Analysis of potassium ion diffusion from neurons to capillaries: Effects of astrocyte endfeet geometry.

Neurovascular coupling (NVC) refers to a local increase in cerebral blood flow in response to increased neuronal activity. Mechanisms of communication between neurons and blood vessels remain unclear. Astrocyte endfeet almost completely cover cerebral capillaries, suggesting that astrocytes play a role in NVC by releasing vasoactive substances near capillaries. An alternative hypothesis is that direct diffusion through the extracellular space of potassium ions (K+ ) released by neurons contributes to NVC. Here, the goal is to determine whether astrocyte endfeet present a barrier to K+ diffusion from neurons to capillaries. Two simplified 2D geometries of extracellular space, clefts between endfeet, and perivascular space are used: (i) a source 1 µm from a capillary; (ii) a neuron 15 µm from a capillary. K+ release is modelled as a step increase in [K+ ] at the outer boundary of the extracellular space. The time-dependent diffusion equation is solved numerically. In the first geometry, perivascular [K+ ] approaches its final value within 0.05 s. Decreasing endfeet cleft width or increasing perivascular space width slows the rise in [K+ ]. In the second geometry, the increase in perivascular [K+ ] occurs within 0.5 s and is insensitive to changes in cleft width or perivascular space width. Predicted levels of perivascular [K+ ] are sufficient to cause vasodilation, and the rise time is within the time for flow increase in NVC. These results suggest that direct diffusion of K+ through the extracellular space is a possible NVC signalling mechanism.

Estimation of shear stress heterogeneity along capillary segments in angiogenic rat mesenteric microvascular networks.

OBJECTIVE: Fluid shear stress is thought to be a regulator of endothelial cell behavior during angiogenesis. The link, however, requires an understanding of stress values at the capillary level in angiogenic microvascular networks. Critical questions remain. What are the stresses? Do capillaries experience similar stress magnitudes? Can variations explain vessel-specific behavior? The objective of this study was to estimate segment-specific shear stresses in angiogenic networks. METHODS: Images of angiogenic networks characterized by increased vascular density were obtained from rat mesenteric tissues stimulated by compound 48/80-induced mast cell degranulation. Vessels were identified by perfusion of a 40 kDa fixable dextran prior to harvesting and immunolabeling for PECAM. Using a network flow-based segment model with physiologically relevant parameters, stresses were computed per vessel for regions across multiple networks. RESULTS: Stresses ranged from 0.003 to 2328.1 dyne/cm2 and varied dramatically at the capillary level. For all regions, the maximum segmental shear stresses were for capillary segments. Stresses along proximal capillaries branching from arteriole inlets were increased compared to stresses along capillaries in more distal regions. CONCLUSIONS: The results highlight the variability of shear stresses along angiogenic capillaries and motivate new discussions on how endothelial cells may respond in vivo to segment-specific microenvironment during angiogenesis.

The dependence of maximum oxygen uptake and utilization (V̇O2 max) on hemoglobin-oxygen affinity and altitude.

Oxygen transport from the lungs to peripheral tissue is dependent on the affinity of hemoglobin for oxygen. Recent experimental data have suggested that the maximum human capacity for oxygen uptake and utilization (V̇O2 max) at sea level and altitude (~3000 m) is sensitive to alterations in hemoglobin-oxygen affinity. However, the effect of such alterations on V̇O2 max at extreme altitudes remains largely unknown due to the rarity of mutations affecting hemoglobin-oxygen affinity. This work uses a mathematical model that couples pulmonary oxygen uptake with systemic oxygen utilization under conditions of high metabolic demand to investigate the effect of hemoglobin-oxygen affinity on V̇O2 max as a function of altitude. The model includes the effects of both diffusive and convective limitations on oxygen transport. Pulmonary oxygen uptake is calculated using a spatially-distributed model that accounts for the effects of hematocrit and hemoglobin-oxygen affinity. Systemic oxygen utilization is calculated assuming Michaelis-Menten kinetics. The pulmonary and systemic model components are solved iteratively to compute predicted arterial and venous oxygen levels. Values of V̇O2 max are predicted for several values of hemoglobin-oxygen affinity and hemoglobin concentration based on data from humans with hemoglobin mutations. The model predicts that increased hemoglobin-oxygen affinity leads to increased V̇O2 max at altitudes above ~4500 m.

Cortical microvascular blood flow velocity mapping by combining dynamic light scattering optical coherence tomography and two-photon microscopy.

Significance: The accurate large-scale mapping of cerebral microvascular blood flow velocity is crucial for a better understanding of cerebral blood flow (CBF) regulation. Although optical imaging techniques enable both high-resolution microvascular angiography and fast absolute CBF velocity measurements in the mouse cortex, they usually require different imaging techniques with independent system configurations to maximize their performances. Consequently, it is still a challenge to accurately combine functional and morphological measurements to co-register CBF speed distribution from hundreds of microvessels with high-resolution microvascular angiograms. Aim: We propose a data acquisition and processing framework to co-register a large set of microvascular blood flow velocity measurements from dynamic light scattering optical coherence tomography (DLS-OCT) with the corresponding microvascular angiogram obtained using two-photon microscopy (2PM). Approach: We used DLS-OCT to first rapidly acquire a large set of microvascular velocities through a sealed cranial window in mice and then to acquire high-resolution microvascular angiograms using 2PM. The acquired data were processed in three steps: (i) 2PM angiogram coregistration with the DLS-OCT angiogram, (ii) 2PM angiogram segmentation and graphing, and (iii) mapping of the CBF velocities to the graph representation of the 2PM angiogram. Results: We implemented the developed framework on the three datasets acquired from the mice cortices to facilitate the coregistration of the large sets of DLS-OCT flow velocity measurements with 2PM angiograms. We retrieved the distributions of red blood cell velocities in arterioles, venules, and capillaries as a function of the branching order from precapillary arterioles and postcapillary venules from more than 1000 microvascular segments. Conclusions: The proposed framework may serve as a useful tool for quantitative analysis of large microvascular datasets obtained by OCT and 2PM in studies involving normal brain functioning, progression of various diseases, and numerical modeling of the oxygen advection and diffusion in the realistic microvascular networks.

An autonomous mathematical model for the mammalian cell cycle.

A mathematical model for the mammalian cell cycle is developed as a system of 13 coupled nonlinear ordinary differential equations. The variables and interactions included in the model are based on detailed consideration of available experimental data. A novel feature of the model is inclusion of cycle tasks such as origin licensing and initiation, nuclear envelope breakdown and kinetochore attachment, and their interactions with controllers (molecular complexes involved in cycle control). Other key features are that the model is autonomous, except for a dependence on external growth factors; the variables are continuous in time, without instantaneous resets at phase boundaries; mechanisms to prevent rereplication are included; and cycle progression is independent of cell size. Eight variables represent cell cycle controllers: the Cyclin D1-Cdk4/6 complex, APCCdh1, SCFßTrCP, Cdc25A, MPF, NuMA, the securin-separase complex, and separase. Five variables represent task completion, with four for the status of origins and one for kinetochore attachment. The model predicts distinct behaviors corresponding to the main phases of the cell cycle, showing that the principal features of the mammalian cell cycle, including restriction point behavior, can be accounted for in a quantitative mechanistic way based on known interactions among cycle controllers and their coupling to tasks. The model is robust to parameter changes, in that cycling is maintained over at least a five-fold range of each parameter when varied individually. The model is suitable for exploring how extracellular factors affect cell cycle progression, including responses to metabolic conditions and to anti-cancer therapies.

Simulation of Angiogenesis in Three Dimensions: Development of the Retinal Circulation.

A theoretical model is used to describe the three-dimensional development of the retinal circulation in the human eye, which occurs after the initial spread of vasculature across the inner surface of the retina. In the model, random sprouting angiogenesis is driven by a growth factor that is produced in tissue at a rate dependent on oxygen level and diffuses to existing vessels. Vessel sprouts connect to form pathways for blood flow and undergo remodeling and pruning. These processes are controlled by known or hypothesized vascular responses to hemodynamic and biochemical stimuli, including conducted responses along vessel walls. The model shows regression of arterio-venous connections on the surface of the retina, allowing perfusion of the underlying tissue. A striking feature of the retinal circulation is the formation of two vascular plexuses located at the inner and outer surfaces of the inner nuclear layer within the retina. The model is used to test hypotheses regarding the formation of these structures. A mechanism based on local production and diffusion of growth factor is shown to be ineffective. However, sprout guidance by localized structures on the boundaries of the inner nuclear layer can account for plexus formation. The resulting networks have vascular density, perfusion and oxygen transport characteristics consistent with observed properties. The model shows how stochastic generation of vascular sprouts combined with a set of biologically based response mechanisms can lead to the generation of a specialized three-dimensional vascular structure with a high degree of organization.

A fast computational model for circulatory dynamics: effects of left ventricle-aorta coupling.

The course of diseases such as hypertension, systolic heart failure and heart failure with a preserved ejection fraction is affected by interactions between the left ventricle (LV) and the vasculature. To study these interactions, a computationally efficient, biophysically based mathematical model for the circulatory system is presented. In a four-chamber model of the heart, the LV is represented by a previously described low-order, wall volume-preserving model that includes torsion and base-to-apex and circumferential wall shortening and lengthening, and the other chambers are represented using spherical geometries. Active and passive myocardial mechanics of all four chambers are included. The cardiac model is coupled with a wave propagation model for the aorta and a closed lumped-parameter circulation model. Parameters for the normal heart and aorta are determined by fitting to experimental data. Changes in the timing and magnitude of pulse wave reflections by the aorta are demonstrated with changes in compliance and taper of the aorta as seen in aging (decreased compliance, increased diameter and length), and resulting effects on LV pressure-volume loops and LV fiber stress and sarcomere shortening are predicted. Effects of aging of the aorta combined with reduced LV contractile force (failing heart) are examined. In the failing heart, changes in aortic properties with aging affect stroke volume and sarcomere shortening without appreciable augmentation of aortic pressure, and the reflected pressure wave contributes an increased proportion of aortic pressure.

Conditions for Kir-induced bistability of membrane potential in capillary endothelial cells.

A simplified model for electrophysiology of endothelial cells is used to examine the conditions that can lead to bistability of membrane resting potential. The model includes the effects of inward-rectifying potassium (Kir) ion channels, whose current-voltage relationship shows an interval of negative slope and whose maximum conductance is dependent on the extracellular potassium concentration. The background current resulting from other types of channels is assumed to be linearly related to membrane potential. A method is presented for identifying the boundaries in the parameter space for the background currents of the regions of bistability. It is shown that these regions are relatively narrow and depend on extracellular potassium concentration. The results are used to define conditions leading to transitions between depolarized and hyperpolarized membrane states. These behaviors can influence the properties of conducted responses, in which changes in membrane potential are propagated along blood vessel walls. Conducted responses are important in the local regulation of blood flow in the brain and other tissues.

Spreading mechanics and differentiation of astrocytes during retinal development.

The retinal vasculature supplies oxygen to the inner layers of the retina, the light-sensitive tissue in the eye. During development, formation of the retinal vasculature depends on prior establishment of a mesh of astrocytes, a type of glial cell, which guide the growth of the vascular network. Astrocytes emerge from the optic nerve head and proliferate and spread, forming a mesh-like layer over the retinal surface. The initially formed cells are termed astrocyte precursor cells (APCs), which differentiate into immature perinatal astrocytes (IPAs) during the prenatal period. A continuum model is developed to describe the proliferation, differentiation, and migration these cells. Effects of oxygen and growth factor levels on proliferation and differentiation are included. Cell migration is driven by gradients in tension in the astrocyte mesh, which varies inversely with total density. The resulting governing equations have the form of a nonlinear diffusion-like equation. The model can account for the observed radial spread over time of the astrocyte disk. Experimental observations show that the APCs form a narrow rim around the edge of this disk, with IPAs in the interior. The model predicts this behavior if the mobility of the APCs is assumed to be higher than that of the IPAs under a given tension gradient. Thus, the model shows how tension-driven cell motions can account for separation of cell types in a cell layer spreading over a substrate.

Novel method for kinetic analysis applied to transport by the uniporter OCT2.

The kinetics of solute transport shed light on the roles these processes play in cellular physiology, and the absolute values of the kinetic parameters that quantitatively describe transport are increasingly used to model its impact on drug clearance. However, accurate assessment of transport kinetics is challenging. Although most carrier-mediated transport is adequately described by the Michaelis-Menten equation, its use presupposes that the rates of uptake used in the analysis of maximal rates of transport (Jmax) and half-saturation constants (Kt) reflect true unidirectional rates of influx from known concentrations of substrate. Most experimental protocols estimate the initial rate of transport from net substrate accumulation determined at a single time point (typically between 0.5 and 5 min) and assume it reflects unidirectional influx. However, this approach generally results in systematic underestimates of Jmax and overestimates of Kt; the former primarily due to the unaccounted impact of efflux of accumulated substrate, and the latter due to the influence of unstirred water layers. Here, we describe the bases of these time-dependent effects and introduce a computational model that analyzes the time course of net substrate uptake at several concentrations to calculate Jmax and Kt for unidirectional influx, taking into account the influence of unstirred water layers and mediated efflux. This method was then applied to calculate the kinetics of transport of 1-methyl-4-phenylpryridinium and metformin by renal organic cation transporter 2 as expressed in cultured Chinese hamster ovary cells.NEW & NOTEWORTHY Here, we describe a mathematical model that uses the time course of net substrate uptake into cells from several increasing concentrations to calculate unique kinetic parameters [maximal rates of transport (Jmax) and half-saturation constants (Kt)] of the process. The method is the first to take into consideration the common complicating factors of unstirred layers and carrier-mediated efflux in the experimental determination of transport kinetics.

Functional implications of microvascular heterogeneity for oxygen uptake and utilization.

In the vascular system, an extensive network structure provides convective and diffusive transport of oxygen to tissue. In the microcirculation, parameters describing network structure, blood flow, and oxygen transport are highly heterogeneous. This heterogeneity can strongly affect oxygen supply and organ function, including reduced oxygen uptake in the lung and decreased oxygen delivery to tissue. The causes of heterogeneity can be classified as extrinsic or intrinsic. Extrinsic heterogeneity refers to variations in oxygen demand in the systemic circulation or oxygen supply in the lungs. Intrinsic heterogeneity refers to structural heterogeneity due to stochastic growth of blood vessels and variability in flow pathways due to geometric constraints, and resulting variations in blood flow and hematocrit. Mechanisms have evolved to compensate for heterogeneity and thereby improve oxygen uptake in the lung and delivery to tissue. These mechanisms, which involve long-term structural adaptation and short-term flow regulation, depend on upstream responses conducted along vessel walls, and work to redistribute flow and maintain blood and tissue oxygenation. Mathematically, the variance of a functional quantity such as oxygen delivery that depends on two or more heterogeneous variables can be reduced if one of the underlying variables is controlled by an appropriate compensatory mechanism. Ineffective regulatory mechanisms can result in poor oxygen delivery even in the presence of adequate overall tissue perfusion. Restoration of endothelial function, and specifically conducted responses, should be considered when addressing tissue hypoxemia and organ failure in clinical settings.

Accurate Three-Dimensional Thermal Dosimetry and Assessment of Physiologic Response Are Essential for Optimizing Thermoradiotherapy.

Numerous randomized trials have revealed that hyperthermia (HT) + radiotherapy or chemotherapy improves local tumor control, progression free and overall survival vs. radiotherapy or chemotherapy alone. Despite these successes, however, some individuals fail combination therapy; not every patient will obtain maximal benefit from HT. There are many potential reasons for failure. In this paper, we focus on how HT influences tumor hypoxia, since hypoxia negatively influences radiotherapy and chemotherapy response as well as immune surveillance. Pre-clinically, it is well established that reoxygenation of tumors in response to HT is related to the time and temperature of exposure. In most pre-clinical studies, reoxygenation occurs only during or shortly after a HT treatment. If this were the case clinically, then it would be challenging to take advantage of HT induced reoxygenation. An important question, therefore, is whether HT induced reoxygenation occurs in the clinic that is of radiobiological significance. In this review, we will discuss the influence of thermal history on reoxygenation in both human and canine cancers treated with thermoradiotherapy. Results of several clinical series show that reoxygenation is observed and persists for 24-48 h after HT. Further, reoxygenation is associated with treatment outcome in thermoradiotherapy trials as assessed by: (1) a doubling of pathologic complete response (pCR) in human soft tissue sarcomas, (2) a 14 mmHg increase in pO2 of locally advanced breast cancers achieving a clinical response vs. a 9 mmHg decrease in pO2 of locally advanced breast cancers that did not respond and (3) a significant correlation between extent of reoxygenation (as assessed by pO2 probes and hypoxia marker drug immunohistochemistry) and duration of local tumor control in canine soft tissue sarcomas. The persistence of reoxygenation out to 24-48 h post HT is distinctly different from most reported rodent studies. In these clinical series, comparison of thermal data with physiologic response shows that within the same tumor, temperatures at the higher end of the temperature distribution likely kill cells, resulting in reduced oxygen consumption rate, while lower temperatures in the same tumor improve perfusion. However, reoxygenation does not occur in all subjects, leading to significant uncertainty about the thermal-physiologic relationship. This uncertainty stems from limited knowledge about the spatiotemporal characteristics of temperature and physiologic response. We conclude with recommendations for future research with emphasis on retrieving co-registered thermal and physiologic data before and after HT in order to begin to unravel complex thermophysiologic interactions that appear to occur with thermoradiotherapy.

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.

Coalescent angiogenesis-evidence for a novel concept of vascular network maturation.

Angiogenesis describes the formation of new blood vessels from pre-existing vascular structures. While the most studied mode of angiogenesis is vascular sprouting, specific conditions or organs favor intussusception, i.e., the division or splitting of an existing vessel, as preferential mode of new vessel formation. In the present study, sustained (33-h) intravital microscopy of the vasculature in the chick chorioallantoic membrane (CAM) led to the hypothesis of a novel non-sprouting mode for vessel generation, which we termed "coalescent angiogenesis." In this process, preferential flow pathways evolve from isotropic capillary meshes enclosing tissue islands. These preferential flow pathways progressively enlarge by coalescence of capillaries and elimination of internal tissue pillars, in a process that is the reverse of intussusception. Concomitantly, less perfused segments regress. In this way, an initially mesh-like capillary network is remodeled into a tree structure, while conserving vascular wall components and maintaining blood flow. Coalescent angiogenesis, thus, describes the remodeling of an initial, hemodynamically inefficient mesh structure, into a hierarchical tree structure that provides efficient convective transport, allowing for the rapid expansion of the vasculature with maintained blood supply and function during development.

Analysis of flow resistance in the pulmonary arterial circulation: implications for hypoxic pulmonary vasoconstriction.

Hypoxic pulmonary vasoconstriction (HPV) plays an essential role in distributing blood in the lung to enhance ventilation-perfusion matching and blood oxygenation. In this study, a theoretical model of the pulmonary vasculature is used to predict the effects of vasoconstriction over specified ranges of vessel diameters on pulmonary vascular resistance (PVR). The model is used to evaluate the ability of hypothesized mechanisms of HPV to account for observed levels of PVR elevation during hypoxia. The vascular structure from pulmonary arteries to capillaries is represented using scaling laws. Vessel segments are modeled as resistive elements and blood flow rates are computed from physical principles. Direct vascular responses to intravascular oxygen levels have been proposed as a mechanism of HPV. In the lung, significant changes in oxygen level occur only in vessels less than 60 µm in diameter. The model shows that observed levels of hypoxic vasoconstriction in these vessels alone cannot account for the elevation of PVR associated with HPV. However, the elevation in PVR associated with HPV can be accounted for if larger upstream vessels also constrict. These results imply that upstream signaling by conducted responses to engage constriction of arterioles plays an essential role in the elevation of PVR during HPV.NEW & NOTEWORTHY A theoretical model of the pulmonary vasculature is used to predict the effects of vasoconstriction over specified ranges of vessel diameters on pulmonary vascular resistance (PVR). The model shows that observed levels of hypoxic vasoconstriction in terminal vessels cannot account for the elevation of PVR associated with hypoxic pulmonary vasoconstriction (HPV). Upstream signaling by conducted responses to engage constriction of arterioles, therefore, plays an essential role in the elevation of PVR during HPV.

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.

Distinct roles of red-blood-cell-derived and wall-derived mechanisms in metabolic regulation of blood flow.

OBJECTIVE: A theoretical model is used to analyze combinations of RBC-derived and wall-derived (RBC-independent) mechanisms for metabolic blood flow regulation, with regard to their oxygen transport properties. METHODS: Heterogeneous microvascular network structures are derived from observations in rat mesentery and hamster cremaster. The effectiveness of metabolic blood flow regulation using combinations of RBC-dependent and RBC-independent mechanisms is simulated in these networks under conditions of reduced oxygen delivery and increased oxygen demand. RESULTS: Metabolic regulation by a wall-derived mechanism results in higher predicted total blood flow rate and number of flowing vessels, and lower tissue hypoxic fraction, than regulation by combinations of RBC-derived and wall-derived signals. However, a combination of RBC-derived and wall-derived signals results in a higher predicted median tissue PO2 than either mechanism acting alone. CONCLUSIONS: Model results suggest complementary roles for RBC-derived and wall-derived mechanisms of metabolic flow regulation, with the wall-derived mechanism responsible for avoiding hypoxia, and the RBC-derived mechanism responsible for maintaining PO2 levels high enough for optimal tissue function.

The Oxygen Cascade During Exercise in Health and Disease.

The oxygen transport cascade describes the physiological steps that bring atmospheric oxygen into the body where it is delivered and consumed by metabolically active tissue. As such, the oxygen cascade is fundamental to our understanding of exercise in health and disease. Our narrative review will highlight each step of the oxygen transport cascade from inspiration of atmospheric oxygen down to mitochondrial consumption in both healthy active males and females along with clinical conditions. We will focus on how different steps interact along with principles of homeostasis, physiological redundancies, and adaptation. In particular, we highlight some of the parallels between elite athletes and clinical conditions in terms of the oxygen cascade.

Simulation of oxygen transport and estimation of tissue perfusion in extensive microvascular networks: Application to cerebral cortex.

Advanced imaging techniques have made available extensive three-dimensional microvascular network structures. Simulation of oxygen transport by such networks requires information on blood flow rates and oxygen levels in vessels crossing boundaries of the imaged region, which is difficult to obtain experimentally. Here, a computational method is presented for estimating blood flow rates, oxygen levels, tissue perfusion and oxygen extraction, based on incomplete boundary conditions. Flow rates in all segments are estimated using a previously published method. Vessels crossing the region boundary are classified as arterioles, capillaries or venules. Oxygen levels in inflowing capillaries are assigned based on values in outflowing capillaries, and similarly for venules. Convective and diffusive oxygen transport is simulated. Contributions of each vessel to perfusion are computed in proportion to the decline in oxygen concentration along that vessel. For a vascular network in the mouse cerebral cortex, predicted tissue oxygen levels show a broad distribution, with 99% of tissue in the range of 20 to 80 mmHg under reference conditions, and steep gradients near arterioles. Perfusion and extraction estimates are consistent with experimental values. A 30% reduction in perfusion or a 30% increase in oxygen demand, relative to reference levels, is predicted to result in tissue hypoxia.

Effects of impaired microvascular flow regulation on metabolism-perfusion matching and organ function.

Impaired tissue oxygen delivery is a major cause of organ damage and failure in critically ill patients, which can occur even when systemic parameters, including cardiac output and arterial hemoglobin saturation, are close to normal. This review addresses oxygen transport mechanisms at the microcirculatory scale, and how hypoxia may occur in spite of adequate convective oxygen supply. The structure of the microcirculation is intrinsically heterogeneous, with wide variations in vessel diameters and flow pathway lengths, and consequently also in blood flow rates and oxygen levels. The dynamic processes of structural adaptation and flow regulation continually adjust microvessel diameters to compensate for heterogeneity, redistributing flow according to metabolic needs to ensure adequate tissue oxygenation. A key role in flow regulation is played by conducted responses, which are generated and propagated by endothelial cells and signal upstream arterioles to dilate in response to local hypoxia. Several pathophysiological conditions can impair local flow regulation, causing hypoxia and tissue damage leading to organ failure. Therapeutic measures targeted to systemic parameters may not address or may even worsen tissue oxygenation at the microvascular level. Restoration of tissue oxygenation in critically ill patients may depend on restoration of endothelial cell function, including conducted responses.