×
Trejo, Imelda; Kojouharov, Hristo V.

Understanding the fundamental molecular mechanism of osteogenic differentiation from mesenchymal stem cells. (English) Zbl 1433.34068

Appl. Appl. Math. 14, No. 2, 687-698 (2019).
Summary: A mathematical model is presented to study the regulatory effects of growth factors in osteoblastogenesis. The model incorporates the interactions among mesenchymal stem cells, osteoblasts, and growth factors. The resulting system of nonlinear ordinary differential equations is studied analytically and numerically. Mathematical conditions for successful osteogenic differentiation and optimal osteoblasts population are formulated, which can be used in practice to accelerate bone formation. Numerical simulations are also presented to support the theoretical results and to explore different medical interventions to enhance osteoblastogenesis.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34C23 Bifurcation theory for ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
92C37 Cell biology
92C50 Medical applications (general)
92C40 Biochemistry, molecular biology
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Keywords:

bone fracture healing; growth factors; Hopf bifurcation; mesenchymal stem cell differentiation; osteoblasts; osteogenesis; stability
Cite Review PDF
Full Text: Link

References:

[1] Bailon-Plaza, A. and Van Der Meulen, M.C. (2001). A mathematical framework to study the effects of growth factor influences on fracture healing, Journal of Theoretical Biology, Vol. 212, No. 2, pp. 191-209.
[2] Carlier, A., Geris, L., Van Gastel, N., Carmeliet, G. and Van Oosterwyck, H. (2015). Oxygen as a critical determinant of bone fracture healing-a multiscale model, Journal of Theoretical Biology, Vol. 365, pp. 247-264. · Zbl 1314.92040
[3] Devescovi, V., Leonardi, E., Ciapetti, G. and Cenni, E. (2008). Growth factors in bone repair, La Chirurgia degli organi di movimento, Vol. 92, No. 3, pp. 161-168.
[4] Dimitriou, R., Tsiridis, E. and Giannoudis, P.V. (2005). Current concepts of molecular aspects of bone healing, Injury, Vol. 36, No. 12, pp. 1392-1404.
[5] Doblaré, M., García, J.M. and Gómez, M.J. (2004). Modelling bone tissue fracture and healing: a review, Engineering Fracture Mechanics, Vol. 71, No. 13, pp. 1809-1840.
[6] Fakhry, M., Hamade, E., Badran, B., Buchet, R. and Magne, D. (2013). Molecular mechanisms of mesenchymal stem cell differentiation towards osteoblasts, World Journal of Stem Cells, Vol. 5, No. 4, pp. 136.
[7] Florencio-Silva, R., Sasso, G.R.D.S., Sasso-Cerri, E., Simões, M.J. and Cerri, P.S. (2015). Biology of bone tissue: structure, function, and factors that influence bone cells, BioMed Research International, Vol. 2015.
[8] Garg, P., Mazur, M.M., Buck, A.C., Wandtke, M.E., Liu, J. and Ebraheim, N.A. (2017). Prospective review of mesenchymal stem cells differentiation into osteoblasts, Orthopaedic Surgery, Vol. 9, No. 1, pp. 13-19.
[9] Ghiasi, M.S. and Chen, J., Vaziri, A., Rodriguez, E.K. and Nazarian, A. (2017). Bone fracture healing in mechanobiological modeling: A review of principles and methods, Bone Reports, Vol. 6, pp. 87-100.
[10] Lin, H., Sohn, J., Shen, H., Langhans, M.T. and Tuan, R.S. (2019). Bone marrow mesenchymal stem cells: Aging and tissue engineering applications to enhance bone healing, Biomaterials, Vol. 203, pp. 96-110.
[11] Moreo, P., García-Aznar, J.M. and Doblaré, M. (2009). Bone ingrowth on the surface of endosseous implants, Part 1: Mathematical model, Journal of Theoretical Biology, Vol. 260, No. 1, pp. 1- 12. · Zbl 1402.92249
[12] Trejo, I., Kojouharov, H. and Chen-Charpentier, B. (2019). Modeling the macrophage-mediated inflammation involved in the bone fracture healing process, Mathematical and Computational Applications, Vol. 24, No. 1, pp. 12.
[13] Via, A.G., Frizziero, A. and Oliva, F. (2012). Biological properties of mesenchymal stem cells from different sources, Muscles, Ligaments and Tendons Journal, Vol. 2, No. 3, pp. 154.
[14] Wiggins, S. (2003).Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer Science & Business Media. · Zbl 1027.37002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.