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

A Numerical Comparison of Petri Net and Ordinary Differential Equation SIR Component Models

Petri nets are a promising modeling framework for epidemiology, including the spread of disease across populations or within an individual. In particular, the Susceptible-Infectious-Recovered (SIR) compartment model is foundational for population epidemiological modeling and has been implemented in several prior Petri net studies. However, the SIR model is generally stated as a system of ordinary differential equations (ODEs) with continuous time and variables, while Petri nets are discrete event simulations. To our knowledge, no prior study has investigated the numerical equivalence of Petri net SIR models to the classical ODE formulation. We introduce crucial numerical techniques for implementing SIR models in the GPenSim package for Petri net simulations. We show that these techniques are critical for Petri net SIR models and show a relative root mean squared error of less than 1% compared to ODE simulations for biologically relevant parameter ranges. We conclude that Petri nets provide a valid framework for modeling SIR-type dynamics using biologically relevant parameter values, provided that the other PN structures we outline are also implemented.

Gompertz models with periodical treatment and applications to prostate cancer

In this paper, Gompertz type models are proposed to understand the temporal tumor volume behavior of prostate cancer when a periodical treatment is provided. Existence, uniqueness, and stability of periodic solutions are established. The models are used to fit the data and to forecast the tumor growth behavior based on prostate cancer treatments using capsaicin and docetaxel anticancer drugs. Numerical simulations show that the combination of capsaicin and docetaxel is the most efficient treatment of prostate cancer.

Involvement of FAM83 Family Proteins in the Development of Solid Tumors: An Update Review

FAM83 family members are a group of proteins that have been implicated in various solid tumors. In this updated review, we mainly focus on the cellular localization, molecular composition, and biological function of FAM83 family proteins in solid tumors. We discussed the factors that regulate abnormal protein expression and alterations in the functional activities of solid tumor cells (including non-coding microRNAs and protein modifiers) and potential mechanisms of tumorigenesis (including the MAPK, WNT, and TGF-β signaling pathways). Further, we highlighted the application of FAM83 family proteins in the diagnoses and treatment of different cancers, such as breast, lung, liver, and ovarian cancers from two aspects: molecular marker diagnosis and tumor drug resistance. We described the overexpression of FAM83 genes in various human malignant tumor cells and its relationship with tumor proliferation, migration, invasion, transformation, and drug resistance. Moreover, we explored the prospects and challenges of using tumor treatments based on the FAM83 proteins. Overall, we provide a theoretical basis for harnessing FAM83 family proteins as novel targets in cancer treatment. We believe that this review opens up open new directions for solid tumor treatment in clinical practice.

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.

A hybrid spatiotemporal model of PCa dynamics and insights into optimal therapeutic strategies

Using a hybrid cellular automaton with stochastic elements, we investigate the effectiveness of multiple drug therapies on prostate cancer (PCa) growth. The ability of Androgen Deprivation Therapy to reduce PCa growth represents a milestone in prostate cancer treatment, nonetheless most patients eventually become refractory and develop castration-resistant prostate cancer. In recent years, a "second generation" drug called enzalutamide has been used to treat advanced PCa, or patients already exposed to chemotherapy that stopped responding to it. However, tumour resistance to enzalutamide is not well understood, and in this context, preclinical models and in silico experiments (numerical simulations) are key to understanding the mechanisms of resistance and to assessing therapeutic settings that may delay or prevent the onset of resistance. In our mathematical system, we incorporate cell phenotype switching to model the development of increased drug resistance, and consider the effect of the micro-environment dynamics on necrosis and apoptosis of the tumour cells. The therapeutic strategies that we explore include using a single drug (enzalutamide), and drug combinations (enzalutamide and everolimus or cabazitaxel) with different treatment schedules. Our results highlight the effectiveness of alternating therapies, especially alternating enzalutamide and cabazitaxel over a year, and a comparison is made with data taken from TRAMP mice to verify our findings.

High Accuracy Indicators of Androgen Suppression Therapy Failure for Prostate Cancer-A Modeling Study

Simple Summary

Hormonal therapy for prostate cancer is often applied past the point of resistance, hence losing any future clinical value to the evolution of resistant strains. If the undesirable outcome of the treatment is forewarned, then clinicians can have an opportunity to adjust the treatment, which can result in better management of the cancer. Using a mechanistic mathematical model, we introduce two methods to enhance the accuracy of classical biomarkers for hormonal therapy failure. Our results show the value in measuring both prostate-specific antigen and androgen during hormonal treatment, which can potentially allow for better management of prostate cancer.

Abstract

Prostate cancer is a serious public health concern in the United States. The primary obstacle to effective long-term management for prostate cancer patients is the eventual development of treatment resistance. Due to the uniquely chaotic nature of the neoplastic genome, it is difficult to determine the evolution of tumor composition over the course of treatment. Hence, a drug is often applied continuously past the point of effectiveness, thereby losing any potential treatment combination with that drug permanently to resistance. If a clinician is aware of the timing of resistance to a particular drug, then they may have a crucial opportunity to adjust the treatment to retain the drug’s usefulness in a potential treatment combination or strategy. In this study, we investigate new methods of predicting treatment failure due to treatment resistance using a novel mechanistic model built on an evolutionary interpretation of Droop cell quota theory. We analyze our proposed methods using patient PSA and androgen data from a clinical trial of intermittent treatment with androgen deprivation therapy. Our results produce two indicators of treatment failure. The first indicator, proposed from the evolutionary nature of the cancer population, is calculated using our mathematical model with a predictive accuracy of 87.3% (sensitivity: 96.1%, specificity: 65%). The second indicator, conjectured from the implication of the first indicator, is calculated directly from serum androgen and PSA data with a predictive accuracy of 88.7% (sensitivity: 90.2%, specificity: 85%). Our results demonstrate the potential and feasibility of using an evolutionary tumor dynamics model in combination with the appropriate data to aid in the adaptive management of prostate cancer.