The Hidden Mathematics to Treat Cancer
Authors: A. Mageed Ismail 
Published: January 2025

Mathematics is essential in cancer research and treatment because it helps scientists analyze complex data, such as genetic mutations in tumors, to understand cancer progression and estimate how long it has been developing. Mathematical models are used to improve treatment strategies, like determining the best combination of drugs to combat resistant cancer cells and optimizing immunotherapy approaches, such as CAR-T cell therapy. By applying these mathematical concepts, researchers can enhance the effectiveness of cancer treatments and tailor them to individual patients&rsquo; needs. Mathematical models, such as differential equations, are essential tools in cancer research for understanding and predicting how tumors grow over time. Models like the Gompertz and logistic growth models describe the dynamics of tumor growth, helping researchers simulate how cancer cells multiply, interact, and respond to various treatments. By using these models, scientists can gain insights into cancer progression and improve treatment strategies, ultimately enhancing patient outcomes. Dosimetry is a crucial aspect of radiation therapy that uses mathematical calculations to determine the right amount of radiation needed to effectively target tumors while protecting healthy tissues from damage. Advanced treatment planning software employs algorithms and simulations to figure out the best angles and intensities for delivering radiation, ensuring that the treatment is both effective and safe for the patient. This mathematical approach helps optimize cancer treatment by maximizing tumor destruction and minimizing side effects. Pharmacokinetics and pharmacodynamics are important concepts in understanding how drugs work in the body. Pharmacokinetics focuses on how a drug is absorbed, distributed, metabolized, and eliminated, which helps determine the best dosage and timing for chemotherapy. On the other hand, response models use statistical methods to predict how tumors will react to specific chemotherapy drugs, allowing doctors to create personalized treatment plans that are more effective for individual patients. Mathematics plays a crucial role in designing clinical trials for cancer treatments by helping researchers determine how many patients to include (sample size), how to randomly assign them to different treatment groups (randomization methods), and how to analyze the results statistically to see if the treatments are effective. Additionally, survival analysis techniques, like Kaplan-Meier estimation and Cox proportional hazards modeling, are used to study patient survival data, allowing researchers to identify which factors influence how long patients live after treatment. These mathematical tools are essential for ensuring that clinical trials are well-structured and that the findings are reliable. Bioinformatics is a field that uses mathematical and statistical techniques to analyze genomic data, which includes information about a person&rsquo;s DNA. In cancer research, bioinformatics helps identify genetic mutations and biological pathways that contribute to the disease, allowing scientists to understand how cancer develops and progresses. This information is crucial for developing targeted therapies, which are treatments designed to specifically attack the mutations found in cancer cells, improving treatment effectiveness. The current exposition offers new insights into the cancer research community, as well as providing open problems which offer bridging the gaps to gain more knowledge about the influential role of mathematics to advance next generation cancer treatment.