Advertisement

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

Abstract

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.

Keywords

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

\(\mathbf{E}=(\mathbf{C}-\mathbf{I})/2\)

Green–Lagrange strain tensor

\(\mathbf{I}\)

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(\(\theta )\)

\(S_\mathrm{ens}\)

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

\(E_\mathrm{cutoff}\)

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

a

Exponent of the elastin ensembles along the circumferential direction

b

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

Notes

Acknowledgements

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.

References

  1. Aggarwal A, Sacks MS (2015) A framework for determination of heart valves’ mechanical properties using inverse-modeling approach. Lect Notes Comput Sci 9126:285–294CrossRefGoogle Scholar
  2. Aggarwal A, Pouch AM, Lai E, Lesicko J, Yushkevich PA et al (2016) In-vivo heterogeneous functional and residual strains in human aortic valve leaflets. J Biomech 49:2481–2490CrossRefGoogle Scholar
  3. Amini R, Eckert CE, Koomalsingh K, McGarvey J, Minakawa M et al (2012) On the in vivo deformation of the mitral valve anterior leaflet: effects of annular geometry and referential configuration. Ann Biomed Eng 40:1455–1467CrossRefGoogle Scholar
  4. Balachandran K, Konduri S, Sucosky P, Jo H, Yoganathan A (2006) An ex vivo study of the biological properties of porcine aortic valves in response to circumferential cyclic stretch. Ann Biomed Eng 34:1655–1665CrossRefGoogle Scholar
  5. Balachandran K, Sucosky P, Jo H, Yoganathan AP (2009) Elevated cyclic stretch alters matrix remodeling in aortic valve cusps: implications for degenerative aortic valve disease. Am J Physiol Heart Circ Physiol 296:H756–764CrossRefGoogle Scholar
  6. Bouma W, Lai EK, Levack MM, Shang EK, Pouch AM et al (2016) Preoperative three-dimensional valve analysis predicts recurrent ischemic mitral regurgitation after mitral annuloplasty. Ann Thorac Surg 101:567–575CrossRefGoogle Scholar
  7. Braunberger E, Deloche A, Berrebi A, Abdallah F, Celestin JA et al (2001) Very long-term results (more than 20 years) of valve repair with carpentier’s techniques in nonrheumatic mitral valve insufficiency. Circulation 104:I8–11CrossRefGoogle Scholar
  8. Cardamone L, Valentin A, Eberth JF, Humphrey JD (2009) Origin of axial prestretch and residual stress in arteries. Biomech Model Mechanobiol 8:431–446CrossRefGoogle Scholar
  9. Carpentier A (1983) Cardiac valve surgery-the “french correction”. J Thorac Cardiovasc Surg 86:323–337Google Scholar
  10. Carruthers CA, Alfieri CM, Joyce EM, Watkins SC, Yutzey KE et al (2012a) Gene expression and collagen fiber micromechanical interactions of the semilunar heart valve interstitial cell. Cell Mol Bioeng 5:254–265CrossRefGoogle Scholar
  11. Carruthers CA, Good B, D’Amore A, Liao J, Amini R et al (2012b) Alterations in the microstructure of the anterior mitral valve leaflet under physiological stress. In: ASME 2012 summer bioengineering conference, 2012b. American Society of Mechanical Engineers, pp 227–228Google Scholar
  12. Chandran PL, Barocas VH (2006) Affine versus non-affine fibril kinematics in collagen networks: theoretical studies of network behavior. J Biomech Eng 128:259–270CrossRefGoogle Scholar
  13. Chuong CJ, Fung YC (1986a) On residual stress in arteries. J Biomech Eng 108:189–192CrossRefGoogle Scholar
  14. Chuong CJ, Fung YC (1986b) Residual stress in arteries. In: Schmid-Schonbein G, Woo SLY, Zweifach B (eds) Frontiers in biomechanics. Springer, New York, pp 117–129CrossRefGoogle Scholar
  15. Dahl KN, Ribeiro AJ, Lammerding J (2008) Nuclear shape, mechanics, and mechanotransduction. Circ Res 102:1307–1318CrossRefGoogle Scholar
  16. Eckert CE, Zubiate B, Vergnat M, Gorman JH 3rd, Gorman RC et al (2009) In vivo dynamic deformation of the mitral valve annulus. Ann Biomed Eng 37:1757–1771CrossRefGoogle Scholar
  17. Fan R, Sacks MS (2014) Simulation of planar soft tissues using a structural constitutive model: finite element implementation and validation. J Biomech 47:2043–2054CrossRefGoogle Scholar
  18. Flameng W, Herijgers P, Bogaerts K (2003) Recurrence of mitral valve regurgitation after mitral valve repair in degenerative valve disease. Circulation 107:1609–1613CrossRefGoogle Scholar
  19. Flameng W, Meuris B, Herijgers P, Herregods M-C (2008) Durability of mitral valve repair in Barlow disease versus fibroelastic deficiency. J Thorac Cardiovas Surg 135:274–282CrossRefGoogle Scholar
  20. Fung YC (1991) What are the residual stresses doing in our blood vessels? Ann Biomed Eng 19:237–249CrossRefGoogle Scholar
  21. Fung YC (1993) Biomechanics: mechanical properties of living tissues, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  22. Fung YC, Liu SQ (1991) Changes of zero-stress state of rat pulmonary arteries in hypoxic hypertension. J Appl Physiol 70:2455–2470CrossRefGoogle Scholar
  23. Gilbert TW, Sacks MS, Grashow JS, Woo SL, Badylak SF et al (2006) Fiber kinematics of small intestinal submucosa under biaxial and uniaxial stretch. J Biomech Eng 128:890–898CrossRefGoogle Scholar
  24. Gillinov AM, Blackstone EH, Nowicki ER, Slisatkorn W, Al-Dossari G et al (2008) Valve repair versus valve replacement for degenerative mitral valve disease. J Thorac Cardiovas Surg 135:885–893 e882CrossRefGoogle Scholar
  25. Gorman JH 3rd, Gupta KB, Streicher JT, Gorman RC, Jackson BM et al (1996) Dynamic three-dimensional imaging of the mitral valve and left ventricle by rapid sonomicrometry array localization. J Thorac Cardiovasc Surg 112:712–726CrossRefGoogle Scholar
  26. Grashow JS (2005) Evaluation of the biaxial mechanical properties of the mitral valve anterior leaflet under physiological loading conditions. Master’s Thesis, University of PittsburghGoogle Scholar
  27. Grashow JS, Sacks MS, Liao J, Yoganathan AP (2006a) Planar biaxial creep and stress relaxation of the mitral valve anterior leaflet. Ann Biomed Eng 34:1509–1518CrossRefGoogle Scholar
  28. Grashow JS, Yoganathan AP, Sacks MS (2006b) Biaixal stress-stretch behavior of the mitral valve anterior leaflet at physiologic strain rates. Ann Biomed Eng 34:315–325CrossRefGoogle Scholar
  29. Jassar AS, Brinster CJ, Vergnat M, Robb JD, Eperjesi TJ et al (2011) Quantitative mitral valve modeling using real-time three-dimensional echocardiography: technique and repeatability. Ann Thorac Surg 91:165–171CrossRefGoogle Scholar
  30. Kunzelman KS, Cochran RP, Chuong C, Ring WS, Verrier ED et al (1993) Finite element analysis of the mitral valve. J Heart Valve Dis 2:326–340Google Scholar
  31. Lee CH, Amini R, Gorman RC, Gorman JH 3rd, Sacks MS (2014) An inverse modeling approach for stress estimation in mitral valve anterior leaflet valvuloplasty for in-vivo valvular biomaterial assessment. J Biomech 47:2055–2063CrossRefGoogle Scholar
  32. Lee C-H, Amini R, Sakamoto Y, Carruthers CA, Aggarwal A et al (2015a) Mitral valves: A computational framework. In: Multiscale modeling in biomechanics and mechanobiology. Springer, pp 223–255Google Scholar
  33. Lee C-H, Carruthers CA, Ayoub S, Gorman RC, Gorman JH et al (2015b) Quantification and simulation of layer-specific mitral valve interstitial cells deformation under physiological loading. J Theor Biol 373:26–39CrossRefzbMATHGoogle Scholar
  34. Lee CH, Rabbah JP, Yoganathan AP, Gorman RC, Gorman JH 3rd et al (2015c) On the effects of leaflet microstructure and constitutive model on the closing behavior of the mitral valve. Biomech Model Mechanobiol 14:1281–1302CrossRefGoogle Scholar
  35. Lee CH, Zhang W, Liao J, Carruthers CA, Sacks JI et al (2015d) On the presence of affine fibril and fiber kinematics in the mitral valve anterior leaflet. Biophys J 108:2074–2087CrossRefGoogle Scholar
  36. Liao J, Yang L, Grashow J, Sacks MS (2005) Collagen fibril kinematics in mitral valve leaflet under biaxial elongation, creep, and stress relaxation. In: Society for Heart Valve Disease Third Biennial Meeting, Vancouver. SHVDGoogle Scholar
  37. Liao J, Yang L, Grashow J, Sacks MS (2007) The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet. J Biomech Eng 129:78–87CrossRefGoogle Scholar
  38. May-Newman K, Yin FC (1995) Biaxial mechanical behavior of excised porcine mitral valve leaflets. Am J Physiol 269:H1319–1327Google Scholar
  39. Nevo E, Lanir Y (1994) The effect of residual strain on the diastolic function of the left ventricle as predicted by a structural model. J Biomech 27:1433–1446CrossRefGoogle Scholar
  40. Pierlot CM, Lee JM, Amini R, Sacks MS, Wells SM (2014) Pregnancy-induced remodeling of collagen architecture and content in the mitral valve. Ann Biomed Eng 42:2058–2071CrossRefGoogle Scholar
  41. Pierlot CM, Moeller AD, Lee JM, Wells SM (2015) Pregnancy-induced remodeling of heart valves. Am J Physiol Heart Circ Physiol 309:H1565–1578CrossRefGoogle Scholar
  42. Prot V, Skallerud B (2016) Contributions of prestrains, hyperelasticity, and muscle fiber activation on mitral valve systolic performance Int J Numer Meth Biomed Eng. doi: 10.1002/cnm.2806
  43. Prot V, Skallerud B, Holzapfel G (2007) Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation. Int J Numer Methods Eng 71:987–1008MathSciNetCrossRefzbMATHGoogle Scholar
  44. Prot V, Haaverstad R, Skallerud B (2009) Finite element analysis of the mitral apparatus: Annulus shape effect and chordal force distribution. Biomech Model Mechanobiol 8:43–55CrossRefGoogle Scholar
  45. Rausch MK, Bothe W, Kvitting JP, Goktepe S, Miller DC et al (2011) In vivo dynamic strains of the ovine anterior mitral valve leaflet. J Biomech 44:1149–1157CrossRefGoogle Scholar
  46. Rausch MK, Famaey N, Shultz TO, Bothe W, Miller DC et al (2013) Mechanics of the mitral valve: A critical review, an in vivo parameter identification, and the effect of prestrain. Biomech Model Mechanobiol 12:1053–1071CrossRefGoogle Scholar
  47. Rego BV, Wells SM, Lee CH, Sacks MS (2016) Mitral valve leaflet remodelling during pregnancy: Insights into cell-mediated recovery of tissue homeostasis. J R Soc Interface 13(125):20160709. doi: 10.1098/rsif.2016.0709 CrossRefGoogle Scholar
  48. Sacks MS, Smith DB, Hiester ED (1997) A small angle light scattering device for planar connective tissue microstructural analysis. Ann Biomed Eng 25:678–689CrossRefGoogle Scholar
  49. Sacks MS, He Z, Baijens L, Wanant S, Shah P et al (2002) Surface strains in the anterior leaflet of the functioning mitral valve. Ann Biomed Eng 30:1281–1290CrossRefGoogle Scholar
  50. Sacks MS, Enomoto Y, Graybill JR, Merryman WD, Zeeshan A et al (2006) In-vivo dynamic deformation of the mitral valve anterior leaflet. Ann Thorac Surg 82:1369–1377CrossRefGoogle Scholar
  51. Sacks MS, Zhang W, Wognum S (2016) A novel fibre-ensemble level constitutive model for exogenous cross-linked collagenous tissues. Interface focus 6(1):20150090. doi: 10.1098/rsfs.2015.0090 CrossRefGoogle Scholar
  52. Sakamoto Y, Buchana RM, Sanchez-Adams J, Guilak F, Sacks MS (2017) On the functional role of valve interstitial cell stress fibers: a continuum modeling approach. J Biomech Eng 139:021007CrossRefGoogle Scholar
  53. Votta E, Caiani E, Veronesi F, Soncini M, Montevecchi FM et al (2008) Mitral valve finite-element modelling from ultrasound data: a pilot study for a new approach to understand mitral function and clinical scenarios. Philos Trans A Math Phys Eng Sci 366:3411–3434CrossRefGoogle Scholar
  54. Wang Q, Sun W (2013) Finite element modeling of mitral valve dynamic deformation using patient-specific multi-slices computed tomography scans. Ann Biomed Eng 41:142–153CrossRefGoogle Scholar
  55. Wells SM, Pierlot CM, Moeller AD (2012) Physiological remodeling of the mitral valve during pregnancy. Am J Physiol Heart Circ Physiol 303:H878–892CrossRefGoogle Scholar
  56. Zhang W, Ayoub S, Liao J, Sacks MS (2016) A meso-scale layer-specific structural constitutive model of the mitral heart valve leaflets. Acta Biomater 32:238–255CrossRefGoogle Scholar

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

Personalised recommendations