Improving brain-cancer therapies through mathematical modelling

Cancer therapies are various modes of treatment, such as surgery, radiation therapy, and chemotherapy that are administered to cancer patients.
However, cancer treatments can pose several challenges, as therapies used to kill cancer cells are generally also toxic to normal cells. Moreover, cancer cells mutate rapidly and can develop resistance to chemical agents or radiation therapy. Besides, all types of cancer cells may not respond to the same therapy. Some cancer cells respond to one...

Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...

The targeted cancer therapies, also known as “molecular targeted therapies,” take advantage of the molecular and genetic differences between the cancer cells and the normal cells. It needs a thorough understanding of the cancer cells to develop drugs that can target specific molecular aspects that drive the growth, progression, and spread of cancer cells without affecting the growth and survival of other normal cells in the body.
There are several types of targeted therapies against...

Modeling, a key technique in therapy, uses observational learning to help clients acquire and practice new skills by watching therapists demonstrate desired behaviors. This approach, rooted in Albert Bandura's concept of vicarious learning, plays a significant role in therapeutic interventions for various psychological conditions, including social anxiety, ADHD, and depression.
Participant Modeling
Participant modeling involves therapists demonstrating calm and effective behaviors in...

Mathematical induction is a structured method of proof used to confirm the truth of statements involving natural numbers. Consider the sum of the first n natural numbers:This formula describes a pattern that appears to hold true as more terms are added. To verify that it is valid for all natural numbers, mathematical induction proceeds in two essential steps. The first is the base case, where the formula is tested for the initial value, typically n = 1. Substituting into both sides confirms the...

Mathematical principles play a crucial role in pharmacokinetics, providing a framework for understanding and quantifying drug distribution and elimination dynamics in the body. By utilizing mathematical expressions and units, pharmacologists can accurately characterize the behavior of drugs, optimize dosing regimens, and predict therapeutic outcomes.
One significant application of mathematics in pharmacokinetics is the characterization of drug distribution through the volume of distribution...