Cancer is one of the five leading causes of death. And yet, despite decades of research, there is no standardized first-line treatment for most cancers. In addition, disappointing results from predominant second-line treatments like chemotherapy have established the need for alternative methods.
Mathematical modeling of cancer usually involves describing the evolution of tumors in terms of differential equations and stochastic or agent-based models, and testing the effectiveness of various treatments within the chosen mathematical framework. Tumor progression (or regression) is evaluated by studying the dynamics of tumor cells under different treatments, such as immune therapy, chemotherapy and drug therapeutics while optimizing dosage, duration and frequencies.
In a paper published last month in the SIAM Journal on Applied Mathematics, 'Controlled Drug Delivery in Cancer Immunotherapy: Stability, Optimization, and Monte Carlo Analysis,' authors Andrea Minelli, Francesco Topputo, and Franco Bernelli-Zazzera propose a differential equation model to describe tumorimmune interactions. "We study the dynamics of the competition between the tumor and the immune system," Topputo explains.
The relationship between cancers and the immune system has been studied for many years, and immune therapy has been known to influence tumor regression. Clinically called immunotherapy, it involves using external factors to induce, enhance, or suppress a patient's immune response for treatment of disease. In this study, the therapy consists of injecting a type of immune cells called dendritic cells, which generate tumor-specific immunity by presenting tumor-associated antigens.
"In particular, cancer immunotherapy has the purpose of identifying and killing tumor cells," says Topputo. "Our research considers a model that describes the interaction between the neoplasia [or tumor], the immune system, and drug administration." Such modeling
|Contact: Karthika Muthukumaraswamy|
Society for Industrial and Applied Mathematics