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Development of a Functionally Equivalent Model of the Mitral Valve Chordae Tendineae Through Topology Optimization

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Abstract

Ischemic mitral regurgitation (IMR) is a currently prevalent disease in the US that is projected to become increasingly common as the aging population grows. In recent years, image-based simulations of mitral valve (MV) function have improved significantly, providing new tools to refine IMR treatment. However, clinical implementation of MV simulations has long been hindered as the in vivo MV chordae tendineae (MVCT) geometry cannot be captured with sufficient fidelity for computational modeling. In the current study, we addressed this challenge by developing a method to produce functionally equivalent MVCT models that can be built from the image-based MV leaflet geometry alone. We began our analysis using extant micron-resolution 3D imaging datasets to first build anatomically accurate MV models. We then systematically simplified the native MVCT structure to generate a series of synthetic models by consecutively removing key anatomic features, such as the thickness variations, branching patterns, and chordal origin distributions. In addition, through topology optimization, we identified the minimal structural complexity required to capture the native MVCT behavior. To assess the performance and predictive power of each synthetic model, we analyzed their performance by comparing the mismatch in simulated MV closed shape, as well as the strain and stress tensors, to ground-truth MV models. Interestingly, our results revealed a substantial redundancy in the anatomic structure of native chordal anatomy. We showed that the closing behavior of complete MV apparatus under normal, diseased, and surgically repaired scenarios can be faithfully replicated by a functionally equivalent MVCT model comprised of two representative papillary muscle heads, single strand chords, and a uniform insertion distribution with a density of 15 insertions/cm2. Hence, even though the complete sub-valvular structure is mostly missing in in vivo MV images, we believe our approach will allow for the development of patient-specific complete MV models for surgical repair planning.

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Acknowledgments

Research reported in this publication was supported by National Heart, Lung, and Blood Institute of the National Institutes of Health under Award Number R01-HL119297, National Science Foundation Grant No. DGE-1610403 to BVR, and the American Heart Association Grant No. 18PRE34030258 to BVR.

Conflict of interest

The authors declare no conflict of interest.

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Authors and Affiliations

  1. James T. Willerson Center for Cardiovascular Modeling and Simulation, Institute for Computational Engineering and Sciences, Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX, USA

    Amir H. Khalighi, Bruno V. Rego, Andrew Drach & Michael S. Sacks

  2. Gorman Cardiovascular Research Group, Department of Surgery, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA

    Robert C. Gorman & Joseph H. Gorman III

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  1. Amir H. Khalighi
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  2. Bruno V. Rego
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  3. Andrew Drach
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  6. Michael S. Sacks
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Correspondence to Michael S. Sacks.

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Associate Editor Elena S. Di Martino oversaw the review of this article.

Appendix

Appendix

We performed our analysis presented in this work on 3 valves that were randomly selected from our extant dataset of micro-CT based MV models (Fig. 10). The optimal models developed for all valves faithfully reproduced the effect of native chordal anatomy in terms of organ-level simulations of the MV closure under normal, dilated, and repaired conditions (Figs. 11 and 12). This consistency further indicates that functionally equivalent MVCT models allow performing predictive simulations of the MV apparatus to simulate clinically important conditions of the MV.

Figure 10
figure 10

The study was performed on 3 specimens to reproduce the results of functionally equivalent models of the MVCT on multiple valves.

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Figure 11
figure 11

Closure simulations of MV2 are shown for a functionally equivalent MVCT and the ground truth models.

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Figure 12
figure 12

Closure simulations of MV3 are shown for a functionally equivalent MVCT and the ground truth models.

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Khalighi, A.H., Rego, B.V., Drach, A. et al. Development of a Functionally Equivalent Model of the Mitral Valve Chordae Tendineae Through Topology Optimization. Ann Biomed Eng 47, 60–74 (2019). https://doi.org/10.1007/s10439-018-02122-y

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