Abstract
Embryonic heart valves develop under continuous and demanding hemodynamic loading. The particular contributions of fluid pressure and shear tractions in valve morphogenesis are difficult to decouple experimentally. To better understand how fluid loads could direct valve formation, we developed a computational model of avian embryonic atrioventricular (AV) valve (cushion) growth and remodeling using experimentally derived parameters for the blood flow and the cushion stiffness. Through an iterative scheme, we first solved the fluid loads on the axisymmetric AV canal and cushion model geometry. We then applied the fluid loads to the cushion and integrated the evolution equations to determine the growth and remodeling. After a set time of growth, we updated the fluid domain to reflect the change in cushion geometry and resolved for the fluid forces. The rate of growth and remodeling was assumed to be a function of the difference between the current stress and an isotropic homeostatic stress state. The magnitude of the homeostatic stress modulated the rate of volume addition during the evolution. We found that the pressure distribution on the AV cushion was sufficient to generate leaflet-like elongation in the direction of flow, through inducing tissue resorption on the inflow side of cushion and expansion on the outflow side. Conversely, shear tractions minimally altered tissue volume, but regulated the remodeling of tissue near the cushion surface, particular at the leading edge. Significant shear and circumferential residual stresses developed as the cushion evolved. This model offers insight into how natural and perturbed mechanical environments may direct AV valvulogenesis and provides an initial framework on which to incorporate more mechano-biological details.
Similar content being viewed by others
References
Al-Roubaie S, Jahnsen ED, Mohammed M, Henderson-Toth C, Jones EA (2011) Rheology of embryonic avian blood. Am J Physiol Heart C 301(6): H2473–H2481
Ambrosi D, Ateshian GA, Arruda EM, Cowin SC, Dumais J, Goriely A, Holzapfel GA, Humphrey JD, Kemkemer R, Kuhl E, Olberding JE, Taber LA, Garikipati K (2011) Perspectives on biological growth and remodeling. J Mech Phys Solids 59(4): 863–883
Ambrosi D, Guillou A (2007) Growth and dissipation in biological tissues. Continuum Mech Thermodyn 5: 245–251
Bartman T, Walsh EC, Wen KK, McKane M, Ren J, Alexander J, Rubenstein PA, Stainier DY (2004) Early myocardial function affects endocardial cushion development in zebrafish. PLoS Biol 2(5): E129
Bartram U, Molin DG, Wisse LJ, Mohamad A, Sanford LP, Doetschman T, Speer CP, Poelmann RE, Gittenberger de Groot AC (2001) Double-outlet right ventricle and overriding tricuspid valve reflect disturbances of looping, myocardialization, endocardial cushion differentiation, and apoptosis in tgf-beta(2)-knockout mice. Circulation 103(22): 2745–2752
Beloussov LV, Grabovsky VI (2006) Morphomechanics: goals, basic experiments and models. Int J Dev Biol 50(2–3): 81–92
Beloussov LV, Luchinskaia NN (1995) Biomechanical feedback in morphogenesis, as exemplified by stretch responses of amphibian embryonic tissues. Biochem Cell Biol 73(7–8): 555–563
Biechler SV, Potts JD, Yost MJ, Junor L, Goodwin RL, Weidner JW (2010) Mathematical modeling of flow-generated forces in an in vitro system of cardiac valve development. Ann Biomed Eng 38(1): 109–117
Buskohl PR, Gould RA, Butcher JT (2012) Quantification of embryonic atrioventricular valve biomechanics during morphogenesis. J Biomech 45(5): 895–902
Butcher JT, Markwald RR (2007) Valvulogenesis: the moving target. Philos Trans R Soc B 362(1484): 1489–1503
Butcher JT, McQuinn TC, Sedmera D, Turner D, Markwald RR (2007) Transitions in early embryonic atrioventricular valvular function correspond with changes in cushion biomechanics that are predictable by tissue composition. Circ Res 100(10): 1503–1511
Chuong CJ, Fung YC (1986) On residual stresses in arteries. J Biomech Eng 108(2): 189–192
Cowin SC, Van Buskirk WC (1979) Surface bone remodeling induced by a medullary pin. J Biomech 12(4): 269–276
de Lange FJ, Moorman AF, Anderson RH, Manner J, Soufan AT, de Gier-de Vries C, Schneider MD, Webb S, van den Hoff MJ, Christoffels VM (2004) Lineage and morphogenetic analysis of the cardiac valves. Circ Res 95(6): 645–654
Eisenberg LM, Markwald RR (1995) Molecular regulation of atrioventricular valvuloseptal morphogenesis. Circ Res 77(1): 1–6
Forouhar AS, Liebling M, Hickerson A, Nasiraei-Moghaddam A, Tsai HJ, Hove JR, Fraser SE, Dickinson ME, Gharib M (2006) The embryonic vertebrate heart tube is a dynamic suction pump. Science 312(5774): 751–753
Garikipati K, Arruda EM, Grosh K, Narayanan H, Calve S (2004) A continuum treatment of growth in biological tissue: mass transport coupled with mechanics. J Mech Phys Solids 52((7): 1595–1625
Gonzalez-Sanchez A, Bader D (1990) In vitro analysis of cardiac progenitor cell differentiation. Dev Biol 139(1): 197–209
Groenendijk BC, Hierck BP, Vrolijk J, Baiker M, Pourquie MJ, Gittenbergerde Groot AC, Poelmann RE (2005) Changes in shear stress-related gene expression after experimentally altered venous return in the chicken embryo. Circ Res 96(12): 1291–1298
Hinton RB, Lincoln J, Deutsch GH, Osinska H, Manning PB, Benson DW, Yutzey KE (2006) Extracellular matrix remodeling and organization in developing and diseased aortic valves. Circ Res 98(11): 1431–1438
Hogers B, DeRuiter MC, Gittenberger de Groot AC, Poelmann RE (1997) Unilateral vitelline vein ligation alters intracardiac blood flow patterns and morphogenesis in the chick embryo. Circ Res 80(4): 473–481
Hove JR, Koster RW, Forouhar AS, Acevedo-Bolton G, Fraser SE, Gharib M (2003) Intracardiac fluid forces are an essential epigenetic factor for embryonic cardiogenesis. Nature 421(6919): 172–177
Hu N, Clark EB (1989) Hemodynamics of the stage 12 to stage 29 chick embryo. Circ Res 65(6): 1665–1670
Humphrey JD, Rajagopal KR (2003) A constrained mixture model for arterial adaptations to a sustained step change in blood flow. Biomech Model Mech 2(2): 109–126
Kruithof BP, Krawitz SA, Gaussin V (2007) Atrioventricular valve development during late embryonic and postnatal stages involves condensation and extracellular matrix remodeling. Dev Biol 302(1): 208–217
Lin IE, Taber LA (1995) A model for stress-induced growth in the developing heart. J Biomech Eng 117(3): 343–349
Lincoln J, Alfieri CM, Yutzey KE (2004) Development of heart valve leaflets and supporting apparatus in chicken and mouse embryos. Dev Dyn 230(2): 239–250
Lincoln J, Florer JB, Deutsch GH, Wenstrup RJ, Yutzey KE (2006) Colva1 and colxia1 are required for myocardial morphogenesis and heart valve development. Dev Dyn 235(12): 3295–3305
Lubarda VA, Hoger A (2002) On the mechanics of solids with a growing mass. Int J Solids Struct 39(18): 4627–4664
Miller LA (2011) Fluid dynamics of ventricular filling in the embryonic heart. Cell Biochem Biophys 61(1): 33–45
Munoz JJ, Conte V, Miodownik M (2010) Stress-dependent morphogenesis: continuum mechanics and truss systems. Biomech Model Mech 9(4): 451–467
Person AD, Klewer SE, Runyan RB (2005) Cell biology of cardiac cushion development. Int Rev Cytol 243: 287–335
Rachev A, Gleason RL Jr (2011) Theoretical study on the effects of pressure-induced remodeling on geometry and mechanical non-homogeneity of conduit arteries. Biomech Model Mech 10(1): 79–93
Ramasubramanian A, Nerurkar NL, Achtien KH, Filas BA, Voronov DA, Taber LA (2008) On modeling morphogenesis of the looping heart following mechanical perturbations. J Biomech Eng 130(6): 061018
Ramasubramanian A, Taber LA (2008) Computational modeling of morphogenesis regulated by mechanical feedback. Biomech Model Mech 7(2): 77–91
Rodriguez EK, Hoger A, McCulloch AD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27(4): 455–467
Santhanakrishnan A, Miller LA (2011) Fluid dynamics of heart development. Cell Biochem Biophys 61(1): 1–22
Schroeder JA, Jackson LF, Lee DC, Camenisch TD (2003) Form and function of developing heart valves: coordination by extracellular matrix and growth factor signaling. J Mol Med 81(7): 392–403
Sedmera D, Pexieder T, Rychterova V, Hu N, Clark EB (1999) Remodeling of chick embryonic ventricular myoarchitecture under experimentally changed loading conditions. Anat Rec 254(2): 238–252
Snider P, Hinton RB, Moreno-Rodriguez RA, Wang J, Rogers R, Lindsley A, Li F, Ingram DA, Menick D, Field L, Firulli AB, Molkentin JD, Markwald R, Conway SJ (2008) Periostin is required for maturation and extracellular matrix stabilization of noncardiomyocyte lineages of the heart. Circ Res 102(7): 752–760
Taber LA (2008) Theoretical study of beloussov’s hyper-restoration hypothesis for mechanical regulation of morphogenesis. Biomech Model Mech 7(6): 427–441
Taber LA (2009) Towards a unified theory for morphomechanics. Philos Trans R Soc A 367(1902): 3555–3583
Taber LA, Humphrey LA (2001) Stress-modulated growth, residual stress, and vascular heterogeneity. J Biomech Eng 123(6): 528–535
Taber LA, Zhang J, Perucchio R (2007) Computational model for the transition from peristaltic to pulsatile flow in the embryonic heart tube. J Biomech Eng 129(3): 441–449
Vermot J, Forouhar AS, Liebling M, Wu D, Plummer D, Gharib M, Fraser SE (2009) Reversing blood flows act through klf2a to ensure normal valvulogenesis in the developing heart. PLoS Biol 7(11): e1000246
Yalcin HC, Shekhar A, McQuinn TC, Butcher JT (2011) Hemodynamic patterning of the avian atrioventricular valve. Dev Dyn 240(1): 23–35
Author information
Authors and Affiliations
Corresponding author
Electronic Supplementary Material
The Below is the Electronic Supplementary Material.
Rights and permissions
About this article
Cite this article
Buskohl, P.R., Jenkins, J.T. & Butcher, J.T. Computational simulation of hemodynamic-driven growth and remodeling of embryonic atrioventricular valves. Biomech Model Mechanobiol 11, 1205–1217 (2012). https://doi.org/10.1007/s10237-012-0424-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10237-012-0424-5