Abstract
Mechanical forces cause changes in form during embryogenesis and likely play a role in regulating these changes. This paper explores the idea that changes in homeostatic tissue stress (target stress), possibly modulated by genes, drive some morphogenetic processes. Computational models are presented to illustrate how regional variations in target stress can cause a range of complex behaviors involving the bending of epithelia. These models include growth and cytoskeletal contraction regulated by stress-based mechanical feedback. All simulations were carried out using the commercial finite element code ABAQUS, with growth and contraction included by modifying the zero-stress state in the material constitutive relations. Results presented for bending of bilayered beams and invagination of cylindrical and spherical shells provide insight into some of the mechanical aspects that must be considered in studying morphogenetic mechanisms.
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References
ABAQUS/Standard User’s Manual. Volumes I and III (2003) ABAQUS, Inc. Providence, RI
Agoram B, Barocas VH (2001) Coupled macroscopic and microscopic scale modeling of fibrillar tissues and tissue equivalents. J Biomech Eng 123:362–369
Barocas VH, Tranquillo RT (1997) An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance. J Biomech Eng 119:137–145
Belintsev BN, Beloussov LV, Zaraisky AG (1987) Model of pattern formation in epithelial morphogenesis. J Theor Biol 129:369–394
Beloussov LV, Dorfman JG, Cherdantzev VG (1975) Mechanical stresses and morphological patterns in amphibian embryos. J Embryol Exp Morphol 34:559–574
Beloussov LV (1998) The dynamic architecture of a developing organism: an interdisciplinary approach to the development of organisms. Kluwer, Dordrecht
Beysens DA, Forgacs, G, Glazier JA (2000) Cell sorting is analogous to phase ordering in fluids. Proc Nat Acad Sci 97:9467–9471
Brodland GW (2002) The differential interfacial tension hypothesis (DITH): a comprehensive theory for the self-rearrangement of embryonic cells and tissues. J Biomech Eng 124:188–197
Brodland GW, Chen HH (2000) The mechanics of heterotypic cell aggregates: Insights from computer simulations. J Biomech Eng 122:402–407
Brodland GW, Clausi DA (1994) Embryonic tissue morphogenesis modeled by FEM. J Biomech Eng 116:164–155
Chen HH, Brodland GW (2000) Cell-level finite element studies of viscous cells in planar aggregates. J Biomech Eng 122:394–401
Clausi DA, Brodland GW (1993) Mechanical evaluation of theories of neurulation using computer simulations. Development 118:1013–1023
Davidson LA, Koehl MAR, Keller R, Oster GF (1995) How do sea urchins invaginate? Using biomechanics to distinguish between mechanisms of primary invagination. Development 121:2005–2018
Davidson LA, Oster GF, Keller RE, Koehl MAR (1999) Measurements of mechanical properties of the blastula wall reveal which hypothesized mechanisms of primary invagination are physically plausible in the sea urchin stronglylocentrotus purpuratus. Dev Biol 209:221–238
Davies JA (2005) Mechanics of morphogenesis. Elsevier Academic Press, New York
Forgacs G, Foty RA, Shafrir Y, Steinberg MS (1998) Viscoelastic properties of living embryonic tissues: a quantitative study. Biophys J 74:2227–2234
Franklin GF, Powell JD, Workman ML (1997) Digital control of dynamic systems, 3rd edn. Addison Wesley Longman, Menlo Park
Gilbert SF (2006) Developmental biology, 8th edn. Sinauer Associates, Sunderland
Gordon R (2006) Mechanics in embryogenesis and embryonics: prime mover or epiphenomenon?. Int J Dev Biol 50:245–253
Holzapfel GA (2001) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, West Sussex
Keller R, Davidson LA, Shook DR (2003) How we are shaped: the biomechanics of gastrulation. Differentiation 71:171–205
Lubarda VA, Hoger A (2002) On the mechanics of solids with a growing mass. Int J Solids Struct 39:4627–4664
Manoussaki D, Lubkin SR, Vernon RB, Murray JD (1996) A mechanical model for the formation of vascular networks in vitro. Acta Biotheor 44:271–282
Munoz JJ, Barrett K, Mindownik M (2006) A deformation gradient decomposition method for the analysis of the mechanics of morphogenesis. J Biomech (in press)
Murray JD (1993) Mathematical Biology. Springer, New York
Murray JD, Oster GF (1984) Cell traction models for generating pattern and form in morphogenesis. J Math Biol 19:265–280
Namy P, Ohayon J, Tracqui P (2004) Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields. J Theor Biol 227:103–120
Odell GM, Oster G, Alberch P, Burnside B (1981) The mechanical basis of morphogenesis. I. epithelial folding and investigation. Dev Biol 85:446–462
Oster GF, Murray JD, Harris AK (1983) Mechanical aspects of mesenchymal morphogenesis. J Embryol Exp Morphol 78:83–125
Ramasubramanian A, Latacha KS, Benjamin JM, Voronov DA, Ravi A, and Taber LA (2006) Computational model for early cardiac looping. Ann Biomed Eng 34:1355–1369
Rodriguez EK, Hoger A, McCulloch AD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27: 455–467
Taber LA, Hu N, Pexieder T, Clark EB, Keller BB (1993) Residual strain in the ventricle of the stage 16–24 chick embryo. Circul Res 72:455–462
Taber LA (1995) Biomechanics of growth, remodeling, and morphogenesis. Appl Mech Rev 48:487–545
Taber LA (2000) Pattern formation in a nonlinear membrane model for epithelial morphogenesis. Acta Biotheoretica 48:47–63
Taber LA (2001) Biomechanics of cardiovascular development. Ann Rev Biomed Eng 3:1–25
Taber LA (2004) Nonlinear theory of elasticity: Applications in biomechanics. World Scientific, Singapore
Taber LA (2005) Biophysical mechanisms of cardiac looping. Int J Dev Biol 50:323–332
Taber LA, Perucchio R (2000) Modeling heart development. J Elast 61:165–197
Taber LA, Zahalak GI (2001) Theoretical model for myocardial trabeculation. Dev Dyn 220:226–237
Viamontes GI, Kirk DL (1977) Cell shape changes and the mechanism of inversion in volvox. J Cell Biol 75:719–730
Viamontes GI, Fochtmann LJ, Kirk DL (1979) Morphogenesis in volvox: analysis of critical variables. Cell 17:537–550
Weliky M, Oster G (1990) The mechanical basis of cell rearrangement: I. Epithelial morphogenesis during fundulus epiboly. Development 109:373–386
Yang WH, Feng WW (1970) On axisymmetrical deformations of nonlinear membranes. J Appl Mech 37:1002–1011
Zamir EA, Srinivasan V, Perucchio R, Taber LA (2003) Mechanical asymmetry in the embryonic chick heart during looping. Ann Biomed Eng 31:1327–1336
Zamir EA, Taber LA (2004) Mechanical properties and residual stress in the stage 12 chick heart. J Biomech Eng 126:823–830
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Ramasubramanian, A., Taber, L.A. Computational modeling of morphogenesis regulated by mechanical feedback. Biomech Model Mechanobiol 7, 77–91 (2008). https://doi.org/10.1007/s10237-007-0077-y
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DOI: https://doi.org/10.1007/s10237-007-0077-y