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

Linking Vascular Structure and Function: Image-Based Virtual Populations of the Retina

Purpose

This study explored the relationship among microvascular parameters as delineated by optical coherence tomography angiography (OCTA) and retinal perfusion. Here, we introduce a versatile framework to examine the interplay between the retinal vascular structure and function by generating virtual vasculatures from central retinal vessels to macular capillaries. Also, we have developed a hemodynamics model that evaluates the associations between vascular morphology and retinal perfusion.

Methods

The generation of the vasculature is based on the distribution of four clinical parameters pertaining to the dimension and blood pressure of the central retinal vessels, constructive constrained optimization, and Voronoi diagrams. Arterial and venous trees are generated in the temporal retina and connected through three layers of capillaries at different depths in the macula. The correlations between total retinal blood flow and macular flow fraction and vascular morphology are derived as Spearman rank coefficients, and uncertainty from input parameters is quantified.

Results

A virtual cohort of 200 healthy vasculatures was generated. Means and standard deviations for retinal blood flow and macular flow fraction were 20.80 ± 7.86 µL/min and 15.04% ± 5.42%, respectively. Retinal blood flow was correlated with vessel area density, vessel diameter index, fractal dimension, and vessel caliber index. The macular flow fraction was not correlated with any morphological metrics.

Conclusions

The proposed framework is able to reproduce vascular networks in the macula that are morphologically and functionally similar to real vasculature. The framework provides quantitative insights into how macular perfusion can be affected by changes in vascular morphology delineated on OCTA.

Lessons From The Glaucoma Foundation Think Tank 2023: A Patient-Centric Approach to Glaucoma

PRCIS

The main takeaways also included that BIG DATA repositories and AI are important combinatory tools to foster novel strategies to prevent and stabilize glaucoma and, in the future, recover vision loss from the disease.

PURPOSE

To summarize the main topics discussed during the 28th Annual Glaucoma Foundation Think Tank Meeting "A Patient-Centric Approach to Glaucoma" held in New York on June 9 and 10, 2023.

METHODS

The highlights of the sessions on BIG DATA, genetics, modifiable lifestyle risk factors, female sex hormones, and neuroprotection in the field of primary open angle glaucoma (POAG) were summarized.

RESULTS

The researchers discussed the importance of BIG DATA repositories available at national and international levels for POAG research, including the United Kingdom Biobank. Combining genotyped large cohorts worldwide, facilitated by artificial intelligence (AI) and machine-learning approaches, led to the milestone discovery of 312 genome-wide significant disease loci for POAG. While these loci could be combined into a polygenic risk score with clinical utility, Think Tank meeting participants also provided analytical epidemiological evidence that behavioral risk factors modify POAG polygenetic risk, citing specific examples related to caffeine and alcohol use. The impact of female sex hormones on POAG pathophysiology was discussed, as was neuroprotection and the potential use of AI to help mitigate specific challenges faced in clinical trials and speed approval of neuroprotective agents.

CONCLUSIONS

The experts agreed on the importance of genetics in defining individual POAG risk and highlighted the additional crucial role of lifestyle, gender, blood pressure, and vascular risk factors. The main takeaways also included that BIG DATA repositories and AI are important combinatory tools to foster novel strategies to prevent and stabilize glaucoma and, in the future, recover vision loss from the disease.

Variability in Capillary Perfusion Is Increased in Regions of Retinal Ischemia Due to Branch Retinal Vein Occlusion

Purpose

To investigate alterations in macular perfusion variability due to branch retinal vein occlusion (BRVO) using a novel approach based on optical coherence tomography angiography (OCTA) coefficient of variation (CoV) analysis.

Methods

Thirteen eyes of 13 patients with macular ischemia due to BRVO were studied. Multiple consecutive en face OCTA images were acquired. Bias field correction, spatial alignment, and normalization of intensities across the images were performed followed by pixelwise computation of standard deviation divided by the mean to generate a CoV map. Region of interest-based CoV values, derived from this map, for arterioles, venules, and the microvasculature were compared between regions with macular ischemia and control areas of the same eye. Control areas were regions of the same macula that were not affected by the BRVO and had normal retinal vascular structure as seen on multimodal imaging and normal retinal vascular density measurements as quantified using OCTA.

Results

CoV increased by a mean value of 17.6% within the microvasculature of ischemic regions compared to the control microvasculature (P < 0.0001). CoV measurements of microvasculature were consistently greater in the ischemic area of all 13 eyes compared to control. There were no differences in CoV measurements between ischemic and control areas for arterioles (P = 0.13) and venules (P = 1.0).

Conclusions

Greater variability in microvasculature perfusion occurs at sites of macular ischemia due to BRVO. We report a novel way for quantifying macular perfusion variability using OCTA. This technique may have applicability for studying the pathophysiology of other retinal vascular diseases.

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.

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

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

Evaluation of retinal vessel and perfusion density in migraine patients by optical coherence tomography angiography

BACKGROUND

Migraine is a neurovascular disease and has been reported as a risk factor for ocular vascular complications. Our study aimed to compare the retinal vessel density and perfusion density between migraine patients and healthy subjects by optical coherence tomography angiography (OCTA).

METHODS

In this prospective study, 23 patients with migraine with aura (MWA) and 31 patients with migraine without aura (MWOA), and 32 age- and gender-matched healthy controls (HC) were enrolled. The vessel density (VD) and perfusion density (PD) were evaluated in a 6 × 6 mm scan of the macula and optic nerve head (ONH) with the Cirrus HD-OCT 5000 device. The measurement area is divided into three areas: center (c), inner ring (ir), outer ring (or) (with diameters of 1, 3, and 6 mm respectively), and nine subfields, according to the Early Treatment Retinopathy Study grid.

RESULTS

The macular cVD, cPD, and temporal orVD in MWA and MWOA groups were significantly reduced than those of HC. On optic nerve head OCTA, patients with MWA had decreased cVD, average irVD, inferior irVD, and temporal orVD compared with HCs while MWOA had reduced cVD than HC group. In addition, PD was not significantly different among MWA, MWOA, and HC groups in any measure in the optic nerve head. The Migraine Disability Assessment Score (MIDAS) and attack frequency were significantly inversely correlated with cVD, cPD, irVD, and irPD of macula and ONH.

CONCLUSIONS

Vessel and perfusion density of macula were reduced in both MWA and MWOA. Vessel density, but not perfusion density of ONH was decreased in MWA. The migraine severity and attack frequency were significantly inversely correlated with vessel and perfusion density of macula and ONH.

Subretinal fluid disturbs the retinal venous blood flow in central serous chorioretinopathy

The significance of subretinal fluid in the retinal blood flow is unclear. Here, we evaluated the association between subretinal fluid (SRF) and retinal blood flow in eyes with central serous chorioretinopathy (CSC) using a retinal functional imager (RFI) and optical coherence tomography angiography (OCTA). In this retrospective case–control study involving 26 eyes from 18 CSC patients and 25 eyes from 21 age- and sex-matched controls, we found that the CSC group showed significant differences from the control group in terms of the retinal venule blood flow velocity (3.60 ± 0.43 vs 3.96 ± 0.56 mm/s; p = 0.030), retinal venule blood flow rate (8.75 ± 2.67 vs 12.51 ± 7.12 nl/s; p = 0.040), and the diameter of retinal venules (118.26 ± 14.25 vs 126.92 ± 35.31 μm; p = 0.045). Linear regression analysis showed that SRF thickness accounted for a 36.9% reduction in venous BFR (p = 0.013). The difference in the O₂ saturation between retinal arteries and veins was greater in the CSC group. There was no correlation between SRF thickness and capillary densities in OCTA. Our findings suggest that disturbance in venous return and the associated altered oxygen may be significant changes in the retinal blood flow dynamics in eyes with SRF.

A multi-scale/multi-physics model for the theoretical study of the vascular configuration of retinal capillary plexuses based on OCTA data

The retinal tissue is highly metabolically active and is responsible for translating the visual stimuli into electrical signals to be delivered to the brain. A complex vascular structure ensures an adequate supply of blood and oxygen, which is essential for the function and survival of the retinal tissue. To date, a complete understanding of the configuration of the retinal vascular structures is still lacking. Optical coherence tomography angiography has made available a huge amount of imaging data regarding the main retinal capillary plexuses, namely the superficial capillary plexuses (SCP), intermediate capillary plexuses (ICP) and deep capillary plexuses (DCP). However, the interpretation of these data is still controversial. In particular, the question of whether the three capillary plexuses are connected in series or in parallel remains a matter of debate. In this work, we address this question by utilizing a multi-scale/multi-physics mathematical model to quantify the impact of the two hypothesized vascular configurations on retinal hemodynamics and oxygenation. The response to central retinal vein occlusion (CRVO) and intraocular pressure (IOP) elevation is also simulated depending on whether the capillary plexuses are connected in series or in parallel. The simulation results show the following: (i) in the in series configuration, the plexuses exhibit a differential response, with DCP and ICP experiencing larger pressure drops than SCP; and (ii) in the in parallel configuration, the blood flow redistributes uniformly in the three plexuses. The different vascular configurations show different responses also in terms of oxygen profiles: (i) in the in series configuration, the outer nuclear layer, outer plexiform layer and inner nuclear layer (INL) are those most affected by CRVO and IOP elevation; and (ii) in the in parallel configuration the INL and ganglion cell layer are those most affected. The in series results are consistent with studies on paracentral acute middle maculopathy, secondary to CRVO and with studies on IOP elevation, in which DCP and ICP and the retinal tissues surrounding them are those most affected by ischemia. These findings seem to suggest that the in series configuration better describes the physiology of the vascular retinal capillary network in health and disease.

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.

Chronic social defeat stress causes retinal vascular dysfunction

PURPOSE

The roles of vascular dysfunction and chronic stress have been extensively discussed in the pathophysiology of glaucoma. Our aim was to test whether chronic stress causes retinal vascular dysfunction and therewith induces retinal ganglion cells (RGCs) loss.

METHODS

Twelve mice underwent chronic social defeat (CSD) stress, while 12 mice received control treatment only. Intraocular pressure (IOP) was measured with a rebound tonometer. Blood plasma corticosterone concentration and adrenal gland weight were used to assess stress levels. Brn-3a staining in retinas and PPD staining in optic nerve cross sections were conducted to assess the survival of RGCs and axons respectively. The ET-1 and α-SMA levels were determined in retina. Retinal vascular autoregulation, functional response to various vasoactive agents and vascular mechanics were measured using video microscopy.

RESULTS

No significant difference in IOP levels was observed during and after CSD between CSD mice and controls. CSD stress caused hypercortisolemia 2 days post-CSD. However, increased corticosterone levels went back to normal 8 months after CSD. CSD-exposed mice developed adrenal hyperplasia 3 days post-CSD, which was normalized by 8 months. RGC and axon survival were similar between CSD mice and controls. However, CSD stress caused irreversible, impaired autoregulation and vascular dysfunction of retinal arterioles in CSD mice. In addition, impaired maximal dilator capacity of retinal arterioles was observed 8 months post-CSD rather than 3 days post-CSD. Remarkably, ET-1 levels were increased 3 days post-CSD while α-SMA levels were decreased 8 months post-CSD.

CONCLUSIONS

We found that CSD stress does not cause IOP elevation, nor loss of RGCs and their axons. However, it strikingly causes irreversible impaired autoregulation and endothelial function in murine retinal arterioles. In addition, CSD changed vascular mechanics on a long-term basis. Increased ET-1 levels and loss of pericytes in retina vessels may involve in this process.

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.

Physics-based modeling of Age-related Macular Degeneration-A theoretical approach to quantify retinal and choroidal contributions to macular oxygenation

We developed a mathematical model to characterize how macular oxygenation may be affected by abnormalities in the retinal and choroidal oxygen supplies. The macular region is modeled as a layered structure including: ganglion cell and nerve fiber layers, inner plexiform layer, inner nuclear layer, outer plexiform layer, outer nuclear layer, inner segment of photoreceptors layer and retinal pigmented epithelium. Each layer is characterized by specific levels of oxygen consumption. The vitreous and the choroid are located at the macula boundary and provide oxygen via boundary conditions of Dirichlet type. The three capillary plexi (superficial, intermediate, and deep) of the retinal circulation pierce the macular layers and provide oxygen via a volumetric source that depends on the retinal blood flow. Oxygen profiles through the macular tissue are calculated by simulating the balance among oxygen supply, consumption and diffusion in: (a) physiological baseline conditions; (b) retinal blood flow reduced by 10%, 30% and 50% with respect to baseline; (c) choroidal oxygen level diminished by 10%, 30% and 50% with respect to baseline. Model simulations predict that: (1) the oxygenation of the foveal avascular zone is not affected by reduction in retinal blood flow; (2) a reduction in choroidal oxygen supply significantly affects the outer layers, especially the photoreceptors and outer nuclear layers; (3) the impact of reduction in choroidal oxygen supply is larger in the region more proximal to the macular center; (4) the impact of reduction in retinal blood flow is larger in the region more proximal to the macular periphery. The proposed mathematical model suggests that changes in retinal and choroidal oxygen supplies impact the oxygenation of the macular tissue differentially. These results may help better understand the pathogenesis of macular degeneration.

Retinal microvascular density modifications during the water drinking test

PURPOSE

The water drinking test (WDT) is a well-known stress test that increases intraocular pressure (IOP) momentarily and can indicate risk of glaucoma progression. This study focuses on correlating changes in the retinal microvascular plexus with the WDT in young healthy subjects.

METHODS

A total of 20 eyes of 20 healthy young subjects (mean age 24.37 ± 2.17 years) were included in this study. In our protocol, WDT consisted of drinking 1 L of water within 5 min. Outcome measures in this prospective observational study were mean arterial pressure (MAP), heart rate (HR), IOP, and retinal vessel density of both superficial and deep macular retina using optical coherence tomography angiography (OCTA), which were assessed before water ingestion and four times after at 15-min intervals. OCTA images were later quantified by fractal analysis (box counting [D_box]). One-way repeated measures analysis of variance (ANOVA) was used to assess the effects of WDT on each of the parameters.

RESULTS

The WDT resulted in significant peak changes of the following parameters compared to baseline: IOP: 15.63 ± 3.37 versus 18.38 ± 4.53 mmHg at 30 min, p < 0.001; HR: 75.74 ± 12.23 versus 64.95 ± 11.37 bpm at 15 min, p < 0.001; deep retinal vessel density 1.758 ± 0.14 versus 1.749 ± 0.16 at 15 min, p = 0.040.

CONCLUSIONS

Besides IOP elevation and systemic effects in HR, WDT is associated with temporary modifications of the deep vascular plexus in young healthy subjects.

Distinct roles of red-blood-cell-derived and wall-derived mechanisms in metabolic regulation of blood flow

OBJECTIVE

A theoretical model is used to analyze combinations of RBC-derived and wall-derived (RBC-independent) mechanisms for metabolic blood flow regulation, with regard to their oxygen transport properties.

METHODS

Heterogeneous microvascular network structures are derived from observations in rat mesentery and hamster cremaster. The effectiveness of metabolic blood flow regulation using combinations of RBC-dependent and RBC-independent mechanisms is simulated in these networks under conditions of reduced oxygen delivery and increased oxygen demand.

RESULTS

Metabolic regulation by a wall-derived mechanism results in higher predicted total blood flow rate and number of flowing vessels, and lower tissue hypoxic fraction, than regulation by combinations of RBC-derived and wall-derived signals. However, a combination of RBC-derived and wall-derived signals results in a higher predicted median tissue P_O2 than either mechanism acting alone.

CONCLUSIONS

Model results suggest complementary roles for RBC-derived and wall-derived mechanisms of metabolic flow regulation, with the wall-derived mechanism responsible for avoiding hypoxia, and the RBC-derived mechanism responsible for maintaining P_O2 levels high enough for optimal tissue function.

Neurodegenerative Disorders of the Eye and of the Brain: A Perspective on Their Fluid-Dynamical Connections and the Potential of Mechanism-Driven Modeling

Neurodegenerative disorders (NDD) such as Alzheimer's and Parkinson's diseases are significant causes of morbidity and mortality worldwide. The pathophysiology of NDD is still debated, and there is an urgent need to understand the mechanisms behind the onset and progression of these heterogenous diseases. The eye represents a unique window to the brain that can be easily assessed via non-invasive ocular imaging. As such, ocular measurements have been recently considered as potential sources of biomarkers for the early detection and management of NDD. However, the current use of ocular biomarkers in the clinical management of NDD patients is particularly challenging. Specifically, many ocular biomarkers are influenced by local and systemic factors that exhibit significant variation among individuals. In addition, there is a lack of methodology available for interpreting the outcomes of ocular examinations in NDD. Recently, mathematical modeling has emerged as an important tool capable of shedding light on the pathophysiology of multifactorial diseases and enhancing analysis and interpretation of clinical results. In this article, we review and discuss the clinical evidence of the relationship between NDD in the brain and in the eye and explore the potential use of mathematical modeling to facilitate NDD diagnosis and management based upon ocular biomarkers.

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.

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.

Retinal oximetry in glaucoma: investigations and findings reviewed

Abnormalities of the retinal blood supply have been widely implicated in primary open-angle glaucoma (POAG). Impaired blood supply to the retina and optic nerve head (ONH) may be a primary pathophysiologic mechanism contributing to POAG ('vascular hypothesis'). However, the decreased metabolic activity of atrophic tissue is itself known to induce both vascular changes and decreased blood flow due to reduced oxygen demand. Therefore, primary nonvascular factors could potentially induce glaucomatous atrophy, with subsequent secondary vascular pathology ('mechanical hypothesis'). Retinal oximetry holds great promise in the investigation of glaucoma pathogenesis, as it can provide useful data on retinal metabolic oxygen demand, especially when combined with measurements of retinal blood flow. This review surveys the research on retinal metabolism in POAG using spectroscopic retinal oximetry. The use of mathematical models in combination with oximetric data to investigate the role of retinal metabolism and oxygen supply in POAG is also discussed.

Modeling acute blood flow responses to a major arterial occlusion

OBJECTIVE

The development of earlier and less invasive treatments for peripheral arterial disease requires a more complete understanding of vascular responses following a major arterial occlusion. A mechanistic model of the vasculature of the rat hindlimb is developed to predict acute (immediate) changes in vessel diameters and smooth muscle tone following femoral arterial occlusion.

METHODS

Vascular responses of collateral arteries and distal arterioles to changes in pressure, shear stress, and metabolism are assessed before and after occlusion. The effects of exercise are also simulated and compared with venous flow measurements from WKY rats.

RESULTS

The model identifies collateral arteries as the primary contributors to flow compensation following occlusion. Increasing the number of capillaries has minimal effect on blood flow while increasing the number of collateral arteries significantly increases flow, since the primary site of resistance shifts upstream to the collateral arteries following occlusion. Despite significant collateral dilation, calf flow remains below pre-occlusion levels and the deficit becomes more severe with increased activity.

CONCLUSIONS

Although unable to compensate fully for an occlusion, the model demonstrates the importance of the shear response in collateral arteries and the metabolic response in the distal microcirculation in acute adaptations to a major arterial occlusion.

Ocular blood flow as a clinical observation: Value, limitations and data analysis

Alterations in ocular blood flow have been identified as important risk factors for the onset and progression of numerous diseases of the eye. In particular, several population-based and longitudinal-based studies have provided compelling evidence of hemodynamic biomarkers as independent risk factors for ocular disease throughout several different geographic regions. Despite this evidence, the relative contribution of blood flow to ocular physiology and pathology in synergy with other risk factors and comorbidities (e.g., age, gender, race, diabetes and hypertension) remains uncertain. There is currently no gold standard for assessing all relevant vascular beds in the eye, and the heterogeneous vascular biomarkers derived from multiple ocular imaging technologies are non-interchangeable and difficult to interpret as a whole. As a result of these disease complexities and imaging limitations, standard statistical methods often yield inconsistent results across studies and are unable to quantify or explain a patient's overall risk for ocular disease. Combining mathematical modeling with artificial intelligence holds great promise for advancing data analysis in ophthalmology and enabling individualized risk assessment from diverse, multi-input clinical and demographic biomarkers. Mechanism-driven mathematical modeling makes virtual laboratories available to investigate pathogenic mechanisms, advance diagnostic ability and improve disease management. Artificial intelligence provides a novel method for utilizing a vast amount of data from a wide range of patient types to diagnose and monitor ocular disease. This article reviews the state of the art and major unanswered questions related to ocular vascular anatomy and physiology, ocular imaging techniques, clinical findings in glaucoma and other eye diseases, and mechanistic modeling predictions, while laying a path for integrating clinical observations with mathematical models and artificial intelligence. Viable alternatives for integrated data analysis are proposed that aim to overcome the limitations of standard statistical approaches and enable individually tailored precision medicine in ophthalmology.

Elevated Intraocular Pressure Causes Abnormal Reactivity of Mouse Retinal Arterioles

Objective

Glaucoma is a leading cause of severe visual impairment and blindness. Although high intraocular pressure (IOP) is an established risk factor for the disease, the role of abnormal ocular vessel function in the pathophysiology of glaucoma gains more and more attention. We tested the hypothesis that elevated intraocular pressure (IOP) causes vascular dysfunction in the retina.

Methods

High IOP was induced in one group of mice by unilateral cauterization of three episcleral veins. The other group received sham surgery only. Two weeks later, retinal vascular preparations were studied by video microscopy in vitro. Reactive oxygen species (ROS) levels and expression of hypoxia markers and of prooxidant and antioxidant redox genes as well as of inflammatory cytokines were determined.

Results

Strikingly, responses of retinal arterioles to stepwise elevation of perfusion pressure were impaired in the high-IOP group. Moreover, vasodilation responses to the endothelium-dependent vasodilator, acetylcholine, were markedly reduced in mice with elevated IOP, while no differences were seen in response to the endothelium-independent nitric oxide donor, sodium nitroprusside. Remarkably, ROS levels were increased in the retinal ganglion cell layer including blood vessels. Expression of the NADPH oxidase isoform, NOX2, and of the inflammatory cytokine, TNF-α, was increased at the mRNA level in retinal explants. Expression of NOX2, but not of the hypoxic markers, HIF-1α and VEGF-A, was increased in the retinal ganglion cell layer and in retinal blood vessels at the protein level.

Conclusion

Our data provide first-time evidence that IOP elevation impairs autoregulation and induces endothelial dysfunction in mouse retinal arterioles. Oxidative stress and inflammation, but not hypoxia, appear to be involved in this process.

Biofluid modeling of the coupled eye-brain system and insights into simulated microgravity conditions

This work aims at investigating the interactions between the flow of fluids in the eyes and the brain and their potential implications in structural and functional changes in the eyes of astronauts, a condition also known as spaceflight associated neuro-ocular syndrome (SANS). To this end, we propose a reduced (0-dimensional) mathematical model of fluid flow in the eyes and brain, which is embedded into a simplified whole-body circulation model. In particular, the model accounts for: (i) the flows of blood and aqueous humor in the eyes; (ii) the flows of blood, cerebrospinal fluid and interstitial fluid in the brain; and (iii) their interactions. The model is used to simulate variations in intraocular pressure, intracranial pressure and blood flow due to microgravity conditions, which are thought to be critical factors in SANS. Specifically, the model predicts that both intracranial and intraocular pressures increase in microgravity, even though their respective trends may be different. In such conditions, ocular blood flow is predicted to decrease in the choroid and ciliary body circulations, whereas retinal circulation is found to be less susceptible to microgravity-induced alterations, owing to a purely mechanical component in perfusion control associated with the venous segments. These findings indicate that the particular anatomical architecture of venous drainage in the retina may be one of the reasons why most of the SANS alterations are not observed in the retina but, rather, in other vascular beds, particularly the choroid. Thus, clinical assessment of ocular venous function may be considered as a determinant SANS factor, for which astronauts could be screened on earth and in-flight.

Comparison of retinal vascular geometry in obese and non-obese children

Purpose

Childhood obesity is associated with adult cardiometabolic disease. We postulate that the underlying microvascular dysfunction begins in childhood. We thus aimed to compare retinal vascular parameters between obese and non-obese children.

Methods

This was a cross-sectional study involving 166 children aged 6 to 12 years old in Malaysia. Ocular examination, biometry, retinal photography, blood pressure and body mass index measurement were performed. Participants were divided into two groups; obese and non-obese. Retinal vascular parameters were measured using validated software.

Results

Mean age was 9.58 years. Approximately 51.2% were obese. Obese children had significantly narrower retinal arteriolar caliber (F_(1,159) = 6.862, p = 0.010), lower arteriovenous ratio (F_(1,159) = 17.412, p < 0.001), higher venular fractal dimension (F_(1,159) = 4.313, p = 0.039) and higher venular curvature tortuosity (F_(1,158) = 5.166, p = 0.024) than non-obese children, after adjustment for age, gender, blood pressure and axial length.

Conclusions

Obese children have abnormal retinal vascular geometry. These findings suggest that childhood obesity is characterized by early microvascular abnormalities that precede development of overt disease. Further research is warranted to determine if these parameters represent viable biomarkers for risk stratification in obesity.

Reactive oxygen species, oxidative stress, glaucoma and hyperbaric oxygen therapy

This review examines the role of oxidative stress in damage to cells of the trabecular meshwork and associated impaired aqueous drainage as well as damage to retinal ganglion cells and associated visual field losses. Consideration is given to the interaction between vascular and mechanical explanations for pathological changes in glaucoma. For example, elevated intraocular pressure (IOP) forces may contribute to ischaemia but there is increasing evidence that altered blood flow in a wider sense is also involved. Both vascular and mechanical theories are involved through fluctuations in intraocular pressure and dysregulation of blood flow. Retinal function is very sensitive to changes in haemoglobin oxygen concentration and the associated variations in the production of reactive oxygen species. Reperfusion injury and production of reactive oxygen species occurs when IOP is elevated or blood pressure is low and beyond the capacity for blood flow autoregulation to maintain appropriate oxygen concentration. Activities such as those associated with postural changes, muscular effort, eye wiping and rubbing which cause IOP fluctuation, may have significant vascular, mechanical, reperfusion and oxidative stress consequences. Hyperbaric oxygen therapy exposes the eye to increased oxygen concentration and the risk of oxidative damage in susceptible individuals. However, oxygen concentration in aqueous humour, and the risk of damage to trabecular meshwork cells may be greater if hyperbaric oxygen is delivered by a hood which exposes the anterior ocular surface to higher than normal oxygen levels. Oronasal mask delivery of hyperbaric oxygen therapy appears to be indicated in these cases.

Retinal Microvascular Network and Microcirculation Assessments in High Myopia

PURPOSE

To investigate the changes of the retinal microvascular network and microcirculation in high myopia.

DESIGN

A cross-sectional, matched, comparative clinical study.

PARTICIPANTS

Twenty eyes of 20 subjects with nonpathological high myopia (28 ± 5 years of age) with a refractive error of -6.31 ± 1.23 D (mean ± SD) and 20 eyes of 20 age- and sex-matched control subjects (30 ± 6 years of age) with a refractive error of -1.40 ± 1.00 D were recruited.

METHODS

Optical coherence tomography angiography (OCTA) was used to image the retinal microvascular network, which was later quantified by fractal analysis (box counting [D_box], representing vessel density) in both superficial and deep vascular plexuses. The Retinal Function Imager was used to image the retinal microvessel blood flow velocity (BFV). The BFV and microvascular density in the myopia group were corrected for ocular magnification using Bennett's formula.

RESULTS

The density of both superficial and deep microvascular plexuses was significantly decreased in the myopia group in comparison to the controls (P < .05). The decrease of the microvessel density of the annular zone (0.6-2.5 mm), measured as D_box, was 2.1% and 2.9% in the superficial and deep vascular plexuses, respectively. Microvessel density reached a plateau from 0.5 mm to 1.25 mm from the fovea in both groups, but that in the myopic group was about 3% lower than the control group. No significant differences were detected between the groups in retinal microvascular BFV in either arterioles or venules (P > .05). Microvascular densities in both superficial (r = -0.45, P = .047) and deep (r = -0.54, P = .01) vascular plexuses were negatively correlated with the axial lengths in the myopic eye. No correlations were observed between BFV and vessel density (P > .05).

CONCLUSIONS

Retinal microvascular decrease was observed in the high myopia subjects, whereas the retinal microvessel BFV remained unchanged. The retinal microvascular network alteration may be attributed to ocular elongation that occurs with the progression of myopia. The novel quantitative analyses of the retinal microvasculature may help to characterize the underlying pathophysiology of myopia and enable early detection and prevention of myopic retinopathy.

Understanding Glaucomatous Optic Neuropathy: The Synergy Between Clinical Observation and Investigation

Glaucoma is a complex disorder of aging defined by the death of retinal ganglion cells and remodeling of connective tissues at the optic nerve head. Intraocular pressure-induced axonal injury at the optic nerve head leads to apoptosis. Loss of retinal ganglion cells follows a slowly progressive sequence. Clinical features of the disease have suggested and corroborated pathological events. The death of retinal ganglion cells causes secondary loss of neurons in the brain, but only as a by-product of injury to the retinal ganglion cells. Although therapy to lower intraocular pressure is moderately effective, new treatments are being developed to alter the remodeling of ocular connective tissue, to interrupt the injury signal from axon to soma, and to upregulate a variety of survival mechanisms.

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.

Theoretical Model of Coronary Blood Flow Regulation: Role of Myocardium Compressive Forces

OBJECTIVE

Auto-regulatory reserve of coronary blood flow is nonuniformly distributed across the ventricular wall. MCF are thought to play an important role in determining the transmural distribution of myocardium blood flow. Here, impacts of MCF on coronary flow regulation are analyzed using a theoretical model.

METHODS

Coronary microvessels at various depths in the ventricular wall are represented by parallel segments. Nine vessel regions are connected in series to represent one parallel segment, which includes four vasoactive regions regulated by the wall tension, the shear stress and the metabolic demand. The nonuniform distribution of MCF is modeled and its effects on coronary flow regulation are taken into consideration by using a modified tension model and a vessel collapse model. Flow regulation behaviors in both normal and obstructed coronary circulation are simulated.

RESULTS

Model-predicted auto-regulatory curve is shifted to the high pressure region by including the effect of MCF. Model-predicted flow distributions in obstructed coronary circulation show that severe stenosis in coronary artery would first impede myocardial blood flow in subendocardial layer.

CONCLUSIONS

The model results indicate that MCF plays an important role in coronary flow regulation and also in determining the transmural distribution of myocardium blood flow.

A MATHEMATICAL AND COMPUTATIONAL MODEL OF BLOOD FLOW REGULATION IN MICROVESSELS: APPLICATION TO THE EYE RETINA CIRCULATION

This paper presents a mathematical model and a computational framework for the resolution of large networks of distensible blood microvessels characterized by a hierarchy of different diameters. We analyze the contribution of different distensibility relations, representing both active and passive responses in the case of the microvascular network in the eye retina. Model predictions indicate that, depending on the geometrical (hierarchical) location in the network, distensibility effects may be significantly different and lead, over long times, to possible geometrically-driven remodeling processes.

Microgravity-induced fluid shift and ophthalmic changes

Although changes to visual acuity in spaceflight have been observed in some astronauts since the early days of the space program, the impact to the crew was considered minor. Since that time, missions to the International Space Station have extended the typical duration of time spent in microgravity from a few days or weeks to many months. This has been accompanied by the emergence of a variety of ophthalmic pathologies in a significant proportion of long-duration crewmembers, including globe flattening, choroidal folding, optic disc edema, and optic nerve kinking, among others. The clinical findings of affected astronauts are reminiscent of terrestrial pathologies such as idiopathic intracranial hypertension that are characterized by high intracranial pressure. As a result, NASA has placed an emphasis on determining the relevant factors and their interactions that are responsible for detrimental ophthalmic response to space. This article will describe the Visual Impairment and Intracranial Pressure syndrome, link it to key factors in physiological adaptation to the microgravity environment, particularly a cephalad shifting of bodily fluids, and discuss the implications for ocular biomechanics and physiological function in long-duration spaceflight.

Intraocular pressure, blood pressure, and retinal blood flow autoregulation: a mathematical model to clarify their relationship and clinical relevance

PURPOSE

This study investigates the relationship between intraocular pressure (IOP) and retinal hemodynamics and predicts how arterial blood pressure (BP) and blood flow autoregulation (AR) influence this relationship.

METHODS

A mathematical model is developed to simulate blood flow in the central retinal vessels and retinal microvasculature as current flowing through a network of resistances and capacitances. Variable resistances describe active and passive diameter changes due to AR and IOP. The model is validated by using clinically measured values of retinal blood flow and velocity. The model simulations for six theoretical patients with high, normal, and low BP (HBP-, NBP-, LBP-) and functional or absent AR (-wAR, -woAR) are compared with clinical data.

RESULTS

The model predicts that NBPwAR and HBPwAR patients can regulate retinal blood flow (RBF) as IOP varies between 15 and 23 mm Hg and between 23 and 29 mm Hg, respectively, whereas LBPwAR patients do not adequately regulate blood flow if IOP is 15 mm Hg or higher. Hemodynamic alterations would be noticeable only if IOP changes occur outside of the regulating range, which, most importantly, depend on BP. The model predictions are consistent with clinical data for IOP reduction via surgery and medications and for cases of induced IOP elevation.

CONCLUSIONS

The theoretical model results suggest that the ability of IOP to induce noticeable changes in retinal hemodynamics depends on the levels of BP and AR of the individual. These predictions might help to explain the inconsistencies found in the clinical literature concerning the relationship between IOP and retinal hemodynamics.

Parametric transfer function analysis and modeling of blood flow autoregulation in the optic nerve head

The aim of the study was to establish a parametric transfer function to describe the relationship between ocular perfusion pressure (OPP) and blood flow (BF) in the optic nerve head (ONH). A third-order parametric theoretical model was proposed to describe the ONH OPP-BF relationship within the lower OPP range of the autoregulation curve (< 80 mmHg) based on experimentally induced BF response to a rapid intraocular pressure (IOP) increase in 6 rhesus monkeys. The theoretical and actual data fitted well and suggest that this parametric third-order transfer function can effectively describe both the linear and nonlinear feature in dynamic and static autoregulation in the ONH within the OPP range studied. It shows that the BF autoregulation fully functions when the OPP was > 40 mmHg and becomes incomplete when the OPP was < 40 mmHg. This model may be used to help investigating the features of autoregulation in the ONH under different experimental conditions.

Mathematical modeling approaches in the study of glaucoma disparities among people of African and European descents

Open angle glaucoma (OAG) is a severe ocular disease characterized by progressive and irreversible vision loss. While elevated intraocular pressure (IOP) is a well-established risk factor for OAG, the progression of OAG in many cases, despite IOP treatment, suggests that other risk factors must play significant roles in the development of the disease. For example, various structural properties of the eye, ocular blood flow properties, and systemic conditions have been identified as risk factors for OAG. Ethnicity has also been indicated as a relevant factor that affects the incidence and prevalence of OAG; in fact, OAG is the leading cause of blindness among people of African descent. Numerous clinical studies have been designed to examine the possible correlation and causation between OAG and these factors; however, these studies are met with the challenge of isolating the individual role of multiple interconnected factors. Over the last decade, various mathematical modeling approaches have been implemented in combination with clinical studies in order to provide a mechanical and hemodynamical description of the eye in relation to the entire human body and to assess the contribution of single risk factors to the development of OAG. This review provides a summary of the clinical evidence of ocular structural differences, ocular vascular differences and systemic vascular differences among people of African and European descent, describes the mathematical approaches that have been proposed to study ocular mechanics and hemodynamics while discussing how they could be used to investigate the relevance to OAG of racial disparities, and outlines possible new directions of research.