A computational study of the effect of capillary network anastomoses and tortuosity on oxygen transport

Characterization of Retinal Microvascular Abnormalities in Birdshot Chorioretinopathy Using OCT Angiography

Objective

To characterize changes in the retinal microvasculature in eyes with birdshot chorioretinopathy (BCR) using OCT angiography (OCTA).

Design

Retrospective, observational, single center.

Subjects

Twenty-eight patients (53 eyes) with BCR and 59 age-matched controls (110 eyes).

Methods

En face OCTA images of the superficial capillary plexus (SCP) and deep capillary plexus (DCP) of each eye were assessed for the presence of microvascular abnormalities and used to measure the vessel and foveal avascular zone (FAZ) areas. A longitudinal analysis was performed with a representative cohort of 23 BCR eyes (16 patients) at baseline and at a 2-year time point.

Main Outcome Measures

Whole-image vessel density (VD, %), extrafoveal avascular zone (extra-FAZ) VD (%), and FAZ area (%) were calculated and compared between control and BCR eyes. The frequency of microvascular abnormalities in BCR eyes was recorded.

Results

In the SCP, increased intercapillary space and capillary loops were common features present on OCTA images. Whole-image and extra-FAZ VD were lower in the BCR group compared with controls (P < 0.0001 [SCP and DCP]). Foveal avascular zone area was enlarged in BCR eyes (P = 0.0008 [DCP]). Worsening best-corrected visual acuity was associated with a decrease in whole-image and extra-FAZ VD in the SCP (P < 0.0001 for both) and the DCP (P < 0.005 for both). Multivariable analysis, with vessel analysis parameters as outcomes, demonstrated that increasing age, increasing disease duration, lower central subfield thickness, and treatment-naive eyes (compared with those on only biologics) were associated with a significant decrease in both DCP whole-image and extra-FAZ VD. Increasing disease duration was associated with a significant decrease in both SCP whole-image and extra-FAZ VD. Longitudinal analysis demonstrated no significant difference in any vessel analysis parameters except for an increase in DCP FAZ area.

Conclusions

Our results demonstrate a significant a decrease in VD in BCR eyes and an association on multivariable analysis with disease duration. Quantifying VD in the retinal microvasculature may be a useful biomarker for monitoring disease severity and progression in patients with BCR. Further studies with extended longitudinal follow-up are needed to characterize its utility in monitoring disease progression and treatment response.

Financial Disclosures

Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

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.

A constrained constructive optimization model of branching arteriolar networks in rat skeletal muscle

Blood flow regulation within the microvasculature reflects a complex interaction of regulatory mechanisms and varies spatially and temporally according to conditions such as metabolism, growth, injury, and disease. Understanding the role of microvascular flow distributions across conditions is of interest to investigators spanning multiple disciplines; however, data collection within networks can be labor-intensive and challenging due to limited resolution. To overcome these experimental challenges, computational network models that can accurately simulate vascular behavior are highly beneficial. Constrained constructive optimization (CCO) is a commonly used algorithm for vascular simulation, particularly well known for its adaptability toward vascular modeling across tissues. The present work demonstrates an implementation of CCO aimed to simulate a branching arteriolar microvasculature in healthy skeletal muscle, validated against literature including comprehensive rat gluteus maximus vasculature datasets, and reviews a list of user-specified adjustable model parameters to understand how their variability affects the simulated networks. Network geometric properties, including mean element diameters, lengths, and numbers of bifurcations per order, Horton's law ratios, and fractal dimension, demonstrate good validation once model parameters are adjusted to experimental data. This model successfully demonstrates hemodynamic properties such as Murray's law and the network Fahraeus effect. Application of centrifugal and Strahler ordering schemes results in divergent descriptions of identical simulated networks. This work introduces a novel CCO-based model focused on generating branching skeletal muscle microvascular arteriolar networks based on adjustable model parameters, thus making it a valuable tool for investigations into skeletal muscle microvascular structure and tissue perfusion.NEW & NOTEWORTHY The present work introduces a CCO-based algorithm for generating branching arteriolar networks, with adjustable model parameters to enable modeling in varying skeletal muscle tissues. The geometric and hemodynamic parameters of the generated networks have been comprehensively validated using experimental data collected previously in-house and from literature. This is one of few validated CCO-based models to specialize in skeletal muscle microvasculature and acts as a beneficial tool for investigating the microvasculature for hypothesis testing and validation.

Thromboxane-induced cerebral microvascular rarefaction predicts depressive symptom emergence in metabolic disease

Previous studies have suggested that the loss of microvessel density in the peripheral circulation with evolving metabolic disease severity represents a significant contributor to impaired skeletal muscle oxygenation and fatigue-resistance. Based on this and our recent work, we hypothesized that cerebral microvascular rarefaction was initiated from the increased prooxidant and proinflammatory environment with metabolic disease and is predictive of the severity of the emergence of depressive symptoms in obese Zucker rats (OZRs). In male OZR, cerebrovascular rarefaction followed the emergence of elevated oxidant and inflammatory environments characterized by increased vascular production of thromboxane A2 (TxA2). The subsequent emergence of depressive symptoms in OZR was associated with the timing and severity of the rarefaction. Chronic intervention with antioxidant (TEMPOL) or anti-inflammation (pentoxifylline) therapy blunted the severity of rarefaction and depressive symptoms, although the effectiveness was limited. Blockade of TxA2 production (dazmegrel) or action (SQ-29548) resulted in a stronger therapeutic effect, suggesting that vascular production and action represent a significant contributor to rarefaction and the emergence of depressive symptoms with chronic metabolic disease (although other pathways clearly contribute as well). A de novo biosimulation of cerebrovascular oxygenation in the face of progressive rarefaction demonstrates the increased probability of generating hypoxic regions within the microvascular networks, which could contribute to impaired neuronal metabolism and the emergence of depressive symptoms. The results of the present study also implicate the potential importance of aggressive prodromic intervention in reducing the severity of chronic complications arising from metabolic disease.NEW & NOTEWORTHY With clinical studies linking vascular disease risk to depressive symptom emergence, we used obese Zucker rats, a model of chronic metabolic disease, to identify potential mechanistic links between these two negative outcomes. Depressive symptom severity correlated with the extent of cerebrovascular rarefaction, after increased vascular oxidant stress/inflammation and TxA2 production. Anti-TxA2 interventions prevasculopathy blunted rarefaction and depressive symptoms, while biosimulation indicated that cerebrovascular rarefaction increased hypoxia within capillary networks as a potential contributing mechanism.

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.

A physicochemical model of X-ray induced photodynamic therapy (X-PDT) with an emphasis on tissue oxygen concentration and oxygenation

X-PDT is one of the novel cancer treatment approaches that uses high penetration X-ray radiation to activate photosensitizers (PSs) placed in deep seated tumors. After PS activation, some reactive oxygen species (ROS) like singlet oxygen (1O2) are produced that are very toxic for adjacent cells. Efficiency of X-PDT depends on 1O2 quantum yield as well as X-ray mortality rate. Despite many studies have been modeled X-PDT, little is known about the investigation of tissue oxygen content in treatment outcome. In the present study, we predicted X-PDT efficiency through a feedback of physiological parameters of tumor microenvironment includes tissue oxygen and oxygenation properties. The introduced physicochemical model of X-PDT estimates 1O2 production in a vascularized and non-vascularized tumor under different tissue oxygen levels to predict cell death probability in tumor and adjacent normal tissue. The results emphasized the importance of molecular oxygen and the presence of a vascular network in predicting X-PDT efficiency.

The dose-related plateau effect of surviving fraction in normal tissue during the ultra-high-dose-rate radiotherapy

Objective.Ultra-high-dose-rate radiotherapy, referred to as FLASH therapy, has been demonstrated to reduce the damage of normal tissue as well as inhibiting tumor growth compared with conventional dose-rate radiotherapy. The transient hypoxia may be a vital explanation for sparing the normal tissue. The heterogeneity of oxygen distribution for different doses and dose rates in the different radiotherapy schemes are analyzed. With these results, the influence of doses and dose rates on cell survival are evaluated in this work.Approach.The two-dimensional reaction-diffusion equations are used to describe the heterogeneity of the oxygen distribution in capillaries and tissue. A modified linear quadratic model is employed to characterize the surviving fraction at different doses and dose rates.Main results.The reduction of the damage to the normal tissue can be observed if the doses exceeds a minimum dose threshold under the ultra-high-dose-rate radiation. Also, the surviving fraction exhibits the 'plateau effect' under the ultra-high dose rates radiation, which signifies that within a specific range of doses, the surviving fraction either exhibits minimal variation or increases with the dose. For a given dose, the surviving fraction increases with the dose rate until tending to a stable value, which means that the protection in normal tissue reaches saturation.Significance.The emergence of the 'plateau effect' allows delivering the higher doses while minimizing damage to normal tissue. It is necessary to develop appropriate program of doses and dose rates for different irradiated tissue to achieve more efficient protection.

Myocardial infarction and oxidative damage in animal models: objective and expectations from the application of cysteine derivatives

Reactive oxygen species (ROS) and associated oxidative stress are the main contributors to pathophysiological changes following myocardial infarction (MI), which is the principal cause of death from cardiovascular disease. The glutathione (GSH)/glutathione peroxidase (GPx) system appears to be the main and most active cardiac antioxidant mechanism. Hence, enhancement of the myocardial GSH system might have protective effects in the setting of MI. It follows that by increasing antioxidant capacity, the heart will be able to reduce the damage associated with MI and even prevent/weaken the occurrence of oxidative stress, which is highly ranked among the factors responsible for the occurrence of acute MI. For these reasons, the primary goal of future investigations should be to address the effects of different antioxidative compounds and especially cysteine derivatives like N-acetyl cysteine (NAC) and L-2-oxothiazolidine-4-carboxylic acid (OTC) as precursors responsible for the enhancement of the GSH-related antioxidant system's capacity. It is assumed that this will lay down the basis for elucidation of the mechanisms throughout which applicable doses of OTC will manifest a potentially positive impact in the reduction of adverse effects of acute MI. The inclusion of OTC in the models for prediction of the distribution of oxygen in infarcted animal hearts can help to upgrade existing computational models. Such a model would be based on computational geometries of the heart, but the inclusion of biochemical redox features in addition to angiogenic therapy, despite improvement of the post-infarcted oxygenated outcome could enhance the accuracy of the predictive values of oxygenation.

Optical method to determine in vivo capillary hematocrit, hemoglobin concentration, and 3-D network geometry in skeletal muscle

OBJECTIVE

The aim of this study was to develop a tool to visualize and quantify hemodynamic information, such as hemoglobin concentration and hematocrit, within microvascular networks recorded in vivo using intravital video microscopy. Additionally, we aimed to facilitate the 3-D reconstruction of the microvascular networks.

METHODS

Digital images taken from an intravital video microscopy preparation of the extensor digitorum longus muscle in rats for 25 capillary segments were used. The developed algorithm was used to delineate capillaries of interest, calculate the optical density for each pixel in the image, and reconstruct the 3-D capillary geometry using the calculated light path-lengths. Subsequently, the mean corpuscular hemoglobin concentration (MCHC), hemoglobin concentration, and hematocrit for these capillaries were calculated. We evaluated the hematocrit values determined by our methodology by comparing them to those obtained using a previously published method.

RESULTS

The hematocrit values from the proposed optical method were strongly correlated with those calculated using published methods r² (25) = .92, p < .001, and demonstrated excellent agreement with a mean difference of 1.3% and a coefficient of variation (CV) of 11%. The average MCHC, hemoglobin concentration, and light path-lengths were 23.83 g/dl, 8.06 g/dl, and 3.92 µm, respectively.

CONCLUSION

The proposed methodology can quantify hemodynamic measurements and produce functional images for visualization of the microcirculation in vivo.

Association of retinal fractal dimension and vessel tortuosity with impaired renal function among healthy Chinese adults

Purpose

This study investigated the association of retinal fractal dimension (FD) and blood vessel tortuosity (BVT) with renal function [assessed by estimated glomerular filtrate rate (eGFR)] in healthy Chinese adults using swept-source optical coherence tomographic angiography (SS-OCTA).

Materials and methods

This cross-sectional study was conducted among ocular treatment–naïve healthy participants from Guangzhou, China. FD and BVT in the superficial capillary plexus and deep capillary plexus were measured by SS-OCTA with a 3 × 3 macula model. eGFR was calculated using the Xiangya equation, and impaired renal function (IRF) was defined as eGFR = 90 mL/min/1.73 m2. Linear regression was performed to evaluate the relationships between SS-OCTA metrics and renal function.

Results

A total of 729 participants with a mean age of 57.6 ± 9.1 years were included in the final analysis. Compared to participants with normal renal function, those with IRF had lower FD both in the superficial capillary plexus (1.658 ± 0.029 vs. 1.666 ± 0.024, p = 0.001) and deep capillary plexus (1.741 ± 0.016 vs. 1.746 ± 0.016, p = 0.0003), while the deep BVT was larger in participants with IRF than those with normal renal function (1.007 ± 0.002 vs. 1.006 ± 0.002, p = 0.028). The superficial FD was linearly and positively associated with eGFR after adjusting for confounders (β = 0.2257; 95% CI 0.0829–0.3685; p = 0.002), while BVT was not associated with eGFR (all p ≥ 0.05).

Conclusion

The patients with IRF had lower FD and larger BVT than those with normal renal function. The superficial FD decreased linearly with renal function deterioration. Our study suggests that the retinal microvasculature can represent a useful indicator of subclinical renal microvascular abnormalities and serve as a useful non-invasive assessment to predict and monitor the progression of renal function.

Arteriolar dysgenesis in ischemic, regenerating skeletal muscle revealed by automated micro-morphometry, computational modeling, and perfusion analysis

Rebuilding the local vasculature is central to restoring the health of muscles subjected to ischemic injury. Arteriogenesis yields remodeled collateral arteries that circumvent the obstruction, and angiogenesis produces capillaries to perfuse the regenerating myofibers. However, the vital intervening network of arterioles that feed the regenerated capillaries is poorly understood and an investigative challenge. We used machine learning and automated micro-morphometry to quantify the arteriolar landscape in distal hindlimb muscles in mice that have regenerated after femoral artery excision. Assessment of 1546 arteriolar sections revealed a striking (> 2-fold) increase in arteriolar density in regenerated muscle 14 and 28 days after ischemic injury. Lumen caliber was initially similar to that of control arterioles but after 4 weeks lumen area was reduced by 46%. In addition, the critical smooth muscle layer was attenuated throughout the arteriolar network, across a 150 to 5 µm diameter range. To understand the consequences of the reshaped distal hindlimb arterioles, we undertook computational flow modeling which revealed blunted flow augmentation. Moreover, impaired flow reserve was confirmed in vivo by laser Doppler analyses of flow in response to directly applied sodium nitroprusside. Thus, in hindlimb muscles regenerating after ischemic injury, the arteriolar network is amplified, inwardly remodels, and is diffusely under-muscularized. These defects and the associated flow restraints could contribute to the deleterious course of peripheral artery disease and merit attention when considering therapeutic innovations.

Dermal Lymphatic Capillaries Do Not Obey Murray's Law

Lymphatic vessels serve as a major conduit for the transport of interstitial fluid, immune cells, lipids and drugs. Therefore, increased knowledge about their development and function is relevant to clinical issues ranging from chronic inflammation and edema, to cancer metastasis to targeted drug delivery. Murray's Law is a widely-applied branching rule upheld in diverse circulatory systems including leaf venation, sponge canals, and various human organs for optimal fluid transport. Considering the unique and diverse functions of lymphatic fluid transport, we specifically address the branching of developing lymphatic capillaries, and the flow of lymph through these vessels. Using an empirically-generated dataset from wild type and genetic lymphatic insufficiency mouse models we confirmed that branching blood capillaries consistently follow Murray's Law. However surprisingly, we found that the optimization law for lymphatic vessels follows a different pattern, namely a Murray's Law exponent of ~1.45. In this case, the daughter vessels are smaller relative to the parent than would be predicted by the hypothesized radius-cubed law for impermeable vessels. By implementing a computational fluid dynamics model, we further examined the extent to which the assumptions of Murray's Law were violated. We found that the flow profiles were predominantly parabolic and reasonably followed the assumptions of Murray's Law. These data suggest an alternate hypothesis for optimization of the branching structure of the lymphatic system, which may have bearing on the unique physiological functions of lymphatics compared to the blood vascular system. Thus, it may be the case that the lymphatic branching structure is optimized to enhance lymph mixing, particle exchange, or immune cell transport, which are particularly germane to the use of lymphatics as drug delivery routes.

A two-layer continuously distributed capillary O2 transport model applied to blood flow regulation in resting skeletal muscle

The microcirculation is the site of direct oxygen transfer from blood to tissue, and also of oxygen delivery control via regulation of local blood flow. In addition, a number of diseases including type II diabetes mellitus (DMII) and sepsis are known to produce microcirculatory dysfunction in their early phases. Given the complexity of microvascular structure and physiology, and the difficulty of measuring tissue oxygenation at the micro-scale, mathematical modelling has been necessary for understanding the physiology and pathophysiology of O₂ transport in the microcirculation and for interpreting in vivo experiments. To advance this area, a model of blood-tissue O₂ transport in skeletal muscle was recently developed which uses continuously distributed capillaries and includes O₂ diffusion, convection, and consumption. The present work extends this model to two adjacent layers of skeletal muscle with different blood flow rates and applies it to study steady-state O₂ transport when flow regulation is stimulated using an O₂ exchange chamber. To generate a model which may be validated through in vivo experiments, an overlying O₂ permeable membrane is included. The model is solved using traditional methods including separation of variables and Fourier decomposition, and to ensure smooth profiles at the muscle-muscle and muscle-membrane interfaces matching conditions are developed. The study presents qualitative verification for the model, using visualizations of tissue PO₂ distributions for varying capillary density (CD), and presents capillary velocity response values in the near layer for varying chamber PO₂ under the assumption that outlet capillary O₂ saturation is equalized between adjacent layers. These compensatory velocity profiles, along with effective 'no-flux' chamber PO₂ values, are presented for varying CD and tissue O₂ consumption values. Insights gained from the two-layer model provide guidance for interpreting and planning future in-vivo experiments, and also provide motivation for further development of the model to improve understanding of the interaction between O₂ transport and blood flow regulation.

Morphological and Functional Relationship Between OCTA and FA/ICGA Quantitative Features in AMD-Related Macular Neovascularization

Background: The aim was to study the relationship between quantitative information provided by optical coherence tomography (OCT) angiography (OCTA) and conventional angiography in macular neovascularization (MNV) secondary to age-related macular degeneration (AMD).

Methods: The research was designed as an interventional, prospective study. We included 66 eyes (66 patients) affected by naïve MNV. Multimodal imaging included structural OCT, OCTA, fluorescein angiography (FA), and indocyanine green angiography (ICGA). The follow-up lasted 1 year. Patients were treated by PRN anti-VEGF injections. Based on FA/ICGA examinations, we divided the patients into two categories: low vessel tortuosity (VT) (<8.40) and high VT (>8.40), correlating VT with the MNV area, leakage area, speckled fluorescence (SF) quadrants and MNV area/leakage area ratio.

Results: Mean baseline BCVA was 0.50 ± 0.61 LogMAR, improved to 0.31 ± 0.29 LogMAR after 1 year (p < 0.01), with a mean number of 7 ± 2 anti-VEGF injections. The patients revealed type-1 MNV in 36 eyes (55%), mixed type 1 and 2 MNV in 18 eyes (27%), and type-2 MNV in 12 eyes (18%). MNV eyes in high-VT MNV featured poorer BCVA, CMT, and OCTA parameters, higher SF quadrants, and less exudation, compared with low-VT MNV (p < 0.01). Moreover, 30% of high-VT MNV eyes developed outer retinal atrophy.

Conclusions: Low VT MNV turned out to be more exudative at the baseline but less damaging to the outer retinal structures, whereas high VT MNV proved to be less exudative but more prone to lead to atrophic changes and visual function deterioration. VT may be usefully applied to artificial intelligence-based models designed to characterize MNV secondary to AMD.

Vessel Evaluation in Patients with Primary Open-Angle Glaucoma, Normal Tension Glaucoma and Healthy Controls

Purpose

To compare changes in central retinal arterial equivalent (CRAE), central retinal vein equivalent (CRVE), arteriovenous ratio (AVR), tortuosity and fractal dimension in primary open-angle glaucoma (POAG), normal-tension glaucoma (NTG) and in a control group (CG) on fundus photographs. Further, to provide further evidence of vascular change in glaucoma patients using a novel method of tortuosity.

Patients and Methods

The primary endpoint was the change in CRAE, CRVE, AVR, fractal dimension and tortuosity of the retinal vasculature from baseline, retrospectively analyzed from 2011 to 2017 at the University Eye Hospital Tuebingen. Fundus photos of POAG (N = 49), NTG (N = 38) and CG (N = 18) were computer evaluated and analyzed in the quantities mentioned above.

Results

CRAE in NTG and POAG and CRVE in NTG significantly decreased (P = 0.02, P = 0.01; P = 0.03) whereas CRVE in POAG increased insignificantly (P = 0.72). In NTG, AVR decreased significantly (P = 0.05), but to a lesser extent than in POAG (P < 0.001). In CG, CRAE decreased insignificantly (P = 0.10), CRVE decreased significantly (P = 0.03) and AVR increased insignificantly (P = 0.77). In POAG tortuosity calculated using standard methods as well as our novel method, increased significantly (P = 0.015-0.04), whereas it did not occur in NTG (P = 0.18-0.57) and CG (P = 0.11-0.21). Fractal dimensions in POAG decreased significantly (P = 0.001-0.002), whereas in NTG and CG changes were insignificant (P = 0.33-0.92).

Conclusion

Based on a retrospective analysis of fundus photographs, specific retinal vasculature features of the retinal vasculature display significant alterations associated with NTG and POAG. The assessment of tortuosity using our novel method was consistent with previously established methods for analyzing tortuosity.

QUANTITATIVE OPTICAL COHERENCE TOMOGRAPHY ANGIOGRAPHY PARAMETER VARIATIONS AFTER TREATMENT OF MACULAR NEOVASCULARIZATION SECONDARY TO AGE-RELATED MACULAR DEGENERATION

PURPOSE

Macular neovascularization (MNV) secondary to age-related macular degeneration can be characterized by quantitative optical coherence tomography angiography. The aim of the study was to assess the evolution of quantitative optical coherence tomography angiography parameters after 1 year of antivascular endothelial growth factor injections.

METHODS

Naive age-related macular degeneration-related MNV eyes were prospectively recruited to analyze optical coherence tomography and optical coherence tomography angiography parameters, including MNV vessel tortuosity (VT) and reflectivity, at baseline and at the end of the follow-up. Macular neovascularization eyes were categorized by a MNV VT cutoff, and quantitative parameter variations were documented after 1 year of treatment. We divided MNV eyes into Group 1 (MNV VT < 8.40) and Group 2 (MNV VT > 8.40).

RESULTS

Thrity naive age-related macular degeneration-related MNV eyes (30 patients) were included. Our cohort included 18 Type 1 MNV and 12 Type 2 MNV lesions. Baseline central macular thickness (411 ± 85 µm) improved to 323 ± 54 µm at 1 year (P < 0.01). Only Group 1 MNV displayed significant visual improvement. Macular neovascularization VT values remained stable over the follow-up in both subgroups. Group 2 MNV eyes showed increased MNV reflectivity and increased MNV area at the end of the follow-up. Quantitative retinal capillary plexa parameters were found to be worse in Group 2 MNV. Outer retinal atrophy occurred in 2 of the 18 eyes in MNV Group 1 (11%) and in 6 of the 12 eyes in MNV Group 2 (50%) after 1 year. Vessel density proved to be always worse in Group 2 than in Group 1.

CONCLUSION

Macular neovascularization VT provides information on the blood flow and identifies two subgroups with different final anatomical and visual outcomes, regardless of the treatment effect.

A Mesoscale Computational Model for Microvascular Oxygen Transfer

We address a mathematical model for oxygen transfer in the microcirculation. The model includes blood flow and hematocrit transport coupled with the interstitial flow, oxygen transport in the blood and the tissue, including capillary-tissue exchange effects. Moreover, the model is suited to handle arbitrarily complex vascular geometries. The purpose of this study is the validation of the model with respect to classical solutions and the further demonstration of its adequacy to describe the heterogeneity of oxygenation in the tissue microenvironment. Finally, we discuss the importance of these effects in the treatment of cancer using radiotherapy.

Regenerated Microvascular Networks in Ischemic Skeletal Muscle

Skeletal muscle is the largest organ in humans. The viability and performance of this metabolically demanding organ are exquisitely dependent on the integrity of its microcirculation. The architectural and functional attributes of the skeletal muscle microvasculature are acquired during embryonic and early postnatal development. However, peripheral vascular disease in the adult can damage the distal microvasculature, together with damaging the skeletal myofibers. Importantly, adult skeletal muscle has the capacity to regenerate. Understanding the extent to which the microvascular network also reforms, and acquires structural and functional competence, will thus be critical to regenerative medicine efforts for those with peripheral artery disease (PAD). Herein, we discuss recent advances in studying the regenerating microvasculature in the mouse hindlimb following severe ischemic injury. We highlight new insights arising from real-time imaging of the microcirculation. This includes identifying otherwise hidden flaws in both network microarchitecture and function, deficiencies that could underlie the progressive nature of PAD and its refractoriness to therapy. Recognizing and overcoming these vulnerabilities in regenerative angiogenesis will be important for advancing treatment options for PAD.

Lamina Cribrosa Capillaries Straighten as Intraocular Pressure Increases

Purpose

The purpose of this study was to visualize the lamina cribrosa (LC) capillaries and collagenous beams, measure capillary tortuosity (path length over straight end-to-end length), and determine if capillary tortuosity changes when intraocular pressure (IOP) increases.

Methods

Within 8 hours of sacrifice, 3 pig heads were cannulated via the external ophthalmic artery, perfused with PBS to remove blood, and then perfused with a fluorescent dye to label the capillaries. The posterior pole of each eye was mounted in a custom-made inflation chamber for control of IOP with simultaneous imaging. Capillaries and collagen beams were visualized with structured light illumination enhanced imaging at IOPs from 5 to 50 mm Hg at each 5 mm Hg increment. Capillary tortuosity was measured from the images and paired two-sample t-tests were used to assess for significant changes in relation to changes in IOP.

Results

Capillaries were highly tortuous at 15 mm Hg (up to 1.45). In all but one eye, tortuosity decreased significantly as IOP increased from 15 to 25 mm Hg (P < 0.01), and tortuosity decreased significantly in every eye as IOP increased from 15 to 40 mm Hg (P < 0.01). In only 16% of capillaries, tortuosity increased with elevated IOP. Capillaries had a surprisingly different topology from the collagen beams.

Conclusions

Although high capillary tortuosity is sometimes regarded as potentially problematic because it can reduce blood flow, LC capillary tortuosity may provide slack that mitigates against reduced flow and structural damage caused by excessive stretch under elevated IOP. We speculate that low capillary tortuosity could be a risk factor for damage under high IOP.

The capillary fascicle in skeletal muscle: Structural and functional physiology of RBC distribution in capillary networks

KEY POINTS

The capillary module, consisting of parallel capillaries from arteriole to venule, is classically considered as the building block of complex capillary networks. In skeletal muscle, this structure fails to address how blood flow is regulated along the entire length of the synchronously contracting muscle fibres. Using intravital video microscopy of resting extensor digitorum longus muscle in rats, we demonstrated the capillary fascicle as a series of interconnected modules forming continuous columns that align naturally with the dimensions of the muscle fascicle. We observed structural heterogeneity for module topology, and functional heterogeneity in space and time for capillary-red blood cell (RBC) haemodynamics within a module and between modules. We found that module RBC haemodynamics were independent of module resistance, providing direct evidence for microvascular flow regulation at the level of the capillary module. The capillary fascicle is an updated paradigm for characterizing blood flow and RBC distribution in skeletal muscle capillary networks.

ABSTRACT

Capillary networks are the fundamental site of oxygen exchange in the microcirculation. The capillary module (CM), consisting of parallel capillaries from terminal arteriole (TA) to post-capillary venule (PCV), is classically considered as the building block of complex capillary networks. In skeletal muscle, this structure fails to address how blood flow is regulated along the entire length of the synchronously contracting muscle fibres, requiring co-ordination from numerous modules. It has previously been recognized that TAs and PCVs interact with multiple CMs, creating interconnected networks. Using label-free intravital video microscopy of resting extensor digitorum longus muscle in rats, we found that these networks form continuous columns of linked CMs spanning thousands of microns, herein denoted as the capillary fascicle (CF); this structure aligns naturally with the dimensions of the muscle fascicle. We measured capillary-red blood cell (RBC) haemodynamics and module topology (n = 9 networks, 327 modules, 1491 capillary segments). The average module had length 481 μm, width 157 μm and 9.51 parallel capillaries. We observed structural heterogeneity for CM topology, and functional heterogeneity in space and time for capillary-RBC haemodynamics within a module and between modules. There was no correlation between capillary RBC velocity and lineal density. A passive inverse relationship between module length and haemodynamics was remarkably absent, providing direct evidence for microvascular flow regulation at the level of the CM. In summary, the CF is an updated paradigm for characterizing RBC distribution in skeletal muscle, and strengthens the theory of capillary networks as major contributors to the signal that regulates capillary perfusion.

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

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

Do skeletal muscle motor units and microvascular units align to help match blood flow to metabolic demand?

PURPOSE

We explore the motor unit recruitment and control of perfusion of microvascular units in skeletal muscle to determine whether they coordinate to match blood flow to metabolic demand.

METHODS

The PubMed database was searched for historical, current and relevant literature.

RESULTS

A microvascular, or capillary unit consists of 2-20 individual capillaries. Individual capillaries within a capillary unit cannot increase perfusion independently of other capillaries within the unit. Capillary units perfuse a short segment of approx. 12 muscle fibres located beside each other. Motor units consist of muscle fibres that can be dispersed widely within the muscle volume. During a contraction, where not all motor units are recruited, muscle fibre contraction will result in increased perfusion of associated capillaries as well as all capillaries within that capillary unit. Perfusion of the entire capillary unit will result in an increased blood flow delivery to muscle fibres associated with active motor unit plus approximately 11 other inactive muscle fibres within the same region. This will result in an overperfusion of the muscle resulting in blood flow in excess of the muscle fibre needs.

CONCLUSIONS

Given the architecture of the capillary units and the dispersed nature of muscle fibres within a motor unit, during submaximal contractions, where not all motor units are recruited, there will be a greater perfusion to the muscle than that predicted by the number of active muscle fibres. Such overperfusion brings into question if blood flow and metabolic demand are as tightly matched as previously assumed.

Determining the parameter space for effective oxygen depletion for FLASH radiation therapy

There has been a recent revival of interest in the FLASH effect, after experiments have shown normal tissue sparing capabilities of ultra-high-dose-rate radiation with no compromise on tumour growth restraint. A model has been developed to investigate the relative importance of a number of fundamental parameters considered to be involved in the oxygen depletion paradigm of induced radioresistance. An example eight-dimensional parameter space demonstrates the conditions under which radiation may induce sufficient depletion of oxygen for a diffusion-limited hypoxic cellular response. Initial results support experimental evidence that FLASH sparing is only achieved for dose rates on the order of tens of Gy/s or higher, for a sufficiently high dose, and only for tissue that is slightly hypoxic at the time of radiation. We show that the FLASH effect is the result of a number of biological, radiochemical and delivery parameters. Also, the threshold dose for a FLASH effect occurring would be more prominent when the parameterisation was optimised to produce the maximum effect. The model provides a framework for further FLASH-related investigation and experimental design. An understanding of the mechanistic interactions producing an optimised FLASH effect is essential for its translation into clinical practice.

A two-compartment model of oxygen transport in skeletal muscle using continuously distributed capillaries

For future application to studying regulation of microvascular oxygen delivery, a model is developed for O₂ transport within an idealized volume of tissue, that is perfused by a continuous distribution of capillaries. Considering oxygen diffusion, convection, and consumption, an O₂-dependent transfer term between the capillaries and tissue is used to extend previous single-compartment approaches to include separate tissue and capillary compartments. The coupled tissue-capillary PDE system is considered for unidirectional capillary flow in z, as a simplified model of O₂ transport in skeletal muscle, and steady-state 2D solutions are obtained using boundary conditions in x that are consistent with two experimental situations of interest. To validate the continuous capillary model, comparisons are made of an exact nonlinear solution (for no flux at x=0) to results of an established discrete capillary model (solved via finite differences) for varying capillary density, O₂ consumption rate, and red blood cell velocity. In addition, comparisons of an approximate linearized solution (for fixed PO₂ at x=0) are made to the corresponding discrete capillary solution. Results of the continuous capillary model are presented for varying inlet O₂ saturation, showing the utility of the new model for studying physiological problems. Numerical solution of the new model for problems with time dependence and complex geometry is expected to be substantially more efficient than for the corresponding discrete capillary problems.

Optical Coherence Tomography Angiography Quantitative Assessment of Macular Neovascularization in Best Vitelliform Macular Dystrophy

Purpose

To describe quantitative characteristics of macular neovascularization (MNV) in vitelliform macular dystrophy (VMD) patients by means of optical coherence tomography angiography (OCTA).

Methods

The study design was a prospective case series. All patients underwent complete ophthalmologic assessment, optical coherence tomography, and OCTA. The quantitative OCTA parameters examined included vessel tortuosity and vessel dispersion of the MNV. The primary outcome was OCTA characterization of MNV in VMD. Secondary outcomes included the evolution of MNV over the follow-up.

Results

A total of 78 eyes were recruited for the study. MNV was identified in 50 eyes (64%) at baseline and in 51 eyes (65%) at the end of the follow-up (mean follow-up, 24.7 ± 9.7 months). MNV was detected in four out of the 30 eyes classified as stages 2 and 3 (13%), showing exudative manifestations and undergoing ranibizumab treatment, leading to clinical stabilization. OCTA detected MNV in 46 out of 48 eyes (96%) classified as stages 4 and 5, showing no evidence of exudative manifestation. All of the non-exudative MNVs were merely observed over the follow-up and received no treatment. At the end of the follow-up, 47 out of 48 eyes displayed MNV (98%). Non-exudative MNVs remained stable over the follow-up. Statistically significant differences were found when comparing vessel tortuosity and vessel dispersion in the two MNV subforms.

Conclusions

VMD is characterized by two MNV subforms. Exudative MNV is rare and may develop in the early stages of the disease, in association with bleeding and fluid formation. Non-exudative MNV develops very commonly in the advanced stage of VMD, without any exudative manifestation.

Vessel-on-a-chip models for studying microvascular physiology, transport, and function in vitro

To understand how the microvasculature grows and remodels, researchers require reproducible systems that emulate the function of living tissue. Innovative contributions toward fulfilling this important need have been made by engineered microvessels assembled in vitro with microfabrication techniques. Microfabricated vessels, commonly referred to as "vessels-on-a-chip," are from a class of cell culture technologies that uniquely integrate microscale flow phenomena, tissue-level biomolecular transport, cell-cell interactions, and proper three-dimensional (3-D) extracellular matrix environments under well-defined culture conditions. Here, we discuss the enabling attributes of microfabricated vessels that make these models more physiological compared with established cell culture techniques and the potential of these models for advancing microvascular research. This review highlights the key features of microvascular transport and physiology, critically discusses the strengths and limitations of different microfabrication strategies for studying the microvasculature, and provides a perspective on current challenges and future opportunities for vessel-on-a-chip models.

Steady-State Tissue Oxygen Distributions Calculated by a Green's Function Method and a Finite Difference Method: A Comparison

Simulations that are meant to determine the steady-state distribution of a diffusible solute such as oxygen in tissues have typically used finite difference methods to solve the diffusion equation. Finite difference methods require a tissue mesh with enough points to resolve oxygen gradients near and between discrete blood vessels. The large number of points that are typically required can make these calculations very slow. In this paper, we investigate a numerical method known as the Green's function method which is not bound by the same constraint. The Green's function method is expected to yield an accurate oxygen distribution more quickly by requiring fewer mesh points. Both methods were applied to calculate the steady state oxygen distribution in a model simulation region. When the Green's function calculation used meshes with 1/2, 1/4 and, 1/8 of the resolution required for the finite-difference mesh, there was good agreement with the finite difference calculation in all cases. When the volume of the domain was increased 8-fold the Green's function method was able to calculate the O₂ field in 22 minutes, whereas the finite difference calculation is expected to take approximately 1 week. The number of steps required for the Green's function calculation increases quadratically with the number of points in the tissue mesh. As a result, small meshes are calculated very quickly using Green's functions, while for larger mesh sizes this method experiences a significant decrease in efficiency.

Quantitative Optical Coherence Tomography Angiography Parameters in Type 1 Macular Neovascularization Secondary to Age-Related Macular Degeneration

Purpose

The purpose of this paper was to study type 1 macular neovascularization (MNV) quantitative optical coherence tomography (OCT) angiography (OCTA) features by means of advanced postprocessing analyses.

Methods

We recruited patients affected by naïve type 1 MNV secondary to age-related macular degeneration (AMD) and age-matched controls. All patients underwent ophthalmologic examination and multimodal imaging. They were treated with pro-re-nata anti-VEGF injections. The ensuing follow-up lasted 24 months. Quantitative OCT and OCTA parameters were statistically analyzed to obtain cutoff values able to distinguish two clinically different patient subgroups. Main outcome measures were best-corrected visual acuity (BCVA), central macular thickness, vessel density of superficial, deep and choriocapillaris plexa, vessel tortuosity (VT) of MNV, vessel dispersion of MNV, number of injections, blooding, pigment epithelium detachment, subretinal fluid, photoreceptor elongation, subretinal fibrosis, and outer retinal atrophy.

Results

Ninety-one eyes (91 patients; 49 men; mean age 78 ± 7 years) and 91 control eyes were included. Mean logarithm of the minimum angle of resolution (logMAR) BCVA was 0.46 ± 0.56 at baseline, increasing up to 0.29 ± 0.30 after 2 years of treatment (P < 0.01). The mean number of intravitreal injections was 7.1 ± 2.0 during the first year and 4.5 ± 1.4 during the second year. A baseline VT cutoff of 8.40 detected two patients’ subgroups differing significantly in terms of BCVA improvement after 2 years of treatment.

Conclusions

OCTA-based classification of type 1 MNV, performed at baseline, provided useful information in terms of the functional outcome achievable after 24 months of anti-VEGF treatment.

Translational Relevance

Quantitative OCTA-based classification of type 1 MNV, performed at baseline, provided useful information in terms of the functional outcome achievable after 24 months of anti-VEGF treatment.

Retinal Arteriolar Narrowing in Young Adults With Glaucomatous Optic Disc

PURPOSE

Glaucomatous optic disc (GOD) might represent various subclinical processes. However, whether the presence of GOD is related to vascular processes is less clear. This study aimed to assess the retinal vessel diameter, as surrogate markers of vascular regulation, in healthy young adults with GOD compared with normal.

MATERIALS AND METHODS

This was a clinic-based case-control study of 54 participants, aged between 18 and 30 years. We included patients with GOD (confirmed with slit-lamp and optical coherence tomography examination having cup-to-disc ratio ≥0.5), intraocular pressure ≤21 mm Hg, no history of hypertension, cardiovascular and kidney disease, anemia, diabetes mellitus, and spherical correction of ≤-1.5 D. Controls were healthy subjects with similar criteria but no sign of GOD. Retinal vessel diameters were measured using semiautomated program [Singapore I Vessel Assessment (SIVA) version 4.0] and expressed as central retinal arteriolar equivalent (CRAE) and central retinal venular equivalent.

RESULTS

The mean CRAE was significantly narrower in patients with GOD than controls (110.6±12.16 vs. 118.6±12.17; P=0.019). Central retinal venular equivalent was not significantly different. A CRAE narrower than 107.1 μm was significantly associated with GOD (odds ratio, 8.59; 95% confidence interval, 1.68-43.9; P<0.001) compared with controls.

CONCLUSIONS

Retinal arterioles were narrower in young adults with GOD compared with normal, suggesting that the presence of GOD might be associated with subclinical changes in retinal vascularization even in the absence of increased intraocular pressure. However, the clinical significance of these findings deserves further studies.

Hyperinsulinemia does not cause de novo capillary recruitment in rat skeletal muscle

Objective

The effect of insulin on blood flow distribution within muscle microvasculature has been suggested to be important for glucose metabolism. However, the “capillary recruitment” hypothesis is still controversial and relies on studies using indirect contrast‐enhanced ultrasound (CEU) methods.

Methods

We studied how hyperinsulinemia effects capillary blood flow in rat extensor digitorum longus (EDL) muscle during euglycemic hyperinsulinemic clamp using intravital video microscopy (IVVM). Additionally, we modeled blood flow and microbubble distribution within the vascular tree under conditions observed during euglycemic hyperinsulinemic clamp experiments.

Results

Euglycemic hyperinsulinemia caused an increase in erythrocyte (80 ± 25%, P < .01) and plasma (53 ± 12%, P < .01) flow in rat EDL microvasculature. We found no evidence of de novo capillary recruitment within, or among, capillary networks supplied by different terminal arterioles; however, erythrocyte flow became slightly more homogenous. Our computational model predicts that a decrease in asymmetry at arteriolar bifurcations causes redistribution of microbubble flow among capillaries already perfused with erythrocytes and plasma, resulting in 25% more microbubbles flowing through capillaries.

Conclusions

Our model suggests increase in CEU signal during hyperinsulinemia reflects a redistribution of arteriolar flow and not de novo capillary recruitment. IVVM experiments support this prediction showing increases in erythrocyte and plasma flow and not capillary recruitment.

Edward F. Adolph Distinguished Lecture. Contemporary model of muscle microcirculation: gateway to function and dysfunction

This review strikes at the very heart of how the microcirculation functions to facilitate blood-tissue oxygen, substrate, and metabolite fluxes in skeletal muscle. Contemporary evidence, marshalled from animals and humans using the latest techniques, challenges iconic perspectives that have changed little over the past century. Those perspectives include the following: the presence of contractile or collapsible capillaries in muscle, unitary control by precapillary sphincters, capillary recruitment at the onset of contractions, and the notion of capillary-to-mitochondrial diffusion distances as limiting O₂ delivery. Today a wealth of physiological, morphological, and intravital microscopy evidence presents a completely different picture of microcirculatory control. Specifically, capillary red blood cell (RBC) and plasma flux is controlled primarily at the arteriolar level with most capillaries, in healthy muscle, supporting at least some flow at rest. In healthy skeletal muscle, this permits substrate access (whether carried in RBCs or plasma) to a prodigious total capillary surface area. Pathologies such as heart failure or diabetes decrease access to that exchange surface by reducing the proportion of flowing capillaries at rest and during exercise. Capillary morphology and function vary disparately among tissues. The contemporary model of capillary function explains how, following the onset of exercise, muscle O₂ uptake kinetics can be extremely fast in health but slowed in heart failure and diabetes impairing contractile function and exercise tolerance. It is argued that adoption of this model is fundamental for understanding microvascular function and dysfunction and, as such, to the design and evaluation of effective therapeutic strategies to improve exercise tolerance and decrease morbidity and mortality in disease.

Tumor Ensemble-Based Modeling and Visualization of Emergent Angiogenic Heterogeneity in Breast Cancer

There is a critical need for new tools to investigate the spatio-temporal heterogeneity and phenotypic alterations that arise in the tumor microenvironment. However, computational investigations of emergent inter- and intra-tumor angiogenic heterogeneity necessitate 3D microvascular data from 'whole-tumors' as well as "ensembles" of tumors. Until recently, technical limitations such as 3D imaging capabilities, computational power and cost precluded the incorporation of whole-tumor microvascular data in computational models. Here, we describe a novel computational approach based on multimodality, 3D whole-tumor imaging data acquired from eight orthotopic breast tumor xenografts (i.e. a tumor 'ensemble'). We assessed the heterogeneous angiogenic landscape from the microvascular to tumor ensemble scale in terms of vascular morphology, emergent hemodynamics and intravascular oxygenation. We demonstrate how the abnormal organization and hemodynamics of the tumor microvasculature give rise to unique microvascular niches within the tumor and contribute to inter- and intra-tumor heterogeneity. These tumor ensemble-based simulations together with unique data visualization approaches establish the foundation of a novel 'cancer atlas' for investigators to develop their own in silico systems biology applications. We expect this hybrid image-based modeling framework to be adaptable for the study of other tissues (e.g. brain, heart) and other vasculature-dependent diseases (e.g. stroke, myocardial infarction).

Brain Capillary Networks Across Species: A few Simple Organizational Requirements Are Sufficient to Reproduce Both Structure and Function

Despite the key role of the capillaries in neurovascular function, a thorough characterization of cerebral capillary network properties is currently lacking. Here, we define a range of metrics (geometrical, topological, flow, mass transfer, and robustness) for quantification of structural differences between brain areas, organs, species, or patient populations and, in parallel, digitally generate synthetic networks that replicate the key organizational features of anatomical networks (isotropy, connectedness, space-filling nature, convexity of tissue domains, characteristic size). To reach these objectives, we first construct a database of the defined metrics for healthy capillary networks obtained from imaging of mouse and human brains. Results show that anatomical networks are topologically equivalent between the two species and that geometrical metrics only differ in scaling. Based on these results, we then devise a method which employs constrained Voronoi diagrams to generate 3D model synthetic cerebral capillary networks that are locally randomized but homogeneous at the network-scale. With appropriate choice of scaling, these networks have equivalent properties to the anatomical data, demonstrated by comparison of the defined metrics. The ability to synthetically replicate cerebral capillary networks opens a broad range of applications, ranging from systematic computational studies of structure-function relationships in healthy capillary networks to detailed analysis of pathological structural degeneration, or even to the development of templates for fabrication of 3D biomimetic vascular networks embedded in tissue-engineered constructs.

A computational model for microcirculation including Fahraeus-Lindqvist effect, plasma skimming and fluid exchange with the tissue interstitium

We present a two-phase model for microcirculation that describes the interaction of plasma with red blood cells. The model takes into account of typical effects characterizing the microcirculation, such as the Fahraeus-Lindqvist effect and plasma skimming. Besides these features, the model describes the interaction of capillaries with the surrounding tissue. More precisely, the model accounts for the interaction of capillary transmural flow with the surrounding interstitial pressure. Furthermore, the capillaries are represented as one-dimensional channels with arbitrary, possibly curved configuration. The latter two features rely on the unique ability of the model to account for variations of flow rate and pressure along the axis of the capillary, according to a local differential formulation of mass and momentum conservation. Indeed, the model stands on a solid mathematical foundation, which is also addressed in this work. In particular, we present the model derivation, the variational formulation, and its approximation using the finite element method. Finally, we conclude the work with a comparative computational study of the importance of the Fahraeus-Lindqvist, plasma skimming, and capillary leakage effects on the distribution of flow in a microvascular network.

Endogenous dipeptidyl peptidase IV modulates skeletal muscle arteriolar diameter in rats

The purpose of this study is to investigate that dipeptidyl peptidase IV (DPP‐IV) released from skeletal and vascular smooth muscle can increase arteriolar diameter in a skeletal muscle vascular bed by reducing neuropeptide Y (NPY)‐mediated vasoconstriction. We hypothesized that the effect of myokine DPP‐IV would be greatest in the smallest and least in the largest arterioles. Eight male Sprague Dawley rats (age 7–9 weeks; mass, mean ± SD: 258 ± 41 g) were anesthetized and the gluteus maximus dissected in situ for intravital microscopy analysis of arteriolar diameter of the vascular network. Computational modeling was performed on the diameter measurements to evaluate the overall impact of diameter changes on network resistance and flow distribution. In the first set of experiments, whey protein isolate powder was added to physiological saline solution, put in a heated reservoir, and applied to the preparation to induce release of DPP‐IV from the muscle. This resulted in an order‐dependent increase in arteriolar diameter, with the largest change in the 6A arterioles (63% more reactive than 1A arterioles; P < 0.05). This effect was abolished by adding the DPP‐IV inhibitor, Diprotin A. To test if the DPP‐IV released was affecting NPY‐mediated vasoconstriction, we applied NPY and whey protein, which resulted in attenuated vasoconstriction. These findings suggest that DPP‐IV is released from muscle and has a unique effect on blood flow, which appears to act on NPY to attenuate vasoconstriction. The findings suggest that DPP‐IV released from the skeletal or smooth muscle can alter muscle blood flow.

Numerical simulations of the microvascular fluid balance with a non-linear model of the lymphatic system

Fluid homeostasis is required for life. Processes involved in fluid balance are strongly related to exchanges at the microvascular level. Computational models have been presented in the literature to analyze the microvascular-interstitial interactions. As far as we know, none of those models consider a physiological description for the lymphatic drainage-interstitial pressure relation. We develop a computational model that consists of a network of straight cylindrical vessels and an isotropic porous media with a uniformly distributed sink term acting as the lymphatic system. In order to describe the lymphatic flow rate, a non-linear function of the interstitial pressure is defined, based on literature data on the lymphatic system. The proposed model of lymphatic drainage is compared to a linear one, as is typically used in computational models. To evaluate the response of the model, the two are compared with reference to both physiological and pathological conditions. Differences in the local fluid dynamic description have been observed using the non-linear model. In particular, the distribution of interstitial pressure is heterogeneous in all the cases analyzed. The resulting averaged values of the interstitial pressure are also different, and they agree with literature data when using the non-linear model. This work highlights the key role of lymphatic drainage and its modeling when studying the fluid balance in microcirculation for both to physiological and pathological conditions, e.g. uremia.

Reduced fibre size, capillary supply and mitochondrial activity in constitutional thinness' skeletal muscle

AIM

Constitutional thinness (CT) is a rare condition of natural low body weight, with no psychological issues, no marker of undernutrition and a resistance to weight gain. This study evaluated the skeletal muscle phenotype of CT women by comparison with a normal BMI control group.

METHODS

Ten CT women (BMI < 17.5 kg/m² ) and 10 female controls (BMI: 18.5-25 kg/m² ) underwent metabolic and hormonal assessment along with muscle biopsies to analyse the skeletal muscular fibres pattern, capillarity, enzymes activities and transcriptomics.

RESULTS

Constitutional thinness displayed similar energy balance metabolic and hormonal profile to controls. Constitutional thinness presented with lower mean area of all the skeletal muscular fibres (-24%, P = .01) and percentage of slow-twitch type I fibres (-25%, P = .02, respectively). Significant downregulation of the mRNA expression of several mitochondrial-related genes and triglycerides metabolism was found along with low cytochrome c oxidase (COX) activity and capillary network in type I fibres. Pre- and post-mitochondrial respiratory chain enzymes levels were found similar to controls. Transcriptomics also revealed downregulation of cytoskeletal-related genes.

CONCLUSION

Diminished type I fibres, decreased mitochondrial and metabolic activity suggested by these results are discordant with normal resting metabolic rate of CT subjects. Downregulated genes related to cytoskeletal proteins and myocyte differentiation could account for CT's resistance to weight gain.

The Relation Between Capillary Transit Times and Hemoglobin Saturation Heterogeneity. Part 2: Capillary Networks

Brain metabolism is highly dependent on continuous oxygen supply. Cortical microvascular networks exhibit heterogeneous blood flow, leading to non-uniform tissue oxygenation and capillary hemoglobin saturation. We recently proposed capillary outflow saturation heterogeneity (COSH) to represent effects of heterogeneity on oxygen supply to tissue regions most vulnerable to hypoxia, and showed that diffusive oxygen exchange among red blood cells within capillaries and among capillaries (diffusive interaction) significantly reduces COSH in simplified geometrical configurations. Here, numerical simulations of oxygen transport in capillary network geometries derived from mouse somatosensory cortex are presented. Diffusive interaction was found to reduce COSH by 41 to 62% compared to simulations where diffusive interaction was excluded. Hemoglobin saturation drop across the microvascular network is strongly correlated with red blood cell transit time, but the coefficient of variation of saturation drop is approximately one third lower. Unexpectedly, the radius of the tissue cylinder supplied by a capillary correlates weakly with the anatomical tissue cylinder radius, but strongly with hemoglobin saturation. Thus, diffusive interaction contributes greatly to the microcirculation's ability to achieve tissue oxygenation, despite heterogeneous capillary transit time and hematocrit distribution. These findings provide insight into the effects of cerebral small vessel disease on tissue oxygenation and brain function.

Scaling behavior of drug transport and absorption in in silico cerebral capillary networks

Drug delivery to the brain is challenging due to the presence of the blood-brain barrier. Mathematical modeling and simulation are essential tools for the deeper understanding of transport processes in the blood, across the blood-brain barrier and within the tissue. Here we present a mathematical model for drug delivery through capillary networks with increasingly complex topologies with the goal to understand the scaling behavior of model predictions on a coarse-to-fine sequence of grids. We apply our model to the delivery of L-Dopa, the primary drug used in the therapy of Parkinson’s Disease. Our model replicates observed blood flow rates and ratios between plasma and tissue concentrations. We propose an optimal network grain size for the simulation of tissue volumes of 1 cm³ that allows to make reliable predictions with reasonable computational costs.

QUANTIFICATION OF RETINAL VESSEL TORTUOSITY IN DIABETIC RETINOPATHY USING OPTICAL COHERENCE TOMOGRAPHY ANGIOGRAPHY

PURPOSE

To investigate the association of vessel tortuosity with severity of diabetic retinopathy (DR) using optical coherence tomography angiography.

METHODS

We retrospectively analyzed 30 healthy eyes and 121 eyes of diabetic subjects with no DR, mild nonproliferative DR (NPDR), moderate to severe NPDR and proliferative DR (PDR). Binarized images were used to quantify the vessel tortuosity, vessel density, foveal avascular zone (FAZ) area, and FAZ acircularity. The vessels were divided vertically as superficial retinal layer and deep retinal layer, and horizontally as circular areas with 3 mm and 1.5 mm diameters. Analysis of variance was performed for multiple comparisons. Correlation analysis evaluated the association between the quantified parameters.

RESULTS

Compared with healthy eyes, vessel tortuosity increased as DR severity was more in NPDR, but decreased in PDR (P = 0.033). The decrease in vessel density and the increase in both FAZ area and FAZ acircularity were consistent, while DR approached PDR. Among all parameters, statistically significant difference between no DR and mild NPDR was observed only in vessel tortuosity, especially within the 1.5 mm area of superficial retinal layer (P = 0.011). Correlations of vessel tortuosity with FAZ area and acircularity were confined to the 3 mm and 1.5 mm areas of superficial retinal layer (r = -0.185, P = 0.023 for FAZ area; r = 0.268, P = 0.001 for FAZ acircularity), while vessel density strongly correlated with FAZ parameters in the superficial retinal layer and deep retinal layer.

CONCLUSION

Vessel tortuosity increased as the stage of NPDR was more severe, but decreased in PDR. The vessel tortuosity determined using optical coherence tomography angiography might be a useful parameter indicating the progression to PDR, circumventing the risk from invasive conventional angiography.

Investigation of microvascular morphological measures for skeletal muscle tissue oxygenation by image-based modelling in three dimensions

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, especially for skeletal muscle during exercise. Traditionally, microvascular oxygen supply capability is assessed by the analysis of morphological measures on transverse cross-sections of muscle, e.g. capillary density or capillary-to-fibre ratio. In this work, we investigate the relationship between microvascular structure and muscle tissue oxygenation in mice. Phase contrast imaging was performed using synchrotron radiation computed tomography (SR CT) to visualize red blood cells (RBCs) within the microvasculature in mouse soleus muscle. Image-based mathematical modelling of the oxygen diffusion from the RBCs into the muscle tissue was subsequently performed, as well as a morphometric analysis of the microvasculature. The mean tissue oxygenation was then compared with the morphological measures of the microvasculature. RBC volume fraction and spacing (mean distance of any point in tissue to the closest RBC) emerged as the best predictors for muscle tissue oxygenation, followed by length density (summed RBC length over muscle volume). The two-dimensional measures of capillary density and capillary-to-fibre ratio ranked last. We, therefore, conclude that, in order to assess the states of health of muscle tissue, it is advisable to rely on three-dimensional morphological measures rather than on the traditional two-dimensional measures.

The relative influence of hematocrit and red blood cell velocity on oxygen transport from capillaries to tissue

OBJECTIVE

Oxygen transport to parenchymal cells occurs mainly at the microvascular level and depends on convective RBC flux, which is proportional in an individual capillary to the product of capillary hematocrit and RBC velocity. This study investigates the relative influence of these two factors on tissue PO₂ .

METHODS

A simple analytical model is used to quantify the respective influences of hematocrit, RBC velocity, and RBC flow on tissue oxygenation around capillaries. Predicted tissue PO₂ levels are compared with a detailed computational model.

RESULTS

Hematocrit is shown to have a larger influence on tissue PO₂ than RBC velocity. The effect of RBC velocity increases with distance from the arterioles. Good agreement between analytical and numerical results is obtained, and the discrepancies are explained. Significant dependence of MTCs on RBC velocity at low hematocrit is demonstrated.

CONCLUSIONS

For a given RBC flux in a capillary, the PO₂ in the surrounding tissue increases with increasing hematocrit, as a consequence of decreasing IVR to diffusive oxygen transport from RBCs to tissue. These results contribute to understanding the effects of blood flow changes on oxygen transport, such as those that occur in functional hyperemia in the brain.

Multiscale systems biology of trauma-induced coagulopathy

Trauma with hypovolemic shock is an extreme pathological state that challenges the body to maintain blood pressure and oxygenation in the face of hemorrhagic blood loss. In conjunction with surgical actions and transfusion therapy, survival requires the patient's blood to maintain hemostasis to stop bleeding. The physics of the problem are multiscale: (a) the systemic circulation sets the global blood pressure in response to blood loss and resuscitation therapy, (b) local tissue perfusion is altered by localized vasoregulatory mechanisms and bleeding, and (c) altered blood and vessel biology resulting from the trauma as well as local hemodynamics control the assembly of clotting components at the site of injury. Building upon ongoing modeling efforts to simulate arterial or venous thrombosis in a diseased vasculature, computer simulation of trauma-induced coagulopathy is an emerging approach to understand patient risk and predict response. Despite uncertainties in quantifying the patient's dynamic injury burden, multiscale systems biology may help link blood biochemistry at the molecular level to multiorgan responses in the bleeding patient. As an important goal of systems modeling, establishing early metrics of a patient's high-dimensional trajectory may help guide transfusion therapy or warn of subsequent later stage bleeding or thrombotic risks. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Regulatory Biology Models of Systems Properties and Processes > Mechanistic Models.

Increased capillary tortuosity and pericapillary basement membrane thinning in skeletal muscle of mice undergoing running wheel training

To work out which microvascular remodeling processes occur in murine skeletal muscle during endurance exercise, we subjected C57BL/6 mice to voluntary running wheel training for 1 week (1 wk-t) or 6 weeks (6 wks-t). By means of morphometry, the capillarity as well as the compartmental and sub-compartmental structure of the capillaries were quantitatively described at the light microscopy level and at the electron microscopy level, respectively, in the plantaris (PLNT) muscle of the exercising mice in comparison to untrained littermates. In the early phase of the training (1 wk-t), angiogenesis [32% higher capillary/fiber (C/F) ratio; P<0.05] in PLNT muscle was accompanied by a tendency for capillary lumen enlargement (30%; P=0.06) and a reduction of the pericapillary basement membrane thickness [(CBMT) 12.7%; P=0.09] as well as a 21% shortening of intraluminal protrusion length (P<0.05), all compared with controls. After long-term training (6 wks-t), when the mice reached a steady state in running activity, additional angiogenesis (C/F ratio: 76%; P<0.05) and a 16.3% increase in capillary tortuosity (P<0.05) were established, accompanied by reversal of the lumen expansion (23%; P>0.05), further reduction of the CBMT (16.5%; P<0.05) and additional shortening of the intraluminal protrusion length (23%; P<0.05), all compared with controls. Other structural indicators, such as capillary profile sizes, profile area densities, perimeters of the capillary compartments and concentrations of endothelium-pericyte peg-socket junctions, were not significantly different between the mouse groups. Besides angiogenesis, increase of capillary tortuosity and reduction of CBMT represent the most striking microvascular remodeling processes in skeletal muscle of mice that undergo running wheel training.

Image-based modelling of skeletal muscle oxygenation

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, in particular for skeletal muscle during exercise. Disease is often associated with both an inhibition of the microvascular supply capability and is thought to relate to changes in the structure of blood vessel networks. Different methods exist to investigate the influence of the microvascular structure on tissue oxygenation, varying over a range of application areas, i.e. biological in vivo and in vitro experiments, imaging and mathematical modelling. Ideally, all of these methods should be combined within the same framework in order to fully understand the processes involved. This review discusses the mathematical models of skeletal muscle oxygenation currently available that are based upon images taken of the muscle microvasculature in vivo and ex vivo Imaging systems suitable for capturing the blood vessel networks are discussed and respective contrasting methods presented. The review further informs the association between anatomical characteristics in health and disease. With this review we give the reader a tool to understand and establish the workflow of developing an image-based model of skeletal muscle oxygenation. Finally, we give an outlook for improvements needed for measurements and imaging techniques to adequately investigate the microvascular capability for oxygen exchange.

A spectrum of retinal vasculature measures and coronary artery disease

BACKGROUND AND AIMS

We aimed to comprehensively describe a spectrum of retinal vessel measures including fractal dimension (D_f) and their associations with indices of coronary artery disease (CAD) extent and severity, as well as hypertension and diabetes.

METHODS

The Australian Heart Eye Study (AHES) is an observational study that surveyed 1680 participants presenting to a tertiary referral hospital for the evaluation of potential CAD by coronary angiography. A range of newer retinal vessel geometric measures (D_f, curvature tortuosity, and branching angle) were quantified from retinal photographs using semi-automated software, the Singapore 'I' Vessel Assessment (SIVA) tool. A combined retinal score was constructed, aiming to assess the joint effect of multiple retinal vessel parameters on CAD, comprising of those variables that were most strongly significant in multivariate analysis - D_f, arteriolar curvature tortuosity, and retinal arteriolar calibre. CAD was objectively quantified using a range of measures obtained from coronary angiography.

RESULTS

A total of 1187 participants had complete data on retinal vessel measurements and coronary vessel evaluation. Retinal vascular D_f and curvature tortuosity decreased with increasing age; women had significantly lower D_f than men (p<0.003). Straighter retinal vessels were associated with CAD extent and Gensini scores in multivariable analysis (p<0.02). Accounting for media opacity by sub-group analysis in pseudophakic patients, the combined retinal score was associated with stenosis greater than 50% in any coronary artery segment (vessel score) and obstructive coronary stenosis in all three main coronary arteries (segment score) (p = 0.01). Lower D_f and narrower arteriolar branching angle were associated with CAD vessel score (p<0.03). In sex-stratified multivariate analyses, straighter arterioles were associated with greater odds of CAD in men, and narrower venular branching angle was associated with CAD in women.

CONCLUSIONS

A range of retinal vessel measures were associated with CAD extent and severity. A sparser retinal microvascular network (smaller D_f) was associated with older age and female gender. After accounting for the impact of media opacity, retinal vessel measures were associated with more diffuse and severe CAD.

NUMERICAL STUDY OF OXYGEN DIFFUSION FROM CAPILLARY TO TISSUES DURING HYPOXIA WITH EXTERNAL FORCE EFFECTS

A mathematical model to simulate oxygen delivery through a capillary to tissues under the influence of an external force field is presented. The multi-term general fractional diffusion equation containing force terms and a time dependent absorbent term is taken into account. Fractional calculus is applied to describe the phenomenon of sub-diffusion of oxygen in both transverse and longitudinal directions. A new computational algorithm, i.e., the new iterative method (NIM) is employed to solve the spatio-temporal fractional partial differential equation subject to appropriate physical boundary conditions. Validation of NIM solutions is achieved with a modified adomian decomposition method (MADM). A parametric study is conducted for three loading scenarios on the capillary-radial force alone, axial force alone and the combined case of both forces. The results demonstrate that the force terms markedly influence the oxygen diffusion process. For example, the radial force exerts a more profound effect than axial force on sub-diffusion of oxygen indicating that careful manipulation of these forces on capillary-tissues may assist in the effective reduction of hypoxia or other oxygen depletion phenomena.