Modeling the effect of immunotherapies on human castration-resistant prostate cancer

In silico cancer immunotherapy trials uncover the consequences of therapy-specific response patterns for clinical trial design and outcome

Late-stage cancer immunotherapy trials often lead to unusual survival curve shapes, like delayed curve separation or a plateauing curve in the treatment arm. It is critical for trial success to anticipate such effects in advance and adjust the design accordingly. Here, we use in silico cancer immunotherapy trials - simulated trials based on three different mathematical models - to assemble virtual patient cohorts undergoing late-stage immunotherapy, chemotherapy, or combination therapies. We find that all three simulation models predict the distinctive survival curve shapes commonly associated with immunotherapies. Considering four aspects of clinical trial design - sample size, endpoint, randomization rate, and interim analyses - we demonstrate how, by simulating various possible scenarios, the robustness of trial design choices can be scrutinized, and possible pitfalls can be identified in advance. We provide readily usable, web-based implementations of our three trial simulation models to facilitate their use by biomedical researchers, doctors, and trialists.

Practical Understanding of Cancer Model Identifiability in Clinical Applications

Mathematical models are a core component in the foundation of cancer theory and have been developed as clinical tools in precision medicine. Modeling studies for clinical applications often assume an individual's characteristics can be represented as parameters in a model and are used to explain, predict, and optimize treatment outcomes. However, this approach relies on the identifiability of the underlying mathematical models. In this study, we build on the framework of an observing-system simulation experiment to study the identifiability of several models of cancer growth, focusing on the prognostic parameters of each model. Our results demonstrate that the frequency of data collection, the types of data, such as cancer proxy, and the accuracy of measurements all play crucial roles in determining the identifiability of the model. We also found that highly accurate data can allow for reasonably accurate estimates of some parameters, which may be the key to achieving model identifiability in practice. As more complex models required more data for identification, our results support the idea of using models with a clear mechanism that tracks disease progression in clinical settings. For such a model, the subset of model parameters associated with disease progression naturally minimizes the required data for model identifiability.

Dynamics of an Antitumour Model with Pulsed Radioimmunotherapy

In this paper, an antitumour model for characterising radiotherapy and immunotherapy processes at different fixed times is proposed. The global attractiveness of the positive periodic solution for each corresponding subsystem is proved with the integral inequality technique. Then, based on the differentiability of the solutions with respect to the initial values, the eigenvalues of the Jacobian matrix at a fixed point corresponding to the tumour-free periodic solution are determined, resulting in a sufficient condition for local stability. The solutions to the ordinary differential equations are compared, the threshold condition for the global attractiveness of the tumour-free periodic solution is provided in terms of an indicator $R_0$ , and the permanence of a system with at least one tumour-present periodic solution is investigated. Furthermore, the effects of the death rate, effector cell injection dosage, therapeutic period, and effector cell activation rate on indicator $R_0$ are determined through numerical simulations, and the results indicate that radioimmunotherapy is more effective than either radiotherapy or immunotherapy alone.

A Model-Based Framework to Identify Optimal Administration Protocols for Immunotherapies in Castration-Resistance Prostate Cancer

Prostate cancer (PCa) is one of the most frequent cancer in male population. Androgen deprivation therapy is the first-line strategy for the metastatic stage of the disease, but, inevitably, PCa develops resistance to castration (CRPC), becoming incurable. In recent years, clinical trials are testing the efficacy of anti-CTLA4 on CRPC. However, this tumor seems to be resistant to immunotherapies that are very effective in other types of cancers, and, so far, only the dendritic cell vaccine sipuleucel-T has been approved. In this work, we employ a mathematical model of CRPC to determine the optimal administration protocol of ipilimumab, a particular anti-CTLA4, as single treatment or in combination with the sipuleucel-T, by considering both the effect on tumor population and the drug toxicity. To this end, we first introduce a dose-depending function of toxicity, estimated from experimental data, then we define two different optimization problems. We show the results obtained by imposing different constraints, and how these change by varying drug efficacy. Our results suggest administration of high-doses for a brief period, which is predicted to be more efficient than solutions with prolonged low-doses. The model also highlights a synergy between ipilimumab and sipuleucel-T, which leads to a better tumor control with lower doses of ipilimumab. Finally, tumor eradication is also conceivable, but it depends on patient-specific parameters.

Modeling the synergistic properties of drugs in hormonal treatment for prostate cancer

Prostate cancer is one of the most prevalent cancers in men, with increasing incidence worldwide. This public health concern has inspired considerable effort to study various aspects of prostate cancer treatment using dynamical models, especially in clinical settings. The standard of care for metastatic prostate cancer is hormonal therapy, which reduces the production of androgen that fuels the growth of prostate tumor cells prior to treatment resistance. Existing population models often use patients' prostate-specific antigen levels as a biomarker for model validation and for finding optimal treatment schedules; however, the synergistic effects of drugs used in hormonal therapy have not been well-examined. This paper describes the first mathematical model that explicitly incorporates the synergistic effects of two drugs used to inhibit androgen production in hormonal therapy. The drugs are cyproterone acetate, representing the drug family of anti-androgens that affect luteinizing hormones, and leuprolide acetate, representing the drug family of gonadotropin-releasing hormone analogs. By fitting the model to clinical data, we show that the proposed model can capture the dynamics of serum androgen levels during intermittent hormonal therapy better than previously published models. Our results highlight the importance of considering the synergistic effects of drugs in cancer treatment, thus suggesting that the dynamics of the drugs should be taken into account in optimal treatment studies, particularly for adaptive therapy. Otherwise, an unrealistic treatment schedule may be prescribed and render the treatment less effective. Furthermore, the drug dynamics allow our model to explain the delay in the relapse of androgen the moment a patient is taken off treatment, which supports that this delay is due to the residual effects of the drugs.