Numerical simulation of fracture healing_Journal of Biomedical Engineering

Authors：

FU Ruisen ,  YANG Haisheng

Department of Biomedical Engineering, College of Environment and Life Science, Beijing University of Technology, Beijing 100124, P.R.China;

Corresponding author：

Keywords：

fracture healing; mechanobiology; tissue differentiation; numerical model

DOI：

10.7507/1001-5515.202004010

Video：

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Fracture is a common physical injury. Its healing process involves complex biological activities at tissue, cellular and molecular levels and is affected by mechanical and biological factors. Over recent years, numerical simulation methods have been widely used to explore the mechanisms of fracture healing, design fixators and develop novel treatment strategies, etc. This paper mainly recommend the numerical methods used for simulating fracture healing and their latest research progress, which helps people better understand the mechanism of fracture healing, and also provides direction and guidance for the numerical simulation research of fracture healing in the future. First, the fracture healing process and its relationship with mechanical stimulation and biological factors are described. Then, the numerical models used for simulating fracture healing (including mechano-regulatory model, biological regulatory model and mechano-biological regulatory model) and corresponding modeling techniques (mainly including agent-based techniques and fuzzy logic controlling method) were summarized in particular. Finally, the future research directions in numerical simulation of fracture healing were preliminarily prospected.

Citation： FU Ruisen, YANG Haisheng. Numerical simulation of fracture healing. Journal of Biomedical Engineering, 2020, 37(5): 930-935. doi: 10.7507/1001-5515.202004010 Copy

1.	马显志, 韩生寿, 马骏, 等. 股骨干骨折术后骨折不愈合的治疗进展. 中华骨与关节外科杂志, 2018, 11(5): 390-400.
2.	孙再杰, 杨思宇, 张国栋, 等. 动力化治疗下肢长骨骨折术后延迟愈合的研究进展. 中华老年骨科与康复电子杂志, 2019, 5(2): 118-122.
3.	魏娜, 张萍, 于莉, 等. 间充质干细胞在骨折愈合中作用的研究进展. 实用医药杂志, 2018, 35(6): 562-566.
4.	何芬. 促进骨折愈合的物理治疗方法的进展. 中医临床研究, 2018, 10(33): 99-101.
5.	Borgiani E, Duda G N, Checa S. Multiscale modeling of bone healing: toward a systems biology approach. Front Physiol, 2017, 8: 287.
6.	Miramini S, Yang Yi, Zhang Lihai. A probabilistic-based approach for computational simulation of bone fracture healing. Comput Methods Programs Biomed, 2019, 180: 105011.
7.	Ghiasi M S, Chen J, Vaziri A, et al. Bone fracture healing in mechanobiological modeling: a review of principles and methods. Bone Rep, 2017, 6: 87-100.
8.	Wang M, Yang Ning, Wang Xinyu. A review of computational models of bone fracture healing. Med Biol Eng Comput, 2017, 55(11): 1895-1914.
9.	Isaksson H. Recent advances in mechanobiological modeling of bone regeneration. Mech Res Commun, 2012, 42: 22-31.
10.	Kennedy R C, Marmor M, Marcucio R, et al. Simulation enabled search for explanatory mechanisms of the fracture healing process. PLoS Comput Biol, 2018, 14(2): e1005980.
11.	Ghiasi M S, Chen J E, Rodriguez E K, et al. Computational modeling of human bone fracture healing affected by different conditions of initial healing stage. BMC Musculoskelet Disord, 2019, 20(1): 562.
12.	薛徽, 孙瑶. 影响骨折愈合的生物因素研究新进展. 口腔医学, 2018, 38(11): 1043-1047.
13.	Bahney C S, Zondervan R L, Allison P, et al. Cellular biology of fracture healing. J Orthop Res, 2019, 37(1): 35-50.
14.	Wang M, Yang Ning. Three-dimensional computational model simulating the fracture healing process with both biphasic poroelastic finite element analysis and fuzzy logic control. Sci Rep, 2018, 8(1): 6744.
15.	Aziz A U A, Wahab A A, Ramlee M H. Relationship between strain and healing process for the use of external fixator: a short review//2018 2nd International Conference on BioSignal Analysis, Processing and Systems (ICBAPS), Kuching: IEEE, 2018: 87–92.
16.	Reich K M, Tangl S, Heimel P, et al. Histomorphometric analysis of callus formation stimulated by axial dynamisation in a standardised ovine osteotomy model. Biomed Res Int, 2019, 2019: 4250940.
17.	de Barros e Lima Bueno R, Dias A P, Ponce K J, et al. Bone healing response in cyclically loaded implants: comparing zero, one, and two loading sessions per day. Journal of the Mechanical Behavior of Biomedical Materials, 2018, 85: 152-161.
18.	Wilson C J, Schütz M A, Epari D R. Computational simulation of bone fracture healing under inverse dynamisation. Biomech Model Mechanobiol, 2017, 16(1): 5-14.
19.	Vavva M G, Grivas K N, Carlier A, et al. Effect of ultrasound on bone fracture healing: a computational bioregulatory model. Comput Biol Med, 2018, 100: 74-85.
20.	王沫楠. 基于血液供给条件和力学环境的骨折愈合仿真. 自动化学报, 2018, 44(2): 240-250.
21.	王新宇. 力和组织内氧气调控的骨折愈合过程仿真. 哈尔滨: 哈尔滨理工大学, 2019.
22.	Prendergast P J, Huiskes R, Søballe K. Biophysical stimuli on cells during tissue differentiation at implant interfaces. J Biomech, 1997, 30(6): 539-548.
23.	Claes L E, Heigele C A. Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. J Biomech, 1999, 32(3): 255-266.
24.	Ghimire S, Miramini S, Richardson M, et al. Role of dynamic loading on early stage of bone fracture healing. Ann Biomed Eng, 2018, 46(11): 1768-1784.
25.	Lipphaus A, Witzel U. Finite-Element syntheses of callus and bone remodeling: biomechanical study of fracture healing in long bones. Anat Rec (Hoboken), 2018, 301(12): 2112-2121.
26.	Pietsch M, Niemeyer F, Simon U, et al. Modelling the fracture-healing process as a moving-interface problem using an interface-capturing approach. Comput Methods Biomech Biomed Engin, 2018, 21(8): 512-520.
27.	Ren T. Dailey H L. Mechanoregulation modeling of bone healing in realistic fracture geometries. Biomech Model Mechanobiol, 2020. DOI: https://doi.org/10.1007/s10237-020-01340-5.
28.	Borgiani E, Figge C, Kruck B, et al. Age-related changes in the mechanical regulation of bone healing are explained by altered cellular mechanoresponse. J Bone Miner Res, 2019, 34(10): 1923-1937.
29.	Grivas K N, Vavva M G, Polyzos D, et al. Effect of ultrasound on bone fracture healing: a computational mechanobioregulatory model. J Acoust Soc Am, 2019, 145(2): 1048.
30.	Ganadhiepan G, Zhang Lihai, Miramini S, et al. The effects of dynamic loading on bone fracture healing under ilizarov circular fixators. J Biomech Eng, 2019, 141(5): 1-12.
31.	Trejo I, Kojouharov H V, Chen-Charpentier B M. Modeling the effects of growth factors on bone fracture healing. AIP Conf Proc, 2019, 2164(020003): 1-14.
32.	Pauwels F. A new theory on the influence of mechanical stimuli on the differentiation of supporting tissue. The tenth contribution to the functional anatomy and causal morphology of the supporting structure. Z Anat Entwicklungsgesch, 1960, 121(6): 478-515.
33.	Carter D R, Beaupré G S, Giori N J, et al. Mechanobiology of skeletal regeneration. Clin Orthop Relat Res, 1998(355 Suppl): S41-S55.
34.	Checa S, Prendergast P J. A mechanobiological model for tissue differentiation that includes angiogenesis: a lattice-based modeling approach. Ann Biomed Eng, 2009, 37(1): 129-145.
35.	Ament C, Hofer E P. A fuzzy logic model of fracture healing. J Biomech, 2000, 33(8): 961-968.

1. 马显志, 韩生寿, 马骏, 等. 股骨干骨折术后骨折不愈合的治疗进展. 中华骨与关节外科杂志, 2018, 11(5): 390-400.
2. 孙再杰, 杨思宇, 张国栋, 等. 动力化治疗下肢长骨骨折术后延迟愈合的研究进展. 中华老年骨科与康复电子杂志, 2019, 5(2): 118-122.
3. 魏娜, 张萍, 于莉, 等. 间充质干细胞在骨折愈合中作用的研究进展. 实用医药杂志, 2018, 35(6): 562-566.
4. 何芬. 促进骨折愈合的物理治疗方法的进展. 中医临床研究, 2018, 10(33): 99-101.
5. Borgiani E, Duda G N, Checa S. Multiscale modeling of bone healing: toward a systems biology approach. Front Physiol, 2017, 8: 287.
6. Miramini S, Yang Yi, Zhang Lihai. A probabilistic-based approach for computational simulation of bone fracture healing. Comput Methods Programs Biomed, 2019, 180: 105011.
7. Ghiasi M S, Chen J, Vaziri A, et al. Bone fracture healing in mechanobiological modeling: a review of principles and methods. Bone Rep, 2017, 6: 87-100.
8. Wang M, Yang Ning, Wang Xinyu. A review of computational models of bone fracture healing. Med Biol Eng Comput, 2017, 55(11): 1895-1914.
9. Isaksson H. Recent advances in mechanobiological modeling of bone regeneration. Mech Res Commun, 2012, 42: 22-31.
10. Kennedy R C, Marmor M, Marcucio R, et al. Simulation enabled search for explanatory mechanisms of the fracture healing process. PLoS Comput Biol, 2018, 14(2): e1005980.
11. Ghiasi M S, Chen J E, Rodriguez E K, et al. Computational modeling of human bone fracture healing affected by different conditions of initial healing stage. BMC Musculoskelet Disord, 2019, 20(1): 562.
12. 薛徽, 孙瑶. 影响骨折愈合的生物因素研究新进展. 口腔医学, 2018, 38(11): 1043-1047.
13. Bahney C S, Zondervan R L, Allison P, et al. Cellular biology of fracture healing. J Orthop Res, 2019, 37(1): 35-50.
14. Wang M, Yang Ning. Three-dimensional computational model simulating the fracture healing process with both biphasic poroelastic finite element analysis and fuzzy logic control. Sci Rep, 2018, 8(1): 6744.
15. Aziz A U A, Wahab A A, Ramlee M H. Relationship between strain and healing process for the use of external fixator: a short review//2018 2nd International Conference on BioSignal Analysis, Processing and Systems (ICBAPS), Kuching: IEEE, 2018: 87–92.
16. Reich K M, Tangl S, Heimel P, et al. Histomorphometric analysis of callus formation stimulated by axial dynamisation in a standardised ovine osteotomy model. Biomed Res Int, 2019, 2019: 4250940.
17. de Barros e Lima Bueno R, Dias A P, Ponce K J, et al. Bone healing response in cyclically loaded implants: comparing zero, one, and two loading sessions per day. Journal of the Mechanical Behavior of Biomedical Materials, 2018, 85: 152-161.
18. Wilson C J, Schütz M A, Epari D R. Computational simulation of bone fracture healing under inverse dynamisation. Biomech Model Mechanobiol, 2017, 16(1): 5-14.
19. Vavva M G, Grivas K N, Carlier A, et al. Effect of ultrasound on bone fracture healing: a computational bioregulatory model. Comput Biol Med, 2018, 100: 74-85.
20. 王沫楠. 基于血液供给条件和力学环境的骨折愈合仿真. 自动化学报, 2018, 44(2): 240-250.
21. 王新宇. 力和组织内氧气调控的骨折愈合过程仿真. 哈尔滨: 哈尔滨理工大学, 2019.
22. Prendergast P J, Huiskes R, Søballe K. Biophysical stimuli on cells during tissue differentiation at implant interfaces. J Biomech, 1997, 30(6): 539-548.
23. Claes L E, Heigele C A. Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. J Biomech, 1999, 32(3): 255-266.
24. Ghimire S, Miramini S, Richardson M, et al. Role of dynamic loading on early stage of bone fracture healing. Ann Biomed Eng, 2018, 46(11): 1768-1784.
25. Lipphaus A, Witzel U. Finite-Element syntheses of callus and bone remodeling: biomechanical study of fracture healing in long bones. Anat Rec (Hoboken), 2018, 301(12): 2112-2121.
26. Pietsch M, Niemeyer F, Simon U, et al. Modelling the fracture-healing process as a moving-interface problem using an interface-capturing approach. Comput Methods Biomech Biomed Engin, 2018, 21(8): 512-520.
27. Ren T. Dailey H L. Mechanoregulation modeling of bone healing in realistic fracture geometries. Biomech Model Mechanobiol, 2020. DOI: https://doi.org/10.1007/s10237-020-01340-5.
28. Borgiani E, Figge C, Kruck B, et al. Age-related changes in the mechanical regulation of bone healing are explained by altered cellular mechanoresponse. J Bone Miner Res, 2019, 34(10): 1923-1937.
29. Grivas K N, Vavva M G, Polyzos D, et al. Effect of ultrasound on bone fracture healing: a computational mechanobioregulatory model. J Acoust Soc Am, 2019, 145(2): 1048.
30. Ganadhiepan G, Zhang Lihai, Miramini S, et al. The effects of dynamic loading on bone fracture healing under ilizarov circular fixators. J Biomech Eng, 2019, 141(5): 1-12.
31. Trejo I, Kojouharov H V, Chen-Charpentier B M. Modeling the effects of growth factors on bone fracture healing. AIP Conf Proc, 2019, 2164(020003): 1-14.
32. Pauwels F. A new theory on the influence of mechanical stimuli on the differentiation of supporting tissue. The tenth contribution to the functional anatomy and causal morphology of the supporting structure. Z Anat Entwicklungsgesch, 1960, 121(6): 478-515.
33. Carter D R, Beaupré G S, Giori N J, et al. Mechanobiology of skeletal regeneration. Clin Orthop Relat Res, 1998(355 Suppl): S41-S55.
34. Checa S, Prendergast P J. A mechanobiological model for tissue differentiation that includes angiogenesis: a lattice-based modeling approach. Ann Biomed Eng, 2009, 37(1): 129-145.
35. Ament C, Hofer E P. A fuzzy logic model of fracture healing. J Biomech, 2000, 33(8): 961-968.

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