Capillary network formation and structure in a modified discrete mathematical model of angiogenesis

2021 ◽  
Author(s):  
Madjid Soltani
Keyword(s):  
Mathematical Model ◽  
Network Formation ◽  
Initial Conditions ◽  
Capillary Network ◽  
Cancer Development ◽  
Border Effect ◽  
Capillary Networks ◽  
The Matrix ◽  
Discrete Mathematical Model ◽  
Mathematical Foundations

Abstract Angiogenesis, as part of cancer development, involves hierarchical complicated events and processes. Multiple studies have revealed the significance of the formation and structure of tumor-induced capillary networks. In this study, a discrete mathematical model of angiogenesis is studied and modified to capture the realistic physics of capillary network formation. Modifications are performed on the mathematical foundations of an existing discrete model of angiogenesis. The main modifications are the imposition of the matrix density effect, implementation of realistic boundary and initial conditions, and improvement of the method of governing equations based on physical observation. Results show that endothelial cells accelerate angiogenesis and capillary formation as they migrate toward the tumor and clearly exhibit the physical concept of haptotactic movement. On the other hand, consideration of blood flow-induced stress leads to a dynamic adaptive vascular network of capillaries which intelligibly reflects the brush border effect . The present modified model of capillary network formation is based on the physical rationale that defines a clear mathematical and physical interpretation of angiogenesis, which is likely to be used in cancer development modeling and anti-angiogenic therapies.

A DISCRETE MATHEMATICAL MODEL FOR SINGLE AND COLLECTIVE MOVEMENT IN AMOEBOID CELLS

2018 ◽  
Vol 26 (02) ◽  
pp. 275-300
Author(s):  
NICOLETA TARFULEA
Keyword(s):  
Mathematical Model ◽  
Mechanical Model ◽  
Network Formation ◽  
Rigid Surface ◽  
Directed Movement ◽  
Substrate Rigidity ◽  
Cell Substrate ◽  
A Cell ◽  
Discrete Mathematical Model ◽  
Amoeboid Cells

In this paper, we develop a new discrete mathematical model for individual and collective cell motility. We introduce a mechanical model for the movement of a cell on a two-dimensional rigid surface to describe and investigate the cell–cell and cell–substrate interactions. The cell cytoskeleton is modeled as a series of springs and dashpots connected in parallel. The cell–substrate attachments and the cell protrusions are also included. In particular, this model is used to describe the directed movement of endothelial cells on a Matrigel plate. We compare the results from our model with experimental data. We show that cell density and substrate rigidity play an important role in network formation.

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

2009 ◽  
Vol 30 (4) ◽  
pp. 455-462
Author(s):  
Gai-ping Zhao ◽  
Er-yun Chen ◽  
Jie Wu ◽  
Shi-xiong Xu ◽  
M. W. Collins ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Discrete Mathematical Model

scholarly journals Acute ethanol exposure disrupts VEGF receptor cell signaling in endothelial cells

2008 ◽  
Vol 295 (1) ◽  
pp. H174-H184 ◽  
Author(s):  
Katherine A. Radek ◽  
Elizabeth J. Kovacs ◽  
Richard L. Gallo ◽  
Luisa A. DiPietro
Keyword(s):  
Endothelial Cells ◽  
Endothelial Cell ◽  
Cell Signaling ◽  
Network Formation ◽  
Ethanol Exposure ◽  
Capillary Network ◽  
Ethanol Metabolism ◽  
Vegf Receptor ◽  
Acute Ethanol

Physiological angiogenesis is regulated by various factors, including signaling through vascular endothelial growth factor (VEGF) receptors. We previously reported that a single dose of ethanol (1.4 g/kg), yielding a blood alcohol concentration of 100 mg/dl, significantly impairs angiogenesis in murine wounds, despite adequate levels of VEGF, suggesting direct effects of ethanol on endothelial cell signaling (40). To examine the mechanism by which ethanol influences angiogenesis in wounds, we employed two different in vitro angiogenesis assays to determine whether acute ethanol exposure (100 mg/dl) would have long-lasting effects on VEGF-induced capillary network formation. Ethanol exposure resulted in reduced VEGF-induced cord formation on collagen and reduced capillary network structure on Matrigel in vitro. In addition, ethanol exposure decreased expression of endothelial VEGF receptor-2, as well as VEGF receptor-2 phosphorylation in vitro. Inhibition of ethanol metabolism by 4-methylpyrazole partially abrogated the effect of ethanol on endothelial cell cord formation. However, mice treated with t-butanol, an alcohol not metabolized by alcohol dehydrogenase, exhibited no change in wound vascularity. These results suggest that products of ethanol metabolism are important factors in the development of ethanol-induced changes in endothelial cell responsiveness to VEGF. In vivo, ethanol exposure caused both decreased angiogenesis and increased hypoxia in wounds. Moreover, in vitro experiments demonstrated a direct effect of ethanol on the response to hypoxia in endothelial cells, as ethanol diminished nuclear hypoxia-inducible factor-1α protein levels. Together, the data establish that acute ethanol exposure significantly impairs angiogenesis and suggest that this effect is mediated by changes in endothelial cell responsiveness to both VEGF and hypoxia.

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

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.

Optimal Liquidation Strategy Based on Stochastic and Nonlinear Price Impact and Particle Swarm Optimization

2012 ◽  
Vol 452-453 ◽  
pp. 607-612
Author(s):  
Fei Huang ◽  
Jia He Cao
Keyword(s):  
Mathematical Model ◽  
Nonlinear Function ◽  
Liquidity Risk ◽  
Concave Function ◽  
Institutional Investor ◽  
Price Impact ◽  
Swarm Optimization ◽  
Optimal Liquidation ◽  
Horizon Line ◽  
Discrete Mathematical Model

The institutional investor selling a large block of shares in the market usually faces with liquidity risk declining the stock’s prices. In the paper, supposing that temporary impact is stochastic and nonlinear function of trading velocity, we establishes the discrete mathematical model and uses PSO to obtain the optimal liquidation strategies of risk aversion, which is a strict concave function. When analyzing the sensitivity of the parameters, we find that the curve becomes higher and steeper with the increase of the parameters or the decrease of , .As the parameter is tremendous, the curve is close to a horizon line.

scholarly journals AGV Brake System Simulation

2019 ◽  
Vol 10 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Daniel Varecha ◽  
Robert Kohar ◽  
Frantisek Brumercik
Keyword(s):  
Mathematical Model ◽  
Input Data ◽  
Initial Conditions ◽  
Brake System ◽  
Disc Brake ◽  
Hydraulic Control ◽  
Stopping Distance ◽  
Braking Force ◽  
Braking Process ◽  
The Mathematical Model

Abstract The article is focused on braking simulation of automated guided vehicle (AGV). The brake system is used with a disc brake and with hydraulic control. In the first step, the formula necessary for braking force at the start of braking is derived. The stopping distance is 1.5 meters. Subsequently, a mathematical model of braking is created into which the formula of the necessary braking force is applied. The mathematical model represents a motion equation that is solved in the software Matlab by an approximation method. Next a simulation is created using Matlab software and the data of simulation are displayed in the graph. The transport speed of the vehicle is 1 〖m.s〗^(-1) and the weight of the vehicle is 6000 kg including load. The aim of this article is to determine the braking time of the device depending from the input data entered, which represent the initial conditions of the braking process.

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