Next Article in Journal / Special Issue
Evolution of an Exponential Polynomial Family of Discrete Dynamical Systems
Previous Article in Journal
Acknowledgement to Reviewers of MCA in 2018
Previous Article in Special Issue
Block Preconditioning Matrices for the Newton Method to Compute the Dominant λ-Modes Associated with the Neutron Diffusion Equation
Article Menu
Issue 1 (March) cover image

Export Article

Open AccessArticle

Modeling the Macrophage-Mediated Inflammation Involved in the Bone Fracture Healing Process

Department of Mathematics, The University of Texas at Arlington, P.O. Box 19408, Arlington, TX 76019-0408, USA
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(1), 12; https://doi.org/10.3390/mca24010012
Received: 14 November 2018 / Revised: 14 January 2019 / Accepted: 15 January 2019 / Published: 17 January 2019
(This article belongs to the Special Issue Mathematical Modelling in Engineering & Human Behaviour 2018)
  |  
PDF [1309 KB, uploaded 17 January 2019]
  |  

Abstract

A new mathematical model is presented to study the effects of macrophages on the bone fracture healing process. The model consists of a system of nonlinear ordinary differential equations that represents the interactions among classically and alternatively activated macrophages, mesenchymal stem cells, osteoblasts, and pro- and anti-inflammatory cytokines. A qualitative analysis of the model is performed to determine the equilibria and their corresponding stability properties. Numerical simulations are also presented to support the theoretical results, and to monitor the evolution of a broken bone for different types of fractures under various medical interventions. The model can be used to guide clinical experiments and to explore possible medical treatments that accelerate the bone fracture healing process, either by surgical interventions or drug administrations. View Full-Text
Keywords: bone repair; macrophages; immune system; cytokines; stem cells bone repair; macrophages; immune system; cytokines; stem cells
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed
Printed Edition Available!
A printed edition of this Special Issue is available here.

Share & Cite This Article

MDPI and ACS Style

Trejo, I.; Kojouharov, H.; Chen-Charpentier, B. Modeling the Macrophage-Mediated Inflammation Involved in the Bone Fracture Healing Process. Math. Comput. Appl. 2019, 24, 12.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top