Predicting the impact of retinal vessel density on retinal vessel and tissue oxygenation using a theoretical model.

Vascular impairments, including compromised flow regulation, have been identified as significant contributors to glaucomatous disease. Recent studies have shown glaucoma patients with significantly reduced peripapillary, macular, and optic nerve head vessel densities occurring with early glaucomatous structural changes prior to detectable visual field loss. This study aims to quantify the potential impact of decreased vessel densities on retinal perfusion and oxygen metabolism. In our clinical observations, pre-perimetric glaucoma patients exhibited a 10-13% reduction in vessel density compared to healthy individuals. Our theoretical model of the retinal vasculature is adapted in this study to assess the potential impact of this reduction in vessel density on retinal oxygenation. The model predicts a 1% and 38% decrease in mean oxygen saturation in retinal vessels immediately downstream of the capillaries when vessel density is decreased from its reference value by 10% and 50%, respectively. The impact of capillary loss on oxygen extraction fraction and the partial pressure of oxygen in retinal tissue is also predicted. Reductions in vessel density are simulated in combination with impaired flow regulation, and the resulting effects on saturation and flow are predicted. The model results showed a nonlinear relationship between vessel density and downstream saturation, indicating that larger decreases in the density of capillaries have a disproportionate impact on oxygenation. The model further demonstrates that the detrimental effects of minor vessel density reductions are exacerbated when combined with other vascular impairments.

Using Multi-Layer Perceptron Driven Diagnosis to Compare Biomarkers for Primary Open Angle Glaucoma.

Purpose: To use neural network machine learning (ML) models to identify the most relevant ocular biomarkers for the diagnosis of primary open-angle glaucoma (POAG). Methods: Neural network models, also known as multi-layer perceptrons (MLPs), were trained on a prospectively collected observational dataset comprised of 93 glaucoma patients confirmed by a glaucoma specialist and 113 control subjects. The base model used only intraocular pressure, blood pressure, heart rate, and visual field (VF) parameters to diagnose glaucoma. The following models were given the base parameters in addition to one of the following biomarkers: structural features (optic nerve parameters, retinal nerve fiber layer [RNFL], ganglion cell complex [GCC] and macular thickness), choroidal thickness, and RNFL and GCC thickness only, by optical coherence tomography (OCT); and vascular features by OCT angiography (OCTA). Results: MLPs of three different structures were evaluated with tenfold cross validation. The testing area under the receiver operating characteristic curve (AUC) of the models were compared with independent samples t-tests. The vascular and structural models both had significantly higher accuracies than the base model, with the hemodynamic AUC (0.819) insignificantly outperforming the structural set AUC (0.816). The GCC + RNFL model and the model containing all structural and vascular features were also significantly more accurate than the base model. Conclusions: Neural network models indicate that OCTA optic nerve head vascular biomarkers are equally useful for ML diagnosis of POAG when compared to OCT structural biomarker features alone.

Diagnostic Capability of OCTA-Derived Macular Biomarkers for Early to Moderate Primary Open Angle Glaucoma.

Background/Objectives: To investigate macular vascular biomarkers for the detection of primary open-angle glaucoma (POAG). Methods: A total of 56 POAG patients and 94 non-glaucomatous controls underwent optical coherence tomography angiography (OCTA) assessment of macular vessel density (VD) in the superficial (SCP), and deep (DCP) capillary plexus, foveal avascular zone (FAZ) area, perimeter, VD, choriocapillaris and outer retina flow area. POAG patients were classified for severity based on the Glaucoma Staging System 2 of Brusini. ANCOVA comparisons adjusted for age, sex, race, hypertension, diabetes, and areas under the receiver operating characteristic curves (AUCs) for POAG/control differentiation were compared using the DeLong method. Results: Global, hemispheric, and quadrant SCP VD was significantly lower in POAG patients in the whole image, parafovea, and perifovea (p < 0.001). No significant differences were found between POAG and controls for DCP VD, FAZ parameters, and the retinal and choriocapillaris flow area (p > 0.05). SCP VD in the whole image and perifovea were significantly lower in POAG patients in stage 2 than stage 0 (p < 0.001). The AUCs of SCP VD in the whole image (0.86) and perifovea (0.84) were significantly higher than the AUCs of all DCP VD (p < 0.05), FAZ parameters (p < 0.001), and retinal (p < 0.001) and choriocapillaris flow areas (p < 0.05). Whole image SCP VD was similar to the AUC of the global retinal nerve fiber layer (RNFL) (AUC = 0.89, p = 0.53) and ganglion cell complex (GCC) thickness (AUC = 0.83, p = 0.42). Conclusions: SCP VD is lower with increasing functional damage in POAG patients. The AUC for SCP VD was similar to RNFL and GCC using clinical diagnosis as the reference standard.

Regional Vessel Density Reduction in the Macula and Optic Nerve Head of Patients With Pre-Perimetric Primary Open Angle Glaucoma.

PRCIS: Capillary and neuronal tissue loss occur both globally and with regional specificity in pre-perimetric glaucoma patients at the level of the optic nerve and macula, with perifovea regions affected earlier than parafovea areas. PURPOSE: To investigate optic nerve head (ONH) and macular vessel densities (VD) and structural parameters assessed by optical coherence tomography angiography in pre-perimetric open angle glaucoma (ppOAG) patients and healthy controls. MATERIALS AND METHODS: In all, 113 healthy and 79 ppOAG patients underwent global and regional (hemispheric/quadrants) assessments of retinal, ONH, and macular vascularity and structure, including ONH parameters, retinal nerve fiber layer (RNFL) and ganglion cell complex (GCC) thickness. Comparisons between outcomes in ppOAG and controls were adjusted for age, sex, race, BMI, diabetes, and hypertension, with P <0.05 considered statistically significant. RESULTS: In ppOAG compared with healthy controls: RNFL thicknesses were statistically significantly lower for all hemispheres, quadrants, and sectors ( P <0.001-0.041); whole image peripapillary all and small blood vessels VD were statistically significantly lower for all the quadrants ( P <0.001-0.002), except for the peripapillary small vessels in the temporal quadrant (ppOAG: 49.66 (8.40), healthy: 53.45 (4.04); P =0.843); GCC and inner and full macular thicknesses in the parafoveal and perifoveal regions were significantly lower in all the quadrants ( P =0.000- P =0.033); several macular VD were significantly lower ( P =0.006-0.034), with the exceptions of macular center, parafoveal superior and inferior quadrant, and perifoveal superior quadrant ( P >0.05). CONCLUSIONS: In ppOAG patients, VD biomarkers in both the macula and ONH, alongside RNFL, GCC, and macular thickness, were significantly reduced before detectable visual field loss with regional specificity. The most significant VD reduction detected was in the peripheric (perifovea) regions. Macular and ONH decrease in VD may serve as early biomarkers of glaucomatous disease.

Heterogeneity of Ocular Hemodynamic Biomarkers among Open Angle Glaucoma Patients of African and European Descent.

This study investigated the heterogeneity of ocular hemodynamic biomarkers in early open angle glaucoma (OAG) patients and healthy controls of African (AD) and European descent (ED). Sixty OAG patients (38 ED, 22 AD) and 65 healthy controls (47 ED, 18 AD) participated in a prospective, cross-sectional study assessing: intraocular pressure (IOP), blood pressure (BP), ocular perfusion pressure (OPP), visual field (VF) and vascular densities (VD) via optical coherence tomography angiography (OCTA). Comparisons between outcomes were adjusted for age, diabetes status and BP. VF, IOP, BP and OPP were not significantly different between OAG subgroups or controls. Multiple VD biomarkers were significantly lower in OAG patients of ED (p < 0.05) while central macular VD was lower in OAG patients of AD vs. OAG patients of ED (p = 0.024). Macular and parafoveal thickness were significantly lower in AD OAG patients compared to those of ED (p = 0.006-0.049). OAG patients of AD had a negative correlation between IOP and VF index (r = -0.86) while ED patients had a slightly positive relationship (r = 0.26); difference between groups (p < 0.001). Age-adjusted OCTA biomarkers exhibit significant variation in early OAG patients of AD and ED.

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.

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 PO2 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 PO2 levels high enough for optimal tissue function.

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.

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 (Si) 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.

Predicting retinal tissue oxygenation using an image-based theoretical model.

Impaired oxygen delivery and tissue perfusion have been identified as significant factors that contribute to the loss of retinal ganglion cells in glaucoma patients. This study predicts retinal blood and tissue oxygenation using a theoretical model of the retinal vasculature based on confocal microscopy images of the mouse retina. These images reveal a complex and heterogeneous geometry of vessels that are distributed non-uniformly into multiple distinct retinal layers at varying depths. Predicting oxygen delivery and distribution in this irregular arrangement of retinal microvessels requires the use of an efficient theoretical model. The model employed in this work utilizes numerical methods based on a Green's function approach to simulate the spatial distribution of oxygen levels in a network of retinal blood vessels and the tissue surrounding them. Model simulations also predict the blood flow rates and pressures in each of the microvessels throughout the entire network. As expected, the model predicts that average vessel PO2 decreases as oxygen demand is increased. However, the standard deviation of PO2 in the vessels nearly doubles as oxygen demand is increased from 1 to 8 cm3 O2/100 cm3/min, indicating a very wide spread in the predicted PO2 levels, suggesting that average PO2 is not a sufficient indicator of oxygenation in a heterogeneous vascular network. Ultimately, the development of this mathematical model will help to elucidate the important factors associated with blood flow and metabolism that contribute to the vision loss characteristic of glaucoma.

Modeling glucose metabolism and lactate production in the kidney.

The metabolism of glucose provides most of the ATP required for energy-dependent transport processes. In the inner medulla of the mammalian kidney, limited blood flow and O2 supply yield low oxygen tension; therefore, a substantial fraction of the glucose metabolism in that region is anaerobic. Lactate is considered to be a waste product of anaerobic glycolysis, which yields two lactate molecules for each glucose molecule consumed, thereby likely leading to the production and accumulation of a significant amount of lactate in the inner medulla. To gain insights into the transport and metabolic processes in the kidney, we have developed a detailed mathematical model of the renal medulla of the rat kidney. The model represents the radial organization of the renal tubules and vessels, which centers around the vascular bundles in the outer medulla and around clusters of collecting ducts in the inner medulla. Model simulations yield significant radial gradients in interstitial fluid oxygen tension and glucose and lactate concentrations in the outer medulla and upper inner medulla. In the deep inner medulla, interstitial fluid concentrations become much more homogeneous, as the radial organization of tubules and vessels is not distinguishable. Using this model, we have identified parameters concerning glucose transport and basal metabolism, as well as lactate production via anaerobic glycolysis, that yield predicted blood glucose and lactate concentrations consistent with experimental measurements in the papillary tip. In addition, simulations indicate that the radial organization of the rat kidney may affect lactate buildup in the inner medulla.

Modeling Glucose Metabolism in the Kidney.

The mammalian kidney consumes a large amount of energy to support the reabsorptive work it needs to excrete metabolic wastes and to maintain homeostasis. Part of that energy is supplied via the metabolism of glucose. To gain insights into the transport and metabolic processes in the kidney, we have developed a detailed model of the renal medulla of the rat kidney. The model represents water and solute flows, transmural fluxes, and biochemical reactions in the luminal fluid of the nephrons and vessels. In particular, the model simulates the metabolism of oxygen and glucose. Using that model, we have identified parameters concerning glucose transport and basal metabolism that yield predicted blood glucose concentrations that are consistent with experimental measurements. The model predicts substantial axial gradients in blood glucose levels along various medullary structures. Furthermore, the model predicts that in the inner medulla, owing to the relatively limited blood flow and low tissue oxygen tension, anaerobic metabolism of glucose dominates.

Impact of nitric-oxide-mediated vasodilation and oxidative stress on renal medullary oxygenation: a modeling study.

The goal of this study was to investigate the effects of nitric oxide (NO)-mediated vasodilation in preventing medullary hypoxia, as well as the likely pathways by which superoxide (O2(-)) conversely enhances medullary hypoxia. To do so, we expanded a previously developed mathematical model of solute transport in the renal medulla that accounts for the reciprocal interactions among oxygen (O2), NO, and O2(-) to include the vasoactive effects of NO on medullary descending vasa recta. The model represents the radial organization of the vessels and tubules, centered around vascular bundles in the outer medulla and collecting ducts in the inner medulla. Model simulations suggest that NO helps to prevent medullary hypoxia both by inducing vasodilation of the descending vasa recta (thus increasing O2 supply) and by reducing the active sodium transport rate (thus reducing O2 consumption). That is, the vasodilative properties of NO significantly contribute to maintaining sufficient medullary oxygenation. The model further predicts that a reduction in tubular transport efficiency (i.e., the ratio of active sodium transport per O2 consumption) is the main factor by which increased O2(-) levels lead to hypoxia, whereas hyperfiltration is not a likely pathway to medullary hypoxia due to oxidative stress. Finally, our results suggest that further increasing the radial separation between vessels and tubules would reduce the diffusion of NO towards descending vasa recta in the inner medulla, thereby diminishing its vasoactive effects therein and reducing O2 delivery to the papillary tip.

Impacts of nitric oxide and superoxide on renal medullary oxygen transport and urine concentration.

The goal of this study was to investigate the reciprocal interactions among oxygen (O2), nitric oxide (NO), and superoxide (O2 (-)) and their effects on medullary oxygenation and urinary output. To accomplish that goal, we developed a detailed mathematical model of solute transport in the renal medulla of the rat kidney. The model represents the radial organization of the renal tubules and vessels, which centers around the vascular bundles in the outer medulla and around clusters of collecting ducts in the inner medulla. Model simulations yield significant radial gradients in interstitial fluid oxygen tension (Po2) and NO and O2 (-) concentration in the OM and upper IM. In the deep inner medulla, interstitial fluid concentrations become much more homogeneous, as the radial organization of tubules and vessels is not distinguishable. The model further predicts that due to the nonlinear interactions among O2, NO, and O2 (-), the effects of NO and O2 (-) on sodium transport, osmolality, and medullary oxygenation cannot be gleaned by considering each solute's effect in isolation. An additional simulation suggests that a sufficiently large reduction in tubular transport efficiency may be the key contributing factor, more so than oxidative stress alone, to hypertension-induced medullary hypoxia. Moreover, model predictions suggest that urine Po2 could serve as a biomarker for medullary hypoxia and a predictor of the risk for hospital-acquired acute kidney injury.

Renal hemodynamics, function, and oxygenation during cardiac surgery performed on cardiopulmonary bypass: a modeling study.

Acute kidney injury, a prevalent complication of cardiac surgery performed on cardiopulmonary bypass (CPB), is thought to be driven partly by hypoxic damage in the renal medulla. To determine the causes of medullary hypoxia during CPB, we modeled its impact on renal hemodynamics and function, and thus oxygen delivery and consumption in the renal medulla. The model incorporates autoregulation of renal blood flow and glomerular filtration rate and the utilization of oxygen for tubular transport. The model predicts that renal medullary oxygen delivery and consumption are reduced by a similar magnitude during the hypothermic (down to 28°C) phase of CPB. Thus, the fractional extraction of oxygen in the medulla, an index of hypoxia, is increased only by 58% from baseline. However, during the rewarming phase (up to 37°C), oxygen consumption by the medullary thick ascending limb increases 2.3-fold but medullary oxygen delivery increases only by 33%. Consequently, the fractional extraction of oxygen in the medulla is increased 2.7-fold from baseline. Thus, the renal medulla is particularly susceptible to hypoxia during the rewarming phase of CPB. Furthermore, autoregulation of both renal blood flow and glomerular filtration rate is blunted during CPB by the combined effects of hemodilution and nonpulsatile blood flow. Thus, renal hypoxia can be markedly exacerbated if arterial pressure falls below its target level of 50 mmHg. Our findings suggest that tight control of arterial pressure, and thus renal oxygen delivery, may be critical in the prevention of acute kidney injury associated with cardiac surgery performed on CPB.

Oxygen transport in a cross section of the rat inner medulla: impact of heterogeneous distribution of nephrons and vessels.

We have developed a highly detailed mathematical model of oxygen transport in a cross section of the upper inner medulla of the rat kidney. The model is used to study the impact of the structured organization of nephrons and vessels revealed in anatomic studies, in which descending vasa recta are found to lie distant from clusters of collecting ducts. Specifically, we formulated a two-dimensional oxygen transport model, in which the positions and physical dimensions of renal tubules and vessels are based on an image obtained by immunochemical techniques (T. Pannabecker and W. Dantzler, Three-dimensional architecture of inner medullary vasa recta, Am. J. Physiol. Renal Physiol. 290 (2006) F1355-F1366). The model represents oxygen diffusion through interstitium and other renal structures, oxygen consumption by the Na(+)/K(+)-ATPase activities of the collecting ducts, and basal metabolic consumption. Model simulations yield marked variations in interstitial PO2, which can be attributed, in large part, to the heterogeneities in the position and physical dimensions of the collecting ducts. Further, results of a sensitivity study suggest that medullary oxygenation is highly sensitive to medullary blood flow, and that, at high active consumption rates, localized patches of tissue may be vulnerable to hypoxic injury.

Impact of renal medullary three-dimensional architecture on oxygen transport.

We have developed a highly detailed mathematical model of solute transport in the renal medulla of the rat kidney to study the impact of the structured organization of nephrons and vessels revealed in anatomic studies. The model represents the arrangement of tubules around a vascular bundle in the outer medulla and around a collecting duct cluster in the upper inner medulla. Model simulations yield marked gradients in intrabundle and interbundle interstitial fluid oxygen tension (PO2), NaCl concentration, and osmolality in the outer medulla, owing to the vigorous active reabsorption of NaCl by the thick ascending limbs. In the inner medulla, where the thin ascending limbs do not mediate significant active NaCl transport, interstitial fluid composition becomes much more homogeneous with respect to NaCl, urea, and osmolality. Nonetheless, a substantial PO2 gradient remains, owing to the relatively high oxygen demand of the inner medullary collecting ducts. Perhaps more importantly, the model predicts that in the absence of the three-dimensional medullary architecture, oxygen delivery to the inner medulla would drastically decrease, with the terminal inner medulla nearly completely deprived of oxygen. Thus model results suggest that the functional role of the three-dimensional medullary architecture may be to preserve oxygen delivery to the papilla. Additionally, a simulation that represents low medullary blood flow suggests that the separation of thick limbs from the vascular bundles substantially increases the risk of the segments to hypoxic injury. When nephrons and vessels are more homogeneously distributed, luminal PO2 in the thick ascending limb of superficial nephrons increases by 66% in the inner stripe. Furthermore, simulations predict that owing to the Bohr effect, the presumed greater acidity of blood in the interbundle regions, where thick ascending limbs are located, relative to that in the vascular bundles, facilitates the delivery of O2 to support the high metabolic requirements of the thick limbs and raises NaCl reabsorption.

Capillary recruitment in a theoretical model for blood flow regulation in heterogeneous microvessel networks.

In striated muscle, the number of capillaries containing moving red blood cells increases with increasing metabolic demand. This phenomenon, termed capillary recruitment, has long been recognized but its mechanism has been unclear. Here, a theoretical model for metabolic blood flow regulation in a heterogeneous network is used to test the hypothesis that capillary recruitment occurs as a result of active control of arteriolar diameters, combined with unequal partition of hematocrit at diverging microvascular bifurcations. The network structure is derived from published observations of hamster cremaster muscle in control and dilated states. The model for modulation of arteriolar diameters includes length-tension characteristics of vascular smooth muscle and responses of smooth muscle tone to myogenic, shear-dependent, and metabolic stimuli. Blood flow is simulated including non-uniform hematocrit distribution. Convective and diffusive oxygen transport in the network is simulated. Oxygen-dependent metabolic signals are assumed to be conducted upstream from distal vessels to arterioles. With increasing oxygen demand, arterioles dilate, blood flow increases, and the numbers of flowing arterioles and capillaries, as defined by red blood cell flux above a small threshold value, increase. Unequal hematocrit partition at diverging bifurcations contributes to recruitment and enhances tissue oxygenation. The results imply that capillary recruitment, as observed in the hamster cremaster preparations, can occur as a consequence of local control of arteriolar tone and the resulting non-uniform changes in red blood cell fluxes, and provide an explanation for observations of sequential recruitment of individual capillaries in response to modulation of terminal arteriolar diameter.

Estimation of blood flow rates in large microvascular networks.

OBJECTIVE: Recent methods for imaging microvascular structures provide geometrical data on networks containing thousands of segments. Prediction of functional properties, such as solute transport, requires information on blood flow rates also, but experimental measurement of many individual flows is difficult. Here, a method is presented for estimating flow rates in a microvascular network based on incomplete information on the flows in the boundary segments that feed and drain the network. METHODS: With incomplete boundary data, the equations governing blood flow form an underdetermined linear system. An algorithm was developed that uses independent information about the distribution of wall shear stresses and pressures in microvessels to resolve this indeterminacy, by minimizing the deviation of pressures and wall shear stresses from target values. RESULTS: The algorithm was tested using previously obtained experimental flow data from four microvascular networks in the rat mesentery. With two or three prescribed boundary conditions, predicted flows showed relatively small errors in most segments and fewer than 10% incorrect flow directions on average. CONCLUSIONS: The proposed method can be used to estimate flow rates in microvascular networks, based on incomplete boundary data, and provides a basis for deducing functional properties of microvessel networks.