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Critical Reviews™ in Biomedical Engineering

年間 6 å·ç™ºè¡Œ

ISSN 印刷: 0278-940X

ISSN オンライン: 1943-619X

SJR: 0.262 SNIP: 0.372 CiteScore™:: 2.2 H-Index: 56

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A Simplistic Approach to Bone Healing Simulation

巻 50, 発行 6, 2022, pp. 1-12
DOI: 10.1615/CritRevBiomedEng.2022044728
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要約

A simple computational approach to simulation of healing in long bone fractures is presented. In particular, an algorithm that could simulate the formation, maturation, and resorption of fracture callus is developed and validated. The simplicity of the approach lies in the fact that the algorithm uses only the applied load and a single constraint parameter for the entire simulation. The work hypothesizes bone healing as a comprehensive energy minimization process where mechanical stimulation is proposed as the primary precursor for the beginning of different stages (i.e., callus formation, mineralization, and resorption). As such, the hypothesis is derived from the second law of thermodynamics which states that the energy of a closed system should be minimum at equilibrium. Alternatively, each stage of healing bone healing may be termed a state of homeostasis. The validation is done through a multi-material, time-based simulation of bone healing in a damaged tibia. The simulation uses a cross-section-based finite element model and an advanced version of an already validated structural optimization algorithm. The optimization objective is to minimize overall strain energy for the entire process, subject to a polar first moment of mass constraint. The simulation results show different stages of healing, where the algorithm generates a callus geometry similar to those observed experimentally. Eventually, a geometry similar to that in an intact cross-section is achieved by resorption of the callus from the unwanted sites.

Figures

  • Generalized representation of different stages of healing in a typical long bone fracture
  • Pictorial representation of the FE modeling approach. (a) Murine tibia with a defect at anterior mid-diaphysis
section a´-a´. (b) Corresponding cross-section. (c) Prismatic beam model of bone created using the cross-section. (d)
Sixteen-noded hexahedral element used for developing the model.
  • Major tissue lineage curves during cortical bone defect healing. Lineage1 (blue or middle) represents the maturation and resorption of hard callus, Lineage2 (red or top) represents the formation of lamellar bone, and Lineage3
(grey or bottom) represents no bone formation.
  • Distribution of normal strain on defect bearing section obtained using simplifed model (a), and design space
with design and non-design region (b)
  • Qualitative comparison of experimental anterior defect healing with simulation results. Iterative changes in
tissue transformation observed in the simulation (a to f), and schematic representation of an anterior-lateral defect
section 2 and 3 weeks after surgery, respectively (g and h), based on Liu et al.50
  • Experimental versus simulation results in posterior defect healing. simulation results (a to f) and coarse adaptation of the sections with posterior defect at 1 and 4 weeks after surgery (g and h), based on Lim et al.51
  • A comparison of experimental and simulation results in medial cortical defect healing. Iterative changes in
tissue formation and resorption (a to f) and the healing section with medial defect 1 and 3 weeks after surgery (g and
h), based on Lee et al.48
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