Biomechanics and Modeling in Mechanobiology

, Volume 16, Issue 5, pp 1613–1632 | Cite as

On the in vivo function of the mitral heart valve leaflet: insights into tissue–interstitial cell biomechanical coupling

  • Chung-Hao Lee
  • Will Zhang
  • Kristen Feaver
  • Robert C. Gorman
  • Joseph H. GormanIII
  • Michael S. Sacks
Original Paper


There continues to be a critical need for developing data-informed computational modeling techniques that enable systematic evaluations of mitral valve (MV) function. This is important for a better understanding of MV organ-level biomechanical performance, in vivo functional tissue stresses, and the biosynthetic responses of MV interstitial cells (MVICs) in the normal, pathophysiological, and surgically repaired states. In the present study, we utilized extant ovine MV population-averaged 3D fiducial marker data to quantify the MV anterior leaflet (MVAL) deformations in various kinematic states. This approach allowed us to make the critical connection between the in vivo functional and the in vitro experimental configurations. Moreover, we incorporated the in vivo MVAL deformations and pre-strains into an enhanced inverse finite element modeling framework (Path 1) to estimate the resulting in vivo tissue prestresses \((\sigma _\mathrm{CC}\cong \sigma _\mathrm{RR}\cong \, 30\,\hbox {kPa})\) and the in vivo peak functional tissue stresses \((\sigma _\mathrm{CC}\cong 510\, \hbox {kPa}, \sigma _\mathrm{RR}\cong 740\, \hbox {kPa})\). These in vivo stress estimates were then cross-verified with the results obtained from an alternative forward modeling method (Path 2), by taking account of the changes in the in vitro and in vivo reference configurations. Moreover, by integrating the tissue-level kinematic results into a downscale MVIC microenvironment FE model, we were able to estimate, for the first time, the in vivo layer-specific MVIC deformations and deformation rates of the normal and surgically repaired MVALs. From these simulations, we determined that the placement of annuloplasty ring greatly reduces the peak MVIC deformation levels in a layer-specific manner. This suggests that the associated reductions in MVIC deformation may down-regulate MV extracellular matrix maintenance, ultimately leading to reduction in tissue mechanical integrity. These simulations provide valuable insight into MV cellular mechanobiology in response to organ- and tissue-level alternations induced by MV disease or surgical repair. They will also assist in the future development of computer simulation tools for guiding MV surgery procedure with enhanced durability and improved long-term surgical outcomes.


Finite element (FE) inverse modeling Structural constitutive models Collagen fiber recruitment Mitral valve surgical repair Cell mechanotransduction 

List of symbols

\(\Psi _\mathrm{c} \)

Strain energy function component of the collagen fiber network

\(\Psi _\mathrm{e} \)

Strain energy function component of the elastin fiber networks

\(\Psi _\mathrm{m} \)

Strain energy function component of non-fibrous matrix

\(\mathbf{C}=\mathbf{F}^{T}{} \mathbf{F}\)

Right-Cauchy deformation tensor


Green–Lagrange strain tensor


2nd-rank identity tensor

\(I_{4}=\mathbf{n}_\mathrm{c}\cdot \mathbf{Cn}_\mathrm{c}\)

Square of the circumferential stretch associated with elastin fibers

\(I_{6}=\mathbf{n}_\mathrm{R}\cdot \mathbf{Cn}_\mathrm{R}\)

Square of the radial stretch associated with elastin fibers

\({E}_\mathrm{ens}(\theta _{0})=\mathbf{n}(\theta _{0})\cdot \mathbf{En}(\theta _{0})\)

Ensemble fiber strain of the individual collagen fiber in the direction of n(\(\theta )\)


Ensemble fiber stress calculated based on the ensemble fiber stress–strain relation


Cutoff limit of ensemble fiber strain beyond which the ensemble fiber stress–strain relationship becomes linear

\(\mathbf{n}(\theta _{0})\)

Unit vector of collagen fiber orientation w.r.t. \(\beta _{0}\)

\(\mathbf{n}_\mathrm{c}=\mathbf{n}(0^{\circ })\)

Unit vector of elastin fiber orientation along the circumferential direction w.r.t. \(\beta _{0}\)

\(\mathbf{n}_\mathrm{R}=\mathbf{n}(\pi )\)

Unit vector of elastin fiber orientation along the radial direction w.r.t. \(\beta _{0}\)

\(\mu _\mathrm{m}\)

Shear modulus of the non-fibrous matrix represented by a neo-Hookean material

\(\eta _\mathrm{c}\)

Collagen fiber modulus

\(\eta _\mathrm{e}^{a} \)

Elastin fiber modulus of the elastin fibers along the circumferential direction

\(\eta _\mathrm{e}^{b} \)

Elastin fiber modulus of the elastin fibers along the radial direction


Exponent of the elastin ensembles along the circumferential direction


Exponent of the elastin ensembles along the radial direction

\(\Gamma (\theta _0 ;\mu _\mathrm{C} ,\sigma _\mathrm{C} )\)

Orientation density function of the collagen fiber network with a mean fiber direction \(\mu _\mathrm{C}\) and a standard deviation \(\sigma _\mathrm{C}\)

\(D(x;\mu _\mathrm{D} ,\sigma _\mathrm{D},E_\mathrm{lb} ,E_\mathrm{ub})\)

Fiber recruitment distribution function with a mean \(\mu _\mathrm{D}\), a standard deviation \(\sigma _\mathrm{D}\), , a lower-bound limit \(E_\mathrm{lb}\) at which collagen fiber recruitment begins, a lower-bound limit \(E_\mathrm{ub}\) at which collagen fiber is fully recruited



Support from the National Institutes of Health (NIH) Grants R01 HL119297, HL63954, HL103723, and HL73021 is gratefully acknowledged. Dr. Chung-Hao Lee was in part supported by the start-up funds from the School of Aerospace and Mechanical Engineering (AME) at the University of Oklahoma, and the American Heart Association Scientist Development Grant Award (16SDG27760143).

Compliance with ethical standards

Conflict of interest

None of the authors have a conflict of interests with the present work.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Chung-Hao Lee
    • 1
    • 2
  • Will Zhang
    • 2
  • Kristen Feaver
    • 2
  • Robert C. Gorman
    • 3
  • Joseph H. GormanIII
    • 3
  • Michael S. Sacks
    • 2
    • 4
  1. 1.School of Aerospace and Mechanical EngineeringThe University of OklahomaNormanUSA
  2. 2.Department of Biomedical Engineering, Center for Cardiovascular Simulation, Institute for Computational Engineering and SciencesThe University of Texas at AustinAustinUSA
  3. 3.Gorman Cardiovascular Research GroupUniversity of PennsylvaniaPhiladelphiaUSA
  4. 4.W. A. Moncrief, Jr. Simulation-Based Engineering Science Chair I, Department of Biomedical Engineering, Institute for Computational Engineering and SciencesThe University of Texas at AustinAustinUSA

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