[Paper Review] New combinational therapies for cancer using modern statistical mechanics

Jorge A. González, M. Acanda+17 more|arXiv (Cornell University)|Feb 2, 2019

Mathematical Biology Tumor Growth196 references4 citations

TL;DR

This paper proposes a novel dynamical model based on non-extensive statistical mechanics to simulate tumor-host interactions and optimize combinational cancer therapies. By integrating oncogene-targeted therapy, tumor suppressor reactivation, immunotherapy, anti-angiogenesis, and virotherapy with late-intensification scheduling, the model predicts complete tumor eradication through synergistic, multi-pronged treatment sequences, particularly when therapy intensity increases logarithmically over time.

ABSTRACT

We investigate a new dynamical system that describes tumor-host interaction. The equation that describes the untreated tumor growth is based on non-extensive statistical mechanics. Recently, this model has been shown to fit successfully exponential, Gompertz, logistic, and power-law tumor growths. We have been able to include as many hallmarks of cancer as possible. We study also the dynamic response of cancer under therapy. Using our model, we can make predictions about the different outcomes when we change the parameters, and/or the initial conditions. We can determine the importance of different factors to influence tumor growth. We discover synergistic therapeutic effects of different treatments and drugs. Cancer is generally untreatable using conventional monotherapy. We consider conventional therapies, oncogene-targeted therapies, tumor-suppressors gene-targeted therapies, immunotherapies, anti-angiogenesis therapies, virotherapy, among others. We need therapies with the potential to target both tumor cells and the tumors' microenvironment. Drugs that target oncogenes and tumor-suppressor genes can be effective in the treatment of some cancers. However, most tumors do reoccur. We have found that the success of the new therapeutic agents can be seen when used in combination with other cancer-cell-killing therapies. Our results have allowed us to design a combinational therapy that can lead to the complete eradication of cancer.

Motivation & Objective

• To develop a mathematical model of tumor growth and therapy response using non-extensive statistical mechanics to capture complex, non-linear dynamics.
• To address the limitations of conventional monotherapies, which often fail due to drug resistance and tumor recurrence.
• To identify synergistic combinations of therapies targeting both cancer cells and the tumor microenvironment for improved treatment outcomes.
• To design time-dependent treatment schedules—particularly late-intensification strategies—that maximize tumor eradication while minimizing relapse.
• To integrate multiple therapeutic modalities (e.g., immunotherapy, oncolytic virotherapy, p53 modulation) into a sequential, multi-phase treatment protocol.

Proposed method

• The tumor growth dynamics are modeled using a generalized equation derived from non-extensive statistical mechanics, capable of fitting exponential, Gompertz, logistic, and power-law growth patterns.
• The model incorporates multiple hallmarks of cancer, including oncogene activation, tumor suppressor inactivation (e.g., p53), angiogenesis, and cancer stem cell dynamics.
• Therapeutic interventions are simulated by adjusting parameters such as treatment intensity (C(t)), the non-extensivity parameter (q), and carrying capacity (X∞), representing different therapy types.
• Late-intensification therapy is implemented via time-dependent functions such as C(t) = 6(1 + t^0.2) and C(t) = 6(1 + t^2), increasing treatment intensity over time to overcome resistance.
• The model identifies fixed points (P_I and P_II) and uses separatrix analysis to determine conditions under which the system evolves toward complete tumor eradication.
• Combinatorial therapy sequences are designed using phase-space dynamics: first stabilizing a fixed point (P_I), then driving the system past a saddle point (P_II) to achieve permanent tumor control.

Experimental results

Research questions

• RQ1 How can non-extensive statistical mechanics improve the modeling of heterogeneous tumor growth dynamics, including exponential, Gompertz, and power-law patterns?
• RQ2 What are the conditions under which combination therapies—targeting oncogenes, tumor suppressors, angiogenesis, and immune response—can lead to complete tumor eradication?
• RQ3 Can late-intensification scheduling, particularly with logarithmic or polynomially increasing therapy intensity, overcome treatment resistance and prevent relapse?
• RQ4 What is the role of cancer stem cells and p53 reactivation in sustaining or reversing tumor progression under combined therapies?
• RQ5 How do synergistic interactions between immunotherapy, oncolytic virotherapy, and chemo-radiation influence the stability of tumor-free fixed points in the dynamical system?

Key findings

• The model successfully fits diverse tumor growth patterns (exponential, Gompertz, logistic, power-law) using a single framework based on non-extensive statistical mechanics.
• Late-intensification therapy with C(t) = 6(1 + t^0.2) and C(t) = 6(1 + t^2) enables complete tumor eradication even when q < 1, overcoming limitations of constant-dose therapy.
• Combining oncogene-targeted therapy, tumor suppressor reactivation, and cancer stem cell targeting leads to stable, tumor-free fixed points in the model.
• Sequential therapy involving immunotherapy, anti-angiogenesis, and chemotherapy stabilizes fixed point P_I, creating a favorable pre-condition for eradication.
• The third phase—using immunotherapy, oncolytic virotherapy with transgene p53, chemo-radiation, and logarithmic cell-kill function—drives the system past the separatrix of saddle point P_II, ensuring permanent tumor control.
• The model predicts that p53 modulator drugs, when combined with immunotherapy and chemo-radiation, can significantly enhance treatment efficacy and sensitivity to therapy.