P.' ANALYTICAL A':D EXPERR:E'; AL SiDY OF BLOOD
OXYGFNAI'ORS AND PLiiMONARY MASS TR,;SFER
IN LIQU ID BREATHIIC
Ey
JANMZS WIL;.IA-i FALCO
A DISSERTATION P'.ESNTED TO70 h: GRADUATE COUNCIL OF
TlE UN(LRS:I"' OF FIORIPA IN PARTIAL
FULFIl LY;T Or TF REQLIRFMENIS FOS THE DEGREE OF
DCCTOR OF ?HILOSOTY
UNIVERSITY Of FLORLU.-"
1971
ACKNOWLEDGEMENT
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 mu.ch of this research work; and to
Dr. A. K. Varma for generously agreeing to serve on t.is 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 Hospit.al
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
support.
TABLE OF CONTENTS
ACKNO LE uCGE ENT .............................................
LIST OF TABLES ..............................................
LIST OF FIGURES .............................................
NO -ENCLATURE ................................................
A STRACT ....................................................
CHAPTERS:
1. EHE DEVELOPMENT OF ARTIFICIAL BLOOD OXYGENATORS....
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. STIt'LAT.ON OF THE BUBBLE 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 ...............
ii
v
vi
x
xiii
TABLE OF CONTENTS (Continued)
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. GAS TRANSPORT IN LIQUID-FILLED LUNGS................ 133
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
B. SOME OBSERVATIONS ON MEMBRANE OXYGENATORS.......... 191
E.1 On.e-di::.nscnal La-.in.r 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
LIST OF TABLES
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
LIST OF FIGURES
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
LIST OF FIGURES (Continued)
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
LIST OF FIGURES (CortinuRd)
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
viii
LIST OF FIGURES (Continued)
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
NOMENCLATURE
A = interfacial surface area
C = concentration
C. = concentration of component i in a mixture
1i
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
oxygenator
C\ = the amount of component k bound to component M
C. concentration of the ith component in a liquid film
out
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
constituents
CM =- equilibrium relationship whichh equates the amount of
component k, bound to compo..rent 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
1
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
~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
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-
controlled
V- = volume of a stagnant film
I
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
AN ANALYTICAL AND EXPERIMENTAL STUDY OF BLOOD
OXYGENATORS AND PULMONARY MASS
TRANSFER IN LIQUID BREATHING
By
Jar.es 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
cm
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.
CHAPTER 1
THE DEVELOPMENT OF ARTIFICIAL BLOOD OXYGENATORS
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 Mill.er 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
membrar.es 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
developed.
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.
5
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
Lungs
Heart
Waste Products
_<- _-- Kidney ----<------
Capillary
Bed
I.-. -- -
Vein I
0 CO,
2 2
Waste Iateriil
Figure 1.2-1. The Cardiovascular System.
Artery
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
follows:
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
(1.3-5)
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
temperature.
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
KP]I
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
again.
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-
v.-J
SP P37 0
CCO
S2
r.4
S0.200-
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
370
7- = 40.0 mm
CO2
370C
33C
S300C
l !-
20.0 10.0 60.0
02 Partial Pressure
80.0
100.0
Figure 1.3-2.
The Effect of Temperature on
Oxygen Saturation.
1.000
0.800
0.600
G.A00
0.200
0.0
0.0
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.
1.000
0.800
0.600
0.400
0.200
0.0
0.0
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
section.
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
Hib- .NH-COOH Z Hb.NH.COO + H
carbonic
anhydrose
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)
9J
where C is the total concentration of carbon dioxide, S is the
fractional saturation of hemoglobin by oxygen, and P CO is the
Co
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 -~
0.500
0. 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
H o
HJ - .--
' C
M 0r I '0
uE l I 0 '
H *CO U cH
,o
Sr-I -
r ,
H ~ --> ^
H U Cl fl
o o
T-4H
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^
X U
H
H C
o o
ir)
a hC
Li
CJ
1 4
cr
1)
(1
-C)
'-4
o-- --- -
cj-
(3
a
L A rCO
o o
EO
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
reaction
(1.4-1)
or
-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)
ot
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)
it
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
reservoir.
The major advantages of this type of oxygenator are as Follows:
i. the bubble oxygenator is inexpensive and completely
disposable;
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
Blood
02
0
0
i-4
U)
00
o
Z F-
--
o
0 __ (
0
-_ __ ^ (U
-------W_--. -,
S------ C
t --P----
I- 0
111
r--4
--- -i .
i ---
'-
a-
'---4 V - -
'n
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
expensive;
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
axpir.art 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
alveoli.
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 volu.ie 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.
35
alternate model, based upon imperfect mixing theory, which we believe
will describe the functioning of the lung more accurately than models
proposed previously.
CHAPiER 2
SIMULATION OF THE BUBBLE OXYGENATOR
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
T KA
(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
1000
38
x =-.exp t (2.1-4)
where *
C I C*
02 02
x = C _
I
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,
or
V
T
V
where V is the volume flow rate of saline. Thus the final form of
Equation 2.1-3 is
SKA
x = exp (2.1-5)
V
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 lilj.id 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
yields
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)
AYK
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)
AK A
1 + A 1 + A- KT
nV
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
40
: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,
namely,
SV A -
F(AT) =- AT = -- (2.1-11)
Substituting this equation into Equation 2.1-10 gives
d(F())
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,
41
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)
T=O
or
x = exp :] exp[-T/t]dT (2.1-14)
T-=O
Upon integration of Equation 2.1-12,one obtains the result
1
x =- (2.1-15)
KA
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
AK
V
Figure 2.1-1.
Comparison of Concentration Profiles as a
Function of Number of Stages in Series.
1.0
.8
-- Plug Flow
-n= 1
n= 2
1 2 3 4 5
AK
V
Figure 2.1-2.
Comparison of Residence Time Distribution
Functions for Varying Number of Stages in
Series.
1.0 r-
0.8 --
0.6
0.4
0.2
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
coefficient.
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,
Viscosity
of Whole
Blood
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.
4.0
[> .
Microscope
with Camera
Light
Source
Vent
C---3 Reservoir
Pump
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
.C.
o .LJ ., ----
T> a
;O 0
LO
0l,
0 41
r-1 (
=
oCi
Q4.iu
C-)
.- J
Ci
0)
cd o
IP
1,
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
U)
3 6
P
C
a)
4
z
2.
0.0 10.0 20.0 30.0 40.0 50
2
Surface Area (im )
Figure 2.3--1. Distribution of Bubble Sizes by
Surface Area.
12 -- \
10
8
0
6
4
0
2
'K-
0.0 10.0 20.0 30.0 40.0 50.0
Volume (min3)
figure 2.3-2. Distribution of Bubble Sizes by
Volume.
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
2
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
1/2
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
V
C = -c (2.4-1)
V
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 -
Ci
-V.
>1*
0
-4
C'
CO
CO
.1)
il
0
P4
r- -
C
JO
4;
1
--4
CN
o
(u2ot:mI.f s IeuOTej..j.- [) x
6
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)
V D B
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
oxygenators.
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
58
TABLE 2.4-1
COMPARISON OF PROPOSED MODELS WITH EXPERIMENTAL RESULTS
Model
1 CSTR
2 CSTR
Plug Flow
cm
sec
-2
2.29 x 102
4.53 x 10-3
8.51 x 10-3
6K -1
6K (sec )
D
-1
4.65 x 10-
-2
9.22 x 102
1.73 x 10-1
Standard
Deviation
4.7% (5.4% )
8.5%
8.5%
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.
60
150 ---I I
/
125
100 -
| 75 -
50 5
I
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.
61
150 T
150 ------- --- ----T--------
125
75
0
50 L
25
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.
180
18 0 ------- ------r- -----n---^--"- T^--7--
150 -
U
u 120
0
- 90
60
30
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.
2.5
--
---F-- ~~1~~~
250
" 200
,-I
0
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.
'--
,--
r-4
+
-4
U
M +
A
00
'.0
C +
1O1
0 U
S -
O
o +
C- --
z >-
u
0 +
I U C ~
O U
-i-
4I
S> ;5-
0 CM
^ +
I--
-1 4
H r0
NI N N --
0 0 C) -
- -- 0 C 0- -
co o to oa
\C I- 'n C
I I133
,--4
1 0
0 r-I
,---t
1-
N
-S-
CO 4
001 0
0 --
'. '.o
' CM
--4 r-
l
o
0,1 0.
N
Co r--
cn 10
I 0
l--
N
CM
r- \D
-I
0
JJ
. -.1 -.1 ,-1
0 1- C n 1
O l>CD C) C)
LO cr cc c
0000
0 o -o 4 .--
CM L<) CO 00
N T N
CI I I C
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
COOO-
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 I I
I 0- 0 0
,- X X : X
x X
c1
U CM CO
L. 10 00
C Lci -T cO
I I I
co i C Cl
0 0 0 0
0000
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
Sr
1 1-z 1-1 c
-4 I COY
I
0
O
r3
,-'
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
dC
V +AJ r
R+6
or "
d(C ) a(C c )
0 0 0 0
"2 2 A 2 2 -
d- - D -- (2.4-5)
dt V 02 ar
R+6
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
r
Transfer
C
*2
Figure 2.4-6. Thin Film Diffusion Model for
Oxygen Absorption.
Bulk
63
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=l
n (r a)
sn
-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
69
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
D
K (2.4-13)
6
-5 2
Using a value of 2.5 x 10 cm /sec for the diffusivity of oxygen into
-3
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
BOUNDARY LAYER THICKNESS AND PROFILE PARAMETERS
Parameter Value
26
DB
2
2D 2
0
2\
1.1 x 10-3
-2
1.1 x 10
4.9 x 10-3
sec
CHAPTER 3
OBSERVATIONS DURING OPEN-HEART SURGERY
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
72
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)
HbO O2 0 HB,0 HBO HBO RHB
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
2CO V CO,B COH CO V 2
where CO CCO and CCO2 are the concentration of oxygen and
HbCO nCO HbCO Hb bCO
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
S(3.1-8)
(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.
2
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
CO CO, TOT COBCO CO HbCO ,BHbCO
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 )
'CO,c CO TOT A
S 2 1 -- (3.1-13)
(C C AK a,C02 (P P
CO CO TOT COBCO CO CO
2 2 2_2_ 2 2
1 + ---
( CO C0O TOT
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
4J
Q c
4
CC
CIO N*
C MC
*~c-
0
ClO
Na
"00
o3
C)
U0
E EF"
cC
_ 0 I
I-I
>-i
TABLE 3.2-1
SUMITARY OF DATA TAKEN DURING OPEN-HEART SURGERY
Maximum Blood
Flow Capacity ( liter/min)
1.0
2.0
3.0
No. of
Operations
2
5
No. of
Data Points
12
6
6.0 4
Model
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
ACCURACY OF EXPERIMENTAL DATA TAKEN DURING
OPEN-HEART SURGERY
Parameter
02 Partial Pressure
CO2 Partial Pressure
Temperature
pH
Hematocrit
Range of Data
32-590 mm
16-38.5 mm
28-370C
7.2-7.6
0.280-0.385
Accuracy
- 0.5 mm
0.02 mm
t 1.00C
0.007
2%
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- )
O 0 TOT
2 2 6
x = ---- = 1.0 + K (3.3-1)
2 (C C ) 2' BD
O 0 TOT
2 2
and
I *
(C c
SCC CO TOT
x 1.0 + K X (3.3-2)
co C02B B
2 (CC C CO OT 2) B
where
S (P P )
X =0 2 ,-- (3.3-3)
V 2 (C C )
O 02O TOT
2 2
(P PC)
V co CO
H 2 2
X = C (a CO (3.3--4)
V 2(C CC0 )
CO CO 9TOT
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)
and
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)
L
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
P
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
experiments.
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
CO2,B DB
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
02,B
standard deviation for KCO was + 73.3%. The large standard of
CO ,B
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
1.0
co
CO
0.8 0 09
0 0
o 0.6
.4-
L 0
0.4
0
0.2
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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