Agent-based methods facilitate integrative science in cancer

Agent-based modeling in cancer biomedicine: applications and tools for calibration and validation

Computational models are not just appealing because they can simulate and predict the development of biological phenomena across multiple spatial and temporal scales, but also because they can integrate information from well-established in vitro and in vivo models and test new hypotheses in cancer biomedicine. Agent-based models and simulations are especially interesting candidates among computational modeling procedures in cancer research due to the capability to, for instance, recapitulate the dynamics of neoplasia and tumor - host interactions. Yet, the absence of methods to validate the consistency of the results across scales can hinder adoption by turning fine-tuned models into black boxes. This review compiles relevant literature that explores strategies to leverage high-fidelity simulations of multi-scale, or multi-level, cancer models with a focus on verification approached as simulation calibration. We consolidate our review with an outline of modern approaches for agent-based models' validation and provide an ambitious outlook toward rigorous and reliable calibration.

Bridging systems biology and tissue engineering: Unleashing the full potential of complex 3D in vitro tissue models of disease

Rapid advances in tissue engineering have resulted in more complex and physiologically relevant 3D in vitro tissue models with applications in fundamental biology and therapeutic development. However, the complexity provided by these models is often not leveraged fully due to the reductionist methods used to analyze them. Computational and mathematical models developed in the field of systems biology can address this issue. Yet, traditional systems biology has been mostly applied to simpler in vitro models with little physiological relevance and limited cellular complexity. Therefore, integrating these two inherently interdisciplinary fields can result in new insights and move both disciplines forward. In this review, we provide a systematic overview of how systems biology has been integrated with 3D in vitro tissue models and discuss key application areas where the synergies between both fields have led to important advances with potential translational impact. We then outline key directions for future research and discuss a framework for further integration between fields.

Surrogate modeling and control of medical digital twins

The vision of personalized medicine is to identify interventions that maintain or restore a person's health based on their individual biology. Medical digital twins, computational models that integrate a wide range of health-related data about a person and can be dynamically updated, are a key technology that can help guide medical decisions. Such medical digital twin models can be high-dimensional, multi-scale, and stochastic. To be practical for healthcare applications, they often need to be simplified into low-dimensional surrogate models that can be used for optimal design of interventions. This paper introduces surrogate modeling algorithms for the purpose of optimal control applications. As a use case, we focus on agent-based models (ABMs), a common model type in biomedicine for which there are no readily available optimal control algorithms. By deriving surrogate models that are based on systems of ordinary differential equations, we show how optimal control methods can be employed to compute effective interventions, which can then be lifted back to a given ABM. The relevance of the methods introduced here extends beyond medical digital twins to other complex dynamical systems.

Modeling tumors as species-rich ecological communities

Many advanced cancers resist therapeutic intervention. This process is fundamentally related to intra-tumor heterogeneity: multiple cell populations, each with different mutational and phenotypic signatures, coexist within a tumor and its metastatic nodes. Like species in an ecosystem, many cancer cell populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity nor are able to predict its consequences. Here we propose that the Generalized Lotka-Volterra model (GLV), a standard tool to describe complex, species-rich ecological communities, provides a suitable framework to describe the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties, such as outgrowth and multistability, provide a new understanding of the disease. Additionally, we discuss potential extensions of the model and their application to three active areas of cancer research, namely phenotypic plasticity, the cancer-immune interplay and the resistance of metastatic tumors to treatment. Our work outlines a set of questions and a tentative road map for further research in cancer ecology.

Control of Medical Digital Twins with Artificial Neural Networks

The objective of personalized medicine is to tailor interventions to an individual patient's unique characteristics. A key technology for this purpose involves medical digital twins, computational models of human biology that can be personalized and dynamically updated to incorporate patient-specific data collected over time. Certain aspects of human biology, such as the immune system, are not easily captured with physics-based models, such as differential equations. Instead, they are often multi-scale, stochastic, and hybrid. This poses a challenge to existing model-based control and optimization approaches that cannot be readily applied to such models. Recent advances in automatic differentiation and neural-network control methods hold promise in addressing complex control problems. However, the application of these approaches to biomedical systems is still in its early stages. This work introduces dynamics-informed neural-network controllers as an alternative approach to control of medical digital twins. As a first use case for this method, the focus is on agent-based models, a versatile and increasingly common modeling platform in biomedicine. The effectiveness of the proposed neural-network control method is illustrated and benchmarked against other methods with two widely-used agent-based model types. The relevance of the method introduced here extends beyond medical digital twins to other complex dynamical systems.

Incorporating temporal information during feature engineering bolsters emulation of spatio-temporal emergence

MOTIVATION

Emergent biological dynamics derive from the evolution of lower-level spatial and temporal processes. A long-standing challenge for scientists and engineers is identifying simple low-level rules that give rise to complex higher-level dynamics. High-resolution biological data acquisition enables this identification and has evolved at a rapid pace for both experimental and computational approaches. Simultaneously harnessing the resolution and managing the expense of emerging technologies-e.g. live cell imaging, scRNAseq, agent-based models-requires a deeper understanding of how spatial and temporal axes impact biological systems. Effective emulation is a promising solution to manage the expense of increasingly complex high-resolution computational models. In this research, we focus on the emulation of a tumor microenvironment agent-based model to examine the relationship between spatial and temporal environment features, and emergent tumor properties.

RESULTS

Despite significant feature engineering, we find limited predictive capacity of tumor properties from initial system representations. However, incorporating temporal information derived from intermediate simulation states dramatically improves the predictive performance of machine learning models. We train a deep-learning emulator on intermediate simulation states and observe promising enhancements over emulators trained solely on initial conditions. Our results underscore the importance of incorporating temporal information in the evaluation of spatio-temporal emergent behavior. Nevertheless, the emulators exhibit inconsistent performance, suggesting that the underlying model characterizes unique cell populations dynamics that are not easily replaced.

AVAILABILITY AND IMPLEMENTATION

All source codes for the agent-based model, emulation, and analyses are publicly available at the corresponding DOIs: 10.5281/zenodo.10622155, 10.5281/zenodo.10611675, 10.5281/zenodo.10621244, respectively.

Agent-based modeling of the prostate tumor microenvironment uncovers spatial tumor growth constraints and immunomodulatory properties

Inhibiting androgen receptor (AR) signaling through androgen deprivation therapy (ADT) reduces prostate cancer (PCa) growth in virtually all patients, but response may be temporary, in which case resistance develops, ultimately leading to lethal castration-resistant prostate cancer (CRPC). The tumor microenvironment (TME) plays an important role in the development and progression of PCa. In addition to tumor cells, TME-resident macrophages and fibroblasts express AR and are therefore also affected by ADT. However, the interplay of different TME cell types in the development of CRPC remains largely unexplored. To understand the complex stochastic nature of cell-cell interactions, we created a PCa-specific agent-based model (PCABM) based on in vitro cell proliferation data. PCa cells, fibroblasts, "pro-inflammatory" M1-like and "pro-tumor" M2-like polarized macrophages are modeled as agents from a simple set of validated base assumptions. PCABM allows us to simulate the effect of ADT on the interplay between various prostate TME cell types. The resulting in vitro growth patterns mimic human PCa. Our PCABM can effectively model hormonal perturbations by ADT, in which PCABM suggests that CRPC arises in clusters of resistant cells, as is observed in multifocal PCa. In addition, fibroblasts compete for cellular space in the TME while simultaneously creating niches for tumor cells to proliferate in. Finally, PCABM predicts that ADT has immunomodulatory effects on macrophages that may enhance tumor survival. Taken together, these results suggest that AR plays a critical role in the cellular interplay and stochastic interactions in the TME that influence tumor cell behavior and CRPC development.

Tumor-immune metaphenotypes orchestrate an evolutionary bottleneck that promotes metabolic transformation

Introduction

Metabolism plays a complex role in the evolution of cancerous tumors, including inducing a multifaceted effect on the immune system to aid immune escape. Immune escape is, by definition, a collective phenomenon by requiring the presence of two cell types interacting in close proximity: tumor and immune. The microenvironmental context of these interactions is influenced by the dynamic process of blood vessel growth and remodelling, creating heterogeneous patches of well-vascularized tumor or acidic niches.

Methods

Here, we present a multiscale mathematical model that captures the phenotypic, vascular, microenvironmental, and spatial heterogeneity which shapes acid-mediated invasion and immune escape over a biologically-realistic time scale. The model explores several immune escape mechanisms such as i) acid inactivation of immune cells, ii) competition for glucose, and iii) inhibitory immune checkpoint receptor expression (PD-L1). We also explore the efficacy of anti-PD-L1 and sodium bicarbonate buffer agents for treatment. To aid in understanding immune escape as a collective cellular phenomenon, we define immune escape in the context of six collective phenotypes (termed "meta-phenotypes"): Self-Acidify, Mooch Acid, PD-L1 Attack, Mooch PD-L1, Proliferate Fast, and Starve Glucose.

Results

Fomenting a stronger immune response leads to initial benefits (additional cytotoxicity), but this advantage is offset by increased cell turnover that leads to accelerated evolution and the emergence of aggressive phenotypes. This creates a bimodal therapy landscape: either the immune system should be maximized for complete cure, or kept in check to avoid rapid evolution of invasive cells. These constraints are dependent on heterogeneity in vascular context, microenvironmental acidification, and the strength of immune response.

Discussion

This model helps to untangle the key constraints on evolutionary costs and benefits of three key phenotypic axes on tumor invasion and treatment: acid-resistance, glycolysis, and PD-L1 expression. The benefits of concomitant anti-PD-L1 and buffer treatments is a promising treatment strategy to limit the adverse effects of immune escape.

Use of Individual-Based Mathematical Modelling to Understand More About Antibiotic Resistance Within-Host

To model complex systems, individual-based models (IBMs), sometimes called "agent-based models" (ABMs), describe a simplification of the system through an adequate representation of the elements. IBMs simulate the actions and interaction of discrete individuals/agents within a system in order to discover the pattern of behavior that comes from these interactions. Examples of individuals/agents in biological systems are individual immune cells and bacteria that act independently with their own unique attributes defined by behavioral rules. In IBMs, each of these agents resides in a spatial environment and interactions are guided by predefined rules. These rules are often simple and can be easily implemented. It is expected that following the interaction guided by these rules we will have a better understanding of agent-agent interaction as well as agent-environment interaction. Stochasticity described by probability distributions must be accounted for. Events that seldom occur such as the accumulation of rare mutations can be easily modeled.Thus, IBMs are able to track the behavior of each individual/agent within the model while also obtaining information on the results of their collective behaviors. The influence of impact of one agent with another can be captured, thus allowing a full representation of both direct and indirect causation on the aggregate results. This means that important new insights can be gained and hypotheses tested.

Connecting Agent-Based Models with High-Dimensional Parameter Spaces to Multidimensional Data Using SMoRe ParS: A Surrogate Modeling Approach

Across a broad range of disciplines, agent-based models (ABMs) are increasingly utilized for replicating, predicting, and understanding complex systems and their emergent behavior. In the biological and biomedical sciences, researchers employ ABMs to elucidate complex cellular and molecular interactions across multiple scales under varying conditions. Data generated at these multiple scales, however, presents a computational challenge for robust analysis with ABMs. Indeed, calibrating ABMs remains an open topic of research due to their own high-dimensional parameter spaces. In response to these challenges, we extend and validate our novel methodology, Surrogate Modeling for Reconstructing Parameter Surfaces (SMoRe ParS), arriving at a computationally efficient framework for connecting high dimensional ABM parameter spaces with multidimensional data. Specifically, we modify SMoRe ParS to initially confine high dimensional ABM parameter spaces using unidimensional data, namely, single time-course information of in vitro cancer cell growth assays. Subsequently, we broaden the scope of our approach to encompass more complex ABMs and constrain parameter spaces using multidimensional data. We explore this extension with in vitro cancer cell inhibition assays involving the chemotherapeutic agent oxaliplatin. For each scenario, we validate and evaluate the effectiveness of our approach by comparing how well ABM simulations match the experimental data when using SMoRe ParS-inferred parameters versus parameters inferred by a commonly used direct method. In so doing, we show that our approach of using an explicitly formulated surrogate model as an interlocutor between the ABM and the experimental data effectively calibrates the ABM parameter space to multidimensional data. Our method thus provides a robust and scalable strategy for leveraging multidimensional data to inform multiscale ABMs and explore the uncertainty in their parameters.

Mutation divergence over space in tumour expansion

Mutation accumulation in tumour evolution is one major cause of intra-tumour heterogeneity (ITH), which often leads to drug resistance during treatment. Previous studies with multi-region sequencing have shown that mutation divergence among samples within the patient is common, and the importance of spatial sampling to obtain a complete picture in tumour measurements. However, quantitative comparisons of the relationship between mutation heterogeneity and tumour expansion modes, sampling distances as well as the sampling methods are still few. Here, we investigate how mutations diverge over space by varying the sampling distance and tumour expansion modes using individual-based simulations. We measure ITH by the Jaccard index between samples and quantify how ITH increases with sampling distance, the pattern of which holds in various sampling methods and sizes. We also compare the inferred mutation rates based on the distributions of variant allele frequencies under different tumour expansion modes and sampling sizes. In exponentially fast expanding tumours, a mutation rate can always be inferred for any sampling size. However, the accuracy compared with the true value decreases when the sampling size decreases, where small sampling sizes result in a high estimate of the mutation rate. In addition, such an inference becomes unreliable when the tumour expansion is slow, such as in surface growth.

Exploring the Onset and Progression of Prostate Cancer through a Multicellular Agent-based Model

Over 10% of men will be diagnosed with prostate cancer during their lifetime. Arising from luminal cells of the prostatic acinus, prostate cancer is influenced by multiple cells in its microenvironment. To expand our knowledge and explore means to prevent and treat the disease, it is important to understand what drives the onset and early stages of prostate cancer. In this study, we developed an agent-based model of a prostatic acinus including its microenvironment, to allow for in silico studying of prostate cancer development. The model was based on prior reports and in-house data of tumor cells cocultured with cancer-associated fibroblasts (CAF) and protumor and/or antitumor macrophages. Growth patterns depicted by the model were pathologically validated on hematoxylin and eosin slide images of human prostate cancer specimens. We identified that stochasticity of interactions between macrophages and tumor cells at early stages strongly affect tumor development. In addition, we discovered that more systematic deviations in tumor development result from a combinatorial effect of the probability of acquiring mutations and the tumor-promoting abilities of CAFs and macrophages. In silico modeled tumors were then compared with 494 patients with cancer with matching characteristics, showing strong association between predicted tumor load and patients' clinical outcome. Our findings suggest that the likelihood of tumor formation depends on a combination of stochastic events and systematic characteristics. While stochasticity cannot be controlled, information on systematic effects may aid the development of prevention strategies tailored to the molecular characteristics of an individual patient.

Significance

We developed a computational model to study which factors of the tumor microenvironment drive prostate cancer development, with potential to aid the development of new prevention strategies.

Modelling the Tumour Microenvironment, but What Exactly Do We Mean by "Model"?

The Oxford English Dictionary includes 17 definitions for the word "model" as a noun and another 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For instance, "model railways" refer to replicas of railways and trains at a smaller scale and a "model student" refers to an exemplary individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning for model. Even if the context is narrowed, specifically, to research related to the tumour microenvironment, "model" can be understood in a wide variety of ways, from an animal model to a mathematical expression. This paper presents a review of different "models" of the tumour microenvironment, as grouped by different definitions of the word into four categories: model organisms, in vitro models, mathematical models and computational models. Then, the frequencies of different meanings of the word "model" related to the tumour microenvironment are measured from numbers of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequencies of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, particularly xenografts and mouse models, are the most commonly used "models", the number of these entries has been slowly decreasing. Mathematical models, as well as prognostic and risk models, follow in frequency, and these have been growing in use.

Could Mathematics be the Key to Unlocking the Mysteries of Multiple Sclerosis?

Multiple sclerosis (MS) is an autoimmune, neurodegenerative disease that is driven by immune system-mediated demyelination of nerve axons. While diseases such as cancer, HIV, malaria and even COVID have realised notable benefits from the attention of the mathematical community, MS has received significantly less attention despite the increasing disease incidence rates, lack of curative treatment, and long-term impact on patient well-being. In this review, we highlight existing, MS-specific mathematical research and discuss the outstanding challenges and open problems that remain for mathematicians. We focus on how both non-spatial and spatial deterministic models have been used to successfully further our understanding of T cell responses and treatment in MS. We also review how agent-based models and other stochastic modelling techniques have begun to shed light on the highly stochastic and oscillatory nature of this disease. Reviewing the current mathematical work in MS, alongside the biology specific to MS immunology, it is clear that mathematical research dedicated to understanding immunotherapies in cancer or the immune responses to viral infections could be readily translatable to MS and might hold the key to unlocking some of its mysteries.

Quantifying Intratumoral Heterogeneity and Immunoarchitecture Generated In-Silico by a Spatial Quantitative Systems Pharmacology Model

Spatial heterogeneity is a hallmark of cancer. Tumor heterogeneity can vary with time and location. The tumor microenvironment (TME) encompasses various cell types and their interactions that impart response to therapies. Therefore, a quantitative evaluation of tumor heterogeneity is crucial for the development of effective treatments. Different approaches, such as multiregional sequencing, spatial transcriptomics, analysis of autopsy samples, and longitudinal analysis of biopsy samples, can be used to analyze the intratumoral heterogeneity (ITH) and temporal evolution and to reveal the mechanisms of therapeutic response. However, because of the limitations of these data and the uncertainty associated with the time points of sample collection, having a complete understanding of intratumoral heterogeneity role is challenging. Here, we used a hybrid model that integrates a whole-patient compartmental quantitative-systems-pharmacology (QSP) model with a spatial agent-based model (ABM) describing the TME; we applied four spatial metrics to quantify model-simulated intratumoral heterogeneity and classified the TME immunoarchitecture for representative cases of effective and ineffective anti-PD-1 therapy. The four metrics, adopted from computational digital pathology, included mixing score, average neighbor frequency, Shannon's entropy and area under the curve (AUC) of the G-cross function. A fifth non-spatial metric was used to supplement the analysis, which was the ratio of the number of cancer cells to immune cells. These metrics were utilized to classify the TME as "cold", "compartmentalized" and "mixed", which were related to treatment efficacy. The trends in these metrics for effective and ineffective treatments are in qualitative agreement with the clinical literature, indicating that compartmentalized immunoarchitecture is likely to result in more efficacious treatment outcomes.