Development of an image-based network model of retinal vasculature

Simulation of murine retinal hemodynamics in response to tail suspension

The etiology of spaceflight-associated neuro-ocular syndrome (SANS) remains unclear. Recent murine studies indicate there may be a link between the space environment and retinal endothelial dysfunction. Post-fixed control (N = 4) and 14-day tail-suspended (TS) (N = 4) mice eye samples were stained and imaged for the vessel plexus and co-located regions of endothelial cell death. A custom workflow combined whole-mounted and tear reconstructed three-dimensional (3D) spherical retinal plexus models with computational fluid dynamics (CFD) simulation that accounted for the Fåhræus-Lindqvist effect and boundary conditions that accommodated TS fluid pressure measurements and deeper capillary layer blood flow distribution. TS samples exhibited reduced surface area (4.6 ± 0.5 mm2 vs. 3.5 ± 0.3 mm2, P = 0.010) and shorter lengths between branches in small vessels (<10 μm, 69.5 ± 0.6 μm vs. 60.4 ± 1.1 μm, P < 0.001). Wall shear stress (WSS) and pressure were higher in TS mice compared to controls, particularly in smaller vessels (<10 μm, WSS: 6.57 ± 1.08 Pa vs. 4.72 ± 0.67 Pa, P = 0.034, Pressure: 72.04 ± 3.14 mmHg vs. 50.64 ± 6.74 mmHg, P = 0.004). Rates of retinal endothelial cell death were variable in TS mice compared to controls. WSS and pressure were generally higher in cell death regions, both within and between cohorts, but significance was variable and limited to small to medium-sized vessels (<20 μm). These findings suggest a link may exist between emulated microgravity and retinal endothelial dysfunction that may have implications for SANS development. Future work with increased sample sizes of larger species or spaceflight cohorts should be considered.

Pulmonary vasculature development in congenital diaphragmatic hernia: a novel automated quantitative imaging analysis

PURPOSE

Impaired fetal lung vasculature determines the degree of pulmonary hypertension in the congenital diaphragmatic hernia (CDH). This study aims to demonstrate the morphometric measurements that differ in pulmonary vessels of fetuses with CDH.

METHODS

Nitrofen-induced CDH Sprague-Dawley rat fetuses were scanned with microcomputed tomography. The analysis of the pulmonary vascular tree was performed with artificial intelligence.

RESULTS

The number of segments in CDH was significantly lower than that in the control group on the left (U = 2.5, p = 0.004) and right (U = 0, p = 0.001) sides for order 1(O1), whereas there was a significant difference only on the right side for O2 and O3. The pooled element numbers in the control group obeyed Horton's law (R2 = 0.996 left and R2 = 0.811 right lungs), while the CDH group broke it. Connectivity matrices showed that the average number of elements of O1 springing from elements of O1 on the left side and the number of elements of O1 springing from elements of O3 on the right side were significantly lower in CDH samples.

CONCLUSION

According to these findings, CDH not only reduced the amount of small order elements, but also destroyed the fractal structure of the pulmonary arterial trees.

Effects of donor-specific microvascular anatomy on hemodynamic perfusion in human choriocapillaris

Evidence from histopathology and clinical imaging suggest that choroidal anatomy and hemodynamic perfusion are among the earliest changes in retinal diseases such as age-related macular degeneration (AMD). However, how inner choroidal anatomy affects hemodynamic perfusion is not well understood. Therefore, we sought to understand the influences of choroidal microvascular architecture on the spatial distribution of hemodynamic parameters in choriocapillaris from human donor eyes using image-based computational hemodynamic (ICH) simulations. We subjected image-based inner choroid reconstructions from eight human donor eyes to ICH simulation using a kinetic-based volumetric lattice Boltzmann method to compute hemodynamic distributions of velocity, pressure, and endothelial shear stress. Here, we demonstrate that anatomic parameters, including arteriolar and venular arrangements and intercapillary pillar density and distribution exert profound influences on inner choroidal hemodynamic characteristics. Reductions in capillary, arteriolar, and venular density not only reduce the overall blood velocity within choriocapillaris, but also substantially increase its spatial heterogeneity. These first-ever findings improve understanding of how choroidal anatomy affects hemodynamics and may contribute to pathogenesis of retinal diseases such as AMD.

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.

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.

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.

Remodeling of the Microvasculature: May the Blood Flow Be With You

The vasculature ensures optimal delivery of nutrients and oxygen throughout the body, and to achieve this function it must continually adapt to varying tissue demands. Newly formed vascular plexuses during development are immature and require dynamic remodeling to generate well-patterned functional networks. This is achieved by remodeling of the capillaries preserving those which are functional and eliminating other ones. A balanced and dynamically regulated capillary remodeling will therefore ensure optimal distribution of blood and nutrients to the tissues. This is particularly important in pathological contexts in which deficient or excessive vascular remodeling may worsen tissue perfusion and hamper tissue repair. Blood flow is a major determinant of microvascular reshaping since capillaries are pruned when relatively less perfused and they split when exposed to high flow in order to shape the microvascular network for optimal tissue perfusion and oxygenation. The molecular machinery underlying blood flow sensing by endothelial cells is being deciphered, but much less is known about how this translates into endothelial cell responses as alignment, polarization and directed migration to drive capillary remodeling, particularly in vivo. Part of this knowledge is theoretical from computational models since blood flow hemodynamics are not easily recapitulated by in vitro or ex vivo approaches. Moreover, these events are difficult to visualize in vivo due to their infrequency and briefness. Studies had been limited to postnatal mouse retina and vascular beds in zebrafish but new tools as advanced microscopy and image analysis are strengthening our understanding of capillary remodeling. In this review we introduce the concept of remodeling of the microvasculature and its relevance in physiology and pathology. We summarize the current knowledge on the mechanisms contributing to capillary regression and to capillary splitting highlighting the key role of blood flow to orchestrate these processes. Finally, we comment the potential and possibilities that microfluidics offers to this field. Since capillary remodeling mechanisms are often reactivated in prevalent pathologies as cancer and cardiovascular disease, all this knowledge could be eventually used to improve the functionality of capillary networks in diseased tissues and promote their repair.

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.

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.

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.

Characterizing spatial distributions of astrocytes in the mammalian retina

MOTIVATION

In addition to being involved in retinal vascular growth, astrocytes play an important role in diseases and injuries, such as glaucomatous neuro-degeneration and retinal detachment. Studying astrocytes, their morphological cell characteristics and their spatial relationships to the surrounding vasculature in the retina may elucidate their role in these conditions.

RESULTS

Our results show that in normal healthy retinas, the distribution of observed astrocyte cells does not follow a uniform distribution. The cells are significantly more densely packed around the blood vessels than a uniform distribution would predict. We also show that compared with the distribution of all cells, large cells are more dense in the vicinity of veins and toward the optic nerve head whereas smaller cells are often more dense in the vicinity of arteries. We hypothesize that since veinal astrocytes are known to transport toxic metabolic waste away from neurons they may be more critical than arterial astrocytes and therefore require larger cell bodies to process waste more efficiently.

AVAILABILITY AND IMPLEMENTATION

A 1/8th size down-sampled version of the seven retinal image mosaics described in this article can be found on BISQUE (Kvilekval et al., 2010) at http://bisque.ece.ucsb.edu/client_service/view?resource=http://bisque.ece.ucsb.edu/data_service/dataset/6566968.

Regulation of blood flow in the retinal trilaminar vascular network

Light stimulation evokes neuronal activity in the retina, resulting in the dilation of retinal blood vessels and increased blood flow. This response, named functional hyperemia, brings oxygen and nutrients to active neurons. However, it remains unclear which vessels mediate functional hyperemia. We have characterized blood flow regulation in the rat retina in vivo by measuring changes in retinal vessel diameter and red blood cell (RBC) flux evoked by a flickering light stimulus. We found that, in first- and second-order arterioles, flicker evoked large (7.5 and 5.0%), rapid (0.73 and 0.70 s), and consistent dilations. Flicker-evoked dilations in capillaries were smaller (2.0%) and tended to have a slower onset (0.97 s), whereas dilations in venules were smaller (1.0%) and slower (1.06 s) still. The proximity of pericyte somata did not predict capillary dilation amplitude. Expression of the contractile protein α-smooth muscle actin was high in arterioles and low in capillaries. Unexpectedly, we found that blood flow in the three vascular layers was differentially regulated. Flicker stimulation evoked far larger dilations and RBC flux increases in the intermediate layer capillaries than in the superficial and deep layer capillaries (2.6 vs 0.9 and 0.7% dilation; 25.7 vs 0.8 and 11.3% RBC flux increase). These results indicate that functional hyperemia in the retina is driven primarily by active dilation of arterioles. The dilation of intermediate layer capillaries is likely mediated by active mechanisms as well. The physiological consequences of differential regulation in the three vascular layers are discussed.

A one-dimensional mathematical model for studying the pulsatile flow in microvascular networks

Techniques that model microvascular hemodynamics have been developed for decades. While the physiological significance of pressure pulsatility is acknowledged, most of the microcirculatory models use steady flow approaches. To theoretically study the extent and transmission of pulsatility in microcirculation, dynamic models need to be developed. In this paper, we present a one-dimensional model to describe the dynamic behavior of microvascular blood flow. The model is applied to a microvascular network from a rat mesentery. Intravital microscopy was used to record the morphology and flow velocities in individual vessel segments, and boundaries are defined according to the experimental data. The system of governing equations constituting the model is solved numerically using the discontinuous Galerkin method. An implicit integration scheme is adopted to increase computing efficiency. The model allows the simulation of the dynamic properties of blood flow in microcirculatory networks, including the pressure pulsatility (quantified by a pulsatility index) and pulse wave velocity (PWV). From the main input arteriole to the main output venule, the pulsatility index decreases by 66.7%. PWV obtained along arterioles declines with decreasing diameters, with mean values of 77.16, 25.31, and 8.30 cm/s for diameters of 26.84, 17.46, and 13.33 μm, respectively. These results suggest that the 1D model developed is able to simulate the characteristics of pressure pulsatility and wave propagation in complex microvascular networks.

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.

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.

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

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

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.

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

This paper presents the results of a circulation analysis using an image based network model of a murine retinal vasculature, which closely represents the 3D vascular distribution of the retina. The uneven distribution of the red blood cells at vascular network bifurcations (i.e., plasma skimming effect), the microvascular diameter effect (i.e., Fahraeus-Lindqvist effect) and the role of endothelium surface layer (i.e., in vivo viscosity) were considered in determining the viscosity of the blood in the retinal vessel segments. The study yielded detailed distributions of the hemodynamic quantities in the arterial and venous trees shown in various anatomical based contour plots. Quantitative analysis was also carried out based on statistical distributions. The analysis shows that the distribution of the blood hematocrit (H(D)) in the retinal network is very non-uniform, with lower values at the pre-equator region (near the optic disc) and higher values in the equator region of the retina. This has significant influence on the distribution of apparent viscosity, pressure and wall shear stress (WSS) in the vasculature. The viscosity is generally higher in smaller vessels (i.e., pre-capillary vessels) but exceptions occur in some vessels where the H(D) is small. WSS is greater in smaller vessels located near the optic disc than that in the mainstream retinal vessels. The results presented can be directly useful to ophthalmologists and researchers working with retinal vasculature.