The mass transfer coefficient for oxygen transport from blood to tissue in cerebral cortex

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma

Recent progresses in intravital imaging have enabled highly-resolved measurements of periarteriolar oxygen gradients (POGs) within the brain parenchyma. POGs are increasingly used as proxies to estimate the local baseline oxygen consumption, which is a hallmark of cell activity. However, the oxygen profile around a given arteriole arises from an interplay between oxygen consumption and delivery, not only by this arteriole but also by distant capillaries. Integrating such interactions across scales while accounting for the complex architecture of the microvascular network remains a challenge from a modelling perspective. This limits our ability to interpret the experimental oxygen maps and constitutes a key bottleneck toward the inverse determination of metabolic rates of oxygen. We revisit the problem of parenchymal oxygen transport and metabolism and introduce a simple, conservative, accurate and scalable direct numerical method going beyond canonical Krogh-type models and their associated geometrical simplifications. We focus on a two-dimensional formulation, and introduce the concepts needed to combine an operator-splitting and a Green's function approach. Oxygen concentration is decomposed into a slowly-varying contribution, discretized by Finite Volumes over a coarse cartesian grid, and a rapidly-varying contribution, approximated analytically in grid-cells surrounding each vessel. Starting with simple test cases, we thoroughly analyze the resulting errors by comparison with highly-resolved simulations of the original transport problem, showing considerable improvement of the computational-cost/accuracy balance compared to previous work. We then demonstrate the model ability to flexibly generate synthetic data reproducing the spatial dynamics of oxygen in the brain parenchyma, with sub-grid resolution. Based on these synthetic data, we show that capillaries distant from the arteriole cannot be overlooked when interpreting POGs, thus reconciling recent measurements of POGs across cortical layers with the fundamental idea that variations of vascular density within the depth of the cortex may reveal underlying differences in neuronal organization and metabolic load.

Neurovascular coupling is optimized to compensate for the increase in proton production from nonoxidative glycolysis and glycogenolysis during brain activation and maintain homeostasis of pH, pCO2, and pO2

During transient brain activation cerebral blood flow (CBF) increases substantially more than cerebral metabolic rate of oxygen consumption (CMRO2) resulting in blood hyperoxygenation, the basis of BOLD-fMRI contrast. Explanations for the high CBF versus CMRO2 slope, termed neurovascular coupling (NVC) constant, focused on maintenance of tissue oxygenation to support mitochondrial ATP production. However, paradoxically the brain has a 3-fold lower oxygen extraction fraction (OEF) than other organs with high energy requirements, like heart and muscle during exercise. Here, we hypothesize that the NVC constant and the capillary oxygen mass transfer coefficient (which in combination determine OEF) are co-regulated during activation to maintain simultaneous homeostasis of pH and partial pressure of CO2 and O2 (pCO2 and pO2). To test our hypothesis, we developed an arteriovenous flux balance model for calculating blood and brain pH, pCO2, and pO2 as a function of baseline OEF (OEF0), CBF, CMRO2, and proton production by nonoxidative metabolism coupled to ATP hydrolysis. Our model was validated against published brain arteriovenous difference studies and then used to calculate pH, pCO2, and pO2 in activated human cortex from published calibrated fMRI and PET measurements. In agreement with our hypothesis, calculated pH, pCO2, and pO2 remained close to constant independently of CMRO2 in correspondence to experimental measurements of NVC and OEF0. We also found that the optimum values of the NVC constant and OEF0 that ensure simultaneous homeostasis of pH, pCO2, and pO2 were remarkably similar to their experimental values. Thus, the high NVC constant is overall determined by proton removal by CBF due to increases in nonoxidative glycolysis and glycogenolysis. These findings resolve the paradox of the brain's high CBF yet low OEF during activation, and may contribute to explaining the vulnerability of brain function to reductions in blood flow and capillary density with aging and neurovascular disease.

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.

Sublingual Microcirculation Specificity of Sickle Cell Patients: Morphology of the Microvascular Bed, Blood Rheology, and Local Hemodynamics

Patients with sickle cell disease (SCD) have poorly deformable red blood cells (RBC) that may impede blood flow into microcirculation. Very few studies have been able to directly visualize microcirculation in humans with SCD. Sublingual video microscopy was performed in eight healthy (HbAA genotype) and four sickle cell individuals (HbSS genotype). Their hematocrit, blood viscosity, red blood cell deformability, and aggregation were individually determined through blood sample collections. Their microcirculation morphology (vessel density and diameter) and microcirculation hemodynamics (local velocity, local viscosity, and local red blood cell deformability) were investigated. The De Backer score was higher (15.9 mm^-1) in HbSS individuals compared to HbAA individuals (11.1 mm^-1). RBC deformability, derived from their local hemodynamic condition, was lower in HbSS individuals compared to HbAA individuals for vessels < 20 μm. Despite the presence of more rigid RBCs in HbSS individuals, their lower hematocrit caused their viscosity to be lower in microcirculation compared to that of HbAA individuals. The shear stress for all the vessel diameters was not different between HbSS and HbAA individuals. The local velocity and shear rates tended to be higher in HbSS individuals than in HbAA individuals, notably so in the smallest vessels, which could limit RBC entrapment into microcirculation. Our study offered a novel approach to studying the pathophysiological mechanisms of SCD with new biological/physiological markers that could be useful for characterizing the disease activity.

Role of Vitamin D Deficiency in the Pathogenesis of Cardiovascular and Cerebrovascular Diseases

Deficiency in vitamin D (VitD), a lipid-soluble vitamin and steroid hormone, affects approximately 24% to 40% of the population of the Western world. In addition to its well-documented effects on the musculoskeletal system, VitD also contributes importantly to the promotion and preservation of cardiovascular health via modulating the immune and inflammatory functions and regulating cell proliferation and migration, endothelial function, renin expression, and extracellular matrix homeostasis. This brief overview focuses on the cardiovascular and cerebrovascular effects of VitD and the cellular, molecular, and functional changes that occur in the circulatory system in VitD deficiency (VDD). It explores the links among VDD and adverse vascular remodeling, endothelial dysfunction, vascular inflammation, and increased risk for cardiovascular and cerebrovascular diseases. Improved understanding of the complex role of VDD in the pathogenesis of atherosclerotic cardiovascular diseases, stroke, and vascular cognitive impairment is crucial for all cardiologists, dietitians, and geriatricians, as VDD presents an easy target for intervention.

Real-time tracking of brain oxygen gradients and blood flow during functional activation

Significance

Cerebral metabolic rate of oxygen ( CMRO 2 ) consumption is a key physiological variable that characterizes brain metabolism in a steady state and during functional activation.

Aim

We aim to develop a minimally invasive optical technique for real-time measurement of CMRO 2 concurrently with cerebral blood flow (CBF).

Approach

We used a pair of macromolecular phosphorescent probes with nonoverlapping optical spectra, which were localized in the intra- and extravascular compartments of the brain tissue, thus providing a readout of oxygen gradients between these two compartments. In parallel, we measured CBF using laser speckle contrast imaging.

Results

The method enables computation and tracking of CMRO 2 during functional activation with high temporal resolution ( ∼ 7    Hz ). In contrast to other approaches, our assessment of CMRO 2 does not require measurements of CBF or hemoglobin oxygen saturation.

Conclusions

The independent records of intravascular and extravascular partial pressures of oxygen, CBF, and CMRO 2 provide information about the physiological events that accompany neuronal activation, creating opportunities for dynamic quantification of brain metabolism.

Quantification of hypoxic regions distant from occlusions in cerebral penetrating arteriole trees

The microvasculature plays a key role in oxygen transport in the mammalian brain. Despite the close coupling between cerebral vascular geometry and local oxygen demand, recent experiments have reported that microvascular occlusions can lead to unexpected distant tissue hypoxia and infarction. To better understand the spatial correlation between the hypoxic regions and the occlusion sites, we used both in vivo experiments and in silico simulations to investigate the effects of occlusions in cerebral penetrating arteriole trees on tissue hypoxia. In a rat model of microembolisation, 25 μm microspheres were injected through the carotid artery to occlude penetrating arterioles. In representative models of human cortical columns, the penetrating arterioles were occluded by simulating the transport of microspheres of the same size and the oxygen transport was simulated using a Green’s function method. The locations of microspheres and hypoxic regions were segmented, and two novel distance analyses were implemented to study their spatial correlation. The distant hypoxic regions were found to be present in both experiments and simulations, and mainly due to the hypoperfusion in the region downstream of the occlusion site. Furthermore, a reasonable agreement for the spatial correlation between hypoxic regions and occlusion sites is shown between experiments and simulations, which indicates the good applicability of in silico models in understanding the response of cerebral blood flow and oxygen transport to microemboli.

The brain function depends on the continuous oxygen supply through the bloodstream inside the microvasculature. Occlusions in the microvascular network will disturb the oxygen delivery in the brain and result in hypoxic tissues that can lead to infarction and cognitive dysfunction. To aid in understanding the formation of hypoxic tissues caused by micro-occlusions in the penetrating arteriole trees, we use rodent experiments and simulations of human vascular networks to study the spatial correlations between the hypoxic regions and the occlusion locations. Our results suggest that hypoxic regions can form distally from the occlusion site, which agrees with the previous observations in the rat brain. These distant hypoxic regions are primarily due to the lack of blood flow in the brain tissues downstream of the occlusion. Moreover, a reasonable agreement of the spatial relationship is found between the experiments and the simulations, which indicates the applicability of in silico models to study the effects of microemboli on the brain tissue.

Optical measurement of microvascular oxygenation and blood flow responses in awake mouse cortex during functional activation

The cerebral cortex has a number of conserved morphological and functional characteristics across brain regions and species. Among them, the laminar differences in microvascular density and mitochondrial cytochrome c oxidase staining suggest potential laminar variability in the baseline O₂ metabolism and/or laminar variability in both O₂ demand and hemodynamic response. Here, we investigate the laminar profile of stimulus-induced intravascular partial pressure of O₂ (pO2) transients to stimulus-induced neuronal activation in fully awake mice using two-photon phosphorescence lifetime microscopy. Our results demonstrate that stimulus-induced changes in intravascular pO₂ are conserved across cortical layers I-IV, suggesting a tightly controlled neurovascular response to provide adequate O₂ supply across cortical depth. In addition, we observed a larger change in venular O₂ saturation (ΔsO₂) compared to arterioles, a gradual increase in venular ΔsO₂ response towards the cortical surface, and absence of the intravascular "initial dip" previously reported under anesthesia. This study paves the way for quantification of layer-specific cerebral O₂ metabolic responses, facilitating investigation of brain energetics in health and disease and informed interpretation of laminar blood oxygen level dependent functional magnetic resonance imaging signals.

Modelling the effects of cerebral microthrombi on tissue oxygenation and cell death

Thrombectomy, the mechanical removal of a clot, is the most common way to treat ischaemic stroke with large vessel occlusions. However, perfusion cannot always be restored after such an intervention. It has been hypothesised that the absence of reperfusion is at least partially due to the clot fragments that block the downstream vessels. In this paper, we present a new way of quantifying the effects of cerebral microthrombi on oxygen transport to tissue in terms of hypoxia and ischaemia. The oxygen transport was simulated with the Green's function method on physiologically representative microvascular cubes, which was found independent of both microvascular geometry and length scale. The microthrombi occlusions were then simulated in the microvasculature, which were extravasated over time with a new thrombus extravasation model. The tissue hypoxic fraction was fitted as a sigmoidal function of vessel blockage fraction, which was then taken to be a function of time after the formation of microthrombi occlusions. A novel hypoxia-based 3-state cell death model was finally proposed to simulate the hypoxic tissue damage over time. Using the cell death model, the impact of a certain degree of microthrombi occlusions on tissue viability and microinfarct volume can be predicted over time. Quantifying the impact of microthrombi on oxygen transport and tissue death will play an important role in full brain models of ischaemic stroke and thrombectomy.

Simulation of angiogenesis in three dimensions: Application to cerebral cortex

The vasculature is a dynamic structure, growing and regressing in response to embryonic development, growth, changing physiological demands, wound healing, tumor growth and other stimuli. At the microvascular level, network geometry is not predetermined, but emerges as a result of biological responses of each vessel to the stimuli that it receives. These responses may be summarized as angiogenesis, remodeling and pruning. Previous theoretical simulations have shown how two-dimensional vascular patterns generated by these processes in the mesentery are consistent with experimental observations. During early development of the brain, a mesh-like network of vessels is formed on the surface of the cerebral cortex. This network then forms branches into the cortex, forming a three-dimensional network throughout its thickness. Here, a theoretical model is presented for this process, based on known or hypothesized vascular response mechanisms together with experimentally obtained information on the structure and hemodynamics of the mouse cerebral cortex. According to this model, essential components of the system include sensing of oxygen levels in the midrange of partial pressures and conducted responses in vessel walls that propagate information about metabolic needs of the tissue to upstream segments of the network. The model provides insights into the effects of deficits in vascular response mechanisms, and can be used to generate physiologically realistic microvascular network structures.

Brain microvasculature has a common topology with local differences in geometry that match metabolic load

The microvasculature underlies the supply networks that support neuronal activity within heterogeneous brain regions. What are common versus heterogeneous aspects of the connectivity, density, and orientation of capillary networks? To address this, we imaged, reconstructed, and analyzed the microvasculature connectome in whole adult mice brains with sub-micrometer resolution. Graph analysis revealed common network topology across the brain that leads to a shared structural robustness against the rarefaction of vessels. Geometrical analysis, based on anatomically accurate reconstructions, uncovered a scaling law that links length density, i.e., the length of vessel per volume, with tissue-to-vessel distances. We then derive a formula that connects regional differences in metabolism to differences in length density and, further, predicts a common value of maximum tissue oxygen tension across the brain. Last, the orientation of capillaries is weakly anisotropic with the exception of a few strongly anisotropic regions; this variation can impact the interpretation of fMRI data.