bone regeneration; experimental validation; fracture healing; in silico modeling; inflammatory response; multiscale approach
Abstract :
[en] In silico modeling is a powerful strategy to investigate the biological events occurring at tissue, cellular and subcellular level during bone fracture healing. However, most current models do not consider the impact of the inflammatory response on the later stages of bone repair. Indeed, as initiator of the healing process, this early phase can alter the regenerative outcome: if the inflammatory response is too strongly down- or upregulated, the fracture can result in a non-union. This review covers the fundamental information on fracture healing, in silico modeling and experimental validation. It starts with a description of the biology of fracture healing, paying particular attention to the inflammatory phase and its cellular and subcellular components. We then discuss the current state-of-the-art regarding in silico models of the immune response in different tissues as well as the bone regeneration process at the later stages of fracture healing. Combining the aforementioned biological and computational state-of-the-art, continuous, discrete and hybrid modeling technologies are discussed in light of their suitability to capture adequately the multiscale course of the inflammatory phase and its overall role in the healing outcome. Both in the establishment of models as in their validation step, experimental data is required. Hence, this review provides an overview of the different in vitro and in vivo set-ups that can be used to quantify cell- and tissue-scale properties and provide necessary input for model credibility assessment. In conclusion, this review aims to provide hands-on guidance for scientists interested in building in silico models as an additional tool to investigate the critical role of the inflammatory phase in bone regeneration.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Lafuente-Gracia, Laura; Biomechanics Section, Department of Mechanical Engineering, KU Leuven, Leuven, ; Prometheus: Division of Skeletal Tissue Engineering, KU Leuven, Leuven, Belgium.
Borgiani, Edoardo ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Génie biomécanique ; Biomechanics Section, Department of Mechanical Engineering, KU Leuven, Leuven, ; Prometheus: Division of Skeletal Tissue Engineering, KU Leuven, Leuven, Belgium.
Nasello, Gabriele; Biomechanics Section, Department of Mechanical Engineering, KU Leuven, Leuven, ; Prometheus: Division of Skeletal Tissue Engineering, KU Leuven, Leuven, Belgium. ; Skeletal Biology and Engineering Research Center, KU Leuven, Leuven, Belgium.
Geris, Liesbet ; Université de Liège - ULiège > GIGA > GIGA In silico medecine - Biomechanics Research Unit ; Biomechanics Section, Department of Mechanical Engineering, KU Leuven, Leuven, ; Prometheus: Division of Skeletal Tissue Engineering, KU Leuven, Leuven, Belgium. ; Skeletal Biology and Engineering Research Center, KU Leuven, Leuven, Belgium.
Language :
English
Title :
Towards in silico Models of the Inflammatory Response in Bone Fracture Healing.
Adams S. Wuescher L. M. Worth R. Yildirim-Ayan E. (2019). Mechano-Immunomodulation: Mechanoresponsive Changes in Macrophage Activity and Polarization. Ann. Biomed. Eng. 47, 2213–2231. 10.1007/s10439-019-02302-4
Alber M. Chen N. Glimm T. Lushnikov P. M. (2006). Multiscale Dynamics of Biological Cells with Chemotactic Interactions: From a Discrete Stochastic Model to a Continuous Description. Phys. Rev. E 73, 1–11. 10.1103/PhysRevE.73.051901
Alexander K. A. Chang M. K. Maylin E. R. Kohler T. Müller R. Wu A. C. et al. (2011). Osteal Macrophages Promote In Vivo Intramembranous Bone Healing in a Mouse Tibial Injury Model. J. Bone Mineral Res. 26, 1517–1532. 10.1002/jbmr.354
Amini A. R. Laurencin C. T. Nukavarapu S. P. (2012). Bone Tissue Engineering: Recent Advances and Challenges. Crit. ReviewsTM Biomed. Eng. 40, 363–408. 10.1615/critrevbiomedeng.v40.i5.10
Anderson A. R. Chaplain M. A. (1998). Continuous and Discrete Mathematical Models of Tumor-Induced Angiogenesis. Bull. Math. Biol. 60, 857–899. 10.1006/bulm.1998.0042
Anton K. Banerjee D. Glod J. (2012). Macrophage-Associated Mesenchymal Stem Cells Assume an Activated, Migratory, Pro-inflammatory Phenotype with Increased IL-6 and CXCL10 Secretion. PLoS ONE 7, e35036. 10.1371/journal.pone.0035036
Baht G. S. Vi L. Alman B. A. (2018). The Role of the Immune Cells in Fracture Healing. Curr. Osteoporos. Rep. 16, 138–145. 10.1007/s11914-018-0423-2
Bailón-Plaza A. Van Der Meulen M. C. (2001). A Mathematical Framework to Study the Effects of Growth Factor Influences on Fracture Healing. J. Theor. Biol. 212, 191–209. 10.1006/jtbi.2001.2372
Bailón-Plaza A. Van Der Meulen M. C. (2003). Beneficial Effects of Moderate, Early Loading and Adverse Effects of Delayed or Excessive Loading on Bone Healing. J. Biomech. 36, 1069–1077. 10.1016/S0021-9290(03)00117-9
Ballotta V. Driessen-Mol A. Bouten C. V. Baaijens F. P. (2014). Strain-dependent Modulation of Macrophage Polarization within Scaffolds. Biomaterials 35, 4919–4928. 10.1016/j.biomaterials.2014.03.002
Barh D. Azevedo V. (2019). “Single-Cell Omics,” in Technological Advances and Applications (Cambridge, MA: Academic Press), 1. 10.1016/C2017-0-02420-5
Barnes G. L. Kostenuik P. J. Gerstenfeld L. C. Einhorn T. A. (1999). Growth Factor Regulation of Fracture Repair. J. Bone Mineral Res. 14, 1805–1815. 10.1359/jbmr.1999.14.11.1805
Bastian O. Pillay J. Alblas J. Leenen L. Koenderman L. Blokhuis T. (2011). Systemic Inflammation and Fracture Healing. J. Leukoc. Biol. 89, 669–673. 10.1189/jlb.0810446
Bastian O. W. Koenderman L. Alblas J. Leenen L. P. Blokhuis T. J. (2016). Neutrophils Contribute to Fracture Healing by Synthesizing Fibronectin+ Extracellular Matrix Rapidly after Injury. Clin. Immunol. 164, 78–84. 10.1016/j.clim.2016.02.001
Bentley K. Gerhardt H. Bates P. A. (2008). Agent-based Simulation of Notch-Mediated Tip Cell Selection in Angiogenic Sprout Initialisation. J. Theor. Biol. 250, 25–36. 10.1016/j.jtbi.2007.09.015
Birkhold A. I. Razi H. Duda G. N. Weinkamer R. Checa S. Willie B. M. (2014). The Influence of Age on Adaptive Bone Formation and Bone Resorption. Biomaterials 35, 9290–9301. 10.1016/j.biomaterials.2014.07.051
Bittersohl H. Steimer W. (2016). “Intracellular Concentrations of Immunosuppressants,” in Personalized Immunosuppression in Transplantation (Amsterdam, Netherlands: Elsevier), 199–226. 10.1016/B978-0-12-800885-0.00009-6
Borgiani E. Duda G. Willie B. Checa S. (2015). Bone Healing in Mice: Does it Follow Generic Mechano-Regulation Rules? Facta Universitatis, Ser. Mech. Eng. 13, 217–227.
Borgiani E. Duda G. N. Checa S. (2017). Multiscale Modeling of Bone Healing: Toward a Systems Biology Approach. Front. Physiol. 8, 287. 10.3389/fphys.2017.00287
Borgiani E. Figge C. Kruck B. Willie B. M. Duda G. N. Checa S. (2019). Age-Related Changes in the Mechanical Regulation of Bone Healing Are Explained by Altered Cellular Mechanoresponse. J. Bone Mineral Res. 34, 1923–1937. 10.1002/jbmr.3801
Borgiani E. Duda G. N. Willie B. M. Checa S. (2021). Bone Morphogenetic Protein 2-induced Cellular Chemotaxis Drives Tissue Patterning during Critical-Sized Bone Defect Healing: an In Silico Study. Biomech. Model. Mechanobiol. 20, 1627–1644. 10.1007/s10237-021-01466-0
Borgström F. Karlsson L. Ortsäter G. Norton N. Halbout P. Cooper C. et al. (2020). Fragility Fractures in Europe: Burden, Management and Opportunities. Arch. Osteoporos. 15, 1–21. 10.1007/s11657-020-0706-y
Bouchery T. Harris N. (2019). Neutrophil–macrophage Cooperation and its Impact on Tissue Repair. Immunol. Cel Biol. 97, 289–298. 10.1111/imcb.12241
Boussommier-Calleja A. Li R. Chen M. B. Wong S. C. Kamm R. D. (2016). Microfluidics: A New Tool for Modeling Cancer–Immune Interactions. Trends Cancer 2, 6–19. 10.1016/j.trecan.2015.12.003
Britton O. J. Bueno-Orovio A. Van Ammel K. Lu H. R. Towart R. Gallacher D. J. et al. (2013). Experimentally Calibrated Population of Models Predicts and Explains Intersubject Variability in Cardiac Cellular Electrophysiology. Proc. Natl. Acad. Sci. U S A. 110, E2098–E2105. 10.1073/pnas.1304382110
Brown B. Price I. Toapanta F. DeAlmeida D. Wiley C. Ross T. et al. (2011). An Agent-Based Model of Inflammation and Fibrosis Following Particulate Exposure in the Lung. Math. Biosci. 231, 186–196. 10.1016/j.mbs.2011.03.005
Burke D. P. Kelly D. J. (2012). Substrate Stiffness and Oxygen as Regulators of Stem Cell Differentiation during Skeletal Tissue Regeneration: A Mechanobiological Model. PLoS One 7, e40737. 10.1371/journal.pone.0040737
Byrne D. P. Lacroix D. Prendergast P. J. (2011). Simulation of Fracture Healing in the Tibia: Mechanoregulation of Cell Activity Using a Lattice Modeling Approach. J. Orthop. Res. 29, 1496–1503. 10.1002/jor.21362
Calciolari E. Donos N. (2020). Proteomic and Transcriptomic Approaches for Studying Bone Regeneration in Health and Systemically Compromised Conditions. Proteomics – Clin. Appl. 14, 1900084. 10.1002/prca.201900084
Camp J. G. Wollny D. Treutlein B. (2018). Single-cell Genomics to Guide Human Stem Cell and Tissue Engineering. Nat. Methods 15, 661–667. 10.1038/s41592-018-0113-0
Carano R. A. Filvaroff E. H. (2003). Angiogenesis and Bone Repair. Drug Discov. Today 8, 980–989. 10.1016/S1359-6446(03)02866-6
Carlier A. Geris L. Bentley K. Carmeliet G. Carmeliet P. van Oosterwyck H. (2012). MOSAIC: A Multiscale Model of Osteogenesis and Sprouting Angiogenesis with Lateral Inhibition of Endothelial Cells. PLoS Comput. Biol. 8, e1002724. 10.1371/journal.pcbi.1002724
Carlier A. Geris L. van Gastel N. Carmeliet G. Oosterwyck H. V. (2015). Oxygen as a Critical Determinant of Bone Fracture Healing-A Multiscale Model. J. Theor. Biol. 365, 247–264. 10.1016/j.jtbi.2014.10.012
Carlier A. Skvortsov G. A. Hafezi F. Ferraris E. Patterson J. Koc B. et al. (2016). Computational Model-Informed Design and Bioprinting of Cell-Patterned Constructs for Bone Tissue Engineering. Biofabrication 8, 025009. 10.1088/1758-5090/8/2/025009
Carter D. R. Beaupré G. S. (1998). Mechanobiology of Skeletal Regeneration. Clin. Orthop. Relat. Res., S41–S55. 10.1097/00003086-199810001-00006
Carter D. R. Blenman P. R. Beaupré G. S. (1988). Correlations between Mechanical Stress History and Tissue Differentiation in Initial Fracture Healing. J. Orthop. Res. 6, 736–748. 10.1002/jor.1100060517
Celada F. Seiden P. E. (1992). A Computer Model of Cellular Interactions in the Immune System. Immunol. Today 13, 56–62. 10.1016/0167-5699(92)90135-T
Ceresa M. Olivares A. L. Noailly J. Ballester M. A. (2018). Coupled Immunological and Biomechanical Model of Emphysema Progression. Front. Physiol. 9, 2712–2715. 10.3389/fphys.2018.00388
Chaplin D. D. (2010). Overview of the Immune Response. J. Allergy Clin. Immunol. 125, S345. 10.1016/j.jaci.2010.01.002
Checa S. Prendergast P. J. Duda G. N. (2011). Inter-species Investigation of the Mechano-Regulation of Bone Healing: Comparison of Secondary Bone Healing in Sheep and Rat. J. Biomech. 44, 1237–1245. 10.1016/j.jbiomech.2011.02.074
Cilla M. Borgiani E. Martínez J. Duda G. N. Checa S. (2017). Machine Learning Techniques for the Optimization of Joint Replacements: Application to a Short-Stem Hip Implant. PLoS One 12, 1–16. 10.1371/journal.pone.0183755
Claes L. E. Heigele C. A. (1999). Magnitudes of Local Stress and Strain along Bony Surfaces Predict the Course and Type of Fracture Healing. J. Biomech. 32, 255–266. 10.1016/S0021-9290(98)00153-5
Claes L. Recknagel S. Ignatius A. (2012). Fracture Healing under Healthy and Inflammatory Conditions. Nat. Rev. Rheumatol. 8, 133–143. 10.1038/nrrheum.2012.1
Coates B. A. McKenzie J. A. Buettmann E. G. Liu X. Gontarz P. M. Zhang B. et al. (2019). Transcriptional Profiling of Intramembranous and Endochondral Ossification after Fracture in Mice. Bone 127, 577–591. 10.1016/j.bone.2019.07.022
Cointry G. R. Nocciolino L. Ireland A. Hall N. M. Kriechbaumer A. Ferretti J. L. et al. (2016). Structural Differences in Cortical Shell Properties between Upper and Lower Human Fibula as Described by pQCT Serial Scans. A Biomechanical Interpretation. Bone 90, 185–194. 10.1016/j.bone.2016.06.007
Coquim J. Clemenzi J. Salahi M. Sherif A. Avval P. T. Shah S. et al. (2018). Biomechanical Analysis Using FEA and Experiments of Metal Plate and Bone Strut Repair of a Femur Midshaft Segmental Defect. Biomed. Res. Int. 2018, 4650308. 10.1155/2018/4650308
Dagur P. K. McCoy J. P. (2015). Collection, Storage, and Preparation of Human Blood Cells. Curr. Protoc. Cytometry 73, 5.1.1–5.1.16. 10.1002/0471142956.cy0501s73
Del Amo C. Borau C. Gutiérrez R. Asín J. García-Aznar J. M. (2016). Quantification of Angiogenic Sprouting under Different Growth Factors in a Microfluidic Platform. J. Biomech. 49, 1340–1346. 10.1016/j.jbiomech.2015.10.026
Del Amo C. Olivares V. Cóndor M. Blanco A. Santolaria J. Asín J. et al. (2018). Matrix Architecture Plays a Pivotal Role in 3D Osteoblast Migration: The Effect of Interstitial Fluid Flow. J. Mech. Behav. Biomed. Mater. 83, 52–62. 10.1016/j.jmbbm.2018.04.007
Dimitriou R. Tsiridis E. Giannoudis P. V. (2005). Current Concepts of Molecular Aspects of Bone Healing. Injury 36, 1392–1404. 10.1016/j.injury.2005.07.019
Doblaré M. García J. M. Gómez M. J. (2004). Modelling Bone Tissue Fracture and Healing: A Review. Eng. Fracture Mech. 71, 1809–1840. 10.1016/j.engfracmech.2003.08.003
Einhorn T. A. (1998). The Cell and Molecular Biology of Fracture Healing. Clin. Orthop. Relat. Res. 355, S7–S21. 10.1097/00003086-199810001-00003
Eng G. Lee B. W. Parsa H. Chin C. D. Schneider J. Linkov G. et al. (2013). Assembly of Complex Cell Microenvironments Using Geometrically Docked Hydrogel Shapes. Proc. Natl. Acad. Sci. 110, 4551–4556. 10.1073/pnas.1300569110
Epari D. R. Schell H. Bail H. J. Duda G. N. (2006). Instability Prolongs the Chondral Phase during Bone Healing in Sheep. Bone 38, 864–870. 10.1016/j.bone.2005.10.023
Evans S. S. Repasky E. A. Fisher D. T. (2015). Fever and the thermal Regulation of Immunity: The Immune System Feels the Heat. Nat. Rev. Immunol. 15, 335–349. 10.1038/nri3843
Fachada N. Lopes V. Rosa A. (2007). Agent-based Modelling and Simulation of the Immune System: a Review. Epia 2007 Lncs (Lnai) 4874, 300–315.
Fahy N. Menzel U. Alini M. Stoddart M. J. (2019). Shear and Dynamic Compression Modulates the Inflammatory Phenotype of Human Monocytes In Vitro. Front. Immunol. 10, 1–12. 10.3389/fimmu.2019.00383
Faria T. Oliveira J. J. (2020). Global Asymptotic Stability for a Periodic Delay Hematopoiesis Model with Impulses. Appl. Math. Model. 79, 843–864. 10.1016/j.apm.2019.10.063
Fraser D. A. Laust A. K. Nelson E. L. Tenner A. J. (2009). C1q Differentially Modulates Phagocytosis and Cytokine Responses during Ingestion of Apoptotic Cells by Human Monocytes, Macrophages, and Dendritic Cells. J. Immunol. 183, 6175–6185. 10.4049/jimmunol.0902232
Galván-Peña S. O’Neill L. A. (2014). Metabolic Reprograming in Macrophage Polarization. Front. Immunol. 5, 420. 10.3389/fimmu.2014.00420
García-Aznar J. M. Kuiper J. H. Gómez-Benito M. J. Doblaré M. Richardson J. B. (2007). Computational Simulation of Fracture Healing: Influence of Interfragmentary Movement on the Callus Growth. J. Biomech. 40, 1467–1476. 10.1016/j.jbiomech.2006.06.013
Geris L. Gerisch A. Sloten J. V. Weiner R. Oosterwyck H. V. (2008). Angiogenesis in Bone Fracture Healing: A Bioregulatory Model. J. Theor. Biol. 251, 137–158. 10.1016/j.jtbi.2007.11.008
Geris L. Sloten J. V. Oosterwyck H. V. (2010). Connecting Biology and Mechanics in Fracture Healing: An Integrated Mathematical Modeling Framework for the Study of Nonunions. Biomech. Model. Mechanobiol. 9, 713–724. 10.1007/s10237-010-0208-8
Ghiasi M. S. Chen J. Vaziri A. Rodriguez E. K. Nazarian A. (2017). Bone Fracture Healing in Mechanobiological Modeling: A Review of Principles and Methods. Bone Rep. 6, 87–100. 10.1016/j.bonr.2017.03.002
Gianì F. Russo G. Pennisi M. Sciacca L. Frasca F. Pappalardo F. (2018). Computational Modeling Reveals MAP3K8 as Mediator of Resistance to Vemurafenib in Thyroid Cancer Stem Cells. Bioinformatics 35, 2267–2275. 10.1093/bioinformatics/bty969
Gillespie M. T. (2007). Impact of Cytokines and T Lymphocytes upon Osteoclast Differentiation and Function. Arthritis Res. Ther. 9, 7–9. 10.1186/ar2141
Giorgi M. Verbruggen S. W. Lacroix D. (2016). Silico Bone Mechanobiology: Modeling a Multifaceted Biological System. Wiley Interdiscip. Rev. Syst. Biol. Med. 8, 485–505. 10.1002/wsbm.1356
Gómez-Benito M. J. García-Aznar J. M. Kuiper J. H. Doblaré M. (2005). Influence of Fracture gap Size on the Pattern of Long Bone Healing: A Computational Study. J. Theor. Biol. 235, 105–119. 10.1016/j.jtbi.2004.12.023
Gómez-Benito M. J. García-Aznar J. M. Kuiper J. H. Doblaré M. (2006). A 3D Computational Simulation of Fracture Callus Formation: Influence of the Stiffness of the External Fixator. J. Biomech. Eng. 128, 290–299. 10.1115/1.2187045
Godwin J. W. Pinto A. R. Rosenthal N. A. (2017). Chasing the Recipe for a Pro-regenerative Immune System. Semin. Cel Dev. Biol. 61, 71–79. 10.1016/j.semcdb.2016.08.008
Goers L. Freemont P. Polizzi K. M. (2014). Co-culture Systems and Technologies: Taking Synthetic Biology to the Next Level. J. R. Soc. Interf. 11, 20140065. 10.1098/rsif.2014.0065
Gong C. Milberg O. Wang B. Vicini P. Narwal R. Roskos L. et al. (2017). A Computational Multiscale Agent-Based Model for Simulating Spatio-Temporal Tumour Immune Response to PD1 and PDL1 Inhibition. J. R. Soc. Interf. 14, 20170320. 10.1098/rsif.2017.0320
Goodwin S. McPherson J. D. McCombie W. R. (2016). Coming of Age: Ten Years of Next-Generation Sequencing Technologies. Nat. Rev. Genet. 17, 333–351. 10.1038/nrg.2016.49
Grimes R. Jepsen K. J. Fitch J. L. Einhorn T. A. Gerstenfeld L. C. (2011). The Transcriptome of Fracture Healing Defines Mechanisms of Coordination of Skeletal and Vascular Development during Endochondral Bone Formation. J. Bone Mineral Res. 26, 2597–2609. 10.1002/jbmr.486
Groeneveldt L. C. Herpelinck T. Maréchal M. Politis C. van IJcken W. F. J. Huylebroeck D. et al. (2020). The Bone-Forming Properties of Periosteum-Derived Cells Differ between Harvest Sites. Front. Cel Dev. Biol. 8, 554984. 10.3389/fcell.2020.554984
Gruber E. J. Leifer C. A. (2020). Molecular Regulation of TLR Signaling in Health and Disease: Mechano-Regulation of Macrophages and TLR Signaling. Innate Immun. 26, 15–25. 10.1177/1753425919838322
Grundnes O. Reikerås O. (1993). The Importance of the Hematoma for Fracture Healing in Rats. Acta Orthop. Scand. 64, 340–342. 10.3109/17453679308993640
Gu Q. Yang H. Shi Q. (2017). Macrophages and Bone Inflammation. J. Orthop. Transl. 10, 86–93. 10.1016/j.jot.2017.05.002
Guyot Y. Papantoniou I. Chai Y. C. Van Bael S. Schrooten J. Geris L. (2014). A Computational Model for Cell/ECM Growth on 3D Surfaces Using the Level Set Method: a Bone Tissue Engineering Case Study. Biomech. Model. Mechanobiol. 13, 1361–1371. 10.1007/s10237-014-0577-5
Haffner-Luntzer M. Kovtun A. Rapp A. E. Ignatius A. (2016). Mouse Models in Bone Fracture Healing Research. Curr. Mol. Biol. Rep. 2, 101–111. 10.1007/s40610-016-0037-3
Han S. Yan J.-J. Shin Y. Jeon J. J. Won J. Eun Jeong H. et al. (2012). A Versatile Assay for Monitoring In Vivo-like Transendothelial Migration of Neutrophils. Lab. A Chip 12, 3861. 10.1039/c2lc40445a
Harasymowicz N. S. Rashidi N. Savadipour A. Wu C. L. Tang R. Bramley J. et al. (2021). Single-cell RNA Sequencing Reveals the Induction of Novel Myeloid and Myeloid-Associated Cell Populations in Visceral Fat with Long-Term Obesity. FASEB J. 35, 1–17. 10.1096/fj.202001970R
Harwood P. J. Newman J. B. Michael A. L. (2010). (ii) an Update on Fracture Healing and Non-union. Orthop. Trauma 24, 9–23. 10.1016/j.mporth.2009.12.004
Helbling P. M. Piñeiro-Yáñez E. Gerosa R. Boettcher S. Al-Shahrour F. Manz M. G. et al. (2019). Global Transcriptomic Profiling of the Bone Marrow Stromal Microenvironment during Postnatal Development, Aging, and Inflammation. Cel Rep. 29, 3313–3330.e4. 10.1016/j.celrep.2019.11.004
Hoff P. Gaber T. Strehl C. Schmidt-Bleek K. Lang A. Huscher D. et al. (2016). Immunological Characterization of the Early Human Fracture Hematoma. Immunol. Res. 64, 1195–1206. 10.1007/s12026-016-8868-9
Hoff P. Gaber T. Strehl C. Jakstadt M. Hoff H. Schmidt-Bleek K. et al. (2017). A Pronounced Inflammatory Activity Characterizes the Early Fracture Healing Phase in Immunologically Restricted Patients. Int. J. Mol. Sci. 18, 583. 10.3390/ijms18030583
Horst K. Eschbach D. Pfeifer R. Hübenthal S. Sassen M. Steinfeldt T. et al. (2015). Local Inflammation in Fracture Hematoma: Results from a Combined Trauma Model in Pigs. Mediators Inflamm. 2015, 126060. 10.1155/2015/126060
Hundsdorfer W. Verwer J. (2003). Numerical Solution of Time-dependent Advection–Diffusion–Reaction Equations, 33 Heidelberg, Germany: Springer-Verlag Berlin Heidelberg. 10.1007/978-3-662-09017-6
Irimia D. Wang X. (2018). Inflammation-on-a-Chip: Probing the Immune System Ex Vivo. Trends Biotechnol. 36, 923–937. 10.1016/j.tibtech.2018.03.011
Isaksson H. Wilson W. van Donkelaar C. C. Huiskes R. Ito K. (2006). Comparison of Biophysical Stimuli for Mechano-Regulation of Tissue Differentiation during Fracture Healing. J. Biomech. 39, 1507–1516. 10.1016/j.jbiomech.2005.01.037
Isaksson H. van Donkelaar C. C. Huiskes R. Yao J. Ito K. (2008). Determining the Most Important Cellular Characteristics for Fracture Healing Using Design of Experiments Methods. J. Theor. Biol. 255, 26–39. 10.1016/j.jtbi.2008.07.037
Jahn C. Weidinger G. (2017). Regulatory T Cells Know what Is Needed to Regenerate. Dev. Cel. 43, 651–652. 10.1016/j.devcel.2017.12.010
Jain N. Moeller J. Vogel V. (2019). Mechanobiology of Macrophages: How Physical Factors Coregulate Macrophage Plasticity and Phagocytosis. Annu. Rev. Biomed. Eng. 21, 267–297. 10.1146/annurev-bioeng-062117-121224
Jerez S. Díaz-Infante S. Chen B. (2018). Fluctuating Periodic Solutions and Moment Boundedness of a Stochastic Model for the Bone Remodeling Process. Math. Biosci. 299, 153–164. 10.1016/j.mbs.2018.03.006
Karnes J. M. Daffner S. D. Watkins C. M. (2015). Multiple Roles of Tumor Necrosis Factor-Alpha in Fracture Healing. Bone 78, 87–93. 10.1016/j.bone.2015.05.001
Klein P. Schell H. Streitparth F. Heller M. Kassi J. P. Kandziora F. et al. (2003). The Initial Phase of Fracture Healing Is Specifically Sensitive to Mechanical Conditions. J. Orthop. Res. 21, 662–669. 10.1016/s0736-0266(02)00259-0
Könnecke I. Serra A. El Khassawna T. Schlundt C. Schell H. Hauser A. et al. (2014). T and B Cells Participate in Bone Repair by Infiltrating the Fracture Callus in a Two-Wave Fashion. Bone 64, 155–165. 10.1016/j.bone.2014.03.052
Kojouharov H. V. Trejo I. Chen-Charpentier B. M. (2017). “Modeling the Effects of Inflammation in Bone Fracture Healing,” in AIP Conference Proceedings, Albena, Bulgaria, June 21–26, 2017, 1895. 10.1063/1.5007359
Kolar P. Schmidt-Bleek K. Schell H. Gaber T. Toben D. Schmidmaier G. et al. (2010). The Early Fracture Hematoma and its Potential Role in Fracture Healing. Tissue Eng. - B: Rev. 16, 427–434. 10.1089/ten.teb.2009.0687
Kovach T. K. Dighe A. S. Lobo P. I. Cui Q. (2015). Interactions between MSCs and Immune Cells: Implications for Bone Healing. J. Immunol. Res. 2015, 1–17. 10.1155/2015/752510
Kovtun A. Bergdolt S. Wiegner R. Radermacher P. Huber-Lang M. Ignatius A. (2016). The Crucial Role of Neutrophil Granulocytes in Bone Fracture Healing. Eur. Cell Mater. 32, 152–162. 10.22203/eCM.v032a10
Kumar R. Clermont G. Vodovotz Y. Chow C. C. (2004). The Dynamics of Acute Inflammation. J. Theor. Biol. 230, 145–155. 10.1016/j.jtbi.2004.04.044
Lacroix D. Prendergast P. (2002). A Mechano-Regulation Model for Tissue Differentiation during Fracture Healing: Analysis of gap Size and Loading. J. Biomech. 35, 1163–1171. 10.1016/S0021-9290(02)00086-6
Lammens J. Laumen A. Delport H. Vanlauwe J. (2012). The Pentaconcept in Skeletal Tissue Engineering. A Combined Approach for the Repair of Bone Defects. Acta Orthop. Belg. 78, 569–573.
Lammens J. Marechal M. Delport H. Geris L. Luyten F. (2021). A Flowchart for the Translational Research of Cell-Based Therapy in the Treatment of Long Bone Defects. J. Regener. Med. 10, 1. 10.37532/jrgm.2021.10(1).175
Lawson B. A. Drovandi C. C. Cusimano N. Burrage P. Rodriguez B. Burrage K. (2018). Unlocking Data Sets by Calibrating Populations of Models to Data Density: A Study in Atrial Electrophysiology. Sci. Adv. 4. 10.1126/sciadv.1701676
Lisowska B. Kosson D. Domaracka K. (2018). Positives and Negatives of Nonsteroidal Anti-inflammatory Drugs in Bone Healing: The Effects of These Drugs on Bone Repair. Drug Des. Dev. Ther. 12, 1809–1814. 10.2147/dddt.s164565
Liszka T. Orkisz J. (1980). The Finite Difference Method at Arbitrary Irregular Grids and its Application in Applied Mechanics. Comput. Struct. 11, 83–95. Special Issue-Computational Methods in Nonlinear Mechanics. 10.1016/0045-7949(80)90149-2
Lo C. H. Baratchart E. Basanta D. Lynch C. C. (2020). Computational Modeling Reveals a Key Role for Polarized Myeloid Cells in Controlling Osteoclast Activity during Bone Injury Repair. bioRxiv. 10.1101/2020.10.13.338335
Loeffler J. Duda G. N. Sass F. A. Dienelt A. (2018). The Metabolic Microenvironment Steers Bone Tissue Regeneration. Trends Endocrinol. Metab. 29, 99–110. 10.1016/j.tem.2017.11.008
Loi F. Córdova L. A. Pajarinen J. hua Lin T. Yao Z. Goodman S. B. (2016). Inflammation, Fracture and Bone Repair. Bone 86, 119–130. 10.1016/j.bone.2016.02.020
Lüthje F. L. Skovgaard K. Jensen H. E. Kruse Jensen L. (2018). Pigs Are Useful for the Molecular Study of Bone Inflammation and Regeneration in Humans. Lab. Anim. 52, 630–640. 10.1177/0023677218766391
Lux T. (2018). Estimation of Agent-Based Models Using Sequential Monte Carlo Methods. J. Econ. Dyn. Control. 91, 391–408. 10.1016/j.jedc.2018.01.021
Mackey M. Glass L. (1977). Oscillation and Chaos in Physiological Control Systems. Science 197, 287–289. 10.1126/science.267326
Maffioli E. Nonnis S. Angioni R. Santagata F. Calì B. Zanotti L. et al. (2017). Proteomic Analysis of the Secretome of Human Bone Marrow-Derived Mesenchymal Stem Cells Primed by Pro-inflammatory Cytokines. J. Proteomics 166, 115–126. 10.1016/j.jprot.2017.07.012
Malizos K. N. Papatheodorou L. K. (2005). The Healing Potential of the Periosteum: Molecular Aspects. Injury 36, S13–S19. 10.1016/j.injury.2005.07.030
Manabe N. Kawaguchi H. Chikuda H. Miyaura C. Inada M. Nagai R. et al. (2001). Connection between B Lymphocyte and Osteoclast Differentiation Pathways. J. Immunol. 167, 2625–2631. 10.4049/jimmunol.167.5.2625
Marder E. Taylor A. L. (2011). Multiple Models to Capture the Variability in Biological Neurons and Networks. Nat. Neurosci. 14, 133–138. 10.1038/nn.2735
Marsell R. Einhorn T. A. (2011). The Biology of Fracture Healing. Injury 42, 551–555. 10.1016/j.injury.2011.03.031
Marsh D. (1998). Concepts of Fracture union, Delayed union, and Nonunion. Clin. Orthop. Relat. Res. 355, S22–S30. 10.1097/00003086-199810001-00004
Martínez I. V. Gómez E. J. Hernando M. E. Villares R. Mellado M. (2012). Agent-based Model of Macrophage Action on Endocrine Pancreas. Int. J. Data Mining Bioinformatics 6, 355–368. 10.1504/ijdmb.2012.049293
Maruyama M. Rhee C. Utsunomiya T. Zhang N. Ueno M. Yao Z. et al. (2020). Modulation of the Inflammatory Response and Bone Healing. Front. Endocrinol. 11, 386. 10.3389/fendo.2020.00386
Maslin C. Kedzierska K. Webster N. Muller W. Crowe S. (2005). Transendothelial Migration of Monocytes: The Underlying Molecular Mechanisms and Consequences of HIV-1 Infection. Curr. HIV Res. 3, 303–317. 10.2174/157016205774370401
McWhorter F. Y. Wang T. Nguyen P. Chung T. Liu W. F. (2013). Modulation of Macrophage Phenotype by Cell Shape. Proc. Natl. Acad. Sci. U S A. 110, 17253–17258. 10.1073/pnas.1308887110
Medzhitov R. Janeway C. A. (1997). Innate Immunity: Impact on the Adaptive Immune Response. Health San Francisco 9, 4–9. 10.1016/S0952-7915(97)80152-5
Medzhitov R. Janeway C. (2000). Innate Immune Recognition: Mechanisms and Pathways. Immunol Rev. 173, 89–97. 10.1034/j.1600-065x.2000.917309.x
Mehrian M. Guyot Y. Papantoniou I. Olofsson S. Sonnaert M. Misener R. et al. (2018). Maximizing Neotissue Growth Kinetics in a Perfusion Bioreactor: an In Silico Strategy Using Model Reduction and Bayesian Optimization. Biotechnol. Bioeng. 115, 617–629. 10.1002/bit.26500
Mescher A. L. (2017). Macrophages and Fibroblasts during Inflammation and Tissue Repair in Models of Organ Regeneration. Regeneration 4, 39–53. 10.1002/reg2.77
Mestas J. Hughes C. C. W. (2004). Of Mice and Not Men: Differences between Mouse and Human Immunology. J. Immunol. 172, 2731–2738. 10.4049/jimmunol.172.5.2731
Mi Q. Rivière B. Clermont G. Steed D. L. Vodovotz Y. (2007). Agent-based Model of Inflammation and Wound Healing: Insights into Diabetic Foot Ulcer Pathology and the Role of Transforming Growth Factor-Β1. Wound Repair Regen. 15, 671–682. 10.1111/j.1524-475X.2007.00271.x
Middleton K. Al-Dujaili S. Mei X. Günther A. You L. (2017). Microfluidic Co-culture Platform for Investigating Osteocyte-Osteoclast Signalling during Fluid Shear Stress Mechanostimulation. J. Biomech. 59, 35–42. 10.1016/j.jbiomech.2017.05.012
Mills L. A. Simpson A. H. R. W. (2012). In Vivo models of Bone Repair. The J. Bone Jt. Surg., Br. vol. 94-B, 865–874. 10.1302/0301-620x.94b7.27370
Mills L. A. Aitken S. A. Simpson A. H. R. (2017). The Risk of Non-union Per Fracture: Current Myths and Revised Figures from a Population of over 4 Million Adults. Acta Orthop. 88, 434–439. 10.1080/17453674.2017.1321351
Moore S. R. Saidel G. M. Knothe U. Knothe Tate M. L. (2014). Mechanistic, Mathematical Model to Predict the Dynamics of Tissue Genesis in Bone Defects via Mechanical Feedback and Mediation of Biochemical Factors. PLoS Comput. Biol. 10, e1003604. 10.1371/journal.pcbi.1003604
Moreno-Arotzena O. Mendoza G. Cóndor M. Rüberg T. García-Aznar J. M. (2014). Inducing Chemotactic and Haptotactic Cues in Microfluidic Devices for Three-Dimensional In Vitro Assays. Biomicrofluidics 8, 064122. 10.1063/1.4903948
Mosser D. M. Edwards J. P. (2008). Exploring the Full Spectrum of Macrophage Activation. Nat. Rev. Immunol. 8, 958–969. 10.1038/nri2448
Müller R. (2009). Hierarchical Microimaging of Bone Structure and Function. Nat. Rev. Rheumatol. 5, 373–381. 10.1038/nrrheum.2009.107
Murray P. J. Allen J. E. Biswas S. K. Fisher E. A. Gilroy D. W. Goerdt S. et al. (2014). Macrophage Activation and Polarization: Nomenclature and Experimental Guidelines. Immunity 41, 14–20. 10.1016/j.immuni.2014.06.008
Murray J. D. (1989). Mathematical Biology, 19 Heidelberg, Germany: Springer-Verlag Berlin Heidelberg. 10.1007/978-3-662-08539-4
Nagaraja S. Wallqvist A. Reifman J. Mitrophanov A. Y. (2014). Computational Approach to Characterize Causative Factors and Molecular Indicators of Chronic Wound Inflammation. J. Immunol. 192, 1824–1834. 10.4049/jimmunol.1302481
Nagatani Y. Imaizumi H. Fukuda T. Matsukawa M. Watanabe Y. Otani T. (2006). Applicability of Finite-Difference Time-Domain Method to Simulation of Wave Propagation in Cancellous Bone. Jpn. J. Appl. Phys. 45, 7186–7190. 10.1143/jjap.45.7186
Nasello G. Alamán-Díez P. Schiavi J. Pérez M. Á. McNamara L. García-Aznar J. M. (2020). Primary Human Osteoblasts Cultured in a 3D Microenvironment Create a Unique Representative Model of Their Differentiation into Osteocytes. Front. Bioeng. Biotechnol. 8, 336. 10.3389/fbioe.2020.00336
Nasello G. Cóndor M. Vaughan T. Schiavi J. (2021). Designing Hydrogel-Based Bone-On-Chips for Personalized Medicine. Appl. Sci. 11, 4495. 10.3390/app11104495
Occhetta P. Mainardi A. Votta E. Vallmajo-Martin Q. Ehrbar M. Martin I. et al. (2019). Hyperphysiological Compression of Articular Cartilage Induces an Osteoarthritic Phenotype in a Cartilage-On-A-Chip Model. Nat. Biomed. Eng. 3, 545–557. 10.1038/s41551-019-0406-3
Olsen L. Sherratt J. A. Maini P. K. Arnold F. (1997). A Mathematical Model for the Capillary Endothelial Cell-Extracellular Matrix Interactions in Wound-Healing Angiogenesis. IMA J. Math. Appl. Med. Biol. 14, 261–281. 10.1093/imammb/14.4.261
OReilly A. Hankenson K. D. Kelly D. J. (2016). A Computational Model to Explore the Role of Angiogenic Impairment on Endochondral Ossification during Fracture Healing. Biomech. Model. Mechanobiol. 15, 1279–1294. 10.1007/s10237-016-0759-4
Oryan A. Monazzah S. Bigham-Sadegh A. (2015). Bone Injury and Fracture Healing Biology. Biomed. Environ. Sci. 28, 57–71. 10.3967/bes2015.006
Osta B. Benedetti G. Miossec P. (2014). Classical and Paradoxical Effects of TNF-α on Bone Homeostasis. Front. Immunol. 5, 1–9. 10.3389/fimmu.2014.00048
Osuka A. Ogura H. Ueyama M. Shimazu T. Lederer J. A. (2014). Immune Response to Traumatic Injury: harmony and Discordance of Immune System Homeostasis. Acute Med. Surg. 1, 63–69. 10.1002/ams2.17
Pajarinen J. Lin T. Gibon E. Kohno Y. Maruyama M. Nathan K. et al. (2019). Mesenchymal Stem Cell-Macrophage Crosstalk and Bone Healing. Biomaterials 196, 80–89. 10.1016/j.biomaterials.2017.12.025
Papantoniou I. Nilsson Hall G. Loverdou N. Lesage R. Herpelinck T. Mendes L. et al. (2021). Turning Nature’s Own Processes into Design Strategies for Living Bone Implant Biomanufacturing: a Decade of Developmental Engineering. Adv. Drug Deliv. Rev. 169, 22–39. 10.1016/j.addr.2020.11.012
Pape H. C. Evans A. Kobbe P. (2010). Autologous Bone Graft: Properties and Techniques. J. orthop. Trauma 24, S36–S40. 10.1097/bot.0b013e3181cec4a1
Pappalardo F. Pennisi M. Motta S. (2010). “Universal Immune System Simulator Framework (UISS),” in Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology, Niagara Falls, NY, August 2–4, 2010 (Association for Computing Machinery, BCB ’10), 649–650. 10.1145/1854776.1854900
Pappalardo F. Russo G. Pennisi M. Parasiliti Palumbo G. A. Sgroi G. Motta S. et al. (2020). The Potential of Computational Modeling to Predict Disease Course and Treatment Response in Patients with Relapsing Multiple Sclerosis. Cells 9, 586. 10.3390/cells9030586
Parvinian B. Pathmanathan P. Daluwatte C. Yaghouby F. Gray R. A. Weininger S. et al. (2019). Credibility Evidence for Computational Patient Models Used in the Development of Physiological Closed-Loop Controlled Devices for Critical Care Medicine. Front. Physiol. 10, 220. 10.3389/fphys.2019.00220
Patin E. Hasan M. Bergstedt J. Rouilly V. Libri V. Urrutia A. et al. (2018). Natural Variation in the Parameters of Innate Immune Cells Is Preferentially Driven by Genetic Factors. Nat. Immunol. 19, 302–314. 10.1038/s41590-018-0049-7
Peiffer V. Gerisch A. Vandepitte D. Van Oosterwyck H. Geris L. (2011). A Hybrid Bioregulatory Model of Angiogenesis during Bone Fracture Healing. Biomech. Model. Mechanobiol. 10, 383–395. 10.1007/s10237-010-0241-7
Pennisi M. Rajput A. M. Toldo L. Pappalardo F. (2013). Agent Based Modeling of Treg-Teff Cross Regulation in Relapsing-Remitting Multiple Sclerosis. BMC Bioinf. 14 Suppl 16, S9. 10.1186/1471-2105-14-S16-S9
Perier-Metz C. Duda G. N. Checa S. (2020). Mechano-Biological Computer Model of Scaffold-Supported Bone Regeneration: Effect of Bone Graft and Scaffold Structure on Large Bone Defect Tissue Patterning. Front. Bioeng. Biotechnol. 8, 1–15. 10.3389/fbioe.2020.585799
Perren S. M. (2002). Evolution of the Internal Fixation of Long Bone Fractures: the Scientific Basis of Biological Internal Fixation: Choosing a New Balance between Stability and Biology. The J. bone Jt. surg., Br. vol. 84, 1093–1110. 10.1302/0301-620x.84b8.0841093
Plouffe B. D. Murthy S. K. Lewis L. H. (2015). Fundamentals and Application of Magnetic Particles in Cell Isolation and Enrichment: a Review. Rep. Prog. Phys. 78, 016601. 10.1088/0034-4885/78/1/016601
Prendergast P. Huiskes R. Soballe K. (1997). Biophysical Stimuli on Cells during Tissue Differentiation at Implant Interfaces. J. Biomech. 30, 539–548. 10.1016/S0021-9290(96)00140-6
Prokharau P. A. Vermolen F. J. García-Aznar J. M. (2012). A Mathematical Model for Cell Differentiation, as an Evolutionary and Regulated Process. Comput. Methods Biomech. Biomed. Eng. 17, 1051–1070. 10.1080/10255842.2012.736503
Reinke S. Geissler S. Taylor W. R. Schmidt-Bleek K. Juelke K. Schwachmeyer V. et al. (2013). Terminally Differentiated CD8+ T Cells Negatively Affect Bone Regeneration in Humans. Sci. Transl. Med. 5, 177ra36. 10.1126/scitranslmed.3004754
Reppe S. Datta H. K. Gautvik K. M. (2017). Omics Analysis of Human Bone to Identify Genes and Molecular Networks Regulating Skeletal Remodeling in Health and Disease. Bone 101, 88–95. 10.1016/j.bone.2017.04.012
Reynolds A. Rubin J. Clermont G. Day J. Vodovotz Y. Bard Ermentrout G. (2006). A Reduced Mathematical Model of the Acute Inflammatory Response: I. Derivation of Model and Analysis of Anti-inflammation. J. Theor. Biol. 242, 220–236. 10.1016/j.jtbi.2006.02.016
Ribeiro F. O. Gómez-Benito M. J. Folgado J. Fernandes P. R. García-Aznar J. M. (2015). In Silico mechano-chemical Model of Bone Healing for the Regeneration of Critical Defects: The Effect of BMP-2. PLoS One 10, 1–25. 10.1371/journal.pone.0127722
Ribitsch I. Baptista P. M. Lange-Consiglio A. Melotti L. Patruno M. Jenner F. et al. (2020). Large Animal Models in Regenerative Medicine and Tissue Engineering: To Do or Not to Do. Front. Bioeng. Biotechnol. 8, 972. 10.3389/fbioe.2020.00972
Rios F. J. Touyz R. M. Montezano A. C. (2017). “Isolation and Differentiation of Human Macrophages,” in Hypertension (New York, NY: Humana Press), 311–320. 10.1007/978-1-4939-6625-7_24
Russo G. Pennisi M. Fichera E. Motta S. Raciti G. Viceconti M. et al. (2020a). In Silico trial to Test COVID-19 Candidate Vaccines: a Case Study with UISS Platform. BMC Bioinf. 21, 527. 10.1186/s12859-020-03872-0
Russo G. Sgroi G. Parasiliti Palumbo G. A. Pennisi M. Juarez M. A. Cardona P.-J. et al. (2020b). Moving Forward through the In Silico Modeling of Tuberculosis: a Further Step with UISS-TB. BMC Bioinf. 21, 458. 10.1186/s12859-020-03762-5
Sadtler K. Estrellas K. Allen B. W. Wolf M. T. Fan H. Tam A. J. et al. (2016). Developing a Pro-regenerative Biomaterial Scaffold Microenvironment Requires T Helper 2 Cells. Science 352, 366–370. 10.1126/science.aad9272
Schlundt C. Schell H. Goodman S. B. Vunjak-Novakovic G. Duda G. N. Schmidt-Bleek K. (2015). Immune Modulation as a Therapeutic Strategy in Bone Regeneration. J. Exp. Orthop. 2, 1–10. 10.1186/s40634-014-0017-6
Schlundt C. El Khassawna T. Serra A. Dienelt A. Wendler S. Schell H. et al. (2018). Macrophages in Bone Fracture Healing: Their Essential Role in Endochondral Ossification. Bone 106, 78–89. 10.1016/j.bone.2015.10.019
Schmidt-Bleek K. Schell H. Schulz N. Hoff P. Perka C. Buttgereit F. et al. (2012). Inflammatory Phase of Bone Healing Initiates the Regenerative Healing cascade. Cel Tissue Res. 347, 567–573. 10.1007/s00441-011-1205-7
Schmidt-Bleek K. Marcucio R. Duda G. (2016). Future Treatment Strategies for Delayed Bone Healing: An Osteoimmunologic Approach. J. Am. Acad. Orthop. Surg. 24, e134–e135. 10.5435/JAAOS-D-16-00513
Schulte F. A. Zwahlen A. Lambers F. M. Kuhn G. Ruffoni D. Betts D. et al. (2013). Strain-adaptive In Silico Modeling of Bone Adaptation — A Computer Simulation Validated by In Vivo Micro-computed Tomography Data. Bone 52, 485–492. 10.1016/j.bone.2012.09.008
Seiden P. E. Celada F. (1992). A Model for Simulating Cognate Recognition and Response in the Immune System. J. Theor. Biol. 158, 329–357. 10.1016/s0022-5193(05)80737-4
Shi Z. Chapes S. K. Ben-Arieh D. Wu C. H. (2016). An Agent-Based Model of a Hepatic Inflammatory Response to salmonella: A Computational Study under a Large Set of Experimental Data. PLoS One 11, e0161131. 10.1371/journal.pone.0161131
Shiratori H. Feinweber C. Luckhardt S. Linke B. Resch E. Geisslinger G. et al. (2017). THP-1 and Human Peripheral Blood Mononuclear Cell-Derived Macrophages Differ in Their Capacity to Polarize In Vitro. Mol. Immunol. 88, 58–68. 10.1016/j.molimm.2017.05.027
Sierra M. Miana-Mena F. J. Calvo B. Muñoz M. J. Rodríguez J. F. Grasa J. (2015). On Using Model Populations to Determine Mechanical Properties of Skeletal Muscle. Application to Concentric Contraction Simulation. Ann. Biomed. Eng. 43, 2444–2455. 10.1007/s10439-015-1279-6
Sivaraj K. K. Jeong H.-W. Dharmalingam B. Zeuschner D. Adams S. Potente M. et al. (2021). Regional Specialization and Fate Specification of Bone Stromal Cells in Skeletal Development. Cel Rep. 36, 109352. 10.1016/j.celrep.2021.109352
Soltan M. Rohrer M. D. Prasad H. S. (2012). Monocytes: Super Cells for Bone Regeneration. Implant Dent. 21, 13–20. 10.1097/ID.0b013e31823fcf85
Sparks D. S. Saifzadeh S. Savi F. M. Dlaska C. E. Berner A. Henkel J. et al. (2020). A Preclinical Large-Animal Model for the Assessment of Critical-Size Load-Bearing Bone Defect Reconstruction. Nat. Protoc. 15, 877–924. 10.1038/s41596-019-0271-2
Stark R. Grzelak M. Hadfield J. (2019). RNA Sequencing: the Teenage Years. Nat. Rev. Genet. 20, 631–656. 10.1038/s41576-019-0150-2
Stéphanou A. Volpert V. (2016). Hybrid Modelling in Biology: a Classification Review. Math. Model. Nat. Phenom. 11, 37–48. 10.1051/mmnp/201611103
Steeve K. T. Marc P. Sandrine T. Dominique H. Yannick F. (2004). IL-6, RANKL, TNF-alpha/IL-1: Interrelations in Bone Resorption Pathophysiology. Cytokine Growth Factor. Rev. 15, 49–60. 10.1016/j.cytogfr.2003.10.005
Steiner M. Claes L. Ignatius A. Niemeyer F. Simon U. Wehner T. et al. (2013). Prediction of Fracture Healing under Axial Loading, Shear Loading and Bending Is Possible Using Distortional and Dilatational Strains as Determining Mechanical Stimuli. J. R. Soc. Interf. 10, 20130389. 10.1098/rsif.2013.0389
Stewart S. K. (2019). Fracture non-union: A Review of Clinical Challenges and Future Research Needs. Malays. Orthop. J. 13, 1–10. 10.5704/MOJ.1907.001
Stoecklein V. M. Osuka A. Lederer J. A. (2012). Trauma Equals Danger–Damage Control by the Immune System. J. Leukoc. Biol. 92, 539–551. 10.1189/jlb.0212072
Sun X. Su J. Bao J. Peng T. Zhang L. Zhang Y. et al. (2012). Cytokine Combination Therapy Prediction for Bone Remodeling in Tissue Engineering Based on the Intracellular Signaling Pathway. Biomaterials 33, 8265–8276. 10.1016/j.biomaterials.2012.07.041
Toben D. Schroeder I. El Khassawna T. Mehta M. Hoffmann J. E. Frisch J. T. et al. (2011). Fracture Healing Is Accelerated in the Absence of the Adaptive Immune System. J. Bone Mineral Res. 26, 113–124. 10.1002/jbmr.185
Tourolle né Betts D. C. Wehrle E. Paul G. R. Kuhn G. A. Christen P. Hofmann S. et al. (2020). The Association between Mineralised Tissue Formation and the Mechanical Local In Vivo Environment: Time-Lapsed Quantification of a Mouse Defect Healing Model. Sci. Rep. 10, 1100. 10.1038/s41598-020-57461-5
Trejo I. Kojouharov H. Chen-Charpentier B. (2019). Modeling the Macrophage-Mediated Inflammation Involved in the Bone Fracture Healing Process. Math. Comput. Appl. 24, 12. 10.3390/mca24010012
Tsiridis E. Upadhyay N. Giannoudis P. (2007). Molecular Aspects of Fracture Healing: Which Are the Important Molecules? Injury 38, S11–S25. 10.1016/j.injury.2007.02.006
Tsuchiya S. Yamabe M. Yamaguchi Y. Kobayashi Y. Konno T. Tada K. (1980). Establishment and Characterization of a Human Acute Monocytic Leukemia Cell Line (THP-1). Int. J. Cancer 26, 171–176. 10.1002/ijc.2910260208
ASME (2018). Assessing Credibility of Computational Modeling through Verification and Validation: Application to Medical Devices New York, NY: The American Society of Mechanical Engineers.
Vaeyens M.-M. Jorge-Peñas A. Barrasa-Fano J. Steuwe C. Heck T. Carmeliet P. et al. (2020). Matrix Deformations Around Angiogenic Sprouts Correlate to Sprout Dynamics and Suggest Pulling Activity. Angiogenesis 23, 315–324. 10.1007/s10456-020-09708-y
Van Dyke Parunak H. Savit R. Riolo R. L. (1998). “Agent-based Modeling vs. Equation-Based Modeling: A Case Study and Users’ Guide,” in Multi-Agent Systems and Agent-Based Simulation. Editors Sichman J. S. Conte R. Gilbert N. (Berlin, Heidelberg: Springer Berlin Heidelberg), 10–25. 10.1007/10692956_2
Vats D. Mukundan L. Odegaard J. I. Zhang L. Smith K. L. Morel C. R. et al. (2006). Oxidative Metabolism and PGC-1β Attenuate Macrophage-Mediated Inflammation. Cel Metab. 4, 13–24. 10.1016/j.cmet.2006.05.011
Vetter A. Witt F. Sander O. Duda G. N. Weinkamer R. (2012). The Spatio-Temporal Arrangement of Different Tissues during Bone Healing as a Result of Simple Mechanobiological Rules. Biomech. Model. Mechanobiol. 11, 147–160. 10.1007/s10237-011-0299-x
Viceconti M. Henney A. Morley-Fletcher E. (2016). In Silico clinical Trials: How Computer Simulation Will Transform the Biomedical Industry. Int. J. Clin. Trials 3, 37. 10.18203/2349-3259.ijct20161408
Virgilio K. M. Martin K. S. Peirce S. M. Blemker S. S. (2015). Multiscale Models of Skeletal Muscle Reveal the Complex Effects of Muscular Dystrophy on Tissue Mechanics and Damage Susceptibility. Interf. Focus 5, 20140080. 10.1098/rsfs.2014.0080
Vodovotz Y. Chow C. C. Bartels J. Lagoa C. Prince J. M. Levy R. M. et al. (2006). In Silico models of Acute Inflammation in Animals. Shock 26, 235–244. 10.1097/01.shk.0000225413.13866.fo
Wagar L. E. DiFazio R. M. Davis M. M. (2018). Advanced Model Systems and Tools for Basic and Translational Human Immunology. Genome Med. 10, 73. 10.1186/s13073-018-0584-8
Wang M. Yang N. (2018). Three-dimensional Computational Model Simulating the Fracture Healing Process with Both Biphasic Poroelastic Finite Element Analysis and Fuzzy Logic Control. Sci. Rep. 8, 1–13. 10.1038/s41598-018-25229-7
Ward P. A. Lentsch A. B. (1999). The Acute Inflammatory Response and its Regulation. Arch. Surg. 134, 666–669. 10.1001/archsurg.134.6.666
Warrender C. Forrest S. Koster F. (2006). Modeling Intercellular Interactions in Early Mycobacterium Infection. Bull. Math. Biol. 68, 2233–2261. 10.1007/s11538-006-9103-y
Wehrle E. Tourolle né Betts D. C. Kuhn G. A. Scheuren A. C. Hofmann S. Müller R. (2019). Evaluation of Longitudinal Time-Lapsed In Vivo Micro-CT for Monitoring Fracture Healing in Mouse Femur Defect Models. Sci. Rep. 9, 17445. 10.1038/s41598-019-53822-x
Wendelsdorf K. V. Alam M. Bassaganya-Riera J. Bisset K. Eubank S. Hontecillas R. et al. (2012). Enteric Immunity Simulator: A Tool for In Silico Study of Gastroenteric Infections. IEEE Trans. Nanobiosci. 11, 273–288. 10.1109/TNB.2012.2211891
Wendler S. Schlundt C. Bucher C. H. Birkigt J. Schipp C. J. Volk H.-D. et al. (2019). Immune Modulation to Enhance Bone Healing—A New Concept to Induce Bone Using Prostacyclin to Locally Modulate Immunity. Front. Immunol. 10, 713. 10.3389/fimmu.2019.00713
Westman J. Grinstein S. Marques P. E. (2020). Phagocytosis of Necrotic Debris at Sites of Injury and Inflammation. Front. Immunol. 10, 3030. 10.3389/fimmu.2019.03030
Wilkinson D. J. (2009). Stochastic Modelling for Quantitative Description of Heterogeneous Biological Systems. Nat. Rev. Genet. 10, 122–133. 10.1038/nrg2509
Yates A. Chan C. C. Callard R. E. George A. J. Stark J. (2001). An Approach to Modelling in Immunology. Brief. Bioinf. 2, 245–257. 10.1093/bib/2.3.245
Zahedmanesh H. Lally C. (2012). A Multiscale Mechanobiological Modelling Framework Using Agent-Based Models and Finite Element Analysis: Application to Vascular Tissue Engineering. Biomech. Model. Mechanobiol. 11, 363–377. 10.1007/s10237-011-0316-0
Zhang T. Yao Y. (2019). Effects of Inflammatory Cytokines on Bone/cartilage Repair. J. Cell Biochem. 120, 6841–6850. 10.1002/jcb.27953
Zhang Y. Böse T. Unger R. E. Jansen J. A. Kirkpatrick C. J. van den Beucken J. J. J. P. (2017). Macrophage Type Modulates Osteogenic Differentiation of Adipose Tissue MSCs. Cel Tissue Res. 369, 273–286. 10.1007/s00441-017-2598-8
Zhang B. Korolj A. Lai B. F. L. Radisic M. (2018). Advances in Organ-On-A-Chip Engineering. Nat. Rev. Mater. 3, 257–278. 10.1038/s41578-018-0034-7
Zienkiewicz O. C. Taylor R. L. Nithiarasu P. Zhu J. (1977). The Finite Element Method, 3 London, UK: McGraw-Hill.
Zura R. Xiong Z. Einhorn T. Watson J. T. Ostrum R. F. Prayson M. J. et al. (2016). Epidemiology of Fracture Nonunion in 18 Human Bones. JAMA Surg. 151, 1–12. 10.1001/jamasurg.2016.2775
Zysset P. K. Dall’Ara E. Varga P. Pahr D. H. (2013). Finite Element Analysis for Prediction of Bone Strength. BoneKEy Rep. 2, 1–9. 10.1038/bonekey.2013.120
