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.
Article: Ischemic mitral regurgitation: long-term outcome and prognostic implications with quantitative Doppler assessment.[show abstract] [hide abstract]
ABSTRACT: Myocardial infarction (MI) can directly cause ischemic mitral regurgitation (IMR), which has been touted as an indicator of poor prognosis in acute and early phases after MI. However, in the chronic post-MI phase, prognostic implications of IMR presence and degree are poorly defined. We analyzed 303 patients with previous (>16 days) Q-wave MI by ECG who underwent transthoracic echocardiography: 194 with IMR quantitatively assessed in routine practice and 109 without IMR matched for baseline age (71+/-11 versus 70+/-9 years, P=0.20), sex, and ejection fraction (EF, 33+/-14% versus 34+/-11%, P=0.14). In IMR patients, regurgitant volume (RVol) and effective regurgitant orifice (ERO) area were 36+/-24 mL/beat and 21+/-12 mm(2), respectively. After 5 years, total mortality and cardiac mortality for patients with IMR (62+/-5% and 50+/-6%, respectively) were higher than for those without IMR (39+/-6% and 30+/-5%, respectively) (both P<0.001). In multivariate analysis, independently of all baseline characteristics, particularly age and EF, the adjusted relative risks of total and cardiac mortality associated with the presence of IMR (1.88, P=0.003 and 1.83, P=0.014, respectively) and quantified degree of IMR defined by RVol >/=30 mL (2.05, P=0.002 and 2.01, P=0.009) and by ERO >/=20 mm(2) (2.23, P=0.003 and 2.38, P=0.004) were high. In the chronic phase after MI, IMR presence is associated with excess mortality independently of baseline characteristics and degree of ventricular dysfunction. The mortality risk is related directly to the degree of IMR as defined by ERO and RVol. Therefore, IMR detection and quantification provide major information for risk stratification and clinical decision making in the chronic post-MI phase.Circulation 04/2001; 103(13):1759-64. · 14.74 Impact Factor
Article: Impact of papillary muscle relocation as adjunct procedure to mitral ring annuloplasty in functional ischemic mitral regurgitation.[show abstract] [hide abstract]
ABSTRACT: The optimal surgical treatment in functional ischemic mitral regurgitation (FIMR) remains controversial. Recently, a posterior papillary muscle relocation (PMR) technique as adjunct procedure to ring annuloplasty has been proposed to prevent recurrent FIMR. In the present study, we used 3D cardiac MRI to assess the impact of relocating both papillary muscles as adjunct procedure to downsized ring annuloplasty on mitral leaflet coaptation geometry in FIMR pigs. Eleven FIMR pigs were randomized to downsized ring annuloplasty (RA; n=6) or RA combined with PMR (RA+PMR, n=5). In the RA+PMR group, a 2-0 Gore-Tex suture was attached to each trigone, exteriorized through the corresponding papillary muscle, mounted on an epicardial pad, and tightened to relocate the myocardium adjacent to the anterior and posterior papillary muscles 5 and 15 mm, respectively. Using 3D MRI, the impact from these interventions on leaflet geometry was assessed. The distance from the posterior papillary muscle to the anterior trigone was reduced significantly more (median values) in the RA+PMR compared with RA animals at end-diastole (-7.9% versus 3.8%, P<0.01) and end-systole (-9.7% versus 2.5%, P=0.02). Accordingly, lateral tethering of the coaptation point (median values) was reduced significantly more in RA+PMR compared with RA animals (-42.8% versus -29.1%, P<0.01). Adding papillary muscle relocation to downsized ring annuloplasty reduced lateral leaflet tethering in a porcine experimental model of FIMR. Therefore, this technique holds promise for reducing persistent and recurrent FIMR in patients.Circulation 09/2009; 120(11 Suppl):S92-8. · 14.74 Impact Factor
[show abstract] [hide abstract]
ABSTRACT: Functional mitral regurgitation (FMR) is the inability of mitral leaflets to coapt due to a combination of functional and geometrical factors. Valve competence is commonly restored by undersized annuloplasty, reducing the native annulus anteroposterior dimension. In case of severe FMR, this solution may be inadequate. The use of rings specific for the correction of FMR may lead to better results. The performance of the Geoform ring, a recently designed FMR-specific prosthesis, was compared with that of a standard Physio annuloplasty ring. Finite element modeling was used to simulate dilated cardiomyopathy-related FMR and compare, at the systolic peak, the valve's pathologic condition with the postoperative scenario corresponding to both devices. Three degrees of the pathology were simulated by progressively displacing papillary muscles apically, up to 5 mm. Three ring sizes were modeled. Regurgitant area, coaptation length, and stresses acting on valve structures were assessed. When the use of the Geoform was modeled, coaptation length was always longer than 7 mm. In the most unfavorable case, the regurgitant area reduction was 74% with respect to baseline, and leaflets stresses were reduced by 20% when undersizing was simulated. When Physio ring implantation was simulated, coaptation length maximum extent was equal to 4.3 mm, the maximum regurgitant area reduction was equal to 60%, and leaflet stress reduction was observed. Disease-specific prostheses may allow for restoration of valve competence even for significant degrees of leaflets tethering and avoid the need for aggressive undersizing, thus leading to more durable results.The Annals of thoracic surgery 08/2007; 84(1):92-101. · 3.74 Impact Factor
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
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
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 . 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 .
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.  proposed a
modelling approach based on transthoracic real-time
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
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.
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
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
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
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
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
, 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 , 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 . Constant cross-
sectional area values of 0.40, 1.15 and 0.79 mm2 were
assigned to marginal, strut and second order chordae,
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).
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 , 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
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).
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
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.
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).
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.
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
Grigioni F, Enriquez-Sarano M, Zehr KJ, Bailey KR,