A study of tumour growth based on stoichiometric principles: a continuous model and its discrete analogue

M Saleem1, Tanuja Agrawal, Afzal Anees

  • 1a Department of Applied Mathematics , Z.H. College of Engineering and Technology, A.M.U ., Aligarh 202002 , India.

Related Concept Videos

Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
458
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
333
Tumor Progression02:07

Tumor Progression

Tumor progression is a phenomenon where the pre-formed tumor acquires successive mutations to become clinically more aggressive and malignant. In the 1950s, Foulds first described the stepwise progression of cancer cells through successive stages.
Colon cancer is one of the best-documented examples of tumor progression. Early mutation in the APC gene in colon cells causes a small growth on the colon wall called a polyp. With time, this polyp grows into a benign, pre-cancerous tumor. Further...
6.2K
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
164
Adaptive Mechanisms in Cancer Cells02:53

Adaptive Mechanisms in Cancer Cells

Cancer cells accumulate genetic changes at an abnormally rapid rate due to the defects in the DNA repair mechanisms. From an evolutionary perspective, such genetic instability is advantageous for cancer development. Mutant cell lines accumulate a series of beneficial mutations that contribute to their progression into cancer.
Some of the advantages that cancer cells have on normal cells include - enhanced ability to divide without terminally differentiating, induce new blood vessel formation,...
5.7K
Compartment Models: Single-Compartment Model01:14

Compartment Models: Single-Compartment Model

The single-compartment model serves as a simplified representation of the human body. This model assumes that the body functions as a single, well-mixed open compartment. When a drug is administered intravenously, it enters the body and quickly distributes uniformly. The drug then undergoes biotransformation and elimination, ultimately leaving the body. The volume of this compartment is referred to as the apparent volume of distribution into which the drug can uniformly distribute. In this...
3.1K