Mapping 3-D functional capillary geometry in rat skeletal muscle in vivo

Capillary oxygen regulates demand-supply coupling by triggering connexin40-mediated conduction: Rethinking the metabolic hypothesis

Coupling red blood cell (RBC) supply to O2 demand is an intricate process requiring O2 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 (KIR) 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 KIR2.1-/- mice using state-of-the-art live animal imaging where the local tissue O2 environment was manipulated using a custom gas chamber. Second-by-second capillary RBC flow responses were recorded as O2 was altered. A stepwise drop in PO2 at the muscle surface increased RBC supply in capillaries of control animals while elevated O2 elicited the opposite response; capillaries were confirmed to express Cx40. The RBC flow responses were rapid and tightly coupled to O2; computer simulations did not support hypoxia as a driving factor. In contrast, RBC flow responses were significantly diminished in Cx40-/- mice. Endothelial KIR2.1-/- mice, on the other hand, reacted normally to O2 changes, even when the O2 challenge was targeted to a smaller area of tissue with fewer capillaries. Conclusively, microvascular O2 responses depend on coordinated electrical signaling via Cx40 gap junctions, and endothelial KIR2.1 channels do not initiate the event. These findings reconceptualize the paradigm of blood flow regulation in skeletal muscle and how O2 triggers this process in capillaries independent of extracellular K+.

Dynamics of capillary blood flow responses to acute local changes in oxygen and carbon dioxide concentrations

Objectives: We aimed to quantify the magnitude and time transients of capillary blood flow responses to acute changes in local oxygen concentration ([O₂]), and carbon dioxide concentration ([CO₂]) in skeletal muscle. Additionally, we sought to quantify the combined response to both low [O₂] and high [CO₂] to mimic muscle microenvironment changes at the onset of exercise. Methods: 13 Sprague Dawley rats were anaesthetized, mechanically ventilated, and instrumented with indwelling catheters for systemic monitoring. The extensor digitorum longus muscle was blunt dissected, and reflected over a microfluidic gas exchange chamber in the stage of an inverted microscope. Four O₂ challenges, four CO₂ challenges, and a combined low O₂ (7-2%) and high CO₂ (5-10%) challenges were delivered to the surface with simultaneous visualization of capillary blood flow responses. Recordings were made for each challenge over a 1-min baseline period followed by a 2-min step change. The combined challenge employed a 1-min [O₂] challenge followed by a 2-min change in [CO₂]. Mean data for each sequence were fit using least-squared non-linear exponential models to determine the dynamics of each response. Results: 7-2% [O₂] challenges decreased capillary RBC saturation within 2 s following the step change (46.53 ± 19.56% vs. 48.51 ± 19.02%, p < 0.0001, τ = 1.44 s), increased RBC velocity within 3 s (228.53 ± 190.39 μm/s vs. 235.74 ± 193.52 μm/s, p < 0.0003, τ = 35.54 s) with a 52% peak increase by the end of the challenge, hematocrit and supply rate show similar dynamics. 5-10% [CO₂] challenges increased RBC velocity within 2 s following the step change (273.40 ± 218.06 μm/s vs. 276.75 ± 215.94 μm/s, p = 0.007, τ = 79.34s), with a 58% peak increase by the end of the challenge, supply rate and hematocrit show similar dynamics. Combined [O₂] and [CO₂] challenges resulted in additive responses to all microvascular hemodynamic measures with a 103% peak velocity increase by the end of the collection period. Data for mean responses and exponential fitting parameters are reported for all challenges. Conclusion: Microvascular level changes in muscle [O₂] and [CO₂] provoked capillary hemodynamic responses with differing time transients. Simulating exercise via combined [O₂] and [CO₂] challenges demonstrated the independent and additive nature of local blood flow responses to these agents.

Capillary communication: the role of capillaries in sensing the tissue environment, coordinating the microvascular, and controlling blood flow

Historically, capillaries have been viewed as the microvascular site for flux of nutrients to cells and removal of waste products. Capillaries are the most numerous blood vessel segment within the tissue, whose vascular wall consists of only a single layer of endothelial cells and are situated within microns of each cell of the tissue, all of which optimizes capillaries for the exchange of nutrients between the blood compartment and the interstitial space of tissues. There is, however, a growing body of evidence to support that capillaries play an important role in sensing the tissue environment, coordinating microvascular network responses, and controlling blood flow. Much of our growing understanding of capillaries stems from work in skeletal muscle and more recent work in the brain, where capillaries can be stimulated by products released from cells of the tissue during increased activity and are able to communicate with upstream and downstream vascular segments, enabling capillaries to sense the activity levels of the tissue and send signals to the microvascular network to coordinate the blood flow response. This review will focus on the emerging role that capillaries play in communication between cells of the tissue and the vascular network required to direct blood flow to active cells in skeletal muscle and the brain. We will also highlight the emerging central role that disruptions in capillary communication may play in blood flow dysregulation, pathophysiology, and disease.

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.

Spectroscopy detects skeletal muscle microvascular dysfunction during onset of sepsis in a rat fecal peritonitis model

Sepsis is a dysregulated host inflammatory response to infection potentially leading to life-threatening organ dysfunction. The objectives of this study were to determine whether early microvascular dysfunction (MVD) in skeletal muscle can be detected as dynamic changes in microvascular hemoglobin (MVHb) levels using spectroscopy and whether MVD precedes organ histopathology in septic peritonitis. Skeletal muscle of male Sprague-Dawley rats was prepared for intravital microscopy. After intraperitoneal injection of fecal slurry or saline, microscopy and spectroscopy recordings were taken for 6 h. Capillary red blood cell (RBC) dynamics and SO₂ were quantified from digitized microscopy frames and MVHb levels were derived from spectroscopy data. Capillary RBC dynamics were significantly decreased by 4 h after peritoneal infection and preceded macrohemodynamic changes. At the same time, low-frequency oscillations in MVHb levels exhibited a significant increase in Power in parts of the muscle and resembled oscillations in RBC dynamics and SO₂. After completion of microscopy, tissues were collected. Histopathological alterations were not observed in livers, kidneys, brains, or muscles 6 h after induction of peritonitis. The findings of this study show that, in our rat model of sepsis, MVD occurs before detectable organ histopathology and includes ~ 30-s oscillations in MVHb. Our work highlights MVHb oscillations as one of the indicators of MVD onset and provides a foundation for the use of non-invasive spectroscopy to continuously monitor MVD in septic patients.

Localized Oxygen Exchange Platform for Intravital Video Microscopy Investigations of Microvascular Oxygen Regulation

Intravital microscopy has proven to be a powerful tool for studying microvascular physiology. In this study, we propose a gas exchange system compatible with intravital microscopy that can be used to impose gas perturbations to small localized regions in skeletal muscles or other tissues that can be imaged using conventional inverted microscopes. We demonstrated the effectiveness of this system by locally manipulating oxygen concentrations in rat extensor digitorum longus muscle and measuring the resulting vascular responses. A computational model of oxygen transport was used to partially validate the localization of oxygen changes in the tissue, and oxygen saturation of red blood cells flowing through capillaries were measured as a surrogate for local tissue oxygenation. Overall, we have demonstrated that this approach can be used to study dynamic and spatial responses to local oxygen challenges to the microenvironment of skeletal muscle.

Development and validation of a novel microfluidic device for the manipulation of skeletal muscle microvascular blood flow in vivo

OBJECTIVE

To develop and validate a novel liquid microfluidic approach to deliver drugs to microscale regions of tissue while simultaneously allowing for visualization and quantification of microvascular blood flow.

METHODS

Microfluidic devices were fabricated using soft lithographic techniques, molded in polydimethylsiloxane, and bound to a coverslip with a 600 × 300 μm micro-outlet. Sprague-Dawley rats, anesthetized with pentobarbital, were instrumented to monitor systemic parameters. The extensor digitorum longus muscle was dissected, externalized, and reflected across the device mounted on the stage of an inverted microscope. Doses (10^-8 to 10^-3  M) of adenosine triphosphate (ATP), acetylcholine, and phenylephrine (PE) were administered to the muscle via perfusion through the device. Microvascular blood flow directly overlying the micro-outlet was recorded at multiple focal depths. Red blood cell (RBC) velocity, supply rate, and hematocrit were measured from recordings.

RESULTS

ATP significantly increased RBC velocity and supply rate. Increasing concentrations of PE caused a decrease in RBC velocity and supply rate. Perfusion changes were restricted to areas directly overlying the micro-outlet and within 500 μm.

CONCLUSIONS

This novel microfluidic device allows for a controlled delivery of dissolved substances to constrained regions of microvasculature while simultaneously allowing for visualization and measurement of blood flow within discrete vessels and networks.

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.

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.

August Krogh's theory of muscle microvascular control and oxygen delivery: a paradigm shift based on new data

August Krogh twice won the prestigious international Steegen Prize, for nitrogen metabolism (1906) and overturning the concept of active transport of gases across the pulmonary epithelium (1910). Despite this, at the beginning of 1920, the consummate experimentalist was relatively unknown worldwide and even among his own University of Copenhagen faculty. But, in early 1919, he had submitted three papers to Dr Langley, then editor of The Journal of Physiology in England. These papers coalesced anatomical observations of skeletal muscle capillary numbers with O₂ diffusion theory to propose a novel active role for capillaries that explained the prodigious increase in blood-muscle O₂ flux from rest to exercise. Despite his own appraisal of the first two papers as "rather dull" to his friend, the eminent Cambridge respiratory physiologist, Joseph Barcroft, Krogh believed that the third one, dealing with O₂ supply and capillary regulation, was"interesting". These papers, which won Krogh an unopposed Nobel Prize for Physiology or Medicine in 1920, form the foundation for this review. They single-handedly transformed the role of capillaries from passive conduit and exchange vessels, functioning at the mercy of their upstream arterioles, into independent contractile units that were predominantly closed at rest and opened actively during muscle contractions in a process he termed 'capillary recruitment'. Herein we examine Krogh's findings and some of the experimental difficulties he faced. In particular, the boundary conditions selected for his model (e.g. heavily anaesthetized animals, negligible intramyocyte O₂ partial pressure, binary open-closed capillary function) have not withstood the test of time. Subsequently, we update the reader with intervening discoveries that underpin our current understanding of muscle microcirculatory control and place a retrospectroscope on Krogh's discoveries. The perspective is presented that the imprimatur of the Nobel Prize, in this instance, may have led scientists to discount compelling evidence. Much as he and Marie Krogh demonstrated that active transport of gases across the blood-gas barrier was unnecessary in the lung, capillaries in skeletal muscle do not open and close spontaneously or actively, nor is this necessary to account for the increase in blood-muscle O₂ flux during exercise. Thus, a contemporary model of capillary function features most muscle capillaries supporting blood flow at rest, and, rather than capillaries actively vasodilating from rest to exercise, increased blood-myocyte O₂ flux occurs predominantly via elevating red blood cell and plasma flux in already flowing capillaries. Krogh is lauded for his brilliance as an experimentalist and for raising scientific questions that led to fertile avenues of investigation, including the study of microvascular function.

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.

A simple automated method for continuous fieldwise measurement of microvascular hemodynamics

Microvascular perfusion dynamics are vital to physiological function and are frequently dysregulated in injury and disease. Typically studies measure microvascular flow in a few selected vascular segments over limited time, failing to capture spatial and temporal variability. To quantify microvascular flow in a more complete and unbiased way we developed STAFF (Spatial Temporal Analysis of Fieldwise Flow), a macro for FIJI open-source image analysis software. Using high-speed microvascular flow movies, STAFF generates kymographs for every time interval for every vascular segment, calculates flow velocities from red blood cell shadow angles, and outputs the data as color-coded velocity map movies and spreadsheets. In untreated mice, analyses demonstrated profound variation even between adjacent sinusoids over seconds. In acetaminophen-treated mice we detected flow reduction localized to pericentral regions. STAFF is a powerful new tool capable of providing novel insights by enabling measurement of the complex spatiotemporal dynamics of microvascular flow.

Capillary Network Morphometry of Pig Soleus Muscle Significantly Changes in 24 Hours After Death

Capillary network characteristics are invaluable for diagnostics of muscle diseases. Biopsy material is limited in size and mostly not accessible for intensive research. Therefore, especially in human tissue, studies are performed on autopsy material. To approach the problem whether it is reliable to deduce hypotheses from autopsy material to explain physiological and pathological processes, we studied capillarity in pig soleus muscle 1 and 24 hr after death. Capillaries and muscle fibers were immunofluorescently marked, and images were acquired with a confocal microscope. Characteristics of the capillary network were estimated by image analysis methods using several plugins of the Ellipse program. Twenty-four hours after death, the measured characteristics of the capillary network differ by up to 50% when compared with samples excised 1 hr after death. Muscle fiber diameter, the measured capillary length, and tortuosity were reduced, and capillary network became more anisotropic. The main postmortem change that affects capillaries is evidently geometric deformation of muscle tissue. In conclusion, when comparing results from biopsy samples with those from autopsy samples, the effect of postmortem changes on the measured parameters must be carefully considered.

Spin dephasing in a magnetic dipole field around large capillaries: Approximative and exact results

We present an analytical solution of the Bloch-Torrey equation for local spin dephasing in the magnetic dipole field around a capillary and for ensembles of capillaries, and adapt this solution for the study of spin dephasing around large capillaries. In addition, we provide a rigorous mathematical derivation of the slow diffusion approximation for the spin-bearing particles that is used in this regime. We further show that, in analogy to the local magnetization, the transverse magnetization of one MR imaging voxel in the regime of static dephasing (where diffusion effects are not considered) is merely the first term of a series expansion that constitutes the signal in the slow diffusion approximation. Theoretical results are in agreement with experimental data for capillaries in rat muscle at 7T.

Impact of Incremental Perfusion Loss on Oxygen Transport in a Capillary Network Mathematical Model

OBJECTIVES

To quantify how incremental capillary PL, such as that seen in experimental models of sepsis, affects tissue oxygenation using a computation model of oxygen transport.

METHODS

A computational model was applied to capillary networks with dimensions 84 × 168 × 342 (NI) and 70 × 157 × 268 (NII) μm, reconstructed in vivo from rat skeletal muscle. FCD loss was applied incrementally up to ~40% and combined with high tissue oxygen consumption to simulate severe sepsis.

RESULTS

A loss of ~40% FCD loss decreased median tissue PO2 to 22.9 and 20.1 mmHg in NI and NII compared to 28.1 and 27.5 mmHg under resting conditions. Increasing RBC SR to baseline levels returned tissue PO2 to within 5% of baseline. HC combined with a 40% FCD loss, resulted in tissue anoxia in both network volumes and median tissue PO2 of 11.5 and 8.9 mmHg in NI and NII respectively; median tissue PO2 was recovered to baseline levels by increasing total SR 3-4 fold.

CONCLUSIONS

These results suggest a substantial increase in total SR is required in order to compensate for impaired oxygen delivery as a result of loss of capillary perfusion and increased oxygen consumption during sepsis.

Reduced uterine perfusion pressure decreases functional capillary density in skeletal muscle

The purpose of this study was to examine the functional and structural capillary density in the reduced uterine perfusion pressure (RUPP) model, which when performed during pregnancy is an established animal model of preeclampsia. We hypothesized that the RUPP model would be associated with capillary rarefaction and impaired capillary perfusion, which would be more pronounced in the pregnant state. Female Sprague-Dawley rats (n = 32) were randomized to nonpregnancy (Nonpregnant) or breeding (Pregnant) at 12 wk of age and again to RUPP or SHAM surgeries on gestational day (GD) 14 (or equivalent age in nonpregnant rats). On GD 20 (or equivalent), capillary structure and perfusion of the extensor digitorum longus were imaged using digital intravital video microscopy. Functional videos were analyzed by a blinded observer to measure capillary density, expressed as capillaries per millimeter intersecting three staggered reference lines (200 μm). Flow was scored as the percentage of capillaries having 1) continuous, 2) intermittent, or 3) stopped flow. Total capillary density was not different between groups. There was a main effect of RUPP surgery resulting in decreased continuous flow vessels (P < 0.01) and increased stopped flow (P < 0.01), which was driven by differences between pregnant animals (Continuous flow: pregnant SHAM 80.1 ± 7.8% vs. pregnant RUPP 67.8 ± 11.2%, P < 0.05) (Stopped flow: pregnant SHAM 8.7 ± 3.2% vs. pregnant RUPP 17.9 ± 5.7%, P < 0.01). Our results demonstrate that the RUPP surgery is associated with a decrease in functional capillary density in skeletal muscle that is more pronounced in the pregnant state, which may contribute to the vascular pathophysiology observed in preeclampsia.

Krogh-cylinder and infinite-domain models for washout of an inert diffusible solute from tissue

OBJECTIVE

Models based on the Krogh-cylinder concept are developed to analyze the washout from tissue by blood flow of an inert diffusible solute that permeates blood vessel walls. During the late phase of washout, the outflowing solute concentration decays exponentially with time. This washout decay rate is predicted for a range of conditions.

METHODS

A single capillary is assumed to lie on the axis of a cylindrical tissue region. In the classic "Krogh-cylinder" approach, a no-flux boundary condition is applied on the outside of the cylinder. An alternative "infinite-domain" approach is proposed that allows for solute exchange across the boundary, but with zero net exchange. Both models are analyzed, using finite-element and analytical methods.

RESULTS

The washout decay rate depends on blood flow rate, tissue diffusivity and vessel permeability of solute, and assumed boundary conditions. At low blood flow rates, the washout rate can exceed the value for a single well-mixed compartment. The infinite-domain approach predicts slower washout decay rates than the Krogh-cylinder approach.

CONCLUSIONS

The infinite-domain approach overcomes a significant limitation of the Krogh-cylinder approach, while retaining its simplicity. It provides a basis for developing methods to deduce transport properties of inert solutes from observations of washout decay rates.

Comparison of generated parallel capillary arrays to three-dimensional reconstructed capillary networks in modeling oxygen transport in discrete microvascular volumes

OBJECTIVE

We compare RMN to PCA under several simulated physiological conditions to determine how the use of different vascular geometry affects oxygen transport solutions.

METHODS

Three discrete networks were reconstructed from intravital video microscopy of rat skeletal muscle (84 × 168 × 342 μm, 70 × 157 × 268 μm, and 65 × 240 × 571 μm), and hemodynamic measurements were made in individual capillaries. PCAs were created based on statistical measurements from RMNs. Blood flow and O₂ transport models were applied, and the resulting solutions for RMN and PCA models were compared under four conditions (rest, exercise, ischemia, and hypoxia).

RESULTS

Predicted tissue PO₂ was consistently lower in all RMN simulations compared to the paired PCA. PO₂ for 3D reconstructions at rest were 28.2 ± 4.8, 28.1 ± 3.5, and 33.0 ± 4.5 mmHg for networks I, II, and III compared to the PCA mean values of 31.2 ± 4.5, 30.6 ± 3.4, and 33.8 ± 4.6 mmHg. Simulated exercise yielded mean tissue PO₂ in the RMN of 10.1 ± 5.4, 12.6 ± 5.7, and 19.7 ± 5.7 mmHg compared to 15.3 ± 7.3, 18.8 ± 5.3, and 21.7 ± 6.0 in PCA.

CONCLUSIONS

These findings suggest that volume matched PCA yield different results compared to reconstructed microvascular geometries when applied to O₂ transport modeling; the predominant characteristic of this difference being an over estimate of mean tissue PO₂. Despite this limitation, PCA models remain important for theoretical studies as they produce PO₂ distributions with similar shape and parameter dependence as RMN.

Oxygen transport in the microcirculation and its regulation

OBJECTIVE

Cells require energy to carry out their functions and they typically use oxidative phosphorylation to generate the needed ATP. Thus, cells have a continuous need for oxygen, which they receive by diffusion from the blood through the interstitial fluid. The circulatory system pumps oxygen-rich blood through a network of increasingly minute vessels, the microcirculation. The structure of the microcirculation is such that all cells have at least one nearby capillary for diffusive exchange of oxygen and red blood cells release the oxygen bound to hemoglobin as they traverse capillaries.

METHODS

This review focuses first on the historical development of techniques to measure oxygen at various sites in the microcirculation, including the blood, interstitium, and cells.

RESULTS

Next, approaches are described as to how these techniques have been employed to make discoveries about different aspects of oxygen transport. Finally, ways in which oxygen might participate in the regulation of blood flow toward matching oxygen supply to oxygen demand is discussed.

CONCLUSIONS

Overall, the transport of oxygen to the cells of the body is one of the most critical functions of the cardiovascular system and it is in the microcirculation where the final local determinants of oxygen supply, oxygen demand, and their regulation are decided.

Microvascular flow modeling using in vivo hemodynamic measurements in reconstructed 3D capillary networks

OBJECTIVE

We describe a systematic approach to modeling blood flow using reconstructed capillary networks and in vivo hemodynamic measurements. Our goal was to produce flow solutions that represent convective O(2) delivery in vivo.

METHODS

Two capillary networks, I and II (84 × 168 × 342 and 70 × 157 × 268 μm(3)), were mapped using custom software. Total network red blood cell supply rate (SR) was calculated from in vivo data and used as a target metric for the flow model. To obtain inlet hematocrits, mass balances were applied recursively from downstream vessels. Pressure differences across the networks were adjusted to achieve target SR. Baseline flow solutions were used as inputs to existing O(2) transport models. To test the impact of flow redistribution, asymmetric flow solutions (Asym) were generated by applying a ± 20% pressure change to network outlets.

RESULTS

Asym solutions produced a mean absolute difference in SR per capillary of 27.6 ± 33.3% in network I and 33.2 ± 40.1% in network II vs. baseline. The O(2) transport model calculated mean tissue PO(2) of 28.2 ± 4.8 and 28.1 ± 3.5 mmHg for baseline and 27.6 ± 5.2 and 27.7 ± 3.7 mmHg for Asym.

CONCLUSIONS

This outcome illustrates that moderate changes in flow distribution within a capillary network have little impact on tissue PO(2) provided that total SR remains unchanged.

Toward a multiscale description of microvascular flow regulation: o(2)-dependent release of ATP from human erythrocytes and the distribution of ATP in capillary networks

Integration of the numerous mechanisms that have been suggested to contribute to optimization of O₂ supply to meet O₂ need in skeletal muscle requires a systems biology approach which permits quantification of these physiological processes over a wide range of length scales. Here we describe two individual computational models based on in vivo and in vitro studies which, when incorporated into a single robust multiscale model, will provide information on the role of erythrocyte-released ATP in perfusion distribution in skeletal muscle under both physiological and pathophysiological conditions. Healthy human erythrocytes exposed to low O₂ tension release ATP via a well characterized signaling pathway requiring activation of the G-protein, Gi, and adenylyl cyclase leading to increases in cAMP. This cAMP then activates PKA and subsequently CFTR culminating in ATP release via pannexin 1. A critical control point in this pathway is the level of cAMP which is regulated by pathway-specific phosphodiesterases. Using time constants (~100 ms) that are consistent with measured erythrocyte ATP release, we have constructed a dynamic model of this pathway. The model predicts levels of ATP release consistent with measurements obtained over a wide range of hemoglobin O₂ saturations (sO₂). The model further predicts how insulin, at concentrations found in pre-diabetes, enhances the activity of PDE3 and reduces intracellular cAMP levels leading to decreased low O₂-induced ATP release from erythrocytes. The second model, which couples O₂ and ATP transport in capillary networks, shows how intravascular ATP and the resulting conducted vasodilation are affected by local sO₂, convection and ATP degradation. This model also predicts network-level effects of decreased ATP release resulting from elevated insulin levels. Taken together, these models lay the groundwork for investigating the systems biology of the regulation of microvascular perfusion distribution by erythrocyte-derived ATP.