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 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.

scholarly journals Mathematical Model of Muscle Wasting in Cancer Cachexia

2020 ◽  
Author(s):  
Suzan Farhang-Sardroodi ◽  
Kathleen P. Wilkie
Keyword(s):  
Mathematical Model ◽  
Satellite Cell ◽  
Muscle Tissue ◽  
Cancer Cachexia ◽  
Muscle Wasting ◽  
Tissue Growth ◽  
Colon 26 ◽  
Treatment Conditions ◽  
Risk Of Mortality ◽  
Pharmacological Blockade

Cancer cachexia is a debilitating condition characterized by an extreme loss of skeletal muscle mass which negatively impacts patient’s quality of life, reduces their ability to sustain anticancer therapies, and increases the risk of mortality. Recent discoveries have identified the myostatin/activin-ActRIIB pathway as critical to muscle wasting by inducing satellite cell quiescence and increasing muscle-specific ubiquitin ligases responsible for atrophy. Remarkably, pharmacological blockade of the ActRIIB pathway has shown to reverse muscle wasting and prolong the survival time of tumor-bearing animals. To explore the implications of this signaling pathway and potential therapeutic targets in cachexia, we construct a novel mathematical model of muscle tissue subjected to tumor-derived cachexic factors. The model formulation tracks the intercellular interactions between cancer, satellite cell, and muscle cell populations. The model is parameterized by fitting to colon-26 mouse model data, and analysis provides insight into tissue growth in healthy, cancerous, and post-treatment conditions. Model predictions suggest that cachexia fundamentally alters muscle tissue health, as measured by the stem cell ratio, and this is only partially recovered by anti-cachexia treatment. Our mathematical findings suggest that the activation and proliferation of satellite cells, after blocking the myostatin/activin B pathway, is required to partially recover cancer-induced muscle loss.

scholarly journals Mathematical Model of Muscle Wasting in Cancer Cachexia

2020 ◽  
Vol 9 (7) ◽  
pp. 2029 ◽  
Author(s):  
Suzan Farhang-Sardroodi ◽  
Kathleen P. Wilkie
Keyword(s):  
Mathematical Model ◽  
Satellite Cell ◽  
Muscle Tissue ◽  
Cancer Cachexia ◽  
Muscle Wasting ◽  
Functional Differentiation ◽  
Activin A ◽  
Tissue Growth ◽  
Partial Recovery ◽  
Colon 26

Cancer cachexia is a debilitating condition characterized by an extreme loss of skeletal muscle mass, which negatively impacts patients’ quality of life, reduces their ability to sustain anti-cancer therapies, and increases the risk of mortality. Recent discoveries have identified the myostatin/activin A/ActRIIB pathway as critical to muscle wasting by inducing satellite cell quiescence and increasing muscle-specific ubiquitin ligases responsible for atrophy. Remarkably, pharmacological blockade of the ActRIIB pathway has been shown to reverse muscle wasting and prolong the survival time of tumor-bearing animals. To explore the implications of this signaling pathway and potential therapeutic targets in cachexia, we construct a novel mathematical model of muscle tissue subjected to tumor-derived cachectic factors. The model formulation tracks the intercellular interactions between cancer cell, satellite cell, and muscle cell populations. The model is parameterized by fitting to colon-26 mouse model data, and the analysis provides insight into tissue growth in healthy, cancerous, and post-cachexia treatment conditions. Model predictions suggest that cachexia fundamentally alters muscle tissue health, as measured by the stem cell ratio, and this is only partially recovered by anti-cachexia treatment. Our mathematical findings suggest that after blocking the myostatin/activin A pathway, partial recovery of cancer-induced muscle loss requires the activation and proliferation of the satellite cell compartment with a functional differentiation program.

Abstract LB-131: Mathematical model for tumor growth

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