Mitral valve modelling in ischemic patients: Finite element analysis from cardiac magnetic resonance imaging

Abstract

The goal of the present work was to develop a framework for the analysis of time-varying mitral valve (MV) geometry from cardiac magnetic resonance (CMR) imaging, and to integrate these data in a patient-specific simulation of MV closure. CMR imaging of 18 long-axis planes was performed on a healthy subject and on two ischemic patients with MV regurgitation. MV annulus geometry, leaflets surface and papillary muscles position were obtained using custom software. Hyperelastic anisotropic mechanical properties were assigned to the MV tissues, and a pressure load curve was applied to the leaflets. Results concerning healthy MV biomechanics were consistent with previous computational data. Ischemic MV models appear suitable to mimic the pathological malfunctioning of the valve. The proposed models could constitute the basis for the planning of surgical procedures.

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Mitral Valve Modelling in Ischemic Patients: Finite Element Analysis from
Cardiac Magnetic Resonance Imaging
Carlo A Conti1, Marco Stevanella1, Francesco Maffessanti1, Salvatore Trunfio2, Emiliano Votta1,
Alberto Roghi2, Oberdan Parodi2,3, Enrico G Caiani1, Alberto Redaelli1
1Politecnico di Milano, Milano, Italy
2Niguarda Ca' Granda Hospital, Milano, Italy
3CNR Institute of Clinical Physiology, Pisa, Italy
Abstract
The goal of the present work was to develop a
framework for the analysis of time-varying mitral valve
(MV) geometry from cardiac magnetic resonance (CMR)
imaging, and to integrate these data in a patient-specific
simulation of MV closure. CMR imaging of 18 long-axis
planes was performed on a healthy subject and on two
ischemic patients with MV regurgitation. MV annulus
geometry, leaflets surface and papillary muscles position
were obtained using custom software. Hyperelastic
anisotropic mechanical properties were assigned to the
MV tissues, and a pressure load curve was applied to the
leaflets. Results concerning healthy MV biomechanics
were consistent with previous computational data.
Ischemic MV models appear suitable to mimic the
pathological malfunctioning of the valve. The proposed
models could constitute the basis for the planning of
surgical procedures.


1. Introduction
Ischemic mitral regurgitation (IMR) is a common and
important complication of ischemic heart disease,
associated with excess mortality independently of
baseline characteristics and degree of ventricular
dysfunction [1]. Because altered annular geometry often
contributes to leaflet malcoaptation in ischemic mitral
regurgitation, surgical correction is required to restore
proper MV function.
Current standard treatment for IMR is the implantation
of an annuloplasty ring that downsizes the mitral annulus
to increase leaflet coaptation. However, residual or
recurrent mitral regurgitation frequently appears after ring
annuloplasty, as a consequence of a poor prognosis [2].
Thus, models for predicting surgical outcomes of these
repair procedures on the basis of patient preoperative
characteristics can provide valuable tools for clinical
research and practice.
Finite element models (FEMs) has been proven useful
and accurate in the assessment of mitral valve
biomechanics [3,4]. However, most of the previously
proposed MV FEMs are based on animal or ex vivo
measurements and lay over simplifying assumptions on
MV symmetrical shape, idealized leaflets free margin
profile and disregarded papillary muscles (PMs)
contraction. Recently, Votta et al. [5] proposed a
modelling approach based on transthoracic real-time
three-dimensional echocardiography
acquired from a human healthy subject. This strategy
allowed to define the initial MV geometry from the end-
diastolic position of mitral annulus and PMs and to use
the real annular dynamics as boundary conditions during
valve closure.
Cardiac magnetic resonance (CMR) is currently
recognized as the gold standard in the clinical evaluation
of left ventricular volume, function and myocardial mass.
The introduction of the steady-state free precession
(SSFP) technique made CMR not only an useful tool for
the dynamic evaluation of cardiac chambers but also for
the assessment of mitral valve function, as previously
reported in literature [6,7]. As a consequence of high
spatial and temporal resolutions, CMR could constitute
the ideal imaging technique for the detailed quantification
of several nuances of the valvular apparatus, such as
annular and papillary muscle function or leaflet geometry.
The short-term goal of the study is two-fold: 1) to
develop a framework for the quantitative analysis of time-
varying MV geometry from CMR imaging, and 2) to
integrate these data in a patient-specific structural
simulation of MV closure from end-diastole to the
systolic peak. The long-term goal of our work is to use
these regurgitant valve models as a baseline condition to
be compared with different post-operatory scenarios. In
particular, we aim at simulating the effects of different
types of annuloplasty ring (i.e. flexible and rigid) on the
biomechanics of ischemic mitral valves.

(RT3DE) data

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2. Materials and methods
Three models were built using our in home software:
model A for a healthy MV, models B and C for two
regurgitant MVs associated to ischemic diseases.
Moreover, the patient whose dataset was used to build
model B showed also dilated cardiomyopathy.


Figure 1. a) Acquired long-axis CMR cut-planes; b)
Tracing of annulus (red), leaflet (green), papillary muscle
(blue) and position of the aorta (pink) on a cut-plane; c)
Annulus profile as reconstructed through our in home
software; d) Finite element model obtained from the MV
reconstruction algorithm.

2.1. CMR acquisition and processing

CMR imaging of 18 evenly rotated long-axis cut-
planes (one every 10 degrees) was performed. Time
resolution was equal to 55 frames/cardiac cycle, spatial
resolution to 0.78 mm, and slice thickness was 8 mm
(Figure 1.a).
For every frame, on each cut-plane the valvular
substructures were manually obtained using custom
software implemented in MATLAB (The MathWorks
Inc., Natick, MA, United States): first, two annular points
were identified; second, multiple points defining leaflets
profile were selected and connected through cubic
splines; finally, a point was marked for each visible PMs
tips (Figure 1.b). The three-dimensional coordinates of
the points selected on each cut-plane were reconstructed
from the position of the latter with respect to the rotation
axis. The annular profile was reconstructed by
approximating the selected annular points with a 13th
order Fourier function (Figure 1.c) and leaflets surface
was obtained via Delaunay tessellation of leaflets profile
points.

2.2 MV geometrical model

The end-diastolic configuration of the MV was
assumed as its unloaded one; the corresponding geometry
was thus reconstructed.
Three-dimensional annular profile was defined by
Fourier interpolation of the points selected on the mitral
annulus in the end-diastolic frame. Leaflets extent and
inclination were set consistently with the MRI-derived
leaflets free-edge profile. Thirty-nine branched chordae
tendineae of three orders were modeled; their number, the
corresponding branched structure and insertion sites on
the leaflets were defined in accordance to ex vivo findings
[8].

2.3 Tissues mechanical properties

All tissues were assumed non-linear and elastic. Their
mechanical response was described by means of proper
strain energy potentials. Leaflets behaviour was described
through the hyperelastic and transversely isotropic
constitutive model proposed by May-Newman and Yin
[9], in which the mechanical response in the direction of
the collagen fibers (i.e. parallel to the annulus) is much
stiffer than the one in transversal direction (i.e.
perpendicular to the annulus). A regionally varying
thickness distribution was assigned to the leaflets,
consistently with the one proposed in [3], with an average
value of 1.32 mm on the anterior leaflet and 1.26 mm on
the posterior one.
Chordae tendineae response was assumed isotropic and
described through a polynomial strain energy function,
whose parameters were defined via interpolation of
uniaxial test data from literature [10]. Constant cross-
sectional area values of 0.40, 1.15 and 0.79 mm2 were
assigned to marginal, strut and second order chordae,
respectively.

2.4 Boundary conditions

The dynamic contraction of mitral annulus and PMs
was modeled via kinematic boundary conditions, i.e.
imposing time-dependent nodal displacements derived
from annular nodes position at each time-frame.
A physiological transvalvular pressure drop, up to 120
mmHg, was applied on the ventricular side of the leaflets.
The numerical simulations were performed within the
finite element commercial code ABAQUS/Explicit 6.9-1
(SIMULIA, Dassault Systèmes).

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3. Results and discussion
In the healthy valve (model A) complete leaflet
coaptation occurred at a very low value of transvalvular
pressure drop; when a 15 mmHg value was reached, the
valve orifice was already occludedconsistently with in
vivo findings reported in [11], and accordingly with
clinical observations the coaptation region corresponded
to the leaflets rough zone. After reaching 60 mmHg of
transvalvular pressure drop, the valve underwent only
minor further deformations, that were mostly associated
with the motion of the annulus and PMs.
In the ischemic patients’ valves (models B and C),
coaptation was incomplete: regurgitant areas were
identified near the paracommissures. Location and extent
of the regurgitation areas were consistent with CMR
images and leaflets’ profile as reconstructed through our
in home software at peak systole.
The MV tensile state was analysed focusing on systolic
peak, as this timeframe is characterized by the maximum
pressure load. Leaflets maximum principal stresses were
computed (Figure 2). In model A, the region close to the
fibrous trigones was the most stressed with peak values
equal to 430 kPa. The anterior annular region also
showed high tensile values (about 300 kPa), while stress
decreased towards the free margin. The posterior leaflet
showed considerably lower stresses, with a maximum
value of about 120 kPa.
In model B, maximum principal stresses on the leaflet
(Figure 2) showed peak values of almost 500 kPa next to
the fibrous trigones and near the insertion zones of the
strut chordae, and both anterior and posterior leaflet were
overall more stressed than the healthy case (300 kPa and
150 kPa, respectively). In model C, maximum principal
stresses on the leaflet (Figure 2) showed peak values of
almost 290 kPa next to the fibrous trigones, and the
stresses values computed on both anterior and posterior
leaflet were lower than the values in the previous two
cases (i.e. healthy subject and patient with ischemic
dilated cardiomyopathy).
As regards tensions in the subvalvular apparatus, PMs
reaction force evolved during closure following the
transvalvular pressure (Figure 3). In the healthy subject,
peak force values were 6.1 N on the anterolateral PM and
Table 1 Chordae tendineae forces (mean value ± standard deviation) obtained for different chordae types in the three
simulated configurations. Values are expressed in N.
Chordae tendineae Model A Model B Model C
marginal 0.162 ± 0.107 0.256 ± 0.156 0.109 ± 0.062
basal 0.157 ± 0.121 0.302 ± 0.248 0.143 ± 0.102
commissural 0.153 0.279 0.197
paracommissural 0.239 0.372 0.155
strut 0.898 1.197 0.355
Figure 2. Maximum principal stress distribution on the leaflets at the systolic peak (atrial view) for the simulated
healthy valve (model A) and regurgitant valves (models B and C).

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6.9 N on the posteromedial PM, respectively. These
forces were unevenly transmitted to the chordae tendineae
throughout the simulated time course (Table 1), the
average load on a single chorda being highest in the strut
chordae (up to 0.9 N at peak systole).
Forces acting on the PMs in the patient with ischemic
dilated cardiomyopathy (model B) were much higher than
in the healthy one (Figure 3), with systolic peak values of
12.1 N on the posteromedial PM and of 8.3 N on the
anterolateral PM (+75% and +36% with respect to the
corresponding healthy values).
Lower forces were detected on the PMs in the second
ischemic patient (model C) with systolic peak values of
4.2 N on the posteromedial PM and of 5.4 N on the
anterolateral PM.
Computed results suggested
cardiomyopathy following ischemic disease may alter the
functioning of the valve not only in terms of loss of
leaflets coaptation, but also increasing the stresses on the
leaflets and the forces acting on the papillary muscles.

that dilated

Figure 4: Time course of the force acting on the
anterolateral PM (APM, grey) and on the posteromedial
PM (PPM, black) in model A (continuous line), model B
(dotted line) and model C (dashed line).

5. Conclusions
In this study, we demonstrated the feasibility of a MV
model based on patient-specific data obtained from CMR.
This approach could overcome the limitations of
previously proposed models and give new insight into the
complex MV function. These models could constitute the
basis for accurate evaluation of MV pathologic conditions
and for the planning of surgical procedures.

6. Acknowledgements
The research leading to these results has received
funding from the European Community’s Seventh
Framework Programme (FP7/2007-2013) under Grant
Agreement No. 224635.
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Address for correspondence.

Dr Carlo A Conti
Dipartimento di Bioingegneria
Politecnico di Milano
Piazza Leonardo da Vinci 32, Milano, Italy
E-mail: carlo.conti@mail.polimi.it
Grigioni F, Enriquez-Sarano M, Zehr KJ, Bailey KR,