Mathematical Model Creation for Cancer Chemo‐Immunotherapy

Abstract

One of the most challenging tasks in constructing a mathematical model of cancer treatment is the calculation of biological parameters from empirical data. This task becomes increasingly difficult if a model involves several cell populations and treatment modalities. A sophisticated model constructed by de Pillis et al., Mixed immunotherapy and chemotherapy of tumours: Modelling, applications and biological interpretations, J. Theor. Biol. 238 (2006), pp. 841-862; involves tumour cells, specific and non-specific immune cells (natural killer (NK) cells, CD8 þ T cells and other lymphocytes) and employs chemotherapy and two types of immunotherapy (IL-2 supplementation and CD8 þ T-cell infusion) as treatment modalities. Despite the overall success of the aforementioned model, the problem of illustrating the effects of IL-2 on a growing tumour remains open. In this paper, we update the model of de Pillis et al. and then carefully identify appropriate values for the parameters of the new model according to recent empirical data. We determine new NK and tumour antigen-activated CD8 þ T-cell count equilibrium values; we complete IL-2 dynamics; and we modify the model in de Pillis et al. to allow for endogenous IL-2 production, IL-2-stimulated NK cell proliferation and IL-2-dependent CD8 þ T-cell self-regulations. Finally, we show that the potential patient-specific efficacy of immunotherapy may be dependent on experimentally determinable parameters.

Delay Dynamics of Cancer and Immune Cell Model

“…As F increases, the period over which the drug is administered decreases. This is consistent with the concept of availability of more lymphocytes to increase the body's natural immunity, [9]. Therefore, less drug is needed.…”

“…This enables a more accurate approach to treatments [18]. With the collaboration among biologists, mathematicians, and medical professionals, mathematical concepts that were more engineering based have been found to be useful in medical applications, [6,7,8,22,9]. The goal of applying optimal control theory to mathematical models representing the interaction between tumor, immune system, and chemotherapy is to determine the ideal mix of treatments that minimizes both tumor mass and negative effects upon the health of the patient.…”

A Comparison and Catalog of Intrinsic Tumor Growth Models

“…Although future models published by the same authors have also included interleuken-2 (IL-2) dynamics, accounting for a chemical signal that affects CTL proliferation, there are many immunotherapies that affect the IL-2 concentration (de Pillis et al, 2013a(de Pillis et al, , 2009(de Pillis et al, , 2013b. In this model, because the particular immunotherapy we are studying affects IL-2 concentration only indirectly through the proliferation of other cell lines, we reference it only indirectly and remove the IL-2 equation.…”

“…One of the implications of building a CD47 model is the inclusion of tumor types that are not normally associated with successful reactions to immunotherapies. Out of all of the cancer types, only renal cell carcinoma and melanoma have been shown to have success with CD8+ and interleuken-affecting immunotherapies; however, as CD47 treatment has been shown to affect ovarian, breast, colon, bladder, and prostate cancer, as well as glioblastoma and hepatocellular carcinoma, it is necessary for ODE model developers to produce tumor growth parameters for an ever-increasing number of tumor types (de Pillis et al, 2013a(de Pillis et al, , 2009(de Pillis et al, , 2013bWillingham, Stephen B. et al, 2012). The results of this project make these efforts almost trivial, so that future dynamical systems researchers need only develop the parameters for macrophage and dendritic cell terms.…”

Addressing current challenges in cancer immunotherapy with mathematical and computational modelling

“…Modelling can contribute to this process as it can aid in the development of a mechanistic understanding for effectiveness of combination versus monotherapies and make the search for an optimal combination therapy more efficient. For example, de Pillis et al developed a system of six ODEs for combination chemo-and immunotherapy that included tumour, NK, CD8 þ and white blood cells, as well as bloodstream concentrations of chemotherapy (doxorubicin) and immunotherapy drugs, the latter of which include tumour-infiltrating-lymphocyte (TIL) therapy and IL-2 stimulation [53]. The model extended an earlier model by de Pillis et al [54] to include more recent biological findings.…”