A mathematical model of angiogenesis and tumor growth: analysis and application in anti-angiogenesis therapy

2018 ◽  
Vol 77 (5) ◽  
pp. 1589-1622 ◽  
Author(s):  
Xiaoming Zheng ◽  
Mohye Sweidan
Keyword(s):  
Mathematical Model ◽  
Tumor Growth ◽  
Growth Analysis

scholarly journals A mathematical model of tumor growth by diffusion

1989 ◽  
Vol 94 (1) ◽  
pp. 155 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Mathematical Model ◽  
Tumor Growth

scholarly journals Cellular cooperation shapes tumor growth: a statistical mechanics mathematical model

2018 ◽  
Author(s):  
Jeffrey West ◽  
Paul K. Newton
Keyword(s):  
Mathematical Model ◽  
Statistical Mechanics ◽  
Tumor Growth ◽  
Fitness Landscape ◽  
Cellular Level ◽  
Cellular Heterogeneity ◽  
Functional Coupling ◽  
Macroscopic Tumor ◽  
Growth Laws ◽  
Cellular Cooperation

AbstractA tumor is made up of a heterogeneous collection of cell types all competing on a fitness landscape mediated by micro-environmental conditions that dictate their interactions. Despite the fact that much is known about cell signaling and cellular cooperation, the specifics of how the cell-to-cell coupling and the range over which this coupling acts affect the macroscopic tumor growth laws that govern total volume, mass, and carrying capacity remain poorly understood. We develop a statistical mechanics approach that focuses on the total number of possible states each cell can occupy, and show how different assumptions on correlations of these states gives rise to the many different macroscopic tumor growth laws used in the literature. Although it is widely understood that molecular and cellular heterogeneity within a tumor is a driver of growth, here we emphasize that focusing on the functional coupling of these states at the cellular level is what determines macroscopic growth characteristics.Significance statementA mathematical model relating tumor heterogeneity at the cellular level to tumor growth at the macroscopic level is described based on a statistical mechanics framework. The model takes into account the number of accessible states available to each cell as well as their long-range coupling (population cooperation) to other cells. We show that the degree to which cell populations cooperate determine the number of independent cell states, which in turn dictates the macroscopic (volumetric) growth law. It follows that targeting cell-to-cell interactions could be a way of mitigating and controlling tumor growth.

Abstract LB-131: Mathematical model for tumor growth

2010 ◽  
Author(s):  
Jiang ji ◽  
Guangde tu ◽  
Mei zou
Keyword(s):  
Mathematical Model ◽  
Tumor Growth

Stability of a Mathematical Model with Piecewise Constant Arguments for Tumor-Immune Interaction Under Drug Therapy

2019 ◽  
Vol 29 (01) ◽  
pp. 1950009 ◽  
Author(s):  
Zonghong Feng ◽  
Xinxing Wu ◽  
Luo Yang
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Drug Therapy ◽  
Tumor Growth ◽  
Tumor Cells ◽  
Chaotic Behavior ◽  
Sufficient Conditions ◽  
Tumor Growth Rate ◽  
Chaotic Region ◽  
Treatment Parameter

This paper studies a mathematical model for the interaction between tumor cells and Cytotoxic T lymphocytes (CTLs) under drug therapy. We obtain some sufficient conditions for the local and global asymptotical stabilities of the system by using Schur–Cohn criterion and the theory of Lyapunov function. In addition, it is known that the system without any treatment may undergo Neimark–Sacker bifurcation, and there may exist a chaotic region of values of tumor growth rate where the system exhibits chaotic behavior. So it is important to narrow the chaotic region. This may be done by increasing the intensity of the treatment to some extent. Moreover, for a fixed value of tumor growth rate in the chaotic region, a threshold value [Formula: see text] is predicted of the treatment parameter [Formula: see text]. We can see Neimark–Sacker bifurcation of the system when [Formula: see text], and the chaotic behavior for tumor cells ends and the system becomes locally asymptotically stable when [Formula: see text].

Instability and Mitotic Patterns in Tissue Growth

1973 ◽  
Vol 95 (3) ◽  
pp. 324-327 ◽  
Author(s):  
Leon Glass
Keyword(s):  
Mathematical Model ◽  
Tumor Growth ◽  
Mitotic Activity ◽  
Model System ◽  
Tissue Growth ◽  
Dimensionless Number

A mathematical model which reproduces several qualitative features of cancerous tumor growth is proposed. The onset of unstable growth is characterized by a dimensionless number, which is defined in terms of the parameters describing the system. Patterns of mitotic activity of the model system are compared with experimentally observed patterns of mitotic activity in cancerous tissues.

scholarly journals Global Bounded Classical Solutions for a Gradient-Driven Mathematical Model of Antiangiogenesis in Tumor Growth

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Xiaofei Yang ◽  
Bo Lu
Keyword(s):  
Mathematical Model ◽  
Endothelial Cells ◽  
Partial Differential Equations ◽  
Global Existence ◽  
Tumor Growth ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Angiogenic Factors ◽  
Classical Solutions ◽  
Parabolic Partial Differential Equations

In this paper, we consider a gradient-driven mathematical model of antiangiogenesis in tumor growth. In the model, the movement of endothelial cells is governed by diffusion of themselves and chemotaxis in response to gradients of tumor angiogenic factors and angiostatin. The concentration of tumor angiogenic factors and angiostatin is assumed to diffuse and decay. The resulting system consists of three parabolic partial differential equations. In the present paper, we study the global existence and boundedness of classical solutions of the system under homogeneous Neumann boundary conditions.

scholarly journals TMPRSS2-ERG fusions confer efficacy of enzalutamide in an in vivo bone tumor growth model

BMC Cancer ◽  
2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Louie Semaan ◽  
Navneet Mander ◽  
Michael L. Cher ◽  
Sreenivasa R. Chinni
Keyword(s):  
Prostate Cancer ◽  
Tumor Growth ◽  
Bone Tumor ◽  
Bone Tumors ◽  
Growth Analysis ◽  
Biosynthetic Enzyme ◽  
Enzyme Expression ◽  
Oncogenic Signaling ◽  
Androgen Synthesis

Abstract Background Castrate Resistant Prostate Cancer (CRPC) is an advanced disease resistant to systemic traditional medical or surgical castration, and resistance is primarily attributed to reactivation of AR through multiple mechanisms. TMPRSS2-ERG fusions have been shown to regulate AR signaling, interfere with pro-differentiation functions, and mediate oncogenic signaling. We have recently shown that ERG regulates intra-tumoral androgen synthesis and thereby facilitates AR function in prostate cancer cells. We hypothesize that enzalutamide treatment will be more effective in cells/tumors with TMPRSS2-ERG translocations because these tumors have increased AR signaling. Methods ERG knockdown was performed with VCaP cells using lentiviral infections to generate VCaP ERGshRNA cells and control VCaP scr cells with scrambled shRNA. Cell-growth analysis was performed to determine the effect of enzalutamide. Reverse transcription, quantitative real-time PCR (RT-qPCR) was used to determine the expression of AR responsive genes. Luciferase tagged VCaP scr and shRNA infected cells were used in an intra-tibial animal model for bone tumor growth analysis and enzalutamide treatment used to inhibit AR signaling in bone tumors. Western blotting analyzed VCaP bone tumor samples for ERG, AR, AKR1C3 and HSD3B1 and HSD3B2 expression. Results Enzalutamide inhibited the growth of VCaP scr cells more effectively than shERG cells. Analysis of AR responsive genes shows that Enzalutamide treatment at 5 micromolar concentration inhibited by 85–90% in VCaP Scr cells whereas these genes were inhibited to a lesser extent in VCaP shERG cells. Enzalutamide treatment resulted in severe growth inhibition in VCaP scr shRNA cells compared to VCaP shERG cells. In bone tumor growth experiment, VCaP ERG shRNA cells grew at slower than VCaP scr shRNA cells. Androgen biosynthetic enzyme expression is lower VCaP shERG bone tumors compared to VCaP scr shRNA bone tumors and enzalutamide inhibited the enzyme expression in both types of tumors. Conclusions These data suggest that ERG transcription factor regulates androgen biosynthetic enzyme expression that enzalutamide treatment is more effective against VCaP bone tumors with an intact ERG expression, and that knocking down ERG in VCaP cells leads to a lesser response to enzalutamide therapy. Thus, ERG expression status in tumors could help stratify patients for enzalutamide therapy.

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