On numerical modelling of growth, differentiation and damage in structural living tissues

D'Arcy Wentworth Thompson (1997).On growth and form. Cambridge University Press, Cambridge.

S.C. Cowin (2004). Tissue growth and remodeling.Annu. Rev. Biomed. Eng.,6, 77–107.

D.R. Carter and G.S. Beaupre (2001).Skeletal Function and Form. Cambridge University Press.

Marjolein C.H. van der Meulen and Rik Huiskes (2002). Why mechanobiology? A survey article.J. of Biomechanics,35, 401–414.

R.T. Hart (2001).Bone modeling and remodeling: theories and computation. Chapter 31, pp. 31.1–31.42. Bone Mechanics Handbook, 2nd Ed. CRC Press.

H.E. Petermann, T.J. Reiter and F.G. Rammerstorfer (1997). Computational simulation of internal bone remodeling.Archives of Computational Methods in Engineering,4 (4), 295–323.

J.M. García-Aznar, T. Rueberg and M. Doblaré. A bone remodelling model coupling microdamage growth and repairing by 3D BMU-activity.Biomech Model Mechanobiol, In press.

R. Skalak, G. Dasgupta, M. Moss, E. Otten, P. Dullemeijer and H. Vilmann (1982). Analytical description of growth.J. Theor. Biol.,94, 555–577.

J.D. Humphrey (1995). Mechanics of the arterial wall: review and directions.Critic Rev Biomed Engng,23, 1–62.

L.A. Taber (1995). Biomechanics of growth, remodelling and morphogenesis.Appl. Mech. Rev.,48 (8), 487–545.

M. Doblaré, J.M. García and M.J. Gómez (2004). Modelling bone tissue fracture and healing: a review.Engineering Fracture Mechanics,71 (13–14), 1809–1840.

H. Isaksson, W. Wilson, C.C. van Doukelaar, R. Huiskes and K. Ito. Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing.J. Biomech, in press.

V.A. Lubarda, A. Hoger (2002). On the mechanics of solids with a growing mass.Int. J. Solids Struct.,39, 4627–4664.

E. Kuhl and P. Steinmann (2003). Theory and numerics of geometrically non-linear open system mechanics.Int. J. Numer. Metho. Engng.,58.

E. Kuhl and P. Steinmann (2004). Computational modeling of healing: an application of the material force method.Biomech. Model. Mechanobiol.,2 (4).

K. Garikipati, E.M. Arruda, K. Grosh, H. Narayanan and S. Calve (2004). A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics.Journal of the Mechanics and Physics of Solids,52 (7), 1595–1625.

G.F. Oster, J.D. Murray and A.K. Harris (1983). Mechanical aspects of mesenchymal morphogenesis.J Embryol. exp. Morph.,78, 83–125.

D. Manoussaki (2003). A mechanochemical model of angiogenesis and vasculogenesis.Mathematical Modelling and Numerical Analysis,37 (4), 581–599.

P. Namy, J. Ohayon and P. Tracqui (2004). Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields.Journal of Theoretical Biology,227, 103–120.

S. Ramtani (2004). Mechanical modelling of cell/ecm and cell/cell interactions during the contraction of a fibroblast-populated collagen microsphere: theory and model simulation.J. Biomech.,37 (11), 1709–18.

C.J. Hernandez (2001).Simulation of bone remodeling during the development and treatment of osteoporosis. PhD thesis, Stanford University, Stanford, California.

R.B. Martin (2003). Fatigue microdamage as an essential element of bone mechanics and biology.Calcified Tissue International,73 (2), 101–107.

C.H. Turner (2002). Biomechanics of bone: determinants of skeletal fragility and bone quality.Osteoporos Int.,13 (2), 97–104.

J.A. Buckwalter (2002). Articular cartilage injuries.Clin. Orthop.,402, 21–37.

R.G. Breuls, C.V. Bouten, C.W. Oomens, D.L. Bader and F.P. Baaijeus (2003). A theoretical analysis of damage evolution in skeletal muscle tissue with reference to pressure ulcer development.J. Biomech. Eng.,125 (6), 902–909.

R.G. Breuls, C.V. Bouten, C.W. Oomens, D.L. Bader and F.P. Baaijens (2003). Compression induced cell damage in engineered muscle tissue: an in vitro model to study pressure ulcer aetiology.Ann Biomed. Eng.,31 (11), 1357–1364.

J. Lemaitre and J.L. Chaboche (1990).Mechanics of solid materials. Cambridge University Press, Cambridge.

J.C. Simo and J.W. Ju (1987). Strain- and stress-based continuum damage models: I. formulation.International Journal of Solids and Structures,23, 821–840.

J.P. Cordebois and F. Sideroff (1982). Damage induced elastic anisotropy.Mechanical Behavior of Anisotropic Solids. Proc. EUROMECH colloque,115, 761–774.

D.B. Burr, C.H. Turner, P. Naick, M.R. Forwood, W. Ambrosius, M.S. Hasan and R. Pidaparti (1998). Does microdamage accumulation affect the mechanical properties of bone?J. Biomech.,31 (4), 337–345.

J.E. Marsden and T.J.R. Hughes (1983).Mathematical foundations of elasticity. Dover Publications, INC., New York.

E.K. Rodriguez, A. Hoger and A.D. McCulloch (1994). Stress-dependent finite growth in soft elastic tissues.J. Biomech.,27 (4), 455–467.

C. Truesdell and W. Noll (1965).The Non-linear Field Theories, (Handbuch der Physik, Band III). Springer, Berlin.

J.D. Murray and G.F. Oster (1984). Cell traction models for generating pattern and form in morphogenesis.J. Math. Biol.,19 (3), 265–279.

S. Harada and G.A. Rodan (2003). Control of osteoblast function and regulation of bone mass.Nature,423, 349–356.

H.M. Frost (1964).Dynamics of bone remodelling, pages 315–333. Bone biodynamics. Boston, Little, Brown Co..

S.J. Hazelwood, R.B. Martin, M.M. Rashid and J.J. Rodrigo (2001). A mechanistic model for internal bone remodeling exhibits different dynamic responses in disuse and overload?J. Biomech.,34 (3), 299–308.

J. Wolff (1892).The Law of Bone Remodelling. Das Gesetz derTransformation der Kuochen, Kirschwald. Translated by Maquet, P., Furlong, R.

R. Huiskes, H. Weinans, H.J. Grootenboer, M. Dalstra, B. Fudala and T.J. Sloof (1987). Adaptive bone-remodelling theory applied to prosthetic-design analysis.J. Biomech.,20 (11/12), 1135–1150.

D.R. Carter, D.P. Fyhrie and R.T. Whalen (1987). Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy.J. Biomech.,20 (8), 1095–1109.

P.J. Prendergast and D. Taylor (1994). Prediction of bone adaptation using damage accumulation.J. Biomech.,27, 1067–1076.

R.B. Martin (1995). A mathematical model for fatigue damage repair and stress fracture osteonal bone.J. Orhop. Res.,13, 309–316.

C.R. Jacobs, J.C. Simo, G.S. Beaupré and D.R. Carter (1997). Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations.J. Biomech.,30 (6), 603–13.

R.T. Hart and S.P. Fritton (1997). Introduction to finite-element based simulation of the functional adaptation of cancellous bone.Forma,12, 277–299.

P. Fernandes, H. Rodrigues and C.R. Jacobs (1999). A model of bone adaptation using a global optimisation criterion based on the trajectorial theory of wolff.Comput. Methods Biomech. Biomed. Eng.,2 (2), 125–138.

M. Doblaré and J.M. García (2001). Application of an anisotropic bone-remodelling model based on a damage-repair theory to the analysis of the proximal femur before and after total hip replacement.J. Biomech.,34 (9), 1157–70.

M. Doblaré and J.M. García (2002). Anisotropic bone remodelling model based on a continuum damage-repair theory.J. Biomech.,35 (1), 1–17.

S.C. Cowin and D.H. Hegedus (1976). Bone remodeling i: A theory of adaptive elasticity.J. Elasticity,6, 313–326.

R.T. Hart, D.T. Davy and K.G. Heiple (1984). A computational model for stress analysis of adaptive elastic materials with a view toward applications in strain-induced bone remodelling.J. Biomech. Eng.,106, 342–350.

G.S. Beaupré, T.E. Orr and D.R. Carter (1990). An approach for time-dependent bone modeling and remodeling-theoretical development.Journal of Orthopoedic Research,8, 551–651.

H. Weinans, R. Huiskes and H.J. Grootenboer (1992). The behavior of adaptive bone-remodeling simulation models.J. Biomech.,25, 1425–1441.

S. Ramtani and M. Zidi (2001). A theoretical model of the effect of continuum damage on a bone adaptation model.J. Biomech.,34 (4), 471–9.

R. Huiskes, R. Ruimerman, G.H. van Lenthe and J.D. Janssen (2000). Effects of mechanical forces on maintenance and adaptation of form in trabecular bone.Nature,405, 704–706.

C.J. Hernandez, G.S. Beaupré and D.R. Carter (2000). A model of mechanobiologic and metabolic influences on bone adaptation.J. Rehabil. Res. Dev.,37 (2), 235–244.

C.J. Hernandez, G.S. Beaupré, R. Marcus and D.R. Carter (2001). A theoretical analysis of the contributions of remodeling space, mineralization, and bone balance to changes in bone mineral density during alendronate treatment.Bone,29, (6), 511–516.

C.J. Hernandez, G.S. Beaupré and D.R. Carter (2003). A theoretical analysis of the changes in basic multicellular unit activity at menopause.Bone,32, 357–63.

R.B. Martin, D.B. Burr and N.A. Sharkey (1998).Skeletal Tissue Mechanics. New York: Springer-Verlarg.

R.B. Martin (1984).Porosity and specific surface of bone, volume 10 ofCritical Reviews in Biomedical Engineering, Chapter 3, pp. 179–222. CRC Press.

C.J. Hernández, G.S. Beaupré, T.S. Keller and D.R. Carter (2001). The influence of bone volume fraction and ash fraction on bone strength and modulus.Bone,29 (1), 74–78.

C.A. Pattin, W.E. Caler and D.R. Carter (1996). Cyclic mechanical property degradation during fatigue loading of cortical bone.J Biomech,29 (1), 69–79.

P.K. Venesmanaa, H.P. Kroger, J.S. Jurvelin, H.J. Miertinen, O.T. Suomalainen and E.M. Alhava (2003). Periprosthetic bone loss after cemented total hip arthroplasty: a prospective 5-year dual energy radiographic absorptiometry study of 15 patients.Acta Orthop. Scand.,74 (1), 31–36.

D.E. Ashhurst (1986). The influence of mechanical stability on the healing of experimental fractures in the rabbit: a microscopical study. Series B313, 271–302.

M.M. Sandberg, H.T. Aro and E.I. Vuorio (1993). Gene expression during bone repair.Clin. Orthop. Rel. Res.

F. Pauwels (1960). Eine neue theorie über den ernflub mechanischer reize auf die differenzierung der stützgewebe.Z. Anat. Entwicklungsgeschichte,121, 478–515.

S.M. Perren (1979). Physical and biological aspects of fracture healing with special reference to internal fixation.Clin. Orthop. Rel. Res.,138, 175–196.

S.M. Perren and J. Cordey (1980).The concept of interfragmentary strain, pp. 63–77. Currect concepts of internal fixation of fractures. Springer-Verlarg, Berlin.

D.R. Carter, P.R. Bleuman and G.S. Beaupré (1998). Correlations between mechanical stress history and tissue differentiation in initial fracture healing.J. Orthop. Res.,6, 736–748.

D.R. Carter, G.S. Beaupré, N.J. Giori and J.A. Helms (1998). Mechanobiology of skeletal regeneration.Clin. Orthop. Rel. Res.,S355, S41-S55.

L.E. Claes and C.A. Heigele (1999). Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing.J. Biomech., 32:255–266, 1999.

P.J. Prendergast, R. Huiskes and K. Soballe (1997). Biophysical stimuli on cells during tissue differentiation at implant interfaces.J. Biomech.,6, 539–548.

A. Bailón-Plaza and M.C.H. Van Der Meulen (2001). A mathematical framework to study the effects of growth factor influences on fracture healing.J. Theor. Biol.,212, 191–209.

D. Lacroix and P.J. Prendergast (2002). A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading.J. Biomech.,35, 1163–1171.

U. Simon, P. Augat, M. Utz and L. Claes (2002). Dynamical simulation of the fracture healing process including vascularity.Acta of Bioengineering and Biomechanics,4 S1, 772–773.

A. Bailón-Plaza and M.C.H. van der Meulen (2003). A Mathematical Framework to Study the Effects of Growth Factor Influences on Fracture Healing.Journal of Biomechanics,36, 1069–1077.

J.H. Kuiper, J.B. Richardson and B.A. Ashton (2000). Computer simulation to study the effect of fracture site movement on tissue formation and fracture stiffness restoration. InEuropean Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS.

Ch. Ament and E.P. Hofer (2000). A fuzzy logic model of fracture healing.J. Biomech.,33, 961–968.

M.J. Gómez-Benito, J.M. García-Aznar, J.H. Kuiper, M. Doblaré and J.B. Richardson (2005). Influence of fracture gap size on the pattern of long bone healing: A computational study.J. Theor Biol,235 (1), 105–119.

J.H. Kuiper, J.B. Richardson and B.A. Ashton (1996). Mechanical signals in early fracture callus. In J. Vander Sloten, G. Lowet, R. Van Audekercke, and G. Van der Perre, editors,Proc 10th Europ Soc Biomech, page 154.

J.H. Kuiper, B.A. Ashton and J.B. Richardson (2000). Computer simulation of fracture callus formation and stiffness restoration. In P.J. Prendergast, T.C. Lee, and A.J. Carr (Eds.),Proc 12th Europ Soc Biomech, page 61.

D. Lacroix (2000).Simulation of tissue differentiation during fracture healing. PhD thesis, University of Dublin.

D.M. Cullinane, K.T. Salisbury, Y. Alkhiary and S. Eisenberg (2003). Effects of the local mechanical environtment on vertebrate tissue differentiation during repair: does repair recapitulate development.The Journal of Experimental Biology,206, 2459–2471.

G.S. Beaupré, T.E. Orr and D.R. Carter (1990). An approach for time-dependent bone modeling and remodeling-application: A preliminary remodeling simulation.Journal of Orthopaedic Research,8, 662–670.

G.J. Breur, VanEnkevort, C.E. Farnum and N.J. Wilsman (1991). Linear Relationship between the Volume of Hypertrophic Chondrocytes and the Rate of Longitudinal Bone Growth in Growth Plates.Journal of Orthopeadic Research,9, 348–359.

N.J. Wilsman, C.E. Farnum, E.M. Leiferman, M. Fry and C. Barreto (1996). Differential growth by growth plates as a function of multiple parameters of chondrocytic kinetics.Journal of Orthopaedic Research,14, 927–936.

Ch. Ament and E.P. Hofer (1996). On the importance of the osteogenic and vasculative factors in callus healing. InProc. of the 5th Meeting of the International Society for Fracture Repair.

C.R. Jacobs (1994).Numerical simulation of Bone Adaptation to Mechanical Loading. PhD thesis, Stanford University.

J.R. Levick (1987). Flow through interstitium and other fibrous matrices.Quaterly Journal of Experimental Physiology,72, 409–438.

E. Mücke (1993).Shapes and Implementations in Three-Dimensional Geometry. PhD thesis, University of Illinois at Urbana-Champaign.

L. Claes, P. Augat, G. Suger and H.J. Wilke (1997). Influence of size and stability of the osteotomy gap on the success of fracture healing.J. Orthop. Res.,15 (4), 577–584.

H.M. Frost (1988). The biology of fracture healing.Clinical Orhopaedics and Related Research,248, 283–293.

R. Dillon and H.G. Othmer (1999). A mathematical model for outgrowth and spatial patterning of the vertebrate limb bud.Journal of Theoretical Biology,197 (3), 295–330.