Citation
Automated analysis of biological rhythms in the human electroencephalogram /

Material Information

Title:
Automated analysis of biological rhythms in the human electroencephalogram /
Creator:
Keane, Barry Patrick, 1949-
Publication Date:
Copyright Date:
1975
Language:
English
Physical Description:
vii, 247 leaves : ill. ; 28cm.

Subjects

Subjects / Keywords:
Age groups ( jstor )
Autocorrelation ( jstor )
Biological rhythms ( jstor )
Night tables ( jstor )
Phase error ( jstor )
Rapid eye movement sleep ( jstor )
Recordings ( jstor )
Sleep ( jstor )
Spectral energy distribution ( jstor )
Zero ( jstor )
Biological rhythms ( lcsh )
Dissertations, Academic -- Electrical Engineering -- UF
Electrical Engineering thesis Ph. D
Electroencephalography ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 243-246.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Barry Patrick Keane.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
025231541 ( AlephBibNum )
02692739 ( OCLC )
AAS8340 ( NOTIS )

Downloads

This item has the following downloads:


Full Text











AUTOMATED ANALYSIS OF BIOLOGICAL
RHYTHMS IN THE HUMAN ELECTROENCEPHALOGRAM














BY

BARRY PATRICK KEANE


















A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA
19757























































UNIVERSITY OF FLORIDA


3 1262 08666 420 7






























TO

MY WIFE

DEBBIE
















ACKNOWLEDGMENTS


The author would like to thank his supervisory

committee for their guidance and assistance in doing

this work. In particular, the author wishes to thank

Dr. Jack Smith for his close supervision, support, and

continued assistance while working in his laboratory.

Dr. Ismet Karacan, Baylor College of Medicine, provided

the data analyzed in this dissertation. The author would

like to thank Dr. Karacan for providing the data and for

his encouragement and suggestions concerning this research.

In addition, at various times, each person in the

laboratory made contributions or gave advice for which

the author is very greatful--these persons all created

a congenial atmosphere which made it a pleasure to work in

the laboratory and most certainly are in this way partially

responsible for the productivity which this work represents.

This work was supported by Mental Health Grant

MH 16960.
















TABLE OF CONTENTS


ACKNOWLEDGMENTS . . . . . . .

ABSTRACT . . . . . . . . .

CHAPTER

1 INTRODUCTION . . .


The Importance of Biological Rhythms . .
The Need for an Automatic System . . .

2 THE SLEEP ANALYZING HYBRID COMPUTER . .

Introduction . . . . . . . .
Operation of a Typical SAHC Subsystem .
SAHC Organization . . . . . . .
Comments on Zero Crossing Analysis . . .

3 SOFTWARE FOR PROCESSING OF PERIODICITY
DATA . . . . . . . .. .

Introduction . . . . . . . .
Digital Filtering of Periodicity Data . .
Low-Pass Filtering . . . . . . .
Running Average Low-Pass Filtering
of SAHC Data . . . .
High-Pass and Band-Pass Filtering . . .
Determination of Binary Ultradian
Patterns
Patterns . . . . . . . . .
Location of Peaks and Interval
Measurements . . . . . . . .
Treatment of REM . . . . . . .
General . . . . . . . . .

4 NORMAL ADULT PATTERNS . . . . . .


Introduction . . . . . . .
Five-Minute Running Averages . . .
Distribution Over the Night . .
Binary Ultradian Patterns, Cycle Lengths,
etc. . . . . . . . . .
Temporal Relationships ....


Page

. . iii

. . vi


1

1
3

7

7
7
12
16


18

18
21
21

28
30

34

37
38
40

41

41
44


. 49

S. 53
. 66


. .
. .









TABLE OF CONTENTS (Continued)


Page


Correlations, Autocorrelations, Indicated
Periods . . . . . . . . ... 74
Interrelationships Between Different
Activities . . . . . . . .. 77
Summary . . . . . . . . .. . 84

5 ONTOGENETIC TRENDS . . . . . ... 85

Introduction . . . . . . .... .. 85
Qualitative Observations .. . . . 85
Distribution Over the Night . . . .. 86
Binary Patterns, Cycle Length, Period
Length . . . . . . . . . 95
Temporal Relationships . . . . . 110
Correlations, Autocorrelations, Indicated
Periods . . . ..... .... ........ 123
Summary .. . . . . . . . . .123

APPENDIX

1 PROGRAM LISTINGS . . . . . ... 127

2 THE USE OF SPECTRAL TECHNIQUES IN THE
ANALYSIS OF ULTRADIAN BIOLOGICAL RHYTHMS 177

3 DATA FROM ALL AGE GROUPS . . .. . . 197

BIBLIOGRAPHY . . . . . . . . . 243

BIOGRAPHICAL SKETCH . . . . . . ... 247









Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy


AUTOMATED ANALYSIS OF BIOLOGICAL
RHYTHMS IN THE HUMAN ELECTROENCEPHALOGRAM

By

Barry Patrick Keane

June, 1975


Chairman: Dr. Jack R. Smith
Major Department: Electrical Engineering


This dissertation reports on the analysis of biological

rhythms in the human electroencephalogram (EEG) using

modern hardware and software techniques developed expressly

for this type of analysis. Based essentially on their

frequency range, several types of EEG activity are defined,

ranging from delta (.5 to 2.0 Hz.) to beta (15 to 33 Hz.).

Several methods of detection of the above activities

are discussed, including the technique used for this study,

based on zero crossing and pattern detection.

Software for preliminary processing of the above

mentioned raw data is described, including various digital

filters and special purpose software algorithms. Additional

software is described for quantitatively measuring the

tendency of each type of EEG activity to occur rhythmically.

In applying the system to sleep recordings, a care-

fully selected group of normal young adults is analyzed

in order to establish a norm by which to measure older








and younger groups. Next, the same measurements are made

on carefully selected subjects from other age groups,

ranging from 3 to 79 years of age, in order to show

quantitatively the evolution of the various ultradian

rhythms with age.

Results show a number of previously unknown onto-

genetic patterns in the ultradian occurences of alpha,

beta delta, sigma, and rapid eye movement (REM) activity.

The distribution over the night of many types of activity

is found to vary significantly (and predictably) with

age.

The amount of man-hours involved in doing such

studies has been reduced via automation to a small fraction

of what had previously been a prohibitively large value.















CHAPTER ONE
INTRODUCTION


The Importance of Biological Rhythms

From the moment of conception until death,
rhythm is as much part of our structure as
our bones and flesh.....Through studies of bio-
logical rhythms, many aspects of human vari-
ability--in symptoms of illness, our peaks
of strength and productivity, can be antic-
ipated. Moreover, by the end of this decade,
much that is still considered unpredictable in
health and human performance may become fore-
seeable through research into the nature of
biological time cycles. As a result, timing
promises to become an important factor in
preventive health programs and medicine.
(Luce, 1970, p.iv)

This quote by the director of the National Institute of

Mental Health emphasizes just how important biological

rhythms are in our daily lives.

Hormone levels fluctuate, moods change, strengths

and weaknesses vary, in fact "...Life and death may

hang in the balance of timing. Mortality has been

decided, experimentally, not by the amount, but by the

time of day that a rodent received X-rays or was injected

with pneumonia virus, bacteria, or drugs" (Luce, 1970,.p. 1).

In pharmacology, the most effective time to administer a

drug, or the time when it is most needed, may depend

critically upon the patient's biological clock phase.

Replication of experimental data may depend, again crit-








ically, upon the timing of the experiment.

Our emotional and physiological state at any given

time depends upon the relative phases of a number of bio-

logical oscillators. The importance of overall harmony

of these biological rhythms is expressed by Dr. Erwin

Bunning as follows:

...glandular tissue may be in the phase of
hormone production while another organ, being
in a different phase cannot make use of the
hormone; or an enzyme may be active in a
particular time when its substrate is not
available. Every transatlantic air traveler
knows the physiological discomforts that
may arise from such a lack of cooperation.
(Luce, 1970, p.11)

Neuroendocrine rhythms, for example, seem to exhibit

varying degrees of independence, as was shown by Weitzman et

al. in an experiment where the sleep-waking cycle was shifted

by 180 degrees (Weitzman et al., 1968). Some rhythms

adapted immediately to the new schedule, while others

took perhaps two or three weeks to readjust. The proper

phase-locking of these rhythms is then a steady-state

phenomenon; therefore, any abrupt perturbation of the

circadian rhythm will have associated with it a tran-

sient response or recovery period (at least greater

than two or three weeks) during which certain subsystems

are out of phase with each other. It is the steady-

state, phase-locked functioning of these rhythms that

keeps us running on an even keel. A number of studies

have been done showing the normal phase relationships

of concentrations of growth hormone, prolactin, lutein-









izing hormone, 17-OHCS, etc., both during sleep and during

a full 24 hour period (Chase, 1972; Pawel et al., 1972;

Honda et al., 1969; Sassin et al., 1972; Boyar et al., 1972;

Weitzman et al., 1966).

Although the majority of studies involving biological

rhythms have been concerned with neuroendocrine fluctuations,

serious difficulties arise in sampling these rhythms,

as will be explained in the following section of this

chapter.

The critical importance of biological rhythms is

more than enough motivation for looking into new and

more efficient means of analysis.


The Need for an Automatic System

Techniques presently used in analyzing biological

rhythms almost invariably involve an overwhelming amount

of work to produce a time series that adequately shows

the cycling of a given rhythm. If a completely automatic

system could be developed for doing this type of analysis,

a great deal more work could be done in a much shorter time,

thus making it possible to establish a body of normative

data.

Of all the possible parameters that exhibit rhythmical

fluctuations, electrical phenomena are probably the easiest

to monitor. For example, sampling of hormone concentrations

in blood plasma or urine at sufficiently short intervals

requires a tremendous amount of time and effort to collect









and assay the samples. Common practice in such cases has

been to sample at approximately 20-minute intervals

(Chase, 1972; Weitzman et al., 1973). Physical limit-

ations prevent sampling at much shorter intervals, yet

it has been shown in some cases that significant changes

can occur in less than 5 minutes, indicating that the

methods presently used may very well miss major changes

(Chase, 1972).

In addition to this drawback, it would seem that in

measuring hormone levels via the peripheral blood supply

there would necessarily be some integration of the rhythm,

thereby making this method a somewhat questionable indicator

of the actual rhythm of hormone production.

Data collection can be just as cumbersome for EEG

studies when done entirely by hand, for example, counting

REM's or adding up alpha time, etc. Nonautomatic tech-

niques are generally quite accurate for counting phasic

events, but a tremendous amount of time can be spent in

analyzing or marking just one record, let alone an entire

group for an experimental study. Introduction of human

biases that defy replication is also a problem with this

approach, but can be minimized by using multiple scoring.

and cross-checking (Agnew and Webb, 1972).

A number of semiautomatic techniques have been used

which reduce the required man-hours considerably, but

these usually involve a tremendous amount of computer

time. For example, some investigators have used ;!









the technique of doing a direct A/D conversion of the EEG

signal, then doing a spectral analysis using a Fast Fourier

Transform (FFT) program to find the power spectrum of short

epochs, typically 1 or 2 seconds in duration (Lubin et al.,

1973). Each spectrum is then integrated over the desired

frequency range to give the power in that range. In order

to cover a reasonable frequency range, each 2-second epoch

must consist of roughly 500 points. A 512 point FFT must

be calculated for every 1 or 2 seconds of EEG--this requires

a truly spectacular amount of computation time to process

an 8-hour record (Otnes and Enochson, 1972). In addition,

only delta, due to its high amplitude and power, has been

reduced effectively by this method to a series that clearly

depicts a well-defined nightly pattern.

A fully automatic system that could reduce the EEG

record to a relatively small number of values in a

reasonable amount of time would be an invaluable research

tool for analyzing rhythmical EEG phenomena. This need,

along with the critical importance of biological rhythms

in our daily lives, has been the major motivation for

this research.

Chapter Two describes a fully automatic sleep analyzing

computer system and related detection techniques. Also

discussed is the nature of the output data from the com-

puter.

Included in Chapter Three is a detailed description

of a software system for reducing the raw data from the






6


sleep analyzing computer to a relatively small number of

meaningful and descriptive parameters.

Chapters Four and Five are devoted to actual data

collection using the system. Chapter Four is concerned

with only normal young adult subjects, thus establishing

what can be considered to be normal mature patterns. Chap-

ter Five then describes how these patterns vary from age

group to age group, dealing with subjects ranging in age

from three to seventy-nine years.
















CHAPTER TWO
THE SLEEP ANALYZING HYBRID COMPUTER


Introduction

The system described in this dissertation handles

information extracted from EEG recordings by the Sleep

Analyzing Hybrid Computer (SAHC), the product of several

years research by several people working in the lab of

Dr. J. R. Smith at the University of Florida. This

chapter explains the basic operation and organization of

the SAHC and explains briefly why certain techniques of

analysis offer advantages over other methods.


Operation of a Typical SAHC Subsystem

The SAHC contains a number of "event detectors" as

subsystems used to detect the presence of various types

of EEG activity (Smith et al., 1975; Bremer, Smith, and

Karacan, 1970; Smith and Keane, 1973; Keane, 1972). Figure

2.1 is a functional block diagram of a typical event

detector depicting the various decision processes involved

in detection of a particular EEG waveform.

The first step in the processing of the signal is

band-pass filtering to attenuate lower frequency baseline

drifts and higher frequency activity superimposed on the

waveform of interest. A wide-band filter with 12 db/octave




































DETECTION


Figure 2.1 Block Diagram of a SAHC Event
Detector.








roll off is used. Table 2.1 lists the cutoff points for

each SAHC filter. The filter output is connected to both

the A/D circuit and the amplitude measuring circuit. The

amplitude measuring circuit is optional and presently is

only included in the delta detection circuitry. During

each cycle, this circuit determines if a certain amplitude

threshold has been exceeded.

The A/D circuit detects each negative to positive

zero crossing, sending out an indicative pulse that is

synchronized with the system clock cycle. Hysteresis is

included at this point in most of the zero crossing detec-

tors to reject "chatter" due to low amplitude high frequency

noise. Only negative to positive zero crossings are marked,

so that the interval examined between zero crossings is a

full cycle. The full cycle measurement (as opposed to

half cycle measurement) is used since it is not sensitive

to baseline drifts, and it exhibits improved noise charac-

teristics (Gondeck, 1973).

The frequency discriminator circuitry measures the

time interval between consecutive zero crossings and

decides whether a given interval is within preprogrammed

(hardwired) limits. The time interval and corresponding

frequency limits are listed in Table 2.2.

The pattern recognition circuit monitors the activity

of the zero crossing and frequency discriminator circuits

and makes the ultimate decision as to whether or not a

given activity is present. The actual circuitry for real-


























Table 2.1 Corner Frequencies (-3 db) of the
SAHC Analog Filters.


LOWER CUTOFF
FREQUENCY

7.00 Hz.
13.00
0.15
11.00
8.00


UPPER CUTOFF
FREQUENCY

17.00
40.00
3.00
29.00
120.00


ALPHA
BETA
DELTA
SIGMA
ARTIFACT























Frequency and Period Limits of Digital
Frequency Discriminator Circuitry in
the SAHC.


12.00 Hz.
33.00
2.00
16.00


0.0833 sec.
0.0303
0.5000
0.0625


Table 2.2


ALPHA
BETA
DELTA
SIGMA


8.00 Hz.
15.50
0.50
11.75


0.125 sec.
0.645
2.000
0.0851








ization of this decision process varies from detector to

detector, but all perform basically the same function--If

a high percentage (typically 75-80 percent) of the cycle

lengths are within the prescribed limits, then the pattern

recognition circuit signals that the activity is present.


SAHC Organization

Figure 2.2 is a functional block diagram showing the

organization of switching units and subsystems within the

SAHC.

Inputs can be external and on-line if desired, but

usually are taken from the tape recorder, a SANGAMO 3500

14-channel FM recorder. Five channels are selected for

monitoring, and are filtered by the 60 Hz. notch filters

to remove 60-cycle noise. Timing can be selected from

any tape channel, is notch filtered also, and sent to the

time code reader.

Inputs to each of the SAHC detectors may be dialed to

any of the 5 monitored channels, but are connected to the

channels indicated in Table 2.3 except in special cases.

The electrode placements are based on the international

(10-20) electrode placement system.(Strong, 1970; Laidlaw

and Stanton, 1966).

The time code reader reads the elapsed time from the

appropriate tape channel or from the interval timing unit.

The internal timing unit is particularly useful for tapes

with noisy timing channels or for those that have no time

code.
























ENT.
INPUTS


p-'
EXTERNWA CONTROL FROMt POPS W
CASSETTE OUTrPUT BUFFERS
OUTPUT TO PDP 8 UNIT




Figure 2.2 SAHC Architecture.





















Table 2.3 Channel Selection for SAHC Detectors.


GENERAL
CORTICAL ELECTRODE
DETECTOR CHANNEL AREA LEADS

ALPHA 3 OCCIPITAL 03--OZPZ
BETA 1 FRONTAL F1--F7
DELTA 1 FRONTAL F1--F7
SIGMA 2 PARIETAL-TEMPORAL* Pl--T5*
ARTIFACT 1 FRONTAL Fl--F7

*Sigma is sometimes recorded from C3--A2.





15


The total amount of each type of activity is summed

up over an entire minute, then strobed into the output

buffers. Then, while the data for the next minute are

being measured, the information in the buffers is entered

serially onto the cassette tape. The SAHC can operate

real time or, by speeding up the tape recorder, can be

run at 32 times real time, making it possible to run an

entire 8-hour record in about 15 minutes. For alpha, beta,

delta, and artifact, the sums represent (are proportional

to) the total time that each activity is present during

the minute. For REM and sigma, the sums are the total

number of REM's and sigma sleep spindles detected during

that minute.

By monitoring the detectors and summing circuits during

each minute, the sleep stage logic circuits indicate, at

the end of the minute, the appropriate sleep stage for that

minute, based on the sleep scoring rules of Rechtschaffen

and Kales (Rechtschaffen and Kales, 1968). This information

and also the elapsed time from the time code reader are

strobed into the output buffers along with the detector

sums and are also entered onto the cassette tape.

After an entire record has been processed, the cassette

tape may be removed and stored for later processing, or it

can be read immediately, via PDP8 software, onto a DECtape

for permanent storage (Digital Equipment Corporation, 1972).

During the write swquence (or storage sequence) the cassette

unit is controlled by timing signals from the SAHC, but








during the read mode, as information is transferred

onto a DECtape, the unit receives controlling signals

from the PDP8. Once entered on DECtape, the data can

be stored for an indefinite amount of time and may be

referred to or processed at any time.


Comments on Zero Crossing Analysis

Zero crossing analysis has been shown to offer a

number of advantages over frequency analysis or spectral

analysis (Keane, 1972). The most objectionable aspect of

zero crossing analysis seems to be that, intuitively

speaking, a great deal of information appears to be lost

in the binary quantization of the raw data (Evans and

Mulholland, 1969). Further insight would indicate, however,

that such is not necessarily the case. In most EEG wave-

forms, the shape of the waveform between zero crossings

is not usually the same from one cycle to another, but

varies somewhat randomly. This randomness in shape from

cycle to cycle tends to cancel additional information

from amplitude variations between zero crossings--the greater

the randomness, the less the information loss.

It can be shown that for a wide sense stationary,

gaussian process with zero mean and normalized autocorre-

lation function, P (T), a binary quantization or "hard

limiting" yields a process y(t) with autocorrelation

Ry(T) 2 sin- p(t) (Thomas, 1969).

This is to say, the resulting autocorrelation falls off









faster with increasing T--the resulting spectrum has there-

fore been broadened. Working with the zero crossing pattern

of the waveform does not therefore necessarily mean that

such a technique is to be rendered significantly less

effective by a loss of information content.

Perhaps the most significant advantage associated

with this technique of analysis is its insensitivity to

amplitude variations. Amplitude varies widely from sub-

ject to subject, therefore discouraging the use of ampli-

tude sensitive analysis techniques such as spectral analysis

and frequency analysis. In addition, zero crossing is

more easily interpreted for nonstationary data since,

unlike the other techniques mentioned, stationarity is

not a primary prerequisite to this method of analysis.

The incorporation of pattern recognition hardware as

well as period discrimination yields a system that is

quite effective in detecting EEG waveforms for subjects

with vastly different physiological characteristics. This

technique has been applied in a number of EEG studies and

has been demonstrated to produce results showing consid-

erable improvement over other automatic techniques (Smith

and Karacan, 1973).















CHAPTER THREE
SOFTWARE FOR PROCESSING OF PERIODICITY DATA


Introduction

Several different types of information are extracted

from the raw SAHC data and stored on a system data tape.

Figure 3.1 depicts schematically the mechanics of the

software involved in the process. All software is imple-

mented on a Digital Equipment Corporation (DEC) PDP8/e

minicomputer. All stored data, including the raw SAHC

data, are stored on DEC's DECtapes, each of which has

a maximum storage capacity of 1471 blocks, each block

consisting of 128 12-bit words (Digital Equipment Corpor-

ation, 1973).

The top line of boxes in Figure 3.1 represents

information extracted from one night of recorded EEG.

The number above each box gives the relative position of

each section of data on the data tape. For instance,

if information for a particular record begins at block N,

then statistical information concerning that record is

stored in block N+16. Note that each of the sections

of data requires blocks of the DECtape.

Blocks 0 through 4 are set aside for use as a

directory. Information for the first record begins in

block 5.










Each of the programs shown in the lower row of

blocks in Figure 3.1 will be explained in detail in

following sections of this chapter, but their main

functions can be summarized as follows:

RNAV5--Filters raw SAHC data by implementing
a running average low-pass and band-pass
digital filter. Low-passed data go into
block N, band-passed into block N+4.

RNAV6--Does additional smoothing of the data
from block N via a 2-pass running average
filter. Output (to be used by PEAK program)
goes into block N+20.

GATE--Generates binary ultradian pattern by
locating "active" portions of record.
Results go into block N+12.

ULTRAD--Cleans up ultradian pattern (from
block N+12) by removing short duration
transitions. Results are returned to
block N+12.

ULTRD2--Further processes the ultradian pattern
by removing pulses that are not signifi-
cantly higher than surrounding data points.
Results go back into block N+12.

PEAK--Locates peaks within active pulses in
data from block N+20, puts peak locations
into block N+8. Measures distance between
peaks, records this information filed
by hour of occurrence and number of
occurrences. Results go into block N+16,
the first 180 locations.

ULT3--Measures length of each ultradian period
from data in block N+12, stores length
and minute of onset in locations 200
through 240 of block N+16.

REM--Obtains REM binary ultradian pattern
directly from SAHC sleep stage data.
Enters directory information in block N
and binary ultradian sequence in block
N+12.








H424

D


0


Figure 3.1 Software Processing Sequence and Data
Tape Format.









REMULT--Does final processing of REM binary
ultradian sequence by removing short
(less than 5 minutes) bursts of l's and
O's.


Digital Filtering of Periodicity Data

The raw data from the SAHC, consist of 1-minute

sums proportional to the amount of activity present

during that minute. For example, if the ith value of

this time series for beta is n, then there were K times

n seconds of beta activity detected during minute i, where

K is a constant. For beta, K is 60/72, Initial processing

of this raw time series consists basically of 1) low-

passing the data to smooth out high frequency fluctuations,-

that is frequencies above the highest frequency of interest

in periodicity analysis, and 2) band-passing the series

to accentuate any fluctuations of 10-to-20 minute period

length.


Low-Pass Filtering

The simplest method to implement that will produce

a low-pass or smoothing effect is a moving weighting

function or moving average filter (Steiglitz, 1974).

All nonrecursive digital filters are of this type since

they represent a weighted sum of past, present and

future values. There are some particularly appealing

advantages to using moving average or finite impulse

response (FIR) filters. Perhaps the most significant

advantages would be the following: 1) Moving average,








nonrecursive digital filters are always stable,

and 2) Quantization and roundoff problems are generally

negligible for nonrecursive filters (Rabiner, 1971).

This approach may be expressed as

N/2

yi=- akxi-k ,
k=-N/2

where the existence of non-zero ak's for k<0 indicates

a noncausal filter. This imposes some restrictions in

that it is not realizable in real time, but poses

no problems as far as implementing the filter using the

computer, or if the filter is modified to include a

delay so that

N/2

Yi' Yi-N/2= akXi-k-N/2.
k=-N/2

The most readily implemented low-pass filter of this

type would be the case where all the ak's are equal--

the moving average filter given by

N/2

yi= E akxi-k where ak=l/(N+l) for all k
k=-N/2

or

N/2

yi=1/(N+l) E Xi-k

k=-N/2

The weighting coefficients for this filter are given in









Figure 3.2.

This method may be extended from this simple one-pass

nonrecursive case to a two-pass, three-pass, etc. to get

increased attenuation at high frequencies. This would be

equivalent to cascading a number of the simple one-pass

versions. Note that these multiple-pass filters can be

combined to a single one-pass where the ak's are no longer

equal. For example, a two-pass version can be implemented

in either of the following two ways: 1) Cascade two one-

pass windows of lengths N+l (Figure 3.3a). 2) Combine to

a one-pass window of length 2N+1 (Figure 3.3b). For each

one-pass,

N/2

yi=l/(N+l) Xik

k=-N/2

N/2

and zi=l/(N+l) Yi-1

k=-N/2

N/2 N/2

E 1/(N+1) E Xi-l-k
1=-N/2 k--N/2

This is equivalent to the one-pass filter where

N

zi amxi-m

m-N

where the m coefficient, am, is given by letting xi-m

equal unity, all other x's equal zero, and finding the













l-1/(N+1)





a2 ----- aN/2


a-N/2 --- a-2


Figure 3.2 One-Pass Running Average Low-Pass Filter
Coefficients.




















I- iN+l
-ak= 1/(N+1)
ak= 1/(N+1)
4


-- N+ -

ak= 1/(N+1)


2N+1

ak=(1/(N+1)) 2(N+1-k)


Figure 3.3 Two-Pass Running Average Low-Pass Filter
and Its Single-Pass Equivalent.








value of zi (which under these conditions will equal

am) .

To find ao, let xi_0=l, all other x's = 0. Then

N/2 N/2 1
zi= 1/(N+l) 1
1=-N/2 k=-N/2 l+k=0

giving a0=(l/(N+l))(1/(N+1)) (N+) =1/(N+) .

For aN, let xiN=l, all other x's = 0. Then

Z N/2 1/(N+1) N/2 ]
SaN= I/(N+I) 1
1=-N/2 k=-N/2 k+l=N

giving aN=(1/(N+1)) (1/(N+1)) (1)

In this manner it can be shown that the am's are given by

am=(I/(N+1))2(N+l-m) .
These weighting coefficients form a triangular window as

shown in Figure 3.4. By the same approach, any multiple-

pass, nonrecursive filter can be found to be equivalent

to a one-pass with appropriately modified weighting

coefficients and window length.

Although modifying a multiple-pass to a 1-pass

moving average filter involves fewer steps and may appear

simpler, it generally involves considerable computation

time. For instance, if an evenly weighted average filter

(all ak's = 1/(N+1) ) is to be implemented three times

(i.e. three passes are to be made) on a series of 500

data points, the time required can be shown to be approx-

imately (1,000TA + 500TM) x 3, where TA time required to

implement addition, TM = multiplication time (Otnes and
















(1/(N+1)) 2(N+1)


_i ._ (1/--( (N+1))2


a-2 a-1 a0 al a2


Figure 3.4 Coefficients for Single-Pass Version of
Low-Pass Filter from Figure 3.2.


-_ A








Enochson, 1972). Note that this is independent of window

length. The one-pass version of the same filter requires

about 3 x (N+l) x 500(TA+TM) On a machine that uses

software multiplication, TM>>TA, so that the total execu-

tion time for these filters is Te3 1500 TM for the three-

pass and Tel 1500 x (N+1)TM for the one-pass, indicating
el m
that the multiple-pass filter is faster, becoming increas-

ingly superior with increasing N. Even with a hardware

multiplier giving a significant reduction in T the three-

pass version is still independent of window length and soon

becomes faster as N increases. In the limit as TM--*TA,

the execution times would be Te3 Z 4500TA and Tel 3000TA,

for the three-pass and one-pass, respectively, so that

the multiple-pass version still gives a significant decrease

in execution time as N increases. When multiple-pass

filtering is to be used in this processing system, it is

implemented as a multiple-pass and is not modified to a

single-pass.


Running Average Low-Pass Filtering of SAHC Data

As the raw data of 1-minute sums are read from the

SAHC data tapes, it is low-passed by a single-pass running

average filter with a five-minute averaging window. This

smoothes out the data and is effective in attenuating the

high frequency fluctuations present in the raw data without

significantly altering the background trends which are of

interest. Figure 3.5 shows typical plots of beta data









i.
1.0
Raw Beta Activitlr
(Normalized) r .5

Jl.iU I i. i ,
1 2 3 4 5 6 7 Hours
of Sleep




Filtered
Beta Activity A
(Normalized) *A V


1 2 3 4 5 6 7 Hours
of Sleep


Figure 3.5


Low-Pass Filtering (by RNAV5) of Raw
SAHC Data.









from the SAHC. The top plot is the raw data, 1-minute

sums generated by the SAHC. The lower plot is the smoothed

version which would be entered into data block N for this

particular record by the RNAV5 program. To insure that

minute fluctuations do not affect the peak detection algo-

rithm, additional smoothing is done by the RNAV6 program

which implements a two-pass filter using a 3-minute data

window on each pass. The results of two successive 3-

minute smoothings of the beta data from Figure 3.5 are

shown in Figure 3.6. Small high frequency fluctuations

that could disturb or slow down the peak detection program,

PEAK, have been removed, but the trends of interest have

not been significantly altered.

It should perhaps be mentioned at this point that the

RNAV5 program enters directory information into block N

at points above 500. This includes record number, data,

number of minutes of data, type code (alpha, beta, etc.),

scale factor, and lengths of filter windows. Directory

information stored in this manner is readily accessible

during processing without having to make long excursions

on the tape--that is, information concerning each record

is stored right along with all other data. A centralized

directory arrangement would require moving the tape from

each record to the central directory for each reference.


High-Pass and Band-Pass Filtering

A nonrecursive high-pass filter can be implemented













Filtered Beta
(First Pass)


.0


L-i r


1 2 3 4


(Second Pass)











(Third Pass)


5 6 7 Hours
of Sleep


1 2 3 4 5 6 7 Hours
of Sleep


7 Hours
of Sleep


Figure 3.6 Additional Smoothing of SAHC Data.









by the same basic procedure as the low-pass, i.e. by calcu-

lating a moving average of the data. The difference here

is that the filter output is the deviation of the current

input value from a background trend given by the average

of the current point and N surrounding points:

N/2
yi=xi 1/(N+l) E xik
k--N/2

In addition to being easily realized, this filtering

approach offers a number of design advantages over more

involved techniques. In the design of such filters, one

need only determine the proper window length to give a

local trend over the desired neighborhood. Again, he

need not concern himself with instability, frequency

warping and other such problems inherent in the design

of recursive digital filters (Rabiner, 1971).

A band-pass effect can be obtained by combining the

low-pass and high-pass procedures. That is, we can implement

a band-pass filter by taking the output as the difference

between a local average of the current point and N1 sur-

rounding points and a less local average of the current

point and N2 surrounding points where N2>NI:

Nl/2 N2/2

yil1/(Ni+l) 1 xi+k 1/(N2+1) 2 i+1
k=-N1/2 1=-N2/2

The data in Figure 3.7 have been band-pass filtered by

this method using a 5-minute local average and a 20-minute

extended average. Note that the 10-20-minute cycles have






















of Sleep


Figure 3.7 Bandpass Output of RNAV5.
(Same Record as Figures 3.5 and 3.6).








been noticeably accentuated. This band-pass procedure is

implemented by the RNAV5 program at the same time as the

low-pass. (Since the short 5-minute averages are already

available, all that remains is to measure the extended

20-minute averages and calculate the difference.) The

band-passed information is entered into the second data

block (N+4) for each record. This band-passed data can be

used to investigate tendencies to show peaks at 10-20-

minute intervals during active regions. This apparent

tendency has been noted (Aserinsky, 1971) but has never

been quantitatively evaluated.


Determination of Binary Ultradian Patterns

The GATE, ULTRAD, and ULTRD2 programs take the basic

activity information from block N and produce a binary

sequence that points out the active regions. (In this

dissertation, the regions of high beta activity will be

referred to as "active" beta regions or "beta periods".)

The same terminology will be applied to other activities.

The GATE program is essentially an adaptive, zero-

hysteresis comparator. The comparator level being adaptive

allows for widely varying activity levels from subject to

subject. The level is set at 20 percent of the nights

maximum value, then the portions of the record above

the 20 percent level are marked as active periods, and the

portions below are marked as inactive regions. Rapid

transitions or "chattering" at the beginning and end of









each active period are ignored at this time, and results

are put into block N+12. Sample data are shown in Figure

3.8 a and b.

The ULTRAD program removes the "chatter" from the

binary ultradian sequence produced by GATE. The procedure

is as follows: If the comparator output (from GATE) remains

in a given state for at least 10 minutes, then that level

is considered an established state. That is, if the com-

parator level remains high for 10 minutes then it is

established that this is an active region. Once the

state is established as either active or inactive, tran-

sitions from that state will be ignored until a new state

is established by remaining in that new state for at

least 10 minutes. Sample output from ULTRAD is shown in

Figure 3.8 c. The ULTRD2 program further processes the

"active" pulses by requiring each detected pulse to pro-

trude above the local background. This program examines

the binary ultradian sequence at the beginning and end of

each active region. The single-pass filtered data from

block N are examined at points 5 minutes before and after

each transition in the binary ultradian sequence. If

the point 5 minutes inside the active region is not sig-

nificantly higher than the point 5 minutes outside the

active region, the transition is rejected. The pulse is

then made narrower until these requirements are met or

until the active region becomes less than 10 minutes in

which case it is eliminated from the binary sequence. By













RNAV5
a) Output


r



b) GATE
Output
LJ



r-
c) ULTRAD
Output




I

ULTRD2
d) Output i


1 2 3 4 5 6 ,7 -HoaUrs
of Sleep







1 2 3 4 5 67



......}1 -( ^.4 4 1- -4 ,-! J_< I-! . .-1


.1.I


....2 ....-. 3 .... 4.


5 .. -6 ... -..7 -


2 3 4


5 6 7


Figure 3.8 Determining the Binary Ultradian Pattern.









"significantly higher" in this case is meant a difference

of greater than 20/150 of the maximum over the night, so

this measurement is again adaptive and is automatically

adjusted for widely varying subjects. The data processed

by ULTRD2 are shown in Figure 3.8 d.


Location of Peaks and Interval Measurements

Peaks within the active regions are detected in the

ultradian data by the PEAK program. This program finds

peaks in the active regions and measures the lengths between

the peaks. The output from this program is 1) the locations

of the peaks, stored in block N+8 for display purposes, and

2) the length of the interval between these peaks, stored

in block N+16. These interval measurements are grouped

together according to their hours of occurrence. That is,

all intervals occurring during hour 1 are in group 1,

those from hour 2 are in group 2 etc., so'that the data

can be analyzed for variations over the night, or all the

data can be grouped together as a unit.

Peaks are located by the program in the following

manner: Each point of the multiple-pass filtered data is

examined to determine if it is a local maximum. If

2 maxima occur within 2 minutes of each other, the second

is ignored, and only the first is recorded. Intervals

between peaks are next measured and recorded. Intervals

between 2 peaks occurring in different ultradian cycles

are ignored-that is, the entire interval must occur within









the same active period. Output of the PEAK program for

a typical subject is given in Figure 3.9.

In addition to the intervals between peaks within

active periods, ultradian cycle measurements are also

made. The ULT3 program measures the length of each active

period from the binary sequence (block N+12) and records

the length and onset time in the statistics block (block

N+16). With this information, statistics programs can

measure period length, cycle time, etc.


Treatment of REM

Inasmuch as sleep staging has already been computed

by the SAHC and stored on SAHC data tapes, very little

processing is necessary by the REM program to create a

binary ultradian sequence. The REM program merely reads

the sleep stage data from the SAHC data tape and creates

a binary sequence, entering a "1" for REM and a "0"

for all other stages. Directory information is also

read from the SAHC directory and entered in block N

at points above 500 so that the directory conforms to the

cataloguing set up for all other data.

The REMULT program produces the final binary pattern

by removing short bursts that would interfere with the

calculation of average period and cycle lengths etc.

During active regions, an inactive pulse of less than

5 minutes is removed. Similarly, during inactive periods,

a REM period shorter than 5 minutes is removed.















Normalized
Beta
Activity



Peaks


1.0

.5 .


1 2 3 4 5 6 7 Hours

of Sleep


1 2 3 4 5 6 7 Hours
Figure 3.9 Peak Detection Within Active Regions. of Sleep








General

With the exception of the RNAV5 program, the processing

sequence is run for one group of data at a time. If a

group contains 10 records, all 10 records are processed

at once. The RNAV5 program runs records as they are grouped

on the SAHC data tape. If a group of records have been

entered consecutively on the SAHC data tape, they may be

processed simultaneously by RNAV5. Each type of data

processed is stored on its own data tape: All alpha data

are stored on the alpha data tape, all beta data are

recorded on the beta tape, etc.

A number of statistical programs for calculating

means, correlations, distributions, etc. are used to

extract group characteristics from the data. Each of

these programs will be described in Chapters 4 and 5.















CHAPTER FOUR
NORMAL ADULT PATTERNS


Introduction

The different types of activity show varying degrees

of organization in their respective young adult patterns.

A separate chapter is devoted to the young adult patterns

since it is felt that these data best represent the normal

interrelationships of the various EEG activities. The

data for this age group are unobscured by either develop-

mental phenomena or aging.

The experimental design for the age group study,

shown graphically in Figure 4.1, is basically a nested

design of three or four levels (Mendenhall, 1968). At

level one, the data are divided into five age groups.

Table 4.1 lists the ages of various subjects in each

age group. At level two, five normal subjects have

been selected for each age group. This chapter is devoted

to describing the Group 2 data.

At level three, there are two nights of recorded

EEG for each subject. Neither of these recordings has

been taken from the subject's first night in the

laboratory in order to eliminate the "first night

effect" (Agnew et al., 1966).














GROUP 4


LEVEL 1
n1-5


~SUBJ. 5 LEVEL 2
n2-5






LEVEL 3
n3-2





LEVEL 4
n4--variable

Figure 4.1 Design Structure for
Age Group Study.

















Table 4.1 Ages of Subjects in Each Age Group.


GROUP 0

10994 Age 4
10998

10720 Age 4
10724

10350 Age 5
10356

10719 Age 3
10723

10995 Age 3
10999


GROUP 1

10104 Age 13
10114

10110 Age 13
10115

10133 Age 13
10140

10141 Age 13
10147

10164 Age 13
10159


GROUP 2

11742 Age 20
11747

11722 Age 27
11725

6538 Age 30
6546

10250 Age 34
10256

10837 Age 26
10843


GROUP 3

10067 Age 47
10071

10349 Age 43
10352

10927 Age 52
10931

10897 Age 52
10918

10889 Age 53
10896


GROUP 4

11673 Age 79
11677

11740 Age 70
11745

11777 Age 69
11781

11281 Age 78
11286

11365 Age 68
11370








At level four, the data are sampled differently

according to the type of data. For example, for the

temporal statistics, eight samples are taken from each

subject--one measurement for each hour of sleep.


Five-Minute Running Averages

Five-minute running averages (from program RNAV5)

for alpha, beta, delta, and sigma are given in Figures

4.2 through 4.5, respectively. These data were obtained

from SAHC data tapes via RNAV5, as described in Chapter 3.

Perhaps the most striking of these data sets are the

beta data. Beta shows a strong, very well-organized

ultradian pattern throughout the night. Although the

amount of beta appearing in the first half of the night

is clearly less than the amount appearing during the

second half of the night, it is interesting to note

that this is due to shorter period lengths and not due to

a lower amplitude. That is, within any beta period,

the amount of beta per minute does not vary significantly,

but period length does increase over the night. It is

therefore possible at this point to make a statement

concerning the nature of the beta modulation process-

namely that it is the period length that is modulated

in this case. The beta appears periodically over the

entire night and is never suppressed entirely. This

might be :interpreted as meaning that whatever the

physiological processes associated with the appearance

of the beta periods are, they are not scaled down during



















































1 2 3 4 5 6 Hours


Figure 4.2 Plots of Alpha Activity
for Group 2.






















































1 2 3 4 5 6 Hours


Figure 4.3 Plots of Beta Activity
for Group 2.





















































1 2. 3 4 5 6 Hours


Figure 4.4 Plots of Delta Activity
for Group 2.





















































Figure 4.5 Plots of Sigma Activity
for Group 2.






49


the first half of the night, but are proceeding "at full

speed," identically as they do during the second half of

the night.

The modulation of delta activity on the other hand

is of a different nature. During the later two-thirds

of the night, the delta activity is greatly attenuated,

obscuring what seems to be a tendency to continue to

appear periodically over the entire night. In this case

it would seem that the physiological processes themselves

are perhaps being suppressed or scaled down.


Distribution Over the Night

Figure 4.6 shows the calculated "moments about the

midpoint" for several types of activity. This value gives

an indication of how strong the tendency is for a given

type of activity to be greater in either the first or

second half of the night. A negative number (as for

delta and sigma in this case) indicates greater activity

in the first half of the night, whereas a positive

value (beta, alpha) indicates greater activity in the

second half of the night. The values are normalized so

that each record is evenly weighted regardless of the

overall level of activity. For some groups the amounts

of a given activity may be extremely low (i.e. delta

in Group 4 or sigma in Group 0). In these cases it

is felt that the record may not properly reflect the

nightly distribution, so these records are not included

in the calculation of the group moment. The criteria for





50







HOIEHTS BOUT THE MIDPOIHT--GROUP 2
ALPHA. BETA, DELTA, SIGHR


URLUE <== + ==>
-969.00 -480.80 8.80 488.66 968.88
4-----4-----4-----+-----+----------+--- ------ ----






ALPHA *





*BETA


-52. : : .------











: : : : :+-----------
DELTA : *
-1816. :---*---I *







-252 -- : :---------


Figure 4.6 Moments About the Midpoint--Group 2.









exclusion are given in Table 4.2. These criteria have

been established by examining the data to determine

placement of the cutoff points to exclude records

showing extremely low activity.

In order to calculate the moment about the mid-

point, each record is normalized by making the maximum

(in the 5-minute running average) over the night equal

to 150 and scaling all other points appropriately.

Each point then contributes to the overall moment a

value equal to the product of the normalized activity

level just described times the distance from the midpoint.

Points located before the midpoint have been arbitrarily

assigned a negative value, whereas points after the

midpoint contribute a positive value. A listing of this

system program, MOMENT, appears in Appendix 1.

A high positive value for beta and a high negative

value for delta reflect the widely ranging nightly modu-

lations previously described for these activities.

The sigma patterns show a well organized ultradian

rhythm whose modulation is less pronounced than that of

either delta or beta. The group moment for sigma is small,

but shows such wide variation that it is impossible to

make a general statement about the sigma modulation.

The alpha data show no clear ultradian pattern.

Although there seems to be a slight ultradian tendency,

it is often impossible to extract the active regions

from the background "noise." The group moment for alpha
















Table 4.2




SAHC Count

Equivalent
Seconds


Rejection Criteria


BETA DELTA

8 8

9.47 4.13


*SIGMA depends on
to time.


for Moment


SIGMA

5

*count, not


count, not


Calculation.


ALPHA

8

4.13


convertible









indicates that it is fairly evenly distributed. The

variation is small enough in this case that it is not

unreasonable to state that the alpha is distributed evenly

over the night in most cases.


Binary Ultradian Patterns, Cycle Lengths, etc.

In order to find cycle lengths, period lengths, number

of periods, etc., each minute of every record is con-

sidered as part of either an active or inactive region.

A value of 1 is assigned to active minutes, and zero is

assigned to inactive minutes. These active and inactive

regions are determined by a 3-stage process. In stage 1

(system program, GATE) the active regions are selected

as those regions where the 5-minute running averages

are at least 20 percent of the night's maximum. The

next step (system program, ULTRAD) removes short bursts

of inactivity during active regions and vice versa. In

order to be established as an active (or inactive)

region, the input data must remain at 1 (or 0) for 10

consecutive minutes. Shorter bursts within these regions

are reset to the dominant value for that region. The

last step (system program, ULTRD2) checks to be sure that

the active regions protrude significantly above the back-

ground noise. The criterion here is that the difference

between the activity levels five minutes inside the

active region and the level five minutes outside the

region must be greater than 40/150 of the night's maximum,

this value having been chosen heuristically. The program





54


then eliminates pulses that have thus been shortened to

less than 10 minutes.

The length and beginning minute of each active pulse

are measured by system program ULT3. The information is

then stored in block N+16 (see Chapter Three) in the format

indicated in Figure 4.7. Statistical information about

period length and cycle length is measured by system

program GSTATS. In this case "period length" is to

be defined as the width of the active pulse from the

binary ultradian pattern, and "cycle length" is to be

the time between the minutes of onset of two consecutive

active periods. In computing the mean cycle lengths,

the GSTATS program detects "missing" active periods

(missed REM period, beta period, etc.) by excluding from

the ensemble any cycle lengths greater than 140 minutes.

No restrictions are placed on period length; however

periods that extend to the very beginning or end of the

night are excluded from the ensemble since it is felt

that these periods may have been cut short by the temporal

observation window.

The mean cycle lengths for Group 2 are given in

Figure 4.8. It is interesting to note that the mean

cycle length of sigma is somewhat higher than the other

values. The cycle length data have been tested for

significant differences using a paired-difference t-test

(Mendenhall and Sheaffer, 1973). Results (Table 4.3)

indicate that the sigma cycle lengths are significantly
















PERIOD


MINUTES OF


LENGTHS ONSET
200 200+1 220 I 220+1 240


LENGTH
OF Ith
ULTRADIAN
PERIOD


BLANK


BEGINNING
MINUTE
OF Ith
ULTRADIAN
PERIOD


Figure 4.7 Format for Ultradian Period Data Storage
on DECtape.


NO. OF
ULTRADIAN
PERIODS













Average Period

(inns.)
.118.8





104.4






90.0





75.0


BETA DELTA SIGMA
(94.3) (94.2) (106.5)



Figure 4.8 Mean Cycle Lengths for
Group 2 Subjects.


REM
(94.3)




















Table 4.3 Significant Cycle
Group 2 Data.


BETA

*


DELTA

*


Length Differences for


SIGMA


*.

.01
.01


REM


NS

NS

NS
.01


*No ultradian rhythm for alpha.


ALPHA

BETA

DELTA

SIGMA









longer (p<.01) than the beta or delta cycle lengths.

This at first seems astounding, but closer scrutiny

reveals that this is a direct result of the sampling

procedure. For example, consider the 4 cycles of

simulated beta and sigma data in Figure 4.9. If the

beta cycle lengths are all considered to be T seconds

long, but with increased active time during each cycle

(so that P4 >P3 >P2> P) then each corresponding sigma

cycle length will be T seconds plus the next active

period length for beta, minus the last active period

length for beta. The increasing trend in beta periods

results in a net increase in the sigma cycle time for

each sample. For this reason, the sigma cycle time does

not properly reflect the actual ultradian cycle time,

but instead gives an inflated value.

The magnitude of the variance for most types of

activity is sufficiently large to discourage the use

of spectral analysis in analyzing these data. This

subject is discussed in detail in Appendix 2.

Figures 4.10 through 4.13 give mean period lengths

for beta, delta, sigma, and REM. As previously mentioned,

the alpha activity lacks any definite ultradian rhythm,

and therefore did not provide sufficient data for cal-

culating means of period or cycle length.

Other conspicuously absent data points have been

omitted due also to the small amount of data available.

For example, some plots only show periods 1, 2, and 3 or









PI


P2


H1


I: P3 P4
tc------~r c-------


T T T T






I. -I-r, i


T+P2-PI
(O.T. T)


T+P3-P2
(G.T. T)


T+P4-P3
(G.T. T)


Figure 4.9


Simulated Data Showing Cycle
Length Sampling Procedure for
Sigma and Beta.


BETA







SIGMA .





60










HERN LENGTH OF SUCCESSIVE BETR PERIODS
PERIODS 1,2, RND 3--GROUP 2


<== 4 ==>
5.00 15.80 25.00 35.88 45.86
+-----+-----+-----+-----+-----+-----+-----4----------------


S. . + .
+ .



; : a



; ; :
S a . .

I---------------------






+ a

I- -- ---1r---
a a a + S S
5 5 a


*-a----------a-a-,--------a---- ---


Figure 4.10


Mean Lengths of Successive Beta
Periods for Group 2.


URLUE


1st
18.5







2nd
25.1







3rd
37.9
















MERN LENGTH OF SUCCESSIVE DELTR PERIODS
PERIODS 1,2. RND 3--GROUP 2


<(== + =>
8.60 24.80 46.80 56.88 72.88
-----+----+-----+----------+---------+-----+----+-----+


: --*--I


: + :

: + : : :
: .+ : : :
: + : : :
: I---- -- -- ----
: + : :
: + :
: + .


: + :
4 .

:* 4. .
: +


: + :



: + : : :
: .+ :
: + :
4. ..


: + :
I------------------ I

*





: + :


* + *
* + ,
* + C
* 4 .
* + .


Mean Lengths of Successive Delta
Periods for Group 2,


Figure 4.11


VALUE

4







1st
46.8







2nd
46.6







3rd
17.5 :


.-----.-,,,-.-,---.,----.-----.-----.---




62










HEAH LENGTH OF SUCCESSIVE SIGMA PERIODS
PERIODS 2.3, RHD 4 GROUP 2


URLUE <== =
10.80 38.60 58.60 70.8S 96.88
+----------+-----+-----+-----+--------------- ---------






2nd : :
72.7 : + ------ --------+





3rd: +
9. -------------------
4th :
*: + : :












.- -------------- ---------
61.2:


--.2 I------------I- -


Figure 4.12


Mean Lengths of Successive Sigma
Periods for Group 2.





63









MEAN LENGTH OF SUCCESSIVE REM PERIODS
PERIODS 1,2, AND 3--GROUP 2


URLUE <== + ==>
8.80 24.60 48.80 56.88 72.86
+-----+-----+-----+-----+-----+-----+-------------- ---

S + : : : :
: :*
: : : : : : : :
+
: :
1st +
: : + : : : :

S : + : : : :
d : : : : + : : : : :

2915.1 : : ------ -- +
*. : :


3nd: +
: 2 : + .:


: : : : + - :
3rd : : : + : : : :

42.8 : .I---------I-----*--------------I.
... .. . . .. . .


Figure 4.13


Mean Lengths of Successive REM Periods
for Group 2.









perhaps 2, 3, and 4. Points have not been plotted for

other periods in these cases because only a few points

remain in the ensemble after removing periods that

extend to the beginning or end of the record.

The beta plots in Figure 4.10 show a clearly increas-

ing trend in mean period length across the night. As

might be expected, this trend is paralleled by a corres-

ponding trend shown in the REM data. (The correlation

of beta and REM will be discussed later.) The REM data,

as shown in Table 4.4, compare reasonably well with data

from previous investigations.(Dement and Kleitman, 1957;

Verdone, 1968; Williams et al., 1974). The mean period

length of the third REM period is large but in this

case within one standard deviation of previous data. The

fourth and fifth REM periods were often interrupted by

the end of the sleep period. In this case the ensembles

for the fourth and fifth REM periods contained three

members and one member, respectively, and were therefore

omitted from the plots.

The sigma period plots in Figure 4.12 show a slight

decreasing trend over the night, having means ranging

from 72 to 61 minutes.

Figure 4.11 shows that the first two delta periods

have about the same mean value, but the third is signifi-

cantly smaller. Only one of the ten records for Group 2

showed a fourth delta period that stood out distinctly

enough above the background to be detected. Referring to























Table 4.4 Lengths of Successive REM Periods.



Period


Dement and Kleitman


Verdone

Williams et al.

Present Study


13

15.2

15


2

19

27

31.2

29


3

24

30

34.3

42


4

28

33

42.5

*


*Insufficient data available


5

34

31

25.8

*








Figure 4.4 however, it appears that several records had

a tendency to show a fourth delta period, but failed

to rise significantly above the background.

Average alpha, beta, delta, sigma, and REM times as a

percentage of total sleep times are given in Figure 4.14.

Table 4.5 and Table 4.6 show a comparison of these results

with data derived from that of Webb (Colquhoun, 1972).

Since beta occurs both during stage 1 and stage REM, the

sums of stage 1 times and REM times should be roughly

comparable to the active beta time (Keane, 1972). Like-

wise, total active sigma time can be compared with sums

of stages 2, 3, and 4, since considerable sigma activity

occurs during all of these stages (Gondeck, 1973; Silver-

stein, 1974). Finally, stages and 4 can be summed and

compared with total active delta time. REM time is of

course compared directly.


Temporal Relationships

Figures 4.15 through 4.19 show temporal character-

istics of the Group 2 data for alpha, beta, delta, sigma,

and REM. Each value represents the average amount of

active time (in minutes) for a given hour. The generally

low values for hour 8 are a result of sleep times less

than 8 hours.

Alpha time appears to be quite constant over the

night, being lowest during hour 2 and highest during

hour 5.





67












Table 4.5 Total Percent Active Time
for Various Group Data.


Delta

26.2


Sigma

58.6


REM

23.7


Table 4.6 Sleep Stage Percentages for
Young Adult Males (Age 20-29).


2, 3, or 4

70


Beta

35.4


1 or REM

29


3 or 4

20






68

RUERAGE PERCENT TIME PER NIGHT IN ALPHR,
EETAF,)ELIA5..SlIGI, RFD REM--GROUP 2


<== 4 ==>
18.00 38.86 5s0.6 70.8 90.8e
4---- 4 -----4----------------------4 4 --


I------*----I


:ALPHA








]--c--I








1-*-IDELTA:

















--*---J REM


BETA:

















:I---*---I


Figure 4.14 Percent Active Time per Night for
Alpha, Beta, Delta, Sigma, and REM.


:SIGMA




69



TOTRL RCTIUE MINUTES (RUERAGE) OF RLPHR
ERCH HOUR--GROUP 2


URLUE <== =">
-5.00 5.00 15.00 25.08 35.86
+-- ---------------- -- ---------4- 4---4
*
+
(1): : : : +
: : : + : : : : :


5.9 : ------*--- + : : : : :
: : : : : + : : : : :
: : : : + : : : : :
(2) : :
1.5 : --- --- +: :


(3): : : : :
5. 1: I-- ------- -- : : : :
+ : :

(4) :
5.1 ------------ + :
: : : : : : : :
: : : : : : : :
(5) .
8.3 ---------------*---------------
: : : : : : : :
: : : : + : : : :

(6) +
5.3 : ---------- ------------I
: : : : + : : :
: : : : :

(7) : :
5.8: :I-----------*- -------- : :




Figure 4.15 Temporal Distribution of Alpha Activity
for Group 2.









TOTAL RCT1VE MINUTES (RUERAGE) OF BETA
EACH HOUR--GROUP 2


URLUE
8.50
4-----+-----4



(1) :
12. 1-------



(2)
17.8



(3)
15.5




28.5



(5)
23.8



(6)
26.3



(7)
38.7:
a e a ,,,,


<== + ==>
11.56 22.58 33.58 44.56
-- 4---+------4------ ----+-----+-----+ 4-


: : + : : : :
: : : : :



I---------------*-------------
------------- + : : : :


: : : : : :
: : : : : :


I------------------: : : :


: *
: : : : : : :


: : + : : : : :

: : : : : : :
S-------------- : : :








I------------------*-----------------------I:
: : 4* : : : :

. 4 5. 5. .

-------------------I : :



:I----------------<*----------------2


Figure 4.16 Temporal Distribution of [.Beta Activity
for Group 2.










TOTRL RCTIVE MII1UTES (AUERFGE) OF DELTA
ERCH HOUR--GROUP 2


16.80


<== + = >
38.00


44.68


+-----+-----.-----+----- -----+-----+---- +---------- 4 -----


URLUE






(1)
44.5



(2)
23.6



(3)
28.9



(4)
2.7



(5)
3.5


:1----------1--


Figure 4.17 Temporal Distribution of Delta Activity
for Group 2.


2.80


58.e8


+
: : + : : :



:+ --------- ---------
+ :

: : + : : :
: : + : :

---------*----------::



+
+








*
: : + : : :
: : + : : :


I ------------*-----------I :
+*






**.
S + .





: : + : : :
I : : + : : :




72




TOTAL ACTIUE 1IHNUTES AVERAGEE) OF SIGMR
EACH HOUR--GROUP2


<== + ==>
8.80 24.00 48.00 56.86 72.86
-----+----+---------------+-------------------------


URLUE

4.



(1)
56.2



(2)
47.2



(3)
42.9



(4)
45.3



(5)
39.3



(6)
36.8



(7)


28.9 : I-------


Figure 4.18 Temporal Distribution of Sigma Activity
for Group 2.


4 : : : :. :

: : -----------*-----------I :
: : + : : : :


: : + : .
- -I-----*-------I
+ : : : :

: : : : :

------- -------*------------

: : + : :
: : + : : : :
+ : : : :

I: : -----*---- : : :

: : + : : : :


I--------------------I :



: 4 a a
*
------------ --------------I




---*----------I +:
aa





73


TOTAL ACTIVE MINUTES (RUERRGE) OF REM
EACH HOUR--GROUP 2


<== + = >
0.00 18.00 20.80 30. 0e 40.68
*-----+---------- ---+ -------- --- --- ------ 4-


(1)
1.7



(2)
18.1



(3)
7.7



(4)
28.2



(5)
14.7



(6)
23.1



(7)
23.6



(8)
5.4


Figure 4.19 Temporal Distribution of REM Activity for
Group 2.


URLUE


S : : : 4 : : :
S : : 4. : : :

: : : 4 : : :


" 4. : : :

:I----------*----------I+


: : : 4 : :
: : : : : :

: : :


: : :--------------------:


: : : : 4 : : :

I: -- -- -*- -------------I
: : 4. : :

. .


: I- -------------- ------------ -- -------
S a :. : : :



S : ----------- -------------

: : : 4+ : :
: : : : 4 : : :

I-- ------I :








Beta and REM increase markedly across the night as

time asleep increases. The REM data compare quite well

with the results of previous investigations by Webb and

Verdone (Colquhoun, 1972), as shown in Figure 4.20.

There is a sharp decline in the amount of delta as

sleep time increases. This decline in delta activity has

been demonstrated by many investigators, although the

results are most often given in terms of amounts of stage

3 and stage 4 sleep.

The sigma data show a slight decrease over the first

6 hours and a sharp decrease for the 7th hour. The

trend in this temporal data for sigma is much clearer than

for the data collected according to period number.


Correlations, Autocorrelations, Indicated Periods

Program BCOR1 and subroutine BCOR measure the corre-

lation between any two given binary ultradian patterns.

If the programmer so indicates, the program will measure

autocorrelation instead of correlation between two

different patterns. Results are given for values

of lag from zero to one-half the record length of the

shortest record. The correlation (or autocorrelation)

functions are then averaged over each group of 10 records.

Table 4.7 shows the implied period of the ultradian

pattern determined by noting the lag time for which the

group autocorrelation function peaks up, provided that it

shows a periodic component. The periods indicated are












32


28 /


24


20 A /
0

3 16
-4

S 12 Webb
I--

8 ----- Verdone

,'/ Present Study
4 ,/"


S I I
1 2 3 4 5 6 7

Hours of Sleep

Figure 4.20 Hourly Distribution of REM.


























Table 4.7 Ultradian Cycle Time Indicated by
Group 2 Autocorrelation Function.


BETA DELTA SIGMA REM

Cycle Time, T (mins.) 107 101 113 106

Autocorrelation, R(T) .37 .31 .36 .36








slightly higher than those determined by averaging. This

is probably due to the fact that the larger periods will

dominate when using this method. That is, in calculating

the autocorrelation, as the series is shifted, the peaks

will occur where the longer active periods line up,

creating a tendency to favor these larger values and

peaking at slightly higher lag times. The method also

cannot detect "missed" active periods and therefore will

be somewhat sensitive to disturbances of this nature

(Lubin et al., 1973).

The autocorrelation of the alpha patterns showed no

periodicity and was therefore omitted from the table.

All other activities showed quite high autocorrelations

(.31 to .37) for lags of slightly greater than 100

minutes, indicating a strong ultradian component for the

group as a whole.

The correlations were lower and in general not as

clearly periodic for other groups, indicating that this

method is not as useful for the less stable rhythms.


Interrelationships Between Different Activities

A number of interesting correlations were observed

for Group 2. Using BCOR and BCOR1, it is possible to

determine group correlations of any pair of ultradian

patterns. Table 4.8 is a summary of a number of calculated

correlations. Phase relationships are indicated by the

lag times for which the maximum correlation occurred.


























Table 4.8









Beta-REM

Beta-Delta

Beta-Sigma

Delta-Sigma


Maximum and Minimum Correlations and
Periodicities of Group 2 Correlation
Functions.

Maximum Minimum
Correlation Correlation
and and
Associated Associated Indicated
Lag Time Lag Time Period

.76, 13 mins. -.316, 64 mins. 101 mins.

.148, 50 -.427, 3 98

.304, 52 -.75, 0 110

.268, 0 -.086, 42 90









The indicated ultradian period is also given--it has

been calculated by measuring the distance between the

first and second peaks in the correlation function when

a periodic component is clearly present.

A very high correlation of beta and REM (+.76)

occurs at a lag of 12 minutes, indicating a stable

phase relationship between beta and REM where the REM

lags behind the beta by approximately 12 minutes. There

is a strong periodic component of 93 minutes in the

correlation function. This relationship can be seen

very clearly in the Group 2 beta-REM ultradian patterns

shown in Figure 4.21.

Beta and delta are highly negatively correlated

for small lags, that is beta and delta are very emphat-

ically negatively correlated across the night. Notice

this relationship is apparent in Figure 4.22 in the

binary ultradian patterns. There was a very clear

periodicity here of about 98 minutes.

There is yet a stronger negative correlation (-.75)

between beta and sigma, the periodicity in this case

appears to be approximately 110 minutes. The beta and

sigma ultradian patterns are given in Figure 4.23.

Delta and sigma are positively correlated for zero

lag. Referring to the binary ultradian patterns for delta

and sigma (Figure 4.24), the overlapping of the delta

and sigma patterns is obvious. It seems that, were delta

to appear in the second half of the night, it would continue

























1 4





























REM

1 2 3 4' 5 6 7 Hoar


Figure 4.21 Binary Ultradian Patterns for
Beta and REM.













i, .. j n 1l L1- l-

I f 1 1 = + I I I





F J 1 0 1- 1F4



S1I I 1 1 t- I-

Beta
I Delta
1 2 3 4 5 6 7 Hours
Figure 4.22 Binary Ultradian Patterns for
Beta and Delta.


---flF-


nl- i























..t .. ...t h
















1 1 I AI 11 I, i l l



BETA
SIGMA

1 2 3 4 5 6 7 Hours


Figure 4.23 Binary Ultradian Patterns for
Beta and Sigma.


















I1 :1 i | I 1 1









...., ,F n .,
I- 7 .. .11


SIGMA
DELTA
1 2 3 4 5 6 .7 Hours
Figure 4.24 Binary Ultradian Patterns for
Delta and Sigma.








to exhibit the same phase relationship relative to

sigma. The two processes seem therefore to be phase-

locked, under the influence of the same timing cues,

but delta is somehow suppressed in the last two-thirds

of the night.


Summary

In the majority of cases the Group 2 patterns were

the most well organized, most stable, and most easily

defined. Younger age groups were generally in an

interim stage of development, and older groups showed

less stability in most cases. The following chapter will

describe many of the parameters dealt with in this chapter

and how these parameters vary with age.















CHAPTER FIVE
ONTOGENETIC TRENDS


Introduction

This chapter covers essentially the same topics as

described in Chapter 4, but in this case the emphasis

will be placed on the variations or trends across age

groups. Less emphasis will be placed on the actual data

collection procedures, since, for the most part, these

aspects were adequately explained in Chapters 3 and 4.


Qualitative Observations

Five-minute running averages for all age groups are

given in Appendix 3. A number of qualitative character-

istics can be seen in the running averages. These char-

acteristics will be measured quantitatively in the following

sections, but first, here are some general observations.

The young adult group (Group 2) as a whole shows

greater stability. Alpha seems to be the exception here.

As mentioned in Chapter 4, it shows no ultradian rhythm

in the young adults, but it does seem to show a fairly

well-organized ultradian rhythm in a number of the Group 4

subjects.

Beta activity is the best organized overall. Group 1

and Group 3 are both slightly less organized than Group 2.

Group 4 is again less organized than Group 1 or Group 3,








but better organized than Group 0 which still shows

ultradian rhythmicity.

Only in Group 2 does sigma show a clear ultradian

rhythm. The subjects in Group 0 have very little sigma

activity, rendering the 5-minute averages largely meaning-

less. Some records in Group 1 show an ultradian pattern,

but as a whole this group is considerably less organized

than Group 2. Only about 2 records in Group 3 show a

clear ultradian rhythm, but at least 4 records in Group 4

show a good ultradian rhythm.

As previous studies have also shown, delta progres-

sively decreases with age (Feinberg et al., 1967; Colquhoun,

1972) Group 0 shows constant delta throughout the night,

making it difficult to detect any ultradian rhythm. There

is a tendency to show less delta in the second half of

the night (Lubin et al., 1973). Group 1 subjects have a

good ultradian rhythm and frequently have pronounced

active regions or ultradian periods in the second half

of the night. Group 2 shows a well organized rhythm,

but shows fewer active regions in the last two-thirds

of the night, which is consistent with previous inves-

tigations (Lubin et al., 1973; Feinberg et al., 1967).

Degeneration of the ultradian rhythm continues for Group 3

and Group 4 as delta activity continues to fall off.


Distribution Over the Night

Figures 5.1 through 5.4 show moments about the midpoint





87





IOrlfrL I'rD HDrl.t.IITS CIBOUT 1THi MIDPOIHT
FOR tLPHrtlF---GRUPS 8, 1, 2, 3, frill 4


Ufi. tIE
-1208.600
+----..-.....-.--



















-235.6









-38. 6









-4.
^9. t*


< = .- + -->
*(.0c.00 C. 0. C0. % U% .200. 0
_..---4-----+-- --+- 4-----+-----+---_4-----+


Figure 5.1 Normalized Moments About the
Midpoint for Alpha.





















Table 5.1 Significant Group Differences for
Alpha Moment About the Midpoint.


GROUP 1 GROUP 2 GROUP 3 GROUP 4

GROUP 0 *

GROUP 1 .01 NS .05

GROUP 2 NS NS

GROUP 3 NS


*Insufficient data available.











NOrnnLZLlZ MHOll[HTS riBOUT THE MIDPOIHT
FOR F[:E1R--(iGROUlIF; 0, 12, 2, 3, AND 4


-1200.00 -680.600


==- + ==>
.00 c


6C.e. DO


VUALU:











1356.0








9-6.8













20. c




265. 0








-8 (.01


Figure 5.2 Normalized Moments About the
Midpoint for Beta.


1 (?,. 06


4- -...-.-.---..-.-.-..-----+----. _+---- + --- 4_---_4- . 4----- 4--
4 +
4 +
: +

: +
; +
+

+
4-




+
4-


: + C

4- C
S +
S +
S +


+


S+ .
+


C +
+

: + .

+
:: : : / +
+ C C


4


4 C

.C
S C 4





90











Table 5.2 Significant Group Differences for
Beta Moment About the Midpoint.


GROUP 1 GROUP 2 GROUP 3 GROUP 4

GROUP 0 .05 .01 .01 .01

GROUP 1 .05 .01 .01

GROUP 2 .01 .01

GROUP 3 .05





91




NORRnnl.IZrD HMOiNTt FaIOUT 1iHE MIDPOIN7
FOl' DELLf--GROUP'S 0, 1, 2, 3. RID) 4


fILLUE


-1200.00 -600. (0


(=- 4 tr>
0. ('0


600.00


-1006.0 o










-147t8.0















-I4e. C.





- 142.06










*.....;C.... 1


Figure 5.3 Normalized Moments About the
Midpoint for Delta.


I200t. CI


+
+
4-

4.
+
+
+
4
+

+
+
+

+
4

+
+
+
+

+
+

4
+
+
+
+
4





+
+
+


+I:
+
+
+
+
4





+

+

4
4
4
4
+
4


4-


+-----t-----t----- +-----+-----t-----t -----1----~-----~ -----+






92









Table 5.3 Significant Group Differences for
Delta Moment About the Midpoint.


GROUP 1 GROUP 2 GROUP 3 GROUP 4

GROUP 0 .05 NS .01 .01

GROUP 1 .01 .01 .01

GROUP 2 .01 .01

GROUP 3 .05




Full Text

PAGE 1

AUTOMATED ANALYSIS OF BIOLOGICAL RHYTHMS IN THE HUMAN ELECTROENCEPHALOGRAM BY BARRY PATRICK KEANE A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1975-

PAGE 2

UNIVERSITY OF FLORIDA _ _^ 3 1262 08666 420 7

PAGE 3

TO MY WIFE DEBBIE

PAGE 4

ACKNOWLEDGMENTS The author would like to thank his supervisory committee for their guidance and assistance in doing this work. In particular, the author wishes to thank Dr. Jack Smith for his close supervision, support, and continued assistance while working in his laboratory. Dr. Ismet Karacan, Baylor College of Medicine, provided the data analyzed in this dissertation. The author would like to thank Dr. Karacan for providing the data and for his encouragement and suggestions concerning this research. In addition, at various times, each person in the laboratory made contributions or gave advice for which the author is very greatful— these persons all created a congenial atmosphere which made it a pleasure to work in the laboratory and most certainly are in this way partially responsible for the productivity which this work represents. This work was supported by Mental Health Grant MH 16960. iii

PAGE 5

TABLE OF CONTENTS Page ACKNOWLEDGMENTS iii ABSTRACT vi CHAPTER 1 INTRODUCTION 1 The Importance of Biological Rhythms .... 1 The Need for an Automatic System 3 2 THE SLEEP ANALYZING HYBRID COMPUTER .... 7 Introduction 7 Operation of a Typical SAHC Subsystem ... 7 SAHC Organization 12 Comments on Zero Crossing Analysis 16 3 SOFTWARE FOR PROCESSING OF PERIODICITY DATA 18 Introduction 18 Digital Filtering of Periodicity Data ... 21 Low-Pass Filtering 21 Running Average Low-Pass Filtering of SAHC Data 28 High-Pass and Band-Pass Filtering 30 Determination of Binary Ultradian Patterns 34 Location of Peaks and Interval Measurements 37 Treatment of REM 38 General 40 4 NORMAL ADULT PATTERNS .... 41 Introduction 41 Five-Minute Running Averages 44 Distribution Over the Night 49 Binary Ultradian Patterns, Cycle Lengths, etc 53 Temporal Relationships 66 iv

PAGE 6

TABLE OF CONTENTS (Continued) Page Correlations, Autocorrelations, Indicated Periods 74 Interrelationships Between Different Activities . 77 Summary 84 5 ONTOGENETIC TRENDS 85 Introduction 85 Qualitative Observations 85 Distribution Over the Night 86 Binary Patterns, Cycle Length, Period Length 95 Temporal Relationships 110 Correlations, Autocorrelations, Indicated Periods 123 Summary 123 APPENDIX 1 PROGRAM LISTINGS 127 2 THE USE OF SPECTRAL TECHNIQUES IN THE ANALYSIS OF ULTRADIAN BIOLOGICAL RHYTHMS . . 177 3 DATA FROM ALL AGE GROUPS 197 BIBLIOGRAPHY 243 BIOGRAPHICAL SKETCH 247

PAGE 7

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy AUTOMATED ANALYSIS OF BIOLOGICAL RHYTHMS IN THE HUMAN ELECTROENCEPHALOGRAM By Barry Patrick Keane June, 1975 Chairman: Dr. Jack R. Smith Major Department: Electrical Engineering This dissertation reports on the analysis of biological rhythms in the human electroencephalogram (EEG) using modern hardware and software techniques developed expressly for this type of analysis. Based essentially on their frequency range, several types of EEG activity are defined, ranging from delta (.5 to 2.0 Hz.) to beta (15 to 33 Hz.). Several methods of detection of the above activities are discussed, including the technique used for this study, based on zero crossing and pattern detection. Software for preliminary processing of the above mentioned raw data is described, including various digital filters and special purpose software algorithms. Additional software is described for quantitatively measuring the tendency of each type of EEG activity to occur rhythmically. In applying the system to sleep recordings, a carefully selected group of normal young adults is analyzed in order to establish a noz*m by which to measure older vi

PAGE 8

and younger groups. Next, the same measurements are made on carefully selected subjects from other age groups, ranging from 3 to 79 years of age, in order to show quantitatively the evolution of the various ultradian rhythms with age. Results show a number of previously unknown ontogenetic patterns in the ultradian occurences of alpha, beta delta, sigma, and rapid eye movement (REM) activity. The distribution over the night of many types of activity is found to vary significantly (and predictably) with age. The amount of man-hours involved in doing such studies has been reduced via automation to a small fraction of what had previously been a prohibitively large value. vii

PAGE 9

CHAPTER ONE INTRODUCTION The Importance of Biological Rhythms From the momeat of conception until death rhythm is as much part of our structure as our bones and flesh Through studies of biological rhythms, many aspects of human variability—in symptoms of illness, our peaks of strength and productivity, can be anticipated. Moreover, by the end of this decade much that is still considered unpredictable in health and human performance may become foreseeable through research into the nature of biological time cycles. As a result, timing promises to become an important factor in preventive health programs and medicine. (Luce, 1970, p.iv) This quote by the director of the National Institute of Mental Health emphasizes just how important biological rhythms are in our daily lives. Hormone levels fluctuate, moods change, strengths and weaknesses vary, in fact "...Life and death may hang in the balance of timing. Mortality has been decided, experimentally, not by the amount, but by the time of day that a rodent received X-rays or was injected with pneumonia virus, bacteria, or drugs" (Luce, 1970, p. l) In pharmacology, the most effective time to administer a drug, or the time when it is most needed, may depend critically upon the patient's biological clock phase. Replication of experimental data may depend, again crit-

PAGE 10

ically, upon the timing of the experiment. Our emotional and physiological state at any given time depends upon the relative phases of a number of biological oscillators. The importance of overall harmony of these biological rhythms is expressed by Dr. Erwin Bunning as follows: ...glandular tissue may be in the phase of hormone production while another organ, being in a different phase cannot make use of the hormone; or an enzyme may be active in a particular time when its substrate is not available. Every transatlantic air traveler knows the physiological discomforts that may arise from such a lack of cooperation (Luce, 1970, p. 11) Neuroendocrine rhythms, for example, seem to exhibit varying degrees of independence, as was shown by Weitzman et al. in an experiment where the sleep-waking cycle was shifted by 180 degrees (Weitzman et al., 1968). Some rhythms adapted immediately to the new schedule, while others took perhaps two or three weeks to readjust. The proper phase-locking of these rhythms is then a steady-state phenomenon; therefore, any abrupt perturbation of the circadian rhythm will have associated with it a transient response or recovery period (at least greater than two or three weeks) during which certain subsystems are out of phase with each other. It is the steadystate, phase-locked functioning of these rhythms that keeps us running on an even keel. A number of studies have been done showing the normal phase relationships of concentrations of growth hormone, prolactin, lutein-

PAGE 11

izing hormone, 17-OHCS, etc., both during sleep and during a full 24 hour period (Chase, 1972; Pawel et al., 1972;" Honda et al., 1969; Sassin et al., 1972; Boyar et al., 1972; Weitzman et al., 1966). Although the majority of studies involving biological rhythms have been concerned with neuroendocrine fluctuations, serious difficulties arise in sampling these rhythms, as will be explained in the following section of this chapter. The critical importance of biological rhythms is more than enough motivation for looking into new and more efficient means of analysis. The Need for an Automatic System Techniques presently used in analyzing biological rhythms almost invariably involve an overwhelming amount of work to produce a time series that adequately shows the cycling of a given rhythm. If a completely automatic system could be developed for doing this type of analysis, a great deal more work could be done in a much shorter time, thus making it possible to establish a body of normative data. Of all the possible parameters that exhibit rhythmical fluctuations, electrical phenomena are probably the easiest to monitor. For example, sampling of hormone concentrations in blood plasma or urine at sufficiently short intervals requires a tremendous amount of time and effort to collect

PAGE 12

and assay the samples. Common practice in such cases has been to sample at approximately 20-minute intervals (Chase, 1972; Weitzman et al., 1973). Physical limitations prevent sampling at much shorter intervals, yet it has been shown in some cases that significant changes can occur in less than 5 minutes, indicating that the methods presently used may very well miss major changes (Chase, 1972) . In addition to this drawback, it would seem that in measuring hormone levels via the peripheral blood supply there would necessarily be some integration of the rhythm, thereby making this method a somewhat questionable indicator of the actual rhythm of hormone production. Data collection can be just as cumbersome for EEG studies when done entirely by hand, for example, counting REM's or adding up alpha time, etc. Nonautomatic techniques are generally quite accurate for counting phasic events, but a tremendous amount of time can be spent in analyzing or marking just one record, let alone an entire group for an experimental study. Introduction of human biases that defy replication is also a problem with this approach, but can be minimized by using multiple scoring and cross-checking (Agnew and Webb, 1972) . A number of semiautomatic techniques have been used which reduce the required man-hours considerably, but these usually involve a tremendous amount of computer time. For example, some investigators have used :)',

PAGE 13

the technique of doing a direct A/D conversion of the EEG signal, then doing a spectral analysis using a Fast Fourier Transform (FFT) program to find the power spectrum of short epochs, typically 1 or 2 seconds in duration (Lubin et al., 1973) . Each spectrum is then integrated over the desired frequency range to give the power in that range. In order to cover a reasonable frequency range, each 2-second epoch must consist of roughly 500 points. A 512 point FFT must be calculated for every 1 or 2 seconds of EEG— this requires a truly spectacular amount of computation time to process an 8-hour record (Otnes and Enochson, 1972) . In addition, only delta, due to its high amplitude and power, has been reduced effectively by this method to a series that clearly depicts a well-defined nightly pattern. A fully automatic system that could reduce the EEG record to a relatively small number of values in a resonable amount of time would be an invaluable research tool for analyzing rhythmical EEG phenomena. This need, along with the critical importance of biological rhythms in our daily lives, has been the major motivation for this research. Chapter Two describes a fully automatic sleep analyzing computer system and related detection techniques. Also discussed is the nature of the output data from the computer. Included in Chapter Three is a detailed description of a software system for reducing the raw data from the

PAGE 14

sleep analyzing computer to a relatively small number of meaningful and descriptive parameters. Chapters Four and Five are devoted to actual data collection using the system. Chapter Four is concerned with only normal young adult subjects, thus establishing what can be considered to be normal mature patterns. Chapter Five then describes how these patterns vary from age group to age group, dealing with subjects ranging in age from three to seventy-nine years.

PAGE 15

CHAPTER TWO THE SLEEP ANALYZING HYBRID COMPUTER Introduction The system described in this dissertation handles information extracted from EEG recordings by the Sleep Analyzing Hybrid Computer (SAHC) , the product of several years research by several people working in the lab of Dr. J. R. Smith at the University of Florida. This chapter explains the basic operation and organization of the SAHC and explains briefly why certain techniques of analysis offer advantages over other methods. Operation of a Typical SAHC Subsystem The SAHC contains a number of "event detectors" as subsystems used to detect the presence of various types of EEG activity (Smith et al., 1975; Bremer, Smith, and Karacan, 1970; Smith and Keane, 1973; Keane, 1972) . Figure 2.1 is a functional block diagram of a typical event detector depicting the various decision processes involved in detection of a particular EEG waveform. The first step in the processing of the signal is band-pass filtering to attenuate lower frequency baseline drifts and higher frequency activity superimposed on the waveform of interest. A wide-band filter with 12 db/octave 7

PAGE 16

QQ ie

PAGE 17

9 roll off is used. Table 2.1 lists the cutoff points for each SAHC filter. The filter output is connected to both the A/D circuit and the amplitude measuring circuit. The amplitude measuring circuit is optional and presently is only included in the delta detection circuitry. During each cycle, this circuit determines if a certain amplitude threshold has been exceeded. The A/D circuit detects each negative to positive zero crossing, sending out an indicative pulse that is synchronized with the system clock cycle. Hysteresis is included at this point in most of the zero crossing detectors to reject "chatter" due to low amplitude high frequency noise. Only negative to positive zero crossings are marked, so that the interval examined between zero crossings is a full cycle. The full cycle measurement (as opposed to half cycle measurement) is used since it is not sensitive to baseline drifts, and it exhibits improved noise characteristics (Gondeck, 1973). The frequency discriminator circuitry measures the time interval between consecutive zero crossings and decides whether a given interval is within preprogrammed (hardwired) limits. The time interval and corresponding frequency limits are listed in Table 2.2. The pattern recognition circuit monitors the activity of the zero crossing and frequency discriminator circuits and makes the ultimate decision as to whether or not a given activity is present. The actual circuitry for real-

PAGE 18

10 Table 2.1 Corner Frequencies (-3 db) of the SAHC Analog Filters.

PAGE 19

11 Table 2.2 Frequency and Period Limits of Digital Frequency Discriminator Circuitry in the SAHC. fL l/t^ 1/fi ALPHA

PAGE 20

12 ization of this decision process varies from detector to detector, but all perform basically the same function— If a high percentage (typically 75-80 percent) of the cycle lengths are within the prescribed limits, then the pattern recognition circuit signals that the activity is present. SAHC Organization Figure 2.2 is a functional block diagram showing the organization of switching units and subsystems within the SAHC. Inputs can be external and on-line if desired, but usually are taken from the tape recorder, a SANGAMO 3500 14-channel FM recorder. Five channels are selected for monitoring, and are filtered by the 60 Hz. notch filters to remove 60-cycle noise. Timing can be selected from any tape channel, is notch filtered also, and sent to the time code reader. Inputs to each of the SAHC detectors may be dialed to any of the 5 monitored channels, but are connected to the channels indicated in Table 2.3 except in special cases. The electrode placements are based on the international (10-20) electrode placement system. (Strong, 1970; Laidlaw and Stanton, 1966). The time code reader reads the elapsed time from the appropriate tape channel or from the interval timing unit. The internal timing unit is particularly useful for tapes with noisy timing channels or for those that have no time code.

PAGE 21

13 OH SO §5 (0 U H s^^ TT u a u < < CO CI bo •H ^•B

PAGE 22

14 Table 2.3 Channel Selection for SAHC Detectors. DETECTOR CHANNEL GENERAL CORTICAL AREA ELECTRODE LEADS ALPHA 3 OCCIPITAL 03— OZPZ BETA 1 FRONTAL Fl— F7 DELTA 1 FRONTAL F1~F7 SIGMA 2 PARIETAL-TEMPORAL* PI— T5* ARTIFACT 1 FRONTAL Fl — F7 Sigma is sometimes recorded from C3 — A2.

PAGE 23

15 The total amount of each type of activity is summed up over an entire minute, then strobed into the output buffers. Then, while the data for the next minute are being measured, the information in the buffers is entered serially onto the cassette tape. The SAHC can operate real time or, by speeding up the tape recorder, can be run at 32 times real time, making it possible to run an entire 8-hour record in about 15 minutes. For alpha, beta, delta, and artifact, the sums represent (are proportional to) the total time that each activity is present during the minute. For REM and sigma, the sums are the total number of REM's and sigma sleep spindles detected during that minute. By monitoring the detectors and summing circuits during each minute, the sleep stage logic circuits indicate, at the end of the minute, the appropriate sleep stage for that minute, based on the sleep scoring rules of Rechtschaffen and Kales (Rechtschaffen and Kales, 1968) . This information and also the elapsed time from the time code reader are strobed into the output buffers along with the detector sums and are also entered onto the cassette tape. After an entire record has been processed, the cassette tape may be removed and stored for later processing, or it can be read immediately, via PDP8 software, onto a DECtape for permanent storage (Digital Equipment Corporation, 1972) . During the write swquence (or storage sequence) the cassette unit is controlled by timing signals from the SAHC, but

PAGE 24

16 during the read mode, as information is transferred onto a DECtape, the unit receives controlling signals from the PDP8. Once entered on DECtape, the data can be stored for an indefinite amount of time and may be referred to or processed at any time. Comments on Zero Crossing Analysis Zero crossing analysis has been shown to offer a number of advantages over frequency analysis or spectral analysis (Keane, 1972). The most objectionable aspect of zero crossing analysis seems to be that, intuitively speaking, a great deal of information appears to be lost in the binary quantization of the raw data (Evans aDd Mulholland, 1969) . Further insight would indicate, however, that such is not necessarily the case. In most EEG waveforms, the shape of the waveform between zero crossings is not usually the same from one cycle to another, but varies somewhat randomly. This randomness in shape from cycle to cycle tends to cancel additional information from amplitude variations between zero crossings — the greater the randomness, the less the information loss. It can be shown that for a wide sense stationary, gauss ian process with zero mean and normalized autocorrelation function, P (t) , a binary quantization or "hard limiting" yields a process y(t) with autocorrelation 2 1 Ry(T) =Sin"' p(t) (Thomas, 1969). This is to say, the resulting autocorrelation falls off

PAGE 25

17 faster with Increasing t — the resulting spectrum has therefore been broadened. Working with the zero crossing pattern of the waveform does not therefore necessarily mean that such a technique is to be rendered significantly less effective by a loss of information content. Perhaps the most significant advantage associated with this technique of analysis is its insensitivity to amplitude variations. Amplitude varies widely from subject to subject, therefore discouraging the use of amplitude sensitive analysis techniques such as spectral analysis and frequency analysis. In addition, zero crossing is more easily interpretted for nonstationary data since, unlike the other techniques mentioned, stationarity is not a primary prerequisite to this method of analysis. The incorporation of pattern recognition hardware as well as period discrimination yields a system that is quite effective in detecting EEG wavefonas for subjects with vastly different physiological characteristics. This technique has been applied in a number of EEG studies and has been demonstrated to produce results showing considerable improvement over other automatic techniques (Smith and Karacan, 1973) .

PAGE 26

CHAPTER THREE SOFTWARE FOR PROCESSING OF PERIODICITY DATA Introduction Several different types of information are extracted from the raw SAHC data and stored on a system data tape. Figure 3,1 depicts schematically the mechanics of the software involved in the process. All software is implemented on a Digital Equipment Corporation (DEC) PDP8/e minicomputer. All stored data, including the raw SAHC data, are stored on DEC's DECtapes, each of which has a maximum storage capacity of 1471 blocks, each block consisting of 128 12-bit words (Digital Equipment Corporation, 1973) . The top line of boxes in Figure 3.1 represents information extracted from one night of recorded EEG. The number above each box gives the relative position of each section of data on the data tape. For instance, if information for a particular record begins at block N, then statistical information concerning that record is stored in block N+16. Note that each of the sections of data requires 4 blocks of the DECtape. Blocks through 4 are set aside for use as a directory. Information for the first record begins in block 5. 18

PAGE 27

19 Each of the programs shown in the lower row of blocks in Figure 3.1 will be explained in detail in following sections of this chapter, but their main functions can be summarized as follows: RNAV5 — Filters raw SAHC data by implementing a running average low-pass and band-pass digital filter. Low-passed data go into block N, band-passed into block N+4. RNAV6 — Does additional smoothing of the data from block N via a 2-pass running average filter. Output (to be used by PEAK program) goes into block N+20. GATE — Generates binary ultradian pattern by locating "active" portions of record. Results go into block N+12. ULTRAD — Cleans up ultradian pattern (from block N+12) by removing short duration transitions. Results are returned to block N+12. ULTRD2 — Further processes the ultradian pattern by removing pulses that are not significantly higher than surrounding data points. Results go back into block N+12. PEAK — Locates peaks within active pulses in data from block N+20, puts peak locations into block N+8. Measures distance between peaks, records this information filed by hour of occurrence and number of occurrences. Results go into block N+16, the first 180 locations. ULT3 — Measures length of each ultradian period from data in block N+12, stores length and minute of onset in locations 200 through 240 of block N+16. REM — Obtains REM binary ultradian pattern directly from SAHC sleep stage data. Enters directory information in bl6ck N and binary ultradian sequence in block K+12 .

PAGE 28

20

PAGE 29

21 REMULT — Does final processing of REM binary ultradian sequence by removing short (less than 5 minutes) bursts of I's and 0*s. Digital Filtering of Periodicity Data The raw data from the SAHC, consist of 1-minute sums proportional to the amount of activity present during that minute. For example, if the ith value of this time series for beta is n, then there were K times n seconds of beta activity detected during minute i, where K is a constant. For beta, K is 60/72, Initial processing of this raw time series consists basically of 1) lowpassing the data to smooth out high frequency fluctuations.-. that is frequencies above the highest frequency of interest in periodicity analysis, and 2) band-passing the series to accentuate any fluctuations of lO-to-20 minute period length. Low-Pass Filtering The simplest method to implement that will produce a low-pass or smoothing effect is a moving weighting function or moving average filter (Steiglitz, 1974) . All nonrecursive digital filters are of this type since they represent a weighted sum of past, present and future values. There are some particularly appealing advantages to using moving average or finite impulse response (FIR) filters. Perhaps the most significant advantages would be the following: 1) Moving average.

PAGE 30

22 nonrecursive digital filters are always stable, and 2) Quantization and roundoff problems are generally negligible for nonrecursive filters (Rabiner, 1971) . This approach may be expressed as N/2 yi= ^,^ ak^i-k » k=-N/2 where the existence of non-zero aj^'s for k<0 indicates a noncausal filter. This imposes some restrictions in that it is not realizable in real time, but poses no problems as far as implementing the filter using the computer, or if the filter is modified to include a delay so that N/2 yi *=yi-N/2= 2Lj ^k'^i-k-N/2. k=-N/2 The most readily implemented low-pass filter of this type would be the case where all the a, 's are equal — the moving average filter given by N/2 y^= / ^ ^j^x^^jj where aj^=l/(N+l) for all k k=-N/2 or N/2 y,-l/(N^l) 2 x._j^ . k=-N/2 The weighting coefficients for this filter are given in

PAGE 31

23 Figure 3.2. This method may be extended from this simple one-pass nonrecurslve case to a two-pass, three-pass, etc. to get increased attenuation at high frequencies. This would be equivalent to cascading a number of the simple one-pass versions. Note that these multiple-pass filters can be combined to a single one-pass where the ajj.'s are no longer equal. For example, a two-pass version can be implemented in either of the following two ways: 1) Cascade two onepass windows of lengths N+1 (Figure 3.3a) . 2) Combine to a one-pass window of length 2N+1 (Figure 3.3b). For each one-pass, N/2 -k k=-N/2 N/2 7^=1/ (N+1) 22 ^i-1 and Zi=l/(N+1) V^ Yi-i N/2 k=-N/2 N/2 1/(N+1) l=-N/2 This is equivalent to the one-pass filter where N / ^ '^i-l-l . k=-N/2 ;^= 7 a x^ _ . 1 X J m i-m m«=-N th where the m coefficient, a^, is given by letting x. ra ^ D 1— in equal unity, all other x's equal zero, and finding the

PAGE 32

24 N o 08 |3ei m CB I o Q> bO cs U > < bO c 1-1 a • a oQ s -P (U o o OD -H QQ O CB -r* On IH I
PAGE 33

25 i^

PAGE 34

26 value of z^ (which under these conditions will equal To find aQ, let Xj|^_o=l, all other x's = 0. Then l+k=0 giving aQ=(l/(N+l)) (1/(N+1)) (N+1)=1/(N+1) . For ajj, let x^_jj=l, all other x's = 0. Then

PAGE 35

27 + 2 N ^ « <^ ^ ^ cs o (S I ^ CQ o a o n h • > • CO (0 m 0) cs (4 Oi s I be ID -H bo a e •H O 00 (4 O liH m iH (D •H m o m •H cs «H Ai
PAGE 36

28 Eriochson, 1972) . Note that this is independent of window length. The one-pass version of the same filter requires about 3 X (N+1) x 500(T^+Tm). On a machine that uses software multiplication, T^>>Tp^, so that the total execution time for these filters is T^^ = 1500 TJ^, for the threepass and Tg^ = 1500 x (N+1) Tj^ for the one-pass, indicating that the multiple-pass filter is faster, becoming increasingly superior with increasing N. Even with a hardware multiplier giving a significant reduction in T , the threeM pass version is still independent of window length and soon becomes faster as N increases. In the limit as T,.— T. M A ' the execution times would be Tg3 = 450OT and T^^ = SOOOTa, for the three-pass and one-pass, respectively, so that the multiple-pass version still gives a significant decrease in execution time as N increases. When multiple-pass filtering is to be used in this processing system, it is implemented as a multiple-pass and is not modified to a single-pass. Running Average Low-Pass Filtering of SAHC Data As the raw data of 1-minute sums are read from the SAHC data tapes, it is low-passed by a single-pass running average filter with a five-minute averaging window. This smoothes out the data and is effective in attenuating the high frequency fluctuations present in the raw data without significantly altering the background trends which are of interest. Figure 3.5 shows typical plots of beta data

PAGE 37

29 lO

PAGE 38

30 from the SAHC. The top plot is the raw data, l-minute sums generated by the SAHC. The lower plot is the smoothed version which would be entered into data block N for this particular record by the RNAV5 program. To insure that minute fluctuations do not affect the peak detection algorithm, additional smoothing is done by the RNAV6 program which implements a two-pass filter using a 3-minute data window on each pass. The results of two successive 3minute smoothings of the beta data from Figure 3.5 are shown in Figure 3.6. Small high frequency fluctuations that could disturb or slow down the peak detection program, PEAK, have been removed, but the trends of interest have not been significantly altered. It should perhaps be mentioned at this point that the RNAV5 program enters directory information into block N at points above 500. This includes record number, data, number of minutes of data, type code (alpha, beta, etc.), scale factor, and lengths of filter windows. Directory information stored in this manner is readily accessible during processing without having to make long excursions on the tape — that is, information concerning each record is stored right along with all other data. A centralized directory arrangement would require moving the tape from each record to the central directory for each reference. High-Pass and Band-Pass Filtering A nonrecursive high-pass filter can be implemented

PAGE 39

31 ,{D <^. I-^ ^ CO a v CO (S (0 a> 0) en M t< fH -H »..'!• CO esi

PAGE 40

32 by the same basic procedure as the low-pass, i.e. by calculating a moving average of the data. The difference here is that the filter output is the deviation of the current input value from a background trend given by the average of the current point and N surrounding points: N/2 'i=Xi 1/(N+1) ^ x._j^ . k=-N/2 In addition to being easily realized, this filtering approach offers a number of design advantages over more involved techniques. In the design of such filters, one need only determine the proper window length to give a local trend over the desired neighborhood. Again, he need not concern himself with instability, frequency warping and other such problems inherent in the design of recursive digital filters (Rabiner, 1971) . A band-pass effect can be obtained by combining the low-pass and high-pass procedures. That is, we can implement a band-pass filter by taking the output as the difference between a local average of the current point and Nj^ surrounding points and a less local average of the current point and N2 surrounding points where N2>N-: _-^ Ni/2 N2/2 yi=l/(Ni+l) 2J 5^i+k 1/(N2+1) /Z ''i+l * k=-Ni/2 l=-N2/2 The data in Figure 3.7 have been band-pass filtered by this method using a 5-minute local average and a 20-miDUte extended average. Note that the 10-20 -minute cycles have

PAGE 41

33

PAGE 42

34 been noticeably accentuated. This band-pass procedure is implemented by the RNAV5 program at the same time as the low-pass. (Since the short 5-minute averages are already available, all that remains is to measure the extended 20-minute averages and calculate the difference.) The band-passed information is entered into the second data block (N+4) for each record. This band-passed data can be used to investigate tendencies to show peaks at 10-20minute intervals during active regions. This apparent tendency has been noted (Aserinsky, 1971) but has never been quantitatively evaluated. Detex-mination of Binary Ultradian Patterns The GATE, ULTRAD, and ULTRD2 programs take the basic activity information from block N and produce a binary sequence that points out the active regions, (In this dissertation, the regions of high beta activity will be referred to as "active" beta regions or "beta periods".) The same terminology will be applied to other activities. The GATE program is essentially an adaptive, zerohysteresis comparator. The comparator level being adaptive allows for widely varying activity levels from subject to subject. The level is set at 20 percent of the nightJs maximum value, then the portions of the record above the 20 percent level are marked as active periods, and the portions below are marked as inactive regions. Rapid transitions or "chattering" at the beginning and. end of

PAGE 43

35 each active period are ignored at this time, and results are put into block N+12. Sample data are shown in Figure 3.8 a and b. The ULTRAD program removes the "chatter" from the binary ultradian sequence produced by GATE. The procedure is as follows: If the comparator output (from GATE) remains in a given state for at least 10 minutes, then that level is considered an established state. That is, if the comparator level remains high for 10 minutes then it is established that this is an active region. Once the state is established as either active or inactive, transitions from that state will be ignored until a new state is established by remaining in that new state for at least 10 minutes. Sample output from ULTRAD is shown in Figure 3.8 c. The ULTRD2 program further processes the "active" pulses by requiring each detected pulse to protrude above the local background. This program examines the binary ultradian sequence at the beginning and end of each active region. The single-pass filtered data from block N are examined at points 5 minutes before and after each transition in the binary ultradian sequence. If the point 5 minutes inside the active region is not significantly higher than the point 5 minutes outside the active region, the transition is rejected. The pulse is then made narrower until these requirements are met or until the active region becomes less than 10 minutes in which case it is eliminated from the binary sequence. By

PAGE 44

36 -> t.. t* (O 4» » N rl ,-. "* a < -tJ PJ o H 3 < M o 3 o Q +» <; 3 a: a E-I4J ^5 Q 3 cc; a

PAGE 45

37 "significantly higher" in this case is meant a difference of greater than 20/150 of the maximum over the night, so this measurement is again adaptive and is automatically adjusted for widely varying subjects. The data processed by ULTRD2 are shown in Figure 3.8 d. Location of Peaks and Interval Measurements Peaks within the active regions are detected in the ultradian data by the PEAK program. This program finds peaks in the active regions and measures the lengths between the peaks. The output from this program is 1) the locations of the peaks, stored in block N+8 for display purposes, and 2) the length of the interval between these peaks, stored in block N+16. These interval measurements are grouped together according to their hours of occurrence. That is, all intervals occurring during hour 1 are in group 1, those from hour 2 are in group 2 etc., so that the data can be analyzed for variations over the night, or all the data can be grouped together as a unit. Peaks are located by the program in the following manner: Each point of the multiple-pass filtered data is examined to determine if it is a local maximum. If 2 maxima occur within 2 minutes of each other, the second is ignored, and only the first is recorded. Intervals between peaks are next measured and recorded. Intervals between 2 peaks occurring in different ultradian cycles are ignored — that is, the entire interval must occur within

PAGE 46

38 the same active period. Output of the PEAK program for a typical subject is given in Figure 3.9. In addition to the intervals between peaks within active periods, ultradian cycle measurements are also made. The ULT3 program measures the length of each active period from the binary sequence (block N+12) and records the length and onset time in the statistics block (block N+16) . With this information, statistics programs can measure period length, cycle time, etc. Treatment of REM Inasmuch as sleep staging has already been computed by the SAHC and stored on SAHC data tapes, very little processing is necessary by the REM program to create a binary ultradian sequence. The REM program merely reads the sleep stage data from the SAHC data tape and creates a binary sequence, entering a "1" for REM and a "0" for all other stages. Directory information is also read from the SAHC directory and entered in block N at points above 500 so that the directory conforms to the cataloguing set up for all other data. The REMULT program produces the final binary pattern by removing short bursts that would interfere with the calculation of average period and cycle lengths etc. During active regions, an inactive pulse of less than 5 minutes is removed. Similarly, during inactive periods, a REM period shorter than 5 minutes is removed.

PAGE 47

39 (U >, N -M •ri a ft a Qi -H E CQ-W u o DO X CO a> Pi

PAGE 48

40 General With the exception of the RNAV5 program, the processing sequence is run for one group of data at a time. If a group contains 10 records, all 10 records are processed at once. The RNAV5 program runs records as they are grouped on the SAHC data tape. If a group of records have been entered consecutively on the SAHC data tape, they may be processed simultaneously by RNAV5. Each type of data processed is stored on its own data tape: All alpha data are stored on the alpha data tape, all beta data are recorded on the beta tape, etc. A number of statistical programs for calculating means, correlations, distributions, etc. are used to extract group characteristics from the data. Each of these programs will be described in Chapters 4 and 5.

PAGE 49

CHAPTER FOUR NORMAL ADULT PATTERNS Introduction The different types of activity show varying degrees of organization in their respective young adult patterns. A separate chapter is devoted to the young adult patterns since it is felt that these data best represent the normal interrelationships of the various EEG activities. The data for this age group are unobscured by either developmental phenomena or aging. The experimental design for the age group study, shown graphically in Figure 4.1, is basically a nested design of three or four levels (Mendenhall, 1968) . At level one, the data are divided into five age groups. Table 4.1 lists the ages of various subjects in each age group. At level two, five normal subjects have been selected for each age group. This chapter is devoted to describing the Group 2 data. At level three, there are two nights of recorded EEG for each subject. Neither of these recordings has been taken from the subject's first night in the laboratory in order to eliminate the "first night effect" (Agnew et al., 1966). 41

PAGE 50

42 H 8 a c •J n B > N H C •4

PAGE 51

43

PAGE 52

44 At level four, the data are sampled differently according to the type of data. For example, for the temporal statistics, eight samples are taken from each subject — one measurement for each hour of sleep. Five-Minute Running Averages Five-minute running averages (from program RNAV5) for alpha, beta, delta, and sigma are given in Figures 4.2 through 4.5, respectively. These data were obtained from SAHC data tapes via RNAV5, as described in Chapter 3. Perhaps the most striking of these data sets are the beta data. Beta shows a strong, very well-organized ultradian pattern throughout the night. Although the amount of beta appearing in the first half of the night is clearly less than the amount appearing during the second half of the night, it is interesting to note that this is due to shorter period lengths and not due to a lower amplitude. That is, within any beta period, the amount of beta per minute does not vary significantly, but period length does increase over the night. It is therefore possible at this point to make a statement concerning the nature of the beta modulation process — namely that it is the period length that is modulated in this case. The beta appears periodically over the entire night and is never suppressed entirely. This might be interpreted as meaning that whatever the physiological processes associated with the appearance of the beta periods are, they are not scaled down during

PAGE 53

45 4 V.>?-^?^Vn^M^^/^^'^^^ <^jip«y ^M I Ir n/n VTYvrvT; Wr >nNyrf'yi--rn^r^\^^ +— I — I r r^ t f I I i 6 Hours Figure 4.2 Plots of Alpha Activity for Group 2.

PAGE 54

46 :u=.uU\^ \. A. ,. A M. /^ ,,.: ^ "1 r i H<7^ ..» /r>^t > )> > ^ » — | .. (^^'gL^^^ , . (. jBkda ^1 Ur /j.r \ *'< " < tV » nf^i i^. f cVm -* / > — • — > N<< t t ^ft^ r t ^ +-H — h '< »' 6 Hours Figure 4.3 Plots of Beta Activity for Group 2.

PAGE 55

47 / > i V i I i \r^r'f^-r^ T/|V''r^yv ( I T ii f^ i ^^ A /A , , , . 'JaV/^ K )s-i<\vv/X-^ 6 Hours Figure 4.4 Plots of Delta Activity for Group 2.

PAGE 56

48 — I — I ^1 « I — I — H-t — I — > \^ \ I — 1 V ^ " ^ 1 «^i t «L, — I I I — I — I ( V t — I — I | > I jf I — tW"f 'fV^ i > I 4 — I > r I II irv\ f^A ^fX-A, A <^ Ti^^JM I 1^ 1 1 n I I t p I n 1 I N' I I ri I t I v^ ' ^'^fj I I t h^ ' fj i I t V I I I V'^ I I I V --» M I — I 1 I V^ k I I I — I I 1 » I T I I — I i^n 4 — I « 1 — I — t — I — 1 *'> } — I — t *VpT 1 — 1 1 11 — H-l I i i I l^i t r I — I I i^ i I t 1 I I > 1 2 3 4 5 6 Hours Figure 4.5 Plots of Sigma Activity for Group 2.

PAGE 57

49 the first half of the night, but are proceeding "at full speed," identically as they do during the second half of the night. The modulation of delta activity on the other hand is of a different nature. During the later two-thirds of the night, the delta activity is greatly attenuated, obscuring what seems to be a tendency to continue to appear periodically over the entire night. In this case it would seem that the physiological processes themselves are perhaps being suppressed or scaled down. Distribution Over the Night Figure 4.6 shows the calculated "moments about the midpoint" for several types of activity. This value gives an indication of how strong the tendency is for a given type of activity to be greater in either the first or second half of the night. A negative number (as for delta and sigma in this case) indicates greater activity in the first half of the night, whereas a positive value (beta, alpha) indicates greater activity in the second half of the night. The values are normalized so that each record is evenly weighted regardless of the overall level of activity. For some groups the amounts of a given activity may be extremely low (i.e. delta in Group 4 or sigma in Group 0) . In these cases it is felt that the record may not properly reflect the nightly distribution, so these records are not Included in the calculation of the group moment. The criteria for

PAGE 58

50 MOItEHTS neCiUT THE MI DP01HT--GR0LIP 2 ftLPHfl> BETft, DELTA. SIGHR URLUE ALPHA 136. BETA 528. DELTA -1016. SIGMA -252. -968.60 ._4 4. -•486.60 + + . + ==> 6.60 480.66 ._+ +. 966. 66 — 4 4 I * I 4 4 4 4 4 4 4 I *4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 Figure 4.6 Moments About the Midpoint — Group 2.

PAGE 59

51 exclusion are given in Table 4.2. These criteria have been established by examining the data to determine placement of the cutoff points to exclude records showing extremely low activity. In order to calculate the moment about the midpoint, each record is normalized by making the maximum (in the 5-minute running average) over the night equal to 150 and scaling all other points appropriately. Each point then contributes to the overall moment a value equal to the product of the normalized activity level just described times the distance from the midpoint. Points located before the midpoint have been arbitrarily assigned a negative value, whereas points after the midpoint contribute a positive value. A listing of this system program, MOMENT, appears in Appendix 1. A high positive value for beta and a high negative value for delta reflect the widely ranging nightly modulations previously described for these activities. The Sigma patterns show a well organized ultradian rhythm whose modulation is less pronounced than that of either delta or beta. The group moment for sigma is small, but shows such wide variation that it is impossible to make a general statement about the sigma modulation. The alpha data show no clear ultradian pattern. Although there seems to be a slight ultradian tendency, it is often impossible to extract the active regions from the background "noise.** The group moment for alpha

PAGE 60

52 Table 4.2 Rejection Criteria for Moment Calculation. BETA DELTA SIGMA ALPHA SAHC Count 8 8 5 8 Equivalent 9.47 4.13 * 4.13 Seconds SIGMA depends on count, not convertible to time.

PAGE 61

53 indicates that it is fairly evenly distributed. The variation is small enough in this case that it is not unreasonable to state that the alpha is distributed evenly over the night in most cases. Binary Ultradian Patterns, Cycle Lengths, etc. In order to find cycle lengths, period lengths, number of periods, etc., each minute of every record is considered as part of either an active or inactive region. A value of 1 is assigned to active minutes, and zero is assigned to inactive minutes. These active and inactive regions are determined by a 3-stage process, in stage 1 (system program, GATE) the active regions are selected as those regions where the 5-minute running averages are at least 20 percent of the night's maximum. The next step (system program, ULTRAD) removes short bursts of inactivity during active regions and vice versa. In order to be established as an active (or inactive) region, the input data must remain at 1 (or 0) for 10 consecutive minutes. Shorter bursts within these regions are reset to the dominant value for that region. The last step (system program, ULTRD2) checks to be sure that the active regions protrude significantly above the background noise. The criterion here is that the difference between the activity levels five minutes inside the active region and the level five minutes outside the region must be greater than 40/150 of the night's maximum, this value having been chosen heuristically. The program

PAGE 62

54 then eliminates pulses that have thus been shortened to less than 10 minutes. The length and beginning minute of each active pulse are measured by system program ULT3. The information is then stored in block N+16 (see Chapter Three) in the format indicated in Figure 4.7. Statistical information about period length and cycle length is measured by system program GSTATS. In this case "period length" is to be defined as the width of the active pulse from the binary ultradian pattern, and "cycle length" is to be the time between the minutes of onset of two consecutive active periods. In computing the mean cycle lengths, the GSTATS program detects "missing" active periods (missed REM period, beta period, etc.) by excluding from the ensemble any cycle lengths greater than 140 minutes. No restrictions are placed on period length; however periods that extend to the very beginning or end of the night are excluded from the ensemble since it is felt that these periods may have been cut short by the temporal observation window. The mean cycle lengths for Group 2 are given in Figure 4.8. It is interesting to note that the mean cycle length of sigma is somewhat higher than the other values. The cycle length data have been tested for significant differences using a paired-difference t-test (Mendenhall and Sheaffer, 1973). Results (Table 4.3) indicate that the sigma cycle lengths are significantly

PAGE 63

55 4r o H Eh O , H CO H » to D O o N O iz; !z; < M w x; w Q a Eh -tJft O R P M < tH M ^ K PS O HH li, Eh W fas cs (^ o •M 09 CS 4^ OS Q •o o •H tH Q) (^ a cs •H •D CS U CO OS OEh a: s /_ Eh -M iz; S x: M Q Eh -mQO A/ o o iz: oc e H {>« H H < CO OQO < ft -a OS OH H u o o o. 1-i CS tsfn sn o c fLi o

PAGE 64

56 -OM •

PAGE 65

57 Table 4.3 Significant Cycle Length Differences for Group 2 Data.

PAGE 66

58 longer (p < .01) than the beta or delta cycle lengths. This at first seems astounding, but closer scrutiny reveals that this is a direct result of the sampling procedure. For example, consider the 4 cycles of simulated beta and sigma data in Figure 4.9. If the beta cycle lengths are all considered to be T seconds long, but with increased active time during each cycle (so that P4 >P3 >P2>Pi) , then each corresponding sigma cycle length will be T seconds plus the next active period length for beta, minus the last active period length for beta. The increasing trend in beta periods results in a net increase in the sigma cycle time for each sample. For this reason, the sigma cycle time does not properly reflect the actual ultradian cycle time, but instead gives an inflated value. The magnitude of the variance for most types of activity is sufficiently large to discourage the use of spectral analysis in analyzing these data. This subject is discussed in detail in Appendix 2. Figures 4.10 through 4.13 give mean period lengths for beta, delta, sigma, and REM. As previously mentioned, the alpha activity lacks any definite ultradian rhythm, and therefore did not provide sufficient data for calculating means of period or cycle length. Other conspicuously absent data points have been omitted due also to the small amount of data available. For example, some plots only show periods 1, 2, and 3 or

PAGE 67

59 o o o >> o s tSD'O s o ^ o CQ ca c OS P -H 4^ c8iH O Q acQ e _ ffiCQ s 4J cs A x: r-i *» a s bo s S e bo CQ tJ CQ o s bfi » o

PAGE 68

60 MEHN LENGTH OF SUCCESSIUE BETR PERIODS PERIODS 1.2, BND 3~GR0UP 2 UftLUE s.eo 15.00 + ==> 25.60 35.ee -+ 1st 18.5 2Dd 25.1 3rd 37.9 J * 1 Figure 4.10 Mean Lengths of Successive Beta Periods for Group 2^

PAGE 69

61 MERN LENGTH OF SUCCESSIUE DELTR PERIODS PERIODS 1,2* RND 3~GR0UP 2 UftLUE 8.eo .+ — — +. 24.60 . + ^ 46.60 5€..ee 72.ee 1st 46.8 2nd 4S.& 3rd 1?.5 I— •—I Figure 4.11 Mean Lengths of Successive Delta Periods for Group 2,

PAGE 70

62 HERH LETNGTH OF SUCCESSIUE SIGKR PERIODS PERIODS 2>3, RHD 4 GROUP 2 URLUE 18.60 -4 4-. 3e.eo -+ — + ==> 58.60 70.66 96.86 -+ 4 2nd 72.7 3rd 69.8 4th 61.2 Figure 4.12 Mean Lengths of Successive Sigma Periods for Group 2.

PAGE 71

63 MERN LENGTH OF SUCCESSIUE REK. PERIODS PERIODS 1.2. fiHD 3— GROUP 2 URLUE 8.60 24.80 . + + + +. 46.60 56.66 72.66 1st 15.1 2nd 29.7 3rd 42.8 I * 1 + f + + . 4 + + + 1 + * 4 + . 4 4 4 Figure 4.13 Mean Lengths of Successive REM Periods for Group 2.

PAGE 72

64 perhaps 2, 3, and 4. Points have not been plotted for other periods in these cases because only a few points remain in the ensemble after removing periods that extend to the beginning or end of the record. The beta plots in Figure 4.10 show a clearly increasing trend in mean period length across the night. As might be expected, this trend is paralleled by a corresponding trend shown in the REM data. (The correlation of beta and REM will be discussed later.) The REM data, as shown in Table 4.4, compare reasonably well with data from previous investigations. (Dement and Kleitman, 1957; Verdone, 1968; Williams et al., 1974). The mean period length of the third REM period is large but in this case within one standard deviation of previous data. The fourth and fifth REM periods were often interrupted by the end of the sleep period. In this case the ensembles for the fourth and fifth REM periods contained three members and one member, respectively, and were therefore omitted frcMn the plots. The Sigma period plots in Figure 4.12 show a slight decreasing trend over the night, having means ranging from 72 to 61 minutes. Figure 4.11 shows that the first two delta periods have about the same mean value, but the third is significantly smaller. Only one of the ten records for Group 2 showed a fourth delta period that stood out distinctly enough above the background to be detected. Referring to

PAGE 73

65 Table 4.4 Lengths of Successive REM Periods.

PAGE 74

66 Figure 4.4 however, it appears that several records had a tendency to show a fourth delta period, but failed to rise significantly above the background. Average alpha, beta, delta, sigma, and REM times as a percentage of total sleep times are given in Figure 4.14. Table 4.5 and Table 4.6 show a comparison of these results with data derived from that of Webb (Colquhoun, 1972). Since beta occurs both during stage 1 and stage REM, the sums of stage 1 times and REM times should be roughly comparable to the active beta time (Keane, 1972) . Likewise, total active sigma time can be compared with sums of stages 2, 3, and 4, since considerable sigma activity occurs during all of these stages (Gondeck, 1973; Silverstein, 1974) . Finally, stages 3 and 4 can be summed and compared with total active delta time. REM time is of course compared directly. Temporal Relationships Figures 4.15 through 4.19 show temporal characteristics of the Group 2 data for alpha, beta, delta, sigma, and REM. Each value represents the average amount of active time (in minutes) for a given hour. The generally low values for hour 8 are a result of sleep times less than 8 hours. Alpha time appears to be quite constant over the night, being lowest during hour 2 and highest during hour 5.

PAGE 75

67 Table 4.5 Total Percent Active Time for Various Group Data. Beta Delta Sigma REM 35.4 26.2 58.6 23.7 Table 4.6 Sleep Stage Percentages for Toung Adult Males (Age 20-29) 1 or REM 3 or 4 2, 3, or 4 REM 29 20 70 24

PAGE 76

68 RUERnGE PERCENT TH1E PER NIGHT IN ftLPHR.. BETA.. DELI fl.. SI GMR.. RND REM — GKOUP 2 le.eo 30.cie. .+ 56.86 76. ee 4 + . 96.06 + + J * 1 ALPHA I— *~1 BETA 1~*I DELTA 1 * J jjjgjj I * 1 SIGMA Figure 4.14 Percent Active Time per Night for Alpha, Beta, Delta, Sigma, and REM.

PAGE 77

€9 TOTRL HCTIUE I1IHUTES
PAGE 78

70 TOTftL RC71UE HIHUTES OF BETR EnCH HOUR— GROUP 2 UfiLUE (1) n.e (2) 1?.8 (3) 15.5 (4) 26.5 (5) 23.6 (6) 2e.3 (7) 38.7 <== 6.50 11.56 + ==> 22.56 33.56 + 1 + + 4I + + I 44.56 + 4 Figure 4.16 Temporal Distribution of /.Beta Activity for Group 2.

PAGE 79

71 TOTRL RCTIUE MIHUTES CftUERflGE> OF DELTA ERCH HOUR—GROUP 2 URLUE <«== (X) 44.5 (2) 23. & (3) 28.9 (4) 2.7 (5) 3.5 (6) 4.6 2.00 .+ +. 16.60 .+ + = = > 30.00 I * 1 I « 1 I * , 44.08 .+ +. 58. ee •++ + + I + + + * 1 Hi Figure 4.17 Temporal Distribution of Delta Activity for Group 2.

PAGE 80

72 TOTftL nCTlUE I1IHUTES (flUERRGE) OF SIGKR ERCH H0UR--GR0UP2 URLUE e.eo 24. eO 46.00 56.66 ?2.6e (1) 56.2 (2) 4?. 2 (3) 42.9 (4) 45.3 (5) 39.3 (6) 36.6 (7) 28.9 4 + I •• 4+ 1 1 Figure 4.18 Temporal Distribution of Sigma Activity for Group 2.

PAGE 81

73 TOTftL RCTIVE MlHirjES (RUERRGE) OF REM ERCH HOUR—GROUP 2 ' (1) 1.7 (2) le. 1 (3) 7.7 (4) 26.2 (5) 14.7 (6) 23.1 (7) 23.0 (8) 5.4 UfiLUE <== + ==> B.eo 18. eo 20.80 3e.e6 + + 4 + + f 1 + + 4 4 4 4 4 4 4 4 1 * 1 40.66 -4--4 Figure 4.19 Temporal Distribution of REM Activity for Group 2. • .

PAGE 82

74 Beta and REM increase markedly across the night as time asleep increases. The REM data compare quite well with the results of previous investigations by Webb and Verdone (Colquhoun, 1972), as shown in Figure 4.20. There is a sharp decline in the amount of delta as sleep time increases. This decline in delta activity has been demonstrated by many investigators, although the results are most often given in terms of amounts of stage 3 and stage 4 sleep. The Sigma data show a slight decrease over the first 6 hours and a sharp decrease for the 7th hour. The trend in this temporal data for sigma is much clearer than for the data collected according to period number. Correlations, Autocorrelations, Indicated Periods Program BCORl and subroutine BCOR measure the correlation between any two given binary ultradian patterns. If the programmer so indicates, the program will measure autocorrelation instead of correlation between two different patterns. Results are given for values of lag from zero to one-half the record length of the shortest record. The correlation (or autocorrelation) functions are then averaged over each group of 10 records. Table 4.7 shows the implied period of the ultradian pattern determined by noting the lag time for which the group autocorrelation function peaks up, provided that it shows a periodic component. The periods indicated are

PAGE 83

75

PAGE 84

76 Table 4.7 Ultradian Cycle Time Indicated by Group 2 Autocorrelation Function. BETA DELTA SIGMA REM Cycle Time, T (mins.) 107 101 113 106 Autocorrelation, R(T) .37 .31 .36 .36

PAGE 85

77 slightly higher than those determined by averaging. This is probably due to the fact that the larger periods will dominate when using this method. That is, in calculating the autocorrelation, as the series is shifted, the peaks will occur where the longer active periods line up, creating a tendency to favor these larger values and peaking at slightly higher lag times. The method also cannot detect "missed" active periods and therefore will be somewhat sensitive to disturbances of this nature (Lubin et al., 1973) . The autocorrelation of the alpha patterns showed no periodicity and was therefore omitted from the table. All other activities showed quite high autocorrelations (.31 to .37) for lags of slightly greater than 100 minutes, indicating a strong ultradian component for the group as a whole. The correlations were lower and in general not as clearly periodic for other groups, indicating that this method is not as useful for the less stable rhythms. Interrelationships Between Different Activities A number of interesting correlations were observed for Group 2. Using BCOR and BCORl, it is possible to determine group correlations of any pair of ultradian patterns. Table 4.8 is a summary of a number of calculated correlations. Phase relationships are indicated by the lag times for which the maximum correlation occurred.

PAGE 86

78 Table 4.8 Maximum and Minimum Correlations and Periodicities of Group 2 Correlation Functions. Maximum Minimum Correlation Correlation and and Associated Associated Indicated Lag Time Lag Time Period Beta-REM .76, 13 mins. -.316, 64 mins. 101 mins Beta-Delta .148, 50 -.427, 3 98 Beta-Sigma .304, 52 -.75, HO Delta-Sigma .268, -.086, 42 90

PAGE 87

79 The indicated ultradian period is also given — it has been calculated by measuring the distance between the first and second peaks in the correlation function when a periodic component is clearly present. A very high correlation of betia and REM (+.76) occurs at a lag of 12 minutes, indicating a stable phase relationship between beta and REM where the REM lags behind the beta by approximately 12 minutes. There is a strong periodic component of 93 minutes in the correlation function. This relationship can be seen very clearly in the Group 2 beta-REM ultradian patterns shown in Figure 4.21. Beta and delta are highly negatively correlated for small lags, that is beta and delta are very emphatically negatively correlated across the night. Notice this relationship is apparent In Figure 4.22 in the binary ultradian patterns. There was a very clear periodicity here of about 98 minutes. There is yet a stronger negative correlation (-.75) between beta and sigma, the periodicity in this case appears to be approximately 110 minutes. The beta and Sigma ultradian patterns are given in Figure 4.23. Delta and sigma are positively correlated for zero lag. Referring to the binary ultradian patterns for delta and Sigma (Figure 4.24) , the overlapping of the delta and Sigma patterns is obvious. It seems that, were delta to appear in the second half of the night, it would continue

PAGE 88

80 ..n.. rii -H — M-4 — I — I — > I f 11 \ . +-H — J — \ — ( — f — Mil < I ' I' •4 h H — I — I — y m jji — I — } — pj. H — h 4 — Ixn 4 — H-+. , ni] ,,, JJi -j — ^— f. H — h+ -I — I M ri -I — I — j-a-f ^ — HH — ^ yj — I — M-j — I — i^-fU. f-H — J-J — > — f. I — p I t -? — I — M-f I t I -i — tH — h iH, , , 4 — J< ' I" { t — j... Ml ' ' 4 "i I' ' *— * tt: — »— *+-4. «— 4-»-+ 'I f M — I — {' f^ V H — h— »— f -<— i 1 i ! ! i' I ^ t ! I r . .n. i — I — K-H H — h t } I ? » f t I BETA REB < ! \ i ^M > I -4 & 7 Hours Figure 4.21 Binary Ultradian Patterns for Beta and REM.

PAGE 89

81 — t — hL. < — h '' t I I 4— JU H — 1-4 -J — f — h -i — I — M4 n i — ^-H — h 1 -l4 — ). +— -* ~f— 4— t — fD <— H +-H4—4" ^ — I — h n — I — (. n +»-4 •4—4. bJJ H — H-f4 — I — I I 'I — P f I D ! — h -H — f 4 — I — »I t i H — H I — H 4— ^ — I — I — I — I — i * » H < — t^ — ! »-f-n.: r~lni -« — f I ' I — I — {' II — i< {I < 'I 4 — I « r 4—4 — fr— t4 — h n D H H "In. . tTH n I < *—+ 4— > ! I f 4— »-{ — hH — ( — >— H Beta Delta < 1 4 — 7 Hours Figure 4.22 Binary Ultradian Patterns for Beta and Delta.

PAGE 90

82 7 Hours Figure 4.23 Binary Ultradian Patterns for Beta and Sigma.

PAGE 91

B3 * — 1 — t' M i 1 i-i4Jj — t•i — I — Jj: M 1 — j f. .n. . . n I' M} \ HH — M H — i-M — H— * -* — f1+ I — h Llj — ,_4 — j nj i — h4— +• I — I — p f i 'I — « ft} i t 4 — I — M++-H — » f| i ! ' 1 i U •+-H — I — I — H -' — t 'I ' t I — I— i -< — !+— f. H — Min, ,u -< — f' t t I I } »• J C i < ' n t { i 1 ' ii > « ) e "« — f-H — i — !-H — J — I . I ^ < — fH — h 'i t 1 I — i — 1 a -t — t i-H — J — »-I — ft— ^ — hH— f I 1 t ; I1 ; I H t I i — ! r I t 1 I a i • H — 5 — ^ tilt 4—11 — ^ } — J li , 1 , < — f — I I I SIGMA DELTA -»-H 1 < 1 . 1 7 Hoars Figure 4.24 Binary Ultradian Patterns for Delta and Sigma.

PAGE 92

84 to exhibit the same phase relationship relative to Sigma. The two processes seem therefore to be phaselocked, under the influence of the same timing cues, but delta is somehow suppressed in the last two-thirds of the night. Summary In the majority of cases the Group 2 patterns were the most well organized, most stable, and most easily defined. Younger age groups were generally in an interim stage of development, and older groups showed less stability in most cases. The following chapter will describe many of the parameters dealt with in this chapter and how these parameters vary with age.

PAGE 93

CHAPTER FIVE ONTOGENETIC TRENDS Introduction This chapter covers essentially the same topics as described in Chapter 4, but in this case the emphasis will be placed on the variations or trends across age groups. Less emphasis will be placed on the actual data collection procedures, since, for the most part, these aspects were adequately explained in Chapters 3 and 4. Qualitative Observations Five-minute running averages for all age groups are given in Appendix 3. A number of qualitative characteristics can be seen in the running averages. These characteristics will be measured quantitatively in the following sections, but first, here are some general observations. The young adult group (Group 2) as a whole shows greater stability. Alpha seems to be the exception here. As mentioned in Chapter 4, it shows no ultradian rhythm in the young adults, but it does seem to show a fairly well-organized ultradian rhythm in a number of the Group 4 subjects. Beta activity is the best organized overall. Group 1 and Group 3 are both slightly less organized than Group 2. Group 4 is again less organized than Group 1 or Group 3, 85

PAGE 94

86 but better organized than Group which still shows ultradian rhythmicity . Only in Group 2 does sigma show a clear ultradian rhythm. The subjects in Group have very little sigma activity, rendering the 5-minute averages largely meaningless. Some records in Group 1 show an ultradian pattern, but as a whole this group is considerably less organized than Group 2. Only about 2 records in Group 3 show a clear ultradian rhythm, but at least 4 records in Group 4 show a good ultradian rhythm. As previous studies have also shown, delta progressively decreases with age (Feinberg et al., 1967; Colquhoun, 1972) . Group shows constant delta throughout the night, making it difficult to detect any ultradian rhythm. There is a tendency to show less delta in the second half of the night (Lubin et al., 1973). Group 1 subjects have a good ultradian rhythm and frequently have pronounced active regions or ultradian periods in the second half of the night. Group 2 shows a well organized rhythm, but shows fewer active regions in the last two-thirds of the night, which is consistent with previous investigations (Lubin et al., 1973; Feinberg et al., 1967). Degeneration of the ultradian rhythm continues for Group 3 and Group 4 as delta activity continues to fall off. Distribution Over the Night Figures 5.1 through 5.4 show moments about the midpoint

PAGE 95

87 HOKnriLirri) hokiiitc ftBOUT Tur MJDroiHT FOR RtPHFl-GROUPS e> 1/ ?' 3' f«KI> 4 UftlUF JSfiCi.OO < = = (•.ecu 00 -3?6.6 -235.6 i?e.e -4.11 'j'iKb e. no — + •» + + + + + + +. j?ct'..ep Figure 5.1 Normalized Moments About the Midpoint for Alpha.

PAGE 96

88 Table 5.1 Significant Group Differences for Alpha Moment About the Midpoint.

PAGE 97

89 NORnnLizFt) Hor.f HTr rbout the mjdpoiht FUR F;E;TH--f>ROHF-:; t«/ 1/2, ?i HND A UflLlU 120ei. GO — 4 ^ 4 + , i35e..0 96f..e f.2e.6 2er.. e • st..o Figure 5.2 Normalized Moments About the Midpoint for Beta.

PAGE 98

90 Table 5.2 Significant Group Differences for Beta Moment About the Midpoint. GROUP 1 GROUP 2 GROUP 3 GROUP 4 GROUP .05 .01 .01 .01 GROUP 1 .05 .01 .01 GROUP 2 .01 .01 GROUP 3 .05

PAGE 99

91 NDKnni.lZrn HDKfiNT'J ffOOUT TMi: MIDPOINT FOU [>tLTM-~GROUPi> G, 1, 2* 3* RUl> 4 unLut -+ 4 -6tiCi,00 e.oo 6oe!.eo 4 + lepc.ci -i47e.e -J0I6.6 ?4?. e •45'e«.e + + + + + + 4 f + + + + + + + + ' + + + + •f + I+ + + + + + + + + + Figure 5.3 Normalized Moments About the Midpoint for Delta.

PAGE 100

92 Table 5.3 Significant Group Differences for Delta Moment About the Midpoint.

PAGE 101

93 NORflfil IZFf) MOiafJTS ftBOUT TUC HIDPOINT FOR f;IGMft ---GNTiUpr. 1/ 2/ 3/ OHD 4 ufji ur 1208. eo 4 4 -4 -f e.oci f.CC.CiH -4 •«• i:^(it;. Oft __4 »4 -nf:.e ?53.e 123.0 " I 55 . Figure 5.4 Normalized Moments About the Midpoint for Sigma.

PAGE 102

94 for alpha, beta, delta, and sigma. The procedure for calculating this value as well as criteria for exclusion of a record are given in Chapter 4. Significant group differences have been calculated using a paired-difference t-test; confidence intervals are given for each type of activity. Moments about the midpoint for alpha are small by comparison with beta and delta, but a few significant differences exist (in Table 5.1) between age groups. Little significance can be attached to the Group values, since all but three records have been eliminated from the calculations due to veiry small amounts of alpha (see Chapter 4). The Group 1 moment, however, is seen to be significantly lower than the va-lues for Group 2 (p<.01) and Group 4 (p<.05>. The beta activity has a high positive moment for Group 0, but this moment becomes progressively smaller until, in Group 4, there is actually a slightly negative moment. This shows that although beta activity shows an ultradian rhythm from childhood to old age, it becomes progressively more evenly distributed temporally with age. All group differences are significant for the beta distribution, as shown in Table 5.2— this is obviously a very strongly age-dependent variable. Groups 0, 1, and 2 have highly negative momeats for delta, the most pronounced of these being the Group 1 value. Proceeding to Group 3, however, the value drops

PAGE 103

95 off sharply and remains quite small for Group 4 also. Table 5.3 shows that all group differences are significant except for the comparison of Group with Group 2 which from Figure 5.3 can be seen to have equal moments. Since very little sigma occurs for Group 0, values are only given for Groups 1 through 4. Thehighest value is the moment for Group 2, with the values for Groups 1 and 3 dropping by about 50 percent, and a very small value for Group 4. Results of the paired-difference t-tests for group comparisons of the sigma moments have revealed that no significant differences occur between the various groups. Figure 5.5 shows relative values for moments in each age group. The most obvious feature here is the mutual convergence toward an even distribution (zero moment) with increasing age. Binary Patterns, Cycle Length, Period Length Binary patterns for all age groups are arrived at by the 3-stage procedure described in Chapter 4 and are given in Appendix 3. Cycle lengths have been calculated in the same manner described in Chapter 4 and are summarized in Table 5.4. There seems to be no discernible pattern across age groups or activity types. Average active time per night (as a percent of total sleep time) for all age groups is given in Table 5.5.

PAGE 104

.96 / / /

PAGE 105

97

PAGE 106

98 c E « JO W CO CO "Vl
PAGE 107

99 Figures 5.6 through 5.10 show the ontogenetic trends in percents of alpha, beta, delta, sigma, and REM, respectively, per night. Significant group differences have again been calculated using the paired-difference t-test. Figure 5.6 shows the ontogenetic trend in percent alpha per night. Significant group differences are given in Table 5.6. The percent of alpha for Group would effectively be zero since subjects from this age group generally show no alpha activity. No actual quantitative measurements have been made, however, since this process, due to its adaptive nature, yields meaningless results if no alpha occurs at any time during the night. (The records in this group have thus been eliminated according to the exclusion criteria given in Chapter 4.) Alpha shows a continual increase with age, showing a significant increase for Group 3 and a tremendous increase for Group 4. As previously mentioned, several of the Group 4 subjects also show a rather well organized ultradian alpha pattern. Percent beta per night, given in Figure 5.7, shows striking consistency with age. It is interesting, though, to contrast this with the beta moment about the midpoint (Figure 5.2) which shows highly significant changes in the way the beta is distributed over the night. None of the group differences for percent beta per night were significant at the .05 level (Table 5.7) . The most outstanding feature of the delta plot in

PAGE 108

100 RVERflGE PERCENT RLPHR PER NIGHT le.eo 38.00. . + 50, ee + +_ 76. ee .+ 96. ee Figure 5.6 Percent Active Time per Night for Alpha.

PAGE 109

101 Table 5.6 Significant Group Differences in Percent Alpha per Night.

PAGE 110

102 RUERftGC PERCENT BETR PER HIGHT 4 + ^. 30. 6G + ==> + 470.00 + + 90. 00 "t + Figure 5.7 Percent Active Time per Night for Beta.

PAGE 111

103 Table 5.7 Significant Group Differences in Percent Beta per Night.

PAGE 112

104 RMERnCE PERCENT DELTR PER NIGHT le.eo <== + ==> .+ + + ^. 70.60 + + . 90. 60 -4 + Figure 5.8 Percent Active Time per Night for Delta.

PAGE 113

105 Table 5.8 Significant Group Differences in Percent Delta per Night. GROUP 1 GROUP 2 GROUP 3 GROUP 4 GROUP .01 .01 .01 .01 GROUP 1 .05 NS .01 GROUP 2 NS NS GROUP 3 NS

PAGE 114

106 RVERRGE PERCENT SIGMfl PER NIGHT 16.60 4 + 4 < = = 36. ec •4 + + ==> 50.ee .+ +. 76.66 . + + . 96. 66 + + Figure 5.9 Percent Active Time per Night for Sigma.

PAGE 115

107 Table 5.9 Significant Group Differences in Percent Sigma per Night. GROUP 1 GROUP 2 GROUP 3 GROUP 4 GROUP .05 .01 .01 .05 GROUP 1 .01 NS NS GROUP 2 .05 .05 GROUP 3 NS

PAGE 116

108 ROERRGE PERCENT REM PER NIGHT 10. eo 4 + 43e.ee 4 50.60 4 + 70.00 4 90.00 • 4 4 Figure 5.10 Percent Active Time per Night for REM.

PAGE 117

-109 Table 5.10 Significant Group Differences in Percent REM per Night.

PAGE 118

110 Figure 5.8 is the monumentally high value for Group 0. Percent delta shows much less variability from that point, but continues a slight decreasing trend. Table 5.8 shows that the Group 4 and Group 2 values are both significantly lower than the Group 1 value. The percent sigma per night, shown in Figure 5.9, shows that Group 1, Group 3, and Group 4 all show about the same value — sigma is active over 40 or 50 percent of the night. Group is significantly lower (21 percent) and Group 2 is significantly higher (68.6 percent) . REM data are given in Figure 5.10. Table 5.10 shows that Group 2 is significantly lower than Group 1, but no other group differences quite reach the .05 level of significance. It is important to realize the value of the additional information that comes from calculating moments about the midpoint in addition to the nightly percent of each given type of activity. As has just been pointed out (in the case of beta) , changes in the nightly distribution may cancel each other out so that the nightly percentage of activity does not change significantly from group to group. Temporal Relationships Tables 5.11 through 5.15 summarize temporal distribution data for all activity types. The numbers here represent the average number of active minutes during a given hour of sleep. With the exception of Group values, the averages for hour 8 may be small due to

PAGE 119

Ill lOCOCOtOCOiHOlO • • t* en CO 00 CO 1/5 CO I O N • • • • . • r-itHC>OOiOO>COO r-l o

PAGE 120

112 OOOOONOOOtO ocor-(mo"^*no N CM i-H r-l N i-l i-l CD'^COb-OOt-NiH N Oil OJ N CQ iH •H

PAGE 121

113 eQoroiHpopHcsio C^ r-i r-^ fi C0| csitDNOiincoaotD ou)a>inaotooo CO i-l r-l N iH 4J

PAGE 122

114 ^1 fHeono'^'-»

PAGE 123

115 COtO00CVICSIiH«5t* rH N pH rH 1-1 O Tt^ CO rH CO 00 '*,« i-
PAGE 124

116 sleep times of less than 8 hours (as mentioned in Chapter 4) and therefore must be excluded when analyzing trends temporally over the night. Statistical significance of group data, based on 8 values (1 for each hour) per record, have been calculated using the paired-difference t-test. In Table 5,11 alpha activity for Group is fairly uniform, except that hour 3 seems to stand out as being more active than the rest of the night. In Group 1 the only significant change over Group is the large increase for hour 1. All other hours show very little activity, and the group difference is not statistically significant, as shown in Table 5.16. The Group 2 data no longer show the greatest activity during hour 1, but show increased activity throughout the rest of the night; the group difference again is not statistically significant. Group 3 shows again an increase in alpha activity over the entire night, and is significantly increased over Group 1 (p<:.01) and Group 2 (p<.05) . Group 4 shows a tremendous increase in alpha activity over the whole night. The Group 4 data are significantly higher (p<:.01) than the data of all other groups. Beta activity in Table 5.12 shows very little activity during the first two hours, but increases sharply to very high activity later in the night. Beta activity for the first two hours gradually increases with age. Hour 3 remains constant for Group and Group 1, increases

PAGE 125

117 Table 5.16 Significant Group Differences for Alpha Temporal Data. GROUP 1 GROUP 2 GROUP 3 GROUP 4 GROUP NS NS NS .01 GROUP 1 NS .01 .01 GROUP 2 .05 .01 GROUP 3 .01

PAGE 126

118 slightly over Groups 2 and 3, then falls back to about the same level as for Groups and 1. Activity for hours 4, 5, and 6 shows sharp decreases between Groups and 1, then increases slightly over Groups 2 and 3, then falls back slightly for Group 4. Hour 7 activity falls steadily from Group to Group 3, stays the same for Group 4. The results of the paired-difference t-test for the beta temporal data show no significant changes. It appears that the effect of increasing beta activity in the first half of the night is cancelled by decreasing beta activity during the second half of the night. By analyzing the ' distribution over the night using the moment about the midpoint, it has been shown conclusively that this is in fact a very significant trend. It is very important, therefore, to show both measurements, since one value will show changes in distribution over the night, whereas the other shows trends for increases over the entire' night. In Table 5.13, delta shows practically continuous delta for each hour, with slightly less delta during the last half of the night. For Group 1, delta immediately drops out during the last 3 hours of sleep. The first 3 hours show a continual decrease with age. Hour 4 activity has a somewhat different pattern from the others. It drops drastically from Group to Group 2, but then increases sharply for Group 3 and falls off by about 50 percent for Group 4. Table 5.17 shows significant group differences for

PAGE 127

119 Table 5.17 Significant Group Differences for Delta Temporal Data.

PAGE 128

120 the delta temporal data. As would be expected, the Group values are significantly higher (p<.01) than the values for all other groups. The decrease from Group to Group 1 is significant (p
PAGE 129

121 Table 5.18 Significant Group Differences for Sigma Temporal Data.

PAGE 130

122 Table 5.19 Significant Group Differences for REM Temporal Data.

PAGE 131

123 Group 2 Group 3 and the Group 3 Group 4 comparisons indicated statistically significant (p<:,05) differences in the data (see Table 5.19) . Correlations, Autocorrelations, Indicated Periods Autocorrelations and correlations have been calculated by BCOR and BCORl programs as described in Chapter 4. Table 5.20 shows the period of the ultradian rhythms indicated by the autocorrelation functions of each of the various activity types. The value of the autocorrelation function for a lag time equal to the indicated period length is also listed for each entry. There are a few more omissions here than in Table 5.4, which has been calculated by averaging. The two tables agree reasonable well, although, due to the very low values of the autocorrelation function for some entries, the accuracy of these entries is somewhat questionable. Despite the low correlations though, the indicated periods fall within the expected ultradian period range with remarkable consistency. Table 5.21 lists several values of correlation function maxima for various activities and all age groups. As long as it is possible to obtain such values from the correlation functions, they are fairly consistent over age groups. Summary Throughout this chapter, numerous ontogenetic trends

PAGE 132

124 rf| mpj CDrj< NCO lOf00^ CiiH OIN OiO ON ON c

PAGE 133

125 rrl Tf o cn

PAGE 134

126 have been extracted from the raw SAHC data and expressed in descriptive and illuminating form — completely automatically. What has not yet been emphasized in the chapter is the fact that the system (described in Chapters 2, 3, and 4) makes it possible to do an entire study in a fraction of the time required to do the work in the conventional manner, doing most of the calculations and analyses by hand. In addition to its speed, the system also has the advantage of being totally devoid of human biases, making decisions by prescribed quantitative rules that are invariant from record to record.

PAGE 135

APPENDIX 1 PROGRAM LISTINGS

PAGE 136

128 KHrsus THIS FROGRftH F 1 HDS RUHfnMG RUERflGES OF DESIRED LENGTHS RHi;SU&TKtiiCTt; OFF fi LfiKGtK RLiNiiliiG fivERfiuE fi£ Sr'ECiFIED. RESULTS fJRE STORED ON DRTfi TAPE, UNIT TWO REQUIRED subroutines: VSTORE, SMTH COKMOH I OUT CO K MOM X:=«SUK D} KENS I OH I SI<5K.> .. XXSUIK51 6> .1 0UK51 6> . X<51 6 > WI . FORl'.RTC/'HOUin DflTR TRPE UNIT 1, STORRGE TfiPE UH3T 2'^/> UR1TE<1 .8) RERD<1..3> IFP.. ILB FORKRT CENTER STfiRTING BLOCKS OF. THE FIRST ftHD LRST RECORDS 'TO BE PROCESSED. IN THE FOLLOWIKG MRNNER' >"**** ****'> FORMRT FORMRT<'EHTER CODE. .. '/'-'> RER0 HCODE FORMAT < I 2> WRITE<1 ,fee2> FOr;MRT'> RERD<1.7eo:> NLENl F0RMRT WRITE<1/?81> F0R!1RT»:>>"EWTER LENGTH OF RUG. TO BE REnOUED. . . '^v) RERD<1,76C) NLEH2 CRLL RTflPEC2,6,42S.IpUT> IHt=I0UT<42S> CRLL RTRPE42S,ISl> 1F^9 COKTINUE IF -1FB> 515/7,7 7 CONTINUE S 66f.6 v-SET UP UR1TE<3,5> lSlClF-7>, 1 Sl< lF-6> > ISK IF-5> / ISK lF-4>, 1 ISi ClF-2>, lSl 5 F0KKRT<-<'^//'10X. 'RECORD NUMBER DATE FIRST MIIWTE NUMBER 1 'MjHUTES', 2 /'12X>ie,n ,6X. 14, I2/5X, 13/ 13X,I3^v'> HLEN=HLEM2 IB==1S1<1F) NK3N=lSl C TRUNCATE DRTR IF LONGER THRN 580 MINUTES... iF i2>i2,n 11 HK3N=5eO 12 IE~1B+MC0DE 1 2 e e. 3 tee 662 768 761 5i4

PAGE 137

129 CfiLL RTflPE lOUT) DO leOO 199=1 ,NM1N leee lPliT<199) = IREH<10UT''ieO> 50 CONTINUE C ENTER DIRECTORY I NFORMflTI ON. . . 100T<5e7>=lSl KUK 5e?: "> = 1 S i < I F-4 ) Kil!T<5Gi9) = NC0nE J0l'T=lSl 10UT<514)=ISl I0l=T<515>=HLENl 10liT<516> = NLEH2 DO 75 IJ = l,Nr.IH 75 XXSUK=FL0RT> C PUT DIRECTORY INFO. INTO BOTH OUTPUT flRRRVS. . . DO 76 1.1 = 567,516 76 X<1J>=FL0RT> DO 77 IJ = 567..516 77 XXSUf'',=FL0fa<10UT> xsuM=e.e xx^e.e c C SUK THE FIRST NLEH2 «1 MUTES DO 29 I=1,NLEH2 29 X£i!ii=xsu{i+x:':su«ci> C C FIND SMRLL SUM IN THE MIDDLE OF THE LARGE SUM. Nl>IFF=P1=NDIFF+I NPIFP=HD1FF+NLEN1 DC 30 I=NDP1,KDIFP 38 XX=XX+XXSUM<1> C C CCKPUTE 2 RliJUJlNG RUGS. RKD FIND DIFFERENCE... NlK-NrilN-NLEN2 DO 45 1 = 1, Nl II NEy=I+NLEH2 IPK=I+HD1FF IPKP=1PN+NLEH1 XSUK=XSUM+X>:SUM-XXSUM< I > x>:=xx+xxsurKiPNP)-xxsuri XXSUIK I > = XX>'FL0RT<:MLEH1 > 45 X=XX^FL0flT-XSUM>'FL0flT CRLL VSTORECNIH^XXSUM^INB) INl5=IHB+4 CRLL SMTH<:3>H1«.3*X> NB-e C C C C NOW REMOUE THE MERH SUK=e.8 DO 15 I ''I /HI II

PAGE 138

130 3v. SliH=SUI'S + X Sl'l';-S:U!-1/-FL0ftT DC 16 I-l,K5i; C RL L VST ORE C H i M ^ X . I MB > IKf:-=IKB+2e 1E=-1£1<1F> 1F<1LB-IE:> 51C.>516..520 SaCi COKTIKUE 515 lF--:]F + 9 GO TO 514 51£. COKTIKUE CRLL RTft?-EC2.e,42S, lOUT) 10l'T<42S>-]HB CRLL WTRPEC2,G-:*42S,I01CT) CRLl. EXIT S HLT Els'l:

PAGE 139

131 C GRTE C C PKOGRfiM TO GEWERRTE GRTIH6 FUHCTIOH FROM LEUEL C OF RUNUIHG RUtRRGE IK FIRST DflTR PLOT C c c C: FUNCTIONS RS COMPRRRTOR WITH ZERO HVSTERESIS C C c OIKEHSIOH IK<516>.I0lJT<5i6) UKITE 3Ct3 FOK^'lf^T<>'/'EHTER COMP. LEvEL '//> RERDdiiej) ICOMP wRiTE'^) REftD HREC lei FORMRTCIt) WKlTECI^i82> iei2 FORMRT KI'!IH=IM<512) IF 5,5,4 4 HK3H=5©0 5 COKTIHUE DO e I = i,5e.O c. iouT DO 10 I = l,NI1in 1F Se IB" IB* 12 CfiLL EXIT END

PAGE 140

132 C UL7RRD C C: PR06RRH TO REMOVE SHORT BURSTS C FROH GfiTlNG FUNCTION C C DRTR IS TRKEH FROH RHP REPLfiCED IN RELRTIVE C BLOCK 17. C c DIKiEKSION IX<:516>, I0UT<516> «R1TE<1/ 1000 leee Foi 15/15/20 15 DC it: K=i / ICOuKT 18 1XCI-H>=1RESET GO TO 99 26 lRESET=LftST 99 1 COUNT =1 160 LRST=HEW 1=1 + 1 DO 116 N-I/516 lie IXCH>=0 CRLL UTflPE<2/IB/516/lX> 260 IC^lB+12 CRLL EXIT END

PAGE 141

133 C ULTRD2 C C PRDGRfiK rorFINDING 'RCTIUE' PULSES IN C BJh'nRV ULTRflDlRN SERIES C: C DIMENSION lX. I0UT<516> wunE leGO> lece F0M-;n7 Rfc'RDCl.iGOi> HREC DO 200 Nt<=l..KREC CRLL RTRPEC2, IB.516. IX> KMIH=IX<5i2> 1E:==IB+12 CRLL RTRPE<2, 1B,516. IOUT> C INjTIRLIZE. . . 1=2 ILRST=IOUT 1BEG=I01IT<1> 10 IF < I -500 > 11,11,80 11 IF<10UT... 20 IF-lX 30.40,48 C C CKR'i'Gt TOG SKRLL... 30 1=1-1 C BRCK TO BEGINNING? IFCI) 35,35,3! 31 IF 35,35,28 C: C ELIMIMRTE PULSE OH GRTING FUHCTIOK. .. 35 1=1+1 IFC10UT<1>> 38,38.36 36 10UT<1)=8 GO TO 35 38 ILRST=0 GO TO 10 C C CORRECT GRTING FUNCTION... 10 IEND=I-1 C SHORTEN PULSE IF NECESSRRV... 41 1F<10U7<1)) 43.43*42 42 1OUT
PAGE 142

134 1 = ] + 1 GO TO 41 C TOO SHORT NOl.'? 43 IFClEKD-IEEG-lCi) 45,4S,48 45 DO 46 N=1E:EG. I END 46 I0l?T C 58 lF-46) 51,51>78 C CHRMGE TOD &HRLL. .. 5i 1=I+J 1F<10UT 66,66,65 65 10UTJ 74,74,73 73 10UT=8 GO TO 72 74 ILr:ST = l 1 = 1 BEG CO TO 10 C ee COKTIHUE C C CRLL UTRPE<2, 1B,516,I0UT> 2»e 1B"1B+12 CRLL EXIT EWU

PAGE 143

135 C ULT3 C: C THIS PROGRRM HERSURES LENGTH OF ERCH ULTRftDlfiH C F'EKIOD RHD RECORDS THAT INF0R?1ftT10M IN C DftTfi BLOCK 2i C C DlKENSiON 1X<516>,I0UT<516) UR17E<1. leCC) jeee formrtc^'st. blk='> RRR[) IB lee.i F0RriRT WR3TE<1. i602> ieC';2 FCiRt;RT RERD<1, 1C1C1> KREC DO 100 I1=1,WREC CRLL RTRPE<2. 1B,516.I0UT> lE:=IB-4 CftLL RTfiPE<2.IB,5i6.IX> DC 5 l=20e>5i6 5 IOl-T = e NC.OUK'T = e NLRST=IX<1> NFER=e DO 58 1=1,500 1F> 16/9,18 9 NCOUh'T = NCOU»U+i 60 TO 50 10 1F 38.38,28 20 KI-ER=NPER+1 I0UT<26i2i + HPER> = NC0UNT 1 Ol'T C22e + NPER> = I -NCOUNT 36 HCtiUNT=l 50 HLftST=IX CRLL EXIT END

PAGE 144

136 C RHRU6 C PROGRnn TO SMOOTH RUHHIHG flUERRGE DflTH FROM RELfiTlVE C BLOCK 5. PUT RESULTS IHTO RELflTlUE BLOCK 25— WITH NO C TIKE SHIFT C C C REQUIRED SUBROUTINES: SHTH2 C C C REQUIRED SUBROUTINES: SMTH2 C C COHMOK IX COKMCH X COKMOM V DiKEHSIOU IX<5I6>»X<5i6>»V<516>> yR3TE leee for«rt<^'no. of rec.s='^ RERDie01> NREC li}R3TE iee2 F0KI1RT REfiD IB I eel FORMAT < 1 6) C C DC lOe I1=1.HREC CftLL RTflPE<2iIB,5i6.IX> HHIH=IX(512) DO le I=S.NKIH le x=FLoaT> I9&=HHIiHi DO 20 1=199/516 26 V=e.0 CftLL SHTH20.HMIK.2.}<,V> DO 38 1=1*516 30 ix = iFix IE-lB+2e CftLL UTftPE<2, 1B,516*1X> lee iB=iB+4 CftLL EXIT EHD

PAGE 145

137 C PEBK C C FRCiGRftri 7 FIMD NRX flWD MIN PEfcKS IN C SK.COTKED PtRl ODI CI T V DRTR C C «K]TES DRTR INTO RELRTIVE BLOCK 13. C cor, M OH X COKHOIl lOUT COKMOK l&RTE DU'EHSION' X<516), NPK<5IC.), XSUM<2e • 20) , 1HD<26> . lOUT 1 lGft7E WKITE<1.99> 99 FORKftK/^'DftTft TfiPE...UHIT T«0') WRiTE lee F0KI1RT RF.fi[Ki,16i> HREC lei For 162 FDRHRTOV'tNTtR STRRTIKG BLDCIC OF FIRST RECORD.../') RERr> I ELK DO Se IREC=1.KREC CRLL RTfiFEC2,lBLK,516..KPK> NPTS=HPK<512> WRI TE<3. 1 64 > NPK<5J3> / HPK<514> , NPK<567> > NPK<5e8>/ NPK 1 HPK<5ie>,KPK<589) 164 FORMRTC'^'^-^-i'/'/'ieX, 'REC NO' * lOX, 'DRTE' ^ 10X, 'LI ' . 1 BX, 'L2' . 1 jeX,'PC'/'/',9X,16,U,SX,12,I4,9X,13*9X,I3>18S> 12> lE;LK=IBLI<+2e CRLL RTflPEC2> IBLK,516..NPK> C CLERR OUTPUT RRRRV IHDICRTIHG POSITION OF PERKS... iOL'T(n=i60i C ENTER SCRLE FRCTOR RHD EXP. FOR PLOT PROGRRM. . . I0UT<5UO=l ICii;T<511>=0 lDl'T<512> = 5e«C DO 4 1=2,500 4 ICiUT> 5 X<1>=XX 1X=1 ICODE=e XLMIH=6.e xLKftx=e.e NPK3=HPTS-3 C C STRRT LOOP FOR LOCATING PERKS... C DO 26 I=4,NPH3

PAGE 146

138 lF'3=I+3 XMP:X=X Xtt]M=X-XMfiX> 12,12>11 11 X«r:X=XCN> GO TO 15 12 IF 14,15,15 14 XMIK=X 15 COKTIHUE C C «E KOU Hftl'E THE LOCRL MRX RND HIH C C HEXT^ DETERMIHE IF POINT I IS «RX OR MIH C C DID PERK OCCUR? IF 16,18,18 16 IF 17,17,26 17 IF 20,28,171 171 IF-.8iXL!1flX> 172*172,173 172 XLKIH=X(n ICCDE=e GO TO 20 173 IX=IX-! ICODE=e GO TO 28 18 IFC1C0DE> 20.181,29 181 IF<.8*X 28,28,19 IS NPK(IX>=1 IX=IX+I 1CCDE=1 XLKRX=X 26 CCHTIHUE C C EHlJ OF PERK LOOP... ME NOW HfiWE THE LOCATIONS OF C RLL PERKS C DO 21 1=1,28 21 IN&«e 11 = 8 IBLK=lBLK-8 CRLL RTRPE<2,IBLK,516,I6flTE> DO 28 1=2, IX 1P3=HPK lK3-NPJx' IF<198-5> 27,27,23 23 lF<:i98-35> 26,28,28 26 19<*=1 DO 280 H^ltn, IP3 268 19«'=199'»1GRTE

PAGE 147

139 J I" < 199) ?S.. ?S/2ei H;rT<199)=^f.O K.l?T<19t:> = r.ei 1KI:<199>= IHD<)99> + I 19t-lh'L><:i99> XSUH<199, 19?.> = XX X<]1>=XX GO 10 2S 2? KtK<] >-HPK 2£: COKTIHLIE C RT THIS FOIia.. THE FIRST IX UfiLUES OF X HftUE C RLlTHE lUTERVRL UftLUES <<3> C C C USE IGRTF. RRRFiV TO EHTER ALL THE IHTERUfiL UfiLUES C TC DF. USED FOR" STfiTISTICS LfiTER C DC 55 1=1,516 Z'o I6RTECI> = 6 IGf:TE<2e> = KPM3^&e+l n'.3==16fi1E<26> DC 66 1=1, in3 6e lGnTE=lKDCI> DO 65 I=1,IH3 IF3=IHDC1> DO 65 H=l , IP3 I^i: = 2e*l + H I«;^;=IFIX> 65 16fnE C C WK3TE STRT DRTR IHTO RPPROPRRTE BLOCK C 1E:LK=1BLK+8 CRLL UTRPEC2, IBLK>5i6, IGBTE) 5e. ILLK-IBLK+e CRLL EXIT EHD

PAGE 148

140 C REM C C: C SPECIRL PROGRfiH FOR OBTAINING REM ULTRflDIRN C PftTTEKii FROM SLEEP STRGE DRTfl FROM SRKC C C COKMOM I OUT PIKENSIOH 1&1<516>, IOUT.. IX<516> 1 WK1TE<1.2> 2 FOr IFB>ILB 6 FOkMRT< 'ENTER STARTING BLOCKS OF THE FIRST fiND LRST RECORDS 1 'TO BE PROCESSED, IN THE FOLLOyiKQ MRNHER'^'**-*:* ****•'> 3 FORMRT IKt:=I0UT<42S> CRLL RTRPE<1,6,42S.IS1> IF = 9 514 COKTIHUE IF <1SI-1FB) 515, 7>7 7 COiaiNUE S 666 6 /SET UP WRITE <3,5> lSJ, ISK lF-6> , ISK I F-5> > ISI CIF-4), 1 ISl>ISl 5 FGRKRTC^/X/'IOX, 'RECORD HUKBER DftTE FIRST HIHUTE NUHBER OF 1 'MINUTES', 2 /'12K,I6,n,6X,l4,I2>5X,I3,13X,I3/'>'> KLnH=NLtK2 IB=--1S1 C TRUNCATE DRTR IF LONGER THRH 586 HIHUTES. . . IF 12,12/11 11 NM3H=5DO 12 IB----IB+NCODE CRLL RTRPE<1, IB,516, IX) DO 1000 199=1,NM1N i meI Ol'T < 1 99> = 1 REM< I OUT < I 99>/'l 68) Se CONTINUE C ENTER DIRECTORY INFORMflTION. . . IOI;TC50?)=ISI=ISl = NC0DE 10UT<510)=e I0UT<511)=e 10UT<512)=NMIM I0L'T<513> = 1S1<1F-7)

PAGE 149

141 IGUT<5H) = ISKIF-6) ltiUT<5i£>> = e DO 64 I = l,Nt1IK IF-5> 6e*59>68 59 10UT=8 64 C0K71HUE DO 65 I=NriP/5e8 es iouT=ei CRLL aTfiPEC2/IMB..51S,I0UT> IKlr.= lNB+12 CALL U7BPE<2/1HB>516,10UT> IKf?=INB+J2 IB---IS1 1FCILB-1B> 516*516,520 526 CCKTIHUE 515 IF=lF+9 GO TO 514 516 COh'TJK'UE CRLL R7RPE<2/e,42S/I0UT> I0UT<42£!> = 1H8 CRLL WTRPE<2, 6/428^ IOUT> UK1TE<1 , 1466> 148e FOR'J'.RT GO TO 14&1 CRLL EXIT S HLT EHP

PAGE 150

142 C RFMULT C C PROGRflM TO PROCESS REM ULTRflDIftN PRTTERH FROM SftHC C SLEEP STftGE DRTR C C DIMENSION IX<516> WK3TE 23,23,40 23 COKTIHUE DO 25 N=I, I COUNT 25 1X=1 40 1C0UNT=I 86 1LRST=IX 96 COKTIHUE CRLL UTRPE<2, IB,516,IX) 1 66 1 B" I B+ 1 2 CRLL EXIT END

PAGE 151

143 C MOMENT C C PRDGRftM TO COfiPUTE MOflENT RBOUT THE MIDPOINT C DlSlRfBUTrnV" "*"'*"' '"^ ^^'«'-"«TE SKEWNESS OF RCTIUITV C C GRERTER RCTIUITV IN THE LATER HRLF OF THE NIGHT UILL nuP C PCSITIUE MOnENTS-GRERTER RCTHUITY IN THE F r"t C HRLF OF THE NIGHT WILL GlUE NEGRTIUE MoflpNT '--FOR PERFFrx. V C. BRLRNCED DISTRIBUTIONS, HOMENT WILL BE ziRO? ^^''FECTLV C THE RSERRrp'^in' P^'^S/"^ "^^"^ '^ "^^^ CRLCULRTED, RND C JfERCH GROUP ""^ ''^'''''''' '^ *'"'^'< «"^ ^"^ ^«^ C c C RECUIRED subroutines: STflT2 C WRl'TE!J?9enr^'^^^' ^^"^^'^^>'C«-'"T0T<2e),XM0MC2e> see forhrtcst. BLK. = '> RERD<1,9G1> IB 961 FORMRT 962 FORflRK'NO. OF REC.S PER GROUP='> RERb NREC UR]TE 963 FORMfiT< 'SUBJECT?') RERD<1,964> ISUBJ 9&^ F0r WR1TE<1, 1033> 1633 F0RMRT<'l1flX. COUNT PER MIN. = ') RERD<1,1034> XMRX 1634 F0IVMRT ISUBJ 96e ^^^7f!"^^«i;^?6X,^'REC. N0.',28X,'HCKENT',15X,'T0TRL ', DO 100 11=1,NREC CALL RTflPE<2,IB,516,IX> C SF=FL0ftT>

PAGE 152

144 EXi -Fl ftflKlXvr.l 1 )> J J 9v;, <*s, 1 K'l'2= N!im''2 TCn=^T07*>«:99 XHOf;i=XKf.Mi+X99*FL0fiT*.eei Xt1CM-X«0ni CUKT07=(T0T/158. >*SF CO TO 100 ^^•' COKTIKUE b.!/ IX<513),1X<'5I4>,ISUBT &e *52Ci 1C t; COf'-yERT TO KIKUTES... Xtr.RR^XPftR.-'Vb.oj,. SD--^SD.''Xl1liX ir--*J';jJ'rE<3,le3T.> ISLfBJ, XBRR,SD ' rOR^aT<.,OX.^.UERBOE HI»UTES OP ^,5R1,^ PER REC=^,P,2.4 see: CONTINUE CP.IL EXIT EK'I)

PAGE 153

145 651 PDIFF PRCiGRflK TO PFRFORM PfilREP DIFFERENCE T-TESTS FOR EVERV PRIR OF GROUPS OF HEflSUREMEHTS GIUEH REQUIRED SUBROUTIHES: STRT2 DIK.EHSION DRTRC5, 19) I12<5.5>. 13<5.5) RERD LRBELS WR17E FOR«RT< 'ENTER 2-LIHE REFiD LRBEL.T<5,5>,n<5,5) LRBEL BELOy. WRITE eee formrtc'no. of srmples per 6R0up='> RERD<1,801> HS eei F0RMRT<1€.> WRITE 862 FORMRT<'CRlTICflL T URLUE FOR .1=') RERt>Clie63> TPl 863 F0R«RT WKlTE<1.8e!4> 864 F0RI1RT< "CRITICAL T URLUE FOR .85«'> RERD<1,893> TP05 WRlTE 865 FORMRT<'CRITICflL VALUE FOR .ei='> RERD TPei SQK=FLORT5 JKII, JJ>=JBLRNK 12<1I, JJ> = IE!LHHK 13C11, JJ> = 1E:LRHK T=e.e DO 1 60 I GP= J , 5 I6=1GP-1 WRITE IG FORMRT ,Isl,KS> FORMRT COKTJHUE . ">

PAGE 154

146 C FIKD UfiRIOUS PAIRED DIFFERENCES DO 280 JJ=J^4 1P1=JJ+1 DO 260 I1«=IPI,5 DO 20 N=1.NS 26 X=DftTft-DftTfi C MERH fiHO ST. DEU. CftLL STftT2 XBfiR=ftBS ^ FIWD T VRLUE. . . C T<1 I, JJ>=^SD IF<7 = IfiST IF-TPe5> 286,23,23 23 12CII,JJ>=iftST IF-TPei) 288,24,24 24 I3 ^sfeO FORHRT LRBEL 551 F0RMRT<28X,5CftI> WRITE<3.95e> F0R«flT<^/'/',18X, 'CROUP 8' , 9X, 'GROUP 1 ' ,9X, 'GROUP 2' 19X, 'CROUP 3' -9X, 'GROUP 4'/-) ' DO 380 JJ=i,4 1G«=JJ-1 956 952 368 WR37E<3.952> IG^ , 1 1 < j i , jj) , J2< II , JJi ISe-lT tTs COr?nV.^^''^''°"'* ''I1^2X,5 ''''''^'""''''' CfiLL EXIT END

PAGE 155

147 C STRT C C C C PRDGRRM TO DO STftTlSTlCftL RNflLYSIS OF INTERVBL C DfiTR STOr OK DECTRPE C c DIMENSION IIK'516).XSLlM<2e>,NCNT<20>.XSQ<2e> C C ZERO OUT SUK RRRftV BEFORE STRRTIHC: C DO 10 1=1,20 xsG!=e.e KCN!T = ei WfUTE lee FORMRT<>'x'EHTER HO. OF REC s' TO BE PROCESSED. .. 'x^) REf>D NREC 101 FOrvMflT WKITE 162 FORMRT<^^'EHTER STARTING BLOCK OF FIRST RECORD...'/? RF:RD<1,161> IfK DO 56 1I=1,HREC CftLL RTRPE<2, 1BK,516,IN> WR3TE<3,ie4> lN<5I3>,3H<514>,IN<587>,IH<58e>,INC515>, 1 1N<516>,UK56S> F0RKftT HH«;S=1N<26> C C C ZERO STRTISTlCftL DRTR FOR TH2S RECORD... ICKT=e XBRR=e.e XBSQ=8.e XS&b=6.0 c C FIND SUM FOR EACH HOUR... DO 38 M=1,NHRS C C NO. OF IHTERURLS THIS HOUR IS: N1KTS=1H KCNT+HIHTS HCNTC20>=NCNT<2e>*NlHTS 1CKT=1CNT+HINTS DO 38 1=1, HINTS 19?*=2e*M+I 164

PAGE 156

148 XX=FL0ftT> XBr*R=XBflR+x>: XStiB = XS«t{+X»XX xsuiK2e>=xsufi<2e)+xx XS{v'<20) = XSPk26)+XX*XX XSC.' = XSQCH)+XX*XX 36 XSliM = XSU[1 + XX C C T07RL NO. OF INTERVRLS FOR THIS RECORD IS XNCHT = FLOflT -^ci^lku ii>... XI?RR=XDfiR^XI,'CNT XSftB=XSG>D-^X»CKT XBS:Q=XE:fiR*XBfiR Uf-;r<=XS£)E!-XB£Q SD"VRR**.5 WftITE<3,l5C5) U^wrJ^'TiJ^^vr^^"^"^^^^^^" ^^'^ T"I^ RECORD... '^x> «K 1 7E<3, 1 51 > XBfiR, XBSQ, XSQB, UflR, e:D WKlTE<3,i52> J 52 FORMRK/y^/ieX.'INTERyRL URLUES'^/'i DC 40 M=1,KHRS C C NO. OF INTERMRLS THIS HOUR... NIHTS=IN WK3TE<3,I53> M 1 53 F OR HRT < /^ i CX , ' HOUR NUflBER ',13,'..."', •• ) ' DO 16 l = l,NlinS I9?=28*M+I «RiTE<3,i54> 1K J 54 F0RHRT<18X,ie> '•6 COKTIHOE 50 l&iC=IBK^8 C 150 151 C OUERRL STfiTlSTICS WERE... 155 156 2ee WRITE<3,155> XSlW<2e) WRIT?o!r5efHCHT?2e; ''''''"'' ""^= ' ' ^^«. ^' ^X. 'HINS. '.> nntTe^^'':;^^'"^^^"''^*^O*" IHTERyflLS=',I6^> WRiTE<3,2ee.> xsec2e> F0RMRT Xr-:pR=XSUri<28>/'XX XS«B=XSQ<2e>>'XX XBSQ=XE:AR*XBflR up.r.=xseB-xBSQ SD-URR**. 5 WKITEC3,2ei> XBflR 261 F0r WR1TE<3,159> 262 156.-

PAGE 157

149 159 FCr,MaT^XX XfJSQ^XBftRfXBRF: XSKF:=XSe^XN VriR'=XSGB-XeSQ Sr>"URR**.5 WK J TF C3, 1 6Ci> M* XBftR> SD, HCHT , XSUK<«) , XS6 1 66 FORMRT CI 6X.. 1 4 . 6X. F 1 8. 4 , 3X, F 1 ©. 4 , 1 tX.1 5, 9X, F 1 6. 4 > 7X, F 1 e. 4 > ?e COKTIKUE CftLL EXIT EKP

PAGE 158

150 C PERLEN C C PROGRRM TO MERSURE flUERRGE PERIOD LENGTH OF EACH C ftCTIUE PERIOD OF fi GIVEH TVPE OF flCTIUITV ICOUNT=TOTftL MINS FOR RECORD J. C C XIIERNv'IJ^MERN OF ITH PERIOD C X«tfiH i&ee FORMRTt'ST. BLK.=') REfiDCl>ieoi> IB leei F0RMRTCI6) WR1TE<1, 10e2> 1002 FORMRTC'NO. OF REC.S PER GR0UP='> RERD HREC WRJTECl. 10e.3> 5 663 FOKMflT<'' SUBJECT? '> RERD ISUBJ iee.4 For DO 300 NH=1,5 DC 1 8 I = 1 , 1 x=0.0 XMnRN=0.0 STDCI)=0.6 16 ICOUHT=0 DO 100 11=1,NREC CRLL RTflPE<2.. 1B,516.IX> NM1H«=1X<512> IB-IB-H6 CRLL RTRPE<2,IB,516,IX) NPER=1X<20O>

PAGE 159

151 1F> 25,25,24 24 ICOUNT = NPE.R 25 DO 50 1=1,HPER C DELETE PERIODS AT BEGINNING fiND END OF REC C lBtG=IX<220+J> 1 EKD= lX<22e+l>+ I X<200* I > lF(lBEG-0 5(3.50,40 40 lFClEWt)-Hl1IN> 45,50,50 45 IC0UNT=IC0UNT+1 19«i=IC0UHT X=X+FL0H7) X=FL0R1 > Se COJ'.'TINyE lee ie:=^ie+8 I9*;=IC0UKT<1D> DO 70 N=l , 199 19t=l COUNT DO 60 1=1, 198 66 XX<1>=X CRLL STfiT2 = XBRR 70 STD«SD DO Se 1=1,10 999 F0r^MfiT=x CfiLL STRT2 XKEfiH=SD 1G==HN-1 k5K]TE<3, 1009> 1SUBJ,1G i&es F0RHnT WR]TE<3, ieio> 1010 FOrv»1flT<10X, 'PERIOD', lOX, 'MEAN PER. ' , leX, 'STRNDRRD' , II ex, 'NUMBER ',^1 ex, 'NU«BER',1 IX, 'LENGTH', 1 ex, 'DEUIftTlOK', 2€'X,'1H EHSEHPLE '/•/•> DC 259 1=1,9 WRITE<3, ieil> 1,XMERH<1>,STD,1C0UHT<1> 1011 F0r.MRT<13X, 12, 1 1 X, FS. 3, 1 OX, FS. 3, 1 3X, 14> 250 COKTINUE WRJTE<3, 1012> XMERN,STD<10> 1012 FOrvMRT
PAGE 160

152 C TEMPOR C C PROGRAM TO CftLCULftTE MERHS flHD ST. DEU.S OF RMOUNTS C OF ft GIUEH TVPE OF ftCTJUITV DURING EftCH HOMR OF SLEEP C: C XSl«|-.=SUM OF MIHS. OF RCTIUITV FOR HTH HOUR C OF IITH RECORD C C C REQUIRED SUBROUTIHESI STRT2 DIK/ENSION IX<516>,XSUM<1D,10>.X<16>.. ISUBJC5>,XeftR,XSD WRiTE I SUB J 16^4 F0r PC 380 NM=1,5 PC 10 N=l, 10 DO 16 1-1,10 10 XSUM=e.0 DO 100 11=1,10 IB-^IB+12 CRLL RTfiPE<2, 1B,516, IX> DO 21 1=1,500 IF 21,21,20 26 N=l/'60+l XSUK = XSUM-i-l . 6 21 CONTINUE leO lB-lB+12 DO 460 N=l,10 DC 410 11=1,10 410 X<1I>=XSUM CRLL STRT2 XBRRCNJsXB 460 XSD=SD

PAGE 161

153 WR3TE<3, ie09> ISUBJ^IG JpeS FORMfiKlHl. 19X>'STRTISTICS FOR ',5R1,' GROUP ',!!/'>'•> WRnE<3, I01O> ISUBJ leiCi FORKRT'0F SLEEP', UX, 'PER RECORD' , 12X, 'DEyiRTIOH'/'J DO 256 N=lj-ie 256 WK]TE<3, 181 I> N, XBftR ,XSD leji FOK«1RT<12X.12,13X.F10.3,nX.Fie.3> 3ee CCKTIHUE CRLL EXIT EKI-

PAGE 162

154 C GSTftTS C C PRDGRftM TO COfiPUTE GENERRL STATISTICS. MERNS C RNi; URRIRNCES OF PERIOD LENGTHS, CVCLE TIME, IKTERC PERIOD LENGTHS. C C THE PROGRRH IGNORES LOW LEUEL RECORDS BY EXRMINING C SCRLE FRCTORS. . . C S.F. CRITERION FOR SlGMfl=5.e f^ THERE IS NO RESTRICTION FOR REM t S.F. CRITERION FOR RLL OTHERS IS 8.8 C THE STRTEHENT MUST BE CHRHGED FOR SIGMR RND REM C C C REQUIRED SUBROUTINES: STRTl C C DIKEHSIOH I0UTC516>> IXI<2e8), IX2<26e>, lX3<2e9>.. ISUBJ<6> NKK=e wr Jeei FORMRT REPD NREC Jee«2 F0RMRT WR1TE<1, 1663> iee3 FGRMRT IB C LRn;ELIHG INFO. ... WR'1TE<1,10O4> iee!4 FORMRT RERDie05> I SUB J lees Fcr DO 306 111=1,5 IG=II1-1 WRlTE<3>ie30> ISUBJ,IG 1C30 F0RMRT<1H1, 10X,6fll,' STRTISTICS FOR GROUP '.II^.'^) C C IKITIRLIZRTIOK'S. .. NCl=e NC2=e NC3=0 DO I DO NNN=1,NREC CRLL RTRPE<2, IB,516,I0UT> SF=^FL0ftT EXP=FL0flT> SF-SF*ie.*'»EXP NKIN=I0UT<512> WKJTE<3,95e> 10UT<513>, I0UT<514>, SF 950 F0RMRT<11X,'DRTR FOR REC. HO. ', 16, 1 1 , 18X, 'SCALE FRCTOR 1= '/F10.4/'^> 1E::--IB-M6

PAGE 163

155 C ULT2 C C THIS PROGRftH MERSURES RHO LISTS LENGTHS OF C LILTRfiDIflH PERIODS OF fl GIUEN TVPE OF RCTIUITV C C DJflENSlOW 1SUB<5).. IX<51 6> , IOUT< 15> UKJTE<1 , 1600) lee.e For RERDCl, leOl) ISUB leei F0Rt1RT<5ftl> Wf WRlTE<3,ieC8> lX<5i3>, 1X<514>, IX<567>, IX<5e8> leee forhrtc/^/'iox.'rec. ho '/le.ii. ibx.'drte ', IE!---lB+2e CRLL RTRPE<2.1B,589>IX> NFER=0 HCOUNT=0 NLRST=IX<1> DO 50 1=1 ,500 IF> 10,9.10 S HC0UHT=KC0UHT+1 60 TO 50 10 1F 30/38.20 20 HPER=NPER+1 IOUT=NCOUHT 30 NC0UHT=1 56 HLBST=1X UK'1TE<3> J0O9> , H=J,HPER> 1009 F0RnRT<-'-^10X, 15I6> 100 IB-lB+4 CRLL EXIT EMI)

PAGE 164

156 C ULT3 C C THIS PROGRRM HEflSURES LENGTH OF EftCH ULTRftDIRN C PERIOD BND RECORDS THRT INFORHHTION IN C DftlR BLOCK 21 C C DJMEHSIOK 1X<516>* I0UT<516> uRiTE leee FORtifiTc-^'ST. blk='> REftD IB leei FORMAT < I 6> WR3TE<1^ ie02> 10e.2 FORflRTC^'NO. OF REC.S=') REfiDCl,ieCI> HREC DO 100 ] 1=1, HREC IB"IB+16 CRLL RTftPE<2, 18,516, I0UT> CRLL RTB5=*E<2,IB,516,IX> DO 5 1=290.516 5 10UT=e KC0UHT=8 NLRST=IX<1> Nr-'ER=0 DO 50 1=1,500 IF> ie,9,18 9 NC0UHT=HC0UHT+1 GO TO 58 10 IFCHLft3T> 30,36,26 20 MPER=HPER+1 I OUT <208+NPER ) =NCOUNT I0UT<22e*NPER>=I-NC0UNT 361 NC0UNT = 1 50 NLRST=IXCI> 10UT<206)=HPER IB»IB+4 CRLL WTRPE<2, 1B,516,10UT> lee IB:=IB^8 CRLL EXIT EHD

PAGE 165

157 C THE FOLLOWING STfiTEMEHT IS CHfiMGED FOR SIGMR, RKD LEFT C OUT FOR REH C IF(SF-5.e) 100,100,39 30 CRLL RTRPEC2.IB,516, IOUT> NI'ER=10LlT<2eC> C WR1TE<3,S»51> 951 FOrvflRKl ex, 'PERIOD LENGTHS '•) C RECORD PERIOD LENGTHS IN IXl DO 50 1=1,HPER C IGNORE PERIODS CUT OFF BV BEGINNING RHD END OF SLEEP 1F(IOUT<220+1 >-l> 56,50,48 48 IF+IOUT<200+I>-NMIN> 49,58,56 49 NCi=NCI+l lXl=lOUT<2e0*I> «RITE<3,952> IXKNCO 952 F0RMRT<18X,16> 58 CONTINUE C fn:lTE<3,953> 953 FORMRTC/'/'lDX.. 'INTER-PERIOD LENGTHS. . . '^> C RECORD INTER-PERIOD LENGTHS IN 1X3... DO 78 I=2,HPER C C INTER-PERlOD LENGTHS RRE REQUIRED TO BE FROM C 40 TO 128 HiHUTES I99=I0UTC22e+I>-IOUT<2I9+I>-IOUT<199+I> 1FCI99-I20>e.8,70,76 68 IF<199-4e) 70,78.69 6.9 KC3=NC3+1 IX3=I99 WR3TE<3,952> IX3CNC3) 78 CONTINUE WRITE<3,954> 954 FORMftT<^,'lCX,'CVCLE LENGTHS. .. '>-> C RECORD CVCLE LENGTHS -I0UT<219*I> 1 F < 1 991 4 8 > 78 , 80 , 88 78 lF<199-66) 88,80,79 79 NC2=NC2+1 1X2=I99 WRITE<3,952> IX2 88 CONTINUE C C BLIKP POINTER TO NEXT RECORD BEGINNING... lee IB-IB-i-8 WK1TE<3,968> 968 F0RMRT C C PRINT OUT LENGTHS...

PAGE 166

158 C 96e: F0Rf1ft7<25X. 'PERIOD LENGTHS. .. '••> WK3TE<3,9ei> , I=I,HC1> 9ei FORrmT UK1TE<3,902> 962 F0rcMfl7<.'.'r25X, 'CVCLE LENGTHS. .. '/•> UK-3TE<3,9ei> , H=I,NC2> UftJTE<3>9e3> 903 F0r WRlTE<3,9ei> <1X3> 1=1, HC3) C FIKD HE8NS RHD ST. DEU. 'S. . . li;iiITE<3, ieiO> ISUBJ.IG ICie F0rvHRT WRITE<3.1012> XBfiR,SD,KCl 1612 F0RHRT<2X,'PER. LENGTH' . 3X, FI0. 4,6X, Fie.4,8X, 16) CRLL STflTlXBftR,SD> URITE<3,16I3> XeftR,SD,HC2 1613 F0RHRT<2X,'CVCLE LENGTH' , 2X, FIO. 4, 6X, F18. 4, 8X, 1 6> CRLL STftTlXeRR,SD> WR3TE<3, iei4> XBftR,SD,HC3 36^ COKUHif'''"^""''^''^^"•''^J®-'»'^X.F18.4,7X,I6> CRLL EXIT END

PAGE 167

159 C BCORl C C PRDGRftK TO IMPLEMENT BIHRRV CROSSCORRELflTl ON OF C DIGITAL DRTR (ULTRmDIRH GATING FUNCTIONS) C c REQUIRED subroutines: LPLOT^BCOR C c DIMENSION lXfl<516),X<256>>XT0T<25e>,lXB<516>,IflC5),IB<5) WKJTECl/ 160CO leee ForuiRT RERD <1R, 1=1, 5> leei F0KMRT<5ftl> UR1TEC1,1DC2> ie.e2 FORMRT<^'UNIT 2 SUBJECT...') RERD, 1 = 1, 5> lF+2eU.> 3,2>3 2 IB2=1 60 TO 4 3 IB2=2 4 CONTINUE lees F0R^5ftT<>^'sT. blk='> Kie4 FOr«MftT WRITECI, iee.5> 1665 FORMaT<^'NO. OF REC.S PER CROUP='> RERD RERD HREflD PC 260 111=1,5 1GR0UP=I11-I yR2TE<3,S>25) IGROUP 925 FORKnT'> 1K1H=560 I PL = -560 DO 5 1=1,256 5 XT0T<1>=6.6 DO 180 NMUN-1 ,HREC CRLL RTfiPE lXft<5i3>, lXft<514> 92e F0RHRT<8X, 16, 11> NK:H=IXR<512> CRLL RTflPEClB2,NREftD,516, IXB> lF> 16,10,9 9 N«IN=IXB<512> 16 NRERD=NRERD+12 CRLL RTRPE CRLL RTftPE Nt:2 = Nf1IN^2+l CRLL BCOR
PAGE 168

160 56 XTCT 1F 180.188,99 99 IKlNsNniH lee HRERD=HftEftD+12 IKlN=]lllHr2 X99=FL0ftT DO 168 1 = 1, I Ml N 160 XT0T=XT0T/'X99 DO 299 1=1, IMIN 299 X=FLOftT UR'1TE<3, ie2&> 1R,IB/1GR0UP 162© F0RMfiT' WITH '/5R1, l/'2ex,'F0R CROUP '^ll) CftLL LPLOT<:X,XTOT,IMIH,e> 266 CONTINUE CfsLL EXIT EKD

PAGE 169

161 C BCOR C C SUCROUTIHE FOR FINDING CORRELLRTION BETUEEN THO C PINRRV SEQUENCES 1 'S RND S'S ONLV. C C ROIITIHE IS MUCH FASTER THAN CONUENTIOHRL CORRELRTIOL PROG. C c C NPTS=NO. OF PTS IK EACH RRRflV C HLfl6=PESIRED LRG C COR=OUTPUT C C SUER0U71KE BCORC IX/ I Y^ NPTS,COR> DIMENSION IX<516>, 1V<516>^C0R<259> N02=HPTS/'2+l DO 40 HN=1,K02 C0i=6.8 NLRG^NK-I KSTOP=HPTS-MLRG lXB=e IVB=e 1 xvB=e DO 28 I=1,KST0P 1XB=IXB*1X IVB=IYB+IV IF+IY-l> 2e«26>19 19 IXYB=1XYB+I 26 CONTINUE 1FC1XB-HST0P> 21,40,46 21 IFCIXB) 48,46,22 22 1F<1VB-HST0P> 23,48,49 23 IF<1YB> 48,48,24 24 Xe=FLOAT XYD=FLOAT < I XVB> AFLOAT =COR/'=C0R >•*. 5 48 CONTINUE RETURN END

PAGE 170

162 C SPEC C C C PROGRRM TO FIND SPECTRUM OF 10 RECORDS OF DftTR ftT C SPECIFIED RDDRESS, PLOT OUT fiUG. OF POWER SPECTRR c RECuiRED subroutines: fft,lplot c c COKMON IX COKMOII flX COKMOH RV DIK'ENSIOH IX<5ie>.ftX<516>,flY<5I6>, SP<5I6> «KITE<1.. iOCO) leee formrts'-st. blk.='> RERD(l,10i> IB lei FORHRT NX=9 NrTS=512 00 16 1=1,516 16 sp=e.e DC lee Hn=i, 10 lB-IB+12 CRLL RTRPE<2,lB,NPTg,IX> DO 26 I=1,NPTS ftX=FLORT> 26 RV=6.e CRLL FFT DO 56 I=1,NPTS RX=RX*flXCI>+flV*flV 5e £P=SP+flX DO 96 1=1,55 96 ftV=FL0flT/'512. flX = O.Ci CRLL LPL0T 166 1E«IB+12 N2--HPTS>'2 DO 160 I=1,K2 fiXCI >=FLOftT/'512. 166 SP=SP/'16. C C REMOUE D.C. COMPONENT... SP>Cl>=6.e CRLL LPL0T CRLL EXIT END

PAGE 171

163 C TRPER C C SUBROUTINE TO WEIGHT 16 PERCENT OF PftTft AT BOTH C ENDS OF RECORD WITH R COSINE UIKDOW C SUEROOTINE TRPER DIHEMSION DRTRC516) M=MDRTR'l© DR7a=e.6 Pl-3. 14159 F=PI/<2.e*FL0RT> DC 3 1 = 2, M RRC=F*FLOflT 3 DRTR<1>=DRTR<1>*SINCRRG> H=WDRTR-f1 DO A l=N,NDRTR K=NDftTR-I RRG=F*FLORT 4 DRTR=DflTR*SIH
PAGE 172

164 SUIROUTIHE FFKRX. RV,M> COKItON IX PlK.f M?ION RX/ftV<516>, IX<5ie> DO 7 1=1 /NUl lF25,5/5 25 coktihue t;-;=rx RX=RX RV=RV RX=TX RY=TV 5 K=NU2 £. 1F2e,7,7 26 COKTIh'UE K=K/'2 GO TO 6 7 J=J+K fl-3. 1415926. DC 26 L=1>M LE=2**L LE1=LE^2 ux= I . e UV-e.0 fiPC = PI>'FLORT »X=COS DO 20 J=I,LE1 DO 16 I=J,H>LE IF-^I + LEI TX=RX<1P>*UX-RV*UV TV-=ftX*UY+RVCIP>*UX RX=ftX-TX RV=ftV-TV fiX=fiX+TX le fiV=RV+TV ux-ux*yx-uv*«Y 2fii iiv-ux*wv-*uY*yx KE7URW ENl>

PAGE 173

165 C RBNDU C C SUPROUTIHE TO GENERftTE RRHDOM NOS. C SUOROUTINE RRKDUCIl. 12^13* IV,VFL> IV=I1*£.7+12*23+13*1?3 IF<1Y> 5>e,6 5 IV'^ IV-* 204 7* I e VFL=FLOftT VFL=YFL*.4eS3E-3 RETURN ENr>

PAGE 174

166 C: GftUSS C: C SUIROUTIHE TO GENERATE GRUSSIftN SfiMPLES C WITH MEftH=fiM, ST. C>ty.=S. C SUE ROUT 1 UE GftUSS < I l.I2,I3,S,ftM,y) t>0 5e 1 = 1,12 CftLL RftNDU I1«I2 1 2^-1 3 I3-JV R=ft+V U=Cfl-6. e)*S+ftH RETURN ENI>

PAGE 175

167 C RTTEN C r ^"S22!^l^ ^*^ CRLCULftTE MRGHITUDE SQURRED OF GRUSSIRN C CKP.RftcTERlSTIC FUNCTION FOR GIUEN S7 . DEV. C C RERUIRED SUBROUTINES: LPLOT C C DIIIENSIOH FREQ<5I>, RTTC51) • WRlTE
  • lee-.e formrtcst. deu. of phase error='> RERD SIG leei fomirt F=e.e PI=3. 14159 P1SQ=PI*PI S1G£Q=SIG*SIG DO 100 1=1,51 rrg=-4 . *pi sq* s i gs8*f*f rtt=exp FREQ<1>=F 3 86 F=F+.ee2 CRLL LPLOT CRLL EXIT EHO

    PAGE 176

    168 C STfiT2 C C SUE ROUT I WE TO COMPUTE MERN ftND ST. DEU. C OF M VALUES OF R REAL RRF^flV, X C C SUEROUTJNE STRT2 XEF:R=e.0 SD"0.e XSRB=0.0 IF(N> 161>ieiM6 Je COKTIMUE DO leo 1=1 >N XBRR=XBRR+X*x XBftR=XBftR/FLOAT XSG!B=XSC!B>'FLORT URR=VRR*XN SD=URR**. 5 161 CONTINUE RETURN END

    PAGE 177

    169 C FKFSP C. C PKC'CRP.M TO FIHD RMF-LnUDt RKD PHASE Of RUHHING ftUC C Fll TTRi. . .FIHPi; Mn-GH1TU:>L f FOR VflRIOLIS FKEQUENCIEo. C C F ODES FROL 0.8 TO i.e * HVQUIST FREQ. C C: V = Cf1. . . +CH<2>*X+CMC 1 >*X(Kn + C C2'«=X*X + CPC2)*X. . . +CPCM>x X,C0EF<41>* Cn(26>, RMPd 01 > , PHRSE< 161 > , H kEeC16i> PI=-3. 14159 COKURT--18C'5. -'PI WRiTE REr;D9e3> CZ 963 FDRt1fiT WRITE H 96-1 FC'r TO CP< ' / 12/ ' >«=' > RERD , I=i,H) WKlTE<1.9e5> M 9eti FORMRT<'CfKl > TO CMC ' , 12/ ' > = ' > F<:F-Fi^< 1.963) / 1 = 1 /H> K.2-»1*2+l DC 3 1 = 1 ,11 3 COEF=rCP<:H-I + l> C0tF=C2 [>0 A Ir=l ,H 4 CC!EF<1+M+1 > = CM DO t. 1 = 1/ H2 5 FRFfJ = FLOP.T<:i-M-l> UJRlTE<3/9i6> 916 F0RMRT<1HI / IPX/ -FRECVUtHCV RESPONSE OF RUNHIHG IRVERRGE FILTER'//.''15X.. 'COEFF ICIEHTS. . . '/--^J CRI.L LPL0T'CFRLG!/C0EF,H2/6> DC ?6 J=l /lOl F=. CiKFLORTCvt-O 21KUR=C0S 2IKU1=--SIN GR=-C2 G 1 ^ . D pirx=2iuvr< P1J=21MU1

    PAGE 178

    170 P2R=2]NUR P2J=-2IHUI DC 60 1=1, M 6R«GR+P2R*CP< 1 > + PlR*C!1< I > 63-GI+P21*CP4Pll*CMCI> Xl-Pl IfZlHUR+ZlNUI^PIR P1R=P1R+21NUR-P1 I*ZINyi X2=P2R*2INUR+P21*2INUI P2I=P21*2IKUR-21NUI*P2R" P11=X1 66 P2R=X2 IF-I.E-6> 35,35/40 35 PHF;SE = 9e.*GIyfiBS<60 60 TO 55 46 PHRSECJ? = >*COHURT 55 6R==fiBS Cl'=ftBS<61> ftK.PCJ> = **. 5 FREft=F ?6 COKTmUE CRLL LPLOTCFREG,RMP,iei,I> CRLL LPLOT CRLL EXIT ENP

    PAGE 179

    171 C MfLOT C C C C SUFROUTIHE TO PLOT MERNS ftHD ST. DEU.S OUER RflHGE C HIK. TO MRX. C C ft= HERNS C B-ST. DEV.S C KunOUT=HO. OF POINTS C MII{=LOUEST URLUE OH RflHGE OF PLOT C KRX=K1GHEST URLUE ON RRK6E OF PLOT C HP=1 6IUES NEW PR6E C HP=e PLOTS RT PRESENT POSITION C C SUE ROUT I WE HPL OT < ft . B , NUMO UT . X« I W > KKiRX , KP > DIMENSION R<5»?>,B<5e>.HCHflR<6n DIMENSION VSL<11> iEH[)=fc08 IRSTRIX=-I376 IE.LRNK = -2eU. H1KUS=118.4 I PLUS*1 31 2 IfiKIS=-352 lUP CORE =261^ 3UnRSH= -352 C IF 389 FOr 3lCi FORMRT<' S.D. URLUE ',23X,'<== + « = >') D3U=/'2. VSL<1> = XI1IN DO 363 13=2. 11 3Ct3 VSL + V3NC WRlTE<3iie4) . 11=2.18,2) 10-1 F0RriRT<24X.5> DO 361 L = I.€.l 361 MC.HflR = HlNUS DO 382 L=1.61.6 362 MC.HRR = 1PLUS URITE<3.?60)MCHflR DO 399 Jl=l,NUnOUT C t: CHFlNGE THIS LINE FOR SPACING CHRHGE..flLSO CHRHGE C IF STRTEMENT BELOW

    PAGE 180

    172 DO 399 JJ=1 ,S DO 311 L=l,61 311 MCHflR=IUORSH MCKftR<31>=lRXlS C C CKFiHGE THIS STRTEMEHT FOR SPflClKG CHRNGE. . . RLSO CHRHGE C DO 399 STRTEHENT RBOyE IF^DlU>*3e.>+31.5> H=1FIX< 34e>344,342 340 IFv'I-N-i> 342/344/344 342 U1RITE<3/ ieOO> leeG-i F0r GO 70 395 344 DO 345 L=1,H MCHftR=MIHUS MCHfiR=IEHD RC:HftR 60 TD 399 396 UR3TE<3/26) B< J> / R< J> / MCHRR 26 FOKMRTC '/ F16. 3,.F9. 1 > IX, 61R1 > 399 CONTINUE 999 COKTINUE C C WRITE TERMINRTIOH SEQUENCE C DO 961 L=l,61 961 HCHftR = IlfSCORE DO Sf©2 L=l/61/6 962 MCKRRCL>=IVDflSH WR3TE<3,?60>MCHflR 766 F0Rf1RT<21X,61Rl) RETURN END

    PAGE 181

    173 SlirfvOlfTINE SMTH C SKCOTHIHG ROUT IHE ... COMPUTES RUNHIHG BUGS ^ NRU=LLNGTH OF RUHNIN fiUGS. C HPTS=HO. OF PIS IN RRRfiV X ^ NTS-NO. OF TIMES TO BE flVERftGED ^ X=RRRftV TO BE SMOOTHED C DIKEHSION X<516> HCKT=8 5 NrK=HPTS-NBU suK=e.e DO 10 1=1,NRV 16 SU»<=SUK+X=SUMxFLOftT HPTS=HPM HCWT=HCHT+1 IF 5*5>25 25 CONTINUE RETURN END

    PAGE 182

    174 C STFLOT C C PKC'GRfiM TO PLOT HERNS fiND ST. DEV.S OF GROUP DRTfi C C DRTfi EHTRV VIR TTV C C C REQUIRED SUBROUTINES: MPLOT C C DIKEMSIOH XMERH<25)*XSD<25),ILftBELCie8> WKITE ieC3> ietC.3 FORMAT < 'ENTER 2-LIHE FORHRT'> RERD<1,1604> ILRBEL iee4 FORMAT <:5eifli> WRITE<1.9e5> 965 FORMAT < 'HO. OF PTS.='> RERD HPTS 96e F0RMfiT WR3TE see FORMfiT< 'ENTER MIHIMUH UBLUE'> RERD XMIN Sei FOR«ftT UR3TE 962 FOR«RT< 'ENTER MAX. URLUE'> RERD<1.9ai> XliRX WRiTE leoo leee FOR«aT<'ENTER MERNS. ..'> REfiD , I=1,NPTS> JOei FORMRT WRlTECii 10O2> 1662 FORMRT< 'ENTER STDEU.S. ..'> RERD (XSDCI). I^l^NPTS) C C LRBEL tfR3TE<3/l©Ce> ILRBEL leee format c C PLOT DRTR CRLL nPLOT XMfiX^ 8> CRLL EXIT END

    PAGE 183

    175 C SKTH2 C C THIS PROGRRH RUNS REPEATED SHDOTHIHGS OF X RRRftV C RK'P PUTS RESULTS IMTO Y ftRRflV. C C NL=LENGTH OF RUNHIKG fiUERflCE C NP7S=N0. OF PTS C NTS=NO. OF TIMES TO BE SMOOTHED C x=iHPUT RRRRV C V=OUTPUT RRRRV C C SUBROUTINE Sr4TH2<:Hl. , KPTS. NTS, X, V> DIRENSIOH lX<516>,X<5ie>/V<516> HLI11=NL-1 NK=NLMl-'2 NP=NLKI-NI1 JST=NM-H IF1H=NPTS-NP DO 50 1=1ST,IFIH XSUM=0.0 1K=I-NC1 IP=-1+NP DO 26 H=1M,1P 20 XSUH=XRU«+X 50 V DO 60 l = i.N{1 60 VC1)=V DO 70 1=1, NP ?e V=V RETURN END

    PAGE 185

    APPENDIX 2 THE USE OF SPECTRAL TECHNIQUES IN THE ANALYSIS OF ULTRADIAN BIOLOGICAL RHYTHMS In Chapters 4 and 5, it was shown that the standard deviation of the length of most types of activity cycles was greater than 15 minutes. Large standard deviations in cycle length have been calculated previously by many investigators (Feinberg et al., 1967; Roffwarg et al., 1966; Moses et al., 1972; Chase, 1972). This large error is discouraging when using spectral techniques in analyzing such rhythms. In the following sections a model is assumed for an ideal ultradian series including phase error, and a prediction is made as to the general nature of spectral disturbances to be expected in order to evaluate how well spectral analysis can be expected to work under the assumed conditions. Suppose we characterize a general ultradian series as a number of "pulses" identical in shape except for random additive noise and appearing periodically except for random phase errors. That is, the noisy series can be considered as having been produced from a deterministic series in the manner suggested by Figure A2.1. The final series, y'(t), is the sum of the additive noise, n(t) , and the phase-disturbed series of pulses, y(t) . 177

    PAGE 186

    178

    PAGE 187

    179 That is, y'(t)=y(t)+n(t). The autocorrelation of this series is given by Ry'(T)=E I y'(t)y'(t+T)l =E /ry(t)+n(t) jry(t+T)+n(t+T)j| =E |y(t)y(t+T) + n(t)y(t+T) + a(t+T)y(t) +n(t)n(t+T)|. If y(t) and n(t) are assumed to be independent and have zero means, the cross terms drop out giving Ry'(T)=E |y(t)y(t+T)| + E |n(t)n(t+T)| (Thomas, 1969) . The corresponding power spectral densities would then be Py'(f)=Py(f) + Pn(f) . If the phase error in y(t) distorts or attenuates the spectrum from its undisturbed form, then the composite spectrum may be useless, since the desired spectral components may become buried or overshadowed by the spectral components of the noise. As will now be demonstrated, this may be precisely the case for the model that has been chosen. First, let y(t) , the series with phase error ^ be modelled as shown in Figure A2.2, a series of N+1 pulses equally spaced except for the phase errors, 6±. Let the basic pulse shape be arbitrary, given by x^(t) for -T/2 T/2.

    PAGE 188

    ' 180 The entire series will then consist of N+1 pulses spaced as indicated. The ultradian sequence with phase error can now be written as N/2 y(t)= X! Xm(t-kT-6v) . k=?-N/2 ^ The Fourier transform of this series is given by 00 F|y(t)| = Y(f) = /2 XT(t-kT-6k)e-J2T^*t . -00 It is convenient at this point to make the following substitutions: A=t-kT-6j^ (or, t=X+kT+6jP dX=dt giving F{y(t)} = / i:xT(A)e-J27rf(.X..kT^j^)^j^ •^ k ' Since the summation is not over the variables of integration, the summation may be brought outside the integral, giving Y(f)=( Z e-J2^^Tf^-J2Trf6k) fLx) e'J^^^^aX. Is. -« y ^ XyCf) Note that this expression now includes X.j.(f) , the Fourier transform of the basic pulse, centered about the origin (t=0) . The spectrum of y(t) is obtained from its Fourier transform as

    PAGE 189

    181 FKy(t)V| = Y(f)Y(-f) |(.(.t)}| = ( L e-j27TfkTe-j2trf6^)x^(f) (E e+J27TfkVJ2uf6],)x^(_f) be Then, k=-N/2 l=-N/2 The expected value of the spectrum of y(t) would then E /Y(f)Y(-f) I =P^ (f)-E i EE e-j2^fT(k-l)^-j2Trf(6k-6i)|l ''Tiki^ Note that if the 6^ 's are independent, then Pv(f)=PxT(f)-E |2l} + SZ)E{e"j2'r**< ' ' k ^ k=l ^ •eJ2Tr% e-J2^fT(k-l)l =PxT(f) •( E 1 + EL E |e-j27rf6j^ U/ eJ2^f6i ) .g-j27rfT(k-l)5 Note that -00 where f(6) is the probability density function of the phase errors, 6^ and C^(t) is the characteristic function (Maisel, 1971) . Note that the characteristic function is in this case a function of frequency, f , as a result of these definitions.

    PAGE 190

    182 Assume that the phase errors have zero meaa, are symmetrically distributed ( p(6<-e) = p(6>e)) and stationary so that E|e-j27rf6k |= E{e+J27rf6i I Noting that 2 p *i ^ ?^23 aiaj = E af + XiZ a^a^, the spectrum of y(t) can now be written as Py(f)=P^^(f)| El+(E E{e'^27rf6j^ e-J2^^^T)2 E (E { eJ2Vf 6k } ) ^^^.j-girfkl^ ^l If the phase errors are stationary, E|C6(f) I Vj4TrfkT I so that Py(f)=PxT(f) [ E 1 + I C6(f) |^( Ee-j2TrfkT)2 L k ' k E|c5(f)| V^^f^TJ^ In order to compare this expression with P^^Cf) , the spectrum of the series of equally spaced pulses, it is necessary to refer to Figure A2.2, and recall that the transform of the basic pulse was given as x^(f) . Noting the time shifts of each pulse in x(t) , the transform of X(f) would be

    PAGE 191

    183 X(f) = I]x^(f)e-J2irfkT . k T The spectrum of x(t) would then be Px(f) =X(f) X(-f) =(^XT(f) e-j27rkT) k ^^' (I]x-,(-.f)e+j2TrkT) k ^ =X^(f)X^(.f) (Ee-J^-fkT^ (Ee""''^^'^^) . E^ k k Noting that the two summations are equal, that is, k k ' the expression for P (f) now becomes Px
    PAGE 192

    184 1 cycle per 90 minutes. For further illumination, suppose that the phase errors, 6, are gaussian, with density function f(6>=-(l/ V2iTa2) e-52/2a2^ where a^ is the variance of the phase error (Maisel, 1971), The associated characteristic function, C -(f) , is then C6(f).= /a/>/i;^)e;«^/2°^eJ2^*fi d6 . = (T/ V2Tra2) J g> ( 1/2 a2) ( gZj 4 to2 f 6) ^ 5 . -00 Completing the square in the exponent gives /CO r expL-(l/2.c3^) (§2 -j4TTa2 f 5-.4Tr2a4f ^) -00 -2Tr2a2f2jd = (1/ V2^) e"^""^^^ *^ yrxp[-(l/2a2)(6-.j2Tra2f)^]d6 -co Now let u=6-j2Tra2f, du=d6, so that the integral is then of the form where and K I e du, -00 K=(l/V^i^)e-2^2^2f2 a2 =1/2 a2 . The result of this integration gives Cg(f)=K^Tr/a2 (Selby and Girling, 1964). Substitution for K and a now gives Cfi(f)=(l/V2^) e-27r2a2f2^^^2a2) . Figures A2.3 and A2.4 both show attenuation factor, 2 Cg(f) , for various frequencies and various values for

    PAGE 193

    185 o >> o a (D 3 C 0) Sh • &4 ^ O [Q ;4 m » > 00 c x: o a, •H •P CH CS O 3 c to o » +» 3 •P iH < ca • > c8 m S4 3 p o O -H « u Ot a m > n CM (D 3

    PAGE 194

    186 STANOARD nKVIATlON' OK Kl.KOK (:n) n.) 100 80 60 i 40 20 10 i 8 6 1 4 2 t AiTKMIATION (
    PAGE 195

    •187 the standard deviation of phase error, a , for the gaussian case. A number of simulations of an ultradian biological rhythm were analyzed using a 512-point fast Fourier transform CFFT) algorithm. Phase errors (gaussian) were randomly generated for various values of a . Each ensemble contained 10 records, each consisting of five identical pulses, spaced at 90-minute intervals, except for phase disturbances. The average power spectrum for each group is given in Figures A2.5 through A2.10. Each spectral plot is normalized, the maximum component having been assigned a value of unity; all other values are given in terms of their relative power. Results are summarized in table A2.1. The desired peak in the spectrum occurs at .012 cycles per minute, but peaks at other frequencies become increasingly higher until, at a point between a=lO and a=20 minutes, the peak at .012 is no longer the maximum. It should be pointed out that this model is somewhat ideal, that is all pulses are identical and no additive "noise" disturbance has been assumed. In a real case, i.e. with real data, conditions can only be expected to worsen, so that this model gives an upper limit estimate on the predicted usefulness of spectral analysis in analyzing ultradian rhythms. These results lead one to conclude that phase disturbances with a standard deviation of greater than 10 minutes would certainly tend to accentuate the lower frequency peaks, possibly giving rise to an incorrect choice of the

    PAGE 196

    188 o a 0) D O" 0) u 0) Si s s ^ t^ ;4

    PAGE 197

    189 >>

    PAGE 198

    190

    PAGE 199

    191 o c 0) s a u u (0 Xi E 0) s I o ^4 14 o >>H •H (D 01 01 C C8 (D -S QO, iH Q es s U ft *> OQ U 09 0) S 0< 03 m o • o » s O (U r-l iH bOjD II £8 S • Sh (D Q 0) n • > c oa W OS Hi 3= H M O OS5 0.0 CO CM < o s H

    PAGE 200

    192 ^ •-

    PAGE 201

    193

    PAGE 202

    194 major periodicity. For example, the data of Figure A2.11 have been obtained in exactly the same manner just described, except real data have been used — in this case, the binary ultradian sequence of beta for Group 0. The major peak is at .002, whereas peaks in the expected area (.01 to .012) are much smaller. Figure A2.12, the average power spectrum for beta, Group 2, shows a major peak at .008, indicating a major period of about 125 minutes. The next largest peak is at .002, and the next at .01. It must be inferred then that the results of spectral analysis are of questionable significance when applied to such data and interpreted in this manner. This is not to say that spectral analysis is not a powerful and useful tool, but rather that one must be careful in applying it to ultradian biological rhythms. Table A2.1 Power Spectral Density Peaks for Various Data Sets.

    PAGE 203

    195 >, o c a> s a> u a 3 O (h o I I es 0) CQ U O u u u a> a CO o « e Qi > < < O u s be Eh CO a Q CQ

    PAGE 204

    196 >, o B CD S o* a u a 3 O u o 1 I es 0) CQ U o S 0) Q (S v< 0) a GQ 0) o 0) bO C8 ^4 0) > < CSl 01 u 3 W K M ss H W OO tz; O* H H a Q CO

    PAGE 205

    APPENDIX 3 DATA FROM ALL AGE GROUPS

    PAGE 206

    198 4 ^ I *—!* *' ^»»" ^ ' a kj<^,>^i^\| j I'syNm y . >* I { ' <* 1 i > 'i i?>r^A.tftn^ . j'^^ . i/S^ ., f*"^)!! , <*i i..i^ . .<^ /^^v^/yf t .^ Vv^..r,^ . ^«^ f^^r^?>-rHr^^ ^ rJj^^^j^^^JY"*^^/^.^ ^ j ^1 i \ 1 2 3 4*5 6 7 Hours ALPHA — GROUP

    PAGE 207

    199 1 u n H 1 1 h H 1JI 4—1 1 — J. H — I — ( — h -I — » — J — (H — I — I — f1 I •i — i — I — IH — I I I H — f la t > i -< — J — I — h H — J — J--4-t — i — 5•< — I — i — J4— i — iH — I — h-+ .., — ^^ -\ — i — hH — f — i — I — i — h -J — I — J-4-I — H 4-H — i— {I I » > 7 Hours ALPHA — GROUP

    PAGE 208

    200 -^ -i ^-WWW'V^ ' n-?, ^ ^ * 5 6 7 Hours ALPHA — GROUP 1

    PAGE 209

    201 1 ' ^ i i i i i I ' I « . . f f ( ( , , , J , ~^ ^ ' ' ' ' » .' ' • « " ^ ' " -J I t t I 'i ! t i " ^ ' < » ''' ^ f > B i ^ " I t I }l } ;! J f 1 I 8 t 1 ... . ^ ' ' ' ^ » ^ ^ ' " " ' ' " ' ' t t I t 1 I 1 3 1 . . . hS — i—i — I— i — > --8~ «-8 — » ^»"t 9 t — »— ^-4 — l--i t 1 1 3 p. * > }"i — !*— 4— J — t t d '[ t I • " } " t } 8 ^i-^ -' -i' ^ ^^ ^ i ; t t ( ( i t 1 I i { ? } I I I j , ^ .2 3 4*5 6 7 Hour: Hours ALPHA — GROUP 1

    PAGE 210

    202 J^ait«, ^f j I X^ ^/T^\VV'>Yv/fW^ 6 Hours ALPHA — GROUP 2

    PAGE 211

    203 1 1 -t — h H 1-i — H -i — h 4— +• •i — h 0^ -M — f — H -i — I — h -t — i — I — I — I — I — I — I — I — I — I — I — I — ^ H 1Jj 1-* — k4—+-i — h a -i — i — f4 I ,\ I. ). , ^ a. H — I — f-i — I — I4 — ^i -( — I — I4-H — I^ — h B -f — I — h 4 — I — h H — I — h H — >— +• 4 • -4 — » 1 — h JO. H — ! — III 1 1 H — i — I — f Jl 4-4H — 5-\ — \ — I — h 4 — i-H — H ( I ( +— +• -f—44-44-44—14-4" 4^-44-44-44— «7 Hours ALPHA — GROUP 2

    PAGE 212

    204 ? V-r->W^iV'r^K ALPHA— GROUP 3

    PAGE 213

    205 -4—4 — J — f< — f — f' » 1 t I i ? I > I ; i -HH — h I } U i t i 1 » i i — I — > I 8 t 4 t i i — i — I — J— 4 — > i I { — I — ( {jL ^ . ,if. ? i r i t { ' > t 8 frl nu. I i i -9— M» ^^4 < — »~* — ' — i — } f C ' 9" t J i i C 'M j i' 8 -*— « -*—+ < " i i t * t f l ' { i i I { } t i J J. . .Q I 1 {-t { } i ^ H **—» — ^-H — i-H — ( — M-f a -{ — h4 — >t ! 1 i <].f^ #*-f ^^ {-r ( I I .4•*—4. . 6 •.; :_ .7 Hours ALPHA — GROUP 3

    PAGE 214

    206 \ ^ t I t > 1. t I t H — I 1 I I I t 1 ^? r I 1 I » :,,4&d^fttw!&w.£?!w --H — I — I — I — i--^ 5 — { — it I -J — h-H — I — I I I I ''%. jxJ}uJ:^M 6 Hours ALPHA — GROUP 4

    PAGE 215

    207 -t — I I' I — f4-H ^^ •+— +J H — » — M* — ). h4 — J—'i-H — ! — jXi — I — I — ^__^ ^, i < fII t i I I I -I — 1 — J— f* — I — I — i — I — J — i — H-4 — I4— J4— !« — { — J — 5 — J — f— 4 — 1 — V 1. i 1 t » -8 — J-H — J — J — 1 1 I — f. 8 9 f g "» . .n. r~ -8 — j — 8 — j^— «-4 — S— 4 1 n +~J^-f f-H— =S— f «— — ! — 'r^ — { — { — I — I — j__4 — j_«{ — } — 1_ 7 Hours ALPHA — GROUP 4

    PAGE 216

    208 r~V««P^-*-=?=«?=^4 — t — « — I — { \ ^ V^ < — » — I — I — H-! — ! — s — ; n >>><:>4^3.F , S^rr r ^^>r/^ i Vt^ f-iq — >-~i — » I t T — ^^y^^^tf^K^w i ' ** it"* " '{ — i» ) »ij I li ft «> {<^l t^ > — I — { — ! — } — 1 — J — { — I — f — j -i 4 — I— f — rt,>. j^ >}r" j f it — f — fr--{ — J — ) — ; — f-:^ — I — I ft , , 3 4 5 6 7 Hours BETA— GROUP

    PAGE 217

    209 4-H — h » Ml \ I {I | l i . . ylj I if ,. ! t 1 I ( -H — I ' {i i t jl I (. i — 9 — ^ -< — I — »— +-H — ( — I — i. H — i — J — t a 4-H — ^ { t I 4 — ! — t — t — i — ^ »--J — { — {. f— + •*— f i { { i — { — I ' V I — i — {L +— { — y i j -H— 1-4^ i t } . •*— ! — i t I { -> .. r -i. ^ I* ^' H..,f jl ^ « . ly J .f J J J f -f — f— 4— *H — i — 5— (> } ) < — i I I j L i I t I i i — i ii .« i .„, j — y ^i ] { ' I ' ; fV » i } ! I "* — H-4-H — f — f-H — ( — I — } — J — j — I — }_^ -i — HH — 5 — h [^.... { .. J ( I f> I I j f j ; | .. u , 4„ ^ 3 4 » 5 BETA — GROUP i I i { i -}-~H-}-47 . Hours

    PAGE 218

    210 ^ .=»?»>:Si {— «-^~^g yt J 4 i --i ?*— ; -. <°rr}>>n ,.^ — tTT^L j ^ ;«fr4,.j^ntr ^' I J » . | — 7 Hours BETA— -GROUP 1

    PAGE 219

    211 -* — i — i — ! — h D » '» 'I I t< — f ' ^ * » 1 I I i I 1 «. M ' t ' ' I f I I 1 1 1 1 f--»I i { > .-jj. I i i' JL I ' I I I { 4 -* ' i i . -! — t— +. > » i { t t i t' *--4 — {» 1 I 4 { j -f •^ — { — ^i 8 f i — »— f — I' t ' i t t ij i i . t— fr ^ I LH-~-U»--fr-^v-j^,4^^ W-^ r . I J f ' . L^^J^ ^I g , ^ < — ! — > i } t — 5i ! } > ^ -fr— « 4-4— hU -}— f -1+-H — f t I i ' Ul -f--*-4•? Mi ' > I -I ^-}— + "M-i^— fJ^--4-H--4i.^-.' ->4' J .' I f i t 'i l-H-j-^-H-i7 Hours BETA —GROUP 1

    PAGE 220

    212 W.. ,N^ K^ i^fs fVp/, , VvWi I , 6 Hours BETA — GROUP 2

    PAGE 221

    213 -\ — h n , , , n i — I — I< — I — I — I 'I I — I — I — —< — i — I— + -H 1-I — I — I — 54-4 — t I h -i — I*—* *-H — ( — IH — l i lt H 4 — 1 t « i i I i — H -j — I — t i — I g { — J — I — J 1 < — K --{ — h i — h t a t 1 f-4 -J— f 4— f" f 1 r -i — ( — >— « — I — i \ I M' > 1 1 — M — t i 1 — I — I+-{—*fl i I ' r 1 8 t ? i g" t > ' & 4^-j { ..fr,. { .. if^ l i e 4 -f < I -f— I' t I '8 > t ( ; I I » t t i \ I I •I — h ^ — H-4-H — }< — J«-H — h 4 — M n 4— f-H*-< — ?-4 : 4 — h i — »-H — ^— + ^ — J — ^ -i — I — i' I t }— f i — I i I -I — j — I — f. a ^ — I — ( — f— ^ < — I — f t < I 4 • 5 -H-f 7 Hours BETA— GROUP 2

    PAGE 222

    214 «« J lftOifr^ t«^^*— /.^ I e ' t 4 Hours BETA—GROUP 3

    PAGE 223

    215 . . . nr » I I I n »' I H — K H — I — I — I — It 1 I — I< — I 1 — ». »' 1 I r M ) t I 1 1 I 1 1 K* I I — l-H — t — h 1 • ^ ' ' ' ' ' r I n r I 1 I 1 i ^ t . I f .^», +-+. • ' ' t I >' ? I I I il? { 1 tl I / 1 I f g . -{ — { — t ' y I M { i r t il t 1 | . < ' 8 i I i 1 I I 'f t " t I } i I 4— i— f— I — 1—4 — {— f 4 — }— *F" ' ? " "! iX^ *-iM\ f 1 1 [^ 1 1 rD I ^^ ^-^^^f HHf ( ^ ^ H J ' » I ' ' ' 1 t ' > » 4 . 5 6 7 1 Hours BETA — GROUP 3

    PAGE 224

    216 --fr-*^-M«^~k4~:? ^i?"^ -4=4-i>-H-* 6 Hours BETA— GROUP 4

    PAGE 225

    217 , ,nn, , n, 1 . . . n -i — I — ^ ^ — i — JH — f-H — f--P-I — t-I — I — »-H — I — I — I — { — h ^-H — j — t M j -J — I t t , Jl 4 — I — h +— 4 — F ' M 1 < — I t I *— 4I 1 i' 4— ;» 4—4. '1 i i -J — t — MH — J — J — t t < i — H.r~i t I 1 ^ — » } ( — p— ^ -I — i i i I (M > { >*— i — 5-H — iH — j — h-+— f jt ^t ^ ^' ^ t f i { ..j i^' ^ ( < { ~i . n ={ — j — } — H-I
    PAGE 226

    218 JL^ ' ' J>x ' ' * •' I I I t I t I I t I t { {.-^ * '' ' » t I I I l^ > I > I I I I I I ! j .. | . ' "J^' ' 'I' I » I I I I I I I I I I I I / . :-»» I I I I I I I I I ^ — I I i > . 1 — I I 1 I I ^ — j -' L » ' ' t » I I t 1 I I ! I > I t I 1 I t t ., i_X^^ Jr-t r ^ » '^ ' ' ' > t « I f I I J I I h DELTA — GROUP

    PAGE 227

    219 -* — I — t — J-H — J — h H — J— 1 — i — I — i — h -i — I — i — l-H — t — I-! — J — J — f— J — t — i. -J — J — I — 1 i j , I H — J — I — HH — I — J} -• * ?"* » —» ' < t t H — I — I — HH — I-* — i — HH — I — ! — t-4 — I — HH — ! — ^ -4— I — I — I — i — I — I — I — ; — t -I — HH — J — h-M» t t 1 1 4— f—j — J — )—+t ' t 4 i \ • +-H — h-H — I— "I— H — J— I — I — J — { — k-. i — 5 — { — J-H — I — i{ » } I t I •< — } i 8 t } } 1 i I 1 > { t } i { t { I t f M J] *-H — vn ) 1 ; • } — I { ( — } ( i » 1 I I — f — I — H-i — I } t — I — M' < i I t I I H — J — i — J — h-J»< t I — I — t I I 1 I >i 3 4*5 6 DELTA — GROUP 7 Hours

    PAGE 228

    220 ^^^v^^ rTv^^rio '\QQi-^^^^^^^^d^^^ 7 Hours DELTA — GROUP 1

    PAGE 229

    221 -f-H h H — h i t f 4 — t — h H — iA — I-I — I — I — I— n — f. JjU. -*--+ _L{ 1 1J »— ^ |— *— ! < — h H — • — »-H — I — l-H — I — I 1 . +—1 — fJL. < I t I — I I ! t I t I I 4 — F-+— I — t ill ' t' r I I — I — I f t I I I II 4-4 — h-*a i e ? •i — ! — i. n -t — h r~i. s-^-j — §+— I* -»^ i ; i 1 -« — }" ( — ! — ! — I — H i ^ I j. -f ., } j i i ^ ., | . •J-H — t ' } i 4 — ; ' ». . H — k 1 i (M r I I t i I » t 1 t i t '} i — 8 i t — I — t 1 I — J—i — { — i — { i { <. } 1 i j I j -' t I co^ < < t ! I t f 1 I' 1 2 3 4 • 5 6 7 Hours DELTA — GROUP 1

    PAGE 230

    222 iA.ZV ^'-^ i W^ " ^-rn* "i"" ; '^(V =^^!!!V»^BS ?[vvy\ i n . «^ II ) «}t*^^'*7'^T |t ^ > f ii. f\ ^ pr>-{^« 6 Hours DELTA— GROUP 2

    PAGE 231

    223 < — I' I ' t — IM — h f — H-* -» — I — IM -H — jH — I — I — I — I — I > I — I — I I I I I I I n I I I r I « — V V I I — ( — > ( I t I I I — IJl < — I — I — I — ^-H — I i I I i I i \' t ^ t 8 r » i I t > i 1 f i t t } i t } 1 ZX. ^ 1 r r } i < t I 1 i i g I I i I > I IM t i— H — 1 C 6 8 i 8 } t { i 8 } I I t t f 'I Mi i > i" I t < — I ! I — I 1 I — { — }— «H — Jl -J — 1< — J — f — J — i — i M ff — {i .t .. i> « I 1 1 { t t o. •4 — I— I — f { ' t — fXX. i" t I {ii II { !. { I { I { ' ^ { H — i1 ' Ml i ' i — M8 I I } } i 7 Hours DELTA— GROUP 2

    PAGE 232

    224 .nf< i \r k t/ \^y.rY?r% » ('Onwr'P'rf j V i ^w i. ^'^^rHp'Tl/^^ 4 Hours DELTA — GROUP 3

    PAGE 233

    225 -JX -* — • — • — I — — 4 — J — » — I — 1—4 — h— I — I — I — I — I — 1 t I t »' t < — I — »— ? — til l — H-H — I — J — J — h4 — I t I |, i i — J — IJ — f" ' < t t r I I } I t 8 i I I I { t i, Lh — ( — t-H — Ml i ; I I t* |l 9 +—8 — » t 1 I ( — j t I < -{ — fr^ i 1 I i i r 1 t t t I i I \ {M 'l +-H-H4-"i — I — Mi— I — ^-1 — ? ^ 1 { m a { „»} ,.,.{., I ,| ,; , J , . n . -{ — f . t *! — J — h i — {4 f '> t / /» -J — f— f-H — i — ! — f i I rir J} — hH — ^f — ^ i i 'r 4 — ! — I — i — I — I — i — I — I — { — ) — H-+4 5 6 7 Hours DELTA — GROUP 3

    PAGE 234

    226 ^o^Vv^'^-'^w-M, V^, ,;^y jlT'Vin^ , I B^ w ^tfyr*-y*'^ i \^ n ,) «>«T . /y«i^/ t fLfi» /\ m \ t ?fW I I i i Vr?''"T^iO^Vi^ '^ |ll f» •^l/\„. i^^ t . i f'n» « p . . {«-yrr7Sf7-iryw j rw .^ <-'yfVi ^ rf^ ,i^ 6 Hours DELTA — GROUP 4

    PAGE 235

    227 -» — ysmz -» — I — I — ( — h -* — M-H — I — ^ ' ' « < 1 < I I I l|t t { ; 1 t "^ * — J — S — I — i — J — i — |. I I t 1 I I ' » \ II I { -4< >' i t I I 8 I 1 Ij-^ L * I I { — J. » ' * — I — » } « — K °r I { i' i I | u < I » "*""• — « — »— * f f 11 rf ...r..i.„:„,; 7 Hours DELTA — GROUP 4

    PAGE 236

    228 /.Oj » h \ — p-H \h.jhMx..(Af^.i^. >^aW^ ^^ ,^A^K.,M(k \/r
    PAGE 237

    229 -( h-H 1 1 1 1 >a H — I — H-f\ — »— f-i — I — I — I f t — I — II -J — I — h * — M — i t t < — » I I — I — H 1 . ,u, I , n 1 ' } ' I -f — !— 4-4 — (— 4H — I — I — i-i — I — i — h -i — I — I — h-l — I — y -i — IJl H — I•--h -f— cuxn fM-» — I I' I — ^ a +-H — I — I — h cu H — I — I"4— • — I — I — > -} — I — i — P-Jf-H — M t t n I f < I I t I I — ^H — I — I — I 'I h m M I I a n -! — I — »-H — [ — H-H — i — I — ( — I — I — I — t-J-f — I — fi-H — I — I — ! — M-fl-+1 2 3 4 ' 5 6 7 Hours SIGMA — GROUP

    PAGE 238

    230 =fi2i^^^4::i:iif~^ii^^ ' I • ^ ^ ^ « « «^ r— ^ — r-~f — r— T — r— t — i i | ^'^'>^ ; I rt > tW^i t I i '^ 1 I I t n j'tnr 7 Hours SIGMA — GROUP 1

    PAGE 239

    231 +-M — I — t — -— 4n n r 4 — i-l-H — I 1 — I — h -HA — t4—4" 4—4IL 4 — »4-*44 — h H — H-4Q U 4 *n 4 — H 4 — t4—44 — H 4— 1» 4 — h a 4 — h < — h 4 — I — I — »4 — I — Jl 4 — H 4i-4-H — h M i I M 4—1 — I — *t t I i 4 — f — I — h 4—44 — K a 4— + 4-44— f 4-44—4— 4—44— fa ^ — i — H-f — h a 4—4a 4 — IH — I — M-H< — (^— ? — I — p— V Jl 7 Hours SIGMA — GROUP 1

    PAGE 240

    232 .: — I — 11 I — I 1 — f^H 1 h-V'H 1 !> >' » •*» '^'»<^ ) — »«eL| — I — JLh — I — I — ^i£^ — i — i — l^ J > t \ 4 1 — I — I \'P ' I — ; — I — t »t 4 I — I V "j.* — I — I — F>4 — I — II 1 M — I — I — I — I* I h — It P* — I t tM t I t rv^ < I J — I — p*v-4 — I — I » V { 1 I V'i | hH 1 \^ '\ 1 i 1 1 lUl . /t I \\ at| — 1 i i t — I t i I — I — i I I — I — I — I — I — I — I I TO. t i — t I I — I — »-— < — i — ? — HH — l ^r" I — I — ! — HH — H-« /Am t I I 1 •{ t > » — I — \ > 1^ 1 — I — f-H — I — H-+ 1 2 3.4 5 6 Hours SIGMA — GROUP 2

    PAGE 241

    233 -* — h +—+ H — h 4 — I-i — H ^ — I-» — h 1 — H -4 — »H — I< — i — I 1 1 1 1 M 'l 1 f—M — I — I — 5—4 — »-U — I — J — i -f-H — » — h j — I — J. A — I — I — h-4 — M-4 H — I — h xz: +--+}f77?: IS * — J— + i — f+-H — I — I — f— >* — h J, i — I — J — J — h -4— + H — K H — t H — I — 5 — i ' l ' « • -i — I — IH 1 } J 1— > IM M } \ I 1 I I I I -j I I 1 11 1 > -J — H i — F H — [, -« — ! — > + ! " 1 I > < — lit! «— ^ — i I « I I i II -I — \ — I I M it p {ill 1 I ) M M I I [' 1 I I I I H — t j I — h a * I > < — h-*) — I — I — I — f3 4 • 5 SIGMA — GROUP 2 < t ( I I I 7 Hours

    PAGE 242

    234 S-. f \f^^.. ja^ A>^^A f^h i^fp l^;-^H 1 r I I 1 1 1 1 I r— r , u6uryv^^,Ao 4 Hours SIGMA— GROUP 3

    PAGE 243

    235 4 — I — h JX JX^ H — I — I — y CL. * — I — h i — I — In t_L4. n H — k-i — h 4-H — I — H-*-i — f — ^— }H — I — K-+. -i — K-H — K H — I — »-I — I — h -< — fn -H — i — I — » -H-4H h H — f-j — H i t 1 4 — H H — H 4-4— f1 I P 1 Sl ^<-'i' i 4—4 — H « I i i — \ — fa ^ — M-H-f •4Uh — ! — I — I ! I ( 4-HH — i — h-H — »Jl -< — »n fM — >-« — »-4—4-«-4 — f— 1{ — I — MH — i I I n. r~i.n > ' '} s — y P M ! 4-44 — I — t ' ( I > — I — I — }-H — I — »3 4.5 6 4 »4-47 Hours SIGMA— GROUP 3

    PAGE 244

    236 :AT\jyy}j\i ^ r^ i — I — r^ > r 1 VN^y^VV , : /> \aN ^4— J — i ^rH 1 — J — 1\^ ^ I 1 | \ { — Ki [ 7^f^{rq^ 6 Hours SIGMA — GROUP 4

    PAGE 245

    237 -4-M — h -t — I — »1 — • — I — I — I — I — h -f-H — HH — H-l — J i — t — > > ' ! — t—f -M< — H-i — I — I — h HJ H — ^ H — -»--4I I I P I 4 — I — t4 — I-* — > — I — I — P — » — >-»— + H — ! — ii — *+— f" H — » H — I4 — h OJL I I t H — h ^ — I — H H hf 4 ' -I — I — « — I — h-4H — I — i — h J-4-4 — H-44 — • — I — h I I t i. 4—4H — I I I -< — I — I — IH — I — I — h +— I — f— 47 Hours. SIGMA — GROUP 4

    PAGE 246

    238 +-H 1 J-f— f+— -f J • K -I 1 1 1 h I I I I I H » I I h-H — J 1 1 1— ». H H 4—4-I — IJL 4— *-j—J — H — I — —! — J. 4—1 — I — I — h -< — Ji — (•i — I+-H — il » » I I t I I I I 1 } r *-+ '! I I I M I 1 i I I "4J — -<-H^ — I — I — ^ 1 ' ' ' ' i I > I I 1 I I I I I I j . ' ' < — > > I t ^ I I I 1 I { I I I) < — I — I — i — i — ^-H — I — I I \ 4 ' REM — GROUP « I 'I I I ) « . 5 7 Hours

    PAGE 247

    239 -( — J — h-4 1 1H — I — f-» — } — »•i — i — h H — ( — h a. -i — h i — h -j — h i — p-I — I — » — h 4-H — ! t i — !-H — h -i ! — h i. ( — f — f1* it — I — M-f-l I 4 — j — i — i 1 — H H fQ fi-f4— f -S — h +— + t i ' H — H -*— +• 4 — I — I — h -I — I — I< — h-»+*H-fr\ \ P XL ) M i -M-4^ — H-4^ — J^-^ — } — M-H-f a H — I — f I ' I I H — I — I — I — I — »4 — I — I — h A — >--H -l—f 't ? 1 < a J t i t **-+ -i — h 4— fI J~ H — I — t' I t — h 4— + -f — (— >• 7 Hours REM—GROUP 1

    PAGE 248

    240 -I — I — H +-+-H J-J 1 h . . . . n -I fJ H 1 F — f-U — Uh — , — ^ H — h H — I — "I — I — I — h » » I > ' ' ' 1 I IJ I I 1 1 1 1 I , , [71 -4— + I I »' a •4 — J — h^ H — i 1 H t t I f f • < > 8' ii < — J— 4. I < 'l ' > It — f. H — f ) I I f i — I-{-H — f< — ^n,, . , » f > I I < — h • r t I •» ! I H — I — I — ?~4 4 1JZl MM < — i-LL -^ — »-H — I — I — fi-L» — 1 — , — J a < — HH — I — H-f-H — ! — i ' I » ( — { CI *4 — M. 4 < I -f — I — I — f. -M. . .n -* — { — Ml l < — f. t I t —4—4 < — I — M4 — MH — f — h I 4-^ — [I 1 L . 4 — J — i — I — I — » J — >— *1 2 3 .-Jl li t 7 Hours REM — GROUP 2

    PAGE 249

    241 cn * 1 M-H , ^LH. S 1 h-H — A a. -^~H 1 1 h-H 1 fr. H JM I r --f' < — ' ' ' ' I I I I I I iU a -I — »< I 4 < — > 1 r f — I — M ^"' ' ' ^ ' > J I I I I i > < — J— *l — J — {• < < i i "i > f t I I I I I t *-^< — ' — t — 8 — I — h-j — {.t .j J. H 4-H — * ' > M I 14 -i — f < i i +-4^ > ' I t 1 I i r--' — ^-H — I — I — I — j — (—4 — j.^ ^1 I I I I iN t I I ft "» t t ^ ' ' '' ^ ^' ' ' jin 1 1 ill \ .,14 X14-I — I — ^ > .n .n. . ,n. ,„xi. 4-i -+ a -) — h -I — ) — K-+ -HH — } — I — J. » ' < [ j. 7 Hours REM~GROUP 3

    PAGE 250

    242 — h -» — I — I — \ — i — K—JH — I — » — l-H hI 1 I — ^ flj I ' I I ! ' I r 4 — I — h .r~i J3 4-H — h H — >XL JJ 4--*-4 1 1 — f— 4-• — I — I-H — f. +— +> , ,n, , t > 1 I U t J— I — ^ U I 1 f < — f t f — M I '1 > t -i — f t > I I I j 4 — I" n. . . n r < — i — { — i — ^-H — I — h ' t { — I— +. a < — » -j — f — f--4 — ^ > v I — i t t -( — ^ a ^ — Ii — f — i — t-I — {. XI H — J — I — ^ — HH — H < — H-M— <3 4 •f — ' — J-4-H — ^-H — I — hH — I — h 5 6 7 Hours REM — GROUP 4

    PAGE 251

    BIBLICXlRAPHy Agnew, H.W., Parker, J.C., Webb, W.B. , and Williams, R.L. "The first night effect: an EEG study of sleep." Psychophysiology . 1966, 2: 263-266. Agnew, H.W., and Webb, W.B. Sleep Stage Scoring , Manuscript #293, published by the Journal i>uppiement Abstract Service of the American Psychological Association. May 1972. Aserinsky, E. "Rapid eye movement density and pattern in the sleep of normal young adults." Psychophvsioloev 1971, 8: 361-375. — ^^-^ ^' Boyar, R., Perlow, M. , Hellman, L. , Kapen, S., and Weitzman, E.D. "Twenty-four hour pattern of luteinizing hormone secretion in normal men with sleep stage recording." J. of Clin. Endoc. and Met. , 1972, 35: 73-81. Bremer, G.F., Smith, J.R., and Karacah, I. "Detection of the K-complex in electroencephalograms." IEEE Trans. Bio-med. Engng. , 1970, 17: 314-323. ~ Chase, M.H. (ed.) . The Sleeping Brain , Proceedings of the Symposium of the First International Congress of the Association for the Psychophysiological Study of Sleep, Bruges, Belgium, June 19-24, 1971, Brain Information Service, Brain Research Institute, University of California, 1972. Colquhoun, W. P. (ed.) , Biological Rhythms and Human Performance , London Academic Press, London, England, 1972. Digital Equipment Corporation, PDP-8/e and PDP-8/m Small Computer Handbook , DEC Program Library, Maynard, Massachusetts, 1572. Dement, W.C., and Kleitman, N. "Cyclic variations in EEG during sleep and their relation to eye movements, body motility and dreaming." Elect, and Clin. Neuro. 1957, 9: 673-690. — Evans, C.R., and Mulholland, T.B. (eds.) . Attention in 243

    PAGE 252

    244 yeurophysiology . Appleton-Century-Crof ts. Inc New York, 1969. Feinberg, I., Koresko, R.L. and Heller, N. "EEG sleep patterns as a function of normal and pathological aging in man." J. Psychiat. Res. , 1967, 5: 107-144, Gold, B., and Rader, C. Digital Pr ocessing of Signals McGraw-Hill, New York, 196d. ^ ' Gondeck, A.R. Quantification of the human sleep sigmaspindle , Ph.D. Dissertation, Department of Electrical Engineering, University of Florida, 1973. Honda, Y., Takahashi, K. , Takahashi, S., Azumi, K. , Irie M., Sakuma, M. , Tsushima, T. , Shizume, K. "Growth ' hormone secretion during nocturnal sleep in normal subjects." Clin. Endoc. and Met. . 1969, 29: 20-29. Keane, B.P. Detection and measurement of beta activity in the human eiectroencepnalogram . unpublishecl Master's thesis. University of Florida, 1972. Laidlaw, J., and Stanton, J.B. The EEG in Clin ical Practice E & S Livingstone, Ltd., Edinburgh and London, 1966. ' Lubin, A., Nute, C, Naitoh, P. "EEG delta activity during human sleep as a damped ultradian rhythm." Psychophysiology, 1973, 10: 27-35. Luce, G.G. Biological Rhythms in Psychiatr y and Medicine Public Health Service Publication no. 2088, U.S. Dept of Health, Education, and Welfare, 1970.* Maisel, L. Probability, Statistics, and Rand om Processes, Simon and Schuster, New Vork, 1971. Mendenhall, W. Introduction to Linear Models and t he Design and Analysis of Experiments. Duxburv Press Belmont, California, 1968: Mendenhall, W. , and Sheaffer, R.L. Mathematical Statistics with Applications , Duxbury Pres s, Belmont, California. 1973. " Moses, J., Lubin, A., Naitoh, P., and Johnson, L.C. "Reliability of sleep measures." Psychophysiology , 1972, 9 : 78—82 . —————— ______ Otness, R.K., and Enochson, L. Digital Tim e Series Analysis John Wiley and Sons, New York, 1972. Pawel, M.A., Sassin, J.F., Weitzman, E.D. "The temporal

    PAGE 253

    245 relation between HGH release and sleep stage changes of nocturnal sleep in man." Life Sciences. 1972 11: 587-593. " [ ' Rabiner, L.R. "Techniques for designing finite-duration impulse-response digital filters." IEEE Tra ns. Commun. Technol . , 1971, 19: 188-195. Rechtshaffen, A., and Kales, A. (eds.) . A Manual of Standardized Terminology, Techniques and Scoring H7stem for Sleep Stages of Human Subjects , PuSTxc Health Service, U.S. Government Printing Office, Washington, D.C., 1968. Roffwarg, H.P. , Muzio, J.N., and Dement, F.C. "Ontogenetic development of the human sleep-dream cycle." Science. 1966, 152: 604-619. Sassin, J.F., Frantz, A.G., Weitzman, E.D. "Human prolactin: 24-hour pattern with increased release during sleep." Science , 1972, 177: 1205-1207. Selby, S.M., and Girling, B. (eds.). Standard Mathematical Tables , 14th edition, the Chemical Rubber Company" Cleveland, Ohio, 1964. Silverstein, L.D. Temporal and intra-stage distribution of spindle activity during sleep l unpublished Master's thesis. Department of Psychology, University of Florida, 1974. Smith, J.R., and Karacan, I. "Quantification of the effect of a hypnotic-like drug on slow wave sleep. Sleep physiology, biochemistry, psychology, pharmacology, clinical implications." W.P. Koella and P. Levin (eds.), Proc. First Eur op. Congr. on Sleep Research , Basel, Smith, J.R., and Keane, B. "A method for measuring beta activity in the EEG." Proc. 26th A nn. Conf. Engng. Med . Biol . , 1973, 399. "" ~~~ Smith, J.R., Funke, W.F. , Yeo, W.C., Ambuehl, R.A. "Detection of human sleep EEG waveforms." Elect, and Clin. Neur. , 1975, 38: 435-437. Steiglitz,. K. An Introduction to Discrete Systems , John Wiley and sons, Inc., New York, 1974. Strong, P. Biophysical Measurements, Tektronix Inc., Beaverton, Oregon, 1970. Thomas, J.B. Statistical Communication Theory, John Wiley

    PAGE 254

    246 and Sons, New York, 1969. Verdone, P. "Sleep satiation: Extended sleep in normal subjects." Elect, and Clin. Neuro. , 1968. 24: 417423. Weitzraan, E.D. , Schaumberg, H. , Fishbein, W. "Plasma 17-OHCS levels during sleep in man." J. of C lin. Endoc. and Met. , 1966, 26: 121-127. Weitzman, E.D. , Godamacher, D. , Kripke, D. , MacGregor, P., Kream, J. Hellman, L. "Reversal of sleep-waking cycle: Effect on sleep stage pattern and certain neuroendocrine rhythms." Tran s. Am. Neuro. Assoc, 1968, 93: 153-157. ~~ Weitzman, E.D. ; Discussants: Parker, D. , Sassin, J. "Neuroendocrinologic aspects of the sleep-waking cycle." Taken from: BIS Conference Report #32, 1973. 27-36. \ ' Williams, R.L. , Karacan, I., and Hursch, C.J. EEG of Human Sleep: Clinical Applic ations, John Wiley and Sons. New York, 1974.

    PAGE 255

    BIOGRAPHICAL SKETCH Barry Patrick Keane was born February 26, 1949, in Fort Pierce, Florida. Following his graduation from McArthur High School, Hollywood, Florida, in 1966, he entered MiamiDade Junior College and pursued, under MDJC academic scholarship, an engineering oriented program until 1968. In 1968 he entered the University of Florida where he received the degrees of Bachelor of Science in Electrical Engineering in 1966 and Master of Engineering in Electrical Engineering in 1972. At the University of Florida, Mr. Keane was awarded an academic scholarship as an undergraduate and was an NDEA Title IV fellow from 1972 to 1974. He began pursuing the degree of Doctor of Philosophy in 1973. Mr. Keane is a member of the Institute of Electrical and Electronics Engineers, Sigma Tau, Tau Beta Pi, and Eta Kappa Nu. 247

    PAGE 256

    I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. A. smi'tn, "tThairman Professor of Electrical Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy, Professor of Electrical Engineering and Biophysics (Physics) I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ..%k^^ Graduate Research Professor of Psychology I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. :ang Assistant Profess

    PAGE 257

    Ihi r 1? ^^i^S'' ^^^ submitted to the Graduate Faculty of the College of Engineering and to the Graduate Council and was accepted as partial fulfillment of the requirements t^ the degree of Doctor of Philosophy. 4uirements for June, 1975 ")e^, College 6t Engineering Dean, Graduate School