Daniel Goldman

In this study, a novel algorithm for computing red blood cell (RBC) geometry was developed as the first step of a quantitative model for RBC‐ATP release. This model relied on the developing coordinate‐invariant computational framework of discrete exterior calculus (DEC). The algorithm for the first time in literature was formulated in an implicit manner, utilized a Lie‐derivative based vertex drift contribution to ensure the mesh was well‐behaved throughout deformation, and was able to obtain RBC equilibrium geometries in an efficient manner. This algorithm was shown to be highly stable, quantified through tracking the RBC membrane energy. Equilibrium geometries were shown to agree with literature in in vivo observations, and qualitatively reproduced phenomena seen in in vivo experiments where RBCs are subjected to solutions of varying osmolarity. This DEC algorithm will be applied in future work to fluid–structure interactions of RBCs, and has application to a multitude of open cell biology problems.

Intussusceptive angiogenesis is an increasingly recognized vessel duplication process that generates and reshapes microvascular beds. However, the mechanism by which a vessel splits into two is poorly understood. Particularly vexing is formation of the hallmark transluminal endothelial cell bridge. How an endothelial cell comes to cross a flowing lumen rather than line it is enigmatic. To elucidate this, we used a microvessel-on-a-chip strategy, creating a microconduit coherently lined with flow-sensitive endothelial cells but in which transluminal bridges also formed. Bridge morphologies ranged from filamentous strand to multicellular columns with a central extracellular matrix-containing core. These bridge architectures were found to recapitulate those in microvessels in embryos, tumors, diseased organs, and the dermis of patients with limb-threatening ischemia. Time-lapse, multiplane, three-dimensional (3D) microscopy of the microphysiologic conduit revealed that bridges arose from endothelial cells oriented orthogonal to flow that partially released from the wall while retaining attachments at the ends. This delamination process was blocked by hyperactivation of Rho and augmented by interventions that weaken cell–substrate interactions, including inhibiting nonmuscle myosin II and blocking α5ß1 integrin. Thus, endothelial cells can leave their monolayer and transect a flowing lumen through controlled delamination. This previously unrecognized lumen entry program could explain the launch of intussusceptive angiogenesis and opens a framework for intervening.

Increased amplitude of peripheral vasomotion is a potential early marker of sepsis‐related microcirculatory impairment; however, previous reports relied on clinically unsuitable invasive techniques. Hyperspectral near‐infrared spectroscopy (hsNIRS) and diffuse correlation spectroscopy (DCS) are non‐invasive, bedside techniques that can be paired to continuously monitor tissue hemoglobin content (HbT), oxygenation (StO ₂ ), and perfusion (rBF) to detect vasomotion as low‐frequency microhemodynamic oscillations. While previous studies have primarily focused on the peripheral microcirculation, cerebral injury is also a common occurrence in sepsis and hsNIRS‐DCS could be used to assess cerebral microcirculatory function. This work aimed to use a hybrid hsNIRS‐DCS system to continuously monitor changes in the peripheral and cerebral microcirculation in a rat model of early sepsis. It was hypothesized that the skeletal muscle would be a more sensitive early indicator of sepsis‐related changes in microhemodynamics than the brain. Control animals received saline while the experimental group received fecal slurry to induce sepsis. Subsequently, hsNIRS‐DCS measurements were acquired from the skeletal muscle and brain for 6 h. Peripheral rBF rapidly decreased in septic animals, but there were no significant changes in peripheral HbT or StO ₂ , nor cerebral HbT, rBF, or StO ₂ . The power of low‐frequency peripheral oscillations in all parameters (i.e., HbT, StO ₂ , and rBF) as well as cerebral HbT oscillations were elevated in septic animals during the final 4 h. These findings suggest that in the early stages of sepsis, while vital organs like the brain are partly protected, changes in peripheral perfusion and vasomotor activity can be detected using hsNIRS‐DCS. Future work will apply the technique to ICU patients.

We provide novel insight that the superior maintenance of cerebrovascular endothelial function in female versus male rats with chronic metabolic disease buffers myogenic activation of cerebral resistance arteries/arterioles despite worsening hypertension. As hypertension development is earlier and more severe in females, potentially due to an elevated stress response, the blunted myogenic activation allows greater arterial pressure wave penetrance into the cerebral microcirculation and is associated with accelerated emergence/severity of depressive symptoms in obese female rats.

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.

Coupling red blood cell (RBC) supply to O ₂ demand is an intricate process requiring O ₂ sensing, generation of a stimulus, and signal transduction that alters upstream arteriolar tone. Although actively debated, this process has been theorized to be induced by hypoxia and to involve activation of endothelial inwardly rectifying K ⁺ channels (K _IR ) 2.1 by elevated extracellular K ⁺ to trigger conducted hyperpolarization via connexin40 (Cx40) gap junctions to upstream resistors. This concept was tested in resting healthy skeletal muscle of Cx40 ^−/− and endothelial K _IR 2.1 ^−/− mice using state-of-the-art live animal imaging where the local tissue O ₂ environment was manipulated using a custom gas chamber. Second-by-second capillary RBC flow responses were recorded as O ₂ was altered. A stepwise drop in PO ₂ at the muscle surface increased RBC supply in capillaries of control animals while elevated O ₂ elicited the opposite response; capillaries were confirmed to express Cx40. The RBC flow responses were rapid and tightly coupled to O ₂ ; computer simulations did not support hypoxia as a driving factor. In contrast, RBC flow responses were significantly diminished in Cx40 ^−/− mice. Endothelial K _IR 2.1 ^−/− mice, on the other hand, reacted normally to O ₂ changes, even when the O ₂ challenge was targeted to a smaller area of tissue with fewer capillaries. Conclusively, microvascular O ₂ responses depend on coordinated electrical signaling via Cx40 gap junctions, and endothelial K _IR 2.1 channels do not initiate the event. These findings reconceptualize the paradigm of blood flow regulation in skeletal muscle and how O ₂ triggers this process in capillaries independent of extracellular K ⁺ .

We report a digital pipeline for interrogating the landscape of arterioles in mouse skeletal muscle, using machine learning and automated micromorphometry. This revealed that in muscle regenerating after ischemic injury, the arteriolar density is increased but lumen caliber and smooth muscle content are reduced. Computational modeling and experimental validation reveal this arteriolar network to be functionally compromised, with diminished microvascular flow reserve.

Background. The treatment of coronary stenosis is decided by performing high risk invasive surgery to generate the fractional flow reserve diagnostics index, a ratio of distal to proximal pressures in respect of coronary atherosclerotic plaques. Non-invasive methods are a need of the times that necessitate the use of mathematical models of coronary hemodynamic physiology. This study proposes an extensible mathematical description of the coronary vasculature that provides an estimate of coronary fractional flow reserve. Methods. By adapting an existing computational model of human coronary blood flow, the effects of large vessel stenosis and microvascular disease on fractional flow reserve were quantified. Several simulations generated flow and pressure information, which was used to compute fractional flow reserve under several conditions including focal stenosis, diffuse stenosis, and microvascular disease. Sensitivity analysis was used to uncover the influence of model parameters on fractional flow reserve. The model was simulated as coupled non-linear ordinary differential equations and numerically solved using our implicit higher order method. Results. Large vessel stenosis affected fractional flow reserve. The model predicts that the presence, rather than severity, of microvascular disease affects coronary flow deleteriously. Conclusions. The model provides a computationally inexpensive instrument for future in silico coronary blood flow investigations as well as clinical-imaging decision making. A combination of focal and diffuse stenosis appears to be essential to limit coronary flow. In addition to pressure measurements in the large epicardial vessels, diagnosis of microvascular disease is essential. The independence of the index with respect to heart rate suggests that computationally inexpensive steady state simulations may provide sufficient information to reliably compute the index.

Background. The treatment of coronary stenosis relies on invasive high risk surgical assessment to generate the fractional flow reserve diagnostics index, a ratio of distal to proximal pressures in respect of coronary atherosclerotic plaque causing stenosis. Non-invasive methods are therefore a need of the times. This study proposes an extensible mathematical description of the coronary vasculature that permits rapid estimation of the coronary fractional flow reserve. Methods. By adapting an existing closed loop model of human coronary blood flow, the effects of large vessel stenosis and microvascular disease on fractional flow reserve were quantified. Several simula-tions generated flow and pressure information which was used to compute fractional flow re-serve under a spectrum of conditions including focal stenosis, diffuse stenosis, and microvascular disease. Sensitivity analysis stratified the influence of model parameters on the index. The model was simulated as coupled non-linear ordinary differential equations and numerically solved us-ing an implicit higher order method. Results. Large vessel stenosis affected fractional flow re-serve. The model predicts that the presence, rather than severity, of microvascular disease affect coronary flow deleteriously. Sensitivity analysis revealed that heart rate may not affect the index. Conclusions. The model provides a computationally inexpensive instrument for future in silico coronary blood flow investigations as well as clinical-imaging decision making. A combination of focal and diffuse stenosis appears to be essential in reducing the index. In addition to pressure measurements in the large epicardial vessels, diagnosis of microvascular disease is essential. The independence of the index with respect to heart rate suggests that computationally inexpensive steady state simulations may provide sufficient information to reliably compute the index.

The capillary module (CM), consisting of parallel capillaries from terminal arteriole to post‐capillary venule, is classically considered to be the building block of complex capillary networks. In skeletal muscle, CMs form interconnected columns spanning thousands of microns, which we recently described as the capillary fascicle. However, detailed evaluation of CM haemodynamics has not been described, and may provide insight into mechanisms of blood flow regulation in the microcirculation. We used intravital videomicroscopy from resting extensor digitorum longus muscle in rats (n = 9 networks, 112 capillary modules), as well as dual‐phase computational modelling of blood flow in simulated CM geometries. We found that the mean driving pressure across CMs was 3.236 ± 1.833 mmHg. Red blood cell (RBC) flow was independent of CM resistance, and the ratio of blood flow in adjacent modules was not correlated with their ratio of resistances. In simulated CM geometries, increases to driving pressure produced a direct linear increase to RBC and plasma flow, with no changes to RBC distribution; increases to arteriolar inflow haematocrit resulted in increased RBC flow, but with viscosity‐dependent increases to CM resistance. CM RBC flow heterogeneity was higher than plasma flow heterogeneity in experimental data, in contrast to simulated geometries, suggesting that time‐dependent flow variability may have important consequences for RBC distribution. In summary, these findings suggest that CMs are active participants in microvascular flow regulation, likely achieved through adjustments to CM driving pressure using pre‐ and post‐capillary loci of flow control. Increases to CM viscosity may be important during the regulation of functional hyperaemia.Key points: The capillary module (CM), consisting of parallel capillaries from the arteriole to venule, is classically considered to be the building block of capillary networks in skeletal muscle. A detailed evaluation of module haemodynamics may provide insight into mechanisms of blood flow regulation in the microcirculation. Using experimental data from resting skeletal muscle in rats, as well as dual‐phase computational models of blood flow, we analysed haemodynamic relationships and the impact of variations to boundary conditions on red blood cell and plasma distribution. We showed that driving pressure across CMs is low, and that simulated increases to inflow haematocrit have important viscosity‐dependent effects on module resistance. We found that red blood cell flow was independent from module resistance, which strongly suggests the regulation of driving pressure at the level of the capillary module using pre‐ and post‐capillary loci of flow control. These findings place CMs as central participants in microvascular flow regulation, with important consequences for disease and functional hyperaemia.