The filling mechanism of the human ventricles - ETH E

Diss. ETH No. 16641
The filling mechanism of the
human ventricles during early
diastole: a finite element study
A dissertation submitted to the
Swiss Federal Institute of Technology
Zurich
for the degree of
Doctor of Sciences
presented by
Diane-Elise Bettendorff-Bakman
Ing. phys. dipl. EPF
born November 13th, 1974
citizen of Geneva, Switzerland
accepted on the recommendation of
Prof. Dr. Peter Niederer, examiner
Prof. Dr. Paul Lunkenheimer, co-examiner
2006

Summary
The heart is the pump that circulates blood through all organs of the body. It consists of
four chambers: two ventricles situated below the two atria. The atria and the ventricles
are communicated by the atrioventricular valves which ensure the unidirectional flow of
blood from the atria to the ventricles. The cardiac cycle is constituted by two successive
phases: the systole and the diastole. During systole, both ventricles contract and the
blood is then ejected into the organs of the human body. At the end of the ejection
phase begins the diastolic phase, where both ventricles relax and are subsequently filled
with blood. The coronary circulation, supplying blood to the heart, and the flow through
the lymphatic system are influenced by the cardiac cycle. The blood flow in the coronary
arteries is maximal during diastole and minimal during the systolic phase. Temporal vari-
ations in both coronary and lymphatic fluid flow induce small volume changes of the mass
of the myocardial tissue, thus rendering the cardiac tissue only somewhat incompressible.
Ventricular filling commences with blood flowing in rapidly from the atria in the ven-
tricles in a short period called the rapid filling phase that represents the first third of
diastole. During this period, more than half of the subsequent stroke volume has entered
the ventricles, which are subjected to large strains. The internal volumes of both cavities
approximately double, while the ventricular pressures rise typically only by an amount
of less than 1 kPa. In view of such low pressures, the question arises whether they can
provide the driving force for the large inflow of blood entering the ventricles during this

ii Summary
phase. If it is not the case, it is important to understand which other mechanisms could
play a role in the rapid filling phase. In order to address these issues from a mechanical
point of view, a three-dimensional Finite Element model of both human ventricles has
been developed, utilizing a realistic geometry and taking into account the large defor-
mation occurring during the rapid filling phase as well as the effective compressibility of
the mass of the myocardial tissue. The geometry of the human heart was obtained from
32 short axis slices extending from the apex to the base and taken at end-systole with
Magnetic Resonance Imaging.
In order to investigate whether the ventricular diastolic pressures measured under physio-
logical conditions in the human healthy heart can give rise to the extensive augmentation
in ventricular volumes that occurs during the rapid filling phase, nonlinear elastic Finite
Element analyses with various types of cavity pressure functions applied as boundary
conditions were performed. The calculated evolution of the internal volume for the left
cavity was compared to the filling phase of the human left ventricle as extrapolated from
measurements documented in the literature. Based on the results obtained in the present
work, it can be concluded that the ventricular pressures measured during the rapid filling
phase cannot be the sole cause of the rise of the observed ventricular volumes.
Experiments on cardiac tissue strips of animals have shown that in the absence of active
fiber forces, the myocardium exhibits a nonlinear viscoelastic mechanical behavior. As
the atrioventricular valves open at the start of the rapid filling phase, both ventricles are
subjected to large and abrupt deformations. During this period, it is thus possible that
the viscoelastic response of the heart, depending on the strain velocity of the cardiac
tissue, provides a driving force for ventricular filling. Consequently, the influence of the
viscoelasticity of the myocardium on the rapid filling phase has been analysed by com-
paring the elastic and viscoelastic Finite Element simulations, respectively, as well as to

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the measured evolution of the left ventricular volume during this period. The viscoelastic
Finite Element analysis calculated with short relaxation times yielded a realistic filling of
the left cavity, suggesting that the viscoelastic contribution to the mechanical behavior
of the myocardium should not be neglected when a detailed analysis of the mechanics of
the heart is attempted.
The rapid filling phase can be viewed as the period where the heart recoils from its con-
tracted state. During the systolic contraction, the potential energy of the heart increases
and a part of this energy can be stored in the elastic elements of the myocardium. This
energy is then released through the deformation of the heart when the atrioventricular
valves open at the beginning of diastole, allowing both ventricles to expand naturally, as a
contracted elastic spring tends to return to its resting length when the force of contraction
is removed. The dilatation of both cavities causes the decrease of ventricular pressures
that induces the blood to be rapidly aspirated from the atria into the ventricles. In order
to study the role of this elastic recoil in the rapid filling phase, elastic Finite Element sim-
ulations of ventricular suction were performed. To validate the Finite Element analyses
of ventricular suction calculated with the model utilizing a realistic geometry, the results
for the left ventricle were compared to those obtained with a simpler Finite Element el-
lipsoid model of the left cavity, as well as to the published experimental measurements
for the rapid filling phase of the left ventricle. This study has shown that, under nor-
mal conditions, the ventricular suction plays an important role in the ventricular filling
process.

R´esum´e
Le coeur, assurant la circulation du sang dans le corps, est un organe form´edequatre
chambres: deux ventricules situ´es au-dessous de deux oreillettes. Entre les oreillettes et les
ventricules se trouvent les valves atrioventriculaires, assurant le passage unidirectionnel
du sang des oreillettes aux ventricules. Le cycle cardiaque comporte deux phases: l’une
appel´ee systole, o`u les deux ventricules se contractent et o`u le sang est ensuite eject´edans
les organes du corps humain; l’autre, succ´edant `alasystole,estappel´ee diastole et est
constitu´ee par la relaxation isovolum´etrique et le remplissage successif des ventricules par
le sang. La circulation du sang dans les vaisseaux coronaires, irriguant le coeur, ainsi que
le flux dans le syst`eme lymphatique sont influenc´es par le cycle cardiaque et varient durant
cette p´eriode: le flux sanguin dans les art`eres coronaires est maximal durant la diastole
et minimal durant la systole. Le volume de la masse du tissu cardiaque n’´etant donc pas
constant durant un battement de coeur, il ne peut ˆetre consid´er´e comme incompressible.
Au d´ebut du remplissage ventriculaire, le sang coule rapidement des oreillettes dans les
ventricules. Cette courte p´eriode, appel´ee la phase de remplissage rapide, repr´esente le
premier tiers de la diastole. Durant cette p´eriode, plus de la moiti´eduvolumed’´ejection
entre dans les ventricules qui sont soumis `a de grandes d´eformations. Leurs volumes in-
ternes doublent approximativement, tandis que les pressions ventriculaires augmentent en
g´en´eral de moins de 1 kPa. Etant donn´e que les pressions diastoliques sont si faibles, la
question se pose si elles sont les seules responsables du grand afflux de sang entrant dans