Improving treatment strategies for patients with metastatic castrate resistant prostate cancer through personalized computational modeling

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.

Education and Outreach in Physical Sciences in Oncology

Physical sciences are often overlooked in the field of cancer research. The Physical Sciences in Oncology Initiative was launched to integrate physics, mathematics, chemistry, and engineering with cancer research and clinical oncology through education, outreach, and collaboration. Here, we provide a framework for education and outreach in emerging transdisciplinary fields.

Optimal control to reach eco-evolutionary stability in metastatic castrate-resistant prostate cancer

In the absence of curative therapies, treatment of metastatic castrate-resistant prostate cancer (mCRPC) using currently available drugs can be improved by integrating evolutionary principles that govern proliferation of resistant subpopulations into current treatment protocols. Here we develop what is coined as an 'evolutionary stable therapy', within the context of the mathematical model that has been used to inform the first adaptive therapy clinical trial of mCRPC. The objective of this therapy is to maintain a stable polymorphic tumor heterogeneity of sensitive and resistant cells to therapy in order to prolong treatment efficacy and progression free survival. Optimal control analysis shows that an increasing dose titration protocol, a very common clinical dosing process, can achieve tumor stabilization for a wide range of potential initial tumor compositions and volumes. Furthermore, larger tumor volumes may counter intuitively be more likely to be stabilized if sensitive cells dominate the tumor composition at time of initial treatment, suggesting a delay of initial treatment could prove beneficial. While it remains uncertain if metastatic disease in humans has the properties that allow it to be truly stabilized, the benefits of a dose titration protocol warrant additional pre-clinical and clinical investigations.

Optimizing Cancer Treatment Using Game Theory: A Review

Importance

While systemic therapy for disseminated cancer is often initially successful, malignant cells, using diverse adaptive strategies encoded in the human genome, almost invariably evolve resistance, leading to treatment failure. Thus, the Darwinian dynamics of resistance are formidable barriers to all forms of systemic cancer treatment but rarely integrated into clinical trial design or included within precision oncology initiatives.

Observations

We investigate cancer treatment as a game theoretic contest between the physician's therapy and the cancer cells' resistance strategies. This game has 2 critical asymmetries: (1) Only the physician can play rationally. Cancer cells, like all evolving organisms, can only adapt to current conditions; they can neither anticipate nor evolve adaptations for treatments that the physician has not yet applied. (2) It has a distinctive leader-follower (or "Stackelberg") dynamics; the "leader" oncologist plays first and the "follower" cancer cells then respond and adapt to therapy. Current treatment protocols for metastatic cancer typically exploit neither asymmetry. By repeatedly administering the same drug(s) until disease progression, the physician "plays" a fixed strategy even as the opposing cancer cells continuously evolve successful adaptive responses. Furthermore, by changing treatment only when the tumor progresses, the physician cedes leadership to the cancer cells and treatment failure becomes nearly inevitable. Without fundamental changes in strategy, standard-of-care cancer therapy typically results in "Nash solutions" in which no unilateral change in treatment can favorably alter the outcome.

Conclusions and Relevance

Physicians can exploit the advantages inherent in the asymmetries of the cancer treatment game, and likely improve outcomes, by adopting more dynamic treatment protocols that integrate eco-evolutionary dynamics and modulate therapy accordingly. Implementing this approach will require new metrics of tumor response that incorporate both ecological (ie, size) and evolutionary (ie, molecular mechanisms of resistance and relative size of resistant population) changes.

Hybrid modeling frameworks of tumor development and treatment

Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathways, or variable receptor expression; and extrinsic, such as differences in nutrient supply, crosstalk with stromal or immune cells, or variable composition of the surrounding extracellular matrix. Tumors are also characterized by high cellular heterogeneity and dynamically changing tumor microenvironments. The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. Modeling such complex systems and predicting how tumors will respond to therapies require mathematical models that can handle various types of information and combine diverse theoretical methods on multiple temporal and spatial scales, that is, hybrid models. In this update, we discuss the progress that has been achieved during the last 10 years in the area of the hybrid modeling of tumors. The classical definition of hybrid models refers to the coupling of discrete descriptions of cells with continuous descriptions of microenvironmental factors. To reflect on the direction that the modeling field has taken, we propose extending the definition of hybrid models to include of coupling two or more different mathematical frameworks. Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization, fluid dynamics, game theory, and machine learning. All these methods will be illustrated with applications to tumor development and various anticancer treatments.

This article is characterized under:

Analytical and Computational Methods > Computational Methods

Translational, Genomic, and Systems Medicine > Therapeutic Methods

Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

Computational modelling of resistance and associated treatment response heterogeneity in metastatic cancers

Metastatic cancer patients invariably develop treatment resistance. Different levels of resistance lead to observed heterogeneity in treatment response. The main goal was to evaluate treatment response heterogeneity with a computation model simulating the dynamics of drug-sensitive and drug-resistant cells. Model parameters included proliferation, drug-induced death, transition and proportion of intrinsically resistant cells. The model was benchmarked with imaging metrics extracted from 39 metastatic prostate cancer patients who had ¹⁸F-NaF-PET/CT scans performed at baseline and at three cycles into chemotherapy or hormonal therapy. Two initial model assumptions were evaluated: considering only inter-patient heterogeneity and both inter-patient and intra-patient heterogeneity in the proportion of intrinsically resistant cells. The correlation between the median proportion of intrinsically resistant cells and baseline patient-level imaging metrics was assessed with Spearman's rank correlation coefficient. The impact of model parameters on simulated treatment response was evaluated with a sensitivity study. Treatment response after periods of six, nine, and 12 months was predicted with the model. The median predicted range of response for patients treated with both therapies was compared with a Wilcoxon rank sum test. For each patient, the time was calculated when the proportion of disease with a non-favourable response outperformed a favourable response. By taking into account inter-patient and intra-patient heterogeneity in the proportion of intrinsically resistant cells, the model performed significantly better ([Formula: see text]) than by taking into account only inter-patient heterogeneity ([Formula: see text]). The median proportion of intrinsically resistant cells showed a moderate correlation (ρ  =  0.55) with mean patient-level uptake, and a low correlation (ρ  =  0.36) with the dispersion of mean metastasis-level uptake in a patient. The sensitivity study showed a strong impact of the proportion of intrinsically resistant cells on model behaviour after three cycles of therapy. The difference in the median range of response (MRR) was not significant between cohorts at any time point (p   >  0.15). The median time when the proportion of disease with a non-favourable response outperformed the favourable response was eight months, for both cohorts. The model provides an insight into inter-patient and intra-patient heterogeneity in the evolution of treatment resistance.

Fractionated follow-up chemotherapy delays the onset of resistance in bone metastatic prostate cancer

Prostate cancer to bone metastases are almost always lethal. This results from the ability of metastatic prostate cancer cells to co-opt bone remodeling leading to what is known as the vicious cycle. Understanding how tumor cells can disrupt bone homeostasis through their interactions with the stroma and how metastatic tumors respond to treatment is key to the development of new treatments for what remains an incurable disease. Here we describe an evolutionary game theoretical model of both the homeostatic bone remodeling and its co-option by prostate cancer metastases. This model extends past the evolutionary aspects typically considered in game theoretical models by also including ecological factors such as the physical microenvironment of the bone. Our model recapitulates the current paradigm of the "vicious cycle" driving tumor growth and sheds light on the interactions of heterogeneous tumor cells with the bone microenvironment and treatment response. Our results show that resistant populations naturally become dominant in the metastases under conventional cytotoxic treatment and that novel schedules could be used to better control the tumor and the associated bone disease compared to the current standard of care. Specifically, we introduce fractionated follow up therapy - chemotherapy where dosage is administered initially in one solid block followed by alternating smaller doeses and holidays - and argue that it is better than either a continuous application or a periodic one. Furthermore, we also show that different regimens of chemotherapy can lead to different amounts of pathological bone that are known to correlate with poor quality of life for bone metastatic prostate cancer patients.

Emerging and Established Models of Bone Metastasis

Metastasis is the leading cause of cancer-related death and drives patient morbidity as well as healthcare costs. Bone is the primary site of metastasis for several cancers—breast and prostate cancers in particular. Efforts to treat bone metastases have been stymied by a lack of models to study the progression, cellular players, and signaling pathways driving bone metastasis. In this review, we examine newly described and classic models of bone metastasis. Through the use of current in vivo, microfluidic, and in silico computational bone metastasis models we may eventually understand how cells escape the primary tumor and how these circulating tumor cells then home to and colonize the bone marrow. Further, future models may uncover how cells enter and then escape dormancy to develop into overt metastases. Recreating the metastatic process will lead to the discovery of therapeutic targets for disrupting and treating bone metastasis.

Drug Repositioning for Effective Prostate Cancer Treatment

Drug repositioning has gained attention from both academia and pharmaceutical companies as an auxiliary process to conventional drug discovery. Chemotherapeutic agents have notorious adverse effects that drastically reduce the life quality of cancer patients so drug repositioning is a promising strategy to identify non-cancer drugs which have anti-cancer activity as well as tolerable adverse effects for human health. There are various strategies for discovery and validation of repurposed drugs. In this review, 25 repurposed drug candidates are presented as result of different strategies, 15 of which are already under clinical investigation for treatment of prostate cancer (PCa). To date, zoledronic acid is the only repurposed, clinically used, and approved non-cancer drug for PCa. Anti-cancer activities of existing drugs presented in this review cover diverse and also known mechanisms such as inhibition of mTOR and VEGFR2 signaling, inhibition of PI3K/Akt signaling, COX and selective COX-2 inhibition, NF-κB inhibition, Wnt/β-Catenin pathway inhibition, DNMT1 inhibition, and GSK-3β inhibition. In addition to monotherapy option, combination therapy with current anti-cancer drugs may also increase drug efficacy and reduce adverse effects. Thus, drug repositioning may become a key approach for drug discovery in terms of time- and cost-efficiency comparing to conventional drug discovery and development process.

Homeostasis Back and Forth: An Ecoevolutionary Perspective of Cancer

The role of genetic mutations in cancer is indisputable: They are a key source of tumor heterogeneity and drive its evolution to malignancy. But, the success of these new mutant cells relies on their ability to disrupt the homeostasis that characterizes healthy tissues. Mutated clones unable to break free from intrinsic and extrinsic homeostatic controls will fail to establish a tumor. Here, we will discuss, through the lens of mathematical and computational modeling, why an evolutionary view of cancer needs to be complemented by an ecological perspective to understand why cancer cells invade and subsequently transform their environment during progression. Importantly, this ecological perspective needs to account for tissue homeostasis in the organs that tumors invade, because they perturb the normal regulatory dynamics of these tissues, often coopting them for its own gain. Furthermore, given our current lack of success in treating advanced metastatic cancers through tumor-centric therapeutic strategies, we propose that treatments that aim to restore homeostasis could become a promising venue of clinical research. This ecoevolutionary view of cancer requires mechanistic mathematical models to both integrate clinical with biological data from different scales but also to detangle the dynamic feedback between the tumor and its environment. Importantly, for these models to be useful, they need to embrace a higher degree of complexity than many mathematical modelers are traditionally comfortable with.

Predictive computational modeling to define effective treatment strategies for bone metastatic prostate cancer

The ability to rapidly assess the efficacy of therapeutic strategies for incurable bone metastatic prostate cancer is an urgent need. Pre-clinical in vivo models are limited in their ability to define the temporal effects of therapies on simultaneous multicellular interactions in the cancer-bone microenvironment. Integrating biological and computational modeling approaches can overcome this limitation. Here, we generated a biologically driven discrete hybrid cellular automaton (HCA) model of bone metastatic prostate cancer to identify the optimal therapeutic window for putative targeted therapies. As proof of principle, we focused on TGFβ because of its known pleiotropic cellular effects. HCA simulations predict an optimal effect for TGFβ inhibition in a pre-metastatic setting with quantitative outputs indicating a significant impact on prostate cancer cell viability, osteoclast formation and osteoblast differentiation. In silico predictions were validated in vivo with models of bone metastatic prostate cancer (PAIII and C4-2B). Analysis of human bone metastatic prostate cancer specimens reveals heterogeneous cancer cell use of TGFβ. Patient specific information was seeded into the HCA model to predict the effect of TGFβ inhibitor treatment on disease evolution. Collectively, we demonstrate how an integrated computational/biological approach can rapidly optimize the efficacy of potential targeted therapies on bone metastatic prostate cancer.

Assessing Combinational Drug Efficacy in Cancer Cells by Using Image-based Dynamic Response Analysis

The landscape of translational research has been shifting toward drug combination therapies. Pairing of drugs allows for more types of drug interaction with cells. In order to accurately and comprehensively assess combinational drug efficacy, analytical methods capable of recognizing these alternative reactions will be required to prioritize those drug candidates having better chances of delivering appreciable therapeutic benefits. Traditional efficacy measures are primarily based on the “extent” of drug inhibition, which is the percentage of cells being killed after drug exposure. Here, we introduce a second dimension of evaluation criterion, speed of killing, based on a live cell imaging assay. This dynamic response trajectory approach takes advantage of both “extent” and “speed” information and uncovers synergisms that would otherwise be missed, while also generating hypotheses regarding important mechanistic modes of drug action.

Current and emerging therapies for bone metastatic castration-resistant prostate cancer

BACKGROUND

A paucity of therapeutic options is available to treat men with metastatic castration-resistant prostate cancer (mCRPC). However, recent developments in our understanding of the disease have resulted in several new therapies that show promise in improving overall survival rates in this patient population.

METHODS

Agents approved for use in the United States and those undergoing clinical trials for the treatment of mCRPC are reviewed. Recent contributions to the understanding of prostate biology and bone metastasis are discussed as well as how the underlying mechanisms may represent opportunities for therapeutic intervention. New challenges to delivering effective mCRPC treatment will also be examined.

RESULTS

New and emerging treatments that target androgen synthesis and utilization or the microenvironment may improve overall survival rates for men diagnosed with mCRPC. Determining how factors derived from the primary tumor can promote the development of premetastatic niches and how prostate cancer cells parasitize niches in the bone microenvironment, thus remaining dormant and protected from systemic therapy, could yield new therapies to treat mCRPC. Challenges such as intratumoral heterogeneity and patient selection can potentially be circumvented via computational biology approaches.

CONCLUSIONS

The emergence of novel treatments for mCRPC, combined with improved patient stratification and optimized therapy sequencing, suggests that significant gains may be made in terms of overall survival rates for men diagnosed with this form of cancer.