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Patient-specific finite element analysis of heart failure and the impact of surgical intervention in pulmonary hypertension secondary to mitral valve disease

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Abstract

Pulmonary hypertension (PH), a chronic and complex medical condition affecting 1% of the global population, requires clinical evaluation of right ventricular maladaptation patterns under various conditions. A particular challenge for clinicians is a proper quantitative assessment of the right ventricle (RV) owing to its intimate coupling to the left ventricle (LV). We, thus, proposed a patient-specific computational approach to simulate PH caused by left heart disease and its main adverse functional and structural effects on the whole heart. Information obtained from both prospective and retrospective studies of two patients with severe PH, a 72-year-old female and a 61-year-old male, is used to present patient-specific versions of the Living Heart Human Model (LHHM) for the pre-operative and post-operative cardiac surgery. Our findings suggest that before mitral and tricuspid valve repair, the patients were at risk of right ventricular dilatation which may progress to right ventricular failure secondary to their mitral valve disease and left ventricular dysfunction. Our analysis provides detailed evidence that mitral valve replacement and subsequent chamber pressure unloading are associated with a significant decrease in failure risk post-operatively in the context of pulmonary hypertension. In particular, right-sided strain markers, such as tricuspid annular plane systolic excursion (TAPSE) and circumferential and longitudinal strains, indicate a transition from a range representative of disease to within typical values after surgery. Furthermore, the wall stresses across the RV and the interventricular septum showed a notable decrease during the systolic phase after surgery, lessening the drive for further RV maladaptation and significantly reducing the risk of RV failure.

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Acknowledgements

The authors would like to thank Tehran and Rejaie Heart Centers, in particular Dr. Rabbani, for helping in preparing the draft of the protocol and providing the MRI studies and research. The authors would also like to thank Prof. Luc Mongeau (Department of Mechanical Engineering, McGill) and Prof. Ghyslaine McClure (Department of Civil Engineering, McGill) for providing the Abaqus license. MA’s research is partly supported by NSERC Canada. The authors are grateful for the accommodation of the Living Heart Project and their research. The authors would like to express gratitude to Dr. S. Kelly Sears (Facility for Electron Microscopy Research, McGill) for technical support related to computing and physiological science.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, QC, H3A 0C3, Canada

    Alireza Heidari & Renzo Cecere

  2. Department of Anatomy & Cell Biology, McGill University, Montreal, QC, Canada

    Alireza Heidari, Hojatollah Vali & Sara Sheibani

  3. Department of Mechanical Engineering, American University in Cairo, New Cairo, 11835, Egypt

    Khalil I. Elkhodary & Yousof M. A. Abdel-Raouf

  4. Faculty of Medicine, McGill University, Montreal, QC, Canada

    Cristina Pop

  5. Department of Mechanical Engineering, Future University in Egypt, New Cairo, Egypt

    Mohamed Badran

  6. School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Saeed Torbati

  7. Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada

    Masoud Asgharian & Russell J. Steele

  8. School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Iradj Mahmoudzadeh Kani

  9. Rajaie Cardiovascular Medical and Research Center, Iran University of Medical Sciences, Tehran, Iran

    Hamidreza Pouraliakbar

  10. Faculty of Medicine, Tehran University of Medical Science, Tehran, Iran

    Hakimeh Sadeghian & Hossein Ahmadi Tafti

  11. Department of Surgery, Tehran Heart Center, Tehran, Iran

    Hakimeh Sadeghian & Hossein Ahmadi Tafti

  12. Department of Surgery, Royal Victoria Hospital, McGill University Health Centre, Montreal, QC, Canada

    Renzo Cecere

  13. Departments of Medicine and Diagnostic Radiology, McGill University, Montreal, QC, Canada

    Matthias G. W. Friedrich

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  1. Alireza Heidari
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  2. Khalil I. Elkhodary
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  3. Cristina Pop
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  8. Masoud Asgharian
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  13. Hakimeh Sadeghian
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  16. Hossein Ahmadi Tafti
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Contributions

A. Heidari and H. A. Tafti designed the prospective study, prepared the protocol, and obtained approval for the study. K. Elkhodary developed the expansion method, and A. Heidari developed the shrinkage method to morph the Living Heart Model to represent the heart geometry before and after surgery; both took the lead in manuscript preparation. A. Heidari and Y. M. A. Abdel-Raouf created the computational model with support from M. Badran. A. Heidari and S. Torbati created the computational model for the second patient, and with C. Pop, revised the manuscript. I. M. Kani helped with the morphing concept and resolved the numerical issues in large deformation that led to our finite element analysis for valves and ventricles. H. Vali and S. Sheibani guided the physiological aspects of the model. M. Asgharian and R. Steele helped in tuning the input parameters of the model by suggesting a parametric study to obtain the right ventricle criteria for adapting the model with the patient before and after surgery. H. Pouraliakbar performed the MRI study on the patient, and with M. Friedrich, provided state-of-the-art MRI research for heart failure. H. Sadeghian is responsible for echocardiography. C. Pop and R. Cecere helped with the understanding of cardiac diseases and the interpretation of the MRI images.

Corresponding author

Correspondence to Alireza Heidari.

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Appendix

Appendix

1.1 LHHM active–passive mechanics summary

The mechanical response of the cardiac tissue incorporates an active model that describes the contraction of the fibers due to electrical excitation and a passive model that describes non-excitable material behavior. The active material response is represented as a myofiber-aligned active tension (\(\sigma\)) that is time-varying and instigated post electrical activation [44],

$$\begin{array}{c}{\sigma(\mathrm t,{\mathrm E}_{\mathrm{ff}})}_{\mathrm{active}\mathrm\;\mathrm{fiber}}={\mathrm T}_{max}\frac{\mathrm{Ca}_0^2}{2\left(\mathrm{Ca}_0^2+\mathrm E\mathrm{Ca}_{50}^2\right)}\left(1-\cos\left(\omega\right)\right),\\{\mathrm{ECa}}_{50}=\frac{{\mathrm{Ca}}_{0max}}{\sqrt{\mathrm e^{\mathrm B(\mathrm l-{\mathrm l}_0)}-1}},\\\omega=\left\{\begin{array}{l}\begin{array}{cc}\pi\frac{\mathrm t}{{\mathrm t}_0},&\mathrm{when}\;0\leq\mathrm t\leq{\mathrm t}_0,\end{array}\\\begin{array}{cc}\pi\frac{\mathrm t-{\mathrm t}_0+{\mathrm t}_{\mathrm r}}{{\mathrm t}_{\mathrm r}},&\mathrm{when}\;{\mathrm t}_0\leq\mathrm t\leq{{\mathrm t}_0+\mathrm t}_{\mathrm r},\end{array}\\\begin{array}{cc}0,&\mathrm{when}\;{{\mathrm t}_0+\mathrm t}_{\mathrm r}\leq\mathrm t,\end{array}\end{array}\right.\\{\mathrm t}_{\mathrm r}=\mathrm{ml}+\mathrm b,\\\mathrm l={\mathrm l}_{\mathrm r}\sqrt{2{\mathrm E}_{\mathrm{ff}}+1},\end{array}$$

where \({T}_{max}\) indicates the maximum active stress that can be achieved in a myofiber; \({Ca}_{0}\) and \({Ca}_{0 max}\) represent initial and peak calcium concentrations in the myofiber; \({l}_{0}\) is the minimum sarcomere length at which active stress develops; \({l}_{r}\) is the reference fiber length; \({t}_{0}\) is the time until maximum stress is reached; B, m, and b are phenomenological constants; and \({E}_{ff}\) is the Green–Lagrange strain component in the fiber direction.

The passive response is conversely modeled after the incompressible, anisotropic, hyper-elastic model outlined in [45], given by the strain energy function,

$$\begin{array}{c}{\mathrm\Psi}_{\mathrm{deviatoric}}={\frac{\mathrm a}{2\mathrm b}\mathrm e}^{\mathrm b\left({\mathrm I}_1-3\right)}+\displaystyle\sum_{\mathrm i=\mathrm f,\mathrm s}\frac{{\mathrm a}_{\mathrm i}}{2{\mathrm b}_{\mathrm i}}(\mathrm e^{{\mathrm b}_{\mathrm i}\left({\mathrm I}_{4\mathrm i}-1\right)^2}-1)+{\frac{{\mathrm a}_{\mathrm{fs}}}{2{\mathrm b}_{\mathrm{fs}}}(\mathrm e}^{{\mathrm b}_{\mathrm{fs}}\left({\mathrm I}_{8\mathrm{fs}}\right)^2}-1),\\{\mathrm\Psi}_{\mathrm{volumetric}}=\frac1{\mathrm D}\left(\frac{\mathrm J^2-1}2-\ln(\mathrm J)\right),\end{array}$$

where \(a,b,{a}_{f},{a}_{s},{a}_{fs}\), and \({b}_{fs}\) are material constants. The value of \({I}_{1}\) describes the isotropic response and is the first principle invariant of the right Cauchy-Green tensor, C, and is given by \({I}_{1}=tr(\mathbf{C})\), while the two terms which describe the transversely isotropic response are described by \({I}_{4f}\), \({I}_{4s}\) both evaluated as \({\mathbf{f}}_{0}\bullet \left(\mathbf{C}{\mathbf{f}}_{0}\right)\) and \({\mathbf{s}}_{0}\bullet (\mathbf{C}{\mathbf{s}}_{0})\), respectively. Finally, the orthotropic response is reflected in the term \({I}_{8fs}=\) \({\mathbf{f}}_{0}\bullet \left(\mathbf{C}{\mathbf{s}}_{0}\right)\). \({\mathbf{f}}_{0}\) and \({{\varvec{s}}}_{0}\) are the fiber direction and sheet direction, respectively. The volumetric response is composed of the bulk modulus,\(D\), and the Jacobian (determinant) of the deformation gradient, \(J\).

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Heidari, A., Elkhodary, K.I., Pop, C. et al. Patient-specific finite element analysis of heart failure and the impact of surgical intervention in pulmonary hypertension secondary to mitral valve disease. Med Biol Eng Comput 60, 1723–1744 (2022). https://doi.org/10.1007/s11517-022-02556-6

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