Analysis of retinal circulation using an image-based network model of retinal vasculature

Estimation of shear stress heterogeneity along capillary segments in angiogenic rat mesenteric microvascular networks

OBJECTIVE

Fluid shear stress is thought to be a regulator of endothelial cell behavior during angiogenesis. The link, however, requires an understanding of stress values at the capillary level in angiogenic microvascular networks. Critical questions remain. What are the stresses? Do capillaries experience similar stress magnitudes? Can variations explain vessel-specific behavior? The objective of this study was to estimate segment-specific shear stresses in angiogenic networks.

METHODS

Images of angiogenic networks characterized by increased vascular density were obtained from rat mesenteric tissues stimulated by compound 48/80-induced mast cell degranulation. Vessels were identified by perfusion of a 40 kDa fixable dextran prior to harvesting and immunolabeling for PECAM. Using a network flow-based segment model with physiologically relevant parameters, stresses were computed per vessel for regions across multiple networks.

RESULTS

Stresses ranged from 0.003 to 2328.1 dyne/cm2 and varied dramatically at the capillary level. For all regions, the maximum segmental shear stresses were for capillary segments. Stresses along proximal capillaries branching from arteriole inlets were increased compared to stresses along capillaries in more distal regions.

CONCLUSIONS

The results highlight the variability of shear stresses along angiogenic capillaries and motivate new discussions on how endothelial cells may respond in vivo to segment-specific microenvironment during angiogenesis.

Image-based insilico investigation of hemodynamics and biomechanics in healthy and diabetic human retinas

Retinal hemodynamics and biomechanics play a significant role in understanding the pathophysiology of several ocular diseases. However, these parameters are significantly affected due to changed blood vessel morphology ascribed to pathological conditions, particularly diabetes. In this study, an image-based computational fluid dynamics (CFD) model is applied to examine the effects of changed vascular morphology due to diabetes on blood flow velocity, vorticity, wall shear stress (WSS), and oxygen distribution and compare it with healthy. The 3D patient-specific vascular architecture of diabetic and healthy retina is extracted from Optical Coherence Tomography Angiography (OCTA) images and fundus to extract the capillary level information. Further, Fluid-structure interaction (FSI) simulations have been performed to compare the induced tissue stresses in diabetic and healthy conditions. Results illustrate that most arterioles possess higher velocity, vorticity, WSS, and lesser oxygen concentration than arteries for healthy and diabetic cases. However, an opposite trend is observed for venules and veins. Comparisons show that, on average, the blood flow velocity in the healthy case decreases by 42 % in arteries and 21 % in veins, respectively, compared to diabetic. In addition, the WSS and von Mises stress (VMS) in healthy case decrease by 49 % and 72 % in arteries and by 6 % and 28 % in veins, respectively, when compared with diabetic, making diabetic blood vessels more susceptible to wall rupture and tissue damage. The in-silico results may help predict the possible abnormalities region early, helping the ophthalmologists use these estimates as prognostic tools and tailor patient-specific treatment plans.

Methods to measure blood flow and vascular reactivity in the retina

Disturbances of retinal perfusion are involved in the onset and maintenance of several ocular diseases, including diabetic retinopathy, glaucoma, and retinal vascular occlusion. Hence, knowledge on ocular vascular anatomy and function is highly relevant for basic research studies and for clinical judgment and treatment. The retinal vasculature is composed of the superficial, intermediate, and deep vascular layer. Detection of changes in blood flow and vascular diameter especially in smaller vessels is essential to understand and to analyze vascular diseases. Several methods to evaluate blood flow regulation in the retina have been described so far, but no gold standard has been established. For highly reliable assessment of retinal blood flow, exact determination of vessel diameter is necessary. Several measurement methods have already been reported in humans. But for further analysis of retinal vascular diseases, studies in laboratory animals, including genetically modified mice, are important. As for mice, the small vessel size is challenging requiring devices with high optic resolution. In this review, we recapitulate different methods for retinal blood flow and vessel diameter measurement. Moreover, studies in humans and in experimental animals are described.

Ocular Fluid Mechanics and Drug Delivery: A Review of Mathematical and Computational Models

The human eye is a complex biomechanical structure with a range of biomechanical processes involved in various physiological as well as pathological conditions. Fluid flow inside different domains of the eye is one of the most significant biomechanical processes that tend to perform a wide variety of functions and when combined with other biophysical processes play a crucial role in ocular drug delivery. However, it is quite difficult to comprehend the effect of these processes on drug transport and associated treatment experimentally because of ethical constraints and economic feasibility. Computational modeling on the other hand is an excellent means to understand the associated complexity between these aforementioned processes and drug delivery. A wide range of computational models specific to different types of fluids present in different domains of the eye as well as varying drug delivery modes has been established to understand the fluid flow behavior and drug transport phenomenon in an insilico manner. These computational models have been used as a non-invasive tool to aid ophthalmologists in identifying the challenges associated with a particular drug delivery mode while treating particular eye diseases and to advance the understanding of the biomechanical behavior of the eye. In this regard, the author attempts to summarize the existing computational and mathematical approaches proposed in the last two decades for understanding the fluid mechanics and drug transport associated with different domains of the eye, together with their application to modify the existing treatment processes.

Microcirculatory model predicts blood flow and autoregulation range in the human retina: in vivo investigation with laser speckle flowgraphy

In this study, we mathematically predict retinal vascular resistance (RVR) and retinal blood flow (RBF), we test predictions using laser speckle flowgraphy (LSFG), we estimate the range of vascular autoregulation, and we examine the relationship of RBF with the retinal nerve fiber layer (RNFL) and ganglion cell complex (GCC). Fundus, optical coherence tomography (OCT), and OCT-angiography images, systolic/diastolic blood pressure (SBP/DBP), and intraocular pressure (IOP) measurements were obtained from 36 human subjects. We modeled two circulation markers (RVR and RBF) and estimated individualized lower/higher autoregulation limits (LARL/HARL), using retinal vessel calibers, fractal dimension, perfusion pressure, and population-based hematocrit values. Quantitative LSFG waveforms were extracted from vessels of the same eyes, before and during IOP elevation. LSFG metrics explained most variance in RVR (R² = 0.77/P = 6.9·10^-9) and RBF (R² = 0.65/P = 1.0·10^-6), suggesting that the markers strongly reflect blood flow physiology. Higher RBF was associated with thicker RNFL (P = 4.0·10^-4) and GCC (P = 0.003), thus also verifying agreement with structural measurements. LARL was at SBP/DBP of 105/65 mmHg for the average subject without arterial hypertension and at 115/75 mmHg for the average hypertensive subject. Moreover, during IOP elevation, changes in RBF were more pronounced than changes in RVR. These observations physiologically imply that healthy subjects are already close to LARL, thus prone to hypoperfusion. In conclusion, we modeled two clinical markers and described a novel method to predict individualized autoregulation limits. These findings could improve understanding of retinal perfusion and pave the way for personalized intervention decisions, when treating patients with coexisting ophthalmic and cardiovascular pathologies.NEW & NOTEWORTHY We describe and test a new approach to quantify retinal blood flow, based on standard clinical examinations and imaging techniques, linked together with a physiological model. We use these findings to generate individualized estimates of the autoregulation range. We provide evidence that healthy subjects are closer to the lower autoregulation limit than thought before. This suggests that some retinas are less prepared to withstand hypoperfusion, even after small intraocular pressure rises or blood pressure drops.

Spatial distribution of CD115+ and CD11b+ cells and their temporal activation during oxygen-induced retinopathy in mice

PURPOSE

The model of oxygen-induced retinopathy (OIR) is widely used to analyze pathomechanisms in retinal neovascularization. Previous studies have shown that macrophages (MP) play a key role in vessel formation in OIR, the influence of microglia (MG) having been discussed. The aim of our study was to analyze the spatial and temporal distribution and activation of MP/MG expressing CD115 and CD11b during the process of neovascularization in OIR.

METHODS

We used MacGreen mice expressing the green fluorescence protein (GFP) under the promoter for CD115. CD115⁺ cells were investigated in vivo by scanning laser ophthalmoscopy at postnatal days (P) 17 and 21 in MacGreen mice with OIR (75% oxygen from P7 to P12), and were compared to MacGreen room-air controls. In addition MP/MG were examined ex vivo using immunohistochemistry for CD11b⁺ detection on retinal flatmounts at P14, P17, and P21 of wild type mice with OIR.

RESULTS

In-vivo imaging revealed the highest density of activated MP/MG in tuft areas at P17 of MacGreen mice with OIR. Tufts and regions with a high density of CD115⁺ cells were detected close to veins, rather to arteries. In peripheral, fully vascularized areas, the distribution of CD115⁺ cells in MacGreen mice with OIR was similar to MacGreen room-air controls. Correspondingly, immunohistochemical analyses of retinal flatmounts from wild type mice with OIR induction revealed that the number of CD11b⁺ cells significantly varies between vascular, avascular, and tuft areas as well as between the retinal layers. Activated CD11b⁺ cells were almost exclusively found in avascular areas and tufts of wild type mice with OIR induction; here, the proportion of activated cells related to the total number of CD11b⁺ cells remained stable over the course of time.

CONCLUSIONS

Using two different approaches to monitor MP/MG cells, our findings demonstrated that MP/MG concentrate within pathologically vascularized areas during OIR. We were able to clarify that reactive changes of CD11b⁺ cell distribution to OIR primarily occur in the deep retinal layers. Furthermore, we found the highest proportion of activated CD11b⁺ cells in regions with pathologic neovascularization processes. Our findings support previous reports about activated MP/MG guiding revascularization in avascular areas and playing a key role in the formation and regression of neovascular tufts.

Increased Retinal Oxygen Metabolism Precedes Microvascular Alterations in Type 1 Diabetic Mice

Purpose

To investigate inner retinal oxygen metabolic rate (IRMRO₂) during early stages of type 1 diabetes in a transgenic mouse model.

Methods

In current study, we involved seven diabetic mice (Akita/+, TSP1^−/−) and seven control mice (TSP1^−/−), and applied visible-light optical coherence tomography (vis-OCT) to image functional parameters including retinal blood flow rate, oxygen saturation (sO₂) and the IRMRO₂ value longitudinally from 5 weeks of age to 13 weeks of age. After imaging at 13 weeks of age, we analyzed the imaging results, and examined histology of mouse retina.

Results

Between diabetic mice and the control group, we observed significant differences in venous sO₂ from 9 weeks of age (P = 0.006), and significant increment in IRMRO₂ from 11 weeks of age (P = 0.001) in diabetic mice compared with control group. We did not find significant differences in retinal blood flow rate as well as arterial sO₂ during imaging between diabetic and control mice. Histologic examination of diabetic and control mice at 13 weeks of age also revealed no anatomical retinal alternations.

Conclusions

In diabetic retinopathy, complications in retinal oxygen metabolism may occur before changes of retinal anatomical structure.

Model Microvascular Networks Can Have Many Equilibria

We show that large microvascular networks with realistic topologies, geometries, boundary conditions, and constitutive laws can exhibit many steady-state flow configurations. This is in direct contrast to most previous studies which have assumed, implicitly or explicitly, that a given network can only possess one equilibrium state. While our techniques are general and can be applied to any network, we focus on two distinct network types that model human tissues: perturbed honeycomb networks and random networks generated from Voronoi diagrams. We demonstrate that the disparity between observed and predicted flow directions reported in previous studies might be attributable to the presence of multiple equilibria. We show that the pathway effect, in which hematocrit is steadily increased along a series of diverging junctions, has important implications for equilibrium discovery, and that our estimates of the number of equilibria supported by these networks are conservative. If a more complete description of the plasma skimming effect that captures red blood cell allocation at junctions with high feed hematocrit were to be obtained empirically, then the number of equilibria found by our approach would at worst remain the same and would in all likelihood increase significantly.

Mathematical and computational models of the retina in health, development and disease

The retina confers upon us the gift of vision, enabling us to perceive the world in a manner unparalleled by any other tissue. Experimental and clinical studies have provided great insight into the physiology and biochemistry of the retina; however, there are questions which cannot be answered using these methods alone. Mathematical and computational techniques can provide complementary insight into this inherently complex and nonlinear system. They allow us to characterise and predict the behaviour of the retina, as well as to test hypotheses which are experimentally intractable. In this review, we survey some of the key theoretical models of the retina in the healthy, developmental and diseased states. The main insights derived from each of these modelling studies are highlighted, as are model predictions which have yet to be tested, and data which need to be gathered to inform future modelling work. Possible directions for future research are also discussed. Whilst the present modelling studies have achieved great success in unravelling the workings of the retina, they have yet to achieve their full potential. For this to happen, greater involvement with the modelling community is required, and stronger collaborations forged between experimentalists, clinicians and theoreticians. It is hoped that, in addition to bringing the fruits of current modelling studies to the attention of the ophthalmological community, this review will encourage many such future collaborations.

Inner retinal oxygen metabolism in the 50/10 oxygen-induced retinopathy model

Retinopathy of prematurity (ROP) represents a major cause of childhood vision loss worldwide. The 50/10 oxygen-induced retinopathy (OIR) model mimics the findings of ROP, including peripheral vascular attenuation and neovascularization. The oxygen metabolism of the inner retina has not been previously explored in this model. Using visible-light optical coherence tomography (vis-OCT), we measured the oxygen saturation of hemoglobin and blood flow within inner retinal vessels, enabling us to compute the inner retinal oxygen delivery (irDO₂) and metabolic rate of oxygen (irMRO₂). We compared these measurements between age-matched room-air controls and rats with 50/10 OIR on postnatal day 18. To account for a 61% decrease in the irDO₂ in the OIR group, we found an overall statistically significant decrease in retinal vascular density affecting the superficial and deep retinal vascular capillary networks in rats with OIR compared to controls. Furthermore, matching the reduced irDO₂, we found a 59% decrease in irMRO₂, which we correlated with a statistically significant reduction in retinal thickness in the OIR group, suggesting that the decreased irMRO₂ was due to decreased neuronal oxygen utilization. By exploring these biological and metabolic changes in great detail, our study provides an improved understanding of the pathophysiology of OIR model.

Measurement of Retinal Blood Flow Using Fluorescently Labeled Red Blood Cells

Blood flow is a useful indicator of the metabolic state of the retina. However, accurate measurement of retinal blood flow is difficult to achieve in practice. Most existing optical techniques used for measuring blood flow require complex assumptions and calculations. We describe here a simple and direct method for calculating absolute blood flow in vessels of all sizes in the rat retina. The method relies on ultrafast confocal line scans to track the passage of fluorescently labeled red blood cells (fRBCs). The accuracy of the blood flow measurements was verified by (1) comparing blood flow calculated independently using either flux or velocity combined with diameter measurements, (2) measuring total retinal blood flow in arterioles and venules, (3) measuring blood flow at vessel branch points, and (4) measuring changes in blood flow in response to hyperoxic and hypercapnic challenge. Confocal line scans oriented parallel and diagonal to vessels were used to compute fRBC velocity and to examine velocity profiles across the width of vessels. We demonstrate that these methods provide accurate measures of absolute blood flow and velocity in retinal vessels of all sizes.

Effect of intraocular pressure on the hemodynamics of the central retinal artery: a mathematical model

Retinal hemodynamics plays a crucial role in the pathophysiology of several ocular diseases. There are clear evidences that the hemodynamics of the central retinal artery (CRA) is strongly affected by the level of intraocular pressure (IOP), which is the pressure inside the eye globe. However, the mechanisms through which this occurs are still elusive. The main goal of this paper is to develop a mathematical model that combines the mechanical action of IOP and the blood flow in the CRA to elucidate the mechanisms through which IOP elevation affects the CRA hemodynamics. Our model suggests that the development of radial compressive regions in the lamina cribrosa (a collagen structure in the optic nerve pierced by the CRA approximately in its center) might be responsible for the clinically-observed blood velocity reduction in the CRA following IOP elevation. The predictions of the mathematical model are in very good agreement with experimental and clinical data. Our model also identifies radius and thickness of the lamina cribrosa as major factors affecting the IOP-CRA relationship, suggesting that anatomical differences among individuals might lead to different hemodynamic responses to IOP elevation.

Cerebral malaria in children: using the retina to study the brain

Cerebral malaria is a dangerous complication of Plasmodium falciparum infection, which takes a devastating toll on children in sub-Saharan Africa. Although autopsy studies have improved understanding of cerebral malaria pathology in fatal cases, information about in vivo neurovascular pathogenesis is scarce because brain tissue is inaccessible in life. Surrogate markers may provide insight into pathogenesis and thereby facilitate clinical studies with the ultimate aim of improving the treatment and prognosis of cerebral malaria. The retina is an attractive source of potential surrogate markers for paediatric cerebral malaria because, in this condition, the retina seems to sustain microvascular damage similar to that of the brain. In paediatric cerebral malaria a combination of retinal signs correlates, in fatal cases, with the severity of brain pathology, and has diagnostic and prognostic significance. Unlike the brain, the retina is accessible to high-resolution, non-invasive imaging. We aimed to determine the extent to which paediatric malarial retinopathy reflects cerebrovascular damage by reviewing the literature to compare retinal and cerebral manifestations of retinopathy-positive paediatric cerebral malaria. We then compared retina and brain in terms of anatomical and physiological features that could help to account for similarities and differences in vascular pathology. These comparisons address the question of whether it is biologically plausible to draw conclusions about unseen cerebral vascular pathogenesis from the visible retinal vasculature in retinopathy-positive paediatric cerebral malaria. Our work addresses an important cause of death and neurodisability in sub-Saharan Africa. We critically appraise evidence for associations between retina and brain neurovasculature in health and disease, and in the process we develop new hypotheses about why these vascular beds are susceptible to sequestration of parasitized erythrocytes.

Theoretical analysis of vascular regulatory mechanisms contributing to retinal blood flow autoregulation

PURPOSE

To study whether impaired retinal autoregulation is a risk factor for glaucoma, the relationship between vascular regulatory mechanisms and glaucoma progression needs to be investigated. In this study, a vascular wall mechanics model is used to predict the relative importance of regulatory mechanisms in achieving retinal autoregulation.

METHODS

Resistance vessels are assumed to respond to changes in pressure, shear stress, carbon dioxide (CO2), and the downstream metabolic state communicated via conducted responses. Model parameters governing wall tension are fit to pressure and diameter data from porcine retinal arterioles. The autoregulation pressure range for control and elevated levels of IOP is predicted.

RESULTS

The factor by which flow changes as the blood pressure exiting the central retinal artery is varied between 28 and 40 mm Hg is used to indicate the degree of autoregulation (1 indicates perfect autoregulation). In the presence of only the myogenic response mechanism, the factor is 2.06. In the presence of the myogenic and CO2 responses, the factor is 1.22. The combination of myogenic, shear, CO2, and metabolic responses yields the best autoregulation (factor of 1.10).

CONCLUSIONS

Model results are compared with flow and pressure data from multiple patient studies, and the combined effects of the metabolic and CO2 responses are predicted to be critical for achieving retinal autoregulation. When IOP is elevated, the model predicts a decrease in the autoregulation range toward low perfusion pressure, which is consistent with observations that glaucoma is associated with decreased perfusion pressure.

Regional morphology and pathophysiology of retinal vascular disease

Disturbances in the retinal vascular supply are involved in the pathophysiology of the most frequent diseases causing visual impairment and blindness in the Western World. These diseases are diagnosed by noting how morphological lesions in the retina vary in shape, size, location and dynamics, and subsequently concluding the presence of a specific disease entity. This diagnostic approach can be used to identify the site of a retinal vascular occlusion, to assess whether retinal diseases are primarily due to changes in the larger retinal vessels or the microcirculation, and to differentiate the relative involvement of the choroidal and the retinal vascular systems. However, a number of morphological manifestations of retinal vascular disease cannot presently be related to the underlying pathophysiology. The review concludes that there is a need for developing new methods for assessing vascular structure and function in the ciliary vascular system supplying the choroid and the optic nerve head. Presently, the study of these structures relies on imaging techniques with limited penetration and resolution into the tissue. Secondly, there is a need for studying oscillations in retinal vascular function occurring within days to weeks, and for studying regional manifestations of retinal vascular disease. This may constitute the basis for future research in retinal vascular pathophysiology and for the development of new treatment modalities to reduce blindness secondary to retinal vascular disease.

Ocular hemodynamics and glaucoma: the role of mathematical modeling

PURPOSE

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma.

METHODS

We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation.

RESULTS

Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression.

CONCLUSION

Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

Thioredoxin Interacting Protein (TXNIP) and Pathogenesis of Diabetic Retinopathy

Chronic hyperglycemia (HG)-associated reactive oxygen/nitrogen species (ROS/RNS) stress and low grade inflammation are considered to play critical roles in the development of diabetic retinopathy (DR). Excess glucose metabolic flux through the aldose reductase/polyol pathway, advanced glycation end product (AGE) formation, elevated hexosamine biosynthesis pathway (HBP), diacyl glycerol/PKC activation, and mitochondrial ROS generation are all implicated in DR. In addition, endoplasmic reticulum stress/unfolded protein response (er-UPR) and deregulation of mitochondrial quality control by autophagy/mitophagy are observed causing cellular bioenergetic deficiency and injury. Recently, a pro-oxidant and pro-apoptotic thioredoxin interacting protein (TXNIP) was shown to be highly upregulated in DR and by HG in retinal cells in culture. TXNIP binds to thioredoxin (Trx) inhibiting its oxidant scavenging and thiolreducing capacity. Hence, prolonged overexpression of TXNIP causes ROS/RNS stress, mitochondrial dysfunction, inflammation and premature cell death in DR. Initially, DR was considered as microvascular complications of endothelial dysfunction and pericyte loss characterized by capillary basement membrane thickening, pericyte ghost, blood retinal barrier leakage, acellular capillary and neovascularization. However, it is currently acknowledged that neuro-glia are also affected by HG in diabetes and that neuronal injury, glial activation, innate immunity/sterile inflammation, and ganglion apoptosis occur early in DR. In addition, retinal pigment epithelium (RPE) becomes dysfunctional in DR. Since TXNIP is induced by HG in most cells, its effects are not restricted to a particular cell type in DR. However, depending on the metabolic activity and anti-oxidant capacity, some cells may be affected earlier by TXNIP than others. Identification of TXNIP sensitive cells and elucidating the underlying mechanism(s) will be critical for preventing pre-mature cell death and progression of DR.

A hybrid discrete-continuum mathematical model of pattern prediction in the developing retinal vasculature

Pathological angiogenesis has been extensively explored by the mathematical modelling community over the past few decades, specifically in the contexts of tumour-induced vascularisation and wound healing. However, there have been relatively few attempts to model angiogenesis associated with normal development, despite the availability of animal models with experimentally accessible and highly ordered vascular topologies: for example, growth and development of the vascular plexus layers in the murine retina. The current study aims to address this issue through the development of a hybrid discrete-continuum mathematical model of the developing retinal vasculature in neonatal mice that is closely coupled with an ongoing experimental programme. The model of the functional vasculature is informed by a range of morphological and molecular data obtained over a period of several days, from 6 days prior to birth to approximately 8 days after birth. The spatio-temporal formation of the superficial retinal vascular plexus (RVP) in wild-type mice occurs in a well-defined sequence. Prior to birth, astrocytes migrate from the optic nerve over the surface of the inner retina in response to a chemotactic gradient of PDGF-A, formed at an earlier stage by migrating retinal ganglion cells (RGCs). Astrocytes express a variety of chemotactic and haptotactic proteins, including VEGF and fibronectin (respectively), which subsequently induce endothelial cell sprouting and modulate growth of the RVP. The developing RVP is not an inert structure; however, the vascular bed adapts and remodels in response to a wide variety of metabolic and biomolecular stimuli. The main focus of this investigation is to understand how these interacting cellular, molecular, and metabolic cues regulate RVP growth and formation. In an earlier one-dimensional continuum model of astrocyte and endothelial migration, we showed that the measured frontal velocities of the two cell types could be accurately reproduced by means of a system of five coupled partial differential equations (Aubert et al. in Bull. Math. Biol. 73:2430-2451, 2011). However, this approach was unable to generate spatial information and structural detail for the entire retinal surface. Building upon this earlier work, a more realistic two-dimensional hybrid PDE-discrete model is derived here that tracks the migration of individual astrocytes and endothelial tip cells towards the outer retinal boundary. Blood perfusion is included throughout plexus development and the emergent retinal architectures adapt and remodel in response to various biological factors. The resulting in silico RVP structures are compared with whole-mounted retinal vasculatures at various stages of development, and the agreement is found to be excellent. Having successfully benchmarked the model against wild-type data, the effect of transgenic over-expression of various genes is predicted, based on the ocular-specific expression of VEGF-A during murine development. These results can be used to help inform future experimental investigations of signalling pathways in ocular conditions characterised by aberrant angiogenesis.

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.

Dynamics of angiogenesis during murine retinal development: a coupled in vivo and in silico study

The manner in which the superficial retinal vascular plexus (RVP) develops in neonatal wild-type mice is relatively well documented and poses an interesting challenge to the mathematical modelling community. Prior to birth, astrocyte sprouting and proliferation begin around the edge of the optic nerve head, and subsequent astrocyte migration in response to a chemotactic gradient of platelet-derived growth factor (PDGF)-A results in the formation of a dense scaffold on the surface of the inner retina. Astrocytes express a variety of chemotactic and haptotactic proteins that subsequently induce endothelial cell sprouting and modulate growth of the RVP. An experimentally informed, two-dimensional hybrid partial differential equation-discrete model is derived to track the outward migration of individual astrocyte and endothelial tip cells in response to the appropriate biochemical cues. Blood perfusion is included throughout the development of the plexus, and the evolving retinal trees are allowed to adapt and remodel by means of several biological stimuli. The resulting wild-type in silico RVP structures are compared with corresponding experimental whole mounts taken at various stages of development, and agreement between the respective vascular morphologies is found to be excellent. Subsequent numerical predictions help elucidate some of the key biological processes underlying retinal development and demonstrate the potential of the virtual retina for the investigation of various vascular-related diseases of the eye.

Msx1 is expressed in retina endothelial cells at artery branching sites

Msx1 and Msx2 encode homeodomain transcription factors that play a role in several embryonic developmental processes. Previously, we have shown that in the adult mouse, Msx1(lacZ) is expressed in vascular smooth muscle cells (VSMCs) and pericytes, and that Msx2(lacZ) is also expressed in VSMCs as well as in a few endothelial cells (ECs). The mouse retina and choroid are two highly vascularized tissues. Vessel alterations in the retina are associated with several human diseases and the retina has been intensely used for angiogenesis studies, whereas the choroid has been much less investigated. Using the Msx1(lacZ) and Msx2(lacZ) reporter alleles, we observed that Msx2 is not expressed in the eye vascular tree in contrast to Msx1, for which we establish the spatial and temporal expression pattern in these tissues. In the retina, expression of Msx1 takes place from P3, and by P10, it becomes confined to a subpopulation of ECs at branching points of superficial arterioles. These branching sites are characterized by a subpopulation of mural cells that also show specific expression programs. Specific Msx gene inactivation in the endothelium, using Msx1 and Msx2 conditional mutant alleles together with a Tie2-Cre transgene, did not lead to conspicuous structural defects in the retinal vascular network. Expression of Msx1 at branching sites might therefore be linked to vessel physiology. The retinal blood flow is autonomously regulated and perfusion of capillaries has been proposed to depend on arteriolar precapillary structures that might be the sites for Msx1 expression. On the other hand, branching sites are subject to shear stress that might induce Msx1 expression. In the choroid vascular layer Msx1(lacZ) is expressed more broadly and dynamically. At birth Msx1(lacZ) expression takes place in the endothelium but at P21 its expression has shifted towards the mural layer. We discuss the possible functions of Msx1 in the eye vasculature.

Assessment of Energy Requirement for the Retinal Arterial Network in Normal and Hypertensive Subjects

The retinal arterial network structure can be altered by systemic diseases such as hypertension and diabetes. In order to compare the energy requirement for maintaining retinal blood flow and vessel wall metabolism between normal and hypertensive subjects, 3D hypothetical models of a representative retinal arterial bifurcation were constructed based on topological features derived from retinal images. Computational analysis of blood flow was performed, which accounted for the non-Newtonian rheological properties of blood and peripheral vessel resistance. The results suggested that the rate of energy required to maintain the blood flow and wall metabolism is much lower for normal subjects than for hypertensives, with the latter requiring 49.2% more energy for an entire retinal arteriolar tree. Among the several morphological factors, length-to-diameter ratio was found to have the most significant influence on the overall energy requirement.

Development of an image-based model for capillary vasculature of retina

The paper presents a method of development of a detailed network model to represent retinal capillary vasculature. The capillary model is a circular mesh consisting of concentric rings with an increasing diameter. Each of the rings has uniformly distributed bifurcation nodes to represent capillary vessels. The model is customized using the data that has been measured from confocal microscopic images of a mouse retina. The capillary model developed can be connected to networks of larger vessels of the vasculature such as arterial and venous networks to form a complete model of the retinal network. A method to automate such interface connections between capillary and other vascular networks using connecting vessels (i.e., pre-capillary and post-capillary) is also presented in the paper. Such a detailed image-based capillary model together with the arterial and venular networks can be used for various circulation simulations to obtain accurate information on hemodynamic quantities such as the spatial distribution of pressure and flow in the vasculature for both physiological and pathological conditions. The method presented for the development of the capillary model can also be adopted for vasculatures of other organs.