Multiscale Modeling of Bone Healing: Toward a Systems Biology Approach

Bone is a living part of the body that can, in most situations, heal itself after fracture. However, in some situations, healing may fail. Compromised conditions, such as large bone defects, aging, immuno-deficiency, or genetic disorders, might lead to delayed or non-unions. Treatment strategies for those conditions remain a clinical challenge, emphasizing the need to better understand the mechanisms behind endogenous bone regeneration. Bone healing is a complex process that involves the coordination of multiple events at different length and time scales. Computer models have been able to provide great insights into the interactions occurring within and across the different scales (organ, tissue, cellular, intracellular) using different modeling approaches [partial differential equations (PDEs), agent-based models, and finite element techniques]. In this review, we summarize the latest advances in computer models of bone healing with a focus on multiscale approaches and how they have contributed to understand the emergence of tissue formation patterns as a result of processes taking place at the lower length scales.

[1]  V. Mudera,et al.  Close dependence of fibroblast proliferation on collagen scaffold matrix stiffness , 2009, Journal of tissue engineering and regenerative medicine.

[2]  G. Duda,et al.  BONE HEALING IN MICE: DOES IT FOLLOW GENERIC MECHANO-REGULATION RULES? , 2015 .

[3]  M J Gómez-Benito,et al.  Computational simulation of fracture healing: influence of interfragmentary movement on the callus growth. , 2007, Journal of biomechanics.

[4]  Lutz Claes,et al.  Influence of the fixation stability on the healing time--a numerical study of a patient-specific fracture healing process. , 2010, Clinical biomechanics.

[5]  Lutz Claes,et al.  Fracture healing under healthy and inflammatory conditions , 2012, Nature Reviews Rheumatology.

[6]  L Claes,et al.  A numerical model of the fracture healing process that describes tissue development and revascularisation , 2011, Computer methods in biomechanics and biomedical engineering.

[7]  S. Sen,et al.  Matrix Elasticity Directs Stem Cell Lineage Specification , 2006, Cell.

[8]  Daniel J. Kelly,et al.  A computational model to explore the role of angiogenic impairment on endochondral ossification during fracture healing , 2016, Biomechanics and modeling in mechanobiology.

[9]  G N Duda,et al.  The course of bone healing is influenced by the initial shear fixation stability , 2005, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[10]  Liesbet Geris,et al.  Size Does Matter: An Integrative In Vivo-In Silico Approach for the Treatment of Critical Size Bone Defects , 2014, PLoS Comput. Biol..

[11]  Paul Roschger,et al.  Size and habit of mineral particles in bone and mineralized callus during bone healing in sheep , 2010, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[12]  D. Kelly,et al.  The role of oxygen as a regulator of stem cell fate during fracture repair in TSP2‐null mice , 2013, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[13]  Liesbet Geris,et al.  A hybrid bioregulatory model of angiogenesis during bone fracture healing , 2011, Biomechanics and modeling in mechanobiology.

[14]  M. Dembo,et al.  Cell movement is guided by the rigidity of the substrate. , 2000, Biophysical journal.

[15]  Luke H. Hoeppner,et al.  Wnt signaling during fracture repair , 2009, Current osteoporosis reports.

[16]  G S Beaupré,et al.  Correlations between mechanical stress history and tissue differentiation in initial fracture healing , 1988, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[17]  Melissa L. Knothe Tate,et al.  Mechanistic, Mathematical Model to Predict the Dynamics of Tissue Genesis in Bone Defects via Mechanical Feedback and Mediation of Biochemical Factors , 2014, PLoS Comput. Biol..

[18]  T. Andreassen,et al.  The effect of aging on fracture healing in the rat , 1989, Calcified Tissue International.

[19]  Georg N Duda,et al.  Inter-species investigation of the mechano-regulation of bone healing: comparison of secondary bone healing in sheep and rat. , 2011, Journal of biomechanics.

[20]  G. Vunjak‐Novakovic,et al.  Immune modulation as a therapeutic strategy in bone regeneration , 2015, Journal of Experimental Orthopaedics.

[21]  José Manuel García-Aznar,et al.  In silico Mechano-Chemical Model of Bone Healing for the Regeneration of Critical Defects: The Effect of BMP-2 , 2015, PloS one.

[22]  David R. Gilbert,et al.  Computational methodologies for modelling, analysis and simulation of signalling networks , 2006, Briefings Bioinform..

[23]  J. Jansen,et al.  Signaling pathways involved in osteogenesis and their application for bone regenerative medicine. , 2015, Tissue engineering. Part B, Reviews.

[24]  G. N. Duda,et al.  The spatio-temporal arrangement of different tissues during bone healing as a result of simple mechanobiological rules , 2012, Biomechanics and modeling in mechanobiology.

[25]  J. J. van den Beucken,et al.  Signaling pathways involved in osteogenesis and their application for bone regenerative medicine. , 2015, Tissue engineering. Part B, Reviews.

[26]  M J Gómez-Benito,et al.  Influence of fracture gap size on the pattern of long bone healing: a computational study. , 2005, Journal of theoretical biology.

[27]  F. Su,et al.  Review: Roles of Microenvironment and Mechanical Forces in Cell and Tissue Remodeling , 2011 .

[28]  M J Pearcy,et al.  Simulation of the nutrient supply in fracture healing. , 2009, Journal of biomechanics.

[29]  D. E. Discher,et al.  Matrix elasticity directs stem cell lineage — Soluble factors that limit osteogenesis , 2009 .

[30]  Jiang Yao,et al.  Determining the most important cellular characteristics for fracture healing using design of experiments methods. , 2008, Journal of theoretical biology.

[31]  Jos Vander Sloten,et al.  Occurrence and Treatment of Bone Atrophic Non-Unions Investigated by an Integrative Approach , 2010, PLoS Comput. Biol..

[32]  Liesbet Geris,et al.  MOSAIC: A Multiscale Model of Osteogenesis and Sprouting Angiogenesis with Lateral Inhibition of Endothelial Cells , 2012, PLoS Comput. Biol..

[33]  L. Claes,et al.  Influence of size and stability of the osteotomy gap on the success of fracture healing , 1997, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[34]  Rik Huiskes,et al.  Corroboration of mechanoregulatory algorithms for tissue differentiation during fracture healing: comparison with in vivo results , 2006, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[35]  L. Geris,et al.  Capturing the wide variety of impaired fracture healing phenotypes in Neurofibromatosis Type 1 with eight key factors: a computational study , 2016, Scientific Reports.

[36]  L. Claes,et al.  Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. , 1998, Journal of biomechanics.

[37]  Marjolein C H van der Meulen,et al.  Beneficial effects of moderate, early loading and adverse effects of delayed or excessive loading on bone healing. , 2003, Journal of biomechanics.

[38]  A. Gefen,et al.  Deformations, mechanical strains and stresses across the different hierarchical scales in weight-bearing soft tissues. , 2012, Journal of tissue viability.

[39]  Georg N Duda,et al.  T and B cells participate in bone repair by infiltrating the fracture callus in a two-wave fashion. , 2014, Bone.

[40]  Kay Raum,et al.  Spatial-temporal mapping of bone structural and elastic properties in a sheep model following osteotomy. , 2011, Ultrasound in medicine & biology.

[41]  Ellen Kuhl,et al.  The emergence of extracellular matrix mechanics and cell traction forces as important regulators of cellular self-organization , 2015, Biomechanics and modeling in mechanobiology.

[42]  Olaf Wolkenhauer,et al.  How Modeling Standards, Software, and Initiatives Support Reproducibility in Systems Biology and Systems Medicine , 2016, IEEE Transactions on Biomedical Engineering.

[43]  M. V. D. van der Meulen,et al.  A mathematical framework to study the effects of growth factor influences on fracture healing. , 2001, Journal of theoretical biology.

[44]  G. Duda,et al.  Initiation and early control of tissue regeneration – bone healing as a model system for tissue regeneration , 2014, Expert opinion on biological therapy.

[45]  Darren Paul Burke,et al.  Substrate Stiffness and Oxygen as Regulators of Stem Cell Differentiation during Skeletal Tissue Regeneration: A Mechanobiological Model , 2012, PloS one.

[46]  G. Duda,et al.  BMPs in bone regeneration: Less is more effective, a paradigm-shift. , 2016, Cytokine & growth factor reviews.

[47]  Lutz Claes,et al.  Prediction of fracture healing under axial loading, shear loading and bending is possible using distortional and dilatational strains as determining mechanical stimuli , 2013, Journal of The Royal Society Interface.

[48]  M. Heller,et al.  The initial phase of fracture healing is specifically sensitive to mechanical conditions , 2003, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[49]  E. Nauman,et al.  Multiscale strain analysis of tissue equivalents using a custom-designed biaxial testing device. , 2012, Biophysical journal.

[50]  D. Kelly,et al.  Mechano-regulation of mesenchymal stem cell differentiation and collagen organisation during skeletal tissue repair , 2010, Biomechanics and modeling in mechanobiology.

[51]  D. Lacroix,et al.  Biomechanical model to simulate tissue differentiation and bone regeneration: Application to fracture healing , 2006, Medical and Biological Engineering and Computing.

[52]  S. Mundlos,et al.  Deterioration of fracture healing in the mouse model of NF1 long bone dysplasia. , 2012, Bone.

[53]  Rüdiger Weiner,et al.  Angiogenesis in bone fracture healing: a bioregulatory model. , 2008, Journal of theoretical biology.

[54]  Liesbet Geris,et al.  Oxygen as a critical determinant of bone fracture healing-a multiscale model. , 2015, Journal of theoretical biology.

[55]  G. Duda,et al.  Influence of age and mechanical stability on bone defect healing: age reverses mechanical effects. , 2008, Bone.

[56]  Damien Lacroix,et al.  Simulation of fracture healing in the tibia: Mechanoregulation of cell activity using a lattice modeling approach , 2011, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[57]  L. Geris,et al.  Connecting biology and mechanics in fracture healing: an integrated mathematical modeling framework for the study of nonunions , 2010, Biomechanics and modeling in mechanobiology.