SIAM News Blog

Mathematical Model Advances Immunotherapy Treatments for Cancer

By Lina Sorg

The resilience of malignant tumors significantly complicates cancer treatment. While various types of immunotherapy routinely find initial success, cancerous cells often become resistant to the administered drugs. The genotypic (genetic material) and phenotypic (observable traits or behaviors) heterogeneity of tumors habitually increases during therapy because complex tumor tissues evolve in response to their environment. This adaptability makes them more difficult to treat.

T-cells, white blood cells that are crucial to sustaining the immune system, are used to fight malignant tumors. As part of adoptive cell transfer (ACT) therapy, injected T-cells select and attack target malignant antigens. However, therapy causes inflammation in the malignant cells, triggering the cells to switch their phenotypes and alter their appearance. T-cells no longer recognize the infected cells and cease to attack them, resulting in a relapse.

Using their work with mutating melanoma cells, researchers from the Hausdorff Center for Mathematics and ImmunoSensation at the University of Bonn expanded an individual-based stochastic model for immunotherapy based on adaptive population dynamics. The extended, quantitative model mathematically depicts how malignant tumors change their external appearance, thus expanding the model’s biological applications.

The researchers model T-cells, cancerous cells, and cytokines (small proteins involved in cell signaling) as individual particles in a stochastic system. The model characterizes cancer cells based on their genotypes and phenotypes, simulates multiple immunotherapy procedures – some of which involve the use of numerous types of T-cells – accounts for possible effects of therapy on cancerous cells, and includes a term that lowers the reproductive rate of malignant cells.

By demonstrating the simultaneous growth of both cancerous and immune cells, the model exposes complications associated with genetic mutations and phenotypic switches on varied timescales. In fact, the group’s work showed that under certain circumstances, treatment could increase the probability of cancer cell mutations. A more thorough view of the relationship between therapy and resistance can enable better analysis of the occurrence of such mutations. According to lead scientist Anton Bovier, preliminary results suggest that using several types of immune cells to combat tumors may strengthen immunotherapy treatments. Read Bovier’s explanation here.

Future simulation and analysis of various therapeutic approaches will help scientists understand how tumors resist immunotherapy and familiarize practitioners with mathematical models. A better understanding of resistances can lead to the development of optimal treatment strategies.

The corresponding journal paper is publishing in Scientific Reports.


  Lina Sorg is the associate editor of SIAM News.  


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