An agent-based modeling approach for lung fibrosis in response to COVID-19.

The severity of the COVID-19 pandemic has created an emerging need to investigate the long-term effects of infection on patients. Many individuals are at risk of suffering pulmonary fibrosis due to the pathogenesis of lung injury and impairment in the healing mechanism. Fibroblasts are the central mediators of extracellular matrix (ECM) deposition during tissue regeneration, regulated by anti-inflammatory cytokines including transforming growth factor beta (TGF-ß). The TGF-ß-dependent accumulation of fibroblasts at the damaged site and excess fibrillar collagen deposition lead to fibrosis. We developed an open-source, multiscale tissue simulator to investigate the role of TGF-ß sources in the progression of lung fibrosis after SARS-CoV-2 exposure, intracellular viral replication, infection of epithelial cells, and host immune response. Using the model, we predicted the dynamics of fibroblasts, TGF-ß, and collagen deposition for 15 days post-infection in virtual lung tissue. Our results showed variation in collagen area fractions between 2% and 40% depending on the spatial behavior of the sources (stationary or mobile), the rate of activation of TGF-ß, and the duration of TGF-ß sources. We identified M2 macrophages as primary contributors to higher collagen area fraction. Our simulation results also predicted fibrotic outcomes even with lower collagen area fraction when spatially-localized latent TGF-ß sources were active for longer times. We validated our model by comparing simulated dynamics for TGF-ß, collagen area fraction, and macrophage cell population with independent experimental data from mouse models. Our results showed that partial removal of TGF-ß sources changed the fibrotic patterns; in the presence of persistent TGF-ß sources, partial removal of TGF-ß from the ECM significantly increased collagen area fraction due to maintenance of chemotactic gradients driving fibroblast movement. The computational findings are consistent with independent experimental and clinical observations of collagen area fractions and cell population dynamics not used in developing the model. These critical insights into the activity of TGF-ß sources may find applications in the current clinical trials targeting TGF-ß for the resolution of lung fibrosis.

Elucidating tumor-stromal metabolic crosstalk in colorectal cancer through integration of constraint-based models and LC-MS metabolomics.

Colorectal cancer (CRC) is a major cause of morbidity and mortality in the United States. Tumor-stromal metabolic crosstalk in the tumor microenvironment promotes CRC development and progression, but exactly how stromal cells, in particular cancer-associated fibroblasts (CAFs), affect the metabolism of tumor cells remains unknown. Here we take a data-driven approach to investigate the metabolic interactions between CRC cells and CAFs, integrating constraint-based modeling and metabolomic profiling. Using metabolomics data, we perform unsteady-state parsimonious flux balance analysis to infer flux distributions for central carbon metabolism in CRC cells treated with or without CAF-conditioned media. We find that CAFs reprogram CRC metabolism through stimulation of glycolysis, the oxidative arm of the pentose phosphate pathway (PPP), and glutaminolysis, as well as inhibition of the tricarboxylic acid cycle. To identify potential therapeutic targets, we simulate enzyme knockouts and find that CAF-treated CRC cells are especially sensitive to inhibitions of hexokinase and glucose-6-phosphate, the rate limiting steps of glycolysis and oxidative PPP. Our work gives mechanistic insights into the metabolic interactions between CRC cells and CAFs and provides a framework for testing hypotheses towards CRC-targeted therapies.

OrgDyn: feature- and model-based characterization of spatial and temporal organoid dynamics.

SUMMARY: Organoid model systems recapitulate key features of mammalian tissues and enable high throughput experiments. However, the impact of these experiments may be limited by manual, non-standardized, static or qualitative phenotypic analysis. OrgDyn is an open-source and modular pipeline to quantify organoid shape dynamics using a combination of feature- and model-based approaches on time series of 2D organoid contour images. Our pipeline consists of (i) geometrical and signal processing feature extraction, (ii) dimensionality reduction to differentiate dynamical paths, (iii) time series clustering to identify coherent groups of organoids and (iv) dynamical modeling using point distribution models to explain temporal shape variation. OrgDyn can characterize, cluster and model differences among unique dynamical paths that define diverse final shapes, thus enabling quantitative analysis of the molecular basis of tissue development and disease. AVAILABILITY AND IMPLEMENTATION: https://github.com/zakih/organoidDynamics (BSD 3-Clause License). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

PhysiBoSS: a multi-scale agent-based modelling framework integrating physical dimension and cell signalling.

MOTIVATION: Due to the complexity and heterogeneity of multicellular biological systems, mathematical models that take into account cell signalling, cell population behaviour and the extracellular environment are particularly helpful. We present PhysiBoSS, an open source software which combines intracellular signalling using Boolean modelling (MaBoSS) and multicellular behaviour using agent-based modelling (PhysiCell). RESULTS: PhysiBoSS provides a flexible and computationally efficient framework to explore the effect of environmental and genetic alterations of individual cells at the population level, bridging the critical gap from single-cell genotype to single-cell phenotype and emergent multicellular behaviour. PhysiBoSS thus becomes very useful when studying heterogeneous population response to treatment, mutation effects, different modes of invasion or isomorphic morphogenesis events. To concretely illustrate a potential use of PhysiBoSS, we studied heterogeneous cell fate decisions in response to TNF treatment. We explored the effect of different treatments and the behaviour of several resistant mutants. We highlighted the importance of spatial information on the population dynamics by considering the effect of competition for resources like oxygen. AVAILABILITY AND IMPLEMENTATION: PhysiBoSS is freely available on GitHub (https://github.com/sysbio-curie/PhysiBoSS), with a Docker image (https://hub.docker.com/r/gletort/physiboss/). It is distributed as open source under the BSD 3-clause license. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

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.

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

Many multicellular systems problems can only be understood by studying how cells move, grow, divide, interact, and die. Tissue-scale dynamics emerge from systems of many interacting cells as they respond to and influence their microenvironment. The ideal "virtual laboratory" for such multicellular systems simulates both the biochemical microenvironment (the "stage") and many mechanically and biochemically interacting cells (the "players" upon the stage). PhysiCell-physics-based multicellular simulator-is an open source agent-based simulator that provides both the stage and the players for studying many interacting cells in dynamic tissue microenvironments. It builds upon a multi-substrate biotransport solver to link cell phenotype to multiple diffusing substrates and signaling factors. It includes biologically-driven sub-models for cell cycling, apoptosis, necrosis, solid and fluid volume changes, mechanics, and motility "out of the box." The C++ code has minimal dependencies, making it simple to maintain and deploy across platforms. PhysiCell has been parallelized with OpenMP, and its performance scales linearly with the number of cells. Simulations up to 105-106 cells are feasible on quad-core desktop workstations; larger simulations are attainable on single HPC compute nodes. We demonstrate PhysiCell by simulating the impact of necrotic core biomechanics, 3-D geometry, and stochasticity on the dynamics of hanging drop tumor spheroids and ductal carcinoma in situ (DCIS) of the breast. We demonstrate stochastic motility, chemical and contact-based interaction of multiple cell types, and the extensibility of PhysiCell with examples in synthetic multicellular systems (a "cellular cargo delivery" system, with application to anti-cancer treatments), cancer heterogeneity, and cancer immunology. PhysiCell is a powerful multicellular systems simulator that will be continually improved with new capabilities and performance improvements. It also represents a significant independent code base for replicating results from other simulation platforms. The PhysiCell source code, examples, documentation, and support are available under the BSD license at http://PhysiCell.MathCancer.org and http://PhysiCell.sf.net.

High-throughput cancer hypothesis testing with an integrated PhysiCell-EMEWS workflow.

BACKGROUND: Cancer is a complex, multiscale dynamical system, with interactions between tumor cells and non-cancerous host systems. Therapies act on this combined cancer-host system, sometimes with unexpected results. Systematic investigation of mechanistic computational models can augment traditional laboratory and clinical studies, helping identify the factors driving a treatment's success or failure. However, given the uncertainties regarding the underlying biology, these multiscale computational models can take many potential forms, in addition to encompassing high-dimensional parameter spaces. Therefore, the exploration of these models is computationally challenging. We propose that integrating two existing technologies-one to aid the construction of multiscale agent-based models, the other developed to enhance model exploration and optimization-can provide a computational means for high-throughput hypothesis testing, and eventually, optimization. RESULTS: In this paper, we introduce a high throughput computing (HTC) framework that integrates a mechanistic 3-D multicellular simulator (PhysiCell) with an extreme-scale model exploration platform (EMEWS) to investigate high-dimensional parameter spaces. We show early results in applying PhysiCell-EMEWS to 3-D cancer immunotherapy and show insights on therapeutic failure. We describe a generalized PhysiCell-EMEWS workflow for high-throughput cancer hypothesis testing, where hundreds or thousands of mechanistic simulations are compared against data-driven error metrics to perform hypothesis optimization. CONCLUSIONS: While key notational and computational challenges remain, mechanistic agent-based models and high-throughput model exploration environments can be combined to systematically and rapidly explore key problems in cancer. These high-throughput computational experiments can improve our understanding of the underlying biology, drive future experiments, and ultimately inform clinical practice.

BioFVM: an efficient, parallelized diffusive transport solver for 3-D biological simulations.

MOTIVATION: Computational models of multicellular systems require solving systems of PDEs for release, uptake, decay and diffusion of multiple substrates in 3D, particularly when incorporating the impact of drugs, growth substrates and signaling factors on cell receptors and subcellular systems biology. RESULTS: We introduce BioFVM, a diffusive transport solver tailored to biological problems. BioFVM can simulate release and uptake of many substrates by cell and bulk sources, diffusion and decay in large 3D domains. It has been parallelized with OpenMP, allowing efficient simulations on desktop workstations or single supercomputer nodes. The code is stable even for large time steps, with linear computational cost scalings. Solutions are first-order accurate in time and second-order accurate in space. The code can be run by itself or as part of a larger simulator. AVAILABILITY AND IMPLEMENTATION: BioFVM is written in C ++ with parallelization in OpenMP. It is maintained and available for download at http://BioFVM.MathCancer.org and http://BioFVM.sf.net under the Apache License (v2.0). CONTACT: paul.macklin@usc.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Progress Towards Computational 3-D Multicellular Systems Biology.

Tumors cannot be understood in isolation from their microenvironment. Tumor and stromal cells change phenotype based upon biochemical and biophysical inputs from their surroundings, even as they interact with and remodel the microenvironment. Cancer should be investigated as an adaptive, multicellular system in a dynamical microenvironment. Computational modeling offers the potential to detangle this complex system, but the modeling platform must ideally account for tumor heterogeneity, substrate and signaling factor biotransport, cell and tissue biophysics, tissue and vascular remodeling, microvascular and interstitial flow, and links between all these sub-systems. Such a platform should leverage high-throughput experimental data, while using open data standards for reproducibility. In this chapter, we review advances by our groups in these key areas, particularly in advanced models of tissue mechanics and interstitial flow, open source simulation software, high-throughput phenotypic screening, and multicellular data standards. In the future, we expect a transformation of computational cancer biology from individual groups modeling isolated parts of cancer, to coalitions of groups combining compatible tools to simulate the 3-D multicellular systems biology of cancer tissues.

A review of mechanistic learning in mathematical oncology.

Mechanistic learning refers to the synergistic combination of mechanistic mathematical modeling and data-driven machine or deep learning. This emerging field finds increasing applications in (mathematical) oncology. This review aims to capture the current state of the field and provides a perspective on how mechanistic learning may progress in the oncology domain. We highlight the synergistic potential of mechanistic learning and point out similarities and differences between purely data-driven and mechanistic approaches concerning model complexity, data requirements, outputs generated, and interpretability of the algorithms and their results. Four categories of mechanistic learning (sequential, parallel, extrinsic, intrinsic) of mechanistic learning are presented with specific examples. We discuss a range of techniques including physics-informed neural networks, surrogate model learning, and digital twins. Example applications address complex problems predominantly from the domain of oncology research such as longitudinal tumor response predictions or time-to-event modeling. As the field of mechanistic learning advances, we aim for this review and proposed categorization framework to foster additional collaboration between the data- and knowledge-driven modeling fields. Further collaboration will help address difficult issues in oncology such as limited data availability, requirements of model transparency, and complex input data which are embraced in a mechanistic learning framework.

Drug-loaded nanoparticles for cancer therapy: a high-throughput multicellular agent-based modeling study.

Interactions between biological systems and nanomaterials have become an important area of study due to the application of nanomaterials in medicine. In particular, the application of nanomaterials for cancer diagnosis or treatment presents a challenging opportunity due to the complex biology of this disease spanning multiple time and spatial scales. A system-level analysis would benefit from mathematical modeling and computational simulation to explore the interactions between anticancer drug-loaded nanoparticles (NPs), cells, and tissues, and the associated parameters driving this system and a patient's overall response. Although a number of models have explored these interactions in the past, few have focused on simulating individual cell-NP interactions. This study develops a multicellular agent-based model of cancer nanotherapy that simulates NP internalization, drug release within the cell cytoplasm, "inheritance" of NPs by daughter cells at cell division, cell pharmacodynamic response to the intracellular drug, and overall drug effect on tumor dynamics. A large-scale parallel computational framework is used to investigate the impact of pharmacokinetic design parameters (NP internalization rate, NP decay rate, anticancer drug release rate) and therapeutic strategies (NP doses and injection frequency) on the tumor dynamics. In particular, through the exploration of NP "inheritance" at cell division, the results indicate that cancer treatment may be improved when NPs are inherited at cell division for cytotoxic chemotherapy. Moreover, smaller dosage of cytostatic chemotherapy may also improve inhibition of tumor growth when cell division is not completely inhibited. This work suggests that slow delivery by "heritable" NPs can drive new dimensions of nanotherapy design for more sustained therapeutic response.

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

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

Merging Metabolic Modeling and Imaging for Screening Therapeutic Targets in Colorectal Cancer.

Cancer-associated fibroblasts (CAFs) play a key role in metabolic reprogramming and are well-established contributors to drug resistance in colorectal cancer (CRC). To exploit this metabolic crosstalk, we integrated a systems biology approach that identified key metabolic targets in a data-driven method and validated them experimentally. This process involved high-throughput computational screening to investigate the effects of enzyme perturbations predicted by a computational model of CRC metabolism to understand system-wide effects efficiently. Our results highlighted hexokinase (HK) as one of the crucial targets, which subsequently became our focus for experimental validation using patient-derived tumor organoids (PDTOs). Through metabolic imaging and viability assays, we found that PDTOs cultured in CAF conditioned media exhibited increased sensitivity to HK inhibition. Our approach emphasizes the critical role of integrating computational and experimental techniques in exploring and exploiting CRC-CAF crosstalk.

Forum on immune digital twins: a meeting report.

Medical digital twins are computational models of human biology relevant to a given medical condition, which are tailored to an individual patient, thereby predicting the course of disease and individualized treatments, an important goal of personalized medicine. The immune system, which has a central role in many diseases, is highly heterogeneous between individuals, and thus poses a major challenge for this technology. In February 2023, an international group of experts convened for two days to discuss these challenges related to immune digital twins. The group consisted of clinicians, immunologists, biologists, and mathematical modelers, representative of the interdisciplinary nature of medical digital twin development. A video recording of the entire event is available. This paper presents a synopsis of the discussions, brief descriptions of ongoing digital twin projects at different stages of progress. It also proposes a 5-year action plan for further developing this technology. The main recommendations are to identify and pursue a small number of promising use cases, to develop stimulation-specific assays of immune function in a clinical setting, and to develop a database of existing computational immune models, as well as advanced modeling technology and infrastructure.

Toward mechanistic medical digital twins: some use cases in immunology.

A fundamental challenge for personalized medicine is to capture enough of the complexity of an individual patient to determine an optimal way to keep them healthy or restore their health. This will require personalized computational models of sufficient resolution and with enough mechanistic information to provide actionable information to the clinician. Such personalized models are increasingly referred to as medical digital twins. Digital twin technology for health applications is still in its infancy, and extensive research and development is required. This article focuses on several projects in different stages of development that can lead to specific-and practical-medical digital twins or digital twin modeling platforms. It emerged from a two-day forum on problems related to medical digital twins, particularly those involving an immune system component. Open access video recordings of the forum discussions are available.

An agent-based modeling approach for lung fibrosis in response to COVID-19.

The severity of the COVID-19 pandemic has created an emerging need to investigate the long-term effects of infection on patients. Many individuals are at risk of suffering pulmonary fibrosis due to the pathogenesis of lung injury and impairment in the healing mechanism. Fibroblasts are the central mediators of extracellular matrix (ECM) deposition during tissue regeneration, regulated by anti-inflammatory cytokines including transforming growth factor beta (TGF-ß). The TGF-ß-dependent accumulation of fibroblasts at the damaged site and excess fibrillar collagen deposition lead to fibrosis. We developed an open-source, multiscale tissue simulator to investigate the role of TGF-ß sources in the progression of lung fibrosis after SARS-CoV-2 exposure, intracellular viral replication, infection of epithelial cells, and host immune response. Using the model, we predicted the dynamics of fibroblasts, TGF-ß, and collagen deposition for 15 days post-infection in virtual lung tissue. Our results showed variation in collagen area fractions between 2% and 40% depending on the spatial behavior of the sources (stationary or mobile), the rate of activation of TGF-ß, and the duration of TGF-ß sources. We identified M2 macrophages as primary contributors to higher collagen area fraction. Our simulation results also predicted fibrotic outcomes even with lower collagen area fraction when spatially-localized latent TGF-ß sources were active for longer times. We validated our model by comparing simulated dynamics for TGF-ß, collagen area fraction, and macrophage cell population with independent experimental data from mouse models. Our results showed that partial removal of TGF-ß sources changed the fibrotic patterns; in the presence of persistent TGF-ß sources, partial removal of TGF-ß from the ECM significantly increased collagen area fraction due to maintenance of chemotactic gradients driving fibroblast movement. The computational findings are consistent with independent experimental and clinical observations of collagen area fractions and cell population dynamics not used in developing the model. These critical insights into the activity of TGF-ß sources may find applications in the current clinical trials targeting TGF-ß for the resolution of lung fibrosis. Author summary: COVID-19 survivors are at risk of lung fibrosis as a long-term effect. Lung fibrosis is the excess deposition of tissue materials in the lung that hinder gas exchange and can collapse the whole organ. We identified TGF-ß as a critical regulator of fibrosis. We built a model to investigate the mechanisms of TGF-ß sources in the process of fibrosis. Our results showed spatial behavior of sources (stationary or mobile) and their activity (activation rate of TGF-ß, longer activation of sources) could lead to lung fibrosis. Current clinical trials for fibrosis that target TGF-ß need to consider TGF-ß sources' spatial properties and activity to develop better treatment strategies.

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

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

Digitize your Biology! Modeling multicellular systems through interpretable cell behavior.

Cells are fundamental units of life, constantly interacting and evolving as dynamical systems. While recent spatial multi-omics can quantitate individual cells' characteristics and regulatory programs, forecasting their evolution ultimately requires mathematical modeling. We develop a conceptual framework-a cell behavior hypothesis grammar-that uses natural language statements (cell rules) to create mathematical models. This allows us to systematically integrate biological knowledge and multi-omics data to make them computable. We can then perform virtual "thought experiments" that challenge and extend our understanding of multicellular systems, and ultimately generate new testable hypotheses. In this paper, we motivate and describe the grammar, provide a reference implementation, and demonstrate its potential through a series of examples in tumor biology and immunotherapy. Altogether, this approach provides a bridge between biological, clinical, and systems biology researchers for mathematical modeling of biological systems at scale, allowing the community to extrapolate from single-cell characterization to emergent multicellular behavior.

Multiscale cancer modeling.

Simulating cancer behavior across multiple biological scales in space and time, i.e., multiscale cancer modeling, is increasingly being recognized as a powerful tool to refine hypotheses, focus experiments, and enable more accurate predictions. A growing number of examples illustrate the value of this approach in providing quantitative insights in the initiation, progression, and treatment of cancer. In this review, we introduce the most recent and important multiscale cancer modeling works that have successfully established a mechanistic link between different biological scales. Biophysical, biochemical, and biomechanical factors are considered in these models. We also discuss innovative, cutting-edge modeling methods that are moving predictive multiscale cancer modeling toward clinical application. Furthermore, because the development of multiscale cancer models requires a new level of collaboration among scientists from a variety of fields such as biology, medicine, physics, mathematics, engineering, and computer science, an innovative Web-based infrastructure is needed to support this growing community.

Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): from microscopic measurements to macroscopic predictions of clinical progression.

Ductal carcinoma in situ (DCIS)--a significant precursor to invasive breast cancer--is typically diagnosed as microcalcifications in mammograms. However, the effective use of mammograms and other patient data to plan treatment has been restricted by our limited understanding of DCIS growth and calcification. We develop a mechanistic, agent-based cell model and apply it to DCIS. Cell motion is determined by a balance of biomechanical forces. We use potential functions to model interactions with the basement membrane and amongst cells of unequal size and phenotype. Each cell's phenotype is determined by genomic/proteomic- and microenvironment-dependent stochastic processes. Detailed "sub-models" describe cell volume changes during proliferation and necrosis; we are the first to account for cell calcification. We introduce the first patient-specific calibration method to fully constrain the model based upon clinically-accessible histopathology data. After simulating 45 days of solid-type DCIS with comedonecrosis, the model predicts: necrotic cell lysis acts as a biomechanical stress relief and is responsible for the linear DCIS growth observed in mammography; the rate of DCIS advance varies with the duct radius; the tumour grows 7-10mm per year--consistent with mammographic data; and the mammographic and (post-operative) pathologic sizes are linearly correlated--in quantitative agreement with the clinical literature. Patient histopathology matches the predicted DCIS microstructure: an outer proliferative rim surrounds a stratified necrotic core with nuclear debris on its outer edge and calcification in the centre. This work illustrates that computational modelling can provide new insight on the biophysical underpinnings of cancer. It may 1-day be possible to augment a patient's mammography and other imaging with rigorously-calibrated models that help select optimal surgical margins based upon the patient's histopathologic data.