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A new ecologically inspired paradigm in cancer treatment known as “adaptive therapy” capitalizes on competitive interactions between drug-sensitive and drug-resistant subclones. The goal of adaptive therapy is to maintain a controllable stable tumor burden by allowing a significant population of treatment-sensitive cells to survive. These, in turn, suppress proliferation of the less-fit resistant populations. However, there remain several open challenges in designing adaptive therapies, particularly in extending these therapeutic concepts to multiple treatments. We present a cancer treatment case study (metastatic castrate-resistant prostate cancer) as a point of departure to illustrate three novel concepts to aid the design of multidrug adaptive therapies. First, frequency-dependent “cycles” of tumor evolution can trap tumor evolution in a periodic, controllable loop. Second, the availability and selection of treatments may limit the evolutionary “absorbing region” reachable by the tumor. Third, the velocity of evolution significantly influences the optimal timing of drug sequences. These three conceptual advances provide a path forward for multidrug adaptive therapy.Significance:Driving tumor evolution into periodic, repeatable treatment cycles provides a path forward for multidrug adaptive therapy.

Figure S1, Tables S1, S2. Table S1: Competition parameters for Lupron and Abiraterone treatment; Table S2: Competition parameters for no treatment; Figure S1: After-action analysis of patient-specific subpopulations Normalized subpopulations over time (equation 4) for testosterone-dependent (T+, yellow), testosterone-producing (TP, blue), and testosterone-independent cells (T-, green). Timing of treatment received under clinical protocol is indicated (top) for Lupron & Abiraterone (red) and Lupron only (blue). Parameterization of the model is performed by least-squares fit to PSA data from clinical trial NCT02415621 (see figure 3).

PDF file - 232K, The supporting material describes in more detail the Markov chain model, and includes a full Table and two additional figures. Figure S1. Convergence plot for the lung cancer matrix. Figure S2. Metastatic tumor distributions after two-steps, compared with steady-state. Table S1. Comparative table of top two-step metastatic pathways of all types from Lung.

Bladder cancer (BCa), the 6th commonest cancer in the U.S., is highly lethal when metastatic. Sites and patterns of patient-specific metastatic spread are deemed random and unpredictable. Whether BCa metastatic patterns can be quantified and predicted more accurately is unknown. We used a prospective, longitudinal dataset of 3,505 BCa patients who underwent definitive treatment following diagnosis and were continuously enrolled (1971-2016; mean follow-up 6.13 years). Metastases developed in 30% (n=1,040) of patients, with 5-year survival rate of 18%, compared to 72% in those without metastases (n=2,465). The three commonest metastatic sites at time-of-first progression were pelvis (n=283; 27.2%), bone (n=274; 26.3%), and lung (n=247; 23.8%). We illustrate metastatic pathway progression as color-coded, circular, tree-ring diagrams (primary in the center; metastatic sites outwards). Markov chain modeling, denoting nodes as potential anatomic metastatic sites, indicated higher probability of spread from the bladder to pelvis (15.6%), bone (15.6%), and lung (13.9%), categorizing 4 of 10 anatomical sites as ‘spreaders' and 2 as ‘sponges'. We created a dynamical, data-visualization, web-platform that displays temporal, spatial and Markov modeling figures with predictive capability. For contrasting subgroups, this platform indicated differences in transition probabilities, rank-ordering of metastatic sites, and spreader/sponge node classification. Spatiotemporal patterns of BCa metastasis and sites of spread indicate underlying organotropic mechanisms in the prediction of response. This recognition opens the possibility of organ site-specific therapeutic targeting in the oligo-metastatic disease setting. In the precision medicine era, visualization of complex, time-resolved clinical data will enhance management of post-operative, metastatic BCa patients. Citation Format: Jeremy M. Mason, Zaki Hasnain, Gus Miranda, Karanvir Gill, Paul K. Newton, Inderbir S. Gill, Peter Kuhn. Pathways of metastatic bladder cancer from a longitudinal patient data set [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 4261.

Adrenal gland metastases are common in lung cancer. It is well recognized that aggressive treatment of solitary adrenal metastases leads to improved outcomes but the exact nature of adrenal deposits is not well understood. Controversy exists as to the routing of cancer cells to the adrenal gland with some believing that this transmission is lymphatic, in contrast to the more generally accepted theory of hematogenous spread. Using an autopsy dataset of 3827 untreated cancer patients, we use the metastatic distribution of common primary cancer types to create Markov models of progression. The anatomical sites of spread in the body represent states in the model, while the transition probability between states represents the probability of metastatic spread from one site to another. We then use the Markov models to run Monte Carlo simulations of random walkers representing circulating tumor cells traveling within the body to simulate metastatic spread. We calculate mean first passage times (MFPT) to each site as a representative of time to metastasis formation. Analysis of 6 common cancer types (bladder [n=120 autopsies; 289 metastases], breast [n=432; 2235], colorectal [n=161; 420], lung [n=560; 859], ovarian [n=418; 806], and prostate [n=62; 212]) from the dataset showed distinct metastatic distributions across the populations. MFPT calculations to anatomical sites in the 6 analyzed primary cancer types indicated model progression times to the adrenal gland similar to the regional and distal lymph nodes in only lung cancer. The times associated with adrenal gland in the other primary cancers were similar to other metastatic sites of hematogenous spread. The Markov models created strongly support the lymphatic theory for metastatic spread to the adrenal glands. After performing a literature review to look for the biological plausibility of the simulated results, we believe evidence supports this theory and validates the models. This could explain improved survival for patients in whom solitary adrenal metastases are managed aggressively with surgical or radiation modalities. In order to further validate this theory, we are calling for clinical trials prospectively testing this hypothesis. Citation Format: Jeremy M. Mason, AnneMarie Ciccarella, Lori Marx-Rubiner, Lyudmila Bazhenova, Paul K. Newton, Kelly Bethel, Jorge J. Nieva, Peter Kuhn. Adrenal metastases in lung cancer: Clinical implications of a mathematical model [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2017; 2017 Apr 1-5; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2017;77(13 Suppl):Abstract nr 4532. doi:10.1158/1538-7445.AM2017-4532

We describe a Markov chain mathematical model of lung cancer progression based on a longitudinal dataset of 722 lung cancer patients. Specifically, we investigate the patterns of metastatic spread in lung cancer and how the VEGF inhibitor, bevacizumab, alters these metastatic patterns. Stochastic models were used to simulate metastatic spread by means of random walk processes on directed graphs. We created spatiotemporal diagrams of cancer progression to analyze the differences between patients treated and not treated with bevacizumab. Patients with squamous lung cancer or brain metastases at baseline were ineligible for bevacizumab and excluded from analysis. Our results demonstrated that not only does bevacizumab extend survival, but it also alters patterns of metastatic spread. Patients treated with bevacizumab were characterized by greater heterogeneity in their pathways of metastatic progression, compared to those patients not treated with bevacizumab, which showed more homogeneity in their pathways. Furthermore, we quantify this spread and characterize metastatic sites as ‘spreaders’ and ‘sponges’ based on their probability of spreading the disease. Citation Format: Jeremy M. Mason, Paul K. Newton, Gino K. In, Sonia Lin, Peter Kuhn, Jorge J. Nieva. Spatiotemporal progression patterns in metastatic lung cancer treated with bevacizumab. [abstract]. In: Proceedings of the 107th Annual Meeting of the American Association for Cancer Research; 2016 Apr 16-20; New Orleans, LA. Philadelphia (PA): AACR; Cancer Res 2016;76(14 Suppl):Abstract nr 2711.

Background: Hematogenous metastasis is a poorly understood process that accounts for the lion's share of cancer death. We hypothesize that this process can be explained by circulating tumor cells (CTCs). We endeavor to deconvolute this complex process by means of a mathematical model of CTC population dynamics within the human vascular system. Methods: We have represented the human vasculature as a network with organs represented as nodes and vascular connections as directed edges and written a system of Ordinary Differential Equations to model the dynamics of circulating tumor cells (CTCs) as they populate the body from a source tumor. We have introduced several novel concepts such as a ‘filtration fraction’ which represents the fraction of CTCs that arrest in a given organ, the ‘shedding rate’ which represents the rate at which a primary tumor sheds CTCs into the vasculature and a ‘clearance rate’ which represents the combined effects of CTC apoptosis and immune clearance. Experimental parametrization of this model is accomplished through a clinical trial at The Scripps Institute during which we measure CTC concentrations at each of the most highly connected nodes at several time points before and after definitive surgery for – to include the portal vein, the superior vena cava, peripheral venous and peripheral arterial blood. Results: Initial exploration of the model using clinical data for validation has shown that certain tumor types follow flow driven patterns of metastasis while others seem to ignore the logical spread (e.g. prostate cancer spreading to the bone does not follow the flow directed network while sarcoma to the lungs does). Reasons for this dichotomy are as of yet unknown, though we suspect that both CTC heterogeneity and some form of biological signaling response are at play. We will utilize our theoretical model to investigate this dichotomy by explicitly incorporating CTC heterogeneity and by making specific biological, phenotypic observations of CTCs from different points in the network. Conclusion: We present the first network based, filter and flow model of CTC dynamics. The act of building the theoretical model and comparing it to clinical data alone has inspired several biological hypotheses and we look forward to testing more specific questions through clinical studies. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 102nd Annual Meeting of the American Association for Cancer Research; 2011 Apr 2-6; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2011;71(8 Suppl):Abstract nr 4912. doi:10.1158/1538-7445.AM2011-4912