3D multi-cell simulation of tumor growth and angiogenesis

Chemotaxis effects on the vascular tumor growth: Phase-field model and simulations

In this paper, we propose a vascular tumor growth model that combines a phase-field tumor model with a phase-field angiogenesis model. By incorporating various tumor cell species, we capture the instabilities of the tumor in the presence of evolving neovasculature. The model not only considers different dynamics of tumor cell phase conversions, movement, and pressure effects but also provides a comprehensive representation of angiogenesis, encompassing chemotaxis of endothelial cells, sprouting, anastomoses, and blood flow in capillaries. This study evaluates the impact of chemotaxis on tumor cell movement in both avascular and vascular tumor growth scenarios. The results highlight the acceleration of tumor growth when angiogenesis is stimulated. Additionally, the investigation explores various initial distances of the tumor from neighboring vessels, revealing a critical threshold distance beyond which the angiogenesis factor fails to stimulate angiogenesis, resulting in the tumor maintaining a stable state. The integration of chemotaxis into the growth model induces instabilities, leading to increased nutrient availability and faster growth for the tumor. Furthermore, the study considers anti-angiogenesis therapy as an ideal approach, assuming complete inhibition of angiogenesis from the early stages. In this scenario, the tumor persists in a steady state, adhering to the avascular size limit in the absence of neovasculature. Conversely, when considering chemotaxis, anti-angiogenesis therapy loses efficiency, enabling unrestrained tumor growth towards neighboring vessels. This work sheds light on the intricate interplay among chemotaxis, angiogenesis, and anti-angiogenesis therapy in the context of vascular tumor growth, providing valuable insights for the development of targeted treatment strategies.

Spatiotemporal spread of oncolytic virus in a heterogeneous cell population

Oncolytic (cancer-killing) virus treatment is a promising new therapy for cancer, with many viruses currently being tested for their ability to eradicate tumors. One of the major stumbling blocks to the development of this treatment modality has been preventing spread of the virus to non-cancerous cells. Our recent ability to manipulate RNA and DNA now allows for the possibility of creating designer viruses specifically targeted to cancer cells, thereby significantly reducing unwanted side effects in patients. In this study, we use a partial differential equation model to determine the characteristics of a virus needed to contain spread of an oncolytic virus within a spherical tumor and prevent it from spreading to non-cancerous cells outside the tumor. We find that oncolytic viruses that have different infection rates or different cell death rates in cancer and non-cancerous cells can be made to stay within the tumor. We find that there is a minimum difference in infection rates or cell death rates that will contain the virus and that this threshold value depends on the growth rate of the cancer. Identification of these types of thresholds can help researchers develop safer strains of oncolytic viruses allowing further development of this promising treatment.

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.

Tumor growth and vascular redistribution contributes to the dosimetric preferential effect of microbeam radiotherapy: a Monte Carlo study

The radiobiological mechanisms behind the favorable response of tissues to microbeam radiation therapy (MRT) are not fully described yet. Among other factors, the differential action to tumor and normal tissue vasculature is considered to contribute to MRT efficacy. This computational study evaluates the relevance of tumor growth stage and associated vascular redistribution to this effect. A multiscale approach was employed with two simulation softwares: TOPAS and CompuCell3D. Segmentation images of the angioarchitecture of a non-bearing tumor mouse brain were used. The tumor vasculature at different tumor growth stages was obtained by simulating the tumor proliferation and spatial vascular redistribution. The radiation-induced damage to vascular cells and consequent change in oxygen perfusion were simulated for normal and tumor tissues. The multiscale model showed that oxygen perfusion to tissues and vessels decreased as a function of the tumor proliferation stage, and with the decrease in uniformity of the vasculature spatial distribution in the tumor tissue. This led to an increase in the fraction of hypoxic (up to 60%) and necrotic (10%) tumor cells at advanced tumor stages, whereas normal tissues remained normoxic. These results showed that tumor stage and spatial vascular distribution contribute to the preferential effect of MRT in tumors.

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.

TOPAS-Tissue: A Framework for the Simulation of the Biological Response to Ionizing Radiation at the Multi-Cellular Level

This work aims to develop and validate a framework for the multiscale simulation of the biological response to ionizing radiation in a population of cells forming a tissue. We present TOPAS-Tissue, a framework to allow coupling two Monte Carlo (MC) codes: TOPAS with the TOPAS-nBio extension, capable of handling the track-structure simulation and subsequent chemistry, and CompuCell3D, an agent-based model simulator for biological and environmental behavior of a population of cells. We verified the implementation by simulating the experimental conditions for a clonogenic survival assay of a 2-D PC-3 cell culture model (10 cells in 10,000 µm2) irradiated by MV X-rays at several absorbed dose values from 0-8 Gy. The simulation considered cell growth and division, irradiation, DSB induction, DNA repair, and cellular response. The survival was obtained by counting the number of colonies, defined as a surviving primary (or seeded) cell with progeny, at 2.7 simulated days after irradiation. DNA repair was simulated with an MC implementation of the two-lesion kinetic model and the cell response with a p53 protein-pulse model. The simulated survival curve followed the theoretical linear-quadratic response with dose. The fitted coefficients α = 0.280 ± 0.025/Gy and β = 0.042 ± 0.006/Gy2 agreed with published experimental data within two standard deviations. TOPAS-Tissue extends previous works by simulating in an end-to-end way the effects of radiation in a cell population, from irradiation and DNA damage leading to the cell fate. In conclusion, TOPAS-Tissue offers an extensible all-in-one simulation framework that successfully couples Compucell3D and TOPAS for multiscale simulation of the biological response to radiation.

Bidirectionally validated in silico and in vitro formation of specific depth zone-derived chondrocyte spheroids and clusters

3D multicellular self-organized cluster models, e.g., organoids are promising tools for developing new therapeutic modalities including gene and cell therapies, pharmacological mechanistic and screening assays. Various applications of these models have been used extensively for decades, however, the mechanisms of cluster formation, maintenance, and degradation of these models are not even known over in-vitro-life-time. To explore such advantageous models mimicking native tissues or organs, it is necessary to understand aforementioned mechanisms. Herein, we intend to clarify the mechanisms of the formation of cell clusters. We previously demonstrated that primary chondrocytes isolated from distinct longitudinal depth zones in articular cartilage formed zone-specific spherical multicellular clusters in vitro. To elucidate the mechanisms of such cluster formation, we simulated it using the computational Cellular Potts Model with parameters were translated from gene expression levels and histological characteristics corresponding to interactions between cell and extracellular matrix. This simulation in silico was validated morphologically with cluster formation in vitro and vice versa. Since zone specific chondrocyte cluster models in silico showed similarity with corresponding in vitro model, the in silico has a potential to be used for prediction of the 3D multicellular in vitro models used for development, disease, and therapeutic models.

Impact of stroma remodeling on forces experienced by cancer cells and stromal cells within a pancreatic tumor tissue

Remodeling (re-engineering) of a tumor's stroma has been shown to improve the efficacy of anti-tumor therapies, without destroying the stroma. Even though it still remains unclear which stromal component/-s and what characteristics hinder the reach of nanoparticles deep into cancer cells, we hypothesis that mechanisms behind stroma's resistance to the penetration of nanoparticles rely heavily on extrinsic mechanical forces on stromal cells and cancer cells. Our hypothesis has been formulated on the basis of our previous study which has shown that changes in extracellular matrix (ECM) stiffness with tumor growth influence stresses exerted on fibroblasts and cancer cells, and that malignant cancer cells generate higher stresses on their stroma. This study attempts to establish a distinct identification of the components' remodeling on the distribution and magnitude of stress within a tumor tissue which ultimately will impact the resistance of stroma to treatment. In this study, our objective is to construct a three-dimensional in silico model of a pancreas tumor tissue consisting of cancer cells, stromal cells, and ECM to determine how stromal remodeling alters the stresses distribution and magnitude within the pancreas tumor tissue. Our results show that changes in mechanical properties of ECM significantly alter the magnitude and distribution of stresses within the pancreas tumor tissue. Our results revealed that these stresses are more sensitive to ECM properties as we see the stresses reaching to a maximum of 22,000 Pa for softer ECM with Young's modulus of 250 Pa. The stress distribution and magnitude within the pancreas tumor tissue does not show high sensitivity to the changes in mechanical properties of stromal cells surrounding stiffer cancer cells (PANC-1 with Young's modulus of 2400 Pa). However, softer cancer cells (MIA-PaCa-2 with (Young's modulus of 500 Pa) increase the stresses experienced by stiffer stromal cells and for stiffer ECM. By providing a unique platform to dissect and quantify the impact of individual stromal components on the stress distribution within a tumor tissue, this study serves as an important first step in understanding of which stromal components are vital for an efficient remodeling. This knowledge will be leveraged to overcome a tumor's resistance against the penetration of nanoparticles on a per-patient basis.

Biomaterials-Based Strategies to Enhance Angiogenesis in Diabetic Wound Healing

Amidst the present healthcare issues, diabetes is unique as an emerging class of affliction with chronicity in a majority of the population. To check and control its effects, there have been huge turnover and constant development of management strategies, and though a bigger part of the health care area is involved in achieving its control and the related issues such as the effect of diabetes on wound healing and care and many of the works have reached certain successful outcomes, still there is a huge lack in managing it, with maximum effect yet to be attained. Studying pathophysiology and involvement of various treatment options, such as tissue engineering, application of hydrogels, drug delivery methods, and enhancing angiogenesis, are at constantly developing stages either direct or indirect. In this review, we have gathered a wide field of information and different new therapeutic methods and targets for the scientific community, paving the way toward more settled ideas and research advances to cure diabetic wounds and manage their outcomes.

Modeling Physical Forces Experienced by Cancer and Stromal Cells Within Different Organ-Specific Tumor Tissue

Mechanical force exerted on cancer cells by their microenvironment have been reported to drive cells toward invasive phenotypes by altering cells' motility, proliferation, and apoptosis. These mechanical forces include compressive, tensile, hydrostatic, and shear forces. The importance of forces is then hypothesized to be an alteration of cancer cells' and their microenvironment's biophysical properties as the indicator of a tumor's malignancy state. Our objective is to investigate and quantify the correlation between a tumor's malignancy state and forces experienced by the cancer cells and components of the microenvironment. In this study, we have developed a multicomponent, three-dimensional model of tumor tissue consisting of a cancer cell surrounded by fibroblasts and extracellular matrix (ECM). Our results on three different organs including breast, kidney, and pancreas show that: A) the stresses within tumor tissue are impacted by the organ specific ECM's biophysical properties, B) more invasive cancer cells experience higher stresses, C) in pancreas which has a softer ECM (Young modulus of 1.0 kPa) and stiffer cancer cells (Young modulus of 2.4 kPa and 1.7 kPa) than breast and kidney, cancer cells experienced significantly higher stresses, D) cancer cells in contact with ECM experienced higher stresses compared to cells surrounded by fibroblasts but the area of tumor stroma experiencing high stresses has a maximum length of 40 μm when the cancer cell is surrounded by fibroblasts and 12 μm for when the cancer cell is in vicinity of ECM. This study serves as an important first step in understanding of how the stresses experienced by cancer cells, fibroblasts, and ECM are associated with malignancy states of cancer cells in different organs. The quantification of forces exerted on cancer cells by different organ-specific ECM and at different stages of malignancy will help, first to develop theranostic strategies, second to predict accurately which tumors will become highly malignant, and third to establish accurate criteria controlling the progression of cancer cells malignancy. Furthermore, our in silico model of tumor tissue can yield critical, useful information for guiding ex vivo or in vitro experiments, narrowing down variables to be investigated, understanding what factors could be impacting cancer treatments or even biomarkers to be looking for.

Selected aspects of avascular tumor growth reproduced by a hybrid model of cell dynamics and chemical kinetics

We here propose a hybrid computational framework to reproduce and analyze aspects of the avascular progression of a generic solid tumor. Our method first employs an individual-based approach to represent the population of tumor cells, which are distinguished in viable and necrotic agents. The active part of the disease is in turn differentiated according to a set of metabolic states. We then describe the spatio-temporal evolution of the concentration of oxygen and of tumor-secreted proteolytic enzymes using partial differential equations (PDEs). A differential equation finally governs the local degradation of the extracellular matrix (ECM) by the malignant mass. Numerical realizations of the model are run to reproduce tumor growth and invasion in a number scenarios that differ for cell properties (adhesiveness, duplication potential, proteolytic activity) and/or environmental conditions (level of tissue oxygenation and matrix density pattern). In particular, our simulations suggest that tumor aggressiveness, in terms of invasive depth and extension of necrotic tissue, can be reduced by (i) stable cell-cell contact interactions, (ii) poor tendency of malignant agents to chemotactically move upon oxygen gradients, and (iii) presence of an overdense matrix, if coupled by a disrupted proteolytic activity of the disease.

Modelling cell shape in 3D structured environments: A quantitative comparison with experiments

Cell shape plays a fundamental role in many biological processes, including adhesion, migration, division and development, but it is not clear which shape model best predicts three-dimensional cell shape in structured environments. Here, we compare different modelling approaches with experimental data. The shapes of single mesenchymal cells cultured in custom-made 3D scaffolds were compared by a Fourier method with surfaces that minimize area under the given adhesion and volume constraints. For the minimized surface model, we found marked differences to the experimentally observed cell shapes, which necessitated the use of more advanced shape models. We used different variants of the cellular Potts model, which effectively includes both surface and bulk contributions. The simulations revealed that the Hamiltonian with linear area energy outperformed the elastic area constraint in accurately modelling the 3D shapes of cells in structured environments. Explicit modelling the nucleus did not improve the accuracy of the simulated cell shapes. Overall, our work identifies effective methods for accurately modelling cellular shapes in complex environments.

Computational modeling of angiogenesis: The importance of cell rearrangements during vascular growth

Angiogenesis is the process wherein endothelial cells (ECs) form sprouts that elongate from the pre-existing vasculature to create new vascular networks. In addition to its essential role in normal development, angiogenesis plays a vital role in pathologies such as cancer, diabetes and atherosclerosis. Mathematical and computational modeling has contributed to unraveling its complexity. Many existing theoretical models of angiogenic sprouting are based on the "snail-trail" hypothesis. This framework assumes that leading ECs positioned at sprout tips migrate toward low-oxygen regions while other ECs in the sprout passively follow the leaders' trails and proliferate to maintain sprout integrity. However, experimental results indicate that, contrary to the snail-trail assumption, ECs exchange positions within developing vessels, and the elongation of sprouts is primarily driven by directed migration of ECs. The functional role of cell rearrangements remains unclear. This review of the theoretical modeling of angiogenesis is the first to focus on the phenomenon of cell mixing during early sprouting. We start by describing the biological processes that occur during early angiogenesis, such as phenotype specification, cell rearrangements and cell interactions with the microenvironment. Next, we provide an overview of various theoretical approaches that have been employed to model angiogenesis, with particular emphasis on recent in silico models that account for the phenomenon of cell mixing. Finally, we discuss when cell mixing should be incorporated into theoretical models and what essential modeling components such models should include in order to investigate its functional role. This article is categorized under: Cardiovascular Diseases > Computational Models Cancer > Computational Models.

Enhanced perfusion following exposure to radiotherapy: A theoretical investigation

Tumour angiogenesis leads to the formation of blood vessels that are structurally and spatially heterogeneous. Poor blood perfusion, in conjunction with increased hypoxia and oxygen heterogeneity, impairs a tumour's response to radiotherapy. The optimal strategy for enhancing tumour perfusion remains unclear, preventing its regular deployment in combination therapies. In this work, we first identify vascular architectural features that correlate with enhanced perfusion following radiotherapy, using in vivo imaging data from vascular tumours. Then, we present a novel computational model to determine the relationship between these architectural features and blood perfusion in silico. If perfusion is defined to be the proportion of vessels that support blood flow, we find that vascular networks with small mean diameters and large numbers of angiogenic sprouts show the largest increases in perfusion post-irradiation for both biological and synthetic tumours. We also identify cases where perfusion increases due to the pruning of hypoperfused vessels, rather than blood being rerouted. These results indicate the importance of considering network composition when determining the optimal irradiation strategy. In the future, we aim to use our findings to identify tumours that are good candidates for perfusion enhancement and to improve the efficacy of combination therapies.

A framework for multi-scale intervention modeling: virtual cohorts, virtual clinical trials, and model-to-model comparisons

Computational models of disease progression have been constructed for a myriad of pathologies. Typically, the conceptual implementation for pathology-related in-silico intervention studies has been ad-hoc and similar in design to experimental studies. We introduce a multi-scale interventional design (MID) framework toward two key goals: tracking of disease dynamics from within-body to patient to population scale; and tracking impact(s) of interventions across these same spatial scales. Our MID framework prioritizes investigation of impact on individual patients within virtual pre-clinical trials, instead of replicating the design of experimental studies. We apply a MID framework to develop, organize, and analyze a cohort of virtual patients for the study of tuberculosis (TB) as an example disease. For this study, we use HostSim: our next-generation whole patient-scale computational model of individuals infected with Mycobacterium tuberculosis. HostSim captures infection within lungs by tracking multiple granulomas, together with dynamics occurring with blood and lymph node compartments, the compartments involved during pulmonary TB. We extend HostSim to include a simple drug intervention as an example of our approach and use our MID framework to quantify the impact of treatment at cellular and tissue (granuloma), patient (lungs, lymph nodes and blood), and population scales. Sensitivity analyses allow us to determine which features of virtual patients are the strongest predictors of intervention efficacy across scales. These insights allow us to identify patient-heterogeneous mechanisms that drive outcomes across scales.

Phenotype-structured model of intra-clonal heterogeneity and drug resistance in multiple myeloma

Multiple myeloma (MM) is a genetically complex hematological cancer characterized by the abnormal proliferation of malignant plasma cells in the bone marrow. This disease progresses from a premalignant condition known as monoclonal gammopathy of unknown significance (MGUS) through sequential genetic alterations involving various genes. These genetic changes contribute to the uncontrolled growth of multiple clones of plasma cells. In this study, we present a phenotype-structured model that captures the intra-clonal heterogeneity and drug resistance in multiple myeloma (MM). The model accurately reproduces the branching evolutionary pattern observed in MM progression, aligning with a previously developed multiscale model. Numerical simulations reveal that higher mutation rates enhance tumor phenotype diversity, while access to growth factors accelerates tumor evolution and increases its final size. Interestingly, the model suggests that further increasing growth factor access primarily amplifies tumor size rather than altering clonal dynamics. Additionally, the model emphasizes that higher mutation frequencies and growth factor availability elevate the chances of drug resistance and relapse. It indicates that the timing of the treatment could trajectory of tumor evolution and clonal emergence in the case of branching evolutionary pattern. Given its low computational cost, our model is well-suited for quantitative studies on MM clonal heterogeneity and its interaction with chemotherapeutic treatments.

Physically and Chemically Compartmentalized Polymersomes for Programmed Delivery and Biological Applications

Multicompartment polymersomes (MCPs) refer to polymersomes that not only contain one single compartment, either in the membrane or in the internal cavity, but also mimic the compartmentalized structure of living cells, attracting much attention in programmed delivery and biological applications. The investigation of MCPs may promote the application of soft nanomaterials in biomedicine. This Review seeks to highlight the recent advances of the design principles, synthetic strategies, and biomedical applications of MCPs. The compartmentalization types including chemical, physical, and hybrid compartmentalization are discussed. Subsequently, the design and controlled synthesis of MCPs by the self-assembly of amphiphilic polymers, double emulsification, coprecipitation, microfluidics and particle assembly, etc. are summarized. Furthermore, the diverse applications of MCPs in programmed delivery of various cargoes and biological applications including cancer therapy, antimicrobials, and regulation of blood glucose levels are highlighted. Finally, future perspectives of MCPs from the aspects of controlled synthesis and applications are proposed.

Development and Analysis of Multiscale Models for Tuberculosis: From Molecules to Populations

Although infectious disease dynamics are often analyzed at the macro-scale, increasing numbers of drug-resistant infections highlight the importance of within-host modeling that simultaneously solves across multiple scales to effectively respond to epidemics. We review multiscale modeling approaches for complex, interconnected biological systems and discuss critical steps involved in building, analyzing, and applying such models within the discipline of model credibility. We also present our two tools: CaliPro, for calibrating multiscale models (MSMs) to datasets, and tunable resolution, for fine- and coarse-graining sub-models while retaining insights. We include as an example our work simulating infection with Mycobacterium tuberculosis to demonstrate modeling choices and how predictions are made to generate new insights and test interventions. We discuss some of the current challenges of incorporating novel datasets, rigorously training computational biologists, and increasing the reach of MSMs. We also offer several promising future research directions of incorporating within-host dynamics into applications ranging from combinatorial treatment to epidemic response.

Nanoparticle-mediated cancer cell therapy: basic science to clinical applications

Every sixth person in the world dies due to cancer, making it the second leading severe cause of death after cardiovascular diseases. According to WHO, cancer claimed nearly 10 million deaths in 2020. The most common types of cancers reported have been breast (lung, colon and rectum, prostate cases), skin (non-melanoma) and stomach. In addition to surgery, the most widely used traditional types of anti-cancer treatment are radio- and chemotherapy. However, these do not distinguish between normal and malignant cells. Additional treatment methods have evolved over time for early detection and targeted therapy of cancer. However, each method has its limitations and the associated treatment costs are quite high with adverse effects on the quality of life of patients. Use of individual atoms or a cluster of atoms (nanoparticles) can cause a paradigm shift by virtue of providing point of sight sensing and diagnosis of cancer. Nanoparticles (1-100 nm in size) are 1000 times smaller in size than the human cell and endowed with safer relocation capability to attack mechanically and chemically at a precise location which is one avenue that can be used to destroy cancer cells precisely. This review summarises the extant understanding and the work done in this area to pave the way for physicians to accelerate the use of hybrid mode of treatments by leveraging the use of various nanoparticles.

Angiogenic Microvascular Wall Shear Stress Patterns Revealed Through Three-dimensional Red Blood Cell Resolved Modeling

The wall shear stress (WSS) exerted by blood flowing through microvascular capillaries is an established driver of new blood vessel growth, or angiogenesis. Such adaptations are central to many physiological processes in both health and disease, yet three-dimensional (3D) WSS characteristics in real angiogenic microvascular networks are largely unknown. This marks a major knowledge gap because angiogenesis, naturally, is a 3D process. To advance current understanding, we model 3D red blood cells (RBCs) flowing through rat angiogenic microvascular networks using state-of-the-art simulation. The high-resolution fluid dynamics reveal 3D WSS patterns occurring at sub-endothelial cell (EC) scales that derive from distinct angiogenic morphologies, including microvascular loops and vessel tortuosity. We identify the existence of WSS hot and cold spots caused by angiogenic surface shapes and RBCs, and notably enhancement of low WSS regions by RBCs. Spatiotemporal characteristics further reveal how fluctuations follow timescales of RBC "footprints." Altogether, this work provides a new conceptual framework for understanding how shear stress might regulate EC dynamics in vivo.

Interplay of adherens junctions and matrix proteolysis determines the invasive pattern and growth of squamous cell carcinoma

Cancers, such as squamous cell carcinoma, frequently invade as multicellular units. However, these invading units can be organised in a variety of ways, ranging from thin discontinuous strands to thick 'pushing' collectives. Here we employ an integrated experimental and computational approach to identify the factors that determine the mode of collective cancer cell invasion. We find that matrix proteolysis is linked to the formation of wide strands but has little effect on the maximum extent of invasion. Cell-cell junctions also favour wide strands, but our analysis also reveals a requirement for cell-cell junctions for efficient invasion in response to uniform directional cues. Unexpectedly, the ability to generate wide invasive strands is coupled to the ability to grow effectively when surrounded by extracellular matrix in three-dimensional assays. Combinatorial perturbation of both matrix proteolysis and cell-cell adhesion demonstrates that the most aggressive cancer behaviour, both in terms of invasion and growth, is achieved at high levels of cell-cell adhesion and high levels of proteolysis. Contrary to expectation, cells with canonical mesenchymal traits - no cell-cell junctions and high proteolysis - exhibit reduced growth and lymph node metastasis. Thus, we conclude that the ability of squamous cell carcinoma cells to invade effectively is also linked to their ability to generate space for proliferation in confined contexts. These data provide an explanation for the apparent advantage of retaining cell-cell junctions in squamous cell carcinomas.

Development of a coupled modeling for tumor growth, angiogenesis, oxygen delivery, and phenotypic heterogeneity

Analysis of the evolution and growth dynamics of tumors is crucial for understanding cancer and the development of individually optimized therapies. During tumor growth, a hypoxic microenvironment around cancer cells caused by excessive non-vascular tumor growth induces tumor angiogenesis that plays a key role in the ensuing tumor growth and its progression into higher stages. Various mathematical simulation models have been introduced to simulate these biologically and physically complex hallmarks of cancer. Here, we developed a hybrid two-dimensional computational model that integrates spatiotemporally different components of the tumor system to investigate both angiogenesis and tumor growth/proliferation. This spatiotemporal evolution is based on partial diffusion equations, the cellular automation method, transition and probabilistic rules, and biological assumptions. The new vascular network provided by angiogenesis affects tumor microenvironmental conditions and drives individual cells to adapt themselves to spatiotemporal conditions. Furthermore, some stochastic rules are involved besides microenvironmental conditions. Overall, the conditions promote some commonly observed cellular states, i.e., proliferative, migrative, quiescent, and cell death, depending on the condition of each cell. Altogether, our results offer a theoretical basis for the biological evidence that regions of the tumor tissue near blood vessels are densely populated by proliferative phenotypic variants, while poorly oxygenated regions are sparsely populated by hypoxic phenotypic variants.

Data-driven spatio-temporal modelling of glioblastoma

Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding glioblastoma, a malignant form of brain cancer. For each approach, we summarize the scope, drawbacks and assets. We highlight the potential clinical applications of each modelling technique and discuss the connections between the mathematical models and the molecular and imaging data used to inform them. By doing so, we aim to prime cancer researchers with current and emerging computational tools for understanding tumour progression. By providing an in-depth picture of the different modelling techniques, we also aim to assist researchers who seek to build and develop their own models and the associated inference frameworks. Our article thus strikes a unique balance. On the one hand, we provide a comprehensive overview of the available modelling techniques and their applications, including key mathematical expressions. On the other hand, the content is accessible to mathematicians and biomedical scientists alike to accommodate the interdisciplinary nature of cancer research.

Probing the Interaction Between Supercarrier RBC Membrane and Nanoparticles for Optimal Drug Delivery

Red blood cell (RBC) membrane-hitchhiking nanoparticles (NPs) have been an increasingly popular supercarrier for targeted drug delivery. However, the kinetic details of the shear-induced NP detachment process from RBC in blood flow remain unclear. Here, we perform detailed computational simulations of the traversal dynamics of an RBC-NP composite supercarrier with tunable properties. We show that the detachment of NPs from RBC occurs in a shear-dependent manner which is consistent with previous experiment results. We quantify the NP detachment rate in the microcapillary flow, and our simulation results suggest that there may be an optimal adhesion strength span of 25-40 μJ/m² for rigid spherical NPs to improve the supercarrier performance and targeting efficiency. In addition, we find that the stiffness and the shape of NPs alter the detachment efficiency by changing the RBC-NP contact areas. Together, these findings provide unique insights into the shear-dependent NP release from the RBC surface, facilitating the clinical utility of RBC-NP composite supercarriers in targeted and localized drug delivery with high precision and efficiency.

Multi-scale model of lumen formation via inverse membrane blebbing mechanism during sprouting angiogenesis process

Cancer is one of the leading causes of mortality and morbidity among people worldwide. Cancer appears as solid tumors in many cases. Angiogenesis is the growth of blood vessels from the existing vasculature and is one of the imperative processes in tumor growth. Another vital phenomenon for formation and functionality of this vasculature network is lumen formation. The results of recent studies indicate the importance of blood pressure in this mechanism. Computational modeling can study these processes in different scales. Hence, wide varieties of these models have been proposed during recent years. In this research, a multi-scale model is developed for the angiogenesis process. In the extracellular scale, the growth factor concentration is calculated via the reaction diffusion equation. At the cellular scale, growth, migration, and the adhesion of endothelial cells are modeled by the Potts cellular model. At the intra-cellular scale by considering biochemical signals, a Boolean network model describes migration, division, or apoptosis of endothelial cells. A stochastic model developed for lumen formation via inverse membrane blebbing mechanism. A CFD simulation was also used to investigate the role of pulsated blood pressure in the inverse membrane blebbing mechanism. The lumen formation model shows stochastic behavior in blebs expansion and lumen expansion. Comparing the stochastic model's results with the CFD simulation also shows the vital role of pressure pulse and the topology of the blebs in bleb retraction.

Computational models for generating microvascular structures: Investigations beyond medical imaging resolution

Angiogenesis, arteriogenesis, and pruning are revascularization processes essential to our natural vascular development and adaptation, as well as central players in the onset and development of pathologies such as tumoral growth and stroke recovery. Computational modeling allows for repeatable experimentation and exploration of these complex biological processes. In this review, we provide an introduction to the biological understanding of the vascular adaptation processes of sprouting angiogenesis, intussusceptive angiogenesis, anastomosis, pruning, and arteriogenesis, discussing some of the more significant contributions made to the computational modeling of these processes. Each computational model represents a theoretical framework for how biology functions, and with rises in computing power and study of the problem these frameworks become more accurate and complete. We highlight physiological, pathological, and technological applications that can be benefit from the advances performed by these models, and we also identify which elements of the biology are underexplored in the current state-of-the-art computational models. This article is categorized under: Cancer > Computational Models Cardiovascular Diseases > Computational Models.

Computational Simulation of Tumor-Induced Angiogenesis

Cancer cells require higher oxygen levels and nutrition than normal cells. Cancer cells induce angiogenesis (the development of new blood vessels) from preexisting vessels. This biological process depends on the special, chemical, and physical properties of the microenvironment surrounding tumor tissues. The complexity of these properties hinders an understanding of their mechanisms. Various mathematical models have been developed to describe quantitative relationships related to angiogenesis. We developed a three-dimensional mathematical model that incorporates angiogenesis and tumor growth. We examined angiopoietin, which regulates the spouting and branching events in angiogenesis. The simulation successfully reproduced the transient decrease in new vessels during vascular network formation. This chapter describes the protocol used to perform the simulations.

Efficient Bayesian inference for stochastic agent-based models

The modelling of many real-world problems relies on computationally heavy simulations of randomly interacting individuals or agents. However, the values of the parameters that underlie the interactions between agents are typically poorly known, and hence they need to be inferred from macroscopic observations of the system. Since statistical inference rests on repeated simulations to sample the parameter space, the high computational expense of these simulations can become a stumbling block. In this paper, we compare two ways to mitigate this issue in a Bayesian setting through the use of machine learning methods: One approach is to construct lightweight surrogate models to substitute the simulations used in inference. Alternatively, one might altogether circumvent the need for Bayesian sampling schemes and directly estimate the posterior distribution. We focus on stochastic simulations that track autonomous agents and present two case studies: tumour growths and the spread of infectious diseases. We demonstrate that good accuracy in inference can be achieved with a relatively small number of simulations, making our machine learning approaches orders of magnitude faster than classical simulation-based methods that rely on sampling the parameter space. However, we find that while some methods generally produce more robust results than others, no algorithm offers a one-size-fits-all solution when attempting to infer model parameters from observations. Instead, one must choose the inference technique with the specific real-world application in mind. The stochastic nature of the considered real-world phenomena poses an additional challenge that can become insurmountable for some approaches. Overall, we find machine learning approaches that create direct inference machines to be promising for real-world applications. We present our findings as general guidelines for modelling practitioners.

The modeling study of the effect of morphological behaviors of extracellular matrix fibers on the dynamic interaction between tumor cells and antitumor immune response

Low response rate limits the effective application of immunotherapy, in which the interactions between tumor cells and immune cells play a significant role. The strength of regulation could be mediated by extracellular matrix (ECM) fibers, which is still insufficiently investigated. In the study, the cellular potts model was utilized to explore the role of morphological properties of ECM in tumor-immune interactions. It was observed that high-density random ECM fibers delayed the interaction between tumor cells and T cells. Moreover, the tumor-immune interactions were ECM morphology-specific. Radial ECM fibers exhibited weaker inhibitory role in the process of contact between tumor cells and T cells. This study provided the useful mechanism of tumor-immune interactions from the viewpoint of morphological effect of ECM fibers, facilitating improving the efficiency of immunotherapy.

Replacement in angiogenesis research: Studying mechanisms of blood vessel development by animal-free in vitro, in vivo and in silico approaches

Angiogenesis, the development of new blood vessels from pre-existing ones, is an essential process determining numerous physiological and pathological conditions. Accordingly, there is a high demand for research approaches allowing the investigation of angiogenic mechanisms and the assessment of pro- and anti-angiogenic therapeutics. The present review provides a selective overview and critical discussion of such approaches, which, in line with the 3R principle, all share the common feature that they are not based on animal experiments. They include in vitro assays to study the viability, proliferation, migration, tube formation and sprouting activity of endothelial cells in two- and three-dimensional environments, the degradation of extracellular matrix compounds as well as the impact of hemodynamic forces on blood vessel formation. These assays can be complemented by in vivo analyses of microvascular network formation in the chorioallantoic membrane assay and early stages of zebrafish larvae. In addition, the combination of experimental data and physical laws enables the mathematical modeling of tissue-specific vascularization, blood flow patterns, interstitial fluid flow as well as oxygen, nutrient and drug distribution. All these animal-free approaches markedly contribute to an improved understanding of fundamental biological mechanisms underlying angiogenesis. Hence, they do not only represent essential tools in basic science but also in early stages of drug development. Moreover, their advancement bears the great potential to analyze angiogenesis in all its complexity and, thus, to make animal experiments superfluous in the future.

Mathematical and computational models in spheroid-based biofabrication

Ubiquitous in embryonic development, tissue fusion is of interest to tissue engineers who use tissue spheroids or organoids as building blocks of three-dimensional (3D) multicellular constructs. This review presents mathematical models and computer simulations of the fusion of tissue spheroids. The motivation of this study stems from the need to predict the post-printing evolution of 3D bioprinted constructs. First, we provide a brief overview of differential adhesion, the main morphogenetic mechanism involved in post-printing structure formation. It will be shown that clusters of cohesive cells behave as an incompressible viscous fluid on the time scale of hours. The discussion turns then to mathematical models based on the continuum hydrodynamics of highly viscous liquids and on statistical mechanics. Next, we analyze the validity and practical use of computational models of multicellular self-assembly in live constructs created by tissue spheroid bioprinting. Finally, we discuss the perspectives of the field as machine learning starts to reshape experimental design, and modular robotic workstations tend to alleviate the burden of repetitive tasks in biofabrication. STATEMENT OF SIGNIFICANCE: Bioprinted constructs are living systems, which evolve via morphogenetic mechanisms known from developmental biology. This review presents mathematical and computational tools devised for modeling post-printing structure formation. They help achieving a desirable outcome without expensive optimization experiments. While previous reviews mainly focused on assumptions, technical details, strengths, and limitations of computational models of multicellular self-assembly, this article discusses their validity and practical use in biofabrication. It also presents an overview of mathematical models that proved to be useful in the evaluation of experimental data on tissue spheroid fusion, and in the calibration of computational models. Finally, the perspectives of the field are discussed in the advent of robotic biofabrication platforms and bioprinting process optimization by machine learning.

Extracellular matrix in cancer progression and therapy

The tumor ecosystem with heterogeneous cellular compositions and the tumor microenvironment has increasingly become the focus of cancer research in recent years. The extracellular matrix (ECM), the major component of the tumor microenvironment, and its interactions with the tumor cells and stromal cells have also enjoyed tremendously increased attention. Like the other components of the tumor microenvironment, the ECM in solid tumors differs significantly from that in normal organs and tissues. We review recent studies of the complex roles the tumor ECM plays in cancer progression, from tumor initiation, growth to angiogenesis and invasion. We highlight that the biomolecular, biophysical, and mechanochemical interactions between the ECM and cells not only regulate the steps of cancer progression, but also affect the efficacy of systemic cancer treatment. We further discuss the strategies to target and modify the tumor ECM to improve cancer therapy.

Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2

We extend our established agent-based multiscale computational model of infection of lung tissue by SARS-CoV-2 to include pharmacokinetic and pharmacodynamic models of remdesivir. We model remdesivir treatment for COVID-19; however, our methods are general to other viral infections and antiviral therapies. We investigate the effects of drug potency, drug dosing frequency, treatment initiation delay, antiviral half-life, and variability in cellular uptake and metabolism of remdesivir and its active metabolite on treatment outcomes in a simulated patch of infected epithelial tissue. Non-spatial deterministic population models which treat all cells of a given class as identical can clarify how treatment dosage and timing influence treatment efficacy. However, they do not reveal how cell-to-cell variability affects treatment outcomes. Our simulations suggest that for a given treatment regime, including cell-to-cell variation in drug uptake, permeability and metabolism increase the likelihood of uncontrolled infection as the cells with the lowest internal levels of antiviral act as super-spreaders within the tissue. The model predicts substantial variability in infection outcomes between similar tissue patches for different treatment options. In models with cellular metabolic variability, antiviral doses have to be increased significantly (>50% depending on simulation parameters) to achieve the same treatment results as with the homogeneous cellular metabolism.

A multiscale cell-based model of tumor growth for chemotherapy assessment and tumor-targeted therapy through a 3D computational approach

OBJECTIVES

Computational modeling of biological systems is a powerful tool to clarify diverse processes contributing to cancer. The aim is to clarify the complex biochemical and mechanical interactions between cells, the relevance of intracellular signaling pathways in tumor progression and related events to the cancer treatments, which are largely ignored in previous studies.

MATERIALS AND METHODS

A three-dimensional multiscale cell-based model is developed, covering multiple time and spatial scales, including intracellular, cellular, and extracellular processes. The model generates a realistic representation of the processes involved from an implementation of the signaling transduction network.

RESULTS

Considering a benign tumor development, results are in good agreement with the experimental ones, which identify three different phases in tumor growth. Simulating tumor vascular growth, results predict a highly vascularized tumor morphology in a lobulated form, a consequence of cells' motile behavior. A novel systematic study of chemotherapy intervention, in combination with targeted therapy, is presented to address the capability of the model to evaluate typical clinical protocols. The model also performs a dose comparison study in order to optimize treatment efficacy and surveys the effect of chemotherapy initiation delays and different regimens.

CONCLUSIONS

Results not only provide detailed insights into tumor progression, but also support suggestions for clinical implementation. This is a major step toward the goal of predicting the effects of not only traditional chemotherapy but also tumor-targeted therapies.

The Good, the Bad, and the Ugly: Neutrophils, Angiogenesis, and Cancer

Angiogenesis, the formation of new blood vessels from already existing vasculature, is tightly regulated by pro- and anti-angiogenic stimuli and occurs under both physiological and pathological conditions. Tumor angiogenesis is central for tumor development, and an “angiogenic switch” could be initiated by multiple immune cells, such as neutrophils. Tumor-associated neutrophils promote tumor angiogenesis by the release of both conventional and non-conventional pro-angiogenic factors. Therefore, neutrophil-mediated tumor angiogenesis should be taken into consideration in the design of novel anti-cancer therapy. This review recapitulates the complex role of neutrophils in tumor angiogenesis and summarizes neutrophil-derived pro-angiogenic factors and mechanisms regulating angiogenic activity of tumor-associated neutrophils. Moreover, it provides up-to-date information about neutrophil-targeting therapy, complementary to anti-angiogenic treatment.

Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

Modular microenvironment components reproduce vascular dynamics de novo in a multi-scale agent-based model

Cells do not exist in isolation; they continuously act within and react to their environment. And this environment is not static; it continuously adapts and responds to cells. Here, we investigate how vascular structure and function impact emergent cell population behavior using an agent-based model (ABM). Our ABM enables researchers to "mix and match" cell agents, subcellular modules, and microenvironment components ranging from simple nutrient sources to complex, realistic vascular architectures that accurately capture hemodynamics. We use this ABM to highlight the bilateral relationship between cells and nearby vasculature, demonstrate the effect of vascular structure on environmental heterogeneity, and emphasize the non-linear, non-intuitive relationship between vascular function and the behavior of cell populations over time. Our ABM is well suited to characterizing in vitro and in vivo studies, with applications from basic science to translational synthetic biology and medicine. The model is freely available at https://github.com/bagherilab/ARCADE. A record of this paper's transparent peer review process is included in the supplemental information.

Chemo-mechanistic multi-scale model of a three-dimensional tumor microenvironment to quantify the chemotherapy response of cancer

Exploring efficient chemotherapy would benefit from a deeper understanding of the tumor microenvironment (TME) and its role in tumor progression. As in vivo experimental methods are unable to isolate or control individual factors of the TME, and in vitro models often cannot include all the contributing factors, some questions are best addressed with mathematical models of systems biology. In this study, we establish a multi-scale mathematical model of the TME to simulate three-dimensional tumor growth and angiogenesis and then implement the model for an array of chemotherapy approaches to elucidate the effect of TME conditions and drug scheduling on controlling tumor progression. The hyperglycemic condition as the most common disorder for cancer patients is considered to evaluate its impact on cancer response to chemotherapy. We show that combining antiangiogenic and anticancer drugs improves the outcome of treatment and can decrease accumulation of the drug in normal tissue and enhance drug delivery to the tumor. Our results demonstrate that although both concurrent and neoadjuvant combination therapies can increase intratumoral drug exposure and therapeutic accuracy, neoadjuvant therapy surpasses this, especially against hyperglycemia. Our model provides mechanistic explanations for clinical observations of tumor progression and response to treatment and establishes a computational framework for exploring better treatment strategies.

Multiscale modeling of tumor growth and angiogenesis: Evaluation of tumor-targeted therapy

The dynamics of tumor growth and associated events cover multiple time and spatial scales, generally including extracellular, cellular and intracellular modifications. The main goal of this study is to model the biological and physical behavior of tumor evolution in presence of normal healthy tissue, considering a variety of events involved in the process. These include hyper and hypoactivation of signaling pathways during tumor growth, vessels' growth, intratumoral vascularization and competition of cancer cells with healthy host tissue. The work addresses two distinctive phases in tumor development-the avascular and vascular phases-and in each stage two cases are considered-with and without normal healthy cells. The tumor growth rate increases considerably as closed vessel loops (anastomoses) form around the tumor cells resulting from tumor induced vascularization. When taking into account the host tissue around the tumor, the results show that competition between normal cells and cancer cells leads to the formation of a hypoxic tumor core within a relatively short period of time. Moreover, a dense intratumoral vascular network is formed throughout the entire lesion as a sign of a high malignancy grade, which is consistent with reported experimental data for several types of solid carcinomas. In comparison with other mathematical models of tumor development, in this work we introduce a multiscale simulation that models the cellular interactions and cell behavior as a consequence of the activation of oncogenes and deactivation of gene signaling pathways within each cell. Simulating a therapy that blocks relevant signaling pathways results in the prevention of further tumor growth and leads to an expressive decrease in its size (82% in the simulation).

Repulsive expansion dynamics in colony growth and gene expression

Spatial expansion of a population of cells can arise from growth of microorganisms, plant cells, and mammalian cells. It underlies normal or dysfunctional tissue development, and it can be exploited as the foundation for programming spatial patterns. This expansion is often driven by continuous growth and division of cells within a colony, which in turn pushes the peripheral cells outward. This process generates a repulsion velocity field at each location within the colony. Here we show that this process can be approximated as coarse-grained repulsive-expansion kinetics. This framework enables accurate and efficient simulation of growth and gene expression dynamics in radially symmetric colonies with homogenous z-directional distribution. It is robust even if cells are not spherical and vary in size. The simplicity of the resulting mathematical framework also greatly facilitates generation of mechanistic insights.

Spatiotemporal dynamics are ubiquitous in biology. To understand these phenomena in nature or to program them using synthetic gene circuits, it is critical to resort to mathematical modeling to deduce mechanistic insights or to explore plausible outcomes. Historically, modeling of spatiotemporal dynamics depends on the use of agent-based models or their continuum counterparts consisting of partial differential equations. Here, we show that a class of colony expansion can be treated as being driven by the steric force generated by growing and diving cells. This approximation leads to a drastically simplified framework consisting of only ordinary differential equations. This framework greatly improves the computational efficiency and facilitates development of mechanistic insights into the dynamics of colony growth and pattern formation.

Development of a coupled simulation toolkit for computational radiation biology based on Geant4 and CompuCell3D

Understanding and designing clinical radiation therapy is one of the most important areas of state-of-the-art oncological treatment regimens. Decades of research have gone into developing sophisticated treatment devices and optimization protocols for schedules and dosages. In this paper, we presented a comprehensive computational platform that facilitates building of the sophisticated multi-cell-based model of how radiation affects the biology of living tissue. We designed and implemented a coupled simulation method, including a radiation transport model, and a cell biology model, to simulate the tumor response after irradiation. The radiation transport simulation was implemented through Geant4 which is an open-source Monte Carlo simulation platform that provides many flexibilities for users, as well as low energy DNA damage simulation physics, Geant4-DNA. The cell biology simulation was implemented using CompuCell3D (CC3D) which is a cell biology simulation platform. In order to couple Geant4 solver with CC3D, we developed a 'bridging' module, RADCELL, that extracts tumor cellular geometry of the CC3D simulation (including specification of the individual cells) and ported it to the Geant4 for radiation transport simulation. The cell dose and cell DNA damage distribution in multicellular system were obtained using Geant4. The tumor response was simulated using cell-based tissue models based on CC3D, and the cell dose and cell DNA damage information were fed back through RADCELL to CC3D for updating the cell properties. By merging two powerful and widely used modeling platforms, CC3D and Geant4, we delivered a novel tool that can give us the ability to simulate the dynamics of biological tissue in the presence of ionizing radiation, which provides a framework for quantifying the biological consequences of radiation therapy. In this introductory methods paper, we described our modeling platform in detail and showed how it can be applied to study the application of radiotherapy to a vascularized tumor.

Mathematical simulation of tumour angiogenesis: angiopoietin balance is a key factor in vessel growth and regression

Excessive tumour growth results in a hypoxic environment around cancer cells, thus inducing tumour angiogenesis, which refers to the generation of new blood vessels from pre-existing vessels. This mechanism is biologically and physically complex, with various mathematical simulation models proposing to reproduce its formation. However, although temporary vessel regression is clinically known, few models succeed in reproducing this phenomenon. Here, we developed a three-dimensional simulation model encompassing both angiogenesis and tumour growth, specifically including angiopoietin. Angiopoietin regulates both adhesion and migration between vascular endothelial cells and wall cells, thus inhibiting the cell-to-cell adhesion required for angiogenesis initiation. Simulation results showed a regression, i.e. transient decrease, in the overall length of new vessels during vascular network formation. Using our model, we also evaluated the efficacy of administering the drug bevacizumab. The results highlighted differences in treatment efficacy: (1) earlier administration showed higher efficacy in inhibiting tumour growth, and (2) efficacy depended on the treatment interval even with the administration of the same dose. After thorough validation in the future, these results will contribute to the design of angiogenesis treatment protocols.

Mathematical modelling reveals cellular dynamics within tumour spheroids

Tumour spheroids are widely used as an in vitro assay for characterising the dynamics and response to treatment of different cancer cell lines. Their popularity is largely due to the reproducible manner in which spheroids grow: the diffusion of nutrients and oxygen from the surrounding culture medium, and their consumption by tumour cells, causes proliferation to be localised at the spheroid boundary. As the spheroid grows, cells at the spheroid centre may become hypoxic and die, forming a necrotic core. The pressure created by the localisation of tumour cell proliferation and death generates an cellular flow of tumour cells from the spheroid rim towards its core. Experiments by Dorie et al. showed that this flow causes inert microspheres to infiltrate into tumour spheroids via advection from the spheroid surface, by adding microbeads to the surface of tumour spheroids and observing the distribution over time. We use an off-lattice hybrid agent-based model to re-assess these experiments and establish the extent to which the spatio-temporal data generated by microspheres can be used to infer kinetic parameters associated with the tumour spheroids that they infiltrate. Variation in these parameters, such as the rate of tumour cell proliferation or sensitivity to hypoxia, can produce spheroids with similar bulk growth dynamics but differing internal compositions (the proportion of the tumour which is proliferating, hypoxic/quiescent and necrotic/nutrient-deficient). We use this model to show that the types of experiment conducted by Dorie et al. could be used to infer spheroid composition and parameters associated with tumour cell lines such as their sensitivity to hypoxia or average rate of proliferation, and note that these observations cannot be conducted within previous continuum models of microbead infiltration into tumour spheroids as they rely on resolving the trajectories of individual microbeads.

Tumour spheroids are an experimental assay used to characterise the dynamics and response to treatment of different cancer cell lines. Previous experiments have demonstrated that the localisation of tumour cell proliferation to the spheroid edge (due to the gradient formed by nutrient diffusing from the surrounding medium) causes cells to be pushed from the proliferative rim towards the nutrient-deficient necrotic core. This movement allows inert particles to infiltrate tumour spheroids. We use a hybrid agent-based model to reproduce this data. We show further how data from individual microbead trajectories can be used to infer the composition of simulated tumour spheroids, and to estimate model parameters pertaining to tumour cell proliferation rates and their responses to hypoxia. Since these measurements are possible using modern imaging techniques, this could motivate new experiments in which spheroid composition could be inferred by observing passive infiltration of inert particles.

A hybrid model of tumor growth and angiogenesis: In silico experiments

Tumor associated angiogenesis is the development of new blood vessels in response to proteins secreted by tumor cells. These new blood vessels allow tumors to continue to grow beyond what the pre-existing vasculature could support. Here, we construct a mathematical model to simulate tumor angiogenesis by considering each endothelial cell as an agent, and allowing the vascular endothelial growth factor (VEGF) and nutrient fields to impact the dynamics and phenotypic transitions of each tumor and endothelial cell. The phenotypes of the endothelial cells (i.e., tip, stalk, and phalanx cells) are selected by the local VEGF field, and govern the migration and growth of vessel sprouts at the cellular level. Over time, these vessels grow and migrate to the tumor, forming anastomotic loops to supply nutrients, while interacting with the tumor through mechanical forces and the consumption of VEGF. The model is able to capture collapsing and breaking of vessels caused by tumor-endothelial cell interactions. This is accomplished through modeling the physical interaction between the vasculature and the tumor, resulting in vessel occlusion and tumor heterogeneity over time due to the stages of response in angiogenesis. Key parameters are identified through a sensitivity analysis based on the Sobol method, establishing which parameters should be the focus of subsequent experimental efforts. During the avascular phase (i.e., before angiogenesis is triggered), the nutrient consumption rate, followed by the rate of nutrient diffusion, yield the greatest influence on the number and distribution of tumor cells. Similarly, the consumption and diffusion of VEGF yield the greatest influence on the endothelial and tumor cell numbers during angiogenesis. In summary, we present a hybrid mathematical approach that characterizes vascular changes via an agent-based model, while treating nutrient and VEGF changes through a continuum model. The model describes the physical interaction between a tumor and the surrounding blood vessels, explicitly allowing the forces of the growing tumor to influence the nutrient delivery of the vasculature.

Tumor-on-a-chip for integrating a 3D tumor microenvironment: chemical and mechanical factors

Tumor progression, including metastasis, is significantly influenced by factors in the tumor microenvironment (TME) such as mechanical force, shear stress, chemotaxis, and hypoxia. At present, most cancer studies investigate tumor metastasis by conventional cell culture methods and animal models, which are limited in data interpretation. Although patient tissue analysis, such as human patient-derived xenografts (PDX), can provide important clinical relevant information, they may not be feasible for functional studies as they are costly and time-consuming. Thus, in vitro three-dimensional (3D) models are rapidly being developed that mimic TME and allow functional investigations of metastatic mechanisms and drug responses. One of those new 3D models is tumor-on-a-chip technology that provides a powerful in vitro platform for cancer research, with the ability to mimic the complex physiological architecture and precise spatiotemporal control. Tumor-on-a-chip technology can provide integrated features including 3D scaffolding, multicellular culture, and a vasculature system to simulate dynamic flow in vivo. Here, we review a select set of recent achievements in tumor-on-a-chip approaches and present potential directions for tumor-on-a-chip systems in the future for areas including mechanical and chemical mimetic systems. We also discuss challenges and perspectives in both biological factors and engineering methods for tumor-on-a-chip progress. These approaches will allow in the future for the tumor-on-a-chip systems to test therapeutic approaches for individuals through using their cancerous cells gathered through approaches like biopsies, which then will contribute toward personalized medicine treatments for improving their outcomes.

A multi-scale model for determining the effects of pathophysiology and metabolic disorders on tumor growth

The search for efficient chemotherapy drugs and other anti-cancer treatments would benefit from a deeper understanding of the tumor microenvironment (TME) and its role in tumor progression. Because in vivo experimental methods are unable to isolate or control individual factors of the TME and in vitro models often do not include all the contributing factors, some questions are best addressed with systems biology mathematical models. In this work, we present a new fully-coupled, agent-based, multi-scale mathematical model of tumor growth, angiogenesis and metabolism that includes important aspects of the TME spanning subcellular-, cellular- and tissue-level scales. The mathematical model is computationally implemented for a three-dimensional TME, and a double hybrid continuous-discrete (DHCD) method is applied to solve the governing equations. The model recapitulates the distinct morphological and metabolic stages of a solid tumor, starting with an avascular tumor and progressing through angiogenesis and vascularized tumor growth. To examine the robustness of the model, we simulated normal and abnormal blood conditions, including hyperglycemia/hypoglycemia, hyperoxemia/hypoxemia, and hypercarbia/hypocarbia - conditions common in cancer patients. The results demonstrate that tumor progression is accelerated by hyperoxemia, hyperglycemia and hypercarbia but inhibited by hypoxemia and hypoglycemia; hypocarbia had no appreciable effect. Because of the importance of interstitial fluid flow in tumor physiology, we also examined the effects of hypo- or hypertension, and the impact of decreased hydraulic conductivity common in desmoplastic tumors. The simulations show that chemotherapy-increased blood pressure, or reduction of interstitial hydraulic conductivity increase tumor growth rate and contribute to tumor malignancy.

Notch signaling and taxis mechanisms regulate early stage angiogenesis: A mathematical and computational model

During angiogenesis, new blood vessels sprout and grow from existing ones. This process plays a crucial role in organ development and repair, in wound healing and in numerous pathological processes such as cancer progression or diabetes. Here, we present a mathematical model of early stage angiogenesis that permits exploration of the relative importance of mechanical, chemical and cellular cues. Endothelial cells proliferate and move over an extracellular matrix by following external gradients of Vessel Endothelial Growth Factor, adhesion and stiffness, which are incorporated to a Cellular Potts model with a finite element description of elasticity. The dynamics of Notch signaling involving Delta-4 and Jagged-1 ligands determines tip cell selection and vessel branching. Through their production rates, competing Jagged-Notch and Delta-Notch dynamics determine the influence of lateral inhibition and lateral induction on the selection of cellular phenotypes, branching of blood vessels, anastomosis (fusion of blood vessels) and angiogenesis velocity. Anastomosis may be favored or impeded depending on the mechanical configuration of strain vectors in the ECM near tip cells. Numerical simulations demonstrate that increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands.

Angiogenesis is the process by which new blood vessels grow from existing ones. This process plays a crucial role in organ development, in wound healing and in numerous pathological processes such as cancer growth or in diabetes. Angiogenesis is a complex, multi-step and well regulated process where biochemistry and physics are intertwined. The process entails signaling in vessel cells being driven by both chemical and mechanical mechanisms that result in vascular cell movement, deformation and proliferation. Mathematical models have the ability to bring together these mechanisms in order to explore their relative relevance in vessel growth. Here, we present a mathematical model of early stage angiogenesis that is able to explore the role of biochemical signaling and tissue mechanics. We use this model to unravel the regulating role of Jagged, Notch and Delta dynamics in vascular cells. These membrane proteins have an important part in determining the leading cell in each neo-vascular sprout. Numerical simulations demonstrate that increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands.