From real-time 3D echocardiography to mitral valve finite element analysis: A novel modeling approach

Abstract

Finite element models are an innovative tool for the biomechanical analysis of dynamic cardiac structures, such as the mitral valve. Still, existing models are limited by a simplified description of valve morphology. We aimed at overcoming such limitation by integrating into a mitral valve structural finite element model the information about annulus and papillary muscles geometry and dynamics, obtained in humans by analysis of real time 3D echocardiographic images. The model was used to simulate valve closure from end diastole to systolic peak and to analyze the valve biomechanics. Simulated valvular dynamics and leaflets coaptation were realistic, and all gathered quantitative results were consistent with experimental findings from literature. This novel approach may lead to the development of a patient-specific modeling tool for clinical purposes.

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From Real-Time 3D Echocardiography to Mitral Valve
Finite Element Analysis: A Novel Modeling Approach

E Votta1, A Arnoldi1, M Stevanella1, F Veronesi1, G Tamborini2,
F Alamanni2, EG Caiani1, A Redaelli1

1Politecnico di Milano, Milano, Italy
2Centro Cardiologico Monzino IRCCS, Milano, Italy
Abstract
Finite element models are an innovative tool for the
biomechanical analysis of dynamic cardiac structures,
such as the mitral valve. Still, existing models are limited
by a simplified description of valve morphology.
We aimed at overcoming such limitation by integrating
into a mitral valve structural finite element model the
information about annulus and papillary muscles
geometry and dynamics, obtained in humans by analysis
of real time 3D echocardiographic images.
The model was used to simulate valve closure from
end diastole to systolic peak and to analyze the valve
biomechanics. Simulated valvular dynamics and leaflets
coaptation were realistic, and all gathered quantitative
results were consistent with experimental findings from
literature.
This novel approach may lead to the development of a
patient-specific modeling tool for clinical purposes.

1. Introduction
The mitral valve (MV) is a complex apparatus
consisting of two leaflets, inserted on the valvular plane
through the mitral annulus (MA) and connected to the
ventricular myocardium through a net of branched
chordae tendineae that converge into two papillary
muscles (PMs). The MV guarantees the unidirectional
flow from the left atrium to the left ventricle during
diastole and prevents backward flows during systole. Its
function is driven by several factors: transvalvular
pressure drop, dynamic contraction of MA and PMs and
ventricular hemodynamics.
In the last decade, the high prevalence of MV
pathologies, which require surgical intervention, has
raised the need for more effective surgical techniques and
devices, whose conceiving and application need careful
design and testing. Finite element models (FEMs) are an
innovative and helpful tool to be used in such process.
Indeed, FEMs have the potential to quantitatively analyze
MV biomechanics, with great benefits as compared to
traditional animal models: absence of ethical issues, local
quantification of mechanical parameters, control on the
multiple factors leading the behaviour of the simulated
system and, thus, the capability to answer “what if”
questions. Thanks to such potential, FEMs have been
recently applied to study MV normal function [1-3], the
biomechanics underlying MV diseases [1] and effects of
surgical corrections [4-7]. However, none of the
mentioned studies captures all of the four aspects that
drive MV function: morphology, tissues mechanical
response, dynamic boundary conditions and interaction
between the MV and surrounding blood. In particular,
current FEMs, based on animal or ex vivo data, assume
an idealized, symmetrical valvular structure and neglect
the dynamic contraction of MA and PMs.
Real time 3-D echocardiography (RT3DE) offers the
potential to non invasively assess MV structures over
time, thus providing the information needed to overcome
the abovementioned limitations.
Our aim was to integrate such quantitative information
into a realistic FEM of the MV, which simulates valve
closure from end diastole (ED) to systolic peak (SP).
2. Methods
2.1. Real-time 3D ecocardiography
Transthoracic RT3DE imaging was performed (iE33,
Philips, Andover, MA) from the apical window using a
fully sampled matrix-array transducer (X3), with the
subject in the left lateral decubitus position. RT3DE
datasets were acquired in a single normal subject (male,
age 40) using the wide-angled mode at high frame rate
(31 Hz), wherein 8 wedge-shaped subvolumes were
obtained during 8 cardiac cycles during a single breath
hold with ECG gating.
2.2. RT3DE data analysis
The RT3DE data were analyzed using previously
developed custom software to semiautomatically detect
and track the MA throughout the cardiac cycle, and to
ISSN 0276−6574
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Computers in Cardiology 2008;35:1−4.

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identify the PMs tips [8]. Briefly, on the ED frame, 18
long-axis cut planes evenly rotated around the center of
the MA (10° step) were displayed to complete the
initialization procedure. On each plane, the operator
selected 2 points, one on each side of the MA.
Subsequently, the positions of each initialized point were
automatically tracked frame-by-frame in 3D space, using
optical flow and region-based matching techniques. The
automatically tracked points were displayed in each
frame to verify their position, and manual corrections
were performed when necessary. To identify the PMs tip,
on the ED frame the dataset was analyzed by rotating the
cut plane around the MA center, until the tip of each PM
was best visualized. On the selected plane, the operator
defined a point at the position of the PM tip. Moreover,
on the ED frame additional information regarding leaflets
orientation in space was gathered, measuring their tilting
in an apical 4-chamber cut plane.

Figure 1: a) Valve geometrical model, b) Annular profile,
c) papillary muscles and d) leaflets inclination are
detected on the end diastolic ultrasound frame.
2.3. MV geometrical model
The ED configuration was chosen as the reference one.
The MV geometrical model (Figure 1.a) was
implemented defining i) the annular profile, by
interpolation through 6th order Fourier functions of the 36
points selected on the MA in the ED frame (Figure 1.b).
The continuous profile was than sampled into 404 nodes
that provided the seeding for the mesh to be defined on
leaflets surface; ii) PMs tips, defined as the two points
selected in the ED frame (Figure 1.c); iii) the leaflets,
whose profile, based on ex-vivo data from the literature
[9], was adapted to the subject’s annular size and spatial
orientation (Figure 1.d); iv) the chordal apparatus,
consisting in 39 branched chordae of three orders: 1st
(marginal and commissural chordae), 2nd (including strut
chordae) and 3rd (basal chordae). The number of chordae,
the corresponding branched structure and insertion sites
on the leaflets were defined in accordance to ex vivo
findings [10]. A constant thickness of 1.32 mm and 1.26
mm was defined for anterior and posterior leaflet,
respectively. Two transitional commissural zones with a
thickness of 1.29 mm were also identified. Constant
cross-section area values of 0.4, 1.15 and 0.79 mm2 were
assigned to 1st order, strut and basal chordae.


Figure 2: a) Reconstructed MA time-dependent profile;
the ED configuration is depicted in black, subsequent
configurations are depicted in grey. b) Reconstructed
PMs position. For clarity’s sake the ED configuration of
the MA is also depicted (SH=saddle horn). Axes values
are in mm.
2.4. Tissues mechanical properties
All tissues were assumed non-linear and elastic. Their
mechanical response was described by means of proper
strain energy potentials. Leaflets anisotropic response
was accounted for by means of a Fung-like strain energy
potential [3]. Chordae tendineae response was assumed
isotropic. A second order polynomial strain energy
potential was used for 1st order chordae; a fifth order
Ogden strain energy function was used for 2nd and 3rd
order chordae. The constitutive parameters were defined
via mean-square interpolation of data from the literature
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[11, 12].
2.5. Boundary conditions
The dynamic contraction of MA and PMs was
modelled via kinematic boundary conditions, i.e. imposed
as nodal displacements. A continuous MA profile was
obtained from each RT3DE frame, interpolating the 36
tracked points. After sampling it into 404 nodes, nodal
displacements with respect to the initial ED configuration
were calculated. The motion of PMs tips was estimated
from in vivo data obtained in animal models [13]. The
time-dependent MA profile and PMs position are
depicted in Figure 2.
To simulate the effect of blood pressure from ED to
SP, a physiological time-dependent transvalvular pressure
drop, up to 120 mmHg, was applied on the leaflets.
Simulations were run using the ABAQUS/Explicit
commercial software, version 6.7-1.
3. Results and discussion


Figure 3: Leaflets maximum principal stresses at the
systolic peak (atrial view).

Valve dynamics and leaflets coaptation were
consistent with in-vitro observations: complete coaptation
was obtained for a 18 mmHg transmitral pressure [14]
and, in accordance to clinical observations, the coaptation
region corresponded to the leaflets rough zone.
The MV tensile state was analysed focusing on SP, as
this timeframe is characterized by the maximum pressure
load. Leaflets maximum principal stresses were
computed (Figure 3). Their distribution reflected the
asymmetry of the initial geometrical model. The anterior
leaflet was more stressed than the posterior one, with
peak values of 550 kPa at the insertion of strut chordae.
Leaflets strains (Figure 4) reflected their anisotropic
response, much stiffer in the direction parallel to the MA
(top panel) than orthogonal to it (bottom panel). In
particular, in the belly of the anterior leaflet, stretch ratios
in the two directions were equal to 1.09 and 1.46, in good
agreement with experimental data [15].




Figure 4: Leaflets Green-Lagrange Strains parallel to the
annulus (top) and perpendicular to it (bottom).

Chordae tendineae tension for each type of chorda was
monitored during valve closure (Figure 5 and Table 1).
The average tension on a single chorda was the highest in
strut chordae.


However, marginal chordae as a whole bared the
highest fraction of the entire load experienced by the
chordal apparatus. Good agreement was found with
experimental findings from the literature for the different
chordae types [16].

Table 1: Computed systolic peak chordae tensions,
compared to in vitro data from literature.
Chordae Type

Strut
Anterior Marginal
Posterior Marginal
Posterior 2nd Order
Commissural
Basal
Systolic Peak Tension [N]
FEM Data
1.13 ± 0.25 1.11 ± 0.57
0.13 ± 0.04 0.18 ± 0.16
0.19 ± 0.16 0.08 ± 0.11
0.12 ± 0.10 0.29 ± 0.14
0.45 ± 0.12 0.40 ± 0.31
0.09 ± 0.12 0.48 ± 0.25
In Vitro Data [15]
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Figure 5: Time-course (from ED to PS) of chordae
tendineae tension, averaged on chordae of the same class.
4. Conclusions
With this study, a novel approach to obtain a MV
FEM with beyond-state-of-the-art features was defined
and tested.
Results suggest that the use of RT3DE allows to
overcome most of the limitations of previous MV
models, thus obtaining a more realistic FEM. Although
further testing on more subject-specific data is
mandatory, this strategy may be at the basis for the
development of a patient-specific modelling tool to be
applied in the clinical settings or for surgical planning.
Acknowledgements
The research leading to these results has received
funding from from the European Community's Seventh
Framework Programme (FP7/2007-2013) under grant
agreement n° FP7-224635 and from the Italian Ministry
of Education, University and Research (PRIN 2007
funds, SurgAid Project).
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Address for correspondence

Dr Emiliano Votta
Dipartimento di Bioingegneria
Politecnico di Milano
Piazza Leonardo da Vinci 32, Milano, Italy
E-mail: votta@biomed.polimi.it
Geoform disease-specific
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