PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems

Cell populations simulated in silico within SimulCell accurately reproduce the behaviour of experimental cell cultures

In silico simulations are used to understand cell behaviour by means of different approaches and tools, which range from reproducing average population trends to building lattice-based models to, more recently, creating populations of individual cell agents whose mass, volume and morphology behave according to more or less precise rules and models. In this work, a new agent-based simulator, SimulCell, was conceived, developed and used to predict the behaviour of eukaryotic cell cultures while growing attached to a flat surface. The system, starting from time-lapse microscopy experiments, uses growth, proliferation and migration models to create synthetic populations closely resembling original cultures. Support for cell-cell and cell-environment interaction makes cell agents able to react to changes in medium composition and other events, such as physical damage or chemical modifications occurring in the culture plate. The simulator is accessible through a web application and generates data that can be shown as tables and graphs or exported for further analyses.

Using mathematical modelling and AI to improve delivery and efficacy of therapies in cancer

Mathematical modelling has proven to be a valuable tool in predicting the delivery and efficacy of molecular, antibody-based, nano and cellular therapy in solid tumours. Mathematical models based on our understanding of the biological processes at subcellular, cellular and tissue level are known as mechanistic models that, in turn, are divided into continuous and discrete models. Continuous models are further divided into lumped parameter models - for describing the temporal distribution of medicine in tumours and normal organs - and distributed parameter models - for studying the spatiotemporal distribution of therapy in tumours. Discrete models capture interactions at the cellular and subcellular levels. Collectively, these models are useful for optimizing the delivery and efficacy of molecular, nanoscale and cellular therapy in tumours by incorporating the biological characteristics of tumours, the physicochemical properties of drugs, the interactions among drugs, cancer cells and various components of the tumour microenvironment, and for enabling patient-specific predictions when combined with medical imaging. Artificial intelligence-based methods, such as machine learning, have ushered in a new era in oncology. These data-driven approaches complement mechanistic models and have immense potential for improving cancer detection, treatment and drug discovery. Here we review these diverse approaches and suggest ways to combine mechanistic and artificial intelligence-based models to further improve patient treatment outcomes.

Towards an integrated view and understanding of embryonic signalling during murine gastrulation

At the onset of mammalian gastrulation, secreted signalling molecules belonging to the Bmp, Wnt, Nodal and Fgf signalling pathways induce and pattern the primitive streak, marking the start for the cellular rearrangements that generate the body plan. Our current understanding of how signalling specifies and organises the germ layers in three dimensions, was mainly derived from genetic experimentation using mouse embryos performed over many decades. However, the exact spatiotemporal sequence of events is still poorly understood, both because of a lack of tractable models that allow for real time visualisation of signalling and differentiation and because of the molecular and cellular complexity of these early developmental events. In recent years, a new wave of in vitro embryo models has begun to shed light on the dynamics of signalling during primitive streak formation. Here we discuss the similarities and differences between a widely adopted mouse embryo model, termed gastruloids, and real embryos from a signalling perspective. We focus on the gene regulatory networks that underlie signalling pathway interactions and outline some of the challenges ahead. Finally, we provide a perspective on how embryo models may be used to advance our understanding of signalling dynamics through computational modelling.

Exploring the role of EMT in ovarian cancer progression using a multiscale mathematical model

Epithelial-to-mesenchymal transition (EMT) plays a key role in the progression of cancer tumours, significantly reducing the success of treatment. EMT occurs when a cell undergoes phenotypical changes, resulting in enhanced drug resistance, higher cell plasticity, and increased metastatic abilities. Here, we employ a 3D agent-based multiscale modelling framework using PhysiCell to explore the role of EMT over time in two cell lines, OVCAR-3 and SKOV-3. This approach allows us to investigate the spatiotemporal progression of ovarian cancer and the impacts of the conditions in the microenvironment. OVCAR-3 and SKOV-3 cell lines possess highly contrasting tumour layouts, allowing a wide range of different tumour dynamics and morphologies to be tested and studied. Along with performing sensitivity analysis on the model, simulation results capture the biological observations and trends seen in tumour growth and development, thus helping to obtain further insights into OVCAR-3 and SKOV-3 cell line dynamics.

A hybrid computational model of cancer spheroid growth with ribose-induced collagen stiffening

Metastasis, the leading cause of death in cancer patients, arises when cancer cells disseminate from a primary solid tumour to distant organs. Growth and invasion of the solid tumour often involve collective cell migration, which is profoundly influenced by cell-cell interactions and the extracellular matrix (ECM). The ECM's biochemical composition and mechanical properties, such as stiffness, regulate cancer cell behaviour and migration dynamics. Mathematical modelling serves as a pivotal tool for studying and predicting these complex dynamics, with hybrid discrete-continuous models offering a powerful approach by combining agent-based representations of cells with continuum descriptions of the surrounding microenvironment. In this study, we investigate the impact of ECM stiffness, modulated via ribose-induced collagen cross-linking, on cancer spheroid growth and invasion. We employed a hybrid discrete-continuous model implemented in PhysiCell to simulate spheroid dynamics, successfully replicating three-dimensional in vitro experiments. The model incorporates detailed representations of cell-cell and cell-ECM interactions, ECM remodelling, and cell proliferation. Our simulations align with experimental observations of two breast cancer cell lines, non-invasive MCF7 and invasive HCC 1954, under varying ECM stiffness conditions. The results demonstrate that increased ECM stiffness due to ribose-induced cross-linking inhibits spheroid invasion in invasive cells, whereas non-invasive cells remain largely unaffected. Furthermore, our simulations show that higher ECM degradation by the cells not only enables spheroid growth and invasion but also facilitates the formation of multicellular protrusions. Conversely, increasing the maximum speed that cells can reach due to cell-ECM interactions enhances spheroid growth while promoting single-cell invasion. This hybrid modelling approach enhances our understanding of the interplay between cancer cell migration, proliferation, and ECM mechanical properties, paving the way for future studies incorporating additional ECM characteristics and microenvironmental conditions.

Mathematical modeling of impacts of patient differences on renin-angiotensin system and applications to COVID-19 lung fibrosis outcomes

Patient-specific premorbidity, age, and sex are significant heterogeneous factors that influence the severe manifestation of lung diseases, including COVID-19 fibrosis. The renin-angiotensin system (RAS) plays a prominent role in regulating the effects of these factors. Recent evidence shows patient-specific alterations of RAS peptide homeostasis concentrations with premorbidity and the expression level of angiotensin-converting enzyme 2 (ACE2) during COVID-19. However, conflicting evidence suggests decreases, increases, or no changes in RAS peptides after SARS-CoV-2 infection. A multiscale computational model was developed to quantify the systemic contribution of heterogeneous factors of RAS during COVID-19. Three submodels were connected-an agent-based model for in-host COVID-19 response in the lung tissue, a RAS dynamics model, and a fibrosis dynamics model to investigate the effects of patient-group-specific factors in the systemic alteration of RAS and collagen deposition in the lung. The model results indicated cell death due to inflammatory response as a major contributor to the reduction of ACE and ACE2. The model explained possible mechanisms for conflicting evidence of patient-group-specific changes in RAS peptides in previously published studies. RAS peptides decreased for all virtual patient groups with aging in both sexes. In contrast, large variations in the magnitude of reduction were observed between male and female virtual patients in the older and middle-aged groups. The patient-specific variations in homeostasis RAS peptide concentrations of SARS-CoV-2-negative patients affected the dynamics of RAS during infection. This model may find further applications in patient-specific calibrations of tissue models for acute and chronic lung diseases to develop personalized treatments.

Validating the predictions of mathematical models describing tumor growth and treatment response

Despite advances in methods to interrogate tumor biology, the observational and population-based approach of classical cancer research and clinical oncology does not enable anticipation of tumor outcomes to hasten the discovery of cancer mechanisms and personalize disease management. To address these limitations, individualized cancer forecasts have been shown to predict tumor growth and therapeutic response, inform treatment optimization, and guide experimental efforts. These predictions are obtained via computer simulations of mathematical models that are constrained with data from a patient's cancer and experiments. This book chapter addresses the validation of these mathematical models to forecast tumor growth and treatment response. We start with an overview of mathematical modeling frameworks, model selection techniques, and fundamental metrics. We then describe the usual strategies employed to validate cancer forecasts in preclinical and clinical scenarios. Finally, we discuss existing barriers in validating these predictions along with potential strategies to address them.

A Simple Framework for Agent-Based Modeling with Extracellular Matrix

Extracellular matrix (ECM) is a key component of the cellular microenvironment and critical in multiple disease and developmental processes. Representing ECM and cell-ECM interactions is a challenging multiscale problem as they span molecular-level details to tissue-level dynamics. While several computational frameworks exist for ECM modeling, they often focus on very detailed modeling of individual ECM fibers or represent only a single aspect of the ECM. Using the PhysiCell agent-based modeling platform, we developed a framework of intermediate detail with the ability to capture bidirectional cell-ECM interactions. We represent a small region of ECM, an ECM element, with three variables describing its local microstructure: anisotropy, density, and overall fiber orientation. To spatially model the ECM, we use an array of ECM elements. Cells remodel local ECM microstructure and in turn, local microstructure impacts cellular motility. We demonstrate the utility of this framework and reusability of its core cell-ECM interaction model through examples in cellular invasion, wound healing, basement membrane degradation, and leader-follower collective migration. Despite the relative simplicity of the framework, it is able to capture a broad range of cell-ECM interactions of interest to the modeling community. Furthermore, variables representing the ECM microstructure are accessible through simple programming interfaces. This allows them to impact cell behaviors, such as proliferation and death, without requiring custom code for each interaction, particularly through PhysiCell's modeling grammar, enabling rapid modeling of a diverse range of cell-matrix biology. We make this framework available as a free and open source software package at https://github.com/PhysiCell-Models/collective-invasion .

Numerical modeling of oxygen diffusion in tissue spheroids undergoing fusion using function representation and finite volumes

A three-dimensional cell culture called a spheroid serves as a foundational entity in a wide variety of modern tissue engineering applications, including 3D-bioprinting and preclinical drug testing. Lack of oxygen within tissue spheroids hinders metabolism of cells and eventually leads to cell death. Prevention of necrosis is crucial to success of tissue engineering methods and such prevention requires estimation of cell viability in the spheroid. We propose a novel approach for numerical modeling of diffusion in tissue spheroids during their fusion. The approach is based on numerical solutions of partial differential equations and the application of Function Representation (FRep) framework for geometric modeling. We present modeling of oxygen diffusion based on meshes derived from the geometry of fusing spheroids, a method for selecting optimal spheroid size, and several statistics for estimating cellular viability. Our findings provide insights into oxygen diffusion in three-dimensional cell cultures thus improving the robustness of biotechnological methods that employ tissue spheroids.

Correction: Microglia are essential for tissue contraction in wound closure after brain injury in zebrafish larvae

Although in humans, the brain fails to heal after an injury, young zebrafish are able to restore tissue structural integrity in less than 24 h, thanks to the mechanical action of microglia.

Deficient cell-cell cohesion is linked with lobular localization in simplified models of lobular carcinoma in situ (LCIS)

Lobular carcinoma in situ (LCIS) is a precursor of invasive lobular carcinoma of the breast. LCIS cells lack cell-cell cohesion due to the loss of E-cadherin. LCIS cells grow in mammary lobules rather than in ducts. The etiology of this pattern, especially its dependence on cellular cohesion, is incompletely understood. We simulated passive intra-glandular scattering of carcinoma in situ (CIS) cells in an ultra-simplified hollow mold tissue replica (HMTR) and a discrete-time mathematical model featuring particles of variable sizes representing single cells (LCIS-like particles) or groups of cohesive carcinoma cells (DCIS-like particles). The HMTR features structures reminiscent of a mammary duct with associated lobules. The discrete mathematical model characterizes spatial redistribution over time and includes transition probabilities between ductal or lobular localizations. Redistribution of particles converged toward an equilibrium depending on particle size. Strikingly, equilibrium proportions depended on particle properties, which we also confirm in a continuous-time mathematical model that considers controlling lobular properties such as crowding. Particles of increasing size, representing CIS cells with proficient cohesion, showed increasingly higher equilibrium ductal proportions. Our investigations represent two conceptual abstractions implying a link between loss of cell-cell cohesion and lobular localization of LCIS, which provide a much-needed logical foundation for studying the connections between collective cell behavior and cancer development in breast tissues. In light of the findings from our simplified modeling approach, we discuss multiple avenues for near-future research that can address and evaluate the redistribution hypothesis mathematically and empirically.

A multiphysics hybrid continuum - agent-based model of in vitro vascularized organoids

BACKGROUND

Organoids are 3D in vitro models that fulfill a hierarchical function, representing a small version of living tissues and, therefore, a good approximation of cellular mechanisms. However, one of the main disadvantages of these models is the appearance of a necrotic core due to poor vascularization. The aim of this work is the development of a numerical framework that incorporates the mechanical stimulation as a key factor in organoid vascularization. Parameters, such as fluid velocity and nutrient consumption, are analyzed along the organoid evolution.

METHODS

The mathematical model created for this purpose combines continuum and discrete approaches. In the continuum part, the fluid flow and the diffusion of oxygen and nutrients are modeled using a finite element method approach. Meanwhile, the growth of the organoid, blood vessel evolution, as well as their interaction with the surrounding environment, are modeled using agent-based methods.

RESULTS

Continuum model outcomes include the distribution of shear stress, pressure and fluid velocity around the organoid surface, in addition to the concentration of oxygen and nutrients in its interior. The agent models account for cell proliferation, differentiation, organoid growth and blood vessel morphology, for the different case studies considered.

CONCLUSIONS

Two main conclusions are achieved in this work: (i) the results of the study quantitatively predict in vitro data, with an enhanced blood vessel invasion under high fluid flow and (ii) the diffusion and consumption model parameters of the organoid cells determine the thickness of the proliferative, quiescent, hypoxic and necrotic layers.

In silico modelling of organ-on-a-chip devices: an overview

An organ-on-a-chip (OOAC) is a microscale device designed to mimic the functions and complexity of in vivo human physiology. Different from traditional culture systems, OOACs are capable of replicating the biochemical microenvironment, tissue-tissue interactions, and mechanical dynamics of organs thanks to the precise control offered by microfluidic technology. Diverse OOAC devices specific to different organs have been proposed for experimental research and applications such as disease modelling, personalized medicine and drug screening. Previous studies have demonstrated that the mathematical modelling of OOAC can facilitate the optimization of chips' microenvironments, serving as an essential tool to design and improve microdevices which allow reproducible growth of cell culture, reducing the time and cost of experimental testing. Here, we review recent modelling approaches for various OOAC devices, categorized according to the type of organs. We discuss the opportunities for integrating multiphysics with multicellular computational models to better characterize and predict cell culture dynamics. Additionally, we explore how developing more detailed OOAC models would support a more rapid and effective development of microdevices, and the design of robust protocols to grow and control cell cultures.

Modelling the Impact of HIF on Metabolism and the Extracellular Matrix: Consequences for Tumour Growth and Invasion

The extracellular matrix (ECM) is a complex structure involved in many biological processes with collagen being the most abundant protein. Density of collagen fibers in the matrix is a factor influencing cell motility and migration speed. In cancer, this affects the ability of cells to migrate and invade distant tissues which is relevant for designing new therapies. Furthermore, increased cancer cell migration and invasion have been observed in hypoxic conditions. Interestingly, it has been revealed that the Hypoxia Inducible Factor (HIF) can not only impact the levels of metabolic genes but several collagen remodeling genes as well. The goal of this paper is to explore the impact of the HIF protein on both the tumour metabolism and the cancer cell migration with a focus on the Warburg effect and collagen remodelling processes. Therefore, we present an agent-based model (ABM) of tumour growth combining genetic regulations with metabolic and collagen-related processes involved in HIF pathways. Cancer cell migration is influenced by the extra-cellular collagen through a biphasic response dependant on collagen density. Results of the model showed that extra-cellular collagen within the tumour was mainly influenced by the local cellular density while collagen also influenced the shape of the tumour. In our simulations, proliferation was reduced with higher extra-cellular collagen levels or with lower oxygen levels but reached a maximum in the absence of cell-cell adhesion. Interestingly, combining lower levels of oxygen with higher levels of collagen further reduced the proliferation of the tumour. Since HIF impacts the metabolism and may affect the appearance of the Warburg Effect, we investigated whether different collagen conditions could lead to the adoption of the Warburg phenotype. We found that this was not the case, results suggested that adoption of the Warburg phenotype seemed mainly controlled by inhibition of oxidative metabolism by HIF combined with oscillations of oxygen.

Improving neuroendocrine tumor treatments with mathematical modeling: lessons from other endocrine cancers

Neuroendocrine tumors (NETs) occur sporadically or as part of rare endocrine tumor syndromes (RETSs) such as multiple endocrine neoplasia 1 and von Hippel-Lindau syndromes. Due to their relative rarity and lack of model systems, NETs and RETSs are difficult to study, hindering advancements in therapeutic development. Causal or mechanistic mathematical modeling is widely deployed in disease areas such as breast and prostate cancers, aiding the understanding of observations and streamlining in vitro and in vivo modeling efforts. Mathematical modeling, while not yet widely utilized in NET research, offers an opportunity to accelerate NET research and therapy development. To illustrate this, we highlight examples of how mathematical modeling associated with more common endocrine cancers has been successfully used in the preclinical, translational and clinical settings. We also provide a scope of the limited work that has been done in NETs and map how these techniques can be utilized in NET research to address specific outstanding challenges in the field. Finally, we include practical details such as hardware and data requirements, present advantages and disadvantages of various mathematical modeling approaches and discuss challenges of using mathematical modeling. Through a cross-disciplinary approach, we believe that many currently difficult problems can be made more tractable by applying mathematical modeling and that the field of rare diseases in endocrine oncology is well poised to take advantage of these techniques.

Microglia are essential for tissue contraction in wound closure after brain injury in zebrafish larvae

Wound closure after brain injury is crucial for tissue restoration but remains poorly understood at the tissue level. We investigated this process using in vivo observations of larval zebrafish brain injury. Our findings show that wound closure occurs within the first 24 h through global tissue contraction, as evidenced by live-imaging and drug inhibition studies. Microglia accumulate at the wound site before closure, and computational models suggest that their physical traction could drive this process. Depleting microglia genetically or pharmacologically impairs tissue repair. At the cellular level, live imaging reveals centripetal deformation of astrocytic processes contacted by migrating microglia. Laser severing of these contacts causes rapid retraction of microglial processes and slower retraction of astrocytic processes, indicating tension. Disrupting the lcp1 gene, which encodes the F-actin-stabilising protein L-plastin, in microglia results in failed wound closure. These findings support a mechanical role of microglia in wound contraction and suggest that targeting microglial mechanics could offer new strategies for treating traumatic brain injury.

Optimal control of agent-based models via surrogate modeling

This paper describes and validates an algorithm to solve optimal control problems for agent-based models (ABMs). For a given ABM and a given optimal control problem, the algorithm derives a surrogate model, typically lower-dimensional, in the form of a system of ordinary differential equations (ODEs), solves the control problem for the surrogate model, and then transfers the solution back to the original ABM. It applies to quite general ABMs and offers several options for the ODE structure, depending on what information about the ABM is to be used. There is a broad range of applications for such an algorithm, since ABMs are used widely in the life sciences, such as ecology, epidemiology, and biomedicine and healthcare, areas where optimal control is an important purpose for modeling, such as for medical digital twin technology.

A multiscale model of immune surveillance in micrometastases gives insights on cancer patient digital twins

Metastasis is the leading cause of death in patients with cancer, driving considerable scientific and clinical interest in immunosurveillance of micrometastases. We investigated this process by creating a multiscale mathematical model to study the interactions between the immune system and the progression of micrometastases in general epithelial tissue. We analyzed the parameter space of the model using high-throughput computing resources to generate over 100,000 virtual patient trajectories. We demonstrated that the model could recapitulate a wide variety of virtual patient trajectories, including uncontrolled growth, partial response, and complete immune response to tumor growth. We classified the virtual patients and identified key patient parameters with the greatest effect on the simulated immunosurveillance. We highlight the lessons derived from this analysis and their impact on the nascent field of cancer patient digital twins (CPDTs). While CPDTs could enable clinicians to systematically dissect the complexity of cancer in each individual patient and inform treatment choices, our work shows that key challenges remain before we can reach this vision. In particular, we show that there remain considerable uncertainties in immune responses, unreliable patient stratification, and unpredictable personalized treatment. Nonetheless, we also show that in spite of these challenges, patient-specific models suggest strategies to increase control of clinically undetectable micrometastases even without complete parameter certainty.

A Multicellular Mechanochemical Model to Investigate Tumor Microenvironment Remodeling and Pre-Metastatic Niche Formation

Introduction

Colorectal cancer (CRC) is a major cause of cancer related deaths in the United States, with CRC metastasis to the liver being a common occurrence. The development of an optimal metastatic environment is essential process prior to tumor metastasis. This process, called pre-metastatic niche (PMN) formation, involves activation of key resident liver cells, including fibroblast-like stellate cells and macrophages such as Kupffer cells. Tumor-mediated factors introduced to this environment transform resident cells that secrete additional growth factors and remodel the extracellular matrix (ECM), which is thought to promote tumor colonization and metastasis in the secondary environment.

Methods

To investigate the underlying mechanisms of these dynamics, we developed a multicellular computational model to characterize the spatiotemporal dynamics of the PMN formation in tissue. This modeling framework integrates intracellular and extracellular signaling, and traction and junctional forces into a Cellular Potts model, and represents multiple cell types with varying levels of cellular activation. We perform numerical experiments to investigate the role of key factors in PMN formation and tumor invasiveness, including growth factor concentration, timing of tumor arrival, relative composition of resident cells, and the size of invading tumor cluster.

Results

These parameter studies identified growth factor availability and ECM concentration in the environment as two of the key determinants of tumor invasiveness. We further predict that both the ECM concentration potential and growth factor sensitivity of the stellate cells are key drivers of the PMN formation and associated ECM concentration.

Conclusions

Overall, this modeling framework represents a significant step towards simulating cancer metastasis and investigating the role of key factors on PMN formation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-024-00831-0.

Mathematical Modeling of Impacts of Patient Differences on Renin-Angiotensin System and Applications to COVID-19 Lung Fibrosis Outcomes

Patient-specific premorbidity, age, and sex are significant heterogeneous factors that influence the severe manifestation of lung diseases, including COVID-19 fibrosis. The renin-angiotensin system (RAS) plays a prominent role in regulating the effects of these factors. Recent evidence shows patient-specific alterations of RAS homeostasis concentrations with premorbidity and the expression level of angiotensin-converting enzyme 2 (ACE2) during COVID-19. However, conflicting evidence suggests decreases, increases, or no changes in RAS peptides after SARS-CoV-2 infection. In addition, detailed mechanisms connecting the patient-specific conditions before infection to infection-induced RAS alterations are still unknown. Here, a multiscale computational model was developed to quantify the systemic contribution of heterogeneous factors of RAS during COVID-19. Three submodels were connected-an agent-based model for in-host COVID-19 response in the lung tissue, a RAS dynamics model, and a fibrosis dynamics model to investigate the effects of patient-group-specific factors in the systemic alteration of RAS and collagen deposition in the lung. The model results indicated cell death due to inflammatory response as a major contributor to the reduction of ACE and ACE2. In contrast, there were no significant changes in ACE2 dynamics due to viral-bound internalization of ACE2. The model explained possible mechanisms for conflicting evidence of patient-group-specific changes in RAS peptides in previously published studies. Simulated results were consistent with reported RAS peptide values for SARS-CoV-2-negative and SARS-CoV-2-positive patients. RAS peptides decreased for all virtual patient groups with aging in both sexes. In contrast, large variations in the magnitude of reduction were observed between male and female virtual patients in the older and middle-aged groups. The patient-specific variations in homeostasis RAS peptide concentrations of SARS-CoV-2-negative patients also affected the dynamics of RAS during infection. The model results also showed that feedback between RAS signaling and renin dynamics could restore ANGI homeostasis concentration but failed to restore homeostasis values of RAS peptides downstream of ANGI. In addition, the results showed that ACE2 variations with age and sex significantly altered the concentrations of RAS peptides and led to collagen deposition with slight variations depending on age and sex. This model may find further applications in patient-specific calibrations of tissue models for acute and chronic lung diseases to develop personalized treatments.

Agent-based modeling for the tumor microenvironment (TME)

Cancer is a disease that arises from the uncontrolled growth of abnormal (tumor) cells in an organ and their subsequent spread into other parts of the body. If tumor cells spread to surrounding tissues or other organs, then the disease is life-threatening due to limited treatment options. This work applies an agent-based model to investigate the effect of intra-tumoral communication on tumor progression, plasticity, and invasion, with results suggesting that cell-cell and cell-extracellular matrix (ECM) interactions affect tumor cell behavior. Additionally, the model suggests that low initial healthy cell densities and ECM protein densities promote tumor progression, cell motility, and invasion. Furthermore, high ECM breakdown probabilities of tumor cells promote tumor invasion. Understanding the intra-tumoral communication under cellular stress can potentially lead to the design of successful treatment strategies for cancer.

Foundations of a Compositional Systems Biology

Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes to enable integrative multiscale simulations. Whereas traditional models focus on the structure or dynamics of specific subsystems in controlled conditions, compositional systems biology aims to connect these models, asking critical questions about the space between models: What variables should a submodel expose through its interface? How do coupled models connect and translate across scales? How do domain-specific models connect across biological and physical disciplines to drive the synthesis of new knowledge? This approach requires robust software to integrate diverse datasets and submodels, providing researchers with tools to flexibly recombine, iteratively refine, and collaboratively expand their models. This article offers a comprehensive framework to support this vision, including: a conceptual and graphical framework to define interfaces and composition patterns; standardized schemas that facilitate modular data and model assembly; biological templates that integrate detailed submodels that connect molecular processes to the emergence of the cellular interface; and user-friendly software interfaces that empower research communities to construct and improve multiscale models of cellular systems. By addressing these needs, compositional systems biology will foster a unified and scalable approach to understanding complex cellular systems.

Personalizing computational models to construct medical digital twins

Digital twin technology, pioneered for engineering applications, is being adapted to biomedicine and healthcare; however, several problems need to be solved in the process. One major problem is that of dynamically calibrating a computational model to an individual patient, using data collected from that patient over time. This kind of calibration is crucial for improving model-based forecasts and realizing personalized medicine. The underlying computational model often focuses on a particular part of human biology, combines different modeling paradigms at different scales, and is both stochastic and spatially heterogeneous. A commonly used modeling framework is that of an agent-based model, a computational model for simulating autonomous agents such as cells, which captures how system-level properties are affected by local interactions. There are no standard personalization methods that can be readily applied to such models. The key challenge for any such algorithm is to bridge the gap between the clinically measurable quantities (the macrostate) and the fine-grained data at different physiological scales which are required to run the model (the microstate). In this paper we develop an algorithm which applies a classic data assimilation technique, the ensemble Kalman filter, at the macrostate level. We then link the Kalman update at the macrostate level to an update at the microstate level that produces microstates which are not only compatible with desired macrostates but also highly likely with respect to model dynamics.

An adaptive numerical method for multi-cellular simulations of tissue development and maintenance

In recent years, multi-cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi-cellular modelling tools and to demonstrate which numerical methods are appropriate for simulations of tissue and organ development, maintenance, and disease. The second aim is to introduce an adaptive time-stepping algorithm and to demonstrate it's efficiency and accuracy. We focus on off-lattice, mechanics based, models where cell movement is defined by a series of first order ordinary differential equations, derived by assuming over-damped motion and balancing forces. We see that many numerical methods have been used, ranging from simple Forward Euler approaches through to higher order single-step methods like Runge-Kutta 4 and multi-step methods like Adams-Bashforth 2. Through a series of exemplar multi-cellular simulations, we see that if: care is taken to have events (births deaths and re-meshing/re-arrangements) occur on common time-steps; and boundaries are imposed on all sub-steps of numerical methods or implemented using forces, then all numerical methods can converge with the correct order. We introduce an adaptive time-stepping method and demonstrate that the best compromise between L∞ error and run-time is to use Runge-Kutta 4 with an increased time-step and moderate adaptivity. We see that a judicious choice of numerical method can speed the simulation up by a factor of 10-60 from the Forward Euler methods seen in Osborne et al. (2017), and a further speed up by a factor of 4 can be achieved by using an adaptive time-step.

Characterising Cancer Cell Responses to Cyclic Hypoxia Using Mathematical Modelling

In vivo observations show that oxygen levels in tumours can fluctuate on fast and slow timescales. As a result, cancer cells can be periodically exposed to pathologically low oxygen levels; a phenomenon known as cyclic hypoxia. Yet, little is known about the response and adaptation of cancer cells to cyclic, rather than, constant hypoxia. Further, existing in vitro models of cyclic hypoxia fail to capture the complex and heterogeneous oxygen dynamics of tumours growing in vivo. Mathematical models can help to overcome current experimental limitations and, in so doing, offer new insights into the biology of tumour cyclic hypoxia by predicting cell responses to a wide range of cyclic dynamics. We develop an individual-based model to investigate how cell cycle progression and cell fate determination of cancer cells are altered following exposure to cyclic hypoxia. Our model can simulate standard in vitro experiments, such as clonogenic assays and cell cycle experiments, allowing for efficient screening of cell responses under a wide range of cyclic hypoxia conditions. Simulation results show that the same cell line can exhibit markedly different responses to cyclic hypoxia depending on the dynamics of the oxygen fluctuations. We also use our model to investigate the impact of changes to cell cycle checkpoint activation and damage repair on cell responses to cyclic hypoxia. Our simulations suggest that cyclic hypoxia can promote heterogeneity in cellular damage repair activity within vascular tumours.

AMBER: A Modular Model for Tumor Growth, Vasculature and Radiation Response

Computational models of tumor growth are valuable for simulating the dynamics of cancer progression and treatment responses. In particular, agent-based models (ABMs) tracking individual agents and their interactions are useful for their flexibility and ability to model complex behaviors. However, ABMs have often been confined to small domains or, when scaled up, have neglected crucial aspects like vasculature. Additionally, the integration into tumor ABMs of precise radiation dose calculations using gold-standard Monte Carlo (MC) methods, crucial in contemporary radiotherapy, has been lacking. Here, we introduce AMBER, an Agent-based fraMework for radioBiological Effects in Radiotherapy that computationally models tumor growth and radiation responses. AMBER is based on a voxelized geometry, enabling realistic simulations at relevant pre-clinical scales by tracking temporally discrete states stepwise. Its hybrid approach, combining traditional ABM techniques with continuous spatiotemporal fields of key microenvironmental factors such as oxygen and vascular endothelial growth factor, facilitates the generation of realistic tortuous vascular trees. Moreover, AMBER is integrated with TOPAS, an MC-based particle transport algorithm that simulates heterogeneous radiation doses. The impact of radiation on tumor dynamics considers the microenvironmental factors that alter radiosensitivity, such as oxygen availability, providing a full coupling between the biological and physical aspects. Our results show that simulations with AMBER yield accurate tumor evolution and radiation treatment outcomes, consistent with established volumetric growth laws and radiobiological understanding. Thus, AMBER emerges as a promising tool for replicating essential features of tumor growth and radiation response, offering a modular design for future expansions to incorporate specific biological traits.

Towards verifiable cancer digital twins: tissue level modeling protocol for precision medicine

Cancer exhibits substantial heterogeneity, manifesting as distinct morphological and molecular variations across tumors, which frequently undermines the efficacy of conventional oncological treatments. Developments in multiomics and sequencing technologies have paved the way for unraveling this heterogeneity. Nevertheless, the complexity of the data gathered from these methods cannot be fully interpreted through multimodal data analysis alone. Mathematical modeling plays a crucial role in delineating the underlying mechanisms to explain sources of heterogeneity using patient-specific data. Intra-tumoral diversity necessitates the development of precision oncology therapies utilizing multiphysics, multiscale mathematical models for cancer. This review discusses recent advancements in computational methodologies for precision oncology, highlighting the potential of cancer digital twins to enhance patient-specific decision-making in clinical settings. We review computational efforts in building patient-informed cellular and tissue-level models for cancer and propose a computational framework that utilizes agent-based modeling as an effective conduit to integrate cancer systems models that encode signaling at the cellular scale with digital twin models that predict tissue-level response in a tumor microenvironment customized to patient information. Furthermore, we discuss machine learning approaches to building surrogates for these complex mathematical models. These surrogates can potentially be used to conduct sensitivity analysis, verification, validation, and uncertainty quantification, which is especially important for tumor studies due to their dynamic nature.

Cell density couples tissue mechanics to control the elongation speed of the body axis

The vertebrate body forms by the addition of new tissues at the posterior end. This elongates the body axis, allowing continued anterior segmentation to produce the stereotypic body plan. This balance requires the elongation speed to be constrained. Here we utilized modeling and tissue force microscopy on chicken embryos to show that cell density of the posterior presomitic mesoderm (pPSM) dynamically modulates elongation speed in a negative feedback loop. Elongation alters the cell density in the pPSM, which in turn controls progenitor cell influx through the mechanical coupling of body axis tissues. This enables responsive cell dynamics in over- and under-elongated axes that consequently self-adjust speed to achieve long-term robustness in axial length. Our simulations and experiments further suggest that cell density and FGF activity synergistically drive elongation. Our work supports a simple mechanism of morphogenetic speed control where the cell density relates negatively to progress, and positively to force generation.

PhysiMeSS - a new physiCell addon for extracellular matrix modelling

The extracellular matrix, composed of macromolecules like collagen fibres, provides structural support to cells and acts as a barrier that metastatic cells degrade to spread beyond the primary tumour. While agent-based frameworks, such as PhysiCell, can simulate the spatial dynamics of tumour evolution, they only implement cells as circles (2D) or spheres (3D). To model the extracellular matrix as a network of fibres, we require a new type of agent represented by line segments (2D) or cylinders (3D). Here, we present PhysiMeSS, an addon of PhysiCell, introducing a new agent type to describe fibres and their physical interactions with cells and other fibres. PhysiMeSS implementation is available at https://github.com/PhysiMeSS/PhysiMeSS and in the official PhysiCell repository. We provide examples describing the possibilities of this framework. This tool may help tackle important biological questions, such as diseases linked to dysregulation of the extracellular matrix or the processes leading to cancer metastasis.

Building multiscale models with PhysiBoSS, an agent-based modeling tool

Multiscale models provide a unique tool for analyzing complex processes that study events occurring at different scales across space and time. In the context of biological systems, such models can simulate mechanisms happening at the intracellular level such as signaling, and at the extracellular level where cells communicate and coordinate with other cells. These models aim to understand the impact of genetic or environmental deregulation observed in complex diseases, describe the interplay between a pathological tissue and the immune system, and suggest strategies to revert the diseased phenotypes. The construction of these multiscale models remains a very complex task, including the choice of the components to consider, the level of details of the processes to simulate, or the fitting of the parameters to the data. One additional difficulty is the expert knowledge needed to program these models in languages such as C++ or Python, which may discourage the participation of non-experts. Simplifying this process through structured description formalisms-coupled with a graphical interface-is crucial in making modeling more accessible to the broader scientific community, as well as streamlining the process for advanced users. This article introduces three examples of multiscale models which rely on the framework PhysiBoSS, an add-on of PhysiCell that includes intracellular descriptions as continuous time Boolean models to the agent-based approach. The article demonstrates how to construct these models more easily, relying on PhysiCell Studio, the PhysiCell Graphical User Interface. A step-by-step tutorial is provided as Supplementary Material and all models are provided at https://physiboss.github.io/tutorial/.

Spatially fractionated GRID radiation potentiates immune-mediated tumor control

BACKGROUND

Tumor-immune interactions shape a developing tumor and its tumor immune microenvironment (TIME) resulting in either well-infiltrated, immunologically inflamed tumor beds, or immune deserts with low levels of infiltration. The pre-treatment immune make-up of the TIME is associated with treatment outcome; immunologically inflamed tumors generally exhibit better responses to radio- and immunotherapy than non-inflamed tumors. However, radiotherapy is known to induce opposing immunological consequences, resulting in both immunostimulatory and inhibitory responses. In fact, it is thought that the radiation-induced tumoricidal immune response is curtailed by subsequent applications of radiation. It is thus conceivable that spatially fractionated radiotherapy (SFRT), administered through GRID blocks (SFRT-GRID) or lattice radiotherapy to create areas of low or high dose exposure, may create protective reservoirs of the tumor immune microenvironment, thereby preserving anti-tumor immune responses that are pivotal for radiation success.

METHODS

We have developed an agent-based model (ABM) of tumor-immune interactions to investigate the immunological consequences and clinical outcomes after 2 Gy × 35 whole tumor radiation therapy (WTRT) and SFRT-GRID. The ABM is conceptually calibrated such that untreated tumors escape immune surveillance and grow to clinical detection. Individual ABM simulations are initialized from four distinct multiplex immunohistochemistry (mIHC) slides, and immune related parameter rates are generated using Latin Hypercube Sampling.

RESULTS

In silico simulations suggest that radiation-induced cancer cell death alone is insufficient to clear a tumor with WTRT. However, explicit consideration of radiation-induced anti-tumor immunity synergizes with radiation cytotoxicity to eradicate tumors. Similarly, SFRT-GRID is successful with radiation-induced anti-tumor immunity, and, for some pre-treatment TIME compositions and modeling parameters, SFRT-GRID might be superior to WTRT in providing tumor control.

CONCLUSION

This study demonstrates the pivotal role of the radiation-induced anti-tumor immunity. Prolonged fractionated treatment schedules may counteract early immune recruitment, which may be protected by SFRT-facilitated immune reservoirs. Different biological responses and treatment outcomes are observed based on pre-treatment TIME composition and model parameters. A rigorous analysis and model calibration for different tumor types and immune infiltration states is required before any conclusions can be drawn for clinical translation.

An agent-based model for cell microenvironment simulation using FLAMEGPU2

This work presents an advanced agent-based model developed within the FLAMEGPU2 framework, aimed at simulating the intricate dynamics of cell microenvironments. Our primary objective is to showcase FLAMEGPU2's potential in modelling critical features such as cell-cell and cell-ECM interactions, species diffusion, vascularisation, cell migration, and/or cell cycling. By doing so, we provide a versatile template that serves as a foundational platform for researchers to model specific biological mechanisms or processes. We highlight the utility of our approach as a microscale component within multiscale frameworks. Through four example applications, we demonstrate the model's versatility in capturing phenomena such as strain-stiffening behaviour of hydrogels, cell migration patterns within hydrogels, spheroid formation and fibre reorientation, and the simulation of diffusion processes within a vascularised and deformable domain. This work aims to bridge the gap between computational efficiency and biological fidelity, offering a scalable and flexible platform to advance our understanding of tissue biology and engineering.

Mechanistic modeling of cell viability assays with in silico lineage tracing

Data from cell viability assays, which measure cumulative division and death events in a population and reflect substantial cellular heterogeneity, are widely available. However, interpreting such data with mechanistic computational models is hindered because direct model/data comparison is often muddled. We developed an algorithm that tracks simulated division and death events in mechanistically detailed single-cell lineages to enable such a model/data comparison and suggest causes of cell-cell drug response variability. Using our previously developed model of mammalian single-cell proliferation and death signaling, we simulated drug dose response experiments for four targeted anti-cancer drugs (alpelisib, neratinib, trametinib and palbociclib) and compared them to experimental data. Simulations are consistent with data for strong growth inhibition by trametinib (MEK inhibitor) and overall lack of efficacy for alpelisib (PI-3K inhibitor), but are inconsistent with data for palbociclib (CDK4/6 inhibitor) and neratinib (EGFR inhibitor). Model/data inconsistencies suggest (i) the importance of CDK4/6 for driving the cell cycle may be overestimated, and (ii) that the cellular balance between basal (tonic) and ligand-induced signaling is a critical determinant of receptor inhibitor response. Simulations show subpopulations of rapidly and slowly dividing cells in both control and drug-treated conditions. Variations in mother cells prior to drug treatment all impinging on ERK pathway activity are associated with the rapidly dividing phenotype and trametinib resistance. This work lays a foundation for the application of mechanistic modeling to large-scale cell viability assay datasets and better understanding determinants of cellular heterogeneity in drug response.

Spatial computational modelling illuminates the role of the tumour microenvironment for treating glioblastoma with immunotherapies

Glioblastoma is the most common and deadliest brain tumour in adults, with a median survival of 15 months under the current standard of care. Immunotherapies like immune checkpoint inhibitors and oncolytic viruses have been extensively studied to improve this endpoint. However, most thus far have failed. To improve the efficacy of immunotherapies to treat glioblastoma, new single-cell imaging modalities like imaging mass cytometry can be leveraged and integrated with computational models. This enables a better understanding of the tumour microenvironment and its role in treatment success or failure in this hard-to-treat tumour. Here, we implemented an agent-based model that allows for spatial predictions of combination chemotherapy, oncolytic virus, and immune checkpoint inhibitors against glioblastoma. We initialised our model with patient imaging mass cytometry data to predict patient-specific responses and found that oncolytic viruses drive combination treatment responses determined by intratumoral cell density. We found that tumours with higher tumour cell density responded better to treatment. When fixing the number of cancer cells, treatment efficacy was shown to be a function of CD4 + T cell and, to a lesser extent, of macrophage counts. Critically, our simulations show that care must be put into the integration of spatial data and agent-based models to effectively capture intratumoral dynamics. Together, this study emphasizes the use of predictive spatial modelling to better understand cancer immunotherapy treatment dynamics, while highlighting key factors to consider during model design and implementation.

Kiphynet: an online network simulation tool connecting cellular kinetics and physiological transport

INTRODUCTION

Human metabolism is sustained by functional networks that operate at diverse scales. Capturing local and global dynamics in the human body by hierarchically bridging multi-scale functional networks is a major challenge in physiological modeling.

OBJECTIVES

To develop an interactive, user-friendly web application that facilitates the simulation and visualization of advection-dispersion transport in three-dimensional (3D) microvascular networks, biochemical exchange, and metabolic reactions in the tissue layer surrounding the vasculature.

METHODS

To help modelers combine and simulate biochemical processes occurring at multiple scales, KiPhyNet deploys our discrete graph-based modeling framework that bridges functional networks existing at diverse scales. KiPhyNet is implemented in Python based on Apache web server using MATLAB as the simulator engine. KiPhyNet provides the functionality to assimilate multi-omics data from clinical and experimental studies as well as vascular data from imaging studies to investigate the role of structural changes in vascular topology on the functional response of the tissue.

RESULTS

With the network topology, its biophysical attributes, values of initial and boundary conditions, parameterized kinetic constants, biochemical species-specific transport properties such as diffusivity as inputs, a user can use our application to simulate and view the simulation results. The results of steady-state velocity and pressure fields and dynamic concentration fields can be interactively examined.

CONCLUSION

KiPhyNet provides barrier-free access to perform time-course simulation experiments by building multi-scale models of microvascular networks in physiology, using a discrete modeling framework. KiPhyNet is freely accessible at   http://pallab.cds.iisc.ac.in/kiphynet/ and the documentation is available at   https://deepamahm.github.io/kiphynet_docs/ .

Signatures of selective sweeps in continuous-space populations

Selective sweeps describe the process by which an adaptive mutation arises and rapidly fixes in the population, thereby removing genetic variation in its genomic vicinity. The expected signatures of selective sweeps are relatively well understood in panmictic population models, yet natural populations often extend across larger geographic ranges where individuals are more likely to mate with those born nearby. To investigate how such spatial population structure can affect sweep dynamics and signatures, we simulated selective sweeps in populations inhabiting a two-dimensional continuous landscape. The maximum dispersal distance of offspring from their parents can be varied in our simulations from an essentially panmictic population to scenarios with increasingly limited dispersal. We find that in low-dispersal populations, adaptive mutations spread more slowly than in panmictic ones, while recombination becomes less effective at breaking up genetic linkage around the sweep locus. Together, these factors result in a trough of reduced genetic diversity around the sweep locus that looks very similar across dispersal rates. We also find that the site frequency spectrum around hard sweeps in low-dispersal populations becomes enriched for intermediate-frequency variants, making these sweeps appear softer than they are. Furthermore, haplotype heterozygosity at the sweep locus tends to be elevated in low-dispersal scenarios as compared to panmixia, contrary to what we observe in neutral scenarios without sweeps. The haplotype patterns generated by these hard sweeps in low-dispersal populations can resemble soft sweeps from standing genetic variation that arose from substantially older alleles. Our results highlight the need for better accounting for spatial population structure when making inferences about selective sweeps.

Modeling free tumor growth: Discrete, continuum, and hybrid approaches to interpreting cancer development

Tumor growth dynamics serve as a critical aspect of understanding cancer progression and treatment response to mitigate one of the most pressing challenges in healthcare. The in silico approach to understanding tumor behavior computationally provides an efficient, cost-effective alternative to wet-lab examinations and are adaptable to different environmental conditions, time scales, and unique patient parameters. As a result, this paper explored modeling of free tumor growth in cancer, surveying contemporary literature on continuum, discrete, and hybrid approaches. Factors like predictive power and high-resolution simulation competed against drawbacks like simulation load and parameter feasibility in these models. Understanding tumor behavior in different scenarios and contexts became the first step in advancing cancer research and revolutionizing clinical outcomes.

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

A three-dimensional lattice-free agent-based model of intracellular ice formation and propagation and intercellular mechanics in liver tissues

A successful cryopreservation of tissues and organs is crucial for medical procedures and drug development acceleration. However, there are only a few instances of successful tissue cryopreservation. One of the main obstacles to successful cryopreservation is intracellular ice damage. Understanding how ice spreads can accelerate protocol development and enable model-based decision-making. Previous models of intracellular ice formation in individual cells have been extended to one-cell-wide arrays to establish the theory of intercellular ice propagation in tissues. The current lattice-based ice propagation models do not account for intercellular forces resulting from cell solidification, which could lead to mechanical disruption of tissue structures during freezing. Moreover, these models have not been expanded to include more realistic tissue architectures. In this article, we discuss the development and validation of a stochastic model for the formation and propagation of ice in small tissues using lattice-free agent-based model. We have improved the existing model by incorporating the mechanical effects of water crystallization within cells. Using information from previous research, we have also created a new model that accounts for ice growth in tissue slabs, spheroids and hepatocyte discs. Our model demonstrates that individual cell freezing can have mechanical consequences and is consistent with earlier findings.

Inspiring a convergent engineering approach to measure and model the tissue microenvironment

Understanding the molecular and physical complexity of the tissue microenvironment (TiME) in the context of its spatiotemporal organization has remained an enduring challenge. Recent advances in engineering and data science are now promising the ability to study the structure, functions, and dynamics of the TiME in unprecedented detail; however, many advances still occur in silos that rarely integrate information to study the TiME in its full detail. This review provides an integrative overview of the engineering principles underlying chemical, optical, electrical, mechanical, and computational science to probe, sense, model, and fabricate the TiME. In individual sections, we first summarize the underlying principles, capabilities, and scope of emerging technologies, the breakthrough discoveries enabled by each technology and recent, promising innovations. We provide perspectives on the potential of these advances in answering critical questions about the TiME and its role in various disease and developmental processes. Finally, we present an integrative view that appreciates the major scientific and educational aspects in the study of the TiME.

Building multiscale models with PhysiBoSS, an agent-based modeling tool

Multiscale models provide a unique tool for studying complex processes that study events occurring at different scales across space and time. In the context of biological systems, such models can simulate mechanisms happening at the intracellular level such as signaling, and at the extracellular level where cells communicate and coordinate with other cells. They aim to understand the impact of genetic or environmental deregulation observed in complex diseases, describe the interplay between a pathological tissue and the immune system, and suggest strategies to revert the diseased phenotypes. The construction of these multiscale models remains a very complex task, including the choice of the components to consider, the level of details of the processes to simulate, or the fitting of the parameters to the data. One additional difficulty is the expert knowledge needed to program these models in languages such as C++ or Python, which may discourage the participation of non-experts. Simplifying this process through structured description formalisms - coupled with a graphical interface - is crucial in making modeling more accessible to the broader scientific community, as well as streamlining the process for advanced users. This article introduces three examples of multiscale models which rely on the framework PhysiBoSS, an add-on of PhysiCell that includes intracellular descriptions as continuous time Boolean models to the agent-based approach. The article demonstrates how to easily construct such models, relying on PhysiCell Studio, the PhysiCell Graphical User Interface. A step-by-step tutorial is provided as a Supplementary Material and all models are provided at: https://physiboss.github.io/tutorial/.

A resource-based mechanistic framework for castration-resistant prostate cancer (CRPC)

Cancer therapy often leads to the selective elimination of drug-sensitive cells from the tumour. This can favour the growth of cells resistant to the therapeutic agent, ultimately causing a tumour relapse. Castration-resistant prostate cancer (CRPC) is a well-characterised instance of this phenomenon. In CRPC, after systemic androgen deprivation therapy (ADT), a subset of drug-resistant cancer cells autonomously produce testosterone, thus enabling tumour regrowth. A previous theoretical study has shown that such a tumour relapse can be delayed by inhibiting the growth of drug-resistant cells using biotic competition from drug-sensitive cells. In this context, the centrality of resource dynamics to intra-tumour competition in the CRPC system indicates clear scope for the construction of theoretical models that can explicitly incorporate the underlying mechanisms of tumour ecology. In the current study, we use a modified logistic framework to model cell-cell interactions in terms of the production and consumption of resources. Our results show that steady state composition of CRPC can be understood as a composite function of the availability and utilisation efficiency of two resources-oxygen and testosterone. In particular, we show that the effect of changing resource availability or use efficiency is conditioned by their general abundance regimes. Testosterone typically functions in trace amounts and thus affects steady state behaviour of the CRPC system differently from oxygen, which is usually available at higher levels. Our data thus indicate that explicit consideration of resource dynamics can produce novel and useful mechanistic understanding of CRPC. Furthermore, such a modelling approach also incorporates variables into the system's description that can be directly measured in a clinical context. This is therefore a promising avenue of research in cancer ecology that could lead to therapeutic approaches that are more clearly rooted in the biology of CRPC.

PhysiCell Studio: a graphical tool to make agent-based modeling more accessible

Defining a multicellular model can be challenging. There may be hundreds of parameters that specify the attributes and behaviors of objects. In the best case, the model will be defined using some format specification - a markup language - that will provide easy model sharing (and a minimal step toward reproducibility). PhysiCell is an open-source, physics-based multicellular simulation framework with an active and growing user community. It uses XML to define a model and, traditionally, users needed to manually edit the XML to modify the model. PhysiCell Studio is a tool to make this task easier. It provides a GUI that allows editing the XML model definition, including the creation and deletion of fundamental objects: cell types and substrates in the microenvironment. It also lets users build their model by defining initial conditions and biological rules, run simulations, and view results interactively. PhysiCell Studio has evolved over multiple workshops and academic courses in recent years, which has led to many improvements. There is both a desktop and cloud version. Its design and development has benefited from an active undergraduate and graduate research program. Like PhysiCell, the Studio is open-source software and contributions from the community are encouraged.

Review Study on Mechanical Properties of Cellular Materials

Cellular materials are fundamental elements in civil engineering, known for their porous nature and lightweight composition. However, the complexity of its microstructure and the mechanisms that control its behavior presents ongoing challenges. This comprehensive review aims to confront these uncertainties head-on, delving into the multifaceted field of cellular materials. It highlights the key role played by numerical and mathematical analysis in revealing the mysterious elasticity of these structures. Furthermore, the review covers a range of topics, from the simulation of manufacturing processes to the complex relationships between microstructure and mechanical properties. This review provides a panoramic view of the field by traversing various numerical and mathematical analysis methods. Furthermore, it reveals cutting-edge theoretical frameworks that promise to redefine our understanding of cellular solids. By providing these contemporary insights, this study not only points the way for future research but also illuminates pathways to practical applications in civil and materials engineering.

In silico study of heterogeneous tumour-derived organoid response to CAR T-cell therapy

Chimeric antigen receptor (CAR) T-cell therapy is a promising immunotherapy for treating cancers. This method consists in modifying the patients' T-cells to directly target antigen-presenting cancer cells. One of the barriers to the development of this type of therapies, is target antigen heterogeneity. It is thought that intratumour heterogeneity is one of the leading determinants of therapeutic resistance and treatment failure. While understanding antigen heterogeneity is important for effective therapeutics, a good therapy strategy could enhance the therapy efficiency. In this work we introduce an agent-based model (ABM), built upon a previous ABM, to rationalise the outcomes of different CAR T-cells therapies strategies over heterogeneous tumour-derived organoids. We found that one dose of CAR T-cell therapy should be expected to reduce the tumour size as well as its growth rate, however it may not be enough to completely eliminate it. Moreover, the amount of free CAR T-cells (i.e. CAR T-cells that did not kill any cancer cell) increases as we increase the dosage, and so does the risk of side effects. We tested different strategies to enhance smaller dosages, such as enhancing the CAR T-cells long-term persistence and multiple dosing. For both approaches an appropriate dosimetry strategy is necessary to produce "effective yet safe" therapeutic results. Moreover, an interesting emergent phenomenon results from the simulations, namely the formation of a shield-like structure of cells with low antigen expression. This shield turns out to protect cells with high antigen expression. Finally we tested a multi-antigen recognition therapy to overcome antigen escape and heterogeneity. Our studies suggest that larger dosages can completely eliminate the organoid, however the multi-antigen recognition increases the risk of side effects. Therefore, an appropriate small dosages dosimetry strategy is necessary to improve the outcomes. Based on our results, it is clear that a proper therapeutic strategy could enhance the therapies outcomes. In that direction, our computational approach provides a framework to model treatment combinations in different scenarios and to explore the characteristics of successful and unsuccessful treatments.

A seven-step guide to spatial, agent-based modelling of tumour evolution

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.

Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key experimental observations, linear diffusion fails to predict well-defined sharp fronts that are often observed experimentally. This observation has motivated the use of nonlinear degenerate diffusion; however, these nonlinear models and the associated parameters lack a clear biological motivation and interpretation. Here, we take a different approach by developing a stochastic discrete lattice-based model incorporating biologically inspired mechanisms and then deriving the reaction-diffusion continuum limit. Inspired by experimental observations, agents in the simulation deposit extracellular material, which we call a substrate, locally onto the lattice, and the motility of agents is taken to be proportional to the substrate density. Discrete simulations that mimic a two-dimensional circular barrier assay illustrate how the discrete model supports both smooth and sharp-fronted density profiles depending on the rate of substrate deposition. Coarse-graining the discrete model leads to a novel partial differential equation (PDE) model whose solution accurately approximates averaged data from the discrete model. The new discrete model and PDE approximation provide a simple, biologically motivated framework for modelling the spreading, growth and invasion of cell populations with well-defined sharp fronts. Open-source Julia code to replicate all results in this work is available on GitHub.

Machine learning approach for recognition and morphological analysis of isolated astrocytes in phase contrast microscopy

Astrocytes are glycolytically active cells in the central nervous system playing a crucial role in various brain processes from homeostasis to neurotransmission. Astrocytes possess a complex branched morphology, frequently examined by fluorescent microscopy. However, staining and fixation may impact the properties of astrocytes, thereby affecting the accuracy of the experimental data of astrocytes dynamics and morphology. On the other hand, phase contrast microscopy can be used to study astrocytes morphology without affecting them, but the post-processing of the resulting low-contrast images is challenging. The main result of this work is a novel approach for recognition and morphological analysis of unstained astrocytes based on machine-learning recognition of microscopic images. We conducted a series of experiments involving the cultivation of isolated astrocytes from the rat brain cortex followed by microscopy. Using the proposed approach, we tracked the temporal evolution of the average total length of branches, branching, and area per astrocyte in our experiments. We believe that the proposed approach and the obtained experimental data will be of interest and benefit to the scientific communities in cell biology, biophysics, and machine learning.

Kill rates by immune cells: Ratio-dependent, or mass action?

We describe a cell-based fixed-lattice model to simulate immune cell and tumor cell interaction involving MHC recognition, and FasL vs perforin lysis. We are motivated by open questions about the mechanisms behind observed kill rates of tumor cells by different types of effector cells. These mechanisms play a big role in the effectiveness of many cancer immunotherapies. The model is a stochastic cellular automaton on a hexagonal grid.

BioNexusSentinel: a visual tool for bioregulatory network and cytohistological RNA-seq genetic expression profiling within the context of multicellular simulation research using ChatGPT-augmented software engineering

Summary

Motivated by the need to parameterize ongoing multicellular simulation research, this paper documents the culmination of a ChatGPT augmented software engineering cycle resulting in an integrated visual platform for efficient cytohistological RNA-seq and bioregulatory network exploration. As contrasted to other systems and synthetic biology tools, BioNexusSentinel was developed de novo to uniquely combine these features. Reactome served as the primary source of remotely accessible biological models, accessible using BioNexusSentinel's novel search engine and REST API requests. The innovative, feature-rich gene expression profiler component was developed to enhance the exploratory experience for the researcher, culminating in the cytohistological RNA-seq explorer based on Human Protein Atlas data. A novel cytohistological classifier would be integrated via pre-processed analysis of the RNA-seq data via R statistical language, providing for useful analytical functionality and good performance for the end-user. Implications of the work span prospects for model orthogonality evaluations, gap identification in network modelling, prototyped automatic kinetics parameterization, and downstream simulation and cellular biological state analysis. This unique computational biology software engineering collaboration with generative natural language processing artificial intelligence was shown to enhance worker productivity, with evident benefits in terms of accelerating coding and machine-human intelligence transfer.

Availability and implementation

BioNexusSentinel project releases, with corresponding data and installation instructions, are available at https://github.com/RichardMatzko/BioNexusSentinel.