Group Title: analytical and experimental study of blood oxygenators and pulmonary mass transfer in liquid breathing
Title: An Analytical and experimental study of blood oxygenators and pulmonary mass transfer in liquid breathing
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Title: An Analytical and experimental study of blood oxygenators and pulmonary mass transfer in liquid breathing
Physical Description: Book
Language: English
Creator: Falco, James William, 1942-
Publisher: s.n.
Copyright Date: 1971
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
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Bibliographic ID: UF00097667
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 001024935
oclc - 18000713
notis - AFA6850


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The author wishes to express his sincere appreciation to

Professor R. D. Walker, Jr., Chairman of his Supervisory Commr.ittee,

for his interest and his always helpful suggestions. The author is

indebted to the other members of his Supervisory Committee:

to Dr. R. S. Eliot for his initial encouragement to undertake a study

in the biological area; to Dr. J. H. Model! for extending the facilities

of the Dcpartiernt of Anesthesiology and the cooperation of his staff

for this research work; to Dr. T. >A. Reed for his patient teaching

which provided the basis for of this research work; and to

Dr. A. K. Varma for generously agreeing to serve on co-rinittee as

a representative of the Departmenc of Mathem.atics. The author also

wishes to thank the staff of the Department of An-sthesiology,

particularly Dr. C. A. Hardy, for thoir generous as-sistance.

Thanks go to the pump room crew at Shands Teaching

for their assistance in taking dAta dricag open-heart surgery. Thanks

-also go to Massrs. J. Kalway, >. Jones, T. Lambert and E. Miller for

help witb providing equip-?nen and natorials for this project. Finally

the auth(.r expresses his grateful ipproclarion to Mrs. Karen Walker

for her p;::1ien t '.-crk in typing this di. ration.

The a'ith.r acknowledges the support of the Djpartment of

ChemicaL Erginearing during this study and thanks them for their



ACKNO LE uCGE ENT .............................................

LIST OF TABLES ..............................................

LIST OF FIGURES .............................................

NO -ENCLATURE ................................................

A STRACT ....................................................



1.1 Bistorical Develcpment........................

1.2 The Cacdiovascular-Pulmonary System ...........

1.3 The Properties of Blood.......................

1.4 Description of Oxygenators ....................

1.5 !he Lung as an Oxygenator.....................


2. rachematical Mcdels .................... ......

2.2 Experimental Equip.r.ent and Procedure..........

2.3 Erxperime-,tal Resu1ts--Bubble Diair.eter
1Lsurements ........... .......................

2.4 Expeiieimntal results---0xygenatc Siiiulatinc...

3. C.SERVA ON rO S bUtING OPEN-P-l1ART SURGERY .............

3.1 Theory of Gas Transfer Through bloodd ..........

3.2 Ex:y erimental Frccad e ........................

3.3 Exptrirr antal Results ......... ................

3.4 Conclusions and R.eenr.meidacions ...............







4. THE DISC OXYGENATOR................................ 109

4.1 Description of the Disc Model................. 109

4.2 Analytical Results--Computer Simulation ....... 117

4.3 Conclusion and Recommendations................. 131


5.1 Introduction................................... 133

5.2 Theory of Diffusion........................... 134

5.3 Theory of Imperfect Convective Mixing......... 140

5.4 Transient Dye Penetration in the Lung
Experimental Procedure ........................ 144

5.5 Results and Conclusions....................... 149

APPEN ICES .................................................... 155

A. COMPUTER SIMULATION............................... .. 156


E.1 On.e-di::.nscnal Flow Model ............ 191

3.2 The CSTR Model............................... .. 393

C.. GAS iXCiANGE IN AIR BRKAi ,ING...................... 198

2. I'LR V?:NTAL DATA .................................... 201

ISL 0GPAi HY ................................................ ..212

j' .OGRAPHI. AL SKEICE.. .................................... 216


Table Page

2.4-1 Comparison of Proposed Models with Experimental
Results ........................................... .. 58

2.4-2 Fractional Gas Holdup Volume Vs. Function of 02
and Blood Flow Rates ............................... 64

2.4-3 Boundary Layer Thickness and Profile Parameters.... 70

3.2-1 Summary of Data Taken During Open-Heart Surgery.... 77

3.2-2 Accuracy of Experimental Data Taken During Open-
Heart Surgery...................................... 80

3.3-1 Experimental Values of 02 Mass Transfer Coefficient
and Other Pertinent Parameters..................... 87

D-1 Data Taken During Bubble Measurement Experiment.... 202

D-2 Saline Simulation of a Blood Oxygenator............ 204

D-3 Oxygenation Data from Open-Heart Surgery........... 206

D-4 Transient Liquid-Breathing Experiment with Saline.. 209

D-5 Transient Liquid-Breathing Experiment with
Fluorocarbon (FX-80) ............ ..................... 211


Figure Page

1.2-1 The Cardiovascular System............................ 6

1.3-1 The Effect of Carbon Dioxide Partial Pressure on
Oxygen Saturation in Whole Blood..................... 15

1.3-2 The Effect of Temperature on Oxygen Saturation....... 16

1.3-3 Effect of pH on Oxygen Saturation in Whole Blood ..... 17

1.3-4 The Effect of 02 Saturation on Carbon Dioxide
Concentrate on ........................................ 20

1.3-5 Cascade Mechanism for Thrombosis ..................... 21

1.3-6 Feedback Mechanism for the Growth of Thrombi......... 22

1.4-1 The Bubble Oxygenator ................................ 26

1.4-2 The Disc Oxygenator.................................... 27

2.1-1 Comparison of Concentration Profiles as a Function
of Nurber of Stages in Series........................ 42

2.1-2 Comparison of Residence Time Distribution Functions
for Varying Number of Stages in Series.......... .... 43

2.2-1 ViscosLty of Saline-CMC Solution As a Function of
Composition ......................................... 45

2.2-2 Experimental Apparatus Used to Measure Bubble
Diameters ............................................. 46

2.2-3 Rlood Siu;l tion E.peri..,ent Apparatus................. 48

2.3-1 Distributicn of Bubble Sizes by Surface Area......... 51

2.3--2 Distribution of Bubble Sizes by Volume................ 52

2.4-1 E:perimental Results of the Saline Simultion
Experi ent ........................... .......... .... 56

2.14-2 Gas Holdup Volume as a Function of Gas to Liquid
Volume Flow Rate Ratio in the iLF Bubble Oxygenator.. 60

.4 -3 Gas Huldup Volume as a Function of Gas to Liquid
Volur.,e Flow Rate Ratio in the 2LF Bubble Oxygenator.. 61


Figure use.

2.4-4 Gas Holdup Volume as a Function of Gas to Liquid
Volume Flow Rate Ratio in the 3LF Bubble Oxygenator... 62

2.4-5 Gas Holdup Volume as a Function of Gas to Liquid
Volume Flow Rate Ratio in the 6LF Bubble Oxygenator... 63

2.4-6 Thin Film Diffusion Model for Oxygen Absorption....... 67

3.2-1 Schematic of Surgical Operating Setup ................. 76

3.3-1 Data Taken During Open-Heart Surgery................... 85

3.3-2 The Effect of Temperature on Oxygen Absorption in
the 1LF Bubble Oxygenator............................. 90

3.3-3 The Effect of Temperature on Oxygen Absorption in
the 2LF Bubble Oxygenator............................. 91

3.3-4 Effect of Temperature on Oxygen Absorption in the
3LF Bubble Oxygenator.................................. 92

3.3-5 Effect of Temperature on Oxygen Absorption in the
6LF Bubble Oxygenator................................. 93

3.3-6 The Effect of 02 to Blood Flow Rate Ratio on
Arterial 0 Partial Pressure in the ILF Bubble
Oxygenator ............................................ 95

3.3-7 The Effect of 02 to Blood Flow Rate Ratio on
Arterial 02 Partial Pressure in the 2LF Bubble
Oxygenator............................................ 96

3.3-8 The Effect of 02 to Blood Flow Rate Ratio on
Arterial 02 Partial Pressure in the 3LF Bubble
Oxygenator ............................................ 97

3.3-9 The Effect of 02 to Blood Flow Rate on Arterial
02 Partial Pressure in the 6LF Bubble Oxygenator..... 98

3.3-10 The Effect of 02 to Elood Flow Ratio on Arterial
CO2 Partial Pressure in the 1LF Bubble Oxygenator.... 99

3.3-11 The Effect of 0 to Blood Flow Ratio on the
Arterial COG, Partial Pressure in a 2LF bubble
Oxygen tor..... ........................................ 100


Figure Page

3.3-12 The Effect of 02 to Blood Flow Ratio on the Arterial

CO2 Partial Pressure in the 3LF Bubble Oxygenator... 101

3.3-13 The Effect of 02 to Blood Flow Ratio on the Arterial
CO2 Partial Pressure in the 6LF Bubble Oxygenator... 102

3.3-14 The Effect of Venous 02 Partial Pressure on Oxygen
Absorption in the 1LF Bubble Oxygenator............. 103

3.3-15 The Effect of Venous 02 Partial Pressure on Oxygen
Absorption in the 2LF Bubble Oxygenator............. 104

3.3-16 Effect of Venous 0 Partial Pressure on Oxygen

Absorption in the 3LF Bubble Oxygenator............. 105

3.3-17. Effect of Venous 02 Partial Pressure on Oxygen
Absorption in the 6LF Bubble Oxygenator............. 106

4.1-1 02 Transfer on a Blood Film......................... ill

1&.1-2 Schematic of Perfectly Mixed Stages in a Disc
Oxygenator ........................................... 116

,.2-1 The Effect of Initial 02 Partial Pressure on the

Boundary Layer Concentration Profile. ................ 123

4.2-2 The Effect of Temperature on 02 Absorption in the
Disc Oxygenator ..................................... 125

4.2-3 Carbon Dioxide Boundary Layer Profile ............... 126

4.2-4 The EFfect of Temperature on CO Desorption in the
Disc 0\ygenator ..................................... 127

4.2--5 0,, Partial Pressure as a Function of Stage No. for
a Blood Flow of 40 cc/sec............ ..... .......... 128

4.2-6 02 Partial Pressure as a Functicn of Stage No. for
a Blood Flow of 50 cc/sec........................... 129

4.2-7 02 Partial Pressure as a Furction of Stage No. for
a Blcod Flow of 75 cc/sec........................... 130



Figure Page

5.2-1 Diffusion-Controlled Model of Liquid Breathing
with Plug Flow........................................ 137

5.2-2 Diffusion-Controlled Model of Liquid Breathing
with Perfect Mixing................................... 139

5.3-1 A Model of the Lung as a Series of CSTRs............. 141

5.3-2 Response of the Lung to a Step Change in Dye Conc.
for CSTR Limiting Case............................... 145

3.4-1 Experimental Apparatus for the Liquid-Breathing
Experiment ............................................ 146

5.5-1 Concentration Profiles After 1 Inspiration........... 150

5.5-2 Results of Saline Liquid-Breathing Experiment........ 151

5.5-3 Results of Fluorocarbcn (FX-80) Breathing
Experiment............................................ 153

B2-1 CSTR Model for Turbulent Mass Transfer in Membrane
Oxygenators ........................................... 194

B2-2 Membrane Oxygenator Gas Exchange in CSTR Model....... 196


A = interfacial surface area

C = concentration

C. = concentration of component i in a mixture

C. concentration of component i in the liquid phase that is
in equilibrium with component I in a second phase

(C~) = n-dimensional column matrix containing the concentrations
of the blood constituents at the entrance of the bubble

C\ = the amount of component k bound to component M

C. concentration of the ith component in a liquid film

C = concentration of the ith component in the liquid phase
between two discs

C. = concentration of component i in the inlet stream to a
mixing stage

D = binary diffusion coefficient

[D] = n x n matrix of multicomponent diffusion coefficients

Db = diffusivity of oxygen in blood

D = bubble diameter

D. = diffusivity of component i into a mixture

D, = diffusi"ity of oxygen into plasma

e. = c centration of dye in the alveoli of the ith stage
in the lung

f = equilibrium relationship which equates the total amount
of component k to the concentrationL of the remaining

CM =- equilibrium relationship whichh equates the amount of
component k, bound to M, to the re-naining
species concentraitions in ih.e mixture

H = volume fraction of red cells in the blood, i.e., hematocrit

J. = diffusion flux of component i

K = binary mass transfer coefficient

[K] = n x n matrix of multicomponent mass transfer coefficients

K = equilibrium constant

K. = mass transfer coefficient of species i into species j

N. = mass flux of component i

P = pressure

P. partial pressure of component i

r = radius

R = radius of a bubble

(R) = n-dimensional column matrix of reaction rates

R. = rate of reaction of the ith component

S = fractional oxygen saturation

S = reduced fractional saturation
r arterial 02 saturation venous 02 saturation

saturation at PO = 760 mm venous 0 saturation

= time

tT = enperature

v volume flow rate into alveoli in the ith mixing stage

V = volume

v velocity

V = volume flow rate

V = volu:re in the lung at which transport becomes diffusion-

V- = volume of a stagnant film

VH = gas holdup volume

VTOT = total lung volume

V0 = initial volume of the lungs

x = distance parameter

y = mole fraction of oxygen saturation

Greek Letters

a. = Henry's law constant of component i in a solvent

y = ratio of gas to liquid flow rate in the bubble oxygenator

6 = boundary layer thickness

9j = viscosity

= residence time

0 = residence time of a film at the blood membrane interface

X = effective residence time as defined in Equation 3.3-4

' = effective residence time as defined in Equation 3.3-3

e = angular velocity

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


By William Falco

December, 1971

(.hairmanU: Professor Robert D. Walker, Jr.
Major Department: Chemical Engineering

Mathematical models for blood oxygenation in bubble and

disc oxy.genators have been proposed. In the case of the bubble

oxygenator, na single-stage, perfectly mixed absorber model was

tes.ted and confirmed by a saline simulation experiment which

approximated oxygenator use in open-heart surgery. From data

taken during sixteen open-heart operations, oxygen and carbon dioxide

mass transfer coefficients were estimated as

K = 0.00528 -
'02,B sec

B >0.0131
CO2,B sec

With these results, a computer program was written to simulate trhe

operation of the. bubble oxygenator over a Wide ranfle cf oxygen anc

blood flow rates. During the simulation experiment, it was foUnd

that for each of Lhe four sizes of oxygenators tested, an optimal

Xi i i

ratio of gas to liquid flow rate was obtained. Furthermore, the

oxygenat:ion rate was reduced when gas flow rates exceeded 7 to 8

liters per minute in all four models.

In the case of the disc oxygenator, the equilibrium relation-

ships and other physical constants have been put into subroutine

form for easy substitution in other systems.

The problem of gas transport in liquid-filled lungs was

also considered. It was proposed that oxygen and carbon dioxide

transport through the bulk of the lung by convective mixing instead

of by diffusion as proposed by Kylst.a. A transient breathing

experiment measuring dye penetration in:c saline- and fluorocarbon-

'illed lungs was devised and carried out. From the data obtained,

it was determined that gas transfer through the bulk of the lung

was by convective mixing; the lunrg was appruximatea by Lt-n perfect

mixing stages in series when fluorocarbon was used and twenty

perfect mixing stages in series when saline was used.



1.1 Historical Development

Attempts to oxygenate blood artificially date back to the

nineteenth century. The oxygenation of blood by shaking with air

was reported by Ludwig and Schmidt (1) in 1868, while the first

continuous process for blood oxygenation was attempted by Schorder

(2) in. 18832, who showed that blood could he oxygenated by bubbling air

through it. Zeller (3) in 1908, improved the rate of oxygenation

by using pure oxygen in place of air.

Continued improvement in this method of oxygenation eventually

led to the development of the bubble oxygenator by De Wall and

co-workers (4) in 1956. It is probably the most widely used oxygenator

at this time wing to its relatively low cost, simplicity of -peration

and complete disposability.

Another early method of oxygenating blood, which eventually

evolved into a successful design, was the thin filn transfer unit: it

was studied by Hooker (5) in 1915, and by Drinker and co-workers (6).

fhe basic design consisted of a glass cylinder through which oxygen

was passed. A thin film of blood was distributed on the cylinder

wall, the direction of blood flow induced bring countercurrent to the

direction of oxygen flow. This type cf design eventually evolved

into the screen o*xygenator developed by Miller et al. (7) in 1951.

In the and Gibbon oxygenator, a series of parallel screens

,rc-lace a 'et of concentric cylinders as the blood-filming surface,

but the essential idea of oxygen transfer into a thin blood fiJm is

still the main feature of the design.

Bjork (3) developed an alternate thin film oxygenator in 1948.

His oxygenator consisted of a series of rotating discs, exposed to a

stream of oxygen, which dip into a blood reservoir. This method of

oxygenation is based on oxygen transfer into a thin film which is

constantly being renewed with fresh blood.

These three types of oxygenators, the bubble, screen, and

disc, have been tested experimentally and used clinically. These

ox:ygenators, which might be termed first-generation oxygenators, have

Lwo features and disadvantages in common. Firstly, all of them require

direct contact between gaseous oxygen and blood, and thus protein

denaturation becomes a problem after extended periods of operation.

Secondly.. these methods of oxygenation attempt to minimize resistance

to .:2ass transfer of oxygen into the blood by minimizing di.fusional

resistance in the blood phase.

To date, the principal application of blood oxygenators has

b.:en as cardiac bypass units in open--heart surgery. The three

oxygeriators discussed above have been used for short teim (up to

approxjnm:tely three hours) by-pass of the heart and lungs during either

surgical repair or replacement of sections of the heart. The -urrent

limitation on operating time is the rate of hcmelysis, or red blood

cell Gcscruc-.ion, and the rate of protein denaturation. In an effort

to minimize e p.ctein denaturation new oxygenators, whichh might be

term.led second-generation oxygenators, are in development. All of these

new designs eliminate the direct contact of gaseous oxygen and blood.

It is anticipated that elimination of the blood-gas interface will

reduce protein denaturation and increase the possible bypass time to

the order of days rather than hours. Such a development would be of

value in the treatment of heart and lung damage which cannot be

corrected by surgery.

Therc have been a number of different schemes proposed to

accomplish the oxygenation of blood without direct contact between

gaseous oxygen and blood, two of which appear to be promising. Res._arch

on the use of membranes through which gaseous oxygen can diffuse into

blood has been underway for approximately the last fifteen years.

Kol f and Balzer (9) attempted to oxygenate blood by flowing blood in

polyethylene tubes while oxygen was passed over the tubes. BodelL

and co-workers (10) tried the reverse experiment of immersing tubes,

throughh which oxygen flowed, in blood. Others (11,12) have attempted

to use these cwo methods with different membrane materials. The

material that appears to be most promising at this time is Silastic

(a silicone rubber) tubing. Pierce (13) has also tested a membrane

oxygenator which has blood flow channels embedded in spaced layers of through which oxygen is passed.

Thle second method of blood oxygenation which would eliminate

the direct contact of gasecus oxygen with blood involves the use of

iner;t fluorocarbons as an exchange medium. Basically, the process works

as follows: a fluorocarbon (or other inert, water-insoluble liquid)

is oxygenated by bubbling oxygen through it, then the oxygenated

fluorocarbon is brought into contact with venous blocd. Oxygen is

transferred from the saturated fluorocarbon into the blood and carbon

dioxide is transferred from the blood into the fluorocarbon. Since

fluorocarbon is insoluble in blood, the blood-fluorocarbon mixture can

be separated and the fluorocarbon can be recycled for decarbonation

and reoxygenation. Research in this area is quite recent and the

literature on this method of oxygenation is sparse. Nose and co-workers

(14) have designed a thin film oxygenator using fluorocarbon (FX-80)

as a transfer medium. Dundas (15) has performed simiilar experiments

with FX-80 as well as DC-200 silicone oil. Results so far are

promising, but this method of oxygenation will require a great deal of

further research before a working fluorocarbon oxygenator can be


Although the bubble, disc and screen oxygenators have been in

use for over a decade, no mathematical models have been developed which

describe their operation adequately. Furthermore, only in the case of

the screen oxygenator (16) has there been an attempt to describe

mathematically the rate-limiting process in oxygen transfer.

Significantly, the initial work done thus far with fluorocarbon

o::ygenators does not involve mathematical models. It was the original

goal of this research to develop and test mathematical models for the

disc and bubble oxygenatcrs in the hope that these models would provide

a basis for similar :::odelling of fluorocarbon oxygenators. FurLhermore,

such mathematical mr.odels should pro>.e useful in developing in vitro

expevinments to dterr.rmine the effects of aneschetics and other drugs

on blocd oxkgnaion, and shcu.d provide a clinical tool for open-heart

surge y.


The development of models for membrane oxygenators, in contrast

to other oxygenators, has been the subject of a number of research

studies. Bradley (17) has done a thorough study of gas exchange

through silastic tubes through which blood is pumped. Lightfoot (IS),

and Weisman and Mockros (19) have also constructed models for the

design of membrane oxygenators.

1.2 The Cardiovascular-Pulmonary System

SLnce blood oxygenators are designed to Lake over the functions

normally performed by the heart and lungs, the evaluation of such

artificial oxygenators requires a thorough understanding of the human

cardiovascular-pulmonary system. This system consists of the heart,

lungs and a network of veins, arteries and capillary beds. The function

cf the kidneys is also important to consider as some of the problems

that arise in artificial blood oxygenation are directly attributable

to these organs. A schematic diagram of the cardiovascular system is

shown in figure 1.2.1.

The heart serves as a pump to circulate blood through the

network of veins and arteries to the various points in the body where

oxygen, carbon dioxide, and other blood constituents are exchanged.

It is a four-chambered vessel.: Venous blood flows into the right

atrium and tLence into the right ventricle wh ch acts as a positive

displacement pump to force the blood through the pulmonary system and

into the left atriu.n. Arterial blood flows into the left ventricle

which in turn punps blood through the arteries and veins which

compose the circulatory system.,

CO2 2



Waste Products

_<- _-- Kidney ----<------


I.-. -- -
Vein I

0 CO,
2 2

Waste Iateriil

Figure 1.2-1. The Cardiovascular System.


The arteries are a network of flow channels which transport

blood to the pulmonary capillary bed and to systemic capillary beds

which are distributed throughout the body tissues. Gas exchange

takes place in these capillary beds. In the case of pulmonary

capillaries, oxygen is transferred into the blood while carbon dioxide

is transferred out, and in the case of the systemic capillaries, carbon

dioxide is transferred into the blood while oxygen is transferred into

the tissue. Upon exiting from the systemic capillaries the blood is

transported back to the heart through a network of veins.

The function of the kidneys is to remove waste material from

the blood stream. About 25% of the total blood flow passes through

the renal arteries into these two bean-shaped organs. Once in the

kidney, blood is distributed to approximately 1 million transfer

units called nephrons. A nephron consists of an entrance called

Bowman's capsule and a series of transfer units in which four

processes occur. The first unit, the glomerulus, is an ultrafilter

which separates erythroctes, lipids and plasma proteins from the

remaining plasma constituents. The second unit consists of the

proximal tubule, Henle's loop, and distal tubule. This section is

basically a long tubule folded and looped in sections in which some

plasma constituents and water are reabsorbed and other constituents

are secreted into the tubule. The final unit is the collecting duct

in which, as its name implies, waste products and water are collected

to be eventually excreted from the body.

The details of the phenomena which occur in the kidneys are

quite complex ai.d numerous, and a comprehensive discussion of them is

beyond the scope of this work. There are a number of text and papers

which h treat the kidneys, among which is a recent and concise summary

by Pitts (20).

The lung, of course, also forms an important part of the

cardiovascular-pulmonary system supplying oxygen to the blood and

facilitating carbon dioxide removal from the same. Since it is an

oxygenator in its own right, we have chosen to discuss it in cor.parison

which artificial oxygenators in Section 1.5 rather than in connection

with the cardiovascular-pulmonary system.

1.3 The Properties of Blood

Blocd has been the subject of much research, generally

concentrating on either biochemical interactions or rheolegy. In

the following paragraphs we have drawn heavily from texts by FeruCscn

(21), and Thftmore (22) to collect a pertinent summary.

".'1.ole blood is essentially a suspension of red blood cells in

pla&-.a. Other formed elements in the plasi:-a include white blood cells

ane platelets. The plasma is an aqueous solution containing about

7% proteins, 0.9% inorganic salt, and 2..1% organic substances other

than proteins.

.As st:ated in Section 1.2, blood is distributed throughout the

body through a network of veins and aiceries. In addition to supplying

all body tissues with oxygen and removing carbon dioxide and waste

.r..terials, blood also carries nutrients to the tissues, and it also

serves as a heat transfer Tmedium to control temperature within the

narrow range necessary for normal functioning of the body. Further-

more, blood regulates the fluid balance throughout the body and

provides a defense mechanism against diseases.

The red blood cells, or eyrthrocytes, which carry most of the

oxygen in the blood stream are biconcave discoids. The dimensions of

the human eyrthrocytes quoted by Lehman (23), and Britton (24) are as


diameter = 7.8 microns

thickness = 1.84 -- 2.06 microns

volume = 88 cubimicrons.

The red cell is quite flexible and thus easily distorted. It

is this property that permits the calls to pass through capillaries

thet are smaller in diameter than themselves. It is interesting to

note that the eyrthrocytes pass through the capillaries in slip flow.

Although a number of studies on microcirculation have been reported

by Copley (25), Lew (26), Wells (27,28), and Goldsmith (29), a

mathematical model based upon slip flow has not been proposed or

tested at this time. Since good microcirculation is necessary for

adequate oxygenation of cell tissue and since microcirculation is

affected by hemolysis, that is, cell breakage, during cardiac bypass,

it appears that an understanding of the slip flow mechanism in

capillaries would provide valuable insight into the development of

bett r blood uxyginators.

An erythrocyte consists of a membrane enclosing fluid without

a nucleus. Th; m.emrbrane is formed of a bimolecular layer of lipids and

Lthe ll fluid contains appLcoximacely 33% hemoglobin. Hemoglobin is

t.a constituent which is responsible for the large oxygen-carrying

Capacity of blood, vide infra.

White blood cells, or leucoytes, provide a defense mechanism

against disease. They are classified into three groups according to

size, ranging from 7 to 22 microns. From the smallest to the largest

the three types of leucocytes are lymphocytes, granulocytes, and

monocytes. The total concentration of thece cells in normal blood

is negligible compared to red cell concentration, the ratio of

ey :thocyte to laucocy;e cells being approximately 1000 i:o 1. The

white cell is more rigid than the red cell, but it has a gelatiuou&

membrane which easily deforms to adjust to local conditions.

Platelets are disc-shaped cell remnants much smaller in size

than ccher formed elements and having a diameter between 0.5 and 3

-microns as reported by Bell (30), Merrill (31), and Britton (24).

PlaLelets play an important role in the blood coagulation process, which

we shall discuss shortly.

Plasm., the fluid in which all of these formed elements are

suspended, is both a molecular and ionic solution. The major ions

which are dissolved in the solution are sodium, potassium, calcium,

magnesium, chlorine, and bicarbonate. The principal molecular proteins

in the sollition are fibrinogen, a. ?,, and y globulins, and albumin.

Fibrinogei, .h.ich polynerizes to fibrin during coagulation, is one of

Lhe. largest. of the protein molecules. The globulins, whose specific

functions acee not understood, are extremely important as carries of

lipids anid other water soluble substance. Albumin, the plasma

'r:ct-.i r in highest concentration, is important in maintaining the

balance of -water metabolism.

Having described the constituents of the blood we are now -

prepared to venture into a discussion of how these various components

in che blood combine with oxygen and carbon dioxide, transport these

two gases to the appropriate locations in the body, and then release

them to the body tissue and lungs, respectively. Of major importance

arcthe reactions hemoglobin undergo but we will also comment : on

thrombosis, protein denaturation, and hemolysis which are three

serious problems which may occur during or shortly after cardiac bypass.

Hemoglobin is a large protein molecule with a molecular weight of

67.000 containing approximately 10,000 atoms (32) and an effective

diameter of 50 to 64 A (33). It is a tetramer, each polymeric chain

containing an iron atom combined with a heme group connected to a

polypeptide chain. The heme group is an iron porphyrin complex which

reversibly binds oxygen. It is important to note that heme iron bound

to oxygen remains in the ferrous state (i.e., oxidation of iron by

oxygen does not take place), and consequently the oxygen molecule

maintains itz identity. Both oxygen and hemoglobin are paramagnetic,

but oxyhemogLcbin is diamagnetic, indicating a covalent bond between

iron and oxygen. This bond is, in fact, very weak, and the reaction can

be shifted by 3 slight change in pH. Consider a dissociable hydrogen

ion attached to a hemoglobin molecule.

H.Hb+ (0 HbO H (1.3--1)
.1b IF 0 2 < 1) 2

If the pH of the hemoglobin environment decreases, i.e. the hydrogen

ion concentration Lncreases, the reaction is shifted to the left with

a release of oxygen. If the pH increases, the reaction will shift to

the right and oxygen will be taken up. In the body the pH decreases

..:hen carbon dioxide is released into the blood stream in the form oE

bicarbonate ion

CO2 H20 2 H2CO3 H+ + HCO3 (1.3-2)

Thus, oxygen release to body tissue is facilitated by carbon dioxide

absorption into the blood. In the lungs, where carbon dioxide is

released, the pHi increases and oxygen binding to hemoglobin is

facilitated again by the CO2 transfer.

The kinetics of hemoglobin-oxygen reactions have been the

subject of a number of research studies and several models ha\e been

proposed for the mechanism of reaction. Among the earliest is the

mechanismm proposed by Hill (34)

-1 0
Hb + nO29 Hb(02)n (1.3-3)

for which it can be easily shown that the mole fraction of hemoglobin

saturated is

y =-"- (1.3-4)
1 + kpn

where K is the equiiLibrium constant and P is the partial pressure

of oxygen in the mixture. Since each hemoglobin molecule combines with

4 oxygen :.olecu res, the value of n should be equal to 4, but experimental

values range between .1.4 and 2.9 and they depend on the ionic strength

of che solution. Although this fact undermines the theoretical

basis for Pill's equation, Equation 1.3-4 is still used because of

j is simplicity. ,, of .ourse, is a function of both ionic strength and pH.

Adair (35),in 1925, proposed a four-parameter model for

hencglobin oxygenation involving the following series of steps:

Hb, + 02 Hb 0

Hb 02 + 02 Hb 0
Hb,04 + 0 2 Hb 06

Hb 06 + 02 n Hb08
4 6 2 48

It can be shown after a fair amount of algebra that the fractional

saturation is

2 3 4
KP + 2KKP + 3K K2K3P + 4KlK2K3KP (1.3 )
y 2 2 13 2 4 p4
4(1 + KlP + K +KP2 + KK3P + 1 K 3K P )

where K- through K4 are the equiLibrium constants for the reactions

shown in Equation L.3-5. Note that Equation 1.3-6 does not take

into account pH or ionic concentration and thus the equilibrium

constants must be functions of these two variables in addition to


In 1935, Pauling (17) developed a model which did take into

account pH effects and assumes a heme-heme interaction. His

resulting equilibrium relationship

KP + (2a + 1)K2p2 + 3:2 K p3 + a K P (137)
1 + 4KP + (4a + 2)K2p2 + 4a K 33 + aK 4P

where PTFna is the decrease in free energy due to the interaction of

two groups HbO.. If RTinb is the difference ia the change free

energies of hydrogen ion dissociation from oxyhemoglobin and from

hemoglobin, the pH dependency of K is given by

k = k, (1 + bA/[H+])2
(1 + A/[H]) (3-)

where A is the acid ionization constant. A modification of Pauling's

model was proposed by Margaria (36) in 1963. His final result is

r + kp 3
y = -i (1.3-9)
1 + KP

where m is constant found experimentally to be equal to 125.

It: should be noted that Margaria's equation is a one-parar.eter

model and that K is a function of pH as well as ionic concentration


There are a number of other possible models which have been

's unnarized by Aeeodato de Souza (37). We have chosen to use an updated

version of Adair's equation developed by Kelman (38) to approx..mate the

saturation curve. Th.. modified Adair equation including timipeirature,

p}l and carbon dioxide coacenicration corrections has bcn written as

a subroucine for convenient .computer solution by Kelrian. It is thus

particularly s:ited for chis work. The actual equations used along

with the subroutine are listed in Appendix A. Typical. saturation

curves as functions of oxygen partial pressure, carbon dioxide partial

pressure, temperature, and DH are shown in Figures 1,3-, 1.3-2, and

1..3-3. It. should be noted that as oH increases, the sat,'ratii n clirva

1. 000 --- ------

0.800 Temperature 37C-

SP P37 0



Pressure on Oxygen Saturation in
0.o0l Blocd.
0.0 20.0 40.0 60.0 80.0 100.0

0 2 Partial Pressure (mm)

Figure 1.3-1. The Effect of Carbon Dioxide Partial
Pressure on Oxygen Saturation in
o ol2 BIocd .

pH = 7.4
7- = 40.0 mm




l !-

20.0 10.0 60.0

02 Partial Pressure



Figure 1.3-2.

The Effect of Temperature on
Oxygen Saturation.








20.0 Z0.0 60.0 80.0 100.0

02 Partial

Figure 1.3-3.

Pressure (mm)

Effect of pH on Oxygen Saturation
in Whole Blood.








s h.fts tow..ards lower partial pressures of oxygen. This effect,

known as the Bohr effect, plays a vital role in facilitating the

exchange and transport of oxygen in the body as stated earlier in this


Carbon dioxide also interacts with blood in a number of ways.

The majority of carbon dioxide is carried in both the plasma and

red cells in the form of bicarbonate ions. The reaction of CO2 with

water to form carbonic acid, and subsequently bicarbonate ions, takes

place mainly within the red cell, where the reaction is catalyzed by

carbonic anhydrose. The hydrogen ion released when H."CO dissociates

reacts with the nitrogen of the iridazole group of the hemoglobin

molecule. This reaction buffers the blood and regulates the pH

within a narrow range for large changes in CO2 concentration. CO2

also reacts directly with the amine groups of hemoglobin as wc Ll 3s

proteins in general. These reactions can be sumi.iarizeid as fellows:

CO2 t- ib.NH2 Hb-NH.COOH

CO2 H 120 : H2CO3 (1.3-10)

H2CO3 t H' + HCO,
2 3 -C

H + (ibO2) ; Hb + 02

Bradley (17) suggested that CO2 concentrations car. be represented by

a two -parameter model

C 0.373 0.nI/-85S+ 0.(.0456 P .3-11)

where C is the total concentration of carbon dioxide, S is the

fractional saturation of hemoglobin by oxygen, and P CO is the

partial pressure of carbon dioxide. Since the total CO2 concentration

is not a function of total hemoglobin concentration and does not equal

zero at zero CO2 partial pressure, Equation 1.3-11 must be viewed as

semiemipircal; it is valid for CO2 partial pressures ranging from

approximately 30 to 60 mm. We note in passing that there is a variation

in the CO saturation curve with respect to hemoglobin saturation,

similar to the Bohr effect for oxygen saturation. This is shown in

Figure 1.3-4 and is known as the Haldane effect.

In addition to blood-gas chemistry, we are interested in a

series of reactions triggered by trauma which induce blood clotting

and, more generally, thrombosis. Thrombosis is always triggered by

either chemically or physically induced trauma. The first step in

the process is aggregation of platelets; the next step involves the

polv.ierizaticn of fibrinogen to fibrin, which forms a matrix for the

thrombus. During the physiological changes, a series of chemical

reactions occurs for which a cascade mechanism has been proposed (39,40).

The reaction is aa activation of an enzyme called Hageman factor,

This enzyme acts as a catalyst to activate another enzyme, etc.,

finally forming thrombin which catalyzes the polymerization of tibrincgen

to fibrin (Figure 1.3-5). The formation as growth of thrombi is

enhanced by a rer-dback mechanism as shown in Figure 1.3-6. Since

adenosina (iphosphate and thrombin cause aggregation, their formation

during the cascade reaction provides a feedback mechanism for further

"rc':tn and for"- io1T1n.

0.700 1 1

Temperature = 37C

^ 0.600 -~


0. 0 0 .


0.200 1 s I
20.0 30.0 40.0 50.0 60.0 70.0

CO2 Partial Pressure

Figure 1.3-4. The Effect of 02 Saturation
on Carbon Di.oxide C0nc-nt- it..ion.
on Carbon Dioxide C rictnr-rtion.


H o

HJ - .--
' C
M 0r I '0

uE l I 0 '
H *CO U cH

Sr-I -

r ,
H ~ --> ^
H U Cl fl

o o

S + r- l-
S3 C U U

3 c
J 66 I
o o

0 0

H ri 0
H N i
H 'H -4

*r- H

1-1 U 0^



o o


a hC



1 4



o-- --- -



o o

I 4-J4
A j m'-
t O (-I ', 4

SC-0 0
S0-1 o c

U n
Sa i na w a
I lIZ3 4 0 (U -

a t, 0s
O 0

u do
u -n *

J. (1 0 1
-)- 1 u ic

+ ) -- -- *r

o r1
4 4C
i I -I
c -i c

u0Tq '"J UI D V

The problem of eliminating blood clots is currently surmounted

by the use of anticoagulants such as ACD (acid, Citrate, Dextrose),

and heparin. These anticoagulants do not completely eliminate the

problem as poor oxygen distribution, indicative of embolism and clot

formation, is sometimes observed both during and after surgery.

Research to provide a better understanding of clotting and thrombosis

mechanisms appears to be a prerequisite for improved clinical techniques

in this area.

1.4 Description of Oxygenators

The title oxygenatorr" for artificial heart-lungs is a misnomer,

since both CO and 02 are exchanged in these units; gas exchangers

would appear to be a more descriptive term. In all of the direct

contact exchangers, three processes occur:

1. Oxygen is transported to the blood-gas interface and

carbon dioxide is transported away from this interface

by convection;

2. Oxyger and CO2 are transported through the blood by

diffusion and convective mixing;

3. Chemical reactions involving CO and oxygen take place

within the red blood cell.

T; the design of bluc oxygenators, it is desirable to oxygenate as

much blood as possible in as short a time as possible, and consequently,

vario;,s resistances to .r.ass transfer in both gas and liquid phases

should be mninliized. The gas-phase resistance is essentially

elin'inlated io all c-.cret direct contact cxygeiiatrs by sulppl.ying a

very high gas to liquid volume flow rare (in fact much more oxygen

is supplied than required for complete saturation of the blood).

This leaves the liquid-phase resistance to be dealt with. In

mathematical form, the rate of mass transfer of a gas though a

liquid can be written as (41)

rate of accumulation net flux of component i by diffusion
of component i

+ net flux of component i by convection

+ rate of formation of component i by



-o= .J."- 7.(G.v)-!- R. (1.4-2)
ot ~ ~1 ~ I1 ~ .

Using a ;nulticomponent generalizatio-i of Fick's law and assuming

incouipr'essibiLity, we obtain

= [D]V2(C) v.V(C) + (R) (1.4-3)

Since diffusion is. in general, a rmuch slower process than convection,

the major -csistance to mass transfer occurs in regions which are

stagnant. The ininimization of these diffusion layers is the major

du.ign ccn~iidcation in all oxygcnators. In this stagnant boundary

layer, Equation 1.4-3 reduces to

(C)C) ()
i []V2(C) 2 (R) (1.4-4)

In the bubble oxygenator (Figure 1.4-1), venous blood and

oxygen are pumped cocurrently into the bottom of the oxygenation

chamber. Oxygen enters through a sparger and apparently bubbles

through the chamber in plug flow. Oxygen diffuses into the blood

from the gas bubbles, and CO2 diffuses into the bubbles from the blood.

There is a stagnant layer of blood which surrounds each gas bubble

through which both gases must diffuse. After passing through the

oxygenation chamber, the arterial blood flows through a stainless

steel mesh which defoams the blood and then through a collecting


The major advantages of this type of oxygenator are as Follows:

i. the bubble oxygenator is inexpensive and completely


2. the entire system requires a small blood priming volume;

3. the cocurrent flow of oxygen and blood minimizes the

pressure drop across the system;

4. the equipment is easy to operate;

5. the large number of bubbles provides a large blood-gas

interfacial area for gas exchange.

The major disadvantage of bubble cxygenators is that the turbulent

motion of blood in the oxygenation causes hemolysis and thus liUits

the Lime bypass can be sustained.

The disc oxygenator, as shown in Figure 1.4-2, consists of a

s-ries of discs mounted in a horizontal cylinder. Venous blood is

pumped into one end of the cylinder, the flow rates being regulated

at both ends by -tw.o purmps to maintain the blood level at a depth of

- Degasing Steel Wire

Figure 1.4-1. The Bubble Oxygenator.

Vn ous





Z F-


0 __ (

-_ __ ^ (U
-------W_--. -,

S------ C

t --P----
I- 0


--- -i .
i ---


'---4 V - -


o ;

cne-third the dianeer of the cylinders. As the blood flows through

the chamber, a portion of it is picked up on the rotating discs as

thin films. s the film is carried around by the rotating disc,

oxygen is absorbed from the surrounding atmosphere, and carbon dioxide

is released. It can be shown that blood flow between each of the

discs is turbulent when the equipment is operated at the conditions

normal for surgery.

The diffusion layer which limits gas transfer, in this case,

is the thin blood film on the surface of the discs. This surface

is renewed once every revolution by blood in which the discs are

partially submerged.

The main advantage of the disc oxygenator is that turbulence

is restricted to the spaces between rotating discs. This minimizes

hemolysis due to mechanical breakage of blood cells via turbulence.

The major disadvantages of this oxygenator are as follows:

1. equipment and required resterilization procedures are


2. a large blood priming volume is required.

The screen oxygenator has evolved from a 3eL of concentric

cylinders to an arrargemient of parallel screens. iiood is pumped

to a fixt'ire at Lhe top of the screens wheLe it ii distributed. It

then flows down both sides of each screen contacting oxygen. The thin

film provides efficient gas transfer, particularly if the blood flow

is turbulent.

The major advantage of the screen oxygenator is that small

scale turbulence iainimizes iiemolvsis. The major disadvantages ale

large holdup volumes and intermittent channelling blood flow which

causes variations in oxygen and carbon dioxide transfer.

These three direct contact oxygenators have two limitations

which restrict their operating time as we have stated previously.

Hemolysis, or release of hemoglobin from the red blood cell inuo the

plasma, occurs in cardiac bypass using any of the three oxygenators

now in clinical use. There are two ways in which hemoglobin release

can occur. If red blood cells are placed in distilled water, they

swell, loosing their discoid shape, and become spherical. The cell

membrane expands until it ruptures, releasing hemoglobin into the

surrounding distilled water. The driving force for cell expansion

is osmotic pressure, which is caused by the impermeability of the cell

memb3sne to various electrolytes and proteins.

The other cause of hemolysis is mechanical breakage. This

type of hemolysis is generally due to turbulent flow and mechanical

pui-ping. It appears that since turbulence in pumps is severe this

particular problem will be overcome largely by better pump designs.

The problem of protein denaturation is also common to all

clinically usJd direct contact oxygenators. Protein denaturation is

the alteration of the molecular structure of the protein molecule which

leads to c-anges in the properties of the molecules. The most likely icn for the denaturation caused by exposure of blood to

direct contact .-ith o-xygin is the influence of interfacial forces on

t'ic protein molecules and t:he subsequent reaction of these molecules

with ox:ygn (42). The protein molecule is a surface active agent owing

to the fact choa parts of its molecular chain are hydrophobic and other

parts are hydcophilic. In solution, the hydrophobic sections tend:to

align themselves in the interior of a molecular coil while the hydro-

philic sections tend to lie exposed to the water. At an interface,

the protein molecule tends to unfold or unravel so that the hydrcphobic

sections o-ient themselves toward the gas phase, and the hydrophilic

sections orient themselves toward the liquid phase. This orientation

exposes protein bonds to attack by the gaseous oxygen and thus alters

the protein structure.

The membrane and fluorocarbon oxygenators are supposed to

minimize this problem by eliminating the blood-gas interface.

Although there are a number of feasible designs for both types

of oxygenators, none have been put into clinical use to our knowledge.

The experimental designs all conform to the thin film model. In the

case of the membrane oxygenator, it appears that the most successful

models have erpJoyed small diameter tubes or flow channels surrounded

by flowing oxygen. The tube diameter or cross-sectional area of the

flow channel must be minimized since near the membrane wall gas

transport is diffusion-controlled in a stagnant layer of blood. Also

of importance is resistance to gas transport in the membrane. In

Appendix B, we have presented more detailed co;.re't3 on this problem

rradley (17) has presented a d.-cussion on the effect of
silicone r.e:brane thickness and has .3hown that resistance to CO2

transport through the membrane becomes the rate-limiting step as wall
thickness is increased. The opposite is true il direct contact
oxN genacors in which oxygen transport is the limiting rate process.

along with a simple example to illustrate resistance to transfer

in series.

The major drawback to membr-ane o.xygenators is that the transport

of gases through the membrane and stagnant blood boundary layer is

diffusion-controlled; hence a large priming volume is required to

generate the surface area needed for adequate oxygenation and decarbona-

tion. Attempts to increase efficiency by reducing the diameter of the

tubes must be balanced against increased pumping and resultant hemolvsis.

Further increases in efficiency of gas transport by reducing membrane

thickness are also limited by structural requirements.

The fluorocarbon o--:ygenator has promise as a long term

artificial blood-gas exchanger. As stated earlier, current experimental

designs are limited to the thin film types. Other, more efficient,

methods of contacting oxygen-saturated fluorocarbon and venous blood

are available, and these should be tested. The principal drawback of

these possible irethods, including the thin film process is that there

is some indication that a blood fluorocarbon emulsion forms which is

difficult to bceak. Since more than trace amounts of fluorocarcon

in the blood can cause embolisms (15), anly such emulsion must be

scrupulously removed.

1.5 The LLin: as an Oxygenator

The lung, of course, is an cxvgenator supplying oxygen to the

blood and removing carbon dioxide from the same. The respiratory

system consists of the trachea (air intake and exist), and the right

qnd ift b-nhr.pcli. ich bronchus branches in tree-like fashion into

+ [06
20 to 23 subdivisions, or about 10 terminal tubes. At the end of

each tube are terminal sacks called alveoli of which there are

approximately 3 :- 10 in the entire lung. It is in the alveoli,

which range from 20 to 30 microns in diameter, that gas exchange

with blood occurs. Each of the alveoli are surrounded by thin-walled

capiillary ceds t~rc'ogh which blood passes. The diameter of these

capillaries ranges front 7 to 10 microns and the wall thickness is

less than 0.1 -icron.

The ami-:..t of gas the lung ca, transport is extremely large,

ranging up to aprc.xii.ately 5.5 l/;iin of oxygen during heavy exercise.

In normal breathing, air is pumped in and out of the lungs by movei.enr

of the diaphrrag which movement causes high and :low pressures in the

thorax resulring -n Pitprnate contractions and exp>:l-ions of the


The tra,.sport of gases from the alveoli co the blood is

accomplished by diffusion through the alveolar m;embranrs, which are

.ess than 0.1 micron thick, and the capillary walls. Under normal

rcoi".tions, the volume of air inhaled and exhaled in one breath is

approximately 450 ml in a healthy aJ.ult. This is known as the

tidal volume. U'prn normal expiration, the lungs still ret'.ai about

2.4 of gas. 7his volume is termed the e.xiratop reserve capacity

*n"d rtJ-esiduL volume. The voin:me of the conduct ing airways leading

to the a] eoli :is approxi.racely 130 al.; this is called dead space

All dimeniors, data and physical constant, r-ported in this
-:e.ction were taker. from C~oi-oe (43).

since these airways do not participate to any significant extent in

gas exchange.

The mode of oxygen transport in the lung to the membrane wall

is by convective mixing. Comroe (43) implies chat air passes through

the lung airway- in plug flow and then perfectly mixes with the alveolar

gases. Seagrave (44), in a model of the entire respiratory system,

describes the entire lung as a perfectly mixed stage, thus neglecting

plug flow in the dead space region.

Our interest in the lung is mainly in a liquid-breathing applica-

tion. While studying blood oxygenation by artificial means, we became

aware of attempts to oxygenate blood adequately with the natural lungs

but employing oxygen-saturated liquids instead of air as an exchange

medium. In liquid breathing, the lungs are filled with an oxygen-saturated

liquii-3, and breathing is accomplished by pumping fresh liquid into and out

of the lungs periodically. There are a number of clirical uses to which

such a technique cc.uld be applied, the most important of which appears

to be the treatment of hypoxemia, specifically in cystic fibrosis.

The earliest experiments involving liquid breathing were

performed using normal saline or Ringer's solution saturated with

oxygen. West and co-workers (45) filled canine lungs v:ith degassed

normal saline. After breathing the dcgs a sufficient number of rimes

to ensure removal of all gas, a st.'p-change in the concentration of

a tracer gas was introduced into the lung. One more inspiration was

pera.icted before breathing was termniiated to force some of the tracer

into the lung. The expanded lung was then held fixed for various

periods of time before it was drained and tha concentration of the

tracer was measured as a function of volume drained. From these

concentration profiles, West concluded that oxygen is transported

through liquid-filled lungs by diffusion.

Kylstra (L6) performed steady-state liquid breathing experiments

using oxygenated Ringer's solution, saturated at a partial pressure of

oxygen of 3000 mm. In Kylstra's experiments, canine lungs were filled

with oxygen-saturated Ringer's solution and breathed until steady-

state conditions were obtained. Concentration profiles of 02 and CO2

were then measured as a function of lung volume by draining the lung.

Kylstra fitted these data to a spherical diffusion model assuming the

core of the sphere to be fed by liquid at the entrance composition.

He assumed that the flow of liquid through the airways was in plug flow.

To provide a reasonable agreement between theory and experimental

results, Kylstra adjusted the size and number of hypothetical diffusion

spheres and noted that the diameter of spheres thus obtained compared

S.vcrably within size with the primary lobules of the lung.

More recently Modell and co-workers (47,48,49) and Lowenstein

and co-workers (50) have used fluorocarbon (FX80 and PlD) to ventilate

dogs. The major advantage of fluorocarbon is that itc extremely

high oxygen solubility facilitates the oxygenation of blood at

atmospheric pressure.

The description of gas transport through the lung by diffusion

alone appears to be quite urnsatisfactory and we shall show that

diffusion carr.ot accou-nt for the amounts of oxygen and carbon dioxide

transferred in .iquid-fi..l-ed lungs. Furthermore we shall develop an

A similar d iff-ision model has been proposed for gas-filled
lungs by .Lacrce (51), and supporting data have been quoted by Kylstra
(4C). Th asn-... optin of diffusic-A-ccntrolled transport in gas-filled
li.ngs is i-rth-r frcm reality than in the case of liquid-filled
lurgs and ar:gcurnts for a more realistic model are presented in Appendix C.


alternate model, based upon imperfect mixing theory, which we believe

will describe the functioning of the lung more accurately than models

proposed previously.



2.1 Mathematical Models

From our original observations of the bubble cxvgenator during

open-heart surgery, we concluded that both blood and gas were in

turbulent flow in the oxygenation chamber. We were also able to

ascertain that oxygen gas bubbles passed through the chamber in

essentially plug flow. The blood flow patterns, however, could not be

determined precisely; thus a saline simulation experiment was devised

to investigate liquid flow patterns in the oxygenation chamber. It

was decided to simulate blood with a normal saline solution to which

was added a small amount of carboxy-methyl-cellulose (C.M.C.) to

increase the viscosity of saline to that of whole blood. Since oxygen

d_-.-s not react or physically bind with saline, it was felt that the

flow characteristics of blood could be obtained by measuring the race

of absorption of oxygen into saline, i.e., fluid mechanical effects

would effectively be separated from chemical kinetic effects.

In such an absorption process, occurring in a turbulent flow

channel, there are two limiting cases which are of physical significance.

The first case is plug tlow~ of a liquid through the column. In such

a column, lir:uid and oxygen, entering the bottom and flowing cocurrencly,

wcLld pass through the oxygenating clamber in a slug, and any mixing

As we discovered in the simulation, this is not always the
case when the o:ygenator is cp:rated incorrectly.

which occurred in the liquid phase would be local. In such a situation,

a mass balance across a slug of infinitesimal volume V would predict

the rate of mass transfer as

d(VC )
Ad_ = -KA(C C) (2.1-
dt 0 0
2 2

where C = concentration of the oxygen in the saline solution

C = concentration of oxygen at the gas-liquid interface

K = -ass transfer coefficient

A = 02 bubble-saline interfacial area

V = volume of the slug.

If we further assume that the liquid density is constant and thac the

range of absorption is small compared to the flow rate of gas,

Equation 2.1-1 becomes

d(C C )
2- = 2 (C C ) (2.1-2)
dt V 0 0
2 2

Upon integration of this equation, we obtain

(CO C) = (C' C )P (2.1-3)
2 2 2 2

where the initial condition

C (0) C
s 0

has been used. Equation 2.1-3 can be written in reduced form as



x =-.exp t (2.1-4)

where *
C I C*
02 02
x = C _
C -C
02 02

Now, t is the residence time of a slug of liquid, i.e., the time that

a slug or element of fluid remains in the oxygenation column, and

since these elements are in plug flow, the residence time of any

element of fluid is equal to the average residence time of the liquid, r,



where V is the volume flow rate of saline. Thus the final form of

Equation 2.1-3 is

x = exp (2.1-5)

The other limiting case is a single perfectly mixed stage.

In this model, an element of fluid entering the bottom of the oxygenator

is immediately distributed throughout the oxygenation cha rber. Thus,

all of the in the co'uin is at the exit composition C Of

course, the insantanctous minxi-g of entering liquid is a hypothetical

case which cannot bc physically realized; if, however, the time required

for distribution. of liquid is small compared to the average residence

time, the above ass,': option predicts accurately the physical behavior

of the system. A mass balance across the oxygenator in this case


I *
C C = AK(C C (2.1-6)
2 2 2 2

or following anviogous steps to those taken in the plug flcw case

x (2.1-7)
1 +

We had originally expected that mixing in the oxygenator would

lie between these two extremes and that the best mathematical model

for the system wauld be n perfectly mixed stages in series for which

it can be shown iy extension of Equation 2.1-6 that

S1 (211-8)
1 + A 1 + A- KT

Although the results of our experiments indicated that 1 perfectly

mixed stage described the system accurately, we have included a

comparison of our results with n = 2 for illustrative purposes.

There is an alternate derivation of Equation 2.1-7 which

parallels Kramner and Westerterp's (32) analysis of a 1st order

chemical reaction carried out in a continuously stirred tank reactor

(CSTR). In this development, it is noted the rate of change in

concentration of an element of fluid which remains in the oxygenator

for a given length of time, T, is gien by Equation 2.1-2 and the

concentration of Chis element is given by

x = ex -- T (2.1-9)
(, the elV

No:, the elements which constitute the liquid in the oxygenation column


:emain in the column for different periods of tine. The probability

of an element remaining in the column for a giver time, ,, is given by

the residence time distribution function which, for a CSTR, can be

calculated as follows: Since an element of fluid entering the chamber

mixes perfectly with the bulk liquid, its current position is

independent of its previous history. Consequently, the probability

of it remaining in the column longer than a specified time T + AT,

is the product of the probability of the element remaining longer than

time T and the probability of the element remaining longer than AT.

If F(T) is the volume fraction in the outlet stream having a residence

time less than T, then this probability is given by

1 F(T + AT) = [1 F(r)][1 F(AT)] (2.1-10)

Now, since element position is independent of past history, all elements

have an equal chance of leaving the column in the time period AT,


SV A -
F(AT) =- AT = -- (2.1-11)

Substituting this equation into Equation 2.1-10 gives

S( + -- F(-) = (2.1-12)
d t t

Recognizing that at T = 0, no fluid element has left the o:-ygenatot:, i.e.,

F(0) = 0 (2.1-13)

Equation 2.1--12 becomes, upon integration,


F(T) = 1 exp[-T/t]

Furthermore, since the change in the bulk concentration between the

entrance and exit of the oxygenation chamber is simply the volume

average of the various elements, the bulk concentration is

x = exp VKA T dF(T)

x = exp :] exp[-T/t]dT (2.1-14)

Upon integration of Equation 2.1-12,one obtains the result

x =- (2.1-15)
L + t

which is identical to Ecuation 2.1-7. This second derivation reveals

more about the physical phenomenon of ideal mixing than the first

development since it not only predicts bulk exit concentration but also

the residence time distribution function.

A graphical comparison in Figures 2,1-1 ind 2.1-2, shows the

differences between the three cases under condition. It can be seen

easily from Figure 2.1-1 that, for a given residence time, the greater

the number of mixiog stages, the smaller the value of x, i.e.,

oxygenation is more efficientLly accomplished by a larger number of

:nixing stages. The second salient feature that should be noted is

that as n approaches infinity the resulting x curve approaches the piug

flow curve-.

- -- -- -----

n =

n = 2

n = Plug Flow

2 4 6 8 10


Figure 2.1-1.

Comparison of Concentration Profiles as a
Function of Number of Stages in Series.



-- Plug Flow

-n= 1

n= 2

1 2 3 4 5

Figure 2.1-2.

Comparison of Residence Time Distribution
Functions for Varying Number of Stages in

1.0 r-

0.8 --




2.? Experimental Fqupment and Procedure

The simulation experiments performed were designed primarily

to determine the extent of mixing which occurred in the oxygenator;

secondly,they were designed to yield data from which the mass transfer

coefficient of oxygen in normal saline could be calculated. It was

anticipated that this mass transfer coefficient would be a good

estimate of the mass transfer coefficient of oxygen in blood plasma.

To accomplish these experimental goals two experiments were

attempted. The first experiment was concerned with measurement of the

size of bubbles ejected from the sparger. The second experiment was

designed to ascertain which flow model best described the physical

behavior of the system, and to determine an 0 2-saline mass transfer


In both experiments, normal saline, with small additions of

CMC, was used to simulate whole blood. The solutions were prepared

as fellows: To each liter of distilled water 9 gis of commercial

grade sodium chloride and 2.23 gms of DuPont sodium CMC

(2 W:xH grade) were added and dissolved. This amount of CMC increased

the viscosity' of the saline to that of whole blood as is shown in

Figure 2.2-1. The values shown were obtained by measuring the

viscosity of test samples of saline with varying amounts of CMC.

All measurements were made with a Erookfield variable speed viscosimetcr

at a temperature of 230C.

The experimental apparatus, shown in Figure 2.2-2, used to

measure bubble diameters consisted of a 2-!iter Miniprime Disposable

oygoenatur (Travenrol Labora-tries, Inc.), c high pressure air source,

of Whole

0.0 1.0 2.0

Concentration of CMC (gm/liter)

Figure 2.2-1. Viscosity of Saline-CiC Solution
As a Function of Composition.


[> .

with Camera



C---3 Reservoir

Figure 2.2-2. Experimental Apparatus Used to Measure
Bubble Diameters.

a 12-liter capacity saline reservoir, and a multiple finger variable

drive pump. Accessories included calibrated gas and liquid flow

meters, a pressure-reducing valve, and a thermocouple. Photographs of

rising bubbles were taken using a Unitron Series N Metallograph with

Polaroid camera attachment and auxiliary light source. The magnification

was set at 5X. As it was found that the saline solution corroded

metallic surfaces, Tygon tubing connected by glass and plastic joints

was used exclusively.

The experimental procedure used to measure bubble diameters

was as follows:

1. Saline was pumped through the oxygenator at a flow rate

of 1.4 Z/min.

2. Air flow through the oxygenator was regulated at

5.9 L/min.

3. Three sets of photographs were taken of rising bubbles

at 10, 17, and 30 cm above the sparger entrance. The

camera was focused as closely as possible on the center

of che oxygenation chamber to minimize the distortion of

the rounded surface. Measurements were taken at 23C

(room temperature) and 1 atmosphere pressure.

The experimental apparatus used to determine the mixing model

and to measure 0,-saline mass transfer coefficient is shown in

Figure 2.2-3. It consisted of two Miniprime oxygenacors in series,

three pumps, high pressure oxygen and nitrogen sources, plus all the

accessory equipment used in the bubble r.easurement experiment with the

exception of the microscope aCd camera. The first oxygenator was used


o .LJ ., ----

T> a

;O 0

0 41
r-1 (
= oCi


.- J

cd o


to saturate the saline solution with oxygen, and the second was

used as an oxygen stripper. A bypass was installed between the saline

reservoir and the first oxygenator to vary liquid flow through the

system. Two solenoid valves were also installed between the high

pressure oxygen source ard the sparger entrance, and between the saline

reservoir and the oxygenator entrance. These solenoids were used to

stop simultaneously the flow of oxygen and saline for the purpose of

measuring holdup volumes. Sampling ports were installed at the entrance

and exit of the first oxygenator in order to measure the change in

oxygen content across the oxygenation chamber. A drain was also

provided at the bottom of the oxygenation chamber to facilitate the

measurement of holdup volumes.

A galvanic cell oxygen analyzer was used to measure oxygen

concentration of liquid samples. As the name implies the analyzer

is a galvanic cell with a lead anode and a silver cathode. An

aqueous KOH solution is used as an electrolyte and together with anode

and cathode it is enclosed by a polyethylene membrane which is permeable

to oxygen.

The experimental procedure for testing each of the four

oxygenators (.-, 2-, 3-and 6-liter capacity units) was as follows:

1. -,.ygen flow rate was adjusted to 3 c/min.

2. Saline flow rate was adjusted to a predetermined value.

3. Oxygen flow rate was adjusted to predetermined value.

L. Nitrogen flow rate ,was set at a value not less than

7.0 S./min.

5. After waiting 10 minutes to allow the system to come to

steady state, a 50 ml sample was drawn from the entrance

to the oxygenator and analyzed for oxygen concentration.

6. 50 ml samples were then taken and analyzed until two

successive oxygen readings were recorded which varied

less than 0.6% of the full scale.

7. 50 ml samples were then taken from the oxygenator exit

and analyzed until two successive oxygen readings were

recorded which varied less than 0.6% of the full scale.

8. The temperature of the saline in the oxygenator was

recorded immediately after each 50 ml sample was drawn.

The oxygen analyzer was calibrated at the beginning of each

day in saline solution saturated with air. The analyzer was also

recalibrated at the end of each day for a period of two to three days

after the probe membrane had been changed and electrodes cleaned.

2.3 ExDerinental Results--Bubble Diameter measurementss

The results of the bubble measurement experiment arr- shown in

Figures 2.3-1 and 2.3--2. Actual data are given in Appendix D. From

the photographs taken, it was determined that the rising bubbles were

not perfect spheres but tended to be ell.psoidal in shape. Consequently,

the formulas used to calculate the surface area and volume of each

bubble were, respectively,

S = 2r b2 + -a sin -

S4 2
V - iab


3 6





0.0 10.0 20.0 30.0 40.0 50

Surface Area (im )

Figure 2.3--1. Distribution of Bubble Sizes by
Surface Area.

12 -- \







0.0 10.0 20.0 30.0 40.0 50.0
Volume (min3)
figure 2.3-2. Distribution of Bubble Sizes by

where a = najor radius

b = minor radius

c = eccentricity

As can be seen, both distribution curves for volume and surface area

are skew symmetric. Graphical integration of the distribution curve

for volume gives an average bubble volume of 13.69 mm and an

apparent average spherical diameter of 2.97 mm. Graphical integration

of the surface area distribution function gives an average bubble
surface area of 26.9 mm2 and an apparent average spherical diameter

of 2.93 mm. Since the apparent spherical diameters calculated from

the average volume and average surface area were virtually identical,

it was assumed that the effective spherical diameter of the bubbles

was the average of these two values, i.e., 2.95 mm, in all following

calculations involving blood and saline. Analysis of photographs

of bubbles taken at various heights in the oxygenation chamber

indicated little change in bubble size throughout the column. There

appeared to be a slight increase in the average diameter of approximately

10% from the boLtom to the top of the column, but data points were

too few, particularly at the top of the column, to definitely confirm

this trend. Furthermore a calculation of maximum hydrostatic pressure

.rop across the oxygenation columns of all four Miniprime oxygenator

models predicts a maximum gas volume change of 7%. During normal

operation of the oxygenators even this small change will not be

obtaLned since a fraction of the oxygenation chamber volume is

occupied by gas chus reducing the hydrostatic head. Finally, it is

the total surface of the bubbles in the cxygenator that is important;

including bubble variation as a function of position in the calculation

of the average diameter, as has been dcne, should give a valid

estimate of the surface area for mass transfer coefficient estimation.

A more serious source of error could arise from the assumption

that the bubble diameter is independent of change in gas and liquid

flow rate. The most concrete evidence to support this assumption is

that the term KA was found to be directly proportional to the gas hold-

up volume in the experiments performed to measure the mass transfer

coefficient. If the average bubble diameter varied, this would not

have been the case.

An attempt was made to correlate bubble diameter data with

the single-bubble regime model summarized by Perry (53) which predicts

D 6D /2 (2.3-1)

where DB = bubble diameter

D = orifice diameter

c = gas-liquid interfacial surface tension

p, = liquid density.

The average bubble diameLer size, using Equation 2.3-1, was calculated

to be 7.64 mm which is about twice as large as the estimated value.

The e::perimrentally obtained average diameter was also compared with

the empirical correlation

D = 0.18 D05N 0.33 (2.3-2)
B Re

which was developed by Leibson and co-workers (54). Equati on 2.3-2

Predicts the average bubble diameter to be 0.310 mm or an order of

magnitude too small.

The range of Reynolds numbers for which Equation 2.3-2 is

valid covers flow rates above the single bubble range to Reynolds

numbers below 2000,and this region is known as the transition region.

There is no clear division between the single bubble region and the

transition region, but the low gas Reynolds numbers at which the

oxygenator is operated,

NRe = 30 to NRe = 80

probably lie in the region in which surface tension effects are

important. In such a region, the variation of bubble diameter with

respect to NRe,and thus with flow rate, would be a secondary effect,

no effect at all according to Equation 2.3-1.

2.4 Experimental Results--Oxygenator Simulation

Representative results of the oxygenator simulation experiments

are snown in Figure 2.4-1 and a complete data listing is given in

Appendix D. The variables plotted are % oxygenation, or 1-x,

versus a reduced residence time

C = -c (2.4-1)

The variable V, the holdup volume of oxygen, was chosen since it

was assumed that average bubble diameter was independent of flow

rates. Thus V is related to the interfacial surface area A by the
proprc nalIg
proprut tonality

o o o
.4r (1 C -









r- -




(u2ot:mI.f s IeuOTej..j.- [) x

A = V --
g DB

A least squares fit of the data to a 1 CSTR, 2 CSTR,and plug

flow model was performed. The linear method outlined by Mickley,

Sherwood, and Reed (55) was used by rewriting Equations 2.1-5,

2.1-7, and 2.1-8 as

y 1= 1 + KJ. t (2.4-2)
y --1+ K --'+
x V DB

Y = 1 K D t (2.4-3)

Y = Z.n x = K g- 6 t (2.4-4)

The results of these operations are summarized in Table 2.4-1.

As can be seen, the standard deviations for the 2 CSTR and

plug flow models are almost twice as large as for the 1 CSTR model.

Furthermore, although an F-test indicates nonrandom errors in all

three analyses, a qualitative inspection of the data suggests that the

nonrandom error is greater for the 2 CSTR and plug flow models than

fcr the 1 CSTR model. It was concluded, therefore, that the oxygenatcr

could be apprc .inated by a 1 CSTR moeel for all four sizes of


There appears to be some discrepancy between the model and the

data for smallest size bag, the 1-liter capacity oxygenator. The

data suggest that the o.:ygenation of saline was less than would be

obtained if the system were perfectly mixed. Since both the sparger


TABLE 2.4-1





Plug Flow


2.29 x 102

4.53 x 10-3

8.51 x 10-3

6K -1
6K (sec )

4.65 x 10-
9.22 x 102

1.73 x 10-1


4.7% (5.4% )



Data from the l-liter capacity oxygenator were deleted
from final estimation of K. The value in brackets indicates the
standard deviation with these data omitted.

and chamber for the 1-and 2-liter bags are the same geometrically and,

in fact identical dimensionally, we cannot attribute this phenomenon to

scale up factors, i.e., change in mass transfer coefficient or bubble

diameter. It was noted in later experiments, that any tilting of the

oxygenation chamber caused channelling flow in certain portions of the

oxygenator while in other regions, stagnation and back mixing occurred.

Accompanying this.type of unstable flow was a marked reduction in

oxygenation of saline.

The data from the holdup volume measurements were correlated

as a function of gas flow rate divided by liquid flow rate for each

size oxygenator. rhese reduced data for each case were then fitted to

10th degree polynomials which were subsequently written in the form

of a computer subroutine to be used in blood data analysis. These

results are shown graphically in Figures 2.4-2, 2.4-3, 2.4-4, and 2.4-5.

The final values of the mass transfer coefficients, obtained by the

method of Gauss elimination (56) applied to a least squares fit,

are tabulated in Table 2.4-2. The experimental data are also listed in

Appendix D. The relatively constant value of gas holdup volumes at

high gas flow races is due to fact that as the volume flow rate increases

the velocity of the bubbles increases, and thus, the increase in the

number of bubbles generated per unit time is offset by the speed at

which the bubbles move.

It was also noted that at very high flow rates, bubbles

coalesced into large pockets of gas which rose rapidly through the

oxygenation chamber. This effect could also reduce gas holdup volume,

and, in addition, reduce the surface area available for mass transfer.


150 ---I I



100 -

| 75 -

50 5

25 -

0 _._._--- _--- I - ---
0 2 4 6 8 10

[ Gas Flow Rate (liter/min)
Liquid Flow Rate (liter/min)

Figure 2.4-2. Gas Holdup Volume as a Function of Gas to
Liouid Volume Flow Rate Ratio in the 1LF
Bubble Oxygenator.


150 T

150 ------- --- ----T--------




50 L


0 iL. t I1

0 1 2 3 4 5 6

Gas Flow Rate (liter/min)
Liquid Flow Rate (liter/min) J

Figure 2.4-3. GC- Holdup Volume as a Function of Gas to
Liquid Volume Flow Rate Ratio in the 2LF
Bubble Oxygenator.

18 0 ------- ------r- -----n---^--"- T^--7--

150 -

u 120

- 90



0 I
0 0.5 1. 1.5 2.0

SGas Flow Rate (liter/min)
Liquid Flow Rate (liter/min)

Figure 2.4-4. Gas Hol.dup Volume as a Function of Gas to
liquid Volume Flow Rate Ratio in tha 3,F
Bubble Oxygenator.



---F-- ~~1~~~


" 200


0 150 1

100 -

50 -

0 - -- t I I
0 0.5 1.0 1.5 2.0 2.5

SGas Flow Pate_ (liter/min) 1
[ Liquid Flow Rate (liter/min)

Figure 2.4-5. Gas Holdup Volume as a Function of Gas to
Liquid Volume Flow Rate Ratio in the 6LF
Bubble Oxygenator.





M +



C +

0 U

S -

o +

C- --
z >-


0 +
I U C ~




S> ;5-
0 CM

^ +

-1 4

H r0

NI N N --
0 0 C) -
- -- 0 C 0- -

co o to oa
\C I- 'n C
I I133

1 0

0 r-I

CO 4

001 0

0 --
'. '.o

' CM

--4 r-
0,1 0.


Co r--

cn 10
I 0


r- \D




. -.1 -.1 ,-1
0 1- C n 1

O l>CD C) C)
LO cr cc c


0 o -o 4 .--
CM L<) CO 00


0 0 C'0 0C
,--4 ,-4 -4

-I ,-A "l O 0
CO' O C u
cc co cc I^-
) --1 (D C -1
r o co C

0 C1 1 0'

-I I I 00

ci- on Cn C
r N o0
-1 co 4 Cl c

7o c -4 cc

-1 -1 4 -

cc en r-i 3--

r- Cl CO '.0

o co C
I 0- 0 0

,- X X : X
x X
L. 10 00
C Lci -T cO


co i C Cl
0 0 0 0
,-- X j ; X

.0 C LCG C

C 0 .0 -Z C
I1 Io CO C

Co f-- CO o
,.0 0 0 0
rCl .- l r* l


1 1-z 1-1 c
-4 I COY






It was found that this phenomenon occurred at a gas flow rate of 7.0

to S.0 /nin depending on the size of oxygenator used.

The starting point of our analysis of this absorption process

was Equation 2.1-6. This equation itself is based upon the more

primitive model of diffusion through a thin film or boundary layer.

To derive Equation 2.1-6, it is assumed that the process is

diffusion-controlled, i.e., the rate is controlled by a diffusion

resistance in a thin layer close to the gas-liquid interface; and,

furthermore, that the concentration profile across this boundary layer

is linear. A schematic representation of this model is shown in

Figure 2.4-6.

A mass balance across the diffusion layer gives

V +AJ r

or "
d(C ) a(C c )
0 0 0 0
"2 2 A 2 2 -
d- - D -- (2.4-5)
dt V 02 ar

Suppose that the bulk concentration changes slowly in time in comparison

with the rate of change in concentration profile within thr! boundary

layer, chen, for any small interval of time, C car be assumed as

independent of time and the diffusion of oxygen through the layer can

be described by

DC { 2 (2.4-6)
ot 2 cr 3or



Figure 2.4-6. Thin Film Diffusion Model for
Oxygen Absorption.



with the boundary conditions

C(O,r) = CO a < r < a +

C(t,a) = C (2.4-7)

C(t,6) = C

The solution to this set of equations has been given by

Crank (57) as

aC [(a + 5)C aC ](r a)
C .
C = -+-
r ro

2 (a+6)(CO-C )cos nq a(C -C )


n (r a)

-D2n 2 t/6 (2.4-8)
x e

For values of approaching zero all of the terms in the right-hand

size of Equation 2.4-8 except the first two approach zero.

Differentiating these remaining terms gives

*(C-C [(a + 6)CO ac ]
(C -C ) -a r (.
C + (2.4-9)
;r 2 5 r 2
r r

Moreover, if 5 is much smaller than r,

r a a r < b

and Equation 2?.L- can be app:.oxiriated by


S r C
-C (2.4-10)
cr 6

It should thus be noted that the assumption of a small boundary layer

thickness, such that

2 2 (2.4-11)
6 << r and 6 < D 2 (2.4-11)

yields the linear concentration profile which we required. Substituting

Equation 2.4-10 into Equation 2.4-5 gives

d(C C 2 A (C0 C
2tD (2.4-12)
dt V 02 6

and comparison of this equation with 2.1-6 yields

K (2.4-13)

-5 2
Using a value of 2.5 x 10 cm /sec for the diffusivity of oxygen into
s!line (53), we obtain a bo;undarc layer thickness of 1.1 x 10 cm.

This boundary layer thickness fits the criterion as stated in Equation

2.4-11 for our proposed assumption quite well as shown in Table ?.4-3.

TABLE 2.4-3


Parameter Value


2D 2

1.1 x 10-3

1.1 x 10

4.9 x 10-3




3.1 Theory of Gas Transfer Through Blood

In Chapter 2, oxygen transfer into saline during operation

of the bubble oxygenator was discussed, and it was determined that

the oxygenator could be best characterized, in fact, as a perfectly

mixed stage. This is also true for blood in the oxygenation chamber,

but in this case the oxygen absorption process is more complex owing

to the reactions which take place as discussed in Chapter 1, Section

3. This circumstance increases the complexity of the system and

invalidates the second derivation presented in Chapter 2 of Equation

2.1-7 except for the case of first order reactions.

Since oxygen and carbon dioxide transport must be accounted

for both as dissolved gas and in the chemically bound form, a mass

balance including all of these species must be written. In matrix

form this mass balance is

V{(C) (CI)} = -A[K]{(C) (C*)} + (R) (3.1-1)

where (C) is the column matrix of chemically distinct species

concentl-ations at the exit of the oxygenator, (C ) is the column matrix

of chemically distinct species concentrations at the oxygenator entrance,

(C ) is the column matrix of chemically distinct species concentrations

in equilibrium with the gas phase, and (R) is the column matrix of

chemical reaction coefficients. We shall dismiss out of hand all of

the off-dingonal elements of the matrix [K] arguing thct the solution


is dilute in CO2 and 02, therefore these gases diffuse into the blood

as binary 0 2-blood and CO2-blood pairs. In these circumstances,

Equation 3.1-1 reduces to

I A 1
(C -C ) = K (C C ) + R (3.1-2a)
0, 0 2 0B 0 2 V 02 2 02

I A 1
(C C )=-- K (C C 1+ 2 (3.1-2b)

2 2 V 2 V
I A 1
(C C ) = -- K (C C ) P (3.1-2c)

(Cc bC0) = --2 K Hb (C C2) + R 21HbC02

where CO CCO and CCO2 are the concentration of oxygen and
2 3 2
carbon dioxide bound to each of these chemical species. Addition of

Equations 3.1-2a, 3.1-2b, and 3.1-2c leads to the total oxygen transport

(C C) (K C C )+K (C
0 C TOT ,B + KHbO ,B HbO
2 2 VO2, 2 2 2' 2

Cr1,) (R Hb, + R ) (3.--3)

We furcher assume that the system is in local equilibrium, i.e.,

R bO -R (3.1-4)
consequently, te amount o 0 bound to hemoglobin

andconsequently, the amount of 02 bound to hemoglobin can be related

to the concentration (partial pressure) of dissolved unbound oxygen

by the equilibrium relationship, Equation 1.3-6. Since the red

blood cell has a specific gravity of 1.091 and contains 0.34 weight

fraction hemoglobin, the concentration of hemoglobin in whole blood is

CHb (.34)(1.091).H (3.1-5)

where H = hematocrit = volume fraction of red cells in blood.

Furthermore, since each gram of hemoglobin can bind 1.34 standard cc of

oxygen at saturation, the amount of bound oxygen in the blood is

related to the partial pressure of oxygen by

CHb2 = (.34)(1.091)(l.34)H*S(PO2) (3.1-6)

Finally, we assume that the transport of oxygen bound to hemoglobin

by diffusion is negligible, i.e.,

Kbo2 %0 (3.1-7)

This assumption is based upon the fact that the hemoglobin molecule is

quite large; consequently, it diffuses very slowly through the blood

(58). Incorporating Equations 3.1-4, 3.1-6 and 3.1-7 into Equation

3.1-5 gives the final results, namely,

(C C 0
0 0 'TOT
2 2 1
(C Cc) 0 AK (P P0
2 2 21 2 2
07 2 (C C )
'O 0 TOT
2 2

where Henry's law has been used to relate the partial pressure of

oxygen to the concentration of dissolved gas by

C0= 0 2P0 (3.1-9)

a2 being the Henry's law constant.
The equations for transport of carbon dioxide through blood

are similar to those developed for oxygen. A total mass balance of

CO2 across the oxygenation chamber gives the result

I A KC02
(C -c ) C (C + K (C
2 z V 2 2 2 2

2 O3B 3
CHbCO2 + KHCO3,B((CO CHCO3 (3.1-10)

where ic has already been assumed that all reactions are in local

equilibrium, i.e.,

R O2 + RHCO3+ bCO2 = 0 (3.1-11)

The assumption of negligible transfer by diffusion of hemoglobin-

bound CO2 appears to be valid for the same reason given for HbO2

diffusion. The problem of bicarbonate ion transfer is not so easily

handled. it ,:as the original intent of this work to determine or at

least make a fair estimate of the bicarbonate diffusivity, but data

caken during open-hzart surgery gave differences in inlet and outlet

CO.2 concentration amounting to only a few millimeters partial pressure,

a quantity far too small to make any but an order of magnitude estimate

of the mass-transfer coefficient. Thus, we assuiied

KCO = 0(3.1-12)

Incorporating this last result into Equation 3.1-10 gives

(C C )
S 2 1 -- (3.1-13)

(C C AK a,C02 (P P
2 2 2_2_ 2 2
1 + ---
2 (

which is the same result as obtained in the case of oxygen transfer.

3.2 Experimental Procedure

Sixteen open-heart operations were observed at Shands

Teaching Hospital, the University of Floiida, Gainesville, Florida

during the period from June 18, 1970 to October 3, 1970. In each case

normal operating procedures were followed with the exception that

verous as well as arterial blood samples were drawn from the patient.

In all cases the Miniprime Oxygenators produced by Travenol Corporation

with pumps and a heat exchanger were used, and data were obtained for

each size oxygenator as shown in Table 3.2-1.

A schematic diagram of the operational setup, which was the

same in all of the operations observed, is shown in Figure 3.2-1. The

procedure used in open-heart surgery can be separated into two parts;

(1) the preparation of and surgery on the patient, and (2) the startup

and operation of the oxygenator. The procedure for preparation of the

patient and the surgery is as follows.

1. Before the patient is moved into the operating room a


Q c









_ 0 I



TABLE 3.2-1


Maximum Blood
Flow Capacity ( liter/min)




No. of



No. of
Data Points



6.0 4


sedative, generallyNembutal, and atropine, is administered.

2. Before surgery is begun, an anesthetic such as Pentothal

is administered to the patient. Other anesthetic agents

used are halothane, morphine, and nitrous oxide.

3. Surgery is begun by cannulating the femoral artery located

in the thigh. This artery serves as the arterial return

from the blood oxygenator.

4. Next, the chest cavity is opened and both superior and

inferior vena cava are cannulated. These two veins serve

as the venous supply to the oxygenator.

5. The patient is now placed on 60% bypass, i.e., 60% of

total blood flow is bypassed through the oxygenator. At

this point an anticoagulant,heparin, is administered.

6. The heart is then defibrillated either by electric shock

or by surging cold blood through it.

7. The bypass flow is brought to 100% body perfusicn rate

and surgical repairs are made.

8. After surgery on the heart is completed, the bypass flow

rate is reduced to 60% and the heart is fibrillated by

electric shock.

9. The patient is taken off bypass completely and all wounds

are closed.

The startup and operating procedure for the oxygenator is as follows:

1. The oxygenator, including all tubing, is primed with

Ringor's solution and then whole blood.

2. The blood pumps are sLarteJ and the oxygen flow valve is

opened while the priming solution is circulated around

the oxygenator and heat exchanger in a closed loop. This

is to insure the initial blood entering the patient's body

is saturated with oxygen and at the desired temperature.

4. The blood flow rates are adjusted to 60% desired flow as

the patient is placed on partial cardiac bypass.

Simultaneously a maximum 5% (by volume) flow rate of

halothane is introduced into the oxygen inlet stream.

5. The blood flow rate through the oxygenator is gradually

increased to 100% of desired flow.

6. Venous and arterial blood samples are taken at approximate

20-minute intervals or upon request of the operating

surgeon. These samples are analyzed for oxygen and

carbon dioxide partial pressure, plasma pH, hematocrit,

and plasma bicarbonate concentration. At the time blood

samples are drawn, and blood and oxygen flow rates, as

well as temperature, are recorded.

7. The blood temperature is gradually increase to normal

body temperature, and bypass flow is reduced to 60% of

normal flew.

8. The patient is removed from bypass system.

In addition to these procedures blood hemolysis is also monitored

az various time intervals.

The device used to analyze blood samples w\as an Asterup Type AME1.

Estimated accuracy of the Asterup equipment for various measured

quantities is shown in Table 3.2-2. Blood he;atocrits were measured

TABLE 3.2-2



02 Partial Pressure

CO2 Partial Pressure




Range of Data

32-590 mm

16-38.5 mm





- 0.5 mm

0.02 mm

t 1.00C



by centrifuging two blood samples drawn in capillary tubes for a

period of not less than three minutes and then measuring the volume

fraction cf the separated red cells and plasma. The estimated

accuracy of these measurements is shown in Table 3.2-2.

3.3 Experimental Results

Data taken during the 16 operations referred to above are

listed in Appendix D. Of the 32 data points taken approximately

one-half or 15 were at ratios of oxygen flow to blood flow which

exhibited channelling and stagnating flow in the saline simulation

experiment. These data points were consequently disregarded in a

least square fit to calculate mass transfer coefficients. As

previously stated, a linear least squares fit (56) of the data was

made with Equations 3.1-8 and 3.1-13 written in the form

I *
(C0 C- )
2 2 6
x = ---- = 1.0 + K (3.3-1)
2 (C C ) 2' BD
2 2

I *
(C c
x 1.0 + K X (3.3-2)
co C02B B
2 (CC C CO OT 2) B


S (P P )
X =0 2 ,-- (3.3-3)
V 2 (C C )
2 2

(P PC)
V co CO
H 2 2
X = C (a CO (3.3--4)
V 2(C CC0 )

Both Henry's law constant and the mass transfer coefficient are

functions of temperature and hematocrit, and both of these varied frcm

data point to data point. The temperature dependence of Henry's law

constants was accounted for by fitting data reported by Sendroy et al.

(59), and Davenport (60). For temperatures ranging between 25C and

370C, it was found that the 02 and CO2 solubilities could be predicted

accurately by

02 = (8.971448 0.02566618.T) 02370C (3.3-5)


CO2 = (9.26475738 0.026607855.T) a02,37"C (3.3-6)

where T is the temperature of the blood in degrees Kelvin. The variation

of these constants with respect to hematocrit was also reported by

Sendroy and Da'enport as

a 380 = c H + a (1 H) (3.3-7)
C rc p

where a is the solubility of 02 or CO2 in the ied cell and a is

the solubility of these gases in plasma and H is the volume fraction

of red cells in whole blood. For oxygen, values of 0.0258 cc (STP)/cc-atm

and 0.0209 cc (STP)/cc-arm, were reported for a and a respectively.
rc p
For carbon dioxide, values of 0.423 cc (STP)/cc-atm and 0.509 ca (STP/cc-atm,

were reported for a and a respectively.
Ic p

A correction for the variation in mass transfer coefficient

due to fluctuations in hematocrit was made based on the dLffusivity

correction used by Bradley (17). Bradley, noting that blood was a

suspension of red cells in plasma, drew an analogy for oxygen and carbon

dioxide diffusion into blood to electrical conduction in a suspension

of noninteracting ellipsoids (61). From this analogy he suggested

that the diffusivity of gases in whole blood could be related to the

diffusivity of the same gases in plasma by the equation

D D 1 H(0.65) (3.3-8)
b p = + 0.49H

where Db is the diffusivity of the gas in whole blood and D is the
b P
diffusivity of the gas in plasma. Now, we have already noted that the

mass transfer coefficient is simply

K = D (3.3-9)

where L is the length of the diffusion path. Substituting Equation

3.3-9 into 3.3-8 gives the desired result

b 1 H(0.65) (3.3-10)
K 1 + 0.49H

It was assumed further, that the relationships developed for gas

holdup volume as a function of the ratio of the gas flow rate to the

liquid flow rate in the saline experiment was valid for the blood


UiJng Equations 3.3-1 and 3.3-2 and correcting for temperature

and hem'atocrit variations, it was found that the best least squares

fit of the 17 data points analyzed predicted an oxygen mass transfer

ccefficient of

6 -1
K = 6.44 min
02,B DB

and a carbon dioxide mass transfer coefficient of

K = 15.96 min1

A graph based on these results of percent oxygenation versus residence

time 1 is shown in Figure 3.3-1.

The standard of deviation for K B was + 21%, and the
standard deviation for KCO was + 73.3%. The large standard of
deviation in the case of K should not be surprising since very
C0, ,B
small changes in carbon dioxide partial pressure correspond to a

relatively large change in total carbon dioxide concentration. Since

data reported .wereLo the nearest 0.5 mm, the calculations made could

only predict order of magnitude values for KCO ,B. In addition, we

hive neglected the transport of bicarbonate ion, and this could be a

serious source of error. ihe 2C% standard deviation of the mass

transfer coefficient for oxygen is probably due Dartly to the variation

in mass transfer coefficient with temperature, which ranged from

290C to 37C, and to inaccuracies in flow rate measurements.

The oxygen flow meter used in the open-heart. surgery was

graduated to the nearest liter/min which gave at best a + 0.25 liter/min

estimate of the act,:al flow, rate (as compared to + 0.05 liter/min


0.8 0 09
0 0

o 0.6

L 0



0.0 0.04 0.08 0.12 0.16 0.20

9 (Equivalent Residence Time)

Data Taken During Open-Heart Surgery.

Figure 3.3-1.

estimates obtained in the saline simulation). Although the blood

flow meter was calibrated to + .02 liter/min, readings '.ere reported

by the medical staff to the nearest + 0.2 liter/min (as opposed to

readings of 0.1 liter/min obtained in the saline experiments). If

we consider the variation of the diffusivity of oxygen in plasma for

temperature changes of the order of 29C to 370C, we find a similar

deviation of slightly more than 20%. Finally, it should be noted that

slight deviations of the oxygenation chamber from the vertical also

cause marked differences in the oxygenator performance.

As was done for the saline experiment, a check for the model

of diffusion through a stagnant boundary layer with a linear profile

surrounding each bubble was made. As a test case a representative

hcmatocrit of 0.30 and a temperature of 32C was chosen. Since the

limiting case near total saturation is the situation encountered in

the system when operated normally, it was assumed that Equation 2.4-8

described the transient problem accurately. Using a diffusivity of
-5 2
1,149 x 10 cm /sec, the calculated boundary layer thickness and

time constant obtained are shown in Table 3.3-1. The results, of

course, assume the same average babble diameter as was measured in the

saline experiment.

The somewhat larger boundary layer, estimated at the blood-02

interface as compared with the saline-0, interface, is to be expected

since red cells and the other formed elements of the blood at the blcod:gas

interface would tend co "drag" more fluid with the rising bubble than

the molecular saline solution. Even though the time constant for the

blood. system (2.57 sec ) is smaller than the salina system timn

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