# Aiding cancer therapy by mathematically modeling tumor-immune interactions

January 25, 2012

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 tumor-immune 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 and simulation can be used to assess the impact of drugs and therapies before clinical application.

Using ordinary differential equations, the authors model the progress of different cell populations in the tumor environment as a continuous process. Within the dynamical system presented by the tumor environment, they apply the theory of optimal control--a mathematical optimization method--to design ad-hoc therapies and find an optimal treatment.

The end goal of the control policy is to minimize tumor cells while maximizing effectors, such as immune cells or immune-response chemicals. "The aim is to minimize the tumor concentration while keeping the amount of administered drug below certain thresholds, to avoid toxicity," says Topputo. "In common practice, one searches for effective therapies; in our approach, we look for efficiency and effectiveness."

Elaborating on a prior study where indirect methods used to solve the optimal control problem are not effective, the authors use direct methods that apply algorithms from aerospace engineering to solve the associated optimal control problem in this paper. Optimal protocols are analyzed, and the duration of optimal therapy is determined.

The robustness of the optimal therapies is then assessed. In addition, their applicability toward personalized medicine is discussed, where treatment is customized to each individual based on various factors such as genetic information, family history, social circumstances, environment and lifestyle.

"We have shown that personalized therapy is robust even with uncertain patient conditions. This is relevant as the model coefficients are characterized by uncertainties," Topputo explains. "Further studies would include designing optimal protocols by considering personalized constraints based on individual patient conditions, such as maximum amount of drug, therapy duration, and so on."

Other future directions would be the use of more diverse models and studying the effectiveness of treatment combinations. "More detailed approaches like agent-based models that describe tumor-immune interactions and hybrid therapies that consist of combined chemotherapy-immunotherapy treatments should also be considered," says Topputo.
-end-
About the authors: Andrea Minelli is a researcher in the Applied Aerodynamics Department at ONERA, The French Aerospace Lab in Meudon, France. Francesco Topputo is a post-doctoral research fellow and Franco Bernelli-Zazzera a full professor in the Aerospace Engineering Department at Politecnico di Milano in Milano, Italy.

Source article: Controlled Drug Delivery in Cancer Immunotherapy: Stability, Optimization, and Monte Carlo Analysis
Andrea Minelli, Francesco Topputo, and Franco Bernelli-Zazzera, SIAM Journal on Applied Mathematics, 71, pp 2229-2245 (Online publish date: December 20, 2011)

This paper is part of a Special Section in the SIAM Journal on Applied Mathematics that examines various other mathematical models used in the design and development of controlled drug delivery systems, which are significant in helping us understand physical, chemical and biological processes that influence such systems.

Society for Industrial and Applied Mathematics

## Related Cancer Articles from Brightsurf:

New blood cancer treatment works by selectively interfering with cancer cell signalling
University of Alberta scientists have identified the mechanism of action behind a new type of precision cancer drug for blood cancers that is set for human trials, according to research published in Nature Communications.

UCI researchers uncover cancer cell vulnerabilities; may lead to better cancer therapies
A new University of California, Irvine-led study reveals a protein responsible for genetic changes resulting in a variety of cancers, may also be the key to more effective, targeted cancer therapy.

Breast cancer treatment costs highest among young women with metastic cancer
In a fight for their lives, young women, age 18-44, spend double the amount of older women to survive metastatic breast cancer, according to a large statewide study by the University of North Carolina at Chapel Hill.

Cancer mortality continues steady decline, driven by progress against lung cancer
The cancer death rate declined by 29% from 1991 to 2017, including a 2.2% drop from 2016 to 2017, the largest single-year drop in cancer mortality ever reported.

Stress in cervical cancer patients associated with higher risk of cancer-specific mortality
Psychological stress was associated with a higher risk of cancer-specific mortality in women diagnosed with cervical cancer.

Cancer-sniffing dogs 97% accurate in identifying lung cancer, according to study in JAOA
The next step will be to further fractionate the samples based on chemical and physical properties, presenting them back to the dogs until the specific biomarkers for each cancer are identified.

Moffitt Cancer Center researchers identify one way T cell function may fail in cancer
Moffitt Cancer Center researchers have discovered a mechanism by which one type of immune cell, CD8+ T cells, can become dysfunctional, impeding its ability to seek and kill cancer cells.

More cancer survivors, fewer cancer specialists point to challenge in meeting care needs
An aging population, a growing number of cancer survivors, and a projected shortage of cancer care providers will result in a challenge in delivering the care for cancer survivors in the United States if systemic changes are not made.

New cancer vaccine platform a potential tool for efficacious targeted cancer therapy
Researchers at the University of Helsinki have discovered a solution in the form of a cancer vaccine platform for improving the efficacy of oncolytic viruses used in cancer treatment.

American Cancer Society outlines blueprint for cancer control in the 21st century
The American Cancer Society is outlining its vision for cancer control in the decades ahead in a series of articles that forms the basis of a national cancer control plan.

Read More: Cancer News and Cancer Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.