NUMERICAL SIMULATION OF THE MITRAL
VALVE REPAIR: TOWARD AN OPTIMIZATION OF
THE CLINICAL PRACTICES

Pigeon Tévy Julie, Pascale Kulisa, Benyebka Bou-Saïd

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Pigeon Tévy Julie, Pascale Kulisa, Benyebka Bou-Saïd. NUMERICAL SIMULATION OF THE MITRAL VALVE REPAIR: TOWARD AN OPTIMIZATION OF THE CLINICAL PRACTICES. NAFEMS France Conference, Nov 2024, Senlis, France, France. hal-05362541

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# NUMERICAL SIMULATION OF THE MITRAL VALVE REPAIR: TOWARD AN OPTIMIZATION OF THE CLINICAL PRACTICES

Julie Tévy Pigeon (1), Pascale Kulisa (2), Benyebka Bous-Saïd (1)

1. INSA Lyon, CNRS, LaMCoS, UMR5259, 69100 Villeurbanne, France

2. Ecole Centrale de Lyon, CNRS, LMFA, UMR5509, 69621, Villeurbanne, France

## Abstract

Cardiovascular disease is the leading cause of death worldwide [1], and second only to cancer in France. [2] An estimated 17.7 million deaths are attributable to cardiovascular disease, representing 31% of all deaths worldwide. [1] Mitral regurgitation (MR) is the second most common valve disease in Europe. This pathology is characterized by a leak in the mitral valve (MV) leading to retrograde blood flow from the left ventricle to the left atrium during systole. The annuloplasty is a surgical operation that aims to reduce the valve's diameter and to stabilize the repair, preventing recurrence of mitral regurgitation by means of a prosthetic ring. This prosthetic ring is attached to the native mitral annulus with sewing nitinol threads or anchors. The dehiscence of the anchors after a substantial number of cardiac cycles is conditioned by mechanical and hemodynamical solicitations applied on the system, the healing process at anchors' locations and the tissue and prosthesis' properties. We aim to develop a digital twin of the mitral valve and its environment. The objective is to obtain a prosthetic ring according to patients' physiology and pathology. Commercial Abaqus® software is used to solve this solid mechanics problem. The biological tissue is modelled by a ring representing the junction zone between the myocardium and the mitral leaflets, and the prosthetic ring by a truncated torus imitating the Carpentier-Edwards Physio Ring. The truncated face is attached to the native mitral annulus via fixation points (Figure 1). Ventricular contraction is modelled by a physiological radial displacement boundary condition of 3mm. This simulation enables us to visualize the stress field near the attachment points and the deformed configuration of the VM model under ventricular contraction (Figure 4). We aim to further investigate the tissue response to anchoring forces, taking into account a heterogeneous constitutive law for the biological tissue as well as hemodynamic loads, and to compare several anchoring solutions (size, number and distribution).

**Keywords:** Mitral valve repair, finite element method (FEM), mitral annulus, prosthetic ring, ventricular contraction, anchors.

<figure><img src="image_2.png" /></figure>
**Introduction / Clinical context**

The heart is divided in four main cavities, two on each side of the heart. The two upper cavities are the atriums: They act as a tank of the blood entering the heart. The two lower cavities are the ventricles: They are mainly made up of myocardium and contract themselves to enable the ejection of blood. Cardiac valves are located between and downstream each cavity. They open and close during the cardiac cycle: During the diastole phase, valves between the atrium and the ventricles are open and blood flows from the atrium to the ventricle. During systole, these valves are hermetically sealed, blood is expelled from the heart to the body's organs, and the pressure in the left ventricle reaches 120 mmHg (16 kPa) [3]. We will focus on the mitral valve (MV), located between the left atrium and the left ventricle.

The mitral annulus (MA) is clinically described as fibrous ring made of connective tissue varying in thickness and density along the diameter. It connects the left atrium, left ventricle and the leaflets. Tendinous chords connect the mitral leaflets and the papillary muscles implanted the ventricle. The combined movements of the different parts of the mitral apparatus enable the leaflets to open and close, alternately allowing blood to circulate and stop between the atrium and the ventricle.

Valvopathies are pathologies affecting the heart valves functionality. Secondary valvular diseases do not damage the valve but a change in its environment (tendinous chords rupture, papillary muscles displacement, etc.) leads to the dilatation of the native mitral annulus and the separation of the leaflets. Blood can leak backward through the untight valve: this is called the mitral regurgitation (MR).

Standard surgical treatments exist to repair the MV such as open-heart surgery but are heavy and unsuitable to at-risk patients. Transcatheter techniques are known as minimally invasive as surgeons operate from inside the body without stopping the beating

heart. Another mini-invasive treatment, the MitraClip® partially solves the problem by clamping leaflets together to reduce the MR. We focus on a transcatheter annuloplasty approach, with an emphasis on prosthesis durability.

The study of prosthetic ring durability involves three key actors: the biological tissue, the prosthetic ring and the attachment points. The prosthetic ring durability depends on the position and angle of the attachment points on the native mitral annulus. What are the best positions for maintaining the prosthetic ring attachment points in the biological tissue? We aim to reproduce in-vivo loads and the stress field on the mitral valve near the attachment points in order to optimize their location and angle.

**Methodology / From the physics to the modelling**

The in-vivo loads applied to the system {biological tissue, prosthesis, attachments} are the ventricular contraction, the hemodynamic pressure field and the effect of tendinous chords traction on the mitral annulus during the cardiac cycle. We assume that ventricular contraction has a predominant impact over hemodynamic and tendinous chords effects. Furthermore, we suppose that the maximum efforts take place during the systolic phase, when the mitral valve is closed, the ventricle is contracting and the pressures reached in the ventricular cavity are the highest. We then model ventricular contraction from the diastolic to the systolic phase.

**Geometry.** The finite element method (FEM), using the commercial Abaqus® software, is used to solve this solid mechanics problem. The geometry of the system is represented by a generic, parameterizable model: 1) The heart tissue is represented as the junction between the myocardium and the leaflets, modelled by a hollow disk (Figure 2). It is assumed that, during cardiac contraction, the stiffness of the leaflets offers negligible resistance to the displacement and forces on the biological tissue. The "hole" therefore encompasses the
commissures of the mitral leaflets. 2) The prosthesis inspired by the Carpentier-Edwards Physio Annuloplasty Ring is modelled on a

truncated open torus placed on the mitral annulus (Figure 3).

<figure><img src="image_3.png" /><figcaption>**Figure 2:** Cardiac tissue modelled as the junction between the mitral valve (MV) and the myocardium. The mitral annulus (MA) is located at the convergency of the two biological tissues. Dimensions are set from diameter variation between the systolic and diastole states. [4][6] (left). Cardiac tissue geometry (right).</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 3:** Prosthetic ring dimensions and location inspired by the commercial Carpentier-Edwards Physio Annuloplasty Ring [6] (left). Prosthetic ring geometry (right).</figcaption></figure>

**Materials.** The native mitral annulus is composed of a mixture of muscle tissue, adipose tissue and collagen fibers, the latter being key elements in the holding of the implanted prosthesis. The discontinuous, heterogeneous or even virtually non-existent nature of the native ring makes the prediction of mechanical properties complex [7]. We consider the most critical case by attributing the myocardium mechanical properties to the cardiac tissue, which will have an increased propensity to tear under in-vivo stress. The elastic constitutive law uses coefficients from the literature: density = 1265 kg/m3 [8], Young's modulus of the aorta = 300 kPa [9], Poisson's ratio = 0.45 [10]. The mechanical characteristics of the prosthetic ring were found by reproducing on Abaqus the compression test of a Carpentier Edwards Physio ring [11] and assuming the prosthesis to

be quasi-incompressible: Density = 2300 kg/m3, Young's modulus = 1.785 MPa, Poisson's ratio = 0.45.

**Boundary conditions.** By order of magnitude mitral valve diameter varies by 6mm between early and late systole [5], or between mid-diastole and mid-systole [12]. To model cardiac contraction, a radial displacement of 3mm towards the center of the valve is imposed on the outer circumferential surface of the myocardium. For numerical reasons, this surface is also blocked for vertical translations, while springs of stiffness 2200 N/m connect the earth to four points on the inner circumferential surface of the mitral valve. The tie stress imposed on six 2mm-diameter surfaces models the attachment points between the biological tissue and the prosthetic ring (Figure 1). Contact outside the attachment
points is managed by a "general contact" algorithm.

*Mesh*. The prosthesis is meshed with quadratic tetrahedral elements and the biological tissue with linear tetrahedral elements without reduced integration.

## Results

The outer circumferential surface of the myocardium moves 3mm towards the center of

the valve. A buckling effect of the biological tissue is observed during contraction. This effect is accentuated in the area where the prosthesis is open.

The max principal stress field is greatest in the vicinity of the attachments, particularly those on the open side of the prosthesis. The max amplitude is around 360kPa.

<figure><img src="image_5.png" /><figcaption>**Figure 4:** Ventricular contraction's results: Displacement field with (top left) and without (top right) the prosthetic ring. Max principal stress field without prosthesis (below).</figcaption></figure>

## Conclusion

These simulations of a parametrizable generic mitral annulus under in-vivo loads provide an insight into the tissue response during ventricular contraction.

The distribution of the stress field gives an indication of which areas around the attachment points are most stressed during ventricular contraction after implantation of the prosthesis. Consideration of a yield stress value would help predict at-risk areas regarding prosthesis pull-out. Then, we project
to test different attachment configurations and
compare their lifespan.

Discussion

There are many possibilities to improve this
model:

Firstly, the determination of a heterogeneous
behaviour law for the myocardium around the
mitral annulus. Experimental tests are in
progress to determine the local mechanical
properties of the biological tissue, which is
stiffer at the trigones - fibrous zones shared
with the aortic valve - and more ductile towards
the ventricular wall.

The current geometric model of the mitral
valve has been simplified to fine-tune the
methodology. Once this stage is complete, a
geometry and kinematics closer to anatomical
reality will be required.

The next step is to measure the contribution of
hemodynamic forces and tendinous chords
traction on the mitral valve, in order to validate
the hypothesis of neglecting them in the
calculation.

Finally, the geometry and mechanical
properties of the prosthesis will be refined in
order to test different attachment approaches,
reduce its diameter and test its durability over
time.

Acknowledgment

This work was performed within the
framework of the ICELAND project (ANR-21-
RHUS-0006) coordinated by the Hospices
Civils de Lyon (HCL) within the program
France 2030 operated by the French National
Research Agency (ANR).

References

1. OMS (2017): https://www.who.int/fr/newsroom/fact-sheets/detail/cardiovascular-diseases-(cvds)

2. Website of the French Ministry of Work, Health and Solidarities (sante.gouv.fr) (2023): https://sante.gouv.fr/soins-et-maladies/maladies/maladies-cardiovasculaires/article/maladies-cardiovasculaires

3. The Wright table of the cardiac cycle: a stand-alone supplement to the Wiggers diagram, Wright et al. (2019)

4. Left Ventricular Mid-Diastolic Wall Thickness - Normal Values for Coronary CT angiography, Walpot et al (2019)

5. Dynamic changes in the ischemic mitral annulus: Implications for ring sizing, Owais et al. (2016)

6. Carpentier-Edwards Physio Annuloplasty Ring technical sheet: https://www.kardiochirurgie.cz/dokumenty/edwards physioannuloplastyringsbrochure.pdf

7. Anatomy of mitral annulus insights from non-invasive imaging technique, Faletra et al. (2019)

8. Cardiac left ventricular myocardial tissue evaluated by computed tomography and autopsy, Gheorghe et al. (2019)

9. Biomaterial based cardiac tissue engineering and its applications, Huyer et al. (2015)

10. Passive myocardial mechanical properties: meaning, measurement, models, Emif et al. (2021)

11. A Novel Shape Memory Alloy Annuloplasty Ring for Minimally Invasive Surgery: Design, Fabrication, and Evaluation, Purser et al (2011)

12. A multidimensional dynamic quantification tool for the mitral valve, Hossien et al. (2015)