Tricuspid valve leaflet strains in the beating ovine heart

  • M. Mathur
  • T. Jazwiec
  • W. D. Meador
  • M. Malinowski
  • M. Goehler
  • H. Ferguson
  • T. A. Timek
  • M. K. RauschEmail author
Original Paper


The tricuspid leaflets coapt during systole to facilitate proper valve function and, thus, ensure efficient transport of deoxygenated blood to the lungs. Between their open state and closed state, the leaflets undergo large deformations. Quantification of these deformations is important for our basic scientific understanding of tricuspid valve function and for diagnostic or prognostic purposes. To date, tricuspid valve leaflet strains have never been directly quantified in vivo. To fill this gap in our knowledge, we implanted four sonomicrometry crystals per tricuspid leaflet and six crystals along the tricuspid annulus in a total of five sheep. In the beating ovine hearts, we recorded crystal coordinates alongside hemodynamic data. Once recorded, we used a finite strain kinematic framework to compute the temporal evolutions of area strain, radial strain, and circumferential strain for each leaflet. We found that leaflet strains were larger in the anterior leaflet than the posterior and septal leaflets. Additionally, we found that radial strains were larger than circumferential strains. Area strains were as large as 97% in the anterior leaflet, 31% in the posterior leaflet, and 31% in the septal leaflet. These data suggest that tricuspid valve leaflet strains are significantly larger than those in the mitral valve. Should our findings be confirmed they could suggest either that the mechanobiological equilibrium of tricuspid valve resident cells is different than that of mitral valve resident cells or that the mechanotransductive apparatus between the two varies. Either phenomenon may have important implications for the development of tricuspid valve-specific surgical techniques and medical devices.


Mechanics Kinematics Deformation Right heart Sheep Sonomicrometry 



This study was supported by an internal Grant from the Meijer Heart and Vascular Institute at Spectrum Health.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

Supplementary material 1 (MP4 26454 kb)

Supplementary material 2 (MP4 26388 kb)

Supplementary material 3 (MP4 25270 kb)


  1. Amini R, Eckert CE, Koomalsingh K et al (2012) On the in vivo deformation of the mitral valve anterior leaflet: effects of annular geometry and referential configuration. Ann Biomed Eng 40:1455–1467. CrossRefGoogle Scholar
  2. Beaudoin J, Thai WE, Wai B et al (2013) Assessment of mitral valve adaptation with gated cardiac computed tomography: validation with three-dimensional echocardiography and mechanistic insight to functional mitral regurgitation. Circ Cardiovasc Imaging 6:784–789. CrossRefGoogle Scholar
  3. Benedetto U, Melina G, Angeloni E et al (2012) Prophylactic tricuspid annuloplasty in patients with dilated tricuspid annulus undergoing mitral valve surgery. J Thorac Cardiovasc Surg 143:632–638. CrossRefGoogle Scholar
  4. Bertrand PB, Koppers G, Verbrugge FH et al (2014) Tricuspid annuloplasty concomitant with mitral valve surgery: effects on right ventricular remodeling. J Thorac Cardiovasc Surg 147:1256–1264. CrossRefGoogle Scholar
  5. Bothe W, Kuhl E, Kvitting J-PE, et al (2011a) Rigid, complete annuloplasty rings increase anterior mitral leaflet strains in the normal beating ovine heart. Circulation, vol 124.
  6. Bothe W, Kuhl E, Kvitting JPE et al (2011b) Rigid, complete annuloplasty rings increase anterior mitral leaflet strains in the normal beating ovine heart. Circulation 124:S81–S96. CrossRefGoogle Scholar
  7. Bouleti C, Juliard JM, Himbert D et al (2016) Tricuspid valve and percutaneous approach: no longer the forgotten valve! Arch Cardiovasc Dis 109:55–66. CrossRefGoogle Scholar
  8. Braunwald NS, Ross J, Moruow AG, Morrow AG (1967) Conservative management of tricuspid regurgitation in patients undergoing mitral valve replacement. Circulation 35:I63–I69. CrossRefGoogle Scholar
  9. Chaput M, Handschumacher MD, Guerrero JL et al (2009) Mitral leaflet adaptation to ventricular remodeling prospective changes in a model of ischemic mitral regurgitation. Circulation 120:S99–S103. CrossRefGoogle Scholar
  10. Cirak F, Ortiz M, Schröder P (2000) Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. Int J Numer Methods Eng 47:2039–2072.;2-1 CrossRefzbMATHGoogle Scholar
  11. Dal-Bianco JP, Levine RA (2015) The mitral valve is an actively adapting tissue: new imaging evidence. Eur Heart J Cardiovasc Imaging 16:286–287. CrossRefGoogle Scholar
  12. Göktepe S, Bothe W, Kvitting J-P et al (2010) Anterior mitral leaflet curvature in the beating ovine heart: a case study using videofluoroscopic markers and subdivision surfaces. Biomech Model Mechanobiol 9:281–293. CrossRefGoogle Scholar
  13. Grande-Allen KJ, Liao J (2011) The heterogeneous biomechanics and mechanobiology of the mitral valve: implications for tissue engineering. Curr Cardiol Rep 13:113–120. CrossRefGoogle Scholar
  14. Jazwiec T, Malinowski M, Proudfoot AG et al (2018) Tricuspid valvular dynamics and 3-dimensional geometry in awake and anesthetized sheep. J Thorac Cardiovasc Surg 156:1503–1511. CrossRefGoogle Scholar
  15. Kamensky D, Xu F, Lee C-HH et al (2018) A contact formulation based on a volumetric potential: application to isogeometric simulations of atrioventricular valves. Comput Methods Appl Mech Eng 330:522–546. MathSciNetCrossRefGoogle Scholar
  16. Khoiy K, Biswas D, Decker TN et al (2016) Surface strains of porcine tricuspid valve septal leaflets measured in ex vivo beating hearts. J Biomech Eng 138:111006. CrossRefGoogle Scholar
  17. Kong F, Pham T, Martin C et al (2018) Finite element analysis of tricuspid valve deformation from multi-slice computed tomography images. Ann Biomed Eng 46:1112–1127. CrossRefGoogle Scholar
  18. Loop CT (1987) Smooth subdivision surfaces based on triangles. Department of Mathematics, The University of Utah, Masters ThesisGoogle Scholar
  19. Madukauwa-David ID, Pierce EL, Sulejmani F et al (2018) Suture dehiscence and collagen content in the human mitral and tricuspid annuli. Biomech Model Mechanobiol. Google Scholar
  20. Malinowski M, Wilton P, Khaghani A et al (2016a) The effect of pulmonary hypertension on ovine tricuspid annular dynamics. Eur J Cardio-thoracic Surg 49:40–45. CrossRefGoogle Scholar
  21. Malinowski M, Wilton P, Khaghani A et al (2016b) The effect of acute mechanical left ventricular unloading on ovine tricuspid annular size and geometry. Interact CardioVasc Thorac Surg 23:391–396. CrossRefGoogle Scholar
  22. Malinowski M, Jazwiec T, Goehler M et al (2018) Sonomicrometry derived three-dimensional geometry of the human tricuspid annulus. J Thorac Cardiovasc Surg. Google Scholar
  23. Mascherbauer J, Maurer G (2010) The forgotten valve: lessons to be learned in tricuspid regurgitation. Eur Heart J 31:2841–2843. CrossRefGoogle Scholar
  24. Meador WD, Malinowski M, Jazwiec T et al (2018) A fiduciary marker-based framework to assess heterogeneity and anisotropy of right ventricular epicardial strains in the beating ovine heart. J Biomech 80:179–185. CrossRefGoogle Scholar
  25. Merryman WD, Youn I, Lukoff HD et al (2006) Correlation between heart valve interstitial cell stiffness and transvalvular pressure: implications for collagen biosynthesis. Am J Physiol Heart Circ Physiol 290:224–231. CrossRefGoogle Scholar
  26. Pierlot CM, Lee JM, Amini R, et al (2014) Pregnancy-induced remodeling of collagen architecture and content in the mitral valve. Ann Biomed Eng, vol 42.
  27. Rausch MK, Kuhl E (2013) On the effect of prestrain and residual stress in thin biological membranes. J Mech Phys Solids 61:1955–1969. MathSciNetCrossRefGoogle Scholar
  28. Rausch MK, Bothe W, Kvitting JPE et al (2011) In vivo dynamic strains of the ovine anterior mitral valve leaflet. J Biomech 44:1149–1157. CrossRefGoogle Scholar
  29. Rausch MK, Tibayan FA, Craig Miller D, Kuhl E (2012) Evidence of adaptive mitral leaflet growth. J Mech Behav Biomed Mater 15:208–217. CrossRefGoogle Scholar
  30. Rausch MK, Famaey N, Shultz TOB et al (2013) Mechanics of the mitral valve: a critical review, an in vivo parameter identification, and the effect of prestrain. Biomech Model Mechanobiol 12:1053–1071. CrossRefGoogle Scholar
  31. Rausch MK, Genet M, Humphrey JD (2017a) An augmented iterative method for identifying a stress-free reference configuration in image-based biomechanical modeling. J Biomech 58:227–231. CrossRefGoogle Scholar
  32. Rausch MK, Malinowski M, Wilton P et al (2017b) Engineering analysis of tricuspid annular dynamics in the beating ovine heart. Ann Biomed Eng 9:365–376. Google Scholar
  33. Rausch MK, Malinowski M, Meador WD et al (2018) The effect of acute pulmonary hypertension on tricuspid annular height, strain, and curvature in sheep. Cardiovasc Eng Technol 9:365–376. CrossRefGoogle Scholar
  34. Sacks MS, Yoganathan AP (2007) Heart valve function: a biomechanical perspective. Philos Trans R Soc B Biol Sci 362:1369–1391. CrossRefGoogle Scholar
  35. Sacks MS, He Z, Baijens L et al (2002) Surface strains in the anterior leaflet of the functioning mitral valve. Ann Biomed Eng 30:1281–1290. CrossRefGoogle Scholar
  36. Sacks MS, Enomoto Y, Graybill JR et al (2006) In-vivo dynamic deformation of the mitral valve anterior leaflet. Ann Thorac Surg 82:1369–1377. CrossRefGoogle Scholar
  37. Silver MD, Lam JHC, Ranganathan N, Wigle ED (1971) Morphology of the human tricuspid valve. Circulation 43:333–348. CrossRefGoogle Scholar
  38. Singh-Gryzbon S, Siefert AW, Pierce EL, Yoganathan AP (2019) Tricuspid valve annular mechanics: interactions with and implications for transcatheter devices. Cardiovasc Eng Technol. pp 1–12.
  39. Spinner EM, Buice D, Yap CH, Yoganathan AP (2012) The effects of a three-dimensional, saddle-shaped annulus on anterior and posterior leaflet stretch and regurgitation of the tricuspid valve. Ann Biomed Eng 40:996–1005. CrossRefGoogle Scholar
  40. Stevanella M, Votta E, Lemma M et al (2010) Finite element modelling of the tricuspid valve: a preliminary study. Med Eng Phys 32:1213–1223. CrossRefGoogle Scholar
  41. Taramasso M, Pozzoli A, Guidotti A et al (2017) Percutaneous tricuspid valve therapies: the new frontier. Eur Heart J 38:639–647. CrossRefGoogle Scholar
  42. Taylor PM, Batten P, Brand NJ et al (2003) The cardiac valve interstitial cell. Int J Biochem Cell Biol 35:113–118. CrossRefGoogle Scholar
  43. Ton-Nu TT, Levine RA, Handschumacher MD et al (2006) Geometric determinants of functional tricuspid regurgitation: insights from 3-dimensional echocardiography. Circulation 114:143–149. CrossRefGoogle Scholar
  44. Weinberg EJ, Shahmirzadi D, Mofrad MRK (2010) On the multiscale modeling of heart valve biomechanics in health and disease. Biomech Model Mechanobiol 9:373–387. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • M. Mathur
    • 1
  • T. Jazwiec
    • 2
    • 3
  • W. D. Meador
    • 4
  • M. Malinowski
    • 2
    • 5
  • M. Goehler
    • 2
  • H. Ferguson
    • 2
  • T. A. Timek
    • 2
  • M. K. Rausch
    • 4
    • 6
    • 7
    Email author
  1. 1.Department of Mechanical EngineeringUniversity of Texas at AustinAustinUSA
  2. 2.Division of Cardiothoracic SurgerySpectrum HealthGrand RapidsUSA
  3. 3.Department of Cardiac, Vascular and Endovascular Surgery and TransplantologyMedical University of Silesia in Katowice, Silesian Centre for Heart DiseasesZabrzePoland
  4. 4.Department of Biomedical EngineeringUniversity of Texas at AustinAustinUSA
  5. 5.Department of Cardiac Surgery, School of Medicine in KatowiceMedical University of SilesiaKatowicePoland
  6. 6.Department of Aerospace Engineering and Engineering MechanicsUniversity of Texas at AustinAustinUSA
  7. 7.The Institute for Computational Engineering and SciencesUniversity of Texas at AustinAustinUSA

Personalised recommendations