Dynamic behavior and stabilization of brain cell reconstitution after stroke under the proliferation and differentiation processes for stem cells

Awatif Jahman Alqarni; Azmin Sham Rambely; Sana Abdulkream Alharbi; Ishak Hashim; Awatif Jahman Alqarni; Azmin Sham Rambely; Sana Abdulkream Alharbi; Ishak Hashim

doi:10.3934/mbe.2021314

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 5: 6288-6304. doi: 10.3934/mbe.2021314

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Dynamic behavior and stabilization of brain cell reconstitution after stroke under the proliferation and differentiation processes for stem cells

1.
Department of Mathematics, College of Sciences and Arts in Balqarn, University of Bisha, Bisha 61922, Saudi Arabia
2.
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi Selangor 43600, Malaysia
3.
Department of Mathematics & Statistics, College of Science, Taibah University, Yanbu 41911, Almadinah Almunawarah, Saudi Arabia

Academic Editor: Cristiana J. Silva

Received: 27 May 2021 Accepted: 12 July 2021 Published: 19 July 2021

Stem cells play a critical role in regulatory operations, overseeing tissue regeneration and tissue homeostasis. In this paper, a mathematical model is proposed and analyzed to study the impact of stem cell transplantation on the dynamical behavior of stroke therapy, which is assumed to be based on transplanting dead brain cells following a stroke. We transform the method of using hierarchical cell systems into a method of using different compartment variables by using ordinary differential equations, each of which elucidates a well-defined differentiation stage along with the effect of mature cells in improving the brain function after a stroke. Stem cells, progenitor cells, and the impacts of the stem cells transplanted on brain cells are among the variables considered. The model is studied analytically and solved numerically using the fourth-order Runge-Kutta method. We analyze the structure of equilibria, the ability of neural stem cells to proliferate and differentiate, and the stability properties of equilibria for stem cell transplantation. The model is considered to be stable after transplantation if the stem cells and progenitor cells differentiate into mature nerve cells in the brain. The results of the model analysis and simulation facilitate the identification of various biologically probable parameter sets that can explain the optimal time for stem cell replacement of damaged brain cells. Associating the classified parameter sets with recent experimental and clinical findings contributes to a better understanding of therapeutic mechanisms that promote the reconstitution of brain cells after an ischemic stroke.
- cell replacement,
- eigenvalue stability analysis,
- ischemic stroke,
- numerical simulation,
- system of ordinary differential equations
Citation: Awatif Jahman Alqarni, Azmin Sham Rambely, Sana Abdulkream Alharbi, Ishak Hashim. Dynamic behavior and stabilization of brain cell reconstitution after stroke under the proliferation and differentiation processes for stem cells[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 6288-6304. doi: 10.3934/mbe.2021314

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Abstract

Stem cells play a critical role in regulatory operations, overseeing tissue regeneration and tissue homeostasis. In this paper, a mathematical model is proposed and analyzed to study the impact of stem cell transplantation on the dynamical behavior of stroke therapy, which is assumed to be based on transplanting dead brain cells following a stroke. We transform the method of using hierarchical cell systems into a method of using different compartment variables by using ordinary differential equations, each of which elucidates a well-defined differentiation stage along with the effect of mature cells in improving the brain function after a stroke. Stem cells, progenitor cells, and the impacts of the stem cells transplanted on brain cells are among the variables considered. The model is studied analytically and solved numerically using the fourth-order Runge-Kutta method. We analyze the structure of equilibria, the ability of neural stem cells to proliferate and differentiate, and the stability properties of equilibria for stem cell transplantation. The model is considered to be stable after transplantation if the stem cells and progenitor cells differentiate into mature nerve cells in the brain. The results of the model analysis and simulation facilitate the identification of various biologically probable parameter sets that can explain the optimal time for stem cell replacement of damaged brain cells. Associating the classified parameter sets with recent experimental and clinical findings contributes to a better understanding of therapeutic mechanisms that promote the reconstitution of brain cells after an ischemic stroke.

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