Module-based multiscale simulation of angiogenesis in skeletal muscle

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

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

Simulation of Angiogenesis in Three Dimensions: Development of the Retinal Circulation

A theoretical model is used to describe the three-dimensional development of the retinal circulation in the human eye, which occurs after the initial spread of vasculature across the inner surface of the retina. In the model, random sprouting angiogenesis is driven by a growth factor that is produced in tissue at a rate dependent on oxygen level and diffuses to existing vessels. Vessel sprouts connect to form pathways for blood flow and undergo remodeling and pruning. These processes are controlled by known or hypothesized vascular responses to hemodynamic and biochemical stimuli, including conducted responses along vessel walls. The model shows regression of arterio-venous connections on the surface of the retina, allowing perfusion of the underlying tissue. A striking feature of the retinal circulation is the formation of two vascular plexuses located at the inner and outer surfaces of the inner nuclear layer within the retina. The model is used to test hypotheses regarding the formation of these structures. A mechanism based on local production and diffusion of growth factor is shown to be ineffective. However, sprout guidance by localized structures on the boundaries of the inner nuclear layer can account for plexus formation. The resulting networks have vascular density, perfusion and oxygen transport characteristics consistent with observed properties. The model shows how stochastic generation of vascular sprouts combined with a set of biologically based response mechanisms can lead to the generation of a specialized three-dimensional vascular structure with a high degree of organization.

Dynamic Multiscale Regulation of Perfusion Recovery in Experimental Peripheral Arterial Disease: A Mechanistic Computational Model

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A first-of-a-kind systems biology computational model is presented that describes multiscale regulation of perfusion recovery in experimental peripheral arterial disease.

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Multilevel model calibration and validation enable high-resolution model simulations for experimental peripheral arterial disease (mouse HLI).

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An integrative model-based mechanistic characterization of the intracellular, cellular, and tissue-level features critical for the dynamic reconstitution of perfusion following different patterns of occlusion-induced ischemia in HLI is described.

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Using a model-based virtual HLI mouse population, pharmacologic inhibition of cell necrosis is predicted as a strategy with high therapeutic potential to improve perfusion recovery; in real HLI mice, the positive impact of this new strategy is then experimentally studied and confirmed.

In peripheral arterial disease (PAD), the degree of endogenous capacity to modulate revascularization of limb muscle is central to the management of leg ischemia. To characterize the multiscale and multicellular nature of revascularization in PAD, we have developed the first computational systems biology model that mechanistically incorporates intracellular, cellular, and tissue-level features critical for the dynamic reconstitution of perfusion after occlusion-induced ischemia. The computational model was specifically formulated for a preclinical animal model of PAD (mouse hindlimb ischemia [HLI]), and it has gone through multilevel model calibration and validation against a comprehensive set of experimental data so that it accurately captures the complex cellular signaling, cell–cell communication, and function during post-HLI perfusion recovery. As an example, our model simulations generated a highly detailed description of the time-dependent spectrum-like macrophage phenotypes in HLI, and through model sensitivity analysis we identified key cellular processes with potential therapeutic significance in the pathophysiology of PAD. Furthermore, we computationally evaluated the in vivo effects of different targeted interventions on post-HLI tissue perfusion recovery in a model-based, data-driven, virtual mouse population and experimentally confirmed the therapeutic effect of a novel model-predicted intervention in real HLI mice. This novel multiscale model opens up a new avenue to use integrative systems biology modeling to facilitate translational research in PAD.

Systems biology of angiogenesis signaling: Computational models and omics

Angiogenesis is a highly regulated multiscale process that involves a plethora of cells, their cellular signal transduction, activation, proliferation, differentiation, as well as their intercellular communication. The coordinated execution and integration of such complex signaling programs is critical for physiological angiogenesis to take place in normal growth, development, exercise, and wound healing, while its dysregulation is critically linked to many major human diseases such as cancer, cardiovascular diseases, and ocular disorders; it is also crucial in regenerative medicine. Although huge efforts have been devoted to drug development for these diseases by investigation of angiogenesis‐targeted therapies, only a few therapeutics and targets have proved effective in humans due to the innate multiscale complexity and nonlinearity in the process of angiogenic signaling. As a promising approach that can help better address this challenge, systems biology modeling allows the integration of knowledge across studies and scales and provides a powerful means to mechanistically elucidate and connect the individual molecular and cellular signaling components that function in concert to regulate angiogenesis. In this review, we summarize and discuss how systems biology modeling studies, at the pathway‐, cell‐, tissue‐, and whole body‐levels, have advanced our understanding of signaling in angiogenesis and thereby delivered new translational insights for human diseases.

This article is categorized under:

Cardiovascular Diseases > Computational Models

Cancer > Computational Models

Modeling acute and chronic vascular responses to a major arterial occlusion

OBJECTIVE

To incorporate chronic vascular adaptations into a mathematical model of the rat hindlimb to simulate flow restoration following total occlusion of the femoral artery.

METHODS

A vascular wall mechanics model is used to simulate acute and chronic vascular adaptations in the collateral arteries and collateral-dependent arterioles of the rat hindlimb. On an acute timeframe, the vascular tone of collateral arteries and distal arterioles is determined by responses to pressure, shear stress, and metabolic demand. On a chronic timeframe, sustained dilation of arteries and arterioles induces outward vessel remodeling represented by increased passive vessel diameter (arteriogenesis), and low venous oxygen saturation levels induce the growth of new capillaries represented by increased capillary number (angiogenesis).

RESULTS

The model predicts that flow compensation to an occlusion is enhanced primarily by arteriogenesis of the collateral arteries on a chronic time frame. Blood flow autoregulation is predicted to be disrupted and to occur for higher pressure values following femoral arterial occlusion.

CONCLUSIONS

Structural adaptation of the vasculature allows for increased blood flow to the collateral-dependent region after occlusion. Although flow is still below pre-occlusion levels, model predictions indicate that interventions which enhance collateral arteriogenesis would have the greatest potential for restoring flow.

Simulation of angiogenesis in three dimensions: Application to cerebral cortex

The vasculature is a dynamic structure, growing and regressing in response to embryonic development, growth, changing physiological demands, wound healing, tumor growth and other stimuli. At the microvascular level, network geometry is not predetermined, but emerges as a result of biological responses of each vessel to the stimuli that it receives. These responses may be summarized as angiogenesis, remodeling and pruning. Previous theoretical simulations have shown how two-dimensional vascular patterns generated by these processes in the mesentery are consistent with experimental observations. During early development of the brain, a mesh-like network of vessels is formed on the surface of the cerebral cortex. This network then forms branches into the cortex, forming a three-dimensional network throughout its thickness. Here, a theoretical model is presented for this process, based on known or hypothesized vascular response mechanisms together with experimentally obtained information on the structure and hemodynamics of the mouse cerebral cortex. According to this model, essential components of the system include sensing of oxygen levels in the midrange of partial pressures and conducted responses in vessel walls that propagate information about metabolic needs of the tissue to upstream segments of the network. The model provides insights into the effects of deficits in vascular response mechanisms, and can be used to generate physiologically realistic microvascular network structures.

Sex differences in cancer mechanisms

We now know that cancer is many different diseases, with great variation even within a single histological subtype. With the current emphasis on developing personalized approaches to cancer treatment, it is astonishing that we have not yet systematically incorporated the biology of sex differences into our paradigms for laboratory and clinical cancer research. While some sex differences in cancer arise through the actions of circulating sex hormones, other sex differences are independent of estrogen, testosterone, or progesterone levels. Instead, these differences are the result of sexual differentiation, a process that involves genetic and epigenetic mechanisms, in addition to acute sex hormone actions. Sexual differentiation begins with fertilization and continues beyond menopause. It affects virtually every body system, resulting in marked sex differences in such areas as growth, lifespan, metabolism, and immunity, all of which can impact on cancer progression, treatment response, and survival. These organismal level differences have correlates at the cellular level, and thus, males and females can fundamentally differ in their protections and vulnerabilities to cancer, from cellular transformation through all stages of progression, spread, and response to treatment. Our goal in this review is to cover some of the robust sex differences that exist in core cancer pathways and to make the case for inclusion of sex as a biological variable in all laboratory and clinical cancer research. We finish with a discussion of lab- and clinic-based experimental design that should be used when testing whether sex matters and the appropriate statistical models to apply in data analysis for rigorous evaluations of potential sex effects. It is our goal to facilitate the evaluation of sex differences in cancer in order to improve outcomes for all patients.

Single-Cell Receptor Quantification of an In Vitro Coculture Angiogenesis Model Reveals VEGFR, NRP1, Tie2, and PDGFR Regulation and Endothelial Heterogeneity

Angiogenesis, the formation of new blood vessels from pre-existing ones, is essential for both normal development and numerous pathologies. Systems biology has offered a unique approach to study angiogenesis by profiling tyrosine kinase receptors (RTKs) that regulate angiogenic processes and computationally modeling RTK signaling pathways. Historically, this systems biology approach has been applied on ex vivo angiogenesis assays, however, these assays are difficult to quantify and limited in their potential of temporal analysis. In this study, we adopted a simple two-dimensional angiogenesis assay comprised of human umbilical vein endothelial cells (HUVECs) and human dermal fibroblasts (HDFs) and examined temporal dynamics of a panel of six RTKs and cell heterogeneity up to 17 days. We observed ~2700 VEGFR1 (vascular endothelial growth factor receptor 1) per cell on 24-h-old cocultured HDF plasma membranes, which do not express VEGFR when cultured alone. We observed 4000–8100 VEGFR2 per cell on cocultured HUVEC plasma membranes throughout endothelial tube formation. We showed steady increase of platelet-derived growth factor receptors (PDGFRs) on cocultured HDF plasma membranes, and more interestingly, 1900–2900 PDGFRβ per plasma membrane were found on HUVECs within the first six hours of coculturing. These quantitative findings will offer us insights into molecular regulation during angiogenesis and help assess in vitro tube formation models and their physiological relevance.

Agent-based modeling of morphogenetic systems: Advantages and challenges

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

The importance of geometry in the corneal micropocket angiogenesis assay

The corneal micropocket angiogenesis assay is an experimental protocol for studying vessel network formation, or neovascularization, in vivo. The assay is attractive due to the ease with which the developing vessel network can be observed in the same animal over time. Measurements from the assay have been used in combination with mathematical modeling to gain insights into the mechanisms of angiogenesis. While previous modeling studies have adopted planar domains to represent the assay, the hemispherical shape of the cornea and asymmetric positioning of the angiogenic source can be seen to affect vascular patterning in experimental images. As such, we aim to better understand: i) how the geometry of the assay influences vessel network formation and ii) how to relate observations from planar domains to those in the hemispherical cornea. To do so, we develop a three-dimensional, off-lattice mathematical model of neovascularization in the cornea, using a spatially resolved representation of the assay for the first time. Relative to the detailed model, we predict that the adoption of planar geometries has a noticeable impact on vascular patterning, leading to increased vessel 'merging', or anastomosis, in particular when circular geometries are adopted. Significant differences in the dynamics of diffusible aniogenesis simulators are also predicted between different domains. In terms of comparing predictions across domains, the 'distance of the vascular front to the limbus' metric is found to have low sensitivity to domain choice, while metrics such as densities of tip cells and vessels and 'vascularized fraction' are sensitive to domain choice. Given the widespread adoption and attractive simplicity of planar tissue domains, both in silico and in vitro, the differences identified in the present study should prove useful in relating the results of previous and future theoretical studies of neovascularization to in vivo observations in the cornea.

Agent-based modeling of the interaction between CD8+ T cells and Beta cells in type 1 diabetes

We propose an agent-based model for the simulation of the autoimmune response in T1D. The model incorporates cell behavior from various rules derived from the current literature and is implemented on a high-performance computing system, which enables the simulation of a significant portion of the islets in the mouse pancreas. Simulation results indicate that the model is able to capture the trends that emerge during the progression of the autoimmunity. The multi-scale nature of the model enables definition of rules or equations that govern cellular or sub-cellular level phenomena and observation of the outcomes at the tissue scale. It is expected that such a model would facilitate in vivo clinical studies through rapid testing of hypotheses and planning of future experiments by providing insight into disease progression at different scales, some of which may not be obtained easily in clinical studies. Furthermore, the modular structure of the model simplifies tasks such as the addition of new cell types, and the definition or modification of different behaviors of the environment and the cells with ease.

Image-based modelling of skeletal muscle oxygenation

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, in particular for skeletal muscle during exercise. Disease is often associated with both an inhibition of the microvascular supply capability and is thought to relate to changes in the structure of blood vessel networks. Different methods exist to investigate the influence of the microvascular structure on tissue oxygenation, varying over a range of application areas, i.e. biological in vivo and in vitro experiments, imaging and mathematical modelling. Ideally, all of these methods should be combined within the same framework in order to fully understand the processes involved. This review discusses the mathematical models of skeletal muscle oxygenation currently available that are based upon images taken of the muscle microvasculature in vivo and ex vivo Imaging systems suitable for capturing the blood vessel networks are discussed and respective contrasting methods presented. The review further informs the association between anatomical characteristics in health and disease. With this review we give the reader a tool to understand and establish the workflow of developing an image-based model of skeletal muscle oxygenation. Finally, we give an outlook for improvements needed for measurements and imaging techniques to adequately investigate the microvascular capability for oxygen exchange.

Microvessel Chaste: An Open Library for Spatial Modeling of Vascularized Tissues

Spatial models of vascularized tissues are widely used in computational physiology. We introduce a software library for composing multiscale, multiphysics models for applications including tumor growth, angiogenesis, osteogenesis, coronary perfusion, and oxygen delivery. Composition of such models is time consuming, with many researchers writing custom software. Recent advances in imaging have produced detailed three-dimensional (3D) datasets of vascularized tissues at the scale of individual cells. To fully exploit such data there is an increasing need for software that allows user-friendly composition of efficient, 3D models of vascularized tissues, and comparison of predictions with in vivo or in vitro experiments and alternative computational formulations. Microvessel Chaste can be used to build simulations of vessel growth and adaptation in response to mechanical and chemical stimuli; intra- and extravascular transport of nutrients, growth factors and drugs; and cell proliferation in complex 3D geometries. In addition, it can be used to develop custom software for integrating modeling with experimental data processing workflows, facilitated by a comprehensive Python interface to solvers implemented in C++. This article links to two reproducible example problems, showing how the library can be used to build simulations of tumor growth and angiogenesis with realistic vessel networks.

Fibrosis, low vascularity, and fewer slow fibers after rotator-cuff injury

INTRODUCTION

Rotator-cuff injury (RCI) represents 50% of shoulder injuries, and prevalence increases with age. Even with successful tendon repair, muscle and joint function may not return.

METHODS

To explore the dysfunction, supraspinatus and ipsilateral deltoid (control) muscles were biopsied during arthroscopic RCI repair for pair-wise histological and protein-expression studies.

RESULTS

Supraspinatus showed fiber atrophy (P <  0.0001), fibrosis (by Sirius Red, P = 0.05), reduced vascular density (P <  0.001), and a lower proportion of slow fibers (P <  0.0001) compared with the ipsilateral control muscle. There were also higher levels of atrogin-1 (P = 0.05), vascular endothelial growth factor (VEGF, P <  0.01), and dystrophin (P <  0.008, relative to fiber diameter) versus control.

CONCLUSIONS

Adaptive changes in vascular endothelial growth factor and dystrophin were likely associated with reduced vascular supply, fatigue resistance, and fibrosis, accompanied by disuse atrophy from mechanical unloading of supraspinatus after tendon tear. Treatment to promote growth and vascularity in atrophic supraspinatus muscle may help improve functional outcome after surgical repair. Muscle Nerve 55: 715-726, 2017.

Effects of endothelial cell proliferation and migration rates in a computational model of sprouting angiogenesis

Angiogenesis, the recruitment of new blood vessels, is a critical process for the growth, expansion, and metastatic dissemination of developing tumors. Three types of cells make up the new vasculature: tip cells, which migrate in response to gradients of vascular endothelial growth factor (VEGF), stalk cells, which proliferate and extend the vessels, and phalanx cells, which are quiescent and support the sprout. In this study we examine the contribution of tip cell migration rate and stalk cell proliferation rate on the formation of new vasculature. We calculate several vascular metrics, such as the number of vascular bifurcations per unit volume, vascular segment length per unit volume, and vascular tortuosity. These measurements predict that proliferation rate has a greater effect on the spread and extent of vascular growth compared to migration rate. Together, these findings provide strong implications for designing anti-angiogenic therapies that may differentially target endothelial cell proliferation and migration. Computational models can be used to predict optimal anti-angiogenic therapies in combination with other therapeutics to improve outcome.

Altered Satellite Cell Responsiveness and Denervation Implicated in Progression of Rotator-Cuff Injury

Background

Rotator-cuff injury (RCI) is common and painful; even after surgery, joint stability and function may not recover. Relative contributions to atrophy from disuse, fibrosis, denervation, and satellite-cell responsiveness to activating stimuli are not known.

Methods and Findings

Potential contributions of denervation and disrupted satellite cell responses to growth signals were examined in supraspinatus (SS) and control (ipsilateral deltoid) muscles biopsied from participants with RCI (N = 27). Biopsies were prepared for explant culture (to study satellite cell activity), immunostained to localize Pax7, BrdU, and Semaphorin 3A in satellite cells, sectioning to study blood vessel density, and western blotting to measure the fetal (γ) subunit of acetylcholine receptor (γ-AchR). Principal component analysis (PCA) for 35 parameters extracted components identified variables that contributed most to variability in the dataset. γ-AchR was higher in SS than control, indicating denervation. Satellite cells in SS had a low baseline level of activity (Pax7+ cells labelled in S-phase) versus control; only satellite cells in SS showed increased proliferative activity after nitric oxide-donor treatment. Interestingly, satellite cell localization of Semaphorin 3A, a neuro-chemorepellent, was greater in SS (consistent with fiber denervation) than control muscle at baseline. PCAs extracted components including fiber atrophy, satellite cell activity, fibrosis, atrogin-1, smoking status, vascular density, γAchR, and the time between symptoms and surgery. Use of deltoid as a control for SS was supported by PCA findings since “muscle” was not extracted as a variable in the first two principal components. SS muscle in RCI is therefore atrophic, denervated, and fibrotic, and has satellite cells that respond to activating stimuli.

Conclusions

Since SS satellite cells can be activated in culture, a NO-donor drug combined with stretching could promote muscle growth and improve functional outcome after RCI. PCAs suggest indices including satellite cell responsiveness, atrogin-1, atrophy, and innervation may predict surgical outcome.

An imaging-based computational model for simulating angiogenesis and tumour oxygenation dynamics

Tumour growth, angiogenesis and oxygenation vary substantially among tumours and significantly impact their treatment outcome. Imaging provides a unique means of investigating these tumour-specific characteristics. Here we propose a computational model to simulate tumour-specific oxygenation changes based on the molecular imaging data. Tumour oxygenation in the model is reflected by the perfused vessel density. Tumour growth depends on its doubling time (T d) and the imaged proliferation. Perfused vessel density recruitment rate depends on the perfused vessel density around the tumour (sMVDtissue) and the maximum VEGF concentration for complete vessel dysfunctionality (VEGFmax). The model parameters were benchmarked to reproduce the dynamics of tumour oxygenation over its entire lifecycle, which is the most challenging test. Tumour oxygenation dynamics were quantified using the peak pO2 (pO2peak) and the time to peak pO2 (t peak). Sensitivity of tumour oxygenation to model parameters was assessed by changing each parameter by 20%. t peak was found to be more sensitive to tumour cell line related doubling time (~30%) as compared to tissue vasculature density (~10%). On the other hand, pO2peak was found to be similarly influenced by the above tumour- and vasculature-associated parameters (~30-40%). Interestingly, both pO2peak and t peak were only marginally affected by VEGFmax (~5%). The development of a poorly oxygenated (hypoxic) core with tumour growth increased VEGF accumulation, thus disrupting the vessel perfusion as well as further increasing hypoxia with time. The model with its benchmarked parameters, is applied to hypoxia imaging data obtained using a [(64)Cu]Cu-ATSM PET scan of a mouse tumour and the temporal development of the vasculature and hypoxia maps are shown. The work underscores the importance of using tumour-specific input for analysing tumour evolution. An extended model incorporating therapeutic effects can serve as a powerful tool for analysing tumour response to anti-angiogenic therapies.

Cells as strain-cued automata

We argue in favor of representing living cells as automata and review demonstrations that autonomous cells can form patterns by responding to local variations in the strain fields that arise from their individual or collective motions. An autonomous cell's response to strain stimuli is assumed to be effected by internally-generated, internally-powered forces, which generally move the cell in directions other than those implied by external energy gradients. Evidence of cells acting as strain-cued automata have been inferred from patterns observed in nature and from experiments conducted in vitro. Simulations that mimic particular cases of pattern forming share the idealization that cells are assumed to pass information among themselves solely via mechanical boundary conditions, i.e., the tractions and displacements present at their membranes. This assumption opens three mechanisms for pattern formation in large cell populations: wavelike behavior, kinematic feedback in cell motility that can lead to sliding and rotational patterns, and directed migration during invasions. Wavelike behavior among ameloblast cells during amelogenesis (the formation of dental enamel) has been inferred from enamel microstructure, while strain waves in populations of epithelial cells have been observed in vitro. One hypothesized kinematic feedback mechanism, "enhanced shear motility", accounts successfully for the spontaneous formation of layered patterns during amelogenesis in the mouse incisor. Directed migration is exemplified by a theory of invader cells that sense and respond to the strains they themselves create in the host population as they invade it: analysis shows that the strain fields contain positional information that could aid the formation of cell network structures, stabilizing the slender geometry of branches and helping govern the frequency of branch bifurcation and branch coalescence (the formation of closed networks). In simulations of pattern formation in homogeneous populations and network formation by invaders, morphological outcomes are governed by the ratio of the rates of two competing time dependent processes, one a migration velocity and the other a relaxation velocity related to the propagation of strain information. Relaxation velocities are approximately constant for different species and organs, whereas cell migration rates vary by three orders of magnitude. We conjecture that developmental processes use rapid cell migration to achieve certain outcomes, and slow migration to achieve others. We infer from analysis of host relaxation during network formation that a transition exists in the mechanical response of a host cell from animate to inanimate behavior when its strain changes at a rate that exceeds 10-4-10-3s-1. The transition has previously been observed in experiments conducted in vitro.

Making microvascular networks work: angiogenesis, remodeling, and pruning

The adequate and efficient functioning of the microcirculation requires not only numerous vessels providing a large surface area for transport but also a structure that provides short diffusion distances from capillaries to tissue and efficient distribution of convective blood flow. Theoretical models show how a combination of angiogenesis, remodeling, and pruning in response to hemodynamic and metabolic stimuli, termed "angioadaptation," generates well organized, functional networks.

Systems biology of the microvasculature

The vascular network carries blood throughout the body, delivering oxygen to tissues and providing a pathway for communication between distant organs. The network is hierarchical and structured, but also dynamic, especially at the smaller scales. Remodeling of the microvasculature occurs in response to local changes in oxygen, gene expression, cell-cell communication, and chemical and mechanical stimuli from the microenvironment. These local changes occur as a result of physiological processes such as growth and exercise, as well as acute and chronic diseases including stroke, cancer, and diabetes, and pharmacological intervention. While the vasculature is an important therapeutic target in many diseases, drugs designed to inhibit vascular growth have achieved only limited success, and no drug has yet been approved to promote therapeutic vascular remodeling. This highlights the challenges involved in identifying appropriate therapeutic targets in a system as complex as the vasculature. Systems biology approaches provide a means to bridge current understanding of the vascular system, from detailed signaling dynamics measured in vitro and pre-clinical animal models of vascular disease, to a more complete picture of vascular regulation in vivo. This will translate to an improved ability to identify multi-component biomarkers for diagnosis, prognosis, and monitoring of therapy that are easy to measure in vivo, as well as better drug targets for specific disease states. In this review, we summarize systems biology approaches that have advanced our understanding of vascular function and dysfunction in vivo, with a focus on computational modeling.

Toward modular biological models: defining analog modules based on referent physiological mechanisms

Background

Currently, most biomedical models exist in isolation. It is often difficult to reuse or integrate models or their components, in part because they are not modular. Modular components allow the modeler to think more deeply about the role of the model and to more completely address a modeling project’s requirements. In particular, modularity facilitates component reuse and model integration for models with different use cases, including the ability to exchange modules during or between simulations. The heterogeneous nature of biology and vast range of wet-lab experimental platforms call for modular models designed to satisfy a variety of use cases. We argue that software analogs of biological mechanisms are reasonable candidates for modularization. Biomimetic software mechanisms comprised of physiomimetic mechanism modules offer benefits that are unique or especially important to multi-scale, biomedical modeling and simulation.

Results

We present a general, scientific method of modularizing mechanisms into reusable software components that we call physiomimetic mechanism modules (PMMs). PMMs utilize parametric containers that partition and expose state information into physiologically meaningful groupings. To demonstrate, we modularize four pharmacodynamic response mechanisms adapted from an in silico liver (ISL). We verified the modularization process by showing that drug clearance results from in silico experiments are identical before and after modularization. The modularized ISL achieves validation targets drawn from propranolol outflow profile data. In addition, an in silico hepatocyte culture (ISHC) is created. The ISHC uses the same PMMs and required no refactoring. The ISHC achieves validation targets drawn from propranolol intrinsic clearance data exhibiting considerable between-lab variability. The data used as validation targets for PMMs originate from both in vitro to in vivo experiments exhibiting large fold differences in time scale.

Conclusions

This report demonstrates the feasibility of PMMs and their usefulness across multiple model use cases. The pharmacodynamic response module developed here is robust to changes in model context and flexible in its ability to achieve validation targets in the face of considerable experimental uncertainty. Adopting the modularization methods presented here is expected to facilitate model reuse and integration, thereby accelerating the pace of biomedical research.

Extracellular regulation of VEGF: isoforms, proteolysis, and vascular patterning

The regulation of vascular endothelial growth factor A (VEGF) is critical to neovascularization in numerous tissues under physiological and pathological conditions. VEGF has multiple isoforms, created by alternative splicing or proteolytic cleavage, and characterized by different receptor-binding and matrix-binding properties. These isoforms are known to give rise to a spectrum of angiogenesis patterns marked by differences in branching, which has functional implications for tissues. In this review, we detail the extensive extracellular regulation of VEGF and the ability of VEGF to dictate the vascular phenotype. We explore the role of VEGF-releasing proteases and soluble carrier molecules on VEGF activity. While proteases such as MMP9 can 'release' matrix-bound VEGF and promote angiogenesis, for example as a key step in carcinogenesis, proteases can also suppress VEGF's angiogenic effects. We explore what dictates pro- or anti-angiogenic behavior. We also seek to understand the phenomenon of VEGF gradient formation. Strong VEGF gradients are thought to be due to decreased rates of diffusion from reversible matrix binding, however theoretical studies show that this scenario cannot give rise to lasting VEGF gradients in vivo. We propose that gradients are formed through degradation of sequestered VEGF. Finally, we review how different aspects of the VEGF signal, such as its concentration, gradient, matrix-binding, and NRP1-binding can differentially affect angiogenesis. We explore how this allows VEGF to regulate the formation of vascular networks across a spectrum of high to low branching densities, and from normal to pathological angiogenesis. A better understanding of the control of angiogenesis is necessary to improve upon limitations of current angiogenic therapies.

A systems biology view of blood vessel growth and remodelling

Blood travels throughout the body in an extensive network of vessels – arteries, veins and capillaries. This vascular network is not static, but instead dynamically remodels in response to stimuli from cells in the nearby tissue. In particular, the smallest vessels – arterioles, venules and capillaries – can be extended, expanded or pruned, in response to exercise, ischaemic events, pharmacological interventions, or other physiological and pathophysiological events. In this review, we describe the multi-step morphogenic process of angiogenesis – the sprouting of new blood vessels – and the stability of vascular networks in vivo. In particular, we review the known interactions between endothelial cells and the various blood cells and plasma components they convey. We describe progress that has been made in applying computational modelling, quantitative biology and high-throughput experimentation to the angiogenesis process.

Endothelial cell motility, coordination and pattern formation during vasculogenesis

How vascular networks assemble is a fundamental problem of developmental biology that also has medical importance. To explain the organizational principles behind vascular patterning, we must understand how can tissue level structures be controlled through cell behavior patterns like motility and adhesion that, in turn, are determined by biochemical signal transduction processes? We discuss the various ideas that have been proposed as mechanisms for vascular network assembly: cell motility guided by extracellular matrix alignment (contact guidance), chemotaxis guided by paracrine and autocrine morphogens, and multicellular sprouting guided by cell-cell contacts. All of these processes yield emergent patterns, thus endothelial cells can form an interconnected structure autonomously, without guidance from an external pre-pattern.

A hybrid model of the role of VEGF binding in endothelial cell migration and capillary formation

Vascular endothelial growth factor (VEGF) is the most studied family of soluble, secreted mediators of endothelial cell migration, survival, and proliferation. VEGF exerts its function by binding to specific tyrosine kinase receptors on the cell surface and transducing the effect through downstream signaling. In order to study the influence of VEGF binding on endothelial cell motion, we develop a hybrid model of VEGF-induced angiogenesis, based on the theory of reinforced random walks. The model includes the chemotactic response of endothelial cells to angiogenic factors bound to cell-surface receptors, rather than approximating this as a function of extracellular chemical concentrations. This allows us to capture biologically observed phenomena such as activation and polarization of endothelial cells in response to VEGF gradients across their lengths, as opposed to extracellular gradients throughout the tissue. We also propose a novel and more biologically reasonable functional form for the chemotactic sensitivity of endothelial cells, which is also governed by activated cell-surface receptors. This model is able to predict the threshold level of VEGF required to activate a cell to move in a directed fashion as well as an optimal VEGF concentration for motion. Model validation is achieved by comparison of simulation results directly with experimental data.

Multiscale computational models of complex biological systems

Integration of data across spatial, temporal, and functional scales is a primary focus of biomedical engineering efforts. The advent of powerful computing platforms, coupled with quantitative data from high-throughput experimental methodologies, has allowed multiscale modeling to expand as a means to more comprehensively investigate biological phenomena in experimentally relevant ways. This review aims to highlight recently published multiscale models of biological systems, using their successes to propose the best practices for future model development. We demonstrate that coupling continuous and discrete systems best captures biological information across spatial scales by selecting modeling techniques that are suited to the task. Further, we suggest how to leverage these multiscale models to gain insight into biological systems using quantitative biomedical engineering methods to analyze data in nonintuitive ways. These topics are discussed with a focus on the future of the field, current challenges encountered, and opportunities yet to be realized.

Three-dimensional modeling of angiogenesis in porous biomaterial scaffolds

Vascularization of biomaterial scaffolds is essential for the successful clinical application of engineered tissues. Experimental studies are often performed to investigate the role of scaffold architecture on vascularized tissue formation. However, experiments are expensive and time-consuming and synthesis protocols often do not allow for independent investigation of specific scaffold properties. Computational models allow for rapid screening of potential material designs with control over scaffold properties that is difficult in laboratory settings. We have developed and tested a three-dimensional agent-based framework for investigating the effect of scaffold pore architecture on angiogenesis. Software agents represent endothelial cells, interacting together and with their micro-environment, leading to the invasion of blood vessels into the scaffold. A rule base, driven by experimental findings, governs the behavior of individual agents. 3D scaffold models with well-defined homogeneous and heterogeneous pore architectures were simulated to investigate the impact of various design parameters. Simulation results indicate that pores of larger size with higher interconnectivity and porosity support rapid and extensive angiogenesis. The developed framework can be used to screen biomaterial scaffold designs for optimal vascularization and investigate complex interactions among invading blood vessels and their micro-environment.

MOSAIC: a multiscale model of osteogenesis and sprouting angiogenesis with lateral inhibition of endothelial cells

The healing of a fracture depends largely on the development of a new blood vessel network (angiogenesis) in the callus. During angiogenesis tip cells lead the developing sprout in response to extracellular signals, amongst which vascular endothelial growth factor (VEGF) is critical. In order to ensure a correct development of the vasculature, the balance between stalk and tip cell phenotypes must be tightly controlled, which is primarily achieved by the Dll4-Notch1 signaling pathway. This study presents a novel multiscale model of osteogenesis and sprouting angiogenesis, incorporating lateral inhibition of endothelial cells (further denoted MOSAIC model) through Dll4-Notch1 signaling, and applies it to fracture healing. The MOSAIC model correctly predicted the bone regeneration process and recapitulated many experimentally observed aspects of tip cell selection: the salt and pepper pattern seen for cell fates, an increased tip cell density due to the loss of Dll4 and an excessive number of tip cells in high VEGF environments. When VEGF concentration was even further increased, the MOSAIC model predicted the absence of a vascular network and fracture healing, thereby leading to a non-union, which is a direct consequence of the mutual inhibition of neighboring cells through Dll4-Notch1 signaling. This result was not retrieved for a more phenomenological model that only considers extracellular signals for tip cell migration, which illustrates the importance of implementing the actual signaling pathway rather than phenomenological rules. Finally, the MOSAIC model demonstrated the importance of a proper criterion for tip cell selection and the need for experimental data to further explore this. In conclusion, this study demonstrates that the MOSAIC model creates enhanced capabilities for investigating the influence of molecular mechanisms on angiogenesis and its relation to bone formation in a more mechanistic way and across different time and spatial scales.

Multiscale models of breast cancer progression

Breast cancer initiation, invasion and metastasis span multiple length and time scales. Molecular events at short length scales lead to an initial tumorigenic population, which left unchecked by immune action, acts at increasingly longer length scales until eventually the cancer cells escape from the primary tumor site. This series of events is highly complex, involving multiple cell types interacting with (and shaping) the microenvironment. Multiscale mathematical models have emerged as a powerful tool to quantitatively integrate the convective-diffusion-reaction processes occurring on the systemic scale, with the molecular signaling processes occurring on the cellular and subcellular scales. In this study, we reviewed the current state of the art in cancer modeling across multiple length scales, with an emphasis on the integration of intracellular signal transduction models with pro-tumorigenic chemical and mechanical microenvironmental cues. First, we reviewed the underlying biomolecular origin of breast cancer, with a special emphasis on angiogenesis. Then, we summarized the development of tissue engineering platforms which could provide high-fidelity ex vivo experimental models to identify and validate multiscale simulations. Lastly, we reviewed top-down and bottom-up multiscale strategies that integrate subcellular networks with the microenvironment. We present models of a variety of cancers, in addition to breast cancer specific models. Taken together, we expect as the sophistication of the simulations increase, that multiscale modeling and bottom-up agent-based models in particular will become an increasingly important platform technology for basic scientific discovery, as well as the identification and validation of potentially novel therapeutic targets.

Effects of fiber type and size on the heterogeneity of oxygen distribution in exercising skeletal muscle

The process of oxygen delivery from capillary to muscle fiber is essential for a tissue with variable oxygen demand, such as skeletal muscle. Oxygen distribution in exercising skeletal muscle is regulated by convective oxygen transport in the blood vessels, oxygen diffusion and consumption in the tissue. Spatial heterogeneities in oxygen supply, such as microvascular architecture and hemodynamic variables, had been observed experimentally and their marked effects on oxygen exchange had been confirmed using mathematical models. In this study, we investigate the effects of heterogeneities in oxygen demand on tissue oxygenation distribution using a multiscale oxygen transport model. Muscles are composed of different ratios of the various fiber types. Each fiber type has characteristic values of several parameters, including fiber size, oxygen consumption, myoglobin concentration, and oxygen diffusivity. Using experimentally measured parameters for different fiber types and applying them to the rat extensor digitorum longus muscle, we evaluated the effects of heterogeneous fiber size and fiber type properties on the oxygen distribution profile. Our simulation results suggest a marked increase in spatial heterogeneity of oxygen due to fiber size distribution in a mixed muscle. Our simulations also suggest that the combined effects of fiber type properties, except size, do not contribute significantly to the tissue oxygen spatial heterogeneity. However, the incorporation of the difference in oxygen consumption rates of different fiber types alone causes higher oxygen heterogeneity compared to control cases with uniform fiber properties. In contrast, incorporating variation in other fiber type-specific properties, such as myoglobin concentration, causes little change in spatial tissue oxygenation profiles.

Pattern formation during vasculogenesis

Vasculogenesis, the assembly of the first vascular network, is an intriguing developmental process that yields the first functional organ system of the embryo. In addition to being a fundamental part of embryonic development, vasculogenic processes also have medical importance. To explain the organizational principles behind vascular patterning, we must understand how morphogenesis of tissue level structures can be controlled through cell behavior patterns that, in turn, are determined by biochemical signal transduction processes. Mathematical analyses and computer simulations can help conceptualize how to bridge organizational levels and thus help in evaluating hypotheses regarding the formation of vascular networks. Here, we discuss the ideas that have been proposed to explain the formation of the first vascular pattern: cell motility guided by extracellular matrix alignment (contact guidance), chemotaxis guided by paracrine and autocrine morphogens, and sprouting guided by cell-cell contacts.

Multiscale imaging and computational modeling of blood flow in the tumor vasculature

The evolution in our understanding of tumor angiogenesis has been the result of pioneering imaging and computational modeling studies spanning the endothelial cell, microvasculature and tissue levels. Many of these primary data on the tumor vasculature are in the form of images from pre-clinical tumor models that provide a wealth of qualitative and quantitative information in many dimensions and across different spatial scales. However, until recently, the visualization of changes in the tumor vasculature across spatial scales remained a challenge due to a lack of techniques for integrating micro- and macroscopic imaging data. Furthermore, the paucity of three-dimensional (3-D) tumor vascular data in conjunction with the challenges in obtaining such data from patients presents a serious hurdle for the development and validation of predictive, multiscale computational models of tumor angiogenesis. In this review, we discuss the development of multiscale models of tumor angiogenesis, new imaging techniques capable of reproducing the 3-D tumor vascular architecture with high fidelity, and the emergence of "image-based models" of tumor blood flow and molecular transport. Collectively, these developments are helping us gain a fundamental understanding of the cellular and molecular regulation of tumor angiogenesis that will benefit the development of new cancer therapies. Eventually, we expect this exciting integration of multiscale imaging and mathematical modeling to have widespread application beyond the tumor vasculature to other diseases involving a pathological vasculature, such as stroke and spinal cord injury.

Integration of experimental and computational approaches to sprouting angiogenesis

PURPOSE OF REVIEW

We summarize recent experimental and computational studies that investigate molecular and cellular mechanisms of sprouting angiogenesis. We discuss how experimental tools have unveiled new opportunities for computational modeling by providing detailed phenomenological descriptions and conceptual models of cell-level behaviors underpinned by high-quality molecular data. Using recent examples, we show how new understanding results from bridging computational and experimental approaches.

RECENT FINDINGS

Experimental data extends beyond the tip cell vs. stalk cell paradigm, and involves numerous molecular inputs such as vascular endothelial growth factor and Notch. This data is being used to generate and validate computational models, which can then be used to predict the results of hypothetical experiments that are difficult to perform in the laboratory, and to generate new hypotheses that account for system-wide interactions. As a result of this integration, descriptions of critical gradients of growth factor-receptor complexes have been generated, and new modulators of cell behavior have been described.

SUMMARY

We suggest that the recent emphasis on the different stages of sprouting angiogenesis, and integration of experimental and computational approaches, should provide a way to manage the complexity of this process and help identify new regulatory paradigms and therapeutic targets.

Microfluidic models of vascular functions

In vitro studies of vascular physiology have traditionally relied on cultures of endothelial cells, smooth muscle cells, and pericytes grown on centimeter-scale plates, filters, and flow chambers. The introduction of microfluidic tools has revolutionized the study of vascular physiology by allowing researchers to create physiologically relevant culture models, at the same time greatly reducing the consumption of expensive reagents. By taking advantage of the small dimensions and laminar flow inherent in microfluidic systems, recent studies have created in vitro models that reproduce many features of the in vivo vascular microenvironment with fine spatial and temporal resolution. In this review, we highlight the advantages of microfluidics in four areas: the investigation of hemodynamics on a capillary length scale, the modulation of fluid streams over vascular cells, angiogenesis induced by the exposure of vascular cells to well-defined gradients in growth factors or pressure, and the growth of microvascular networks in biomaterials. Such unique capabilities at the microscale are rapidly advancing the understanding of microcirculatory dynamics, shear responses, and angiogenesis in health and disease as well as the ability to create in vivo-like blood vessels in vitro.

A two-compartment model of VEGF distribution in the mouse

Vascular endothelial growth factor (VEGF) is a key regulator of angiogenesis – the growth of new microvessels from existing microvasculature. Angiogenesis is a complex process involving numerous molecular species, and to better understand it, a systems biology approach is necessary. In vivo preclinical experiments in the area of angiogenesis are typically performed in mouse models; this includes drug development targeting VEGF. Thus, to quantitatively interpret such experimental results, a computational model of VEGF distribution in the mouse can be beneficial. In this paper, we present an in silico model of VEGF distribution in mice, determine model parameters from existing experimental data, conduct sensitivity analysis, and test the validity of the model.

The multiscale model is comprised of two compartments: blood and tissue. The model accounts for interactions between two major VEGF isoforms (VEGF₁₂₀ and VEGF₁₆₄) and their endothelial cell receptors VEGFR-1, VEGFR-2, and co-receptor neuropilin-1. Neuropilin-1 is also expressed on the surface of parenchymal cells. The model includes transcapillary macromolecular permeability, lymphatic transport, and macromolecular plasma clearance. Simulations predict that the concentration of unbound VEGF in the tissue is approximately 50-fold greater than in the blood. These concentrations are highly dependent on the VEGF secretion rate. Parameter estimation was performed to fit the simulation results to available experimental data, and permitted the estimation of VEGF secretion rate in healthy tissue, which is difficult to measure experimentally. The model can provide quantitative interpretation of preclinical animal data and may be used in conjunction with experimental studies in the development of pro- and anti-angiogenic agents. The model approximates the normal tissue as skeletal muscle and includes endothelial cells to represent the vasculature. As the VEGF system becomes better characterized in other tissues and cell types, the model can be expanded to include additional compartments and vascular elements.