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Spatial agent‐based models are frequently used to investigate the evolution of solid tumours subject to localized cell–cell interactions and microenvironmental heterogeneity. As spatial genomic, transcriptomic and proteomic technologies gain traction, spatial computational models are predicted to become ever more necessary for making sense of complex clinical and experimental data sets, for predicting clinical outcomes, and for optimizing treatment strategies. Here we present a non‐technical step by step guide to developing such a model from first principles. Stressing the importance of tailoring the model structure to that of the biological system, we describe methods of increasing complexity, from the basic Eden growth model up to off‐lattice simulations with diffusible factors. We examine choices that unavoidably arise in model design, such as implementation, parameterization, visualization and reproducibility. Each topic is illustrated with examples drawn from recent research studies and state of the art modelling platforms. We emphasize the benefits of simpler models that aim to match the complexity of the phenomena of interest, rather than that of the entire biological system. Our guide is aimed at both aspiring modellers and other biologists and oncologists who wish to understand the assumptions and limitations of the models on which major cancer studies now so often depend. [ABSTRACT FROM AUTHOR]

During embryogenesis, multicellular animals are shaped via cell proliferation, cell rearrangement, and apoptosis. At the end of development, tissue architecture is then maintained through balanced rates of cell proliferation and loss. Here, we take an in silico approach to look for generic systems features of morphogenesis in multicellular animals that arise as a consequence of the evolution of development. Using artificial evolution, we evolved cellular automata-based digital organisms that have distinct embryonic and homeostatic phases of development. Although these evolved organisms use a variety of strategies to maintain their form over time, organisms of different types were all found to rapidly recover from environmental damage in the form of wounds. This regenerative response was most robust in an organism with a stratified tissue-like architecture. An evolutionary analysis revealed that evolution itself contributed to the ability of this organism to maintain its form in the face of genetic and environmental perturbation, confirming the results of previous studies. In addition, the exceptional robustness of this organism to surface injury was found to result from an upward flux of cells, driven in part by cell divisions with a stable niche at the tissue base. Given the general nature of the model, our results lead us to suggest that many of the robust systems properties observed in real organisms, including scar-free wound-healing in well-protected embryos and the layered tissue architecture of regenerating epithelial tissues, may be by-products of the evolution of morphogenesis, rather than the direct result of selection. [ABSTRACT FROM AUTHOR]

Bone-forming osteoblasts and -resorbing osteoclasts control bone injury repair, and myeloid-derived cells such as monocytes and macrophages are known to influence their behavior. However, precisely how these multiple cell types coordinate and regulate each other over time within the bone marrow to restore bone is difficult to dissect using biological approaches. Conversely, mathematical modeling lends itself well to this challenge. Therefore, we generated an ordinary differential equation (ODE) model powered by experimental data (osteoblast, osteoclast, bone volume, pro- and anti-inflammatory myeloid cells) obtained from intra-tibially injured mice. Initial ODE results using only osteoblast/osteoclast populations demonstrated that bone homeostasis could not be recovered after injury, but this issue was resolved upon integration of pro- and anti-inflammatory myeloid population dynamics. Surprisingly, the ODE revealed temporal disconnects between the peak of total bone mineralization/resorption, and osteoblast/osteoclast numbers. Specifically, the model indicated that osteoclast activity must vary greatly (> 17-fold) to return the bone volume to baseline after injury and suggest that osteoblast/osteoclast number alone is insufficient to predict bone the trajectory of bone repair. Importantly, the values of osteoclast activity fall within those published previously. These data underscore the value of mathematical modeling approaches to understand and reveal new insights into complex biological processes. [ABSTRACT FROM AUTHOR]

Small changes to the parameters of a system can lead to abrupt qualitative changes of its behavior, a phenomenon known as bifurcation. Such instabilities are typically considered problematic, however, we show that their power can be leveraged to design novel types of mechanisms. Hysteresis mechanisms use transient changes of system parameters to induce a permanent improvement to its performance via optimal equilibrium selection. Optimal control mechanisms induce convergence to states whose performance is better than even the best equilibrium. We apply these mechanisms in two different settings that illustrate the versatility of bifurcation mechanism design. In the first one we explore how introducing flat taxation could improve social welfare, despite decreasing agent “rationality,” by destabilizing inefficient equilibria. From there we move on to consider a well known game of tumor metabolism and use our approach to derive potential new cancer treatment strategies. [ABSTRACT FROM AUTHOR]

Hypothermia may attenuate the progression of ischemia-induced damage in liver. Here, we determined the effects of a brief cycle of hypothermic preconditioning applied before an ischemic/reperfusion (I/R) episode in isolated perfused rat liver (IPRL) on tissue damage and oxidative stress. Rats (male, 200-250 g) were anaesthetised with sodium pentobarbital (60 mg.kg-1 i.p) and underwent laparatomy. The liver was removed and perfused in a temperature-regulated non-recirculating system. Livers were randomly divided into two groups (n = 6 each group). In the hypothermia-preconditioned group, livers were perfused with hypothermic buffer (cycle of 10 min at 22 °C plus 10 min at 37 °C) and the other group was perfused at 37 °C. Both groups were then submitted to 40 min of warm ischemia and 20 min of warm reperfusion. The level of tissue-damage indicators (alanine amino transferase, ALT; lactate dehydrogenase, LDH; and proteins), oxidative stress markers (thiobarbituric acid-reactive substances, TBARS; advanced oxidation protein products, AOPP; and glutathione, GSH) were measured in aliquots of perfusate sampled at different time intervals. Histological determinations and oxidative stress biomarkers in homogenized liver (AOPP; TBARS; nitric oxide derivatives, NOx; GSH and glutathione disulphide, GSSG) were also made in the tissue at the end. Results showed that both damage and oxidant indicators significantly decreased while antioxidant increased in hypothermic preconditioned livers. In addition, homogenized liver determinations and histological observations at the end of the protocol corroborate the results in the perfusate, confirming the utility of the perfusate as a non-invasive method. In conclusion, hypothermic preconditioning attenuates oxidative damage and appears to be a promising strategy to protect the liver against IR injury. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Natural selection in cancer often results in the emergence of increasingly malignant tumor cells that display many if not all of the hallmarks of cancer. One of the most important traits acquired during cancer progression is angiogenesis. Tumor cells capable of secreting pro-angiogenic factors can be seen as cooperators where the improved oxygenation, nutrient delivery and waste disposal resulting from angiogenesis could be seen as a public good. Under this view, the relatively costly secretion of molecular signals required to orchestrate angiogenesis would be undertaken exclusively by cooperating tumor cells but the benefits of angiogenesis would be felt by neighboring tumor cells regardless of their contribution to the process. In this work we detail a mathematical model to better understand how clones capable of secreting pro-angiogenic factors can emerge in a tumor made of non-cooperative tumor cells. Given the importance of the spatial configuration of the tumor in determining the efficacy of the secretion of pro-angiogenic factors as well as the benefits of angiogenesis we have developed a spatial game theoretic approach where interactions and public good diffusion are described by graphs. The results show that structure of the population affects the evolutionary dynamics of the pro-angiogenic clone. Specifically, when the benefit of angiogenesis is represented by sigmoid function with regards to the number of pro-angiogenic clones then the probability of the coexistence of pro-angiogenic and angiogenesis-neutral clones increases. Our results demonstrate that pro-angiogenic clone equilibrates into clusters that appear from surrounding vascular tissues towards the center of tumor. These clusters appear notably less dense after anti-angiogenic therapy. [ABSTRACT FROM AUTHOR]

Myeloid-derived monocyte and macrophages are key cells in the bone that contribute to remodeling and injury repair. However, their temporal polarization status and control of bone-resorbing osteoclasts and bone-forming osteoblasts responses is largely unknown. In this study, we focused on two aspects of monocyte/macrophage dynamics and polarization states over time: 1) the injury-triggered pro- and anti-inflammatory monocytes/macrophages temporal profiles, 2) the contributions of pro- versus anti-inflammatory monocytes/macrophages in coordinating healing response. Bone healing is a complex multicellular dynamic process. While traditional in vitro and in vivo experimentation may capture the behavior of select populations with high resolution, they cannot simultaneously track the behavior of multiple populations. To address this, we have used an integrated coupled ordinary differential equations (ODEs)-based framework describing multiple cellular species to in vivo bone injury data in order to identify and test various hypotheses regarding bone cell populations dynamics. Our approach allowed us to infer several biological insights including, but not limited to,: 1) anti-inflammatory macrophages are key for early osteoclast inhibition and pro-inflammatory macrophage suppression, 2) pro-inflammatory macrophages are involved in osteoclast bone resorptive activity, whereas osteoblasts promote osteoclast differentiation, 3) Pro-inflammatory monocytes/macrophages rise during two expansion waves, which can be explained by the anti-inflammatory macrophages-mediated inhibition phase between the two waves. In addition, we further tested the robustness of the mathematical model by comparing simulation results to an independent experimental dataset. Taken together, this novel comprehensive mathematical framework allowed us to identify biological mechanisms that best recapitulate bone injury data and that explain the coupled cellular population dynamics involved in the process. Furthermore, our hypothesis testing methodology could be used in other contexts to decipher mechanisms in complex multicellular processes. Author summary: Myeloid-derived monocytes/macrophages are key cells for bone remodeling and injury repair. However, their temporal polarization status and control of bone-resorbing osteoclasts and bone-forming osteoblasts responses is largely unknown. In this study, we focused on two aspects of monocyte/macrophage population dynamics: 1) the injury-triggered pro- and anti-inflammatory monocytes/macrophages temporal profiles, 2) the contributions of pro- versus anti-inflammatory monocytes/macrophages in coordinating healing response. In order to test various hypotheses regarding bone cell populations dynamics, we have integrated a coupled ordinary differential equations-based framework describing multiple cellular species to in vivo bone injury data. Our approach allowed us to infer several biological insights including: 1) anti-inflammatory macrophages are key for early osteoclast inhibition and pro-inflammatory macrophage suppression, 2) pro-inflammatory macrophages are involved in osteoclast bone resorptive activity, whereas osteoblasts promote osteoclast differentiation, 3) Pro-inflammatory monocytes/macrophages rise during two expansion waves, which can be explained by the anti-inflammatory macrophages-mediated inhibition phase between the two waves. Taken together, this mathematical framework allowed us to identify biological mechanisms that recapitulate bone injury data and that explain the coupled cellular population dynamics involved in the process. [ABSTRACT FROM AUTHOR]

Background: Tumour hypoxia is associated with metastatic disease, and while there have been many mechanisms proposed for why tumour hypoxia is associated with metastatic disease, it remains unclear whether one precise mechanism is the key reason or several in concert. Somatic evolution drives cancer progression and treatment resistance, fuelled not only by genetic and epigenetic mutation but also by selection from interactions between tumour cells, normal cells and physical micro-environment. Ecological habitats influence evolutionary dynamics, but the impact on tempo of evolution is less clear.Methods: We explored this complex dialogue with a combined clinical-theoretical approach by simulating a proliferative hierarchy under heterogeneous oxygen availability with an agent-based model. Predictions were compared against histology samples taken from glioblastoma patients, stained to elucidate areas of necrosis and TP53 expression heterogeneity.Results: Results indicate that cell division in hypoxic environments is effectively upregulated, with low-oxygen niches providing avenues for tumour cells to spread. Analysis of human data indicates that cell division is not decreased under hypoxia, consistent with our results.Conclusions: Our results suggest that hypoxia could be a crucible that effectively warps evolutionary velocity, making key mutations more likely. Thus, key tumour ecological niches such as hypoxic regions may alter the evolutionary tempo, driving mutations fuelling tumour heterogeneity. [ABSTRACT FROM AUTHOR]

The Hybrid Automata Library (HAL) is a Java Library developed for use in mathematical oncology modeling. It is made of simple, efficient, generic components that can be used to model complex spatial systems. HAL's components can broadly be classified into: on- and off-lattice agent containers, finite difference diffusion fields, a GUI building system, and additional tools and utilities for computation and data collection. These components are designed to operate independently and are standardized to make them easy to interface with one another. As a demonstration of how modeling can be simplified using our approach, we have included a complete example of a hybrid model (a spatial model with interacting agent-based and PDE components). HAL is a useful asset for researchers who wish to build performant 1D, 2D and 3D hybrid models in Java, while not starting entirely from scratch. It is available on GitHub at https://github.com/MathOnco/HAL under the MIT License. HAL requires the Java JDK version 1.8 or later to compile and run the source code. Author summary: In this paper we introduce the Hybrid Automata Library (HAL) with the purpose of simplifying the implementation and sharing of hybrid models for use in mathematical oncology. Hybrid modeling is used in oncology to create spatial models of tissue, typically by modeling cells using agent-based techniques, and by modeling diffusible chemicals using partial differential equations (PDEs). HAL's key components are designed to run agent-based models, PDEs, and visualization. The components are standardized and are completely decoupled, so models can be built with any combination of them. We first explore the philosophy behind HAL, then summarize the components. Lastly we demonstrate how the components work together with an example of a hybrid model, and a walk-through of the code used to construct it. HAL is open-source and will produce identical results on any machine that supports Java 8 and above, making it highly portable. We recommend HAL to modelers interested in spatial dynamics, even those outside of mathematical oncology, as the components are general enough to facilitate a variety of model types. A community page that provides a download link and online documentation can be found at https://halloworld.org. [ABSTRACT FROM AUTHOR]

Background: Tumours are diverse ecosystems with persistent heterogeneity in various cancer hallmarks like self-sufficiency of growth factor production for angiogenesis and reprogramming of energy metabolism for aerobic glycolysis. This heterogeneity has consequences for diagnosis, treatment and disease progression.Methods: We introduce the double goods game to study the dynamics of these traits using evolutionary game theory. We model glycolytic acid production as a public good for all tumour cells and oxygen from vascularisation via vascular endothelial growth factor production as a club good benefiting non-glycolytic tumour cells. This results in three viable phenotypic strategies: glycolytic, angiogenic and aerobic non-angiogenic.Results: We classify the dynamics into three qualitatively distinct regimes: (1) fully glycolytic; (2) fully angiogenic; or (3) polyclonal in all three cell types. The third regime allows for dynamic heterogeneity even with linear goods, something that was not possible in prior public good models that considered glycolysis or growth factor production in isolation.Conclusions: The cyclic dynamics of the polyclonal regime stress the importance of timing for anti-glycolysis treatments like lonidamine. The existence of qualitatively different dynamic regimes highlights the order effects of treatments. In particular, we consider the potential of vascular normalisation as a neoadjuvant therapy before follow-up with interventions like buffer therapy. [ABSTRACT FROM AUTHOR]

Bone metastasis will impact most men with advanced prostate cancer. The vicious cycle of bone degradation and formation driven by metastatic prostate cells in bone yields factors that drive cancer growth. Mechanistic insights into this vicious cycle have suggested new therapeutic opportunities, but complex temporal and cellular interactions in the bone microenvironment make drug development challenging. We have integrated biologic and computational approaches to generate a hybrid cellular automata model of normal bone matrix homeostasis and the prostate cancer-bone microenvironment. The model accurately reproduces the basic multicellular unit bone coupling process, such that introduction of a single prostate cancer cell yields a vicious cycle similar in cellular composition and pathophysiology to models of prostate-to-bone metastasis. Notably, the model revealed distinct phases of osteolytic and osteogenic activity, a critical role for mesenchymal stromal cells in osteogenesis, and temporal changes in cellular composition. To evaluate the robustness of the model, we assessed the effect of established bisphosphonate and anti-RANKL therapies on bone metastases. At approximately 100% efficacy, bisphosphonates inhibited cancer progression while, in contrast with clinical observations in humans, anti-RANKL therapy fully eradicated metastases. Reducing anti-RANKL yielded clinically similar results, suggesting that better targeting or dosing could improve patient survival. Our work establishes a computational model that can be tailored for rapid assessment of experimental therapies and delivery of precision medicine to patients with prostate cancer with bone metastases. [ABSTRACT FROM AUTHOR]

Since the discovery of tumour initiating cells (TICs) in solid tumours, studies focussing on their role in cancer initiation and progression have abounded. The biological interrogation of these cells continues to yield volumes of information on their pro-tumourigenic behaviour, but actionable generalised conclusions have been scarce. Further, new information suggesting a dependence of tumour composition and growth on the microenvironment has yet to be studied theoretically. To address this point, we created a hybrid, discrete/continuous computational cellular automaton model of a generalised stem-cell driven tissue with a simple microenvironment. Using the model we explored the phenotypic traits inherent to the tumour initiating cells and the effect of the microenvironment on tissue growth. We identify the regions in phenotype parameter space where TICs are able to cause a disruption in homeostasis, leading to tissue overgrowth and tumour maintenance. As our parameters and model are non-specific, they could apply to any tissue TIC and do not assume specific genetic mutations. Targeting these phenotypic traits could represent a generalizable therapeutic strategy across cancer types. Further, we find that the microenvironmental variable does not strongly affect the outcomes, suggesting a need for direct feedback from the microenvironment onto stem-cell behaviour in future modelling endeavours. [ABSTRACT FROM AUTHOR]

Simple Summary: Using a first-principles approach, we demonstrate how standard-of-care therapies for bone metastatic prostate cancer (BMPCa) patients can be optimized with the use of routine measurements to significantly delay the evolution of resistant disease, potentially extending overall patient survival. Background: Bone metastatic prostate cancer (BMPCa), despite the initial responsiveness to androgen deprivation therapy (ADT), inevitably becomes resistant. Recent clinical trials with upfront treatment of ADT combined with chemotherapy or novel hormonal therapies (NHTs) have extended overall patient survival. These results indicate that there is significant potential for the optimization of standard-of-care therapies to delay the emergence of progressive metastatic disease. Methods: Here, we used data extracted from human bone metastatic biopsies pre- and post-abiraterone acetate/prednisone to generate a mathematical model of bone metastatic prostate cancer that can unravel the treatment impact on disease progression. Intra-tumor heterogeneity in regard to ADT and chemotherapy resistance was derived from biopsy data at a cellular level, permitting the model to track the dynamics of resistant phenotypes in response to treatment from biological first-principles without relying on data fitting. These cellular data were mathematically correlated with a clinical proxy for tumor burden, utilizing prostate-specific antigen (PSA) production as an example. Results: Using this correlation, our model recapitulated the individual patient response to applied treatments in a separate and independent cohort of patients (n = 24), and was able to estimate the initial resistance to the ADT of each patient. Combined with an intervention-decision algorithm informed by patient-specific prediction of initial resistance, we propose to optimize the sequence of treatments for each patient with the goal of delaying the evolution of resistant disease and limit cancer cell growth, offering evidence for an improvement against retrospective data. Conclusions: Our results show how minimal but widely available patient information can be used to model and track the progression of BMPCa in real time, offering a clinically relevant insight into the patient-specific evolutionary dynamics of the disease and suggesting new therapeutic options for intervention. Trial registration: NCT # 01953640. Funding: Funded by an NCI U01 (NCI) U01CA202958-01 and a Moffitt Team Science Award. CCL and DB were partly funded by an NCI PSON U01 (U01CA244101). AA was partly funded by a Department of Defense Prostate Cancer Research Program (W81XWH-15-1-0184) fellowship. LC was partly funded by a postdoctoral fellowship (PF-13-175-01-CSM) from the American Cancer Society. [ABSTRACT FROM AUTHOR]

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 doses 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. [ABSTRACT FROM AUTHOR]