{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T20:29:53Z","timestamp":1764880193727,"version":"build-2065373602"},"reference-count":63,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2020,9,5]],"date-time":"2020-09-05T00:00:00Z","timestamp":1599264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000182","name":"Medical Research and Materiel Command","doi-asserted-by":"publisher","award":["W81XWH-17-C-0207"],"award-info":[{"award-number":["W81XWH-17-C-0207"]}],"id":[{"id":"10.13039\/100000182","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJMS"],"abstract":"<jats:p>Surgical simulators and injury-prediction human models require a combination of representative tissue geometry and accurate tissue material properties to predict realistic tool\u2013tissue interaction forces and injury mechanisms, respectively. While biological tissues have been individually characterized, the transition regions between tissues have received limited research attention, potentially resulting in inaccuracies within simulations. In this work, an approach to characterize the transition regions in transversely isotropic (TI) soft tissues using functionally graded material (FGM) modeling is presented. The effect of nonlinearities and multi-regime nature of the TI model on the functional grading process is discussed. The proposed approach has been implemented to characterize the transition regions in the leaflet (LL), chordae tendinae (CT) and the papillary muscle (PM) of porcine tricuspid valve (TV) and mitral valve (MV). The FGM model is informed using high resolution morphological measurements of the collagen fiber orientation and tissue composition in the transition regions, and deformation characteristics predicted by the FGM model are numerically validated to experimental data using X-ray diffraction imaging. The results indicate feasibility of using the FGM approach in modeling soft-tissue transitions and has implications in improving physical representation of tissue deformation throughout the body using a scalable version of the proposed approach.<\/jats:p>","DOI":"10.3390\/ijms21186503","type":"journal-article","created":{"date-parts":[[2020,9,6]],"date-time":"2020-09-06T23:12:49Z","timestamp":1599433969000},"page":"6503","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Functional Grading of a Transversely Isotropic Hyperelastic Model with Applications in Modeling Tricuspid and Mitral Valve Transition Regions"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2795-056X","authenticated-orcid":false,"given":"Rajarshi","family":"Roy","sequence":"first","affiliation":[{"name":"Corvid Technologies, Mooresville, NC 28117, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"suffix":"Jr.","given":"Eric","family":"Warren","sequence":"additional","affiliation":[{"name":"School of Medicine, Duke University, Durham, NC 27708, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaoyao","family":"Xu","sequence":"additional","affiliation":[{"name":"Corvid Technologies, Mooresville, NC 28117, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Caleb","family":"Yow","sequence":"additional","affiliation":[{"name":"Corvid Technologies, Mooresville, NC 28117, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9477-9171","authenticated-orcid":false,"given":"Rama S.","family":"Madhurapantula","sequence":"additional","affiliation":[{"name":"Department of Biology, Illinois Institute of Technology, Chicago, IL 60616, USA"},{"name":"Pritzker Institute of Biomedical Science and Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1050-9391","authenticated-orcid":false,"given":"Joseph P. 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Innov."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2558","DOI":"10.1007\/s10439-015-1546-6","article-title":"Validation of shoulder response of human body finite-element model (GHBMC) under whole body lateral impact condition","volume":"44","author":"Park","year":"2016","journal-title":"Ann. Biomed. Eng."},{"key":"ref_3","first-page":"175","article-title":"Development of the CAVEMAN human body model: Validation of lower extremity sub-injurious response to vertical accelerative loading","volume":"61","author":"Butz","year":"2017","journal-title":"Stapp Car Crash J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1249\/00003677-199101000-00012","article-title":"12 Myotendinous Junction Injury in Relation to Junction Structure and Molecular Composition","volume":"19","author":"Tidball","year":"1991","journal-title":"Exerc. Sport Sci. Rev."},{"key":"ref_5","first-page":"644","article-title":"Failure mechanics of mitral valve chordae tendineae","volume":"11","author":"Sedransk","year":"2002","journal-title":"J. Heart Valve Dis."},{"key":"ref_6","first-page":"133","article-title":"Design optimization of functionally graded dental implant","volume":"14","author":"Hedia","year":"2004","journal-title":"Bio-Med. Mater. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.jmbbm.2007.11.002","article-title":"Engineering functionally graded tissue engineering scaffolds","volume":"1","author":"Leong","year":"2008","journal-title":"J. Mech. Behav. Biomed."},{"key":"ref_8","first-page":"53","article-title":"The development of the myotendinous junction: A review","volume":"2","author":"Charvet","year":"2012","journal-title":"Muscles Ligaments Tendons J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1023\/B:ABME.0000032460.97278.e9","article-title":"Relationship between collagen fibrils, glycosaminoglycans, and stress relaxation in mitral valve chordae tendineae","volume":"32","author":"Liao","year":"2004","journal-title":"Ann. Biomed. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1002\/mus.880070213","article-title":"Regulation of sarcomere number in skeletal muscle: A comparison of hypotheses","volume":"7","author":"Herring","year":"1984","journal-title":"Muscle Nerve"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1146\/annurev-bioeng-062117-121129","article-title":"A contemporary look at biomechanical models of myocardium","volume":"21","author":"Avazmohammadi","year":"2019","journal-title":"Annu. Rev. Biomed. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1002\/nme.1983","article-title":"Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation","volume":"71","author":"Prot","year":"2007","journal-title":"Int. J. Numer. Meth. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.jmbbm.2009.05.004","article-title":"On modelling and analysis of healthy and pathological human mitral valves: Two case studies","volume":"3","author":"Prot","year":"2010","journal-title":"J. Mech. Behav. Biomed."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/0021-9290(87)90279-X","article-title":"Quantification of the mechanical properties of noncontracting canine myocardium under simultaneous biaxial loading","volume":"20","author":"Yin","year":"1987","journal-title":"J. Biomech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1115\/1.2049337","article-title":"Simulated bioprosthetic heart valve deformation under quasi-static loading","volume":"127","author":"Sun","year":"2005","journal-title":"J. Biomech. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1233","DOI":"10.1098\/rsta.2001.0828","article-title":"Modelling cardiac mechanical properties in three dimensions","volume":"359","author":"Costa","year":"2001","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1007\/s10237-005-0075-x","article-title":"Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues","volume":"4","author":"Sun","year":"2005","journal-title":"Biomech. Model. Mechanobiol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"H1243","DOI":"10.1152\/ajpheart.00484.2008","article-title":"Three-dimensional transmural organization of perimysial collagen in the heart","volume":"295","author":"Pope","year":"2008","journal-title":"Am. J. Physiol.-Heart C"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1115\/1.1287158","article-title":"Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: Part II\u2014A structural constitutive model","volume":"122","author":"Billiar","year":"2000","journal-title":"J. Biomech. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1007\/s10237-005-0069-8","article-title":"Invariant formulation for dispersed transverse isotropy in aortic heart valves","volume":"4","author":"Freed","year":"2005","journal-title":"Biomech. Model. Mechanobiol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/A:1010917028671","article-title":"Biaxial mechanical evaluation of planar biological materials","volume":"61","author":"Sacks","year":"2000","journal-title":"J. Elast."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1007\/s10439-015-1385-5","article-title":"Fluid\u2013structure interaction analysis of papillary muscle forces using a comprehensive mitral valve model with 3D chordal structure","volume":"44","author":"Toma","year":"2016","journal-title":"Ann. Biomed. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1098\/rstb.2007.2123","article-title":"Fluid\u2013structure interaction models of the mitral valve: Function in normal and pathological states","volume":"362","author":"Kunzelman","year":"2007","journal-title":"Philos. Trans. R. Soc. B"},{"key":"ref_24","unstructured":"Hunter, P., Nash, M., and Sands, G. (1997). Computational Electromechanics of the Heart. Computational Biology of the Heart, Wiley."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3445","DOI":"10.1098\/rsta.2009.0091","article-title":"Constitutive modelling of passive myocardium: A structurally based framework for material characterization","volume":"367","author":"Holzapfel","year":"2009","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1098\/rsif.2005.0073","article-title":"Hyperelastic modelling of arterial layers with distributed collagen fibre orientations","volume":"3","author":"Gasser","year":"2006","journal-title":"J. R. Soc. Interface"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2766","DOI":"10.1016\/j.jbiomech.2008.05.033","article-title":"A new constitutive model for multi-layered collagenous tissues","volume":"41","author":"Kroon","year":"2008","journal-title":"J. Biomech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.actbio.2015.12.001","article-title":"A meso-scale layer-specific structural constitutive model of the mitral heart valve leaflets","volume":"32","author":"Zhang","year":"2016","journal-title":"Acta Biomater."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1146\/annurev-bioeng-071813-104517","article-title":"Computational modeling of cardiac valve function and intervention","volume":"16","author":"Sun","year":"2014","journal-title":"Annu. Rev. Biomed. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1146\/annurev.bioeng.5.011303.120714","article-title":"Multiaxial mechanical behavior of biological materials","volume":"5","author":"Sacks","year":"2003","journal-title":"Annu. Rev. Biomed. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1115\/1.1695569","article-title":"The structure and mechanical properties of the mitral valve leaflet-strut chordae transition zone","volume":"126","author":"Chen","year":"2004","journal-title":"J. Biomech. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.jbiomech.2017.01.039","article-title":"A functionally graded material model for the transmural stress distribution of the aortic valve leaflet","volume":"54","author":"Rego","year":"2017","journal-title":"J. Biomech."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.euromechsol.2014.04.001","article-title":"The living heart project: A robust and integrative simulator for human heart function","volume":"48","author":"Baillargeon","year":"2014","journal-title":"Eur. J. Mech. A Solid"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.medengphy.2017.06.042","article-title":"A coupled mitral valve\u2014Left ventricle model with fluid\u2013structure interaction","volume":"47","author":"Gao","year":"2017","journal-title":"Med. Eng. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1080\/15389588.2013.799278","article-title":"Validation of simulated chestband data in frontal and lateral loading using a human body finite element model","volume":"15","author":"Hayes","year":"2014","journal-title":"Traffic Inj. Prev."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1016\/j.jbiomech.2016.02.007","article-title":"A validated numerical model of a lower limb surrogate to investigate injuries caused by under-vehicle explosions","volume":"49","author":"Newell","year":"2016","journal-title":"J. Biomech."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"S49","DOI":"10.1080\/15389588.2015.1021418","article-title":"Development of a computationally efficient full human body finite element model","volume":"16","author":"Schwartz","year":"2015","journal-title":"Traffic Inj. Prev."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/0045-7825(96)01035-3","article-title":"Finite element implementation of incompressible, transversely isotropic hyperelasticity","volume":"135","author":"Weiss","year":"1996","journal-title":"Comp. Method Appl. M."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1686","DOI":"10.1016\/j.jbiomech.2005.04.030","article-title":"A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint","volume":"39","author":"Pena","year":"2006","journal-title":"J. Biomech."},{"key":"ref_40","unstructured":"Weiss, J. (1995). A Constitutive Model and Finite Element Representation for Transversely Isotropic Soft Tissues. [Ph.D. Thesis, The University of Utah]."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3598","DOI":"10.1016\/j.jbiomech.2014.10.001","article-title":"Subject-specific finite element analysis to characterize the influence of geometry and material properties in Achilles tendon rupture","volume":"47","author":"Shim","year":"2014","journal-title":"J. Biomech."},{"key":"ref_42","unstructured":"Hallquist, J. (2020, September 04). LS-DYNA Theory Manual. Available online: http:\/\/www.lstc.com\/pdf\/ls-dyna_theory_manual_2006.pdf."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"011005","DOI":"10.1115\/1.4005694","article-title":"FEBio: Finite elements for biomechanics","volume":"134","author":"Maas","year":"2012","journal-title":"J. Biomech. Eng."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Madhurapantula, R., Krell, G., Morfin, B., Roy, R., Lister, K., and Orgel, J. (2020). Advanced methodology and preliminary measurements of molecular and mechanical properties of heart valves under dynamic strain. Int. J. Mol. Sci., 21.","DOI":"10.3390\/ijms21030763"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3657","DOI":"10.1016\/j.ijsolstr.2005.04.011","article-title":"Mechanical behavior of functionally graded material plates under transverse load\u2014Part I: Analysis","volume":"43","author":"Chi","year":"2006","journal-title":"Int. J. Solids Struct."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijmecsci.2015.09.012","article-title":"Stress analysis of thick pressure vessel composed of functionally graded incompressible hyperelastic materials","volume":"104","author":"Anani","year":"2015","journal-title":"Int. J. Mech. Sci."},{"key":"ref_47","first-page":"1","article-title":"New Methodology and Preliminary Data in the Characterization of the Muscle Tendon Junction of Mammalian Muscle Tissues","volume":"1","author":"Madhurapantula","year":"2017","journal-title":"EMS Eng. Sci. J."},{"key":"ref_48","unstructured":"Adams, B., Bohnhoff, W., Dalbey, K., Eddy, J., Eldred, M., Gay, D., Haskell, K., Hough, P., and Swiler, L. (2009). DAKOTA, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 5.0 User\u2019s Manual, Tech. Rep. SAND2010-2183."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"3675","DOI":"10.1016\/j.ijsolstr.2005.04.010","article-title":"Mechanical behavior of functionally graded material plates under transverse load\u2014Part II: Numerical results","volume":"43","author":"Chi","year":"2006","journal-title":"Int. J. Solids Struct"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.actbio.2016.08.027","article-title":"Probing multi-scale mechanical damage in connective tissues using X-ray diffraction","volume":"45","author":"Bianchi","year":"2016","journal-title":"Acta Biomater."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2074","DOI":"10.1016\/j.bpj.2015.03.019","article-title":"On the presence of affine fibril and fiber kinematics in the mitral valve anterior leaflet","volume":"108","author":"Lee","year":"2015","journal-title":"Biophys. J."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1016\/S0021-9290(97)00019-5","article-title":"A method to quantify the fiber kinematics of planar tissues under biaxial stretch","volume":"30","author":"Billiar","year":"1997","journal-title":"J. Biomech."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1115\/1.2401186","article-title":"The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet","volume":"129","author":"Liao","year":"2007","journal-title":"J. Biomech. Eng."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.bpj.2016.05.038","article-title":"Nanomechanics of type I collagen","volume":"111","author":"Varma","year":"2016","journal-title":"Biophys. J."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1006\/jsbi.1998.3966","article-title":"Fibrillar structure and mechanical properties of collagen","volume":"122","author":"Fratzl","year":"1998","journal-title":"J. Struct. Biol."},{"key":"ref_56","unstructured":"Neice, R. (2019). Development and Validation of a Pelvis Finite Element Model for Side Panel Intrusion Threats. [Master\u2019s Thesis, University of Virginia]."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1010835316564","article-title":"A new constitutive framework for arterial wall mechanics and a comparative study of material models","volume":"61","author":"Holzapfel","year":"2000","journal-title":"J. Elast."},{"key":"ref_58","unstructured":"(2020, September 03). Solid 3D Human Heart Model. Available online: https:\/\/www.zygote.com\/cad-models\/solid-3d-human-anatomy\/solid-3d-human-heart."},{"key":"ref_59","first-page":"1551","article-title":"Constitutive modelling of arteries","volume":"466","author":"Holzapfel","year":"2010","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1016\/j.jmbbm.2016.04.024","article-title":"On the accuracy and fitting of transversely isotropic material models","volume":"61","author":"Feng","year":"2016","journal-title":"J. Mech. Behav. Biomed."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1016\/S0969-2126(01)00669-4","article-title":"The in situ supermolecular structure of type I collagen","volume":"9","author":"Orgel","year":"2001","journal-title":"Structure"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Orgel, J., and Irving, T. (2014). Advances in Fiber Diffraction of Macromolecular Assembles. Encyclopedia of Analytical Chemistry: Applications, Theory and Instrumentation, Wiley.","DOI":"10.1002\/9780470027318.a9420"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1016\/j.bpj.2009.05.043","article-title":"Functional grading of mineral and collagen in the attachment of tendon to bone","volume":"97","author":"Genin","year":"2009","journal-title":"Biophys. J."}],"container-title":["International Journal of Molecular Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1422-0067\/21\/18\/6503\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:07:13Z","timestamp":1760177233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1422-0067\/21\/18\/6503"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,5]]},"references-count":63,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["ijms21186503"],"URL":"https:\/\/doi.org\/10.3390\/ijms21186503","relation":{},"ISSN":["1422-0067"],"issn-type":[{"type":"electronic","value":"1422-0067"}],"subject":[],"published":{"date-parts":[[2020,9,5]]}}}