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Immunogenicity against therapeutic proteins frequently causes attrition owing to its potential impact on pharmacokinetics, pharmacodynamics, efficacy, and safety. Predicting immunogenicity is complex because of its multifactorial drivers, including compound properties, subject characteristics, and treatment parameters. To integrate these, the Immunogenicity Simulator was developed using published, predominantly late‐stage trial data from 15 therapeutic proteins. This single‐blinded evaluation with subject‐level data from 10 further monoclonals assesses the Immunogenicity Simulator's credibility for application during the drug development process. [ABSTRACT FROM AUTHOR]

In convergent-extension (CE), a planar-polarized epithelial tissue elongates (extends) in-plane in one direction while shortening (converging) in the perpendicular in-plane direction, with the cells both elongating and intercalating along the converging axis. CE occurs during the development of most multicellular organisms. Current CE models assume cell or tissue asymmetry, but neglect the preferential filopodial activity along the convergent axis observed in many tissues. We propose a cell-based CE model based on asymmetric filopodial tension forces between cells and investigate how cell-level filopodial interactions drive tissue-level CE. The final tissue geometry depends on the balance between external rounding forces and cell-intercalation traction. Filopodial-tension CE is robust to relatively high levels of planar cell polarity misalignment and to the presence of non-active cells. Addition of a simple mechanical feedback between cells fully rescues and even improves CE of tissues with high levels of polarity misalignments. Our model extends easily to three dimensions, with either one converging and two extending axes, or two converging and one extending axes, producing distinct tissue morphologies, as observed in vivo. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially sub-optimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patient-specific multi-modality treatment protocols that may increase patients quality of life. [ABSTRACT FROM AUTHOR]

Objective Insulin resistance and hyperinsulinaemia precede the onset of obesity-induced DM2. The early adaptation of the β-cell during the initial phase of overfeeding and weight gain has only been partly elucidated. We studied the early changes in insulin clearance and β-cell responsivity during a positive and negative energy balance in lean healthy men. Design We studied in nine healthy lean men [age, 37 (27-43) years; BMI, 23·6 (20·6-25·6) kg/m2] insulin sensitivity, insulin clearance, insulin secretion and static and dynamic β-cell responsivity at baseline and after the hypercaloric and subsequent hypocaloric diet. Results Participants gained 7 [5·1-7·6]% of their initial body weight on the hypercaloric diet. Compared to baseline, insulin sensitivity and insulin clearance decreased, while glucose-stimulated insulin secretion was higher. The GLP-1 response to oral glucose did not change. The dynamic β-cell responsivity index increased but the basal and static responsivity indexes did not change. Total and static disposition indexes (DIs) in the hypercaloric state showed a trend towards a decrease. During the hypocaloric diet, insulin sensitivity, glucose-stimulated insulin secretion and insulin clearance returned to baseline. The responsivity and the DIs were not different in the hypocaloric phase compared to baseline. Conclusion A positive energy balance resulting in weight gain in lean men induces hyperinsulinaemia, which is explained by a combined effect on insulin clearance and insulin secretion. Increased insulin secretion was related to insulin resistance-induced higher glucose concentrations but also to increased dynamic β-cell responsivity. Glucose sensitivity of the β-cell did not change. These early adaptations are completely reversible during a negative energy balance after loss of the gained weight. [ABSTRACT FROM AUTHOR]

Motivation: Probability distributions play a central role in mathematical and statistical modelling. The encoding, annotation and exchange of such models could be greatly simplified by a resource providing a common reference for the definition of probability distributions. Although some resources exist, no suitably detailed and complex ontology exists nor any database allowing programmatic access. Results: ProbOnto, is an ontology-based knowledge base of probability distributions, featuring more than 80 uni- and multivariate distributions with their defining functions, characteristics, relationships and re-parameterization formulas. It can be used for model annotation and facilitates the encoding of distribution-based models, related functions and quantities. [ABSTRACT FROM AUTHOR]

Abstract: A central question in developmental biology is how cells interact to organize into tissues? In this paper, we study the role of mesenchyme-ectoderm interaction in the growing chick limb bud using Glazier and Graner''s cellular Potts model, a grid-based stochastic framework designed to simulate cell interactions and movement. We simulate cellular mechanisms including cell adhesion, growth, and division and diffusion of morphogens, to show that differential adhesion between the cells, diffusion of growth factors through the extracellular matrix, and the elastic properties of the apical ectodermal ridge together can produce the proper shape of the limb bud. [Copyright &y& Elsevier]

The formerly distinct fields of lymphocyte signal transduction and cytoskeletal remodeling have recently become linked, as proteins involved in transducing signals downstream of lymphocyte antigen receptors have also been implicated in actin cytoskeleton remodeling, microtubule dynamics and regulation of cell polarity. These discoveries have fuelled interest in understanding both the role of the actin cytoskeleton as an integral component of lymphocyte activation and the interplay between lymphoid cell–cell contact sites (immunological synapse), retractile pole structures (uropod, distal pole complex), and Rho-family GTPases (Rac, Rho, Cdc42), their upstream activators (Dbl-family guanine nucleotide exchange factors) and their downstream effectors (WASp, Arp2/3, ADAP). To understand how these complex regulatory networks are wired, a new breed of computational biologists uses mathematical language to reproduce and simulate signaling circuits ‘in silico’. [Copyright &y& Elsevier]

The kinetic model of Prostaglandin H Synthase-1 (PGHS-1) was developed to investigate its complex network kinetics and non-steroidal anti-inflammatory drugs (NSAIDs) efficacy in different in vitro and in vivo conditions. To correctly describe the complex mechanism of PGHS-1 catalysis, we developed a microscopic approach to modelling of intricate network dynamics of 35 intraenzyme reactions among 24 intermediate states of the enzyme. The developed model quantitatively describes interconnection between cyclooxygenase and peroxidase enzyme activities; substrate (arachidonic acid, AA) and reducing cosubstrate competitive consumption; enzyme self-inactivation; autocatalytic role of AA; enzyme activation threshold; and synthesis of intermediate prostaglandin G2 (PGG2) and final prostaglandin H2 (PGH2) products under wide experimental conditions. In the paper, we provide a detailed description of the enzyme catalytic cycle, model calibration based on a series of in vitro kinetic data, and model validation using experimental data on the regulatory properties of PGHS-1. The validated model of PGHS-1 with a unified set of kinetic parameters is applicable for in silico screening and prediction of the inhibition effects of NSAIDs and their combination on the balance of pro-thrombotic (thromboxane) and anti-thrombotic (prostacyclin) prostaglandin biosynthesis in platelets and endothelial cells expressing PGHS-1. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this study is to build a computational model to investigate the cell dose and cell DNA damage distribution of a multicellular tissue system under the irradiation. Materials and methods: In this work, we developed a computational model for quantifying cell dose and double strand break (DSB) number in a multicellular system by simulating the radiation transport in 2D and 3D cell culture. The model was based on an open-source radiation transport package, Geant4 with Geant4-DNA physics. First, the computational multicellular system was created using a developed program, CelllMaker. Second, the radiation transport simulation for cells was conducted using Geant4 package with the Geant4-DNA physics to obtain the cellular dose and cellular DSB yield. Results: Using the method described in this work, it is possible to obtain the cellular dose and DNA damage simultaneously. The developed model provides a solution for quantifying the cellular dose and cellular DNA damage which are not easily determined in a radiobiological experiment. Conclusions: With limited validation data for the model, this preliminary study provides a roadmap for building a comprehensive toolkit for simulating cellular dose and DNA damage of multicellular tissue systems. [ABSTRACT FROM AUTHOR]

We describe a multi-scale, liver-centric in silico modeling framework for acetaminophen pharmacology and metabolism. We focus on a computational model to characterize whole body uptake and clearance, liver transport and phase I and phase II metabolism. We do this by incorporating sub-models that span three scales; Physiologically Based Pharmacokinetic (PBPK) modeling of acetaminophen uptake and distribution at the whole body level, cell and blood flow modeling at the tissue/organ level and metabolism at the sub-cellular level. We have used standard modeling modalities at each of the three scales. In particular, we have used the Systems Biology Markup Language (SBML) to create both the whole-body and sub-cellular scales. Our modeling approach allows us to run the individual sub-models separately and allows us to easily exchange models at a particular scale without the need to extensively rework the sub-models at other scales. In addition, the use of SBML greatly facilitates the inclusion of biological annotations directly in the model code. The model was calibrated using human in vivo data for acetaminophen and its sulfate and glucuronate metabolites. We then carried out extensive parameter sensitivity studies including the pairwise interaction of parameters. We also simulated population variation of exposure and sensitivity to acetaminophen. Our modeling framework can be extended to the prediction of liver toxicity following acetaminophen overdose, or used as a general purpose pharmacokinetic model for xenobiotics. [ABSTRACT FROM AUTHOR]

Motivation: Currently, there are no ontologies capable of describing both the spatial organization of groups of cells and the behaviors of those cells. The lack of a formalized method for describing the spatiality and intrinsic biological behaviors of cells makes it difficult to adequately describe cells, tissues and organs as spatial objects in living tissues, in vitro assays and in computational models of tissues.Results: We have developed an OWL-2 ontology to describe the intrinsic physical and biological characteristics of cells and tissues. The Cell Behavior Ontology (CBO) provides a basis for describing the spatial and observable behaviors of cells and extracellular components suitable for describing in vivo, in vitro and in silico multicell systems. Using the CBO, a modeler can create a meta-model of a simulation of a biological model and link that meta-model to experiment or simulation results. Annotation of a multicell model and its computational representation, using the CBO, makes the statement of the underlying biology explicit. The formal representation of such biological abstraction facilitates the validation, falsification, discovery, sharing and reuse of both models and experimental data.Availability and implementation: The CBO, developed using Protégé 4, is available at http://cbo.biocomplexity.indiana.edu/cbo/ and at BioPortal (http://bioportal.bioontology.org/ontologies/CBO).Contact: jsluka@indiana.edu or Glazier@indiana.eduSupplementary information: Supplementary data are available at Bioinformatics online. [ABSTRACT FROM PUBLISHER]

Choroidal neovascularization (CNV) of the macular area of the retina is the major cause of severe vision loss in adults. In CNV, after choriocapillaries initially penetrate Bruch's membrane (BrM), invading vessels may regress or expand (CNV initiation). Next, during Early and Late CNV, the expanding vasculature usually spreads in one of three distinct patterns: in a layer between BrM and the retinal pigment epithelium (sub-RPE or Type 1 CNV), in a layer between the RPE and the photoreceptors (subretinal or Type 2 CNV) or in both loci simultaneously (combined pattern or Type 3 CNV). While most studies hypothesize that CNV primarily results from growth-factor effects or holes in BrM, our three-dimensional simulations of multi-cell model of the normal and pathological maculae recapitulate the three growth patterns, under the hypothesis that CNV results from combinations of impairment of: 1) RPE-RPE epithelial junctional adhesion, 2) Adhesion of the RPE basement membrane complex to BrM (RPE-BrM adhesion), and 3) Adhesion of the RPE to the photoreceptor outer segments (RPE-POS adhesion). Our key findings are that when an endothelial tip cell penetrates BrM: 1) RPE with normal epithelial junctions, basal attachment to BrM and apical attachment to POS resists CNV. 2) Small holes in BrM do not, by themselves, initiate CNV. 3) RPE with normal epithelial junctions and normal apical RPE-POS adhesion, but weak adhesion to BrM (e.g. due to lipid accumulation in BrM) results in Early sub-RPE CNV. 4) Normal adhesion of RBaM to BrM, but reduced apical RPE-POS or epithelial RPE-RPE adhesion (e.g. due to inflammation) results in Early sub-retinal CNV. 5) Simultaneous reduction in RPE-RPE epithelial binding and RPEBrM adhesion results in either sub-RPE or sub-retinal CNV which often progresses to combined pattern CNV. These findings suggest that defects in adhesion dominate CNV initiation and progression. [ABSTRACT FROM AUTHOR]

In this paper we present a multiscale, individual-based simulation environment that integrates CompuCell3D for latticebased modelling on the cellular level and Bionetsolver for intracellular modelling. CompuCell3D or CC3D provides an implementation of the lattice-based Cellular Potts Model or CPM (also known as the Glazier-Graner-Hogeweg or GGH model) and a Monte Carlo method based on the metropolis algorithm for system evolution. The integration of CC3D for cellular systems with Bionetsolver for subcellular systems enables us to develop a multiscale mathematical model and to study the evolution of cell behaviour due to the dynamics inside of the cells, capturing aspects of cell behaviour and interaction that is not possible using continuum approaches. We then apply this multiscale modelling technique to a model of cancer growth and invasion, based on a previously published model of Ramis-Conde et al. (2008) where individual cell behaviour is driven by a molecular network describing the dynamics of E-cadherin and β-catenin. In this model, which we refer to as the centre-based model, an alternative individual-based modelling technique was used, namely, a lattice-free approach. In many respects, the GGH or CPM methodology and the approach of the centre-based model have the same overall goal, that is to mimic behaviours and interactions of biological cells. Although the mathematical foundations and computational implementations of the two approaches are very different, the results of the presented simulations are compatible with each other, suggesting that by using individual-based approaches we can formulate a natural way of describing complex multi-cell, multiscale models. The ability to easily reproduce results of one modelling approach using an alternative approach is also essential from a model cross-validation standpoint and also helps to identify any modelling artefacts specific to a given computational approach. [ABSTRACT FROM AUTHOR]

The actions of cell adhesion molecules, in particular, cadherins during embryonic development and morphogenesis more generally, regulate many aspects of cellular interactions, regulation and signaling. Often, a gradient of cadherin expression levels drives collective and relative cell motions generating macroscopic cell sorting. Computer simulations of cell sorting have focused on the interactions of cells with only a few discrete adhesion levels between cells, ignoring biologically observed continuous variations in expression levels and possible nonlinearities in molecular binding. In this paper, we present three models relating the surface density of cadherins to the net intercellular adhesion and interfacial tension for both discrete and continuous levels of cadherin expression. We then use then the Glazier-Graner-Hogeweg (GGH) model to investigate how variations in the distribution of the number of cadherins per cell and in the choice of binding model affect cell sorting. We find that an aggregate with a continuous variation in the level of a single type of cadherin molecule sorts more slowly than one with two levels. The rate of sorting increases strongly with the interfacial tension, which depends both on the maximum difference in number of cadherins per cell and on the binding model. Our approach helps connect signaling at the molecular level to tissue-level morphogenesis. [ABSTRACT FROM AUTHOR]

We present a computer simulation and associated experimental validation of assembly of glial-like support cells into the interweaving hexagonal lattice that spans the Drosophila pupal eye. This process of cell movements organizes the ommatidial array into a functional pattern. Unlike earlier simulations that focused on the arrangements of cells within individual ommatidia, here we examine the local movements that lead to large-scale organization of the emerging eye field. Simulations based on our experimental observations of cell adhesion, cell death, and cell movement successfully patterned a tracing of an emerging wild-type pupal eye. Surprisingly, altering cell adhesion had only a mild effect on patterning, contradicting our previous hypothesis that the patterning was primarily the result of preferential adhesion between IRMclass surface proteins. Instead, our simulations highlighted the importance of programmed cell death (PCD) as well as a previously unappreciated variable: the expansion of cells' apical surface areas, which promoted rearrangement of neighboring cells. We tested this prediction experimentally by preventing expansion in the apical area of individual cells: patterning was disrupted in a manner predicted by our simulations. Our work demonstrates the value of combining computer simulation with in vivo experiments to uncover novel mechanisms that are perpetuated throughout the eye field. It also demonstrates the utility of the Glazier-Graner-Hogeweg model (GGH) for modeling the links between local cellular interactions and emergent properties of developing epithelia as well as predicting unanticipated results in vivo. [ABSTRACT FROM AUTHOR]

Abstract: The detailed kinetic model of Prostaglandin H Synthase-1 (COX-1) was developed to in silico test and predict inhibition effects of nonsteroidal anti-inflammatory drugs (NSAIDs) on target. The model takes into account key features of the complex catalytic mechanism of cyclooxygenase-1, converting arachidonic acid to prostaglandin PGH2, and includes the description of the enzyme interaction with various types of NSAIDs (reversible/irreversible, non-selective and selective to COX-1/COX-2). Two different versions of the model were designed to simulate the inhibition of COX-1 by NSAIDs in two most popular experimental settings –in vitro studies with purified enzyme, and the experiments with platelets. The developed models were applied to calculate the dose-dependence of aspirin and celecoxib action on COX- 1 in vitro and in vivo conditions. The mechanism of the enhancement of aspirin efficiency in platelet as compared to its action on purified COX-1 was elucidated. The dose-dependence of celecoxib simulated with the use of the “in vivo” version of the model predicted potentially strong inhibitory effect of celecoxib on thromboxan production in platelets. Simulation of the combined effect of two NSAIDs, aspirin and celecoxib, on COX-1 allowed us to reveal the mechanism underlying the suppression of aspirin-mediated COX-1 inhibition by celecoxib. We discuss our modelling results in the context of the on-going debates on the potential cardio-vascular risks associated with co-administration of various types of NSAIDs. [Copyright &y& Elsevier]

B Immunogenicity is a major challenge in drug development and patient care. For example, in combination therapies, the mechanism of action of one drug could influence the immune system or the population variability of immune system components in a way that influences the immune response to a second drug. In addition to population parameters already included in Simcyp, the IG Simulator uses human leukocyte antigen (HLA) allele frequencies and variability in the immune system as a function of age or disease will soon be included. This example virtual trial simulation ( B Figure b ) demonstrates that the IG Simulator is capable of simulating clinical population of interest, with accuracy sufficient to inform IG management. [Extracted from the article]

Radiotherapy is a commonly used treatment for cancer and is usually given in varying doses. At low radiation doses relatively few cells die as a direct response to radiation but secondary radiation effects, such as DNA mutation or bystander phenomena, may affect many cells. Consequently it is at low radiation levels where an understanding of bystander effects is essential in designing novel therapies with superior clinical outcomes. In this paper, we use a hybrid multiscale mathematical model to study the direct effects of radiation as well as radiation-induced bystander effects on both tumour cells and normal cells. We show that bystander responses play a major role in mediating radiation damage to cells at low-doses of radiotherapy, doing more damage than that due to direct radiation. The survival curves derived from our computational simulations showed an area of hyper-radiosensitivity at low-doses that are not obtained using a traditional radiobiological model. [ABSTRACT FROM AUTHOR]

In ovarian cancer, metastasis is typically confined to the peritoneum. Surgical removal of the primary tumor and macroscopic secondary tumors is a common practice, but more effective strategies are needed to target microscopic spheroids persisting in the peritoneal fluid after debulking surgery. To treat this residual disease, therapeutic agents can be administered by either intravenous or intraperitoneal infusion. Here, we describe the use of a cellular Potts model to compare tumor penetration of two classes of drugs (cisplatin and pertuzumab) when delivered by these two alternative routes. The model considers the primary route when the drug is administered either intravenously or intraperitoneally, as well as the subsequent exchange into the other delivery volume as a secondary route. By accounting for these dynamics, the model revealed that intraperitoneal infusion is the markedly superior route for delivery of both small-molecule and antibody therapies into microscopic, avascular tumors typical of patients with ascites. Small tumors attached to peritoneal organs, with vascularity ranging from 2% to 10%, also show enhanced drug delivery via the intraperitoneal route, even though tumor vessels can act as sinks during the dissemination of small molecules. Furthermore, we assessed the ability of the antibody to enter the tumor by in silico and in vivo methods and suggest that optimization of antibody delivery is an important criterion underlying the efficacy of these and other biologics. The use of both delivery routes may provide the best total coverage of tumors, depending on their size and vascularity. [ABSTRACT FROM AUTHOR]

Motivation: This article presents libRoadRunner, an extensible, high-performance, cross-platform, open-source software library for the simulation and analysis of models expressed using Systems Biology Markup Language (SBML). SBML is the most widely used standard for representing dynamic networks, especially biochemical networks. libRoadRunner is fast enough to support large-scale problems such as tissue models, studies that require large numbers of repeated runs and interactive simulations. Results: libRoadRunner is a self-contained library, able to run both as a component inside other tools via its C++ and C bindings, and interactively through its Python interface. Its Python Application Programming Interface (API) is similar to the APIs of MATLAB (www.mathworks.com) and SciPy (http://www.scipy.org/), making it fast and easy to learn. libRoadRunner uses a custom Just-In-Time (JIT) compiler built on the widely used LLVM JIT compiler framework. It compiles SBML-specified models directly into native machine code for a variety of processors, making it appropriate for solving extremely large models or repeated runs. libRoadRunner is flexible, supporting the bulk of the SBML specification (except for delay and non-linear algebraic equations) including several SBML extensions (composition and distributions). It offers multiple deterministic and stochastic integrators, as well as tools for steady-state analysis, stability analysis and structural analysis of the stoichiometric matrix. Availability and implementation: libRoadRunner binary distributions are available for Mac OS X, Linux and Windows. The library is licensed under Apache License Version 2.0. libRoadRunner is also available for ARM-based computers such as the Raspberry Pi. http://www.libroadrunner.org provides online documentation, full build instructions, binaries and a git source repository. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 lineargrowth 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]