Mathematical modeling of fracture healing in mice: comparison between experimental data and numerical simulation results

Abstract

The combined use of experimental and mathematical models can lead to a better understanding of fracture healing. In this study, a mathematical model, which was originally established by Bailón-Plaza and van der Meulen (J Theor Biol 212:191-209, 2001), was applied to an experimental model of a semi-stabilized murine tibial fracture. The mathematical model was implemented in a custom finite volumes code, specialized in dealing with the model's requirements of mass conservation and non-negativity of the variables. A qualitative agreement between the experimentally measured and numerically simulated evolution in the cartilage and bone content was observed. Additionally, an extensive parametric study was conducted to assess the influence of the model parameters on the simulation outcome. Finally, a case of pathological fracture healing and its treatment by administration of growth factors was modeled to demonstrate the potential therapeutic value of this mathematical model.

Numerical simulation of two-dimensional and three-dimensional axisymmetric advection–diffusion systems with complex geometries using finite-volume methods

“…(A similar figure but giving the stem cell density is provide in the electronic supplementary material.) It can be seen that the results are very similar thus justifying the approach of Geris et al (2006). Slight differences are seen in the total healing time, which can be attributed mainly to the difference in the modelled callus volume.…”

“…Some groups improve on the allowed shape of Ω by using a non-intersecting union of these large rectangles to make up their domain (e.g. Geris et al 2006). There are several disadvantages to this approach.…”

Sensitivity Analysis by Design of Experiments

“…It is however impossible to study interactions between parameters, and the effect of the parameters resulting from this analysis might be different when choosing a different reference condition [12]. The OAT analysis was used by Lacroix [17] and Geris et al [8] to assess the influence of the value and duration of the initial and boundary conditions on the simulation results of a fracture healing model.…”

Connecting biology and mechanics in fracture healing: an integrated mathematical modeling framework for the study of nonunions

“…For the bioregulatory model, a custom Matlab finite volumes (FV) code is used, paying special attention the model's requirements of mass conservation and non-negativity of the variables (Geris et al 2006). Finite element (FE) analyses are carried out in MSC.Marc (Version 2005r2, Palo Alto, USA), using its soil mechanics capabilities and its user subroutines.…”