Computational analysis of oxygen transport in the retinal arterial network

Potential measurement error from vessel reflex and multiple light paths in dual-wavelength retinal oximetry

PURPOSE

This study aims to characterize the dependence of measured retinal arterial and venous saturation on vessel diameter and central reflex in retinal oximetry, with an ultimate goal of identifying potential causes and suggesting approaches to improve measurement accuracy.

METHODS

In 10 subjects, oxygen saturation, vessel diameter and optical density are obtained using Oxymap Analyzer software without diameter correction. Diameter dependence of saturation is characterized using linear regression between measured values of saturation and diameter. Occurrences of negative values of vessel optical densities (ODs) associated with central vessel reflex are acquired from Oxymap Analyzer. A conceptual model is used to calculate the ratio of optical densities (ODRs) according to retinal reflectance properties and single and double-pass light transmission across fixed path lengths. Model-predicted values are compared with measured oximetry values at different vessel diameters.

RESULTS

Venous saturation shows an inverse relationship with vessel diameter (D) across subjects, with a mean slope of -0.180 (SE = 0.022) %/μm (20 < D < 180 μm) and a more rapid saturation increase at small vessel diameters reaching to over 80%. Arterial saturation yields smaller positive and negative slopes in individual subjects, with an average of -0.007 (SE = 0.021) %/μm (20 < D < 200 μm) across all subjects. Measurements where vessel brightness exceeds that of the retinal background result in negative values of optical density, causing an artifactual increase in saturation. Optimization of model reflectance values produces a good fit of the conceptual model to measured ODRs.

CONCLUSION

Measurement artefacts in retinal oximetry are caused by strong central vessel reflections, and apparent diameter sensitivity may result from single and double-pass transmission in vessels. Improvement in correction for vessel diameter is indicated for arteries however further study is necessary for venous corrections.

Modelling large scale artery haemodynamics from the heart to the eye in response to simulated microgravity

We investigated variations in haemodynamics in response to simulated microgravity across a semi-subject-specific three-dimensional (3D) continuous arterial network connecting the heart to the eye using computational fluid dynamics (CFD) simulations. Using this model we simulated pulsatile blood flow in an upright Earth gravity case and a simulated microgravity case. Under simulated microgravity, regional time-averaged wall shear stress (TAWSS) increased and oscillatory shear index (OSI) decreased in upper body arteries, whilst the opposite was observed in the lower body. Between cases, uniform changes in TAWSS and OSI were found in the retina across diameters. This work demonstrates that 3D CFD simulations can be performed across continuously connected networks of small and large arteries. Simulated results exhibited similarities to low dimensional spaceflight simulations and measured data-specifically that blood flow and shear stress decrease towards the lower limbs and increase towards the cerebrovasculature and eyes in response to simulated microgravity, relative to an upright position in Earth gravity.

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.

Metabolic blood flow regulation in a hybrid model of the human retinal microcirculation

The retinal vascular network supplies perfusion to vital visual structures, including retinal ganglion cells responsible for vision. Impairments in retinal blood flow and oxygenation are involved in the progression of many ocular diseases, including glaucoma. In this study, an established theoretical hybrid model of a retinal microvascular network is extended to include the effects of local blood flow regulation on oxygenation. A heterogeneous representation of the arterioles based on confocal microscopy images is combined with a compartmental description of the downstream capillaries and venules. A Green's function method is used to simulate oxygen transport in the arterioles, and a Krogh cylinder model is applied to the capillary and venular compartments. Acute blood flow regulation is simulated in response to changes in pressure, shear stress, and metabolism. Model results predict that both increased intraocular pressure and impairment of blood flow regulation can cause decreased tissue oxygenation, indicating that both mechanisms represent factors that could lead to impaired oxygenation characteristic of ocular disease. Results also indicate that the metabolic response mechanism reduces the fraction of poorly oxygenated tissue but that the pressure- and shear stress-dependent response mechanisms may hinder the vascular response to changes in oxygenation. Importantly, the heterogeneity of the vascular network demonstrates that traditionally reported average values of tissue oxygen levels hide significant localized defects in tissue oxygenation that may be involved in disease processes, including glaucoma. Ultimately, the model framework presented in this study will facilitate future comparisons to sectorial-specific clinical data to better assess the role of impaired blood flow regulation in ocular disease.

On the identification of hypoxic regions in subject-specific cerebral vasculature by combined CFD/MRI

A long-time exposure to lack of oxygen (hypoxia) in some regions of the cerebrovascular system is believed to be one of the causes of cerebral neurological diseases. In the present study, we show how a combination of magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) can provide a non-invasive alternative for studying blood flow and transport of oxygen within the cerebral vasculature. We perform computer simulations of oxygen mass transfer in the subject-specific geometry of the circle of Willis. The computational domain and boundary conditions are based on four-dimensional (4D)-flow MRI measurements. Two different oxygen mass transfer models are considered: passive (where oxygen is treated as a dilute chemical species in plasma) and active (where oxygen is bonded to haemoglobin) models. We show that neglecting haemoglobin transport results in a significant underestimation of the arterial wall mass transfer of oxygen. We identified the hypoxic regions along the arterial walls by introducing the critical thresholds that are obtained by comparison of the estimated range of Damköhler number (Da ⊂ 〈9; 57〉) with the local Sherwood number. Finally, we recommend additional validations of the combined MRI/CFD approach proposed here for larger groups of subject- or patient-specific brain vasculature systems.

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.

Self-Similar Functional Circuit Models of Arteries and Deterministic Fractal Operators: Theoretical Revelation for Biomimetic Materials

In this paper, the self-similar functional circuit models of arteries are proposed for bioinspired hemodynamic materials design. Based on the mechanical-electrical analogous method, the circuit model can be utilized to mimic the blood flow of arteries. The theoretical mechanism to quantitatively simulate realistic blood flow is developed by establishing a fractal circuit network with an infinite number of electrical components. We have found that the fractal admittance operator obtained from the minimum repeating unit of the fractal circuit can simply and directly determine the blood-flow regulation mechanism. Furthermore, according to the operator algebra, the fractal admittance operator on the aorta can be represented by Gaussian-type convolution kernel function. Similarly, the arteriolar operator can be described by Bessel-type function. Moreover, by the self-similar assembly pattern of the proposed model, biomimetic materials which contain self-similar circuits can be designed to mimic physiological or pathological states of blood flow. Studies show that the self-similar functional circuit model can efficiently describe the blood flow and provide an available and convenient structural theoretical revelation for the preparation of in vitro hemodynamic bionic materials.

Metabolic Signaling in a Theoretical Model of the Human Retinal Microcirculation

Impaired blood flow and oxygenation contribute to many ocular pathologies, including glaucoma. Here, a mathematical model is presented that combines an image-based heterogeneous representation of retinal arterioles with a compartmental description of capillaries and venules. The arteriolar model of the human retina is extrapolated from a previous mouse model based on confocal microscopy images. Every terminal arteriole is connected in series to compartments for capillaries and venules, yielding a hybrid model for predicting blood flow and oxygenation throughout the retinal microcirculation. A metabolic wall signal is calculated in each vessel according to blood and tissue oxygen levels. As expected, a higher average metabolic signal is generated in pathways with a lower average oxygen level. The model also predicts a wide range of metabolic signals dependent on oxygen levels and specific network location. For example, for high oxygen demand, a threefold range in metabolic signal is predicted despite nearly identical PO2 levels. This whole-network approach, including a spatially nonuniform structure, is needed to describe the metabolic status of the retina. This model provides the geometric and hemodynamic framework necessary to predict ocular blood flow regulation and will ultimately facilitate early detection and treatment of ischemic and metabolic disorders of the eye.

Investigating the Upstream and Downstream Hemodynamic Boundary Conditions of Healthy and Growth-Restricted Rat Feto-Placental Arterial Networks

The placenta uniquely develops to orchestrate maternal adaptations and support fetal growth and development. The expansion of the feto-placental vascular network, in part, underpins function. However it is unclear how vascular development is synergistically influenced by hemodynamics and how impairment may lead to fetal growth restriction (FGR). Here, we present a robust framework consisting of ex vivo placental casting, imaging and computational fluid dynamics of rat feto-placental networks where we investigate inlet (steady and transient) and outlet (zero-pressure, Murray's Law, asymmetric fractal trees and porous blocks) boundary conditions in a model of growth-restriction. We show that the Murray's Law flow-split boundary condition is not always appropriate and that mean steady-state inlet conditions produce comparable results to transient flow. However, we conclude that transient simulations should be adopted as they provide a larger amount of valuable data, a necessity to bridge the current knowledge gap in placental biomechanics. We also show preliminary data on changes in flow, shear stress, and flow deceleration between control and growth-restricted feto-placental networks. Our proposed framework provides a standardized approach for structural and hemodynamic analysis of feto-placental vasculature and has the potential to enhance our understanding of placental function.

A fast numerical method for oxygen supply in tissue with complex blood vessel network

Angiogenesis plays an essential role in many pathological processes such as tumor growth, wound healing, and keloid development. Low oxygen level is the main driving stimulus for angiogenesis. In an animal tissue, the oxygen level is mainly determined by three effects—the oxygen delivery through blood flow in a refined vessel network, the oxygen diffusion from blood to tissue, and the oxygen consumption in cells. Evaluation of the oxygen field is usually the bottleneck in large scale modeling and simulation of angiogenesis and related physiological processes. In this work, a fast numerical method is developed for the simulation of oxygen supply in tissue with a large-scale complex vessel network. This method employs an implicit finite-difference scheme to compute the oxygen field. By virtue of an oxygen source distribution technique from vessel center lines to mesh points and a corresponding post-processing technique that eliminate the local numerical error induced by source distribution, square mesh with relatively large mesh sizes can be applied while sufficient numerical accuracy is maintained. The new method has computational complexity which is slightly higher than linear with respect to the number of mesh points and has a convergence order which is slightly lower than second order with respect to the mesh size. With this new method, accurate evaluation of the oxygen field in a fully vascularized tissue on the scale of centimeter becomes possible.

Blood flow regulation and oxygen transport in a heterogeneous model of the mouse retina

Elevated intraocular pressure is the primary risk factor for glaucoma, yet vascular health and ocular hemodynamics have also been established as important risk factors for the disease. The precise physiological mechanisms and processes by which flow impairment and reduced tissue oxygenation relate to retinal ganglion cell death are not fully known. Mathematical modeling has emerged as a useful tool to help decipher the role of hemodynamic alterations in glaucoma. Several previous models of the retinal microvasculature and tissue have investigated the individual impact of spatial heterogeneity, flow regulation, and oxygen transport on the system. This study combines all three of these components into a heterogeneous mathematical model of retinal arterioles that includes oxygen transport and acute flow regulation in response to changes in pressure, shear stress, and oxygen demand. The metabolic signal (S_i) is implemented as a wall-derived signal that reflects the oxygen deficit along the network, and three cases of conduction are considered: no conduction, a constant signal, and a flow-weighted signal. The model shows that the heterogeneity of the downstream signal serves to regulate flow better than a constant conducted response. In fact, the increases in average tissue PO₂ due to a flow-weighted signal are often more significant than if the entire level of signal is increased. Such theoretical work supports the importance of the non-uniform structure of the retinal vasculature when assessing the capability and/or dysfunction of blood flow regulation in the retinal microcirculation.

A computational framework to investigate retinal haemodynamics and tissue stress

The process of vision begins in the retina, yet the role of biomechanical forces in the retina is relatively unknown and only recently being explored. This contribution describes a computational framework involving 3D fluid-structure interaction simulations derived from fundus images that work towards creating unique data on retinal biomechanics. We developed methods to convert 2D fundus photographs into 3D geometries that follow the curvature of the retina. Retina arterioles are embedded into a six-layer representation of the retinal tissue with varying material properties throughout the retinal tissue. Using three different human retinas (healthy, glaucoma, diabetic retinopathy) and by varying our simulation approaches, we report the effects of transient versus steady flow, viscosity assumptions (Newtonian, non-Newtonian and Fåhræus-Lindqvist effect) and rigid versus compliant retinal tissue, on resulting wall shear stress (WSS) and von Mises stress. In the retinal arterioles, the choice of viscosity model is important and WSS obtained from models with the Fåhræus-Lindqvist effect is markedly different from Newtonian and non-Newtonian models. We found little difference in WSS between steady-state and pulsatile simulations (< 5%) and show that WSS varies by about 7% between rigid and deformable models. Comparing the three geometries, we found notably different WSS in the healthy (3.3 ± 1.3 Pa), glaucoma (5.7 ± 1.6 Pa) and diabetic retinopathy cases (4.3 ± 1.1 Pa). Conversely, von Mises stress was similar in each case. We have reported a novel biomechanical framework to explore the stresses in the retina. Despite current limitations and lack of complete subject-specific physiological inputs, we believe our framework is the first of its kind and with further improvements could be useful to better understand the biomechanics of the retina.

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.

Computer simulations reveal complex distribution of haemodynamic forces in a mouse retina model of angiogenesis

There is currently limited understanding of the role played by haemodynamic forces on the processes governing vascular development. One of many obstacles to be overcome is being able to measure those forces, at the required resolution level, on vessels only a few micrometres thick. In this paper, we present an in silico method for the computation of the haemodynamic forces experienced by murine retinal vasculature (a widely used vascular development animal model) beyond what is measurable experimentally. Our results show that it is possible to reconstruct high-resolution three-dimensional geometrical models directly from samples of retinal vasculature and that the lattice-Boltzmann algorithm can be used to obtain accurate estimates of the haemodynamics in these domains. We generate flow models from samples obtained at postnatal days (P) 5 and 6. Our simulations show important differences between the flow patterns recovered in both cases, including observations of regression occurring in areas where wall shear stress (WSS) gradients exist. We propose two possible mechanisms to account for the observed increase in velocity and WSS between P5 and P6: (i) the measured reduction in typical vessel diameter between both time points and (ii) the reduction in network density triggered by the pruning process. The methodology developed herein is applicable to other biomedical domains where microvasculature can be imaged but experimental flow measurements are unavailable or difficult to obtain.

Normative values and predictors of retinal oxygen saturation

PURPOSE

To determine normal retinal oxygen saturation (SO2) values measured with retinal oximetry in a multiethnic group of healthy subjects and to evaluate the association of retinal SO2 with demographic and clinical parameters.

METHODS

Retinal oximetry was performed in both eyes of 61 normal healthy subjects. Global and quadrant venous (SvO2) and arterial oxygen saturation (SaO2), arteriovenous difference in SO2, and venular and arteriolar width were measured. The association of SO2 parameters with age, gender, ethnicity, refraction, iris color, history of controlled systemic hypertension, and smoking was analyzed.

RESULTS

Average SvO2 and SaO2 were 55.3 ± 7.1% and 90.4 ± 4.3%, respectively. All average measurements were comparable in both eyes, both genders, and among ethnic groups. Inferonasal quadrant SaO2 was higher in Asians. Age was associated with decreased SvO2 (β = -0.19; P = 0.001) and SaO2 (β = -0.11; P = 0.003). History of controlled systemic hypertension was associated with an increase in arteriovenous difference in SO2 (β = 3.99; P = 0.013).

CONCLUSION

This is the first description of retinal SO2 in healthy, multiethnic subjects. Aging decreases SvO2 and SaO2 and should be accounted for when interpreting retinal oximetry measurements. Other demographic and clinical parameters studied did not seem to significantly influence retinal SO2 measurements.

FINITE ELEMENT ANALYSIS ON FLUID FILTRATION IN SYSTEM OF PERMEABLE CURVED CAPILLARY AND TISSUE

Fluid filtration across a capillary wall, which is associated with many diseases, is noteworthy for its significant role in cancer treatment. In this study, the coupled fluid dynamic phenomenon within a capillary and its surrounding tissues has been numerically analyzed in order to investigate the effect of capillary geometry, filtration coefficient, and tissue pressure on capillary filtration. The computational domain is composed of a fluid capillary subdomain coupled with a porous tissue subdomain. The flows in the sub-domains are described by the Stokes and Darcy equations, respectively, which are solved in a coupled manner by applying a nodal replacement scheme at the capillary wall. Distributions of pressure and flow velocity are presented, which show that the interfacial pressure drop is strongly influenced by permeability, tissue boundary pressure, and capillary radii. These results provide useful information on the relationship between the interstitial flow pattern and oxygen transport.

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.

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.

Oxygen tension and gradient measurements in the retinal microvasculature of rats

BACKGROUND

Oxygen delivery from the retinal vasculature plays a crucial role in maintaining normal retinal metabolic function. Therefore, measurements of retinal vascular oxygen tension (PO(2)) and PO(2) longitudinal gradients (gPO(2)) along retinal blood vessels may help gain fundamental knowledge of retinal physiology and pathological processes.

METHODS

Three-dimensional retinal vascular PO(2) maps were generated in rats by optical section phosphorescence lifetime imaging. A major retinal artery and vein pair, and a smaller blood vessel (microvessel) between them were segmented, and PO(2) along each blood vessel was measured. In each blood vessel, an average PO(2) (mPO(2)) was calculated, and gPO(2) was determined by linear regression analysis. Reproducibility of measurements was assessed by calculating intraclass correlation coefficient (ICC) of repeated measurements. The correlations of mPO(2) and gPO(2) measurements with systemic arterial oxygen tension (P(a)O(2)) and carbon dioxide tension (P(a)CO(2)) was determined.

RESULTS

Measurements of mPO(2) and gPO(2) in retinal arteries, microvessels and veins were reproducible (ICC > 0.86; p < 0.01; N = 8), except for retinal arterial gPO(2). Retinal arterial, microvessel and venous mPO(2) were 41 ± 8, 32 ± 8 and 25 ± 7 mmHg, respectively (mean ± SD; N = 27). Retinal arterial mPO(2) was correlated with P(a)O(2) and P(a)CO(2) (R > 0.44; p < 0.03), while retinal microvessel and venous mPO(2) were only correlated with P(a)CO(2) (R > 0.68; p < 0.01). Retinal microvessel gPO(2) (-3.8 ± 1.5 mmHg/100 μm) was significantly steeper (more negative) than venous gPO(2) (0.02 ± 0.43 mmHg/100 μm) (p < 0.01; N = 27), and neither were significantly correlated with P(a)O(2) or P(a)CO(2).

CONCLUSIONS

Quantitative measurement of mPO(2) and gPO(2) in the retinal microvasculature was demonstrated. A significant decrease in PO(2) was observed along most retinal microvessels, indicative of substantial oxygen extraction by the retinal tissue. This method has the potential to help elucidate retinal microvascular oxygen transport in health and disease.