A computational model of oxygen transport in skeletal muscle for sprouting and splitting modes of angiogenesis

Vascular phenotyping of the invasive front in breast cancer using a 3D angiogenesis atlas

OBJECTIVE

Vascular remodeling at the invasive tumor front (ITF) plays a critical role in progression and metastasis of triple negative breast cancer (TNBC). Therefore, there is a crucial need to characterize the vascular phenotype (i.e. changes in the structure and function of vasculature) of the ITF and tumor core (TC) in TNBC. This requires high-resolution, 3D structural and functional microvascular data that spans the ITF and TC (i.e. ∼4-5 mm from the tumor's edge). Since such data are often challenging to obtain with most conventional imaging approaches, we employed a unique "3D whole-tumor angiogenesis atlas" derived from orthotopic xenografts to characterize the vascular phenotype of the ITF and TC in TNBC.

METHODS

First, high-resolution (8 μm) computed tomography (CT) images of "whole-tumor" microvasculature were acquired from eight orthotopic TNBC xenografts, of which three tumors were excised at post-inoculation day 21 (i.e. early-stage) and five tumors were excised at post-inoculation day 35 (i.e. advanced-stage). These 3D morphological CT data were combined with soft tissue contrast from MRI as well as functional data generated in silico using image-based hemodynamic modeling to generate a multi-layered "angiogenesis atlas". Employing this atlas, blood vessels were first spatially stratified within the ITF (i.e. ≤1 mm from the tumor's edge) and TC (i.e. >1 mm from the tumor's edge) of each tumor xenograft. Then, a novel method was developed to visualize and characterize microvascular remodeling and perfusion changes in terms of distance from the tumor's edge.

RESULTS

The angiogenesis atlas enabled the 3D visualization of changes in tumor vessel growth patterns, morphology and perfusion within the ITF and TC. Early and advanced stage tumors demonstrated significant differences in terms of their edge-to-center distributions for vascular surface area density, vascular length density, intervessel distance and simulated perfusion density (p ≪ 0.01). Elevated vascular length density, vascular surface area density and perfusion density along the circumference of the ITF was suggestive of a preferential spatial pattern of angiogenic growth in this tumor cohort. Finally, we demonstrated the feasibility of differentiating the vascular phenotypes of ITF and TC in these TNBC xenografts.

CONCLUSIONS

The combination of a 3D angiogenesis atlas and image-based hemodynamic modeling heralds a new approach for characterizing the role of vascular remodeling in cancer and other diseases.

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.

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.

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.

Alternative Vascularization Mechanisms in Tumor Resistance to Therapy

Simple Summary

Tumors rely on blood vessels to grow and metastasize. Malignant tumors can employ different strategies to create a functional vascular network. Tumor cells can use normal processes of vessel formation but can also employ cancer-specific mechanisms, by co-opting normal vessels present in tissues or by turning themselves into vascular cells. These different types of tumor vessels have specific molecular and functional characteristics that profoundly affect tumor behavior and response to therapies, including drugs targeting the tumor vasculature (antiangiogenic therapies). In this review, we discuss how vessels formed by different mechanisms affect the intrinsic sensitivity of tumors to therapy and, on the other hand, how therapies can affect tumor vessel formation, leading to resistance to drugs, cancer recurrence, and treatment failure. Potential strategies to avoid vessel-mediated resistance to antineoplastic therapies will be discussed.

Abstract

Blood vessels in tumors are formed through a variety of different mechanisms, each generating vessels with peculiar structural, molecular, and functional properties. This heterogeneity has a major impact on tumor response or resistance to antineoplastic therapies and is now emerging as a promising target for strategies to prevent drug resistance and improve the distribution and efficacy of antineoplastic treatments. This review presents evidence of how different mechanisms of tumor vessel formation (vasculogenesis, glomeruloid proliferation, intussusceptive angiogenesis, vasculogenic mimicry, and vessel co-option) affect tumor responses to antiangiogenic and antineoplastic therapies, but also how therapies can promote alternative mechanisms of vessel formation, contributing to tumor recurrence, malignant progression, and acquired drug resistance. We discuss the possibility of tailoring treatment strategies to overcome vasculature-mediated drug resistance or to improve drug distribution and efficacy.

Intussusceptive angiogenesis and its counterpart intussusceptive lymphangiogenesis

Intussusceptive angiogenesis (IA) is currently considered an important alternative and complementary form of sprouting angiogenesis (SA). Conversely, intussusceptive lymphangiogenesis (IL) is in an initial phase of study. We compare their morphofunctional characteristics, since many can be shared by both processes. To that end, the following aspects are considered: A) The concept of IA and IL as the mechanism by which blood and lymphatic vessels split, expand and remodel through transluminal pillar formations (hallmarks of intussusception). B) Terminology and historical background, with particular reference to the group of Burri, including Djonov and Patan, who initiated and developed the vessel intussusceptive concept in blood vessels. C) Incidence in normal (e.g. in the sinuses of developing lymph nodes) and pathologic conditions, above all in vessel diseases, such as dilated veins in hemorrhoidal disease, intravascular papillary endothelial hyperplasia (IPEH), sinusoidal hemangioma, lobular capillary hemangioma, lymphangiomas/lymphatic malformations and vascular transformation of lymph nodes. D) Differences and complementarity between vessel sprouting and intussusception. E) Characteristics of the cover (endothelial cells) and core (connective tissue components) of pillars and requirements for pillar identification. F) Structures involved in pillar formation, including endothelial contacts of opposite vessel walls, interendothelial bridges, merged adjacent capillaries, vessel loops and spilt pillars. G) Structures resulting from pillars with intussusceptive microvascular growth, arborization, remodeling and segmentation (compartmentalization). H) Influence of intussusception in the morphogenesis of vessel tumors/ pseudotumors; and I) Hemodynamic and molecular control of vessel intussusception, including VEGF, PDGF BB, Hypoxia, Notch, Endoglobin and Nitric oxide.

Tumor Ensemble-Based Modeling and Visualization of Emergent Angiogenic Heterogeneity in Breast Cancer

There is a critical need for new tools to investigate the spatio-temporal heterogeneity and phenotypic alterations that arise in the tumor microenvironment. However, computational investigations of emergent inter- and intra-tumor angiogenic heterogeneity necessitate 3D microvascular data from 'whole-tumors' as well as "ensembles" of tumors. Until recently, technical limitations such as 3D imaging capabilities, computational power and cost precluded the incorporation of whole-tumor microvascular data in computational models. Here, we describe a novel computational approach based on multimodality, 3D whole-tumor imaging data acquired from eight orthotopic breast tumor xenografts (i.e. a tumor 'ensemble'). We assessed the heterogeneous angiogenic landscape from the microvascular to tumor ensemble scale in terms of vascular morphology, emergent hemodynamics and intravascular oxygenation. We demonstrate how the abnormal organization and hemodynamics of the tumor microvasculature give rise to unique microvascular niches within the tumor and contribute to inter- and intra-tumor heterogeneity. These tumor ensemble-based simulations together with unique data visualization approaches establish the foundation of a novel 'cancer atlas' for investigators to develop their own in silico systems biology applications. We expect this hybrid image-based modeling framework to be adaptable for the study of other tissues (e.g. brain, heart) and other vasculature-dependent diseases (e.g. stroke, myocardial infarction).

A Network Model to Explore the Effect of the Micro-environment on Endothelial Cell Behavior during Angiogenesis

Angiogenesis is an important adaptation mechanism of the blood vessels to the changing requirements of the body during development, aging, and wound healing. Angiogenesis allows existing blood vessels to form new connections or to reabsorb existing ones. Blood vessels are composed of a layer of endothelial cells (ECs) covered by one or more layers of mural cells (smooth muscle cells or pericytes). We constructed a computational Boolean model of the molecular regulatory network involved in the control of angiogenesis. Our model includes the ANG/TIE, HIF, AMPK/mTOR, VEGF, IGF, FGF, PLCγ/Calcium, PI3K/AKT, NO, NOTCH, and WNT signaling pathways, as well as the mechanosensory components of the cytoskeleton. The dynamical behavior of our model recovers the patterns of molecular activation observed in Phalanx, Tip, and Stalk ECs. Furthermore, our model is able to describe the modulation of EC behavior due to extracellular micro-environments, as well as the effect due to loss- and gain-of-function mutations. These properties make our model a suitable platform for the understanding of the molecular mechanisms underlying some pathologies. For example, it is possible to follow the changes in the activation patterns caused by mutations that promote Tip EC behavior and inhibit Phalanx EC behavior, that lead to the conditions associated with retinal vascular disorders and tumor vascularization. Moreover, the model describes how mutations that promote Phalanx EC behavior are associated with the development of arteriovenous and venous malformations. These results suggest that the network model that we propose has the potential to be used in the study of how the modulation of the EC extracellular micro-environment may improve the outcome of vascular disease treatments.

Learning from Mother Nature: Innovative Tools to Boost Endogenous Repair of Critical or Difficult-to-Heal Large Tissue Defects

For repair of chronic or difficult-to-heal tissue lesions and defects, major constraints exist to a broad application of cell therapy and tissue engineering approaches, i.e., transplantation of “ex vivo” expanded autologous stem/progenitor cells, alone or associated with carrier biomaterials. To enable a large number of patients to benefit, new strategies should be considered. One of the main goals of contemporary regenerative medicine is to develop new regenerative therapies, inspired from Mother Nature. In all injured tissues, when platelets are activated by tissue contact, their released factors promote innate immune cell migration to the wound site. Platelet-derived factors and factors secreted by migrating immune cells create an inflammatory microenvironment, in turn, causing the activation of angiogenesis and vasculogenesis processes. Eventually, repair or regeneration of the injured tissue occurs via paracrine signals activating, mobilizing or recruiting to the wound site cells with healing potential, such as stem cells, progenitors, or undifferentiated cells derived from the reprogramming of tissue differentiated cells. This review, largely based on our studies, discusses the identification of new tools, inspired by cellular and molecular mechanisms overseeing physiological tissue healing, that could reactivate dormant endogenous regeneration mechanisms lost during evolution and ontogenesis.

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.

3D microscopic imaging and evaluation of tubular tissue architecture

3D microscopy and image analysis provide reliable measurements of length, branching, density, tortuosity and orientation of tubular structures in biological samples. We present a survey of methods for analysis of large samples by measurement of local differences in geometrical characteristics. The methods are demonstrated on the structure of the capillary bed in a rat brain.

Breast cancer metastasis progression as revealed by intravital videomicroscopy

Metastasis is the spread of cells from a primary tumor to a distant site, where they arrest and grow to form a secondary tumor. Conventional metastasis models have focused primarily on analysis of end point tumor formation following inoculation with tumor cells. This approach can be used to measure the metastatic potential of cell lines, the morphology of metastases and their vasculature and the overall effectiveness of treatment strategies. However, it cannot, reveal the dynamics of metastatic progression, tumor cell interactions with host tissues or the characteristics of blood flow within the tumor microvasculature. Intravital videomicroscopy has been developed to visualize and quantify the movement of tumor cells and their interactions with host tissues as they travel through metastatic pathways within the body and arrest at secondary sites. Intravital videomicroscopy can also be used to quantify the morphology and functional capacity of tumor microvasculature, as well as the timing and dynamic effects of drugs targeted to disrupt tumor vasculaturization. With the development of new fluorescent probes and reporter genes, intravital videomicroscopy has the potential to provide evidence of the timing and location of metabolic processes within the metastatic cascade that may serve as specific targets for the treatment of breast cancer.

A bioimage informatics based reconstruction of breast tumor microvasculature with computational blood flow predictions

Induction of tumor angiogenesis is among the hallmarks of cancer and a driver of metastatic cascade initiation. Recent advances in high-resolution imaging enable highly detailed three-dimensional geometrical representation of the whole-tumor microvascular architecture. This enormous increase in complexity of image-based data necessitates the application of informatics methods for the analysis, mining and reconstruction of these spatial graph data structures. We present a novel methodology that combines ex-vivo high-resolution micro-computed tomography imaging data with a bioimage informatics algorithm to track and reconstruct the whole-tumor vasculature of a human breast cancer model. The reconstructed tumor vascular network is used as an input of a computational model that estimates blood flow in each segment of the tumor microvascular network. This formulation involves a well-established biophysical model and an optimization algorithm that ensures mass balance and detailed monitoring of all the vessels that feed and drain blood from the tumor microvascular network. Perfusion maps for the whole-tumor microvascular network are computed. Morphological and hemodynamic indices from different regions are compared to infer their role in overall tumor perfusion.

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.

Moving domain computational fluid dynamics to interface with an embryonic model of cardiac morphogenesis

Peristaltic contraction of the embryonic heart tube produces time- and spatial-varying wall shear stress (WSS) and pressure gradients (∇P) across the atrioventricular (AV) canal. Zebrafish (Danio rerio) are a genetically tractable system to investigate cardiac morphogenesis. The use of Tg(fli1a:EGFP) (y1) transgenic embryos allowed for delineation and two-dimensional reconstruction of the endocardium. This time-varying wall motion was then prescribed in a two-dimensional moving domain computational fluid dynamics (CFD) model, providing new insights into spatial and temporal variations in WSS and ∇P during cardiac development. The CFD simulations were validated with particle image velocimetry (PIV) across the atrioventricular (AV) canal, revealing an increase in both velocities and heart rates, but a decrease in the duration of atrial systole from early to later stages. At 20-30 hours post fertilization (hpf), simulation results revealed bidirectional WSS across the AV canal in the heart tube in response to peristaltic motion of the wall. At 40-50 hpf, the tube structure undergoes cardiac looping, accompanied by a nearly 3-fold increase in WSS magnitude. At 110-120 hpf, distinct AV valve, atrium, ventricle, and bulbus arteriosus form, accompanied by incremental increases in both WSS magnitude and ∇P, but a decrease in bi-directional flow. Laminar flow develops across the AV canal at 20-30 hpf, and persists at 110-120 hpf. Reynolds numbers at the AV canal increase from 0.07±0.03 at 20-30 hpf to 0.23±0.07 at 110-120 hpf (p< 0.05, n=6), whereas Womersley numbers remain relatively unchanged from 0.11 to 0.13. Our moving domain simulations highlights hemodynamic changes in relation to cardiac morphogenesis; thereby, providing a 2-D quantitative approach to complement imaging analysis.

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.

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.

Multiobjective optimization based-approach for discovering novel cancer therapies

Solid tumors must recruit new blood vessels for growth and maintenance. Discovering drugs that block tumor-induced development of new blood vessels (angiogenesis) is an important approach in cancer treatment. The complexity of angiogenesis presents both challenges and opportunities for cancer therapies. Intuitive approaches, such as blocking VegF activity, have yielded important therapies. But there maybe opportunities to alter nonintuitive targets either alone or in combination. This paper describes the development of a high-fidelity simulation of angiogenesis and uses this as the basis for a parallel search-based approach for the discovery of novel potential cancer treatments that inhibit blood vessel growth. Discovering new therapies is viewed as a multiobjective combinatorial optimization over two competing objectives: minimizing the estimated cost of practically developing the intervention while minimizing the simulated oxygen provided to the tumor by angiogenesis. Results show the effectiveness of the search process by finding interventions that are currently in use, and more interestingly, discovering potential new approaches that are nonintuitive yet effective.

Module-based multiscale simulation of angiogenesis in skeletal muscle

Background

Mathematical modeling of angiogenesis has been gaining momentum as a means to shed new light on the biological complexity underlying blood vessel growth. A variety of computational models have been developed, each focusing on different aspects of the angiogenesis process and occurring at different biological scales, ranging from the molecular to the tissue levels. Integration of models at different scales is a challenging and currently unsolved problem.

Results

We present an object-oriented module-based computational integration strategy to build a multiscale model of angiogenesis that links currently available models. As an example case, we use this approach to integrate modules representing microvascular blood flow, oxygen transport, vascular endothelial growth factor transport and endothelial cell behavior (sensing, migration and proliferation). Modeling methodologies in these modules include algebraic equations, partial differential equations and agent-based models with complex logical rules. We apply this integrated model to simulate exercise-induced angiogenesis in skeletal muscle. The simulation results compare capillary growth patterns between different exercise conditions for a single bout of exercise. Results demonstrate how the computational infrastructure can effectively integrate multiple modules by coordinating their connectivity and data exchange. Model parameterization offers simulation flexibility and a platform for performing sensitivity analysis.

Conclusions

This systems biology strategy can be applied to larger scale integration of computational models of angiogenesis in skeletal muscle, or other complex processes in other tissues under physiological and pathological conditions.

Characterization of the Capillary Network in Skeletal Muscles From 3D Data

In this review we present immunohistochemical methods for visualization of capillaries and muscle fibres in thick muscle sections. Special attention is paid to the procedures that preserve good morphology. Applying confocal microscopy and virtual 3D stereological grids, or tracing of capillaries in virtual reality, length of capillaries within a muscle volume or length of capillaries adjacent to a muscle fibre per fibre length, fibre surface area or fibre volume can be evaluated by an unbiased approach. Moreover, 3D models of capillaries and muscle fibres can be produced. Comparison of the developed methods with counting capillary profiles from 2D sections is discussed and the reader is warned that counting capillary profiles from 2D sections can underestimate the capillary length by as much as 75 percent. Application of the described 3D methodology is illustrated by the anatomical remodelling of capillarity during acute denervation and early reinnervation in the rat soleus and extensor digitorum longus muscles.

Informational dynamics of vasomotion in microvascular networks: a review

Vasomotion refers to spontaneous oscillation of small vessels observed in many microvascular beds. It is an intrinsic phenomenon unrelated to cardiac rhythm or neural and hormonal regulation. Vasomotion is found to be particularly prominent under conditions of metabolic stress. In spite of a significant existent literature on vasomotion, its physiological and pathophysiological roles are not clear. It is thought that modulation of vasomotion by vasoactive substances released by metabolizing tissue plays a role in ensuring optimal delivery of nutrients to the tissue. Vasomotion rhythms exhibit a great variety of temporal patterns from regular oscillations to chaos. The nature of vasomotion rhythm is believed to be significant to its function, with chaotic vasomotion offering several physiological advantages over regular, periodic vasomotion. In this article, we emphasize that vasomotion is best understood as a network phenomenon. When there is a local metabolic demand in tissue, an ideal vascular response should extend beyond local microvasculature, with coordinated changes over multiple vascular segments. Mechanisms of information transfer over a vessel network have been discussed in the literature. The microvascular system may be regarded as a network of dynamic elements, interacting, either over the vascular anatomical network via gap junctions, or physiologically by exchange of vasoactive substances. Drawing analogies with spatiotemporal patterns in neuronal networks of central nervous system, we ask if properties like synchronization/desynchronization of vasomotors have special significance to microcirculation. Thus the contemporary literature throws up a novel view of microcirculation as a network that exhibits complex, spatiotemporal and informational dynamics.

Computational models of VEGF-associated angiogenic processes in cancer

Tumour angiogenesis allows a growing mass of cancer cells to overcome oxygen diffusion limitation and to increase cell survival. The growth of capillaries from pre-existing blood vessels is the result of numerous signalling cascades involving different molecules and of cellular events involving multiple cell and tissue types. Computational models offer insight into the mechanisms governing angiogenesis and provide quantitative information on parameters difficult to assess by experiments alone. In this article, we summarize results from computational models of tumour angiogenic processes with a focus on the molecular-detailed vascular endothelial growth factor-associated models that have been developed in our laboratory, spanning multiple scales from the molecular to whole body.

Physiologically based construction of optimized 3-D arterial tree models

We present an approach to generate 3-D arterial tree models based on physiological principles while at the same time certain morphological properties are enforced at construction time in order to build individual vascular models down to the capillary level. The driving force of our approach is an angiogenesis model incorporating case-specific information about the metabolic activity in the considered domain. Additionally, we enforce morphometrically confirmed bifurcation statistics of vascular networks. The proposed method is able to generate artificial, yet physiologically plausible, arterial tree models that match the metabolic demand of the embedding tissue and fulfill the enforced morphological properties at the same time. We demonstrate the plausibility of our method on synthetic data for different metabolic configurations and analyze physiological and morphological properties of the generated tree models.

A hybrid continuum-discrete modelling approach to predict and control angiogenesis: analysis of combinatorial growth factor and matrix effects on vessel-sprouting morphology

Angiogenesis is crucial during many physiological processes and is influenced by various biochemical and biomechanical factors. Models have proved useful in understanding the mechanisms of angiogenesis and also the characteristics of the capillaries formed as part of the process. We have developed a three-dimensional hybrid, agent-field model where individual cells are modelled as sprout-forming agents in a matrix field. Cell independence, cell-cell communication and stochastic cell response are integral parts of the model. The model simulations incorporate probabilities of an individual cell to transition into one of four stages--quiescence, proliferation, migration and apoptosis. We demonstrate that several features, such as continuous sprouts, cell clustering and branching, that are observed in microfluidic experiments conducted under controlled conditions using few angiogenic factors can be reproduced by this model. We also identify the transition probabilities that result in specific sprout characteristics such as long continuous sprouts and specific branching patterns. Thus, this model can be used to cluster sprout morphology as a function of various influencing factors.

Chronic whole-body hypoxia induces intussusceptive angiogenesis and microvascular remodeling in the mouse retina

Currently, little is known about the response of the adult retinal microvasculature to hypoxia. To test the hypothesis that chronic systemic hypoxia induces angiogenesis and microvascular remodeling in the adult mouse retina, adult 10-week old female C57Bl/6 mice were exposed to 10% O(2) for 2 or 3 weeks. After hypoxia exposure, retinas were harvested, whole-mounted, and processed for immunohistochemistry. Retinas were stained with lectin, anti-smooth muscle alpha-actin antibody, and anti-NG2 antibody to visualize microvascular networks and their cellular components. Confocal microscopy was used to obtain images of superficial retinal networks. Images were analyzed to assess vessel diameter, vascular length density, branch point density, and the presence of vascular loops, a hallmark of intussusceptive angiogenesis. Both 2 and 3 weeks of hypoxia exposure resulted in a significant increase in the diameters of arterioles and post-arteriole capillaries (p<0.003). After 3 weeks of hypoxia, vascular length density and branch point density were significantly increased in retinas exposed to hypoxia as compared to normoxic controls (p<0.001). The number of vascular loops in the superficial retinal networks was significantly greater in hypoxia-exposed retinas (p < or = 0.001). Our results demonstrate, for the first time, intussusceptive angiogenesis as a tissue-level mechanism of vascular adaptation to chronic systemic hypoxia in the adult mouse retina and contribute to our understanding of hypoxia-induced angiogenesis and microvascular remodeling in the adult animal.

Multiscale models of angiogenesis

Vascular disease, cancer, stroke, neurodegeneration, diabetes, inflammation, asthma, obesity, arthritis--the list of conditions that involve angiogenesis reads like main chapters in a book on pathology. Angiogenesis, the growth of capillaries from preexisting vessels, also occurs in normal physiology, in response to exercise or in the process of wound healing.Why and when is angiogenesis prevalent? What controls the process? How can we intelligently control it? These are the key questions driving researchers in fields as diverse as cell biology, oncology, cardiology, neurology, biomathematics, systems biology, and biomedical engineering. As bioengineers, we approach angiogenesis as a complex, interconnected system of events occurring in sequence and in parallel, on multiple levels, triggered by a main stimulus, e.g., hypoxia.

Elongation, proliferation & migration differentiate endothelial cell phenotypes and determine capillary sprouting

BACKGROUND

Angiogenesis, the growth of capillaries from preexisting blood vessels, has been extensively studied experimentally over the past thirty years. Molecular insights from these studies have lead to therapies for cancer, macular degeneration and ischemia. In parallel, mathematical models of angiogenesis have helped characterize a broader view of capillary network formation and have suggested new directions for experimental pursuit. We developed a computational model that bridges the gap between these two perspectives, and addresses a remaining question in angiogenic sprouting: how do the processes of endothelial cell elongation, migration and proliferation contribute to vessel formation?

RESULTS

We present a multiscale systems model that closely simulates the mechanisms underlying sprouting at the onset of angiogenesis. Designed by agent-based programming, the model uses logical rules to guide the behavior of individual endothelial cells and segments of cells. The activation, proliferation, and movement of these cells lead to capillary growth in three dimensions. By this means, a novel capillary network emerges out of combinatorially complex interactions of single cells. Rules and parameter ranges are based on literature data on endothelial cell behavior in vitro. The model is designed generally, and will subsequently be applied to represent species-specific, tissue-specific in vitro and in vivo conditions. Initial results predict tip cell activation, stalk cell development and sprout formation as a function of local vascular endothelial growth factor concentrations and the Delta-like 4 Notch ligand, as it might occur in a three-dimensional in vitro setting. Results demonstrate the differential effects of ligand concentrations, cell movement and proliferation on sprouting and directional persistence.

CONCLUSION

This systems biology model offers a paradigm closely related to biological phenomena and highlights previously unexplored interactions of cell elongation, migration and proliferation as a function of ligand concentration, giving insight into key cellular mechanisms driving angiogenesis.

Theoretical models of microvascular oxygen transport to tissue

To improve understanding of microvascular O(2) transport, theoretical modeling has been pursued for many years. The large number of studies in this area attests to the complexities (i.e., biochemical, structural, and hemodynamic) involved. This article focuses on theoretical studies from the last two decades and, in particular, on models of O(2) transport to tissue by discrete microvessels. A brief discussion of intravascular O(2) transport is first given, highlighting the physiological importance of intravascular resistance to blood-tissue O(2) transfer. This is followed by a description of the Krogh tissue cylinder model of O(2) transport by a single capillary, which is shown to remain relevant in modified forms that relax many of the original biophysical assumptions. However, there are many geometric and hemodynamic complexities that require the consideration of microvascular arrays and networks. Multivessel models are discussed that have shown the physiological importance of heterogeneities in vessel spacing, O(2) supply, red blood cell flow path, as well as interactions between capillaries and arterioles. These realistic models require sophisticated methods for solving the governing partial differential equations, and a range of solution techniques are described. Finally, the issue of experimental validation of microvascular O(2) delivery models is discussed, and new directions in O(2) transport modeling are outlined.

Computational and mathematical modeling of angiogenesis

Over the past two decades, a number of mathematical and computational models have been developed to study different aspects of angiogenesis that span the spatial and temporal scales encompassed by this complex process. For example, models have been built to investigate how growth factors and receptors signal endothelial cell proliferation, how groups of endothelial cells assemble into individual vessels, and how tumors recruit the ingrowth of whole microvascular networks. A prudent question to pose is: "what have we learned from these models?" This review aims to answer this question as it pertains to angiogenesis in the context of normal physiological growth, tumorigenesis, wound healing, tissue engineering, and the design of therapeutic strategies. We also provide a framework for parsing angiogenesis models into categories, according to the type of modeling approach used, the spatial and temporal scales simulated, and the overarching question being posed to the model. Finally, this review introduces some of the simplification strategies and assumptions used in model building, discusses model validation, and makes recommendations for application of modeling approaches to unresolved questions in the field.

Modeling of growth factor-receptor systems from molecular-level protein interaction networks to whole-body compartment models

Most physiological processes are subjected to molecular regulation by growth factors, which are secreted proteins that activate chemical signal transduction pathways through binding of specific cell-surface receptors. One particular growth factor system involved in the in vivo regulation of blood vessel growth is called the vascular endothelial growth factor (VEGF) system. Computational and numerical techniques are well suited to handle the molecular complexity (the number of binding partners involved, including ligands, receptors, and inert binding sites) and multiscale nature (intratissue vs. intertissue transport and local vs. systemic effects within an organism) involved in modeling growth factor system interactions and effects. This chapter introduces a variety of in silico models that seek to recapitulate different aspects of VEGF system biology at various spatial and temporal scales: molecular-level kinetic models focus on VEGF ligand-receptor interactions at and near the endothelial cell surface; mesoscale single-tissue 3D models can simulate the effects of multicellular tissue architecture on the spatial variation in VEGF ligand production and receptor activation; compartmental modeling allows efficient prediction of average interstitial VEGF concentrations and cell-surface VEGF signaling intensities across multiple large tissue volumes, permitting the investigation of whole-body intertissue transport (e.g., vascular permeability and lymphatic drainage). The given examples will demonstrate the utility of computational models in aiding both basic science and clinical research on VEGF systems biology.

Full-field laser-Doppler imaging and its physiological significance for tissue blood perfusion

Using Monte Carlo simulations for a semi-infinite medium representing a skeletal muscle tissue, it is demonstrated that the zero- and first-order moments of the power spectrum for a representative pixel of a full-field laser-Doppler imager behave differently from classical laser-Doppler flowmetry. In particular, the zero-order moment has a very low sensitivity to tissue blood volume changes, and it becomes completely insensitive if the probability for a photon to interact with a moving red blood cell is above 0.05. It is shown that the loss in sensitivity is due to the strong forward scatter of the propagating photons in biological tissues (i.e., anisotropy factor g = 0.9). The first-order moment is linearly related to the root mean square of the red blood cell velocity (the Brownian component), and there is also a positive relationship with tissue blood volume. The most common physiological interpretation of the first-order moment is as tissue blood volume times expectation of the blood velocity (in probabilistic terms). In this sense, the use of the first-order moment appears to be a reasonable approach for qualitative real-time blood flow monitoring, but it does not allow us to obtain information on blood velocity or volume independently. Finally, it is shown that the spatial and temporal resolution trade-off imposed by the CMOS detectors, used in full-field laser-Doppler hardware, may lead to measurements that vary oppositely with the underlying physiological quantities. Further improvements on detectors' sampling rate will overcome this limitation.

A computational framework for modelling solid tumour growth

The biology of cancer is a complex interplay of many underlying processes, taking place at different scales both in space and time. A variety of theoretical models have been developed, which enable one to study certain components of the cancerous growth process. However, most previous approaches only focus on specific aspects of tumour development, largely ignoring the influence of the evolving tumour environment. In this paper, we present an integrative framework to simulate tumour growth, including those model components that are considered to be of major importance. We start by addressing issues at the tissue level, where the phenomena are modelled as continuum partial differential equations. We extend this model with relevant components at the cellular or even sub-cellular level in a vertical fashion. We present an implementation of this framework, covering the major processes and treat the mechanical deformation due to growth, the biochemical response to hypoxia, blood flow, oxygenation and the explicit development of a vascular system in a coupled way. The results demonstrate the feasibility of the approach and its applicability to in silico studies of the influence of different treatment strategies (like the usage of novel anti-cancer drugs) for more effective therapy design.

Emergent vascular network inhomogeneities and resulting blood flow patterns in a growing tumor

Tumors acquire sufficient oxygen and nutrient supply by coopting host vessels and neovasculature created via angiogenesis, thereby transforming a highly ordered network into chaotic heterogeneous tumor specific vasculature. Vessel regression inside the tumor leads to large regions of necrotic tissue interspersed with isolated surviving vessels. We extend our recently introduced model to incorporate Fahraeus-Lindqvist- and phase separation effects, refined tissue oxygen level computation and drug flow computations. We find, unexpectedly, that collapse and regression accelerates rather than diminishes the perfusion and that a tracer substance flowing through the remodeled network reaches all parts of the tumor vasculature very well. The reason for decreased drug delivery well known in tumors should therefore be different from collapse and vessel regression. Implications for drug delivery in real tumors are discussed.

Skeletal muscle VEGF gradients in peripheral arterial disease: simulations of rest and exercise

VEGF is a key promoter of angiogenesis and a major target of proangiogenic therapy for peripheral arterial disease (PAD). Greater understanding of VEGF angiogenic signaling and guidance by gradients for new capillaries will aid in developing new proangiogenic therapies and improving existing treatments. However, in vivo measurements of VEGF concentration gradients at the cell scale are currently impossible. We have developed a computational model to quantify VEGF distribution in extensor digitorum longus skeletal muscle using measurements of VEGF, VEGF receptor (VEGFR), and neuropilin-1 (NRP1) expression in an experimental model of rat PAD. VEGF is secreted by myocytes, diffuses through and interacts with extracellular matrix and basement membranes, and binds VEGFRs and NRP1 on endothelial cell surfaces of blood vessels. We simulate the effects of increased NRP1 expression and of therapeutic exercise training on VEGF gradients, receptor signaling, and angiogenesis. Our study predicts that angiogenic therapy for PAD may be achieved not only through VEGF upregulation but also through modulation of VEGFRs and NRP1. We predict that expression of 10(4) NRP1/cell can increase VEGF binding to receptors by 1.7-fold (vs. no NRP1); in nonexercise-trained muscle with PAD, angiogenesis is hindered due to limited VEGF upregulation, signaling, and gradients; in exercise-trained muscle, VEGF signaling is enhanced by upregulation of VEGFRs and NRP1, and VEGF signaling is strongest within the first week of exercise therapy; and hypoxia-induced VEGF release is important to direct angiogenesis towards unperfused tissue.

Microstructural analysis of deformation-induced hypoxic damage in skeletal muscle

Deep pressure ulcers are caused by sustained mechanical loading and involve skeletal muscle tissue injury. The exact underlying mechanisms are unclear, and the prevalence is high. Our hypothesis is that the aetiology is dominated by cellular deformation (Bouten et al. in Ann Biomed Eng 29:153–63, 2001; Breuls et al. in Ann Biomed Eng 31:1357–364, 2003; Stekelenburg et al. in J App Physiol 100(6):1946–954, 2006) and deformation-induced ischaemia. The experimental observation that mechanical compression induced a pattern of interspersed healthy and dead cells in skeletal muscle (Stekelenburg et al. in J App Physiol 100(6):1946–954, 2006) strongly suggests to take into account the muscle microstructure in studying damage development. The present paper describes a computational model for deformation-induced hypoxic damage in skeletal muscle tissue. Dead cells stop consuming oxygen and are assumed to decrease in stiffness due to loss of structure. The questions addressed are if these two consequences of cell death influence the development of cell injury in the remaining cells. The results show that weakening of dead cells indeed affects the damage accumulation in other cells. Further, the fact that cells stop consuming oxygen after they have died, delays cell death of other cells.

Multi-scale Computational Models of Pro-angiogenic Treatments in Peripheral Arterial Disease

The induction of angiogenesis is a promising therapeutic strategy for the amelioration of peripheral arterial disease (PAD). This occlusive disease results in muscle ischemia, and neovascularization is a route to increasing the perfusion in the tissue. The vascular endothelial growth factor (VEGF) family of potent pro-angiogenic cytokines is a potential therapeutic agent, increasing VEGF-receptor signaling on tissue vasculature. To investigate the effects of possible therapies on the VEGF concentrations and gradients within the tissue, we consider three such strategies: VEGF gene therapy (e.g. by adeno-associated virus); VEGF cell-based therapy (injected myoblasts that overexpress VEGF); and chronic exercise (which upregulates VEGF receptor expression). The multi-scale computational model used to investigate these strategies is an integration of several components: an anatomical description of the muscle geometry and cell types; microvascular blood flow; tissue oxygen distribution; VEGF secretion from muscle fibers; VEGF transport through interstitial space; and VEGF-receptor binding on microvascular endothelial cells. Exercise training, which results in increased VEGF secretion in hypoxic tissue and increased VEGF receptor expression, exhibits increases in both VEGF concentration and VEGF gradients, and is predicted to be more effective than the other, VEGF-only treatments.

VEGF gradients, receptor activation, and sprout guidance in resting and exercising skeletal muscle

Extensive experimental studies have identified vascular endothelial growth factor (VEGF) concentrations and concentration gradients as major factors in angiogenesis; however, localized in vivo measurements of these parameters have not been possible. We developed a three-dimensional computational model of skeletal muscle fibers, blood vessels, and interstitial space. Here it is applied to rat extensor digitorum longus. VEGF isoforms are secreted by myocytes, diffuse through extracellular matrix and basement membranes, and bind endothelial cell surface receptors on blood vessels. In addition, one isoform, VEGF164, binds to proteoglycans in the interstitial space. VEGF secretion rate is determined from the predicted tissue oxygen level through its effect on the hypoxia inducible factor-1alpha transcription factor. We estimate VEGF secretion and its concentrations and gradients in resting muscle and for different levels of exercise. The effects of low levels of inspired oxygen are also studied. We predict that the high spatial heterogeneity of muscle fiber VEGF secretion in hypoxic tissue leads to significant gradients of VEGF concentration and VEGF receptor activation. VEGF concentration gradients are predicted to be significant in both resting and exercising muscle (4% and 6-8% change in VEGF over 10 microm, respectively), sufficient for chemotactic guidance of 50-microm-long sprout tip cells. VEGF gradients also result in heterogeneity in VEGF receptor activation--a possible explanation for the stochasticity of sprout location. In the absence of interstitial flow, gradients are 10-fold steeper in the transverse direction (i.e., perpendicular to the muscle fibers) than in the longitudinal direction. This may explain observed perpendicular anastomoses in skeletal muscle.

Computational model of vascular endothelial growth factor spatial distribution in muscle and pro-angiogenic cell therapy

Members of the vascular endothelial growth factor (VEGF) family of proteins are critical regulators of angiogenesis. VEGF concentration gradients are important for activation and chemotactic guidance of capillary sprouting, but measurement of these gradients in vivo is not currently possible. We have constructed a biophysically and molecularly detailed computational model to study microenvironmental transport of two isoforms of VEGF in rat extensor digitorum longus skeletal muscle under in vivo conditions. Using parameters based on experimental measurements, the model includes: VEGF secretion from muscle fibers; binding to the extracellular matrix; binding to and activation of endothelial cell surface VEGF receptors; and internalization. For 2-D cross sections of tissue, we analyzed predicted VEGF distributions, gradients, and receptor binding. Significant VEGF gradients (up to 12% change in VEGF concentration over 10 mum) were predicted in resting skeletal muscle with uniform VEGF secretion, due to non-uniform capillary distribution. These relative VEGF gradients were not sensitive to extracellular matrix composition, or to the overall VEGF expression level, but were dependent on VEGF receptor density and affinity, and internalization rate parameters. VEGF upregulation in a subset of fibers increased VEGF gradients, simulating transplantation of pro-angiogenic myoblasts, a possible therapy for ischemic diseases. The number and relative position of overexpressing fibers determined the VEGF gradients and distribution of VEGF receptor activation. With total VEGF expression level in the tissue unchanged, concentrating overexpression into a small number of adjacent fibers can increase the number of capillaries activated. The VEGF concentration gradients predicted for resting muscle (average 3% VEGF/10 mum) is sufficient for cellular sensing; the tip cell of a vessel sprout is approximately 50 mum long. The VEGF gradients also result in heterogeneity in the activation of blood vessel VEGF receptors. This first model of VEGF tissue transport and heterogeneity provides a platform for the design and evaluation of therapeutic approaches.