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.
Article: Fluid-structure interaction models of the mitral valve: function in normal and pathological states.[show abstract] [hide abstract]
ABSTRACT: Successful mitral valve repair is dependent upon a full understanding of normal and abnormal mitral valve anatomy and function. Computational analysis is one such method that can be applied to simulate mitral valve function in order to analyse the roles of individual components and evaluate proposed surgical repair. We developed the first three-dimensional finite element computer model of the mitral valve including leaflets and chordae tendineae; however, one critical aspect that has been missing until the last few years was the evaluation of fluid flow, as coupled to the function of the mitral valve structure. We present here our latest results for normal function and specific pathological changes using a fluid-structure interaction model. Normal valve function was first assessed, followed by pathological material changes in collagen fibre volume fraction, fibre stiffness, fibre splay and isotropic stiffness. Leaflet and chordal stress and strain and papillary muscle force were determined. In addition, transmitral flow, time to leaflet closure and heart valve sound were assessed. Model predictions in the normal state agreed well with a wide range of available in vivo and in vitro data. Further, pathological material changes that preserved the anisotropy of the valve leaflets were found to preserve valve function. By contrast, material changes that altered the anisotropy of the valve were found to profoundly alter valve function. The addition of blood flow and an experimentally driven microstructural description of mitral tissue represent significant advances in computational studies of the mitral valve, which allow further insight to be gained. This work is another building block in the foundation of a computational framework to aid in the refinement and development of a truly non-invasive diagnostic evaluation of the mitral valve. Ultimately, it represents the basis for simulation of surgical repair of pathological valves in a clinical and educational setting.Philosophical Transactions of The Royal Society B Biological Sciences 09/2007; 362(1484):1393-406. · 6.40 Impact Factor
Article: Three-dimensional asymmetrical modeling of the mitral valve: a finite element study with dynamic boundaries.[show abstract] [hide abstract]
ABSTRACT: Previous computational studies of the normal mitral valve have been limited because they assumed symmetrical modeling and artificial boundary conditions. The study aim was to model the mitral valve complex asymmetrically with three-dimensional (3-D) dynamic boundaries obtained from in-vivo experimental data. Distance tracings between ultrasound crystals placed in the sheep mitral valve were converted into 3-D coordinates to reconstruct an initial asymmetric mitral model and subsequent dynamic boundary conditions. The non-linear, real-time left ventricular and aortic pressure loads were acquired synchronously. A quasi-static solution was applied over one cardiac cycle. The mitral valve leaflet stress was heterogeneous. The trigones experienced highest stresses, while the mid-anterior annulus between trigones experienced low stress. High leaflet stress was observed during peak pressure loading. During isovolumic relaxation, the leaflets were highly stretched between the anterolateral trigone and the posteromedial commissure, resulting in a prominent secondary leaflet stress re-increment. This has not been observed previously, as symmetric models with artificial boundary conditions were studied only in the ejection phase. Here, the first asymmetrical mitral valve model synchronized with 3-D dynamic boundaries and non-linear pressure loadings over the whole cardiac cycle based on in vivo experimental data is described. Despite its limitations, this model provides new insights into the distribution of leaflet stress in the mitral valve.The Journal of heart valve disease 06/2005; 14(3):386-92. · 0.81 Impact Factor
Article: Finite element analysis of the mitral apparatus: annulus shape effect and chordal force distribution.[show abstract] [hide abstract]
ABSTRACT: This study presents a three-dimensional finite element model of the mitral apparatus using a hyperelastic transversely isotropic material model for the leaflets. The objectives of this study are to illustrate the effects of the annulus shape on the chordal force distribution and on the mitral valve response during systole, to investigate the role of the anterior secondary (strut) chordae and to study the influence of thickness of the leaflets on the leaflets stresses. Hence, analyses are conducted with a moving and fixed saddle shaped annulus and with and without anterior secondary chordae. We found that the tension in the secondary chordae represents 31% of the load carried by the papillary muscles. When removing the anterior secondary chordae, the tension in the primary anterior chordae is almost doubled, the displacement of the anterior leaflet toward the left atrium is also increased. The moving annulus configuration with an increasing annulus saddle height does not give significant changes in the chordal force distribution and in the leaflet stress compared to the fixed annulus. The results also show that the maximum principle stresses in the anterior leaflet are carried by the collagen fibers. The stresses calculated in the leaflets are very sensitive to the thickness employed.Biomechanics and Modeling in Mechanobiology 02/2008; 8(1):43-55. · 3.19 Impact Factor
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
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
This novel approach may lead to the development of a
patient-specific modeling tool for clinical purposes.
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
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  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).
2.1. 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
Computers in Cardiology 2008;35:1−4.
identify the PMs tips . 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
, 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 . 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 . 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
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 . 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 
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 .
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
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 .
Table 1: Computed systolic peak chordae tensions,
compared to in vitro data from literature.
Posterior 2nd Order
Systolic Peak Tension [N]
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 
Figure 5: Time-course (from ED to PS) of chordae
tendineae tension, averaged on chordae of the same class.
With this study, a novel approach to obtain a MV
FEM with beyond-state-of-the-art features was defined
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.
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
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Address for correspondence
Dr Emiliano Votta
Dipartimento di Bioingegneria
Politecnico di Milano
Piazza Leonardo da Vinci 32, Milano, Italy