Advances in Biomedical Engineering. Volume 3

265 Pages·1973·14.709 MB·English

by  J.H.U. Brown, J.F. Dickson

Advances in
BIOMEDICAL
ENGINEERING
Volume 3
Published under the auspices of The Biomédical
Engineering Society
Edited by
j. H. u. BROWN
Department of Health, Education and Welfare
Health Services and
Mental Health Administration
Rockville, Maryland
JAMES F. DICKSON, III
Department of Health, Education and Welfare
National Institutes of Health
Bethesda, Maryland
®
ACADEMIC PRESS 1973
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Contributors
Numbers in parentheses indicate the pages on which the authors' contributions
begin.
MAURICE BENDER, Department of Pathology, School of Medicine, University of
Missouri, Columbia, Missouri (199)
C. F. DALZIEL, Department of Electrical Engineering and Computer Sciences,
University of California, Berkeley, California (223)
EVAN H. GREENER, Department of Biological Materials, Northwestern University,
Chicago, Illinois (141)
E. P. LAUTENSCHLAGER, Department of Biological Materials, Northwestern Uni-
versity, Chicago, Illinois (141)
FRED V. LUCAS, Department of Pathology, School of Medicine, University of
Missouri, Columbia, Missouri (199)
FRANK D. MARK, Department of Pathology, School of Medicine, University of
Missouri, Columbia, Missouri (199)
A. W. PRATT, Division of Computer Research and Technology, National Institutes
of Health, Department of Health, Education and Welfare, Bethesda, Maryland
(97)
MARTIN RUBIN, Department of Biochemistry, Georgetown University School of
Medicine and Dentistry, Washington, D.C. (183)
KIICHI SAGAWA, Department of Biomédical Engineering, School of Medicine,
The Johns Hopkins University, Baltimore, Maryland (1)
ROBERT M. THORNER, Department of Pathology, School of Medicine, University
of Missouri, Columbia, Missouri (199)
DENNIS R. WEBB, Department of Pathology, School of Medicine, University of
Missouri, Columbia, Missouri (199)
VII
Preface
IN Volume 3 of Advances in Biomédical Engineering the Editors have
attempted to continue their policy of a diversified selection of articles.
We have selected an article on circulatory system models (Kiichi
Sagawa) and a study of linguistics applied to computer usage (A. W.
Pratt) as examples of the theoretical approach to biomédical engineering.
The developmental areas of the field are represented by articles on bio-
materials (Evan H. Greener and E. P. Lautenschlager) and the clinical
laboratory (Martin Rubin). The clinical applications have been discussed
in articles on patient monitoring (Fred V. Lucas, Maurice Bender,
Frank D. Mark, Robert M. Thorner, and Dennis R. Webb) and electric
shock (C. F. Dalziel).
We welcome criticism and comments as well as suggestions for future
volumes.
Special thanks are due to Academic Press and their able staff for
their patience and forbearance in the preparation of this volume.
Thanks are also due The Biomédical Engineering Society for moral
support in this undertaking.
J. H. U. BROWN
JAMES F. DICKSON, III
ix
Contents of Previous Volumes
Volume 1
BIOMÉDICAL APPLICATIONS OF ULTRASOUND
Werner Buschmann
SEPARATION OF NEURONAL ACTIVITY BY WAVEFORM ANALYSIS
Edmund M. Glaser
BIOMECHANICAL CHARACTERISTICS OF BONE
8. A. V. Swanson
STRUCTURAL AND MECHANICAL ASPECTS OF CONNECTIVE TISSUE
P. F. Millington, T. Gibson, J. H. Evans, and J. C. Barbenel
SUBJECT INDEX
Volume 2
MODELS OF ADRENAL CORTICAL CONTROL
Donald S. Gann and George L. Cry er
HOSPITAL COMPUTER SYSTEMS—A REVIEW OF USAGE AND FUTURE
REQUIREMENTS AFTER A DECADE OF OVERPROMISE
AND UNDERACHIEVEMENT
William A. Spencer, Robert L. Baker, and Charles L. Moffet
DEVELOPMENT OF FEEDBACK CONTROL PROSTHETIC AND
ORTHOTIC DEVICES
James B. Reswick
ULTRASOUND AS A DIAGNOSTIC TOOL
J. E. Jacobs
GAS-PHASE ANALYTICAL METHODS AND INSTRUMENTS
E. C. Horning and M. G. Horning
AUTHOR INDEX-SUBJECT INDEX
X
Comparative Models of Overall
Circulatory Mechanics
KIICHI SAGAWA
Department of Biomédical Engineering, School of Medicine,
The Johns Hopkins University, Baltimore, Maryland
I. Definition and Use of Modeling 1
II. Models of the Cardiac Pump 3
A. The Cardiac Pump as a Flow Generator 3
B. The Ventricle as a Contractile Chamber 4
C. Cardiac Modeling Synthesized from Myocardial Fiber Mechanics
(Beneken's Model) 33
D. Summarized Comparison of Various Cardiac Models 42
III. Models of the Vascular Systems 44
A. Pulmonary Vascular Bed 44
B. Systemic Vascular Bed 60
IV. Models of Overall Systems Behavior 71
A. Parameter Tests in Various Models 71
B. Models of Circulation as an Oxygen Transport System . . .. 85
References , . 92
I. DEFINITION AND USE OF MODELING
MODELING is one of the fundamental processes in our understanding of
nature. From observations of phenomena we abstract functional relations
(causality) among the substantial elements of a system of interest.
Whether the abstraction is intuitive or mathematical, it is the first step
of modeling. The induced model is then checked against the next obser-
vation through a deductive process and, as a result, discarded, revised,
or further tested. The model may be very elementary, being a verbal
speculation of the cause-and-effect relations among the related elements,
or it may be very formal (mathematical) expressions induced from accu-
rate observations and analytical thoughts. Although both types of model-
ing provide momentum for research, the more quantitative a model is,
the more exact becomes the deduction and the testing. For this reason,
formal modeling is preferable and modern computer techniques make it
far easier than it was decades ago.
The class of models reviewed here provides a mathematically well-
defined analysis of overall circulatory mechanics. The various subsystems
of the circulation are lumped into more or less simplified black boxes,
1
2 KIICHI SAGA WA
and the emphasis is placed on the overall system behavior in which these
coupled subsystems interact with each other. Naturally, isomorphism
has to be greatly sacrificed. Parts of these models, if presented to the
specialists of the respective fields, will not get their approval. One of the
basic questions that those modelers ask is, How much can we simplify
the various portions of the cardiovascular system in order to understand
some specific circulatory phenomenon? Usually a model is built specifi-
cally for the phenomenon (system behavior) that the builder wants to
explain. Whether or not the lumping of components and the reduction of
input-output relations are appropriate depends entirely on the primary
purpose of modeling. In this sense, modeling is an art of simplification
to find the essentials. Does it mean that we can justify one hundred
different models to explain one hundred different phenomena in circula-
tion? The obvious answer is No. A more general model is certainly more
desirable, and the builder should attempt to see how far his model can go
beyond its original aim. The result of this attempt clarifies the limit of
the model's capability. The negative results are as important as the
affirmative ones. Quest of generality causes evolutionary growth of a
model.
The utility of a model can be evaluated by testing it against a
set of known phenomena. There is a serious problem in biological
modeling at this point. One can easily find a spectrum of diverse
experimental results concerning a simple phenomenon. A model there-
fore can claim a good fit with the results obtained by one experimenter
but be criticized on the basis of another experimenter's results. The
variability of biological experimental results stems from different animal
sources or species, anesthesia, methods, skills, time and range of
observation, etc., which are often difficult to identify. Consequently, the
judgment of the fit of a model depends upon two sets of experimental
data: One set that the modeler initially used to synthesize the model
and the other set which he selects to check against. It is often pointed
out that a model of a complex biological system cannot produce a
unique set of system parameters. But even before we consider this
subtle problem we have a problem in the selection of experimental
facts.
Another problem which limits the testing and/or utility of a model
is the lack of access to outputs of a particular model. Most models are
incorporated into complex computer systems, and it is not easy to copy
any one of such models even if the facility exists. Therefore, the model
predictions cannot be known to outsiders beyond the limit of the original
report. Thus, if an experimenter wants to compare his observations
closely related to a particular model, information exchange demands
COMPARATIVE MODELS OF OVERALL CIRCULATORY MECHANICS 3
personal communication. A solution to this problem may require some-
thing like a ''simulation library/ ' supported at a national or international
level, where every major model is stored and, on request, its outputs are
generated under a specified set of conditions and delivered to the inter-
ested experimenter. This would require funds, collaboration from model
builders, and well-trained computer people. But it will surely contribute
to more active and fruitful dialogues between the modeler and the experi-
menter. Without such interactions, modeling tends to be an intellectual
exercise which, however, does not substantially advance our knowledge.
II. MODELS OF THE CARDIAC PUMP
In this section different levels of cardiac models will be described, starting
from the simplest and progressing toward the most detailed. All the heart
models cited were intended for the simulation of overall circulatory
mechanics, and their vascular portions will be described in Section III.
The results of overall simulation will be discussed in Section IV. The
mechanical interactions between the cardiac pump and vascular imped-
ance will be discussed in Sections II and III. In Section II the forcing
of vascular impedance on cardiac pumping will be discussed by represent-
ing the former in pressure terms. The forcing that the heart exerts on the
vascular bed will be represented by the flow that the heart generates.
Physiological regulatory mechanisms via mechanical circulatory loop
structures, and by some of the nervous and humoral controls, are dis-
cussed in Section IV.
A. The Cardiac Pump as a Flow Generator
For years, Guyton and his associates have attempted to build a large-
scale model of the entire circulatory system, with the ultimate goal of
analyzing renal and other forms of hypertension (Guyton and Coleman,
1969; also see Section IV,B,2). For such purposes, the group treated the
heart simply as an active hydraulic element which generates flow (cardiac
output). The most important regulator of cardiac output in their cardiac
model is the Starling mechanism, the major input being mean atrial (or
venous) pressure, P, and the output being ventricular outflow. A curvi-
v
linear relationship curve between the two is used to represent the heart,
with some consideration of heart rate and automatic nerve controls on
the slope and saturation level of the curve (Guyton, 1963). Unfortunately,
the quantitative details of their latest model (Guyton et al., 1972) are not
available. When this group attempted to combine a vast set of mechan-
4 KIICHI SAGA WA
ical, neural, and humoral mechanisms involved in acute and long-term
circulatory regulation, some six hundred equations emerged and quickly
saturated their PDP-9 computer with 16K memory capacity even after
reducing the cardiac performance to such a simplified representation.
This fact raises a serious question as to the application of more detailed
models of circulation to an understanding of the etiology of various
systems diseases. Could any single investigative group ever find a com-
puter large enough, even if there should exist a mathematical model of
the circulation detailed enough to satisfy those specialists in various areas
of the circulatory functions? This again seems to suggest the need for the
simulation library mentioned above.
B. The Ventricle as a Contractile Chamber
1. Grodins1 Early Model
Grodins (1959) attempted to analyze overall circulatory mechanics from
the systems viewpoint. His basic intention was to integrate the respira-
tory and circulatory functions into a single system which he termed a
"respirato-circulatory chemostat" responsible for the homeostasis of the
body (Grodins, 1963). Another popularized version of Starling's law of
the heart was used to define the ventricular performance; it states that the
external work output of the heart is uniquely determined by the end-
diastolic volume of the ventricle :
W = S- V/ (1)
S
in which S denotes the strength of the ventricle and has a dimension of
pressure, and V/ represents end-diastolic ventricular volume. The work
output was approximated by
W = V - P (2)
s 8 a
where V = stroke volume and P = mean arterial pressure.
s a
The relationship between V , V e, and P is then expressed as
8 d a
V = S · V//P (3)
s a
The filling process during ventricular diastole was simplified by assum-
ing that (1) atrial contraction is negligible; (2) phasic variation in venous
pressure is also negligible—that is, mean venous pressure, P is the driv-
V)
ing source pressure for ventricular filling; (3) the ventricular muscle
relaxes instantaneously, the ventricle thereby suddenly becoming a com-
pliant chamber; and (4) the unstressed ventricular volume is zero, and the
volume compliance, (7, is time-invariant and pressure-independent.
COMPARATIVE MODELS OF OVERALL CIRCULATORY MECHANICS 5
Under these assumptions the ventricular filling phase can be expressed
as
(R · V ) + (V /C) = P (4)
d d v
in which R represents overall hindrance to blood flow from the venous
port of the heart, through the atrium and atrioventricular valve, into the
ventricle. It, too, was assumed to be independent of pressure (linear).
Denoting the residual volume of the ventricle by V (= V — V ), we
r d 8
obtain the instantaneous ventricular volume, V , in diastole from Eq. (4) :
d
V = (V - C · P,)e-<i*c + C-P (5)
d r V
in which t is the time from the onset of diastole.
In relating stroke volume to cardiac output per minute, the duration
of ventricular systole was assumed to remain constant at 0.2 second re-
gardless of heart rate, /. The duration of diastole was therefore repre-
sented by (60// — 0.2) second. To simplify the notation, K and A were
used as
K = exp[-(60//-0.2)ÄC]
and
A = 1 - K
Equation (5) therefore becomes
V = ACP[l + K(S/P - 1)] (6)
d v a
From Eqs. (3) and (6), we obtain
V = SCAP/(AP + SK)
s v a
Therefore
V = ACP(P - S)/(AP + SK) (7)
r v a a
Ventricular outflow per minute, Q, is expressed as
Q = / ' V = fSCAP/(AP + SK) (8)
s v a
Note that there are four ventricular system parameters : /, S, Ä, and
C. Besides these, pressure variables P and P„ are necessary to determine
a
the outflow. Also note that the model heart generates a discrete stroke
volume per systole, not an instantaneous aortic flow as a function of time.
Therefore, arterial and venous pressure are not pulsatile, although beat-
to-beat change in stroke volume can be analyzed. It is a beat-to-beat
quantized model of the heart.
Implications of Eq. (8) are that (1) Q increases linearly with P (a
v
linear version of Starling's P — cardiac output curve) but (2) Q decreases
v
hyperbolically with P , provided that ventricular parameters /, S, R, and
a
C are maintained constant. When Grodins tested the case with experimen-