Predicting patient-specific response to adaptive therapy in metastatic castration-resistant prostate cancer using prostate-specific antigen dynamics

A mathematical model for predicting the spatiotemporal response of breast cancer cells treated with doxorubicin

Tumor heterogeneity contributes significantly to chemoresistance, a leading cause of treatment failure. To better personalize therapies, it is essential to develop tools capable of identifying and predicting intra- and inter-tumor heterogeneities. Biology-inspired mathematical models are capable of attacking this problem, but tumor heterogeneity is often overlooked in in-vivo modeling studies, while phenotypic considerations capturing spatial dynamics are not typically included in in-vitro modeling studies. We present a data assimilation-prediction pipeline with a two-phenotype model that includes a spatiotemporal component to characterize and predict the evolution of in-vitro breast cancer cells and their heterogeneous response to chemotherapy. Our model assumes that the cells can be divided into two subpopulations: surviving cells unaffected by the treatment, and irreversibly damaged cells undergoing treatment-induced death. MCF7 breast cancer cells were previously cultivated in wells for up to 1000 hours, treated with various concentrations of doxorubicin and imaged with time-resolved microscopy to record spatiotemporally-resolved cell count data. Images were used to generate cell density maps. Treatment response predictions were initialized by a training set and updated by weekly measurements. Our mathematical model successfully calibrated the spatiotemporal cell growth dynamics, achieving median [range] concordance correlation coefficients of > .99 [.88, >.99] and .73 [.58, .85] across the whole well and individual pixels, respectively. Our proposed data assimilation-prediction approach achieved values of .97 [.44, >.99] and .69 [.35, .79] for the whole well and individual pixels, respectively. Thus, our model can capture and predict the spatiotemporal dynamics of MCF7 cells treated with doxorubicin in an in-vitro setting.

Cell-state transitions and density-dependent interactions together explain the dynamics of spontaneous epithelial-mesenchymal heterogeneity

Cancer cell populations comprise phenotypes distributed among the epithelial-mesenchymal (E-M) spectrum. However, it remains unclear which population-level processes give rise to the observed experimental distribution and dynamical changes in E-M heterogeneity, including (1) differential growth, (2) cell-state switching, and (3) population density-dependent growth or state-transition rates. Here, we analyze the necessity of these three processes in explaining the dynamics of E-M population distributions as observed in PMC42-LA and HCC38 breast cancer cells. We find that, while cell-state transition is necessary to reproduce experimental observations of dynamical changes in E-M fractions, including density-dependent growth interactions (cooperation or suppression) better explains the data. Further, our models predict that treatment of HCC38 cells with transforming growth factor β (TGF-β) signaling and Janus kinase 2/signal transducer and activator of transcription 3 (JAK2/3) inhibitors enhances the rate of mesenchymal-epithelial transition (MET) instead of lowering that of E-M transition (EMT). Overall, our study identifies the population-level processes shaping the dynamics of spontaneous E-M heterogeneity in breast cancer cells.

Integrating Diversity, Equity, and Inclusion into Preclinical, Clinical, and Public Health Mathematical Models

Mathematical modelling applied to preclinical, clinical, and public health research is critical for our understanding of a multitude of biological principles. Biology is fundamentally heterogeneous, and mathematical modelling must meet the challenge of variability head on to ensure the principles of diversity, equity, and inclusion (DEI) are integrated into quantitative analyses. Here we provide a follow-up perspective on the DEI plenary session held at the 2023 Society for Mathematical Biology Annual Meeting to discuss key issues for the increased integration of DEI in mathematical modelling in biology.

The bone ecosystem facilitates multiple myeloma relapse and the evolution of heterogeneous drug resistant disease

Multiple myeloma (MM) is an osteolytic malignancy that is incurable due to the emergence of treatment resistant disease. Defining how, when and where myeloma cell intrinsic and extrinsic bone microenvironmental mechanisms cause relapse is challenging with current biological approaches. Here, we report a biology-driven spatiotemporal hybrid agent-based model of the MM-bone microenvironment. Results indicate MM intrinsic mechanisms drive the evolution of treatment resistant disease but that the protective effects of bone microenvironment mediated drug resistance (EMDR) significantly enhances the probability and heterogeneity of resistant clones arising under treatment. Further, the model predicts that targeting of EMDR deepens therapy response by eliminating sensitive clones proximal to stroma and bone, a finding supported by in vivo studies. Altogether, our model allows for the study of MM clonal evolution over time in the bone microenvironment and will be beneficial for optimizing treatment efficacy so as to significantly delay disease relapse.

Dysregulated FGFR3 signaling alters the immune landscape in bladder cancer and presents therapeutic possibilities in an agent-based model

Bladder cancer is an increasingly prevalent global disease that continues to cause morbidity and mortality despite recent advances in treatment. Immune checkpoint inhibitors (ICI) and fibroblast growth factor receptor (FGFR)-targeted therapeutics have had modest success in bladder cancer when used as monotherapy. Emerging data suggests that the combination of these two therapies could lead to improved clinical outcomes, but the optimal strategy for combining these agents remains uncertain. Mathematical models, specifically agent-based models (ABMs), have shown recent successes in uncovering the multiscale dynamics that shape the trajectory of cancer. They have enabled the optimization of treatment methods and the identification of novel therapeutic strategies. To assess the combined effects of anti-PD-1 and anti-FGFR3 small molecule inhibitors (SMI) on tumor growth and the immune response, we built an ABM that captures key facets of tumor heterogeneity and CD8+ T cell phenotypes, their spatial interactions, and their response to therapeutic pressures. Our model quantifies how tumor antigenicity and FGFR3 activating mutations impact disease trajectory and response to anti-PD-1 antibodies and anti-FGFR3 SMI. We find that even a small population of weakly antigenic tumor cells bearing an FGFR3 mutation can render the tumor resistant to combination therapy. However, highly antigenic tumors can overcome therapeutic resistance mediated by FGFR3 mutation. The optimal therapy depends on the strength of the FGFR3 signaling pathway. Under certain conditions, ICI alone is optimal; in others, ICI followed by anti-FGFR3 therapy is best. These results indicate the need to quantify FGFR3 signaling and the fitness advantage conferred on bladder cancer cells harboring this mutation. This ABM approach may enable rationally designed treatment plans to improve clinical outcomes.

Adaptive therapy: a tumor therapy strategy based on Darwinian evolution theory

Cancer progression is a dynamic process of continuous evolution, in which genetic diversity and heterogeneity are generated by clonal and subclonal amplification based on random mutations. Traditional cancer treatment strategies have a great challenge, which often leads to treatment failure due to drug resistance. Integrating evolutionary dynamics into treatment regimens may be an effective way to overcome the problem of drug resistance. In particular, a potential treatment is adaptive therapy, which strategy advocates containment strategies that adjust the treatment cycles according to tumor evolution to control the growth of treatment-resistant cells. In this review, we first summarize the shortcomings of traditional tumor treatment methods in evolution and then introduce the theoretical basis and research status of adaptive therapy. By analyzing the limitations of adaptive therapy and exploring possible solutions, we can broaden people's understanding of adaptive therapy and provide new insights and strategies for tumor treatment.

Overcoming chemotherapy resistance in low-grade gliomas: A computational approach

Low-grade gliomas are primary brain tumors that arise from glial cells and are usually treated with temozolomide (TMZ) as a chemotherapeutic option. They are often incurable, but patients have a prolonged survival. One of the shortcomings of the treatment is that patients eventually develop drug resistance. Recent findings show that persisters, cells that enter a dormancy state to resist treatment, play an important role in the development of resistance to TMZ. In this study we constructed a mathematical model of low-grade glioma response to TMZ incorporating a persister population. The model was able to describe the volumetric longitudinal dynamics, observed in routine FLAIR 3D sequences, of low-grade glioma patients acquiring TMZ resistance. We used the model to explore different TMZ administration protocols, first on virtual clones of real patients and afterwards on virtual patients preserving the relationships between parameters of real patients. In silico clinical trials showed that resistance development was deferred by protocols in which individual doses are administered after rest periods, rather than the 28-days cycle standard protocol. This led to median survival gains in virtual patients of more than 15 months when using resting periods between two and three weeks and agreed with recent experimental observations in animal models. Additionally, we tested adaptive variations of these new protocols, what showed a potential reduction in toxicity, but no survival gain. Our computational results highlight the need of further clinical trials that could obtain better results from treatment with TMZ in low grade gliomas.

Treatment of evolving cancers will require dynamic decision support

Cancer research has traditionally focused on developing new agents, but an underexplored question is that of the dose and frequency of existing drugs. Based on the modus operandi established in the early days of chemotherapies, most drugs are administered according to predetermined schedules that seek to deliver the maximum tolerated dose and are only adjusted for toxicity. However, we believe that the complex, evolving nature of cancer requires a more dynamic and personalized approach. Chronicling the milestones of the field, we show that the impact of schedule choice crucially depends on processes driving treatment response and failure. As such, cancer heterogeneity and evolution dictate that a one-size-fits-all solution is unlikely-instead, each patient should be mapped to the strategy that best matches their current disease characteristics and treatment objectives (i.e. their 'tumorscape'). To achieve this level of personalization, we need mathematical modeling. In this perspective, we propose a five-step 'Adaptive Dosing Adjusted for Personalized Tumorscapes (ADAPT)' paradigm to integrate data and understanding across scales and derive dynamic and personalized schedules. We conclude with promising examples of model-guided schedule personalization and a call to action to address key outstanding challenges surrounding data collection, model development, and integration.

Evolutionary Dynamics and Intermittent Therapy for Metastatic Cancers

Mathematical models show that the induction period of intermittent cancer therapy drives cancer toward resistance

Autophagy, a critical element in the aging male reproductive disorders and prostate cancer: a therapeutic point of view

Autophagy is a highly conserved, lysosome-dependent biological mechanism involved in the degradation and recycling of cellular components. There is growing evidence that autophagy is related to male reproductive biology, particularly spermatogenic and endocrinologic processes closely associated with male sexual and reproductive health. In recent decades, problems such as decreasing sperm count, erectile dysfunction, and infertility have worsened. In addition, reproductive health is closely related to overall health and comorbidity in aging men. In this review, we will outline the role of autophagy as a new player in aging male reproductive dysfunction and prostate cancer. We first provide an overview of the mechanisms of autophagy and its role in regulating male reproductive cells. We then focus on the link between autophagy and aging-related diseases. This is followed by a discussion of therapeutic strategies targeting autophagy before we end with limitations of current studies and suggestions for future developments in the field.

Effective dose window for containing tumor burden under tolerable level

A maximum-tolerated dose (MTD) reduces the drug-sensitive cell population, though it may result in the competitive release of drug resistance. Alternative treatment strategies such as adaptive therapy (AT) or dose modulation aim to impose competitive stress on drug-resistant cell populations by maintaining a sufficient number of drug-sensitive cells. However, given the heterogeneous treatment response and tolerable tumor burden level of individual patients, determining an effective dose that can fine-tune competitive stress remains challenging. This study presents a mathematical model-driven approach that determines the plausible existence of an effective dose window (EDW) as a range of doses that conserve sufficient sensitive cells while maintaining the tumor volume below a threshold tolerable tumor volume (TTV). We use a mathematical model that explains intratumor cell competition. Analyzing the model, we derive an EDW determined by TTV and the competitive strength. By applying a fixed endpoint optimal control model, we determine the minimal dose to contain cancer at a TTV. As a proof of concept, we study the existence of EDW for a small cohort of melanoma patients by fitting the model to longitudinal tumor response data. We performed identifiability analysis, and for the patients with uniquely identifiable parameters, we deduced patient-specific EDW and minimal dose. The tumor volume for a patient could be theoretically contained at the TTV either using continuous dose or AT strategy with doses belonging to EDW. Further, we conclude that the lower bound of the EDW approximates the minimum effective dose (MED) for containing tumor volume at the TTV.

A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation

Adaptive therapy is a dynamic cancer treatment protocol that updates (or 'adapts') treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.

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.

Adaptive therapy to circumvent drug resistance to tyrosine kinase inhibitors in cancer: is it clinically relevant?

INTRODUCTION

Cancer is highly adaptable and is constantly evolving against current targeted therapies such as tyrosine kinase inhibitors. Despite advances in recent decades, the emergence of drug resistance to tyrosine kinase inhibitors constantly hampers therapeutic efficacy of cancer treatment. Continuous therapy versus intermittent clinical regimen has been a debate in drug administration of cancer patients. An ecologically-inspired shift in cancer treatment known as 'adaptive therapy' intends to improve the drug administration of drugs to cancer patients that can delay emergence of drug resistance.

AREAS COVERED

We discuss improved understanding of the concept of drug resistance, the basis of continuous therapy, intermittent clinical regimens, and adaptive therapy will be reviewed. In addition, we discuss how adaptive therapy provides guidance for future cancer treatment.

EXPERT OPINION

The current understanding of drug resistance in cancer leads to poor prognosis and limited treatment options in patients. Fighting drug resistance mutants is constantly followed by new forms of resistance. In most reported cases, continuous therapy leads to drug resistance and an intermittent clinical regimen vaguely delays it. However, adaptive therapy, conceptually, exploits multiple parameters that can suppress the growth of drug resistance and provides safe treatment for cancer patients in the future.

Range-Bounded Adaptive Therapy in Metastatic Prostate Cancer

Adaptive therapy with abiraterone acetate (AA), whereby treatment is cycled on and off, has been presented as an alternative to continuous therapy for metastatic castration resistant prostate cancer (mCRPC). It is hypothesized that cycling through treatment allows sensitive cells to competitively suppress resistant cells, thereby increasing the amount of time that treatment is effective. It has been proposed that there exists a subset of patients for whom this competition can be enhanced through slight modifications. Here, we investigate how adaptive AA can be modified to extend time to progression using a simple mathematical model of stem cell, non-stem cell, and prostate-specific antigen (PSA) dynamics. The model is calibrated to longitudinal PSA data from 16 mCRPC patients undergoing adaptive AA in a pilot clinical study at Moffitt Cancer Center. Model parameters are then used to simulate range-bounded adaptive therapy (RBAT) whereby treatment is modulated to maintain PSA levels between pre-determined patient-specific bounds. Model simulations of RBAT are compared to the clinically applied adaptive therapy and show that RBAT can further extend time to progression, while reducing the cumulative dose patients received in 11/16 patients. Simulations also show that the cumulative dose can be reduced by up to 40% under RBAT. Through small modifications to the conventional adaptive therapy design, our study demonstrates that RBAT offers the opportunity to improve patient care, particularly in those patients who do not respond well to conventional adaptive therapy.

The Tumor Invasion Paradox in Cancer Stem Cell-Driven Solid Tumors

Cancer stem cells (CSCs) are key in understanding tumor growth and tumor progression. A counterintuitive effect of CSCs is the so-called tumor growth paradox: the effect where a tumor with a higher death rate may grow larger than a tumor with a lower death rate. Here we extend the modeling of the tumor growth paradox by including spatial structure and considering cancer invasion. Using agent-based modeling and a corresponding partial differential equation model, we demonstrate and prove mathematically a tumor invasion paradox: a larger cell death rate can lead to a faster invasion speed. We test this result on a generic hypothetical cancer with typical growth rates and typical treatment sensitivities. We find that the tumor invasion paradox may play a role for continuous and intermittent treatments, while it does not seem to be essential in fractionated treatments. It should be noted that no attempt was made to fit the model to a specific cancer, thus, our results are generic and theoretical.

A Phase 1b Adaptive Androgen Deprivation Therapy Trial in Metastatic Castration Sensitive Prostate Cancer

Background: We hypothesize that cancer survival can be improved through adapting treatment strategies to cancer evolutionary dynamics and conducted a phase 1b study in metastatic castration sensitive prostate cancer (mCSPC). Methods: Men with asymptomatic mCSPC were enrolled and proceeded with a treatment break after achieving > 75% PSA decline with LHRH analog plus an NHA. ADT was restarted at the time of PSA or radiographic progression and held again after achieving >50% PSA decline. This on-off cycling of ADT continued until on treatment imaging progression. Results: At data cut off in August 2022, only 2 of the 16 evaluable patients were off study due to imaging progression at 28 months from first dose of LHRH analog for mCSPC. Two additional patients showed PSA progression at 12.4 and 20.5 months and remain on trial. Since none of the 16 patients developed imaging progression at 12 months, the study succeeded in its primary objective of feasibility. The secondary endpoints of median time to PSA progression and median time to radiographic progression have not been reached at a median follow up of 26 months. Conclusions: It is feasible to use an individual’s PSA response and testosterone levels to guide intermittent ADT in mCSPC.

Clinical Applications of Liquid Biopsy in Prostate Cancer: From Screening to Predictive Biomarker

Prostate cancer (PC) remains the most common malignancy and the second most common cause of cancer death in men. As a result of highly variable biological behavior and development of resistance to available agents under therapeutic pressure, optimal management is often unclear. Traditional surgical biopsies, even when augmented by genomic studies, may fail to provide adequate guidance for clinical decisions as these can only provide a snapshot of a dynamic process. Additionally, surgical biopsies are cumbersome to perform repeatedly and often involve risk. Liquid biopsies (LB) are defined as the analysis of either corpuscular (circulating tumor cells, extracellular vesicles) or molecular (circulating DNA or RNA) tumor-derived material. LB could more precisely identify clinically relevant alterations that characterize the metastatic potential of tumors, predict response to specific treatments or actively monitor for the emergence of resistance. These tests can potentially be repeated as often as deemed necessary and can detect real-time response to treatment with minimal inconvenience to the patient. In the current review, we consider common clinical scenarios to describe available LB assays in PC as a platform to explore existing evidence for their use in guiding decision making and to discuss current limitations to their adoption in the clinic.

Optimizing the future: how mathematical models inform treatment schedules for cancer

For decades, mathematical models have influenced how we schedule chemotherapeutics. More recently, mathematical models have leveraged lessons from ecology, evolution, and game theory to advance predictions of optimal treatment schedules, often in a personalized medicine manner. We discuss both established and emerging therapeutic strategies that deviate from canonical standard-of-care regimens, and how mathematical models have contributed to the design of such schedules. We first examine scheduling options for single therapies and review the advantages and disadvantages of various treatment plans. We then consider the challenge of scheduling multiple therapies, and review the mathematical and clinical support for various conflicting treatment schedules. Finally, we propose how a consilience of mathematical and clinical knowledge can best determine the optimal treatment schedules for patients.

Understanding and targeting prostate cancer cell heterogeneity and plasticity

Prostate cancer (PCa) is a prevalent malignancy that occurs primarily in old males. Prostate tumors in different patients manifest significant inter-patient heterogeneity with respect to histo-morphological presentations and molecular architecture. An individual patient tumor also harbors genetically distinct clones in which PCa cells display intra-tumor heterogeneity in molecular features and phenotypic marker expression. This inherent PCa cell heterogeneity, e.g., in the expression of androgen receptor (AR), constitutes a barrier to the long-term therapeutic efficacy of AR-targeting therapies. Furthermore, tumor progression as well as therapeutic treatments induce PCa cell plasticity such that AR-positive PCa cells may turn into AR-negative cells and prostate tumors may switch lineage identity from adenocarcinomas to neuroendocrine-like tumors. This induced PCa cell plasticity similarly confers resistance to AR-targeting and other therapies. In this review, I first discuss PCa from the perspective of an abnormal organ development and deregulated cellular differentiation, and discuss the luminal progenitor cells as the likely cells of origin for PCa. I then focus on intrinsic PCa cell heterogeneity in treatment-naïve tumors with the presence of prostate cancer stem cells (PCSCs). I further elaborate on PCa cell plasticity induced by genetic alterations and therapeutic interventions, and present potential strategies to therapeutically tackle PCa cell heterogeneity and plasticity. My discussions will make it clear that, to achieve enduring clinical efficacy, both intrinsic PCa cell heterogeneity and induced PCa cell plasticity need to be targeted with novel combinatorial approaches.