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Tumor cell and microvessel densities during the growth of a brain tumor: A theoretical study

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Title Tumor cell and microvessel densities during the growth of a brain tumor: A theoretical study
 
Creator Boruah, Dibyajyoti
Sen, Arijit
 
Subject Angiogenesis efficiency
Energy requirement
Saturated cell density
Saturated tumor cell population
Stress inside the tumor
Tumor saturation factor
 
Description 675-686
Mathematical model for the tumor growth incorporating energy supply and requirement, angiogenesis efficiency and
effect of elasticity of adjacent normal tissue to understand tumor biology and predict saturation status is rare to find. This
study is conducted to address these issues. We propose mathematical expressions to explain alterations of tumor cell density
(nT), microvessel density (MVD), and growth rate(r) during the development of brain tumors. We assume that nT increases
during the growth of the tumor due to the increase of external pressure from the initial cell density (nT0); nT0 is same as the
external normal tissue. The rate of increase in tumor cells (dNT/dt) depends on the rate of energy available for the creation of
new cells and the energy required for a single cell division(γ). Due to the increase of tumor cell density, hypoxia is
developed, which up-regulates the secretion of vascular endothelial growth factor (VEGF) and new capillaries are generated.
Therefore, the surface area density of capillaries (Acs) in tumors increases. Hence, we consider that Acs(t) ∞ nT(t).
A modified logistic equation is developed. Temporal variations of nT(t), Acs(t), r(t) and tumor cell population ‘NT(t)’ are
examined. The expressions of saturated cell density(nTM), saturated microvessel surface area density (AcsM) and tumor
saturation time(Ts) are formulated. An important feature, tumor saturation factor ‘fTS’ is determined. When fTS
 
Date 2022-07-01T10:59:05Z
2022-07-01T10:59:05Z
2022-06
 
Type Article
 
Identifier 0975-0959 (Online); 0301-1208 (Print)
http://nopr.niscpr.res.in/handle/123456789/60008
 
Language en
 
Publisher NIScPR-CSIR, India
 
Source IJBB Vol.59(6) [June 2022]