Multiscale Modeling of Spheroid Tumors: Effect of Nutrient Availability on Tumor Evolution.

Recent years have revealed a large number of complex mechanisms and interactions that drive the development of malignant tumors. Tumor evolution is a framework that explains tumor development as a process driven by survival of the fittest, with tumor cells of different properties competing for limited available resources. To predict the evolutionary trajectory of a tumor, knowledge of how cellular properties influence the fitness of a subpopulation in the context of the microenvironment is required and is often inaccessible. Computational multiscale-modeling of tissues enables the observation of the full trajectory of each cell within the tumor environment. Here, we model a 3D spheroid tumor with subcellular resolution. The fitness of individual cells and the evolutionary behavior of the tumor are quantified and linked to cellular and environmental parameters. The fitness of cells is solely influenced by their position in the tumor, which in turn is influenced by the two variable parameters of our model: cell-cell adhesion and cell motility. We observe the influence of nutrient independence and static and dynamically changing nutrient availability on the evolutionary trajectories of heterogeneous tumors in a high-resolution computational model. Regardless of nutrient availability, we find a fitness advantage of low-adhesion cells, which are favorable for tumor invasion. We find that the introduction of nutrient-dependent cell division and death accelerates the evolutionary speed. The evolutionary speed can be increased by fluctuations in nutrients. We identify a distinct frequency domain in which the evolutionary speed increases significantly over a tumor with constant nutrient supply. The findings suggest that an unstable supply of nutrients can accelerate tumor evolution and, thus, the transition to malignancy.

Multicellular spatial model of RNA virus replication and interferon responses reveals factors controlling plaque growth dynamics.

Respiratory viruses present major public health challenges, as evidenced by the 1918 Spanish Flu, the 1957 H2N2, 1968 H3N2, and 2009 H1N1 influenza pandemics, and the ongoing severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic. Severe RNA virus respiratory infections often correlate with high viral load and excessive inflammation. Understanding the dynamics of the innate immune response and its manifestations at the cell and tissue levels is vital to understanding the mechanisms of immunopathology and to developing strain-independent treatments. Here, we present a novel spatialized multicellular computational model of RNA virus infection and the type-I interferon-mediated antiviral response that it induces within lung epithelial cells. The model is built using the CompuCell3D multicellular simulation environment and is parameterized using data from influenza virus-infected cell cultures. Consistent with experimental observations, it exhibits either linear radial growth of viral plaques or arrested plaque growth depending on the local concentration of type I interferons. The model suggests that modifying the activity of signaling molecules in the JAK/STAT pathway or altering the ratio of the diffusion lengths of interferon and virus in the cell culture could lead to plaque growth arrest. The dependence of plaque growth arrest on diffusion lengths highlights the importance of developing validated spatial models of cytokine signaling and the need for in vitro measurement of these diffusion coefficients. Sensitivity analyses under conditions leading to continuous or arrested plaque growth found that plaque growth is more sensitive to variations of most parameters and more likely to have identifiable model parameters when conditions lead to plaque arrest. This result suggests that cytokine assay measurements may be most informative under conditions leading to arrested plaque growth. The model is easy to extend to include SARS-CoV-2-specific mechanisms or to use as a component in models linking epithelial cell signaling to systemic immune models.

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.

The 2019 mathematical oncology roadmap.

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.

A Computational Model of Peripheral Photocoagulation for the Prevention of Progressive Diabetic Capillary Occlusion.

We developed a computational model of the propagation of retinal ischemia in diabetic retinopathy and analyzed the consequences of various patterns and sizes of burns in peripheral retinal photocoagulation. The model addresses retinal ischemia as a phenomenon of adverse local feedback in which once a capillary is occluded there is an elevated probability of occlusion of adjacent capillaries resulting in enlarging areas of retinal ischemia as is commonly seen clinically. Retinal burns of different sizes and patterns, treated as local oxygen sources, are predicted to have different effects on the propagation of retinal ischemia. The patterns of retinal burns are optimized with regard to minimization of the sum of the photocoagulated retina and computer predicted ischemic retina. Our simulations show that certain patterns of retinal burns are effective at preventing the spatial spread of ischemia by creating oxygenated boundaries across which the ischemia does not propagate. This model makes no statement about current PRP treatment of avascular peripheral retina and notes that the usual spot sizes used in PRP will not prevent ischemic propagation in still vascularized retinal areas. The model seems to show that a properly patterned laser treatment of still vascularized peripheral retina may be able to prevent or at least constrain the propagation of diabetic retinal ischemia in those retinal areas with intact capillaries.

Transcriptome analysis reveals manifold mechanisms of cyst development in ADPKD.

BACKGROUND: Autosomal dominant polycystic kidney disease (ADPKD) causes progressive loss of renal function in adults as a consequence of the accumulation of cysts. ADPKD is the most common genetic cause of end-stage renal disease. Mutations in polycystin-1 occur in 87% of cases of ADPKD and mutations in polycystin-2 are found in 12% of ADPKD patients. The complexity of ADPKD has hampered efforts to identify the mechanisms underlying its pathogenesis. No current FDA (Federal Drug Administration)-approved therapies ameliorate ADPKD progression. RESULTS: We used the de Almeida laboratory's sensitive new transcriptogram method for whole-genome gene expression data analysis to analyze microarray data from cell lines developed from cell isolates of normal kidney and of both non-cystic nephrons and cysts from the kidney of a patient with ADPKD. We compared results obtained using standard Ingenuity Volcano plot analysis, Gene Set Enrichment Analysis (GSEA) and transcriptogram analysis. Transcriptogram analysis confirmed the findings of Ingenuity, GSEA, and published analysis of ADPKD kidney data and also identified multiple new expression changes in KEGG (Kyoto Encyclopedia of Genes and Genomes) pathways related to cell growth, cell death, genetic information processing, nucleotide metabolism, signal transduction, immune response, response to stimulus, cellular processes, ion homeostasis and transport and cofactors, vitamins, amino acids, energy, carbohydrates, drugs, lipids, and glycans. Transcriptogram analysis also provides significance metrics which allow us to prioritize further study of these pathways. CONCLUSIONS: Transcriptogram analysis identifies novel pathways altered in ADPKD, providing new avenues to identify both ADPKD's mechanisms of pathogenesis and pharmaceutical targets to ameliorate the progression of the disease.

Progression of Diabetic Capillary Occlusion: A Model.

An explanatory computational model is developed of the contiguous areas of retinal capillary loss which play a large role in diabetic maculapathy and diabetic retinal neovascularization. Strictly random leukocyte mediated capillary occlusion cannot explain the occurrence of large contiguous areas of retinal ischemia. Therefore occlusion of an individual capillary must increase the probability of occlusion of surrounding capillaries. A retinal perifoveal vascular sector as well as a peripheral retinal capillary network and a deleted hexagonal capillary network are modelled using Compucell3D. The perifoveal modelling produces a pattern of spreading capillary loss with associated macular edema. In the peripheral network, spreading ischemia results from the progressive loss of the ladder capillaries which connect peripheral arterioles and venules. System blood flow was elevated in the macular model before a later reduction in flow in cases with progression of capillary occlusions. Simulations differing only in initial vascular network structures but with identical dynamics for oxygen, growth factors and vascular occlusions, replicate key clinical observations of ischemia and macular edema in the posterior pole and ischemia in the retinal periphery. The simulation results also seem consistent with quantitative data on macular blood flow and qualitative data on venous oxygenation. One computational model applied to distinct capillary networks in different retinal regions yielded results comparable to clinical observations in those regions.

Virtual-tissue computer simulations define the roles of cell adhesion and proliferation in the onset of kidney cystic disease.

In autosomal dominant polycystic kidney disease (ADPKD), cysts accumulate and progressively impair renal function. Mutations in PKD1 and PKD2 genes are causally linked to ADPKD, but how these mutations drive cell behaviors that underlie ADPKD pathogenesis is unknown. Human ADPKD cysts frequently express cadherin-8 (cad8), and expression of cad8 ectopically in vitro suffices to initiate cystogenesis. To explore cell behavioral mechanisms of cad8-driven cyst initiation, we developed a virtual-tissue computer model. Our simulations predicted that either reduced cell-cell adhesion or reduced contact inhibition of proliferation triggers cyst induction. To reproduce the full range of cyst morphologies observed in vivo, changes in both cell adhesion and proliferation are required. However, only loss-of-adhesion simulations produced morphologies matching in vitro cad8-induced cysts. Conversely, the saccular cysts described by others arise predominantly by decreased contact inhibition, that is, increased proliferation. In vitro experiments confirmed that cell-cell adhesion was reduced and proliferation was increased by ectopic cad8 expression. We conclude that adhesion loss due to cadherin type switching in ADPKD suffices to drive cystogenesis. Thus, control of cadherin type switching provides a new target for therapeutic intervention.

Emergent Stratification in Solid Tumors Selects for Reduced Cohesion of Tumor Cells: A Multi-Cell, Virtual-Tissue Model of Tumor Evolution Using CompuCell3D.

Tumor cells and structure both evolve due to heritable variation of cell behaviors and selection over periods of weeks to years (somatic evolution). Micro-environmental factors exert selection pressures on tumor-cell behaviors, which influence both the rate and direction of evolution of specific behaviors, especially the development of tumor-cell aggression and resistance to chemotherapies. In this paper, we present, step-by-step, the development of a multi-cell, virtual-tissue model of tumor somatic evolution, simulated using the open-source CompuCell3D modeling environment. Our model includes essential cell behaviors, microenvironmental components and their interactions. Our model provides a platform for exploring selection pressures leading to the evolution of tumor-cell aggression, showing that emergent stratification into regions with different cell survival rates drives the evolution of less cohesive cells with lower levels of cadherins and higher levels of integrins. Such reduced cohesivity is a key hallmark in the progression of many types of solid tumors.

Multi-scale modeling of tissues using CompuCell3D.

The study of how cells interact to produce tissue development, homeostasis, or diseases was, until recently, almost purely experimental. Now, multi-cell computer simulation methods, ranging from relatively simple cellular automata to complex immersed-boundary and finite-element mechanistic models, allow in silico study of multi-cell phenomena at the tissue scale based on biologically observed cell behaviors and interactions such as movement, adhesion, growth, death, mitosis, secretion of chemicals, chemotaxis, etc. This tutorial introduces the lattice-based Glazier-Graner-Hogeweg (GGH) Monte Carlo multi-cell modeling and the open-source GGH-based CompuCell3D simulation environment that allows rapid and intuitive modeling and simulation of cellular and multi-cellular behaviors in the context of tissue formation and subsequent dynamics. We also present a walkthrough of four biological models and their associated simulations that demonstrate the capabilities of the GGH and CompuCell3D.

Front instabilities and invasiveness of simulated 3D avascular tumors.

We use the Glazier-Graner-Hogeweg model to simulate three-dimensional (3D), single-phenotype, avascular tumors growing in an homogeneous tissue matrix (TM) supplying a single limiting nutrient. We study the effects of two parameters on tumor morphology: a diffusion-limitation parameter defined as the ratio of the tumor-substrate consumption rate to the substrate-transport rate, and the tumor-TM surface tension. This initial model omits necrosis and oxidative/hypoxic metabolism effects, which can further influence tumor morphology, but our simplified model still shows significant parameter dependencies. The diffusion-limitation parameter determines whether the growing solid tumor develops a smooth (noninvasive) or fingered (invasive) interface, as in our earlier two-dimensional (2D) simulations. The sensitivity of 3D tumor morphology to tumor-TM surface tension increases with the size of the diffusion-limitation parameter, as in 2D. The 3D results are unexpectedly close to those in 2D. Our results therefore may justify using simpler 2D simulations of tumor growth, instead of more realistic but more computationally expensive 3D simulations. While geometrical artifacts mean that 2D sections of connected 3D tumors may be disconnected, the morphologies of 3D simulated tumors nevertheless correlate with the morphologies of their 2D sections, especially for low-surface-tension tumors, allowing the use of 2D sections to partially reconstruct medically-important 3D-tumor structures.

3D multi-cell simulation of tumor growth and angiogenesis.

We present a 3D multi-cell simulation of a generic simplification of vascular tumor growth which can be easily extended and adapted to describe more specific vascular tumor types and host tissues. Initially, tumor cells proliferate as they take up the oxygen which the pre-existing vasculature supplies. The tumor grows exponentially. When the oxygen level drops below a threshold, the tumor cells become hypoxic and start secreting pro-angiogenic factors. At this stage, the tumor reaches a maximum diameter characteristic of an avascular tumor spheroid. The endothelial cells in the pre-existing vasculature respond to the pro-angiogenic factors both by chemotaxing towards higher concentrations of pro-angiogenic factors and by forming new blood vessels via angiogenesis. The tumor-induced vasculature increases the growth rate of the resulting vascularized solid tumor compared to an avascular tumor, allowing the tumor to grow beyond the spheroid in these linear-growth phases. First, in the linear-spherical phase of growth, the tumor remains spherical while its volume increases. Second, in the linear-cylindrical phase of growth the tumor elongates into a cylinder. Finally, in the linear-sheet phase of growth, tumor growth accelerates as the tumor changes from cylindrical to paddle-shaped. Substantial periods during which the tumor grows slowly or not at all separate the exponential from the linear-spherical and the linear-spherical from the linear-cylindrical growth phases. In contrast to other simulations in which avascular tumors remain spherical, our simulated avascular tumors form cylinders following the blood vessels, leading to a different distribution of hypoxic cells within the tumor. Our simulations cover time periods which are long enough to produce a range of biologically reasonable complex morphologies, allowing us to study how tumor-induced angiogenesis affects the growth rate, size and morphology of simulated tumors.

Front instabilities and invasiveness of simulated avascular tumors.

We study the interface morphology of a 2D simulation of an avascular tumor composed of identical cells growing in an homogeneous healthy tissue matrix (TM), in order to understand the origin of the morphological changes often observed during real tumor growth. We use the Glazier-Graner-Hogeweg model, which treats tumor cells as extended, deformable objects, to study the effects of two parameters: a dimensionless diffusion-limitation parameter defined as the ratio of the tumor consumption rate to the substrate transport rate, and the tumor-TM surface tension. We model TM as a nondiffusing field, neglecting the TM pressure and haptotactic repulsion acting on a real growing tumor; thus, our model is appropriate for studying tumors with highly motile cells, e.g., gliomas. We show that the diffusion-limitation parameter determines whether the growing tumor develops a smooth (noninvasive) or fingered (invasive) interface, and that the sensitivity of tumor morphology to tumor-TM surface tension increases with the size of the dimensionless diffusion-limitation parameter. For large diffusion-limitation parameters, we find a transition (missed in previous work) between dendritic structures, produced when tumor-TM surface tension is high, and seaweed-like structures, produced when tumor-TM surface tension is low. This observation leads to a direct analogy between the mathematics and dynamics of tumors and those observed in nonbiological directional solidification. Our results are also consistent with the biological observation that hypoxia promotes invasive growth of tumor cells by inducing higher levels of receptors for scatter factors that weaken cell-cell adhesion and increase cell motility. These findings suggest that tumor morphology may have value in predicting the efficiency of antiangiogenic therapy in individual patients.

Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth.

Blood vessels form either when dispersed endothelial cells (the cells lining the inner walls of fully formed blood vessels) organize into a vessel network (vasculogenesis), or by sprouting or splitting of existing blood vessels (angiogenesis). Although they are closely related biologically, no current model explains both phenomena with a single biophysical mechanism. Most computational models describe sprouting at the level of the blood vessel, ignoring how cell behavior drives branch splitting during sprouting. We present a cell-based, Glazier-Graner-Hogeweg model (also called Cellular Potts Model) simulation of the initial patterning before the vascular cords form lumens, based on plausible behaviors of endothelial cells. The endothelial cells secrete a chemoattractant, which attracts other endothelial cells. As in the classic Keller-Segel model, chemotaxis by itself causes cells to aggregate into isolated clusters. However, including experimentally observed VE-cadherin-mediated contact inhibition of chemotaxis in the simulation causes randomly distributed cells to organize into networks and cell aggregates to sprout, reproducing aspects of both de novo and sprouting blood-vessel growth. We discuss two branching instabilities responsible for our results. Cells at the surfaces of cell clusters attempting to migrate to the centers of the clusters produce a buckling instability. In a model variant that eliminates the surface-normal force, a dissipative mechanism drives sprouting, with the secreted chemical acting both as a chemoattractant and as an inhibitor of pseudopod extension. Both mechanisms would also apply if force transmission through the extracellular matrix rather than chemical signaling mediated cell-cell interactions. The branching instabilities responsible for our results, which result from contact inhibition of chemotaxis, are both generic developmental mechanisms and interesting examples of unusual patterning instabilities.