Mathematical Model Creation for Cancer Chemo-Immunotherapy

Model for acid-mediated tumour invasion with chemotherapy intervention II: Spatially heterogeneous populations

This paper extends the model for acid-mediated tumour invasion with chemotherapy intervention examined in part I. The model presented in part I considers the interaction between tumour cells, normal cells, acid and drug in a well mixed (i.e. spatially homogeneous) setting, which is governed by a system of nonlinear differential equations. The model examined here removes the assumption that the populations are spatially homogeneous resulting in a system of nonlinear partial differential equations. Numerical simulations of this model are presented for different treatment methods displaying several possible behaviours. Asymptotic approximations are also derived for a special case of the treatment method and set of parameter values. This analysis then allows us to draw conclusions about the effectiveness of treating acid-mediated tumours with chemotherapy.

Mathematical Modelling and Prediction of the Effect of Chemotherapy on Cancer Cells

Cancer is a class of diseases characterized by out-of-control cells' growth which affect DNAs and make them damaged. Many treatment options for cancer exist, with the primary ones including surgery, chemotherapy, radiation therapy, hormonal therapy, targeted therapy and palliative care. Which treatments are used depends on the type, location, and grade of the cancer as well as the person's health and wishes. Chemotherapy is the use of medication (chemicals) to treat disease. More specifically, chemotherapy typically refers to the destruction of cancer cells. Considering the diffusion of drugs in cancer cells and fractality of DNA walks, in this research we worked on modelling and prediction of the effect of chemotherapy on cancer cells using Fractional Diffusion Equation (FDE). The employed methodology is useful not only for analysis of the effect of special drug and cancer considered in this research but can be expanded in case of different drugs and cancers.

Mathematical model reveals how regulating the three phases of T-cell response could counteract immune evasion

T cells are key players in immune action against the invasion of target cells expressing non-self antigens. During an immune response, antigen-specific T cells dynamically sculpt the antigenic distribution of target cells, and target cells concurrently shape the host's repertoire of antigen-specific T cells. The succession of these reciprocal selective sweeps can result in 'chase-and-escape' dynamics and lead to immune evasion. It has been proposed that immune evasion can be countered by immunotherapy strategies aimed at regulating the three phases of the immune response orchestrated by antigen-specific T cells: expansion, contraction and memory. Here, we test this hypothesis with a mathematical model that considers the immune response as a selection contest between T cells and target cells. The outcomes of our model suggest that shortening the duration of the contraction phase and stabilizing as many T cells as possible inside the long-lived memory reservoir, using dual immunotherapies based on the cytokines interleukin-7 and/or interleukin-15 in combination with molecular factors that can keep the immunomodulatory action of these interleukins under control, should be an important focus of future immunotherapy research.

The effect of intrinsic and acquired resistances on chemotherapy effectiveness

Although chemotherapy is one of the most common treatments for cancer, it can be only partially successful. Drug resistance is the main cause of the failure of chemotherapy. In this work, we present a mathematical model to study the impact of both intrinsic (preexisting) and acquired (induced by the drugs) resistances on chemotherapy effectiveness. Our simulations show that intrinsic resistance could be as dangerous as acquired resistance. In particular, our simulations suggest that tumors composed by even a small fraction of intrinsically resistant cells may lead to an unsuccessful therapy very quickly. Our results emphasize the importance of monitoring both intrinsic and acquired resistances during treatment in order to succeed and the importance of doing more experimental and genetic research in order to develop a pretreatment clinical test to avoid intrinsic resistance.

Control exponential growth of tumor cells with slow spread of oncolytic virus

Great attention has been paid to cancer therapy by means of oncolytic viruses, but the fast virus-spread, which eliminates all tumor cells, cannot be applied to solid tumors. As slow virus-spread is applied, solid tumors are expected to be controlled but complicated dynamical behaviors appear. In this paper we investigate bifurcations of equilibria in the oncolytic virus dynamics model with exponential growth of tumor cells and slow virus-spread. We find conditions of parameters for saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. Those conditions give thresholds for slow virus-spread to control the population of tumor cells within an appropriate range.

Optimal treatment strategy for a tumor model under immune suppression

We propose a mathematical model describing tumor-immune interactions under immune suppression. These days evidences indicate that the immune suppression related to cancer contributes to its progression. The mathematical model for tumor-immune interactions would provide a new methodology for more sophisticated treatment options of cancer. To do this we have developed a system of 11 ordinary differential equations including the movement, interaction, and activation of NK cells, CD8(+)T-cells, CD4(+)T cells, regulatory T cells, and dendritic cells under the presence of tumor and cytokines and the immune interactions. In addition, we apply two control therapies, immunotherapy and chemotherapy to the model in order to control growth of tumor. Using optimal control theory and numerical simulations, we obtain appropriate treatment strategies according to the ratio of the cost for two therapies, which suggest an optimal timing of each administration for the two types of models, without and with immunosuppressive effects. These results mean that the immune suppression can have an influence on treatment strategies for cancer.

Inferring the effect of therapies on tumor growth by using diffusion processes

Modeling the effect of therapies in cancer animal models remains a challenge. This point may be addressed by considering a diffusion process that models the tumor growth and a modified process that includes, in its infinitesimal mean, a time function modeling the effect of the therapy. In the case of a Gompertz diffusion process, where a control group and one or more treated groups are examined, a methodology to estimate this function has been proposed by Albano et al. (2011). This method has been applied to infer the effect of cisplatin and doxorubicin+cyclophosphamide on breast cancer xenografts. Although this methodology can be extended to other diffusion processes, it has an important restriction: it is necessary that a known diffusion process adequately fits the control group. Here, we propose the use of a stochastic process for a hypothetical control group, in such a way that both the control and the treated groups can be modeled by modified processes of the former. Thus, the comparison between models would allow estimating the real effect of the therapy. The new methodology has been validated by inferring the effects in breast cancer models, and we have checked the robustness of the procedure against the choice of stochastic model for the hypothetical control group. Finally, we have also applied the methodology to infer the effect of a therapeutic peptide and ovariectomy on the growth of a breast cancer xenograft, and its efficiency in modeling the effect of different treatments in the absence of control group data is shown.

Bioinformatics for cancer immunology and immunotherapy

Recent mechanistic insights obtained from preclinical studies and the approval of the first immunotherapies has motivated increasing number of academic investigators and pharmaceutical/biotech companies to further elucidate the role of immunity in tumor pathogenesis and to reconsider the role of immunotherapy. Additionally, technological advances (e.g., next-generation sequencing) are providing unprecedented opportunities to draw a comprehensive picture of the tumor genomics landscape and ultimately enable individualized treatment. However, the increasing complexity of the generated data and the plethora of bioinformatics methods and tools pose considerable challenges to both tumor immunologists and clinical oncologists. In this review, we describe current concepts and future challenges for the management and analysis of data for cancer immunology and immunotherapy. We first highlight publicly available databases with specific focus on cancer immunology including databases for somatic mutations and epitope databases. We then give an overview of the bioinformatics methods for the analysis of next-generation sequencing data (whole-genome and exome sequencing), epitope prediction tools as well as methods for integrative data analysis and network modeling. Mathematical models are powerful tools that can predict and explain important patterns in the genetic and clinical progression of cancer. Therefore, a survey of mathematical models for tumor evolution and tumor-immune cell interaction is included. Finally, we discuss future challenges for individualized immunotherapy and suggest how a combined computational/experimental approaches can lead to new insights into the molecular mechanisms of cancer, improved diagnosis, and prognosis of the disease and pinpoint novel therapeutic targets.