The method of lines for the numerical solution of a mathematical model for capillary formation: The role of tumor angiogenic factor in the extra-cellular matrix

: Mesenchymal stem cells because of its high proliferation, differentiation, regenerative capacity, and ease of availability have been a popular choice in cytotherapy. Mesenchymal Stem Cells (MSCs) have a natural tendency to home in a tumor microenvironment and acts against it, owing to the similarity of the latter to an injured tissue environment. Several studies have confirmed the recruitment of MSCs by tumor through various cytokine signaling that brings about phenotypic changes to cancer cells, thereby promoting migration, invasion, and adhesion of cancer cells. The contrasting results on MSCs as a tool for cancer cytotherapy may be due to the complex cell to cell interaction in the tumor microenvironment, which involves various cell types such as cancer cells, immune cells, endothelial cells, and cancer stem cells. Cell to cell communication can be simple or complex and it is transmitted through various cytokines among multiple cell phenotypes, mechano-elasticity of the extra-cellular matrix surrounding the cancer cells, and hypoxic environments. In this article, the role of the extra-cellular matrix proteins and soluble mediators that acts as communicators between mesenchymal stem cells and cancer cells has been reviewed specifically for breast cancer, as it is the leading member of cancer malignancies. The comprehensive information may be beneficial in finding a new combinatorial cytotherapeutic strategy using MSCs by exploiting the cross-talk between mesenchymal stem cells and cancer cells for treating breast cancer.

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A NUMERICAL PROOF THAT CERTAIN CELLS FOLLOW THE TRAILS OF THE DIFFUSIONS OF SOME CHEMICALS IN THE EXTRACELLULAR MATRIX

Journal of Mechanics in Medicine and Biology ◽

10.1142/s0219519421500275 ◽

2021 ◽

pp. 2150027

Author(s):

İREM ÇAY ◽

SERDAL PAMUK

Keyword(s):

Mathematical Model ◽

Extracellular Matrix ◽

Tumor Angiogenesis ◽

Numerical Solutions ◽

Extra Cellular Matrix ◽

The Matrix ◽

Good Agreement ◽

Cellular Matrix

In this work, we obtain the numerical solutions of a 2D mathematical model of tumor angiogenesis originally presented in [Pamuk S, ÇAY İ, Sazci A, A 2D mathematical model for tumor angiogenesis: The roles of certain cells in the extra cellular matrix, Math Biosci 306:32–48, 2018] to numerically prove that the certain cells, the endothelials (EC), pericytes (PC) and macrophages (MC) follow the trails of the diffusions of some chemicals in the extracellular matrix (ECM) which is, in fact, inhomogeneous. This leads to branching, the sprouting of a new neovessel from an existing vessel. Therefore, anastomosis occurs between these sprouts. In our figures we do see these branching and anastomosis, which show the fact that the cells diffuse according to the structure of the ECM. As a result, one sees that our results are in good agreement with the biological facts about the movements of certain cells in the Matrix.

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Stability and Collapsing Mechanism of Cavitation-Induced Nanobubbles in Simulated Extra-Cellular Matrix (ECM) Near Neuron

Volume 3: Biomedical and Biotechnology Engineering ◽

10.1115/imece2016-67806 ◽

2016 ◽

Author(s):

Y.-T. Wu ◽

A. Adnan

Keyword(s):

Extra Cellular Matrix ◽

Bubble Collapse ◽

Experimental Investigations ◽

Perineuronal Nets ◽

Neuron Damage ◽

The Stability ◽

The Relationship ◽

Fluid Interaction ◽

Cellular Matrix

In blast-induced traumatic brain injury, shock waves (SW) play an important role along with cavitation phenomena. Due to the lack of reliable and reproducible experimental investigations, we have a limited understanding of the role of cavitation in brain damage. The present study aims to develop an atomistic simulation model to determine the role of shock-induced impulse and different constituents of the brain’s extra-cellular matrix (ECM) on the formation mechanism, stability and collapsing mechanism of nanobubbles in the ECM. The ECM in the brain can be divided into three major types depending on their location behind the blood-brain barrier, namely (a) the basement membrane (basal lamina), (b) the perineuronal nets and (3) the neural interstitial matrix. In this paper, we have studied the interaction of nanobubbles with bio-molecules of the perineuronal nets. We have chosen this zone of the ECM because we are interested to obtain the role of cavitation bubble collapse in neuron damage. Most biomolecules of perineuronal nets are slender in shape and flexible which is believed to induce special solid-fluid interaction between the fluid domain and the solid domain within the ECM. In addition, perineuronal nets contain a significant number of sodium ions. The relationship between sodium ion and solid-like constituents of perineuronal nets on the stability and the collapsing mechanism of nanobubbles will be discussed.

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