Addressing current challenges in cancer immunotherapy with mathematical and computational modeling

Abstract

The goal of cancer immunotherapy is to boost a patient's immune response to a tumor. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumor microenvironment, immune-modulating effects of conventional treatments, and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modeling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumor classification, optimal treatment scheduling, and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modelers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumor-immune biology. We conclude the review with recommendations for modelers both with respect to methodology and biological direction that might help keep modelers at the forefront of cancer immunotherapy development.

Model predictive control of cancer cellular dynamics: a new strategy for therapy design

“…Computational approaches have been extensively proposed in the search for effective cancer treatments. Initially, mathematical models were used to investigate the pathways within the system, design the inputs themselves, and observe how the system reacts (Konstorum et al, 2017;Cova et al, 2019). Optimisation algorithms have supported the identification of open loop optimal input profiles for target phenotypes (Castiglione and Piccoli, 2006;Kassara, 2006;Piccoli and Castiglione, 2006;Castiglione and Piccoli, 2007;Ledzewicz and Schattler, 2007;Itik et al, 2009;Ghaffari and Naserifar, 2010;Oke et al, 2018).…”

A model of tumor‐immune system interactions with healthy cells and immunotherapies

“…We will neglect the discussion of E 00 in the following since its numerical values depend on r, a, k, c, and d and those parameters are fixed through numerical examinations of no treatment and continuous treatment. Following from the analytical results, our discussion will be based on four parameter regimes: (1)…”

“…The involvement of the immune system in different stages of the tumor development is now recognized as essential issues to understanding cancer progression from a systemic point of view. 1 Adoptive cell therapy (ACT) is a cancer immunotherapy by selecting and expanding patients' own tumor-specific T cells in vitro and then reinfusing back into patients to boost patients' own natural ability to target cancer. Typically, most of the cancer immunotherapies have been attributed to CD8 + T cells because tumor cells express little MHC class II molecules.…”