Roland N. Pittman

Assessment and impact of heterogeneities of convective oxygen transport parameters in capillaries of striated muscle: Experimental and theoretical

Convective oxygen transport parameters were determined in arteriolar (n = 5) and venular (n = 5) capillary networks in the hamster cheek pouch retractor muscle. Simultaneously determined values of red blood cell velocity, lineal density, red blood cell frequency, hemoglobin oxygen saturation (SO2), oxygen flow (QO2), longitudinal SO2 gradient, and diameter were obtained in a total of 73 capillaries, 39 at the arteriolar ends of the network (arteriolar capillaries) and 34 at the venular ends (venular capillaries). We found that the hemodynamic variables were not different at the two ends. However, not unexpectedly, SO2 and QO2 were significantly higher at the upstream end of arteriolar capillaries (60.8 +/- 9.8 (SD)% and 0.150 +/- 0.081 pl/sec, respectively) compared with the downstream end of venular capillaries (39.9 +/- 13.6% and 0.108 +/- 0.095 pl/sec, respectively). Heterogeneities in red blood cell velocity, lineal density, SO2, and QO2, assessed by their coefficients of variation, were significantly greater in venular capillaries. To evaluate the impact of these heterogeneities on oxygen exchange, we incorporated these unique experimental data into a mathematical model of oxygen transport which accounts for variability in red blood cell frequency, lineal density, inlet SO2, capillary diameter, and, to some degree, capillary flow path lengths. An unexpected result of the simulation is that only the incorporation of variability in capillary flow path lengths had any marked effect on the heterogeneity in end-capillary SO2 in resting muscle due to extensive diffusional shunting of oxygen among adjacent capillaries. We subsequently evaluated, through model simulations, the effect of these heterogeneities under conditions of increased flow and high oxygen consumption. Under these conditions, the model predicts that heterogeneities in the hemodynamic parameters will have a marked effect on oxygen transport in this muscle.

Influence of Microvascular Architecture on Oxygen Exchange in Skeletal Muscle

The normal function of skeletal muscle requires that a continuous supply of oxygen be provided by the cardiovascular system. This article reviews the development of our understanding of the role of microvascular architecture on the oxygen transport system, with emphasis on direct microcirculatory observations and mathematical modeling dating from the work of August Krogh to present studies. The contributions of the various elements of the vascular network (i.e., arterioles, capillaries, and venules) and microvascular hemodynamics to oxygen exchange are discussed. Oxygen moves through the microvascular network by convection, almost all of it being reversibly bound to the hemoglobin within red blood cells. Thus, the flow properties and distribution of the red cells within the network can play a significant role in oxygen transport. Because the walls of all the vessels in the microcirculation appear to be permeable to oxygen, it continuously diffuses between the blood and the interstitium, the direction depending on the oxygen partial pressure difference. Because of the high permeability of the vascular wall to oxygen, the complex spatial relationships among the various microvessels lead to correspondingly complex diffusive interactions among them. The proximity of capillaries, arterioles, and venules, along with the anastomotic connections and tortuosity of capillaries, provides the “complex spatial relationships” that lead to diffusive interactions between neighboring capillaries, between capillaries and nearby arterioles and venules, and between paired arterioles and venules. Although there are a number of outstanding problems regarding our understanding of oxygen transport at the microcirculatory level, the most interesting and significant of these has to do with the adjustments that are made in the transition from the resting state to that of sustained aerobic exercise.

Nitric oxide in the vasculature: Where does it come from and where does it go? A quantitative perspective

Nitric oxide (NO) affects two key aspects of O2 supply and demand: It regulates vascular tone and blood flow by activating soluble guanylate cyclase (sGC) in the vascular smooth muscle, and it controls mitochondrial O2 consumption by inhibiting cytochrome c oxidase. However, significant gaps exist in our quantitative understanding of the regulation of NO production in the vascular region. Large apparent discrepancies exist among the published reports that have analyzed the various pathways in terms of the perivascular NO concentration, the efficacy of NO in causing vasodilation (EC50), its efficacy in tissue respiration (IC50), and the paracrine and endocrine NO release. In this study, we review the NO literature, analyzing NO levels on various scales, identifying and analyzing the discrepancies in the reported data, and proposing hypotheses that can potentially reconcile these discrepancies. Resolving these issues is highly relevant to improving our understanding of vascular biology and to developing pharmaceutical agents that target NO pathways, such as vasodilating drugs.

Oxygen transport and exchange in the microcirculation.

The cardiovascular system is responsible for maintaining an adequate convective delivery of oxygen to the smallest branches of the network of blood vessels—the microcirculation—from which oxygen passes to the parenchymal cells by passive diffusion. The aim of this brief review is to trace the development of the study of oxygen transport from the point of view of the microcirculation. August Krogh performed measurements that allowed him to use his keen insight to draw conclusions about oxygen transport that remained the foundations of this field for decades. After an extended period of neglect, Duling rekindled interest in the field of oxygen transport by discovering that substantial amounts of oxygen diffused from the arteriolar network. Subsequent investigations confirmed this finding in various vascular beds and extended these studies to capillaries and venules. The important contributions of computational modeling and new techniques in intravital microscopy continue to led to more advances in our understanding of the role of the microcirculation in the supply of oxygen to tissues. Current work is applying the concepts and principles learned in normal tissues to pathophysiological situations, as well as increasing our understanding of artificial oxygen carriers, oxygen sensing, and the connections between nitric oxide and oxygen transport.

Analysis of phosphorescence in heterogeneous systems using distributions of quencher concentration

A continuous distribution approach, instead of the traditional mono- and multiexponential analysis, for determining quencher concentration in a heterogeneous system has been developed. A mathematical model of phosphorescence decay inside a volume with homogeneous concentration of phosphor and heterogeneous concentration of quencher was formulated to obtain pulse-response fitting functions for four different distributions of quencher concentration: rectangular, normal (Gaussian), gamma, and multimodal. The analysis was applied to parameter estimates of a heterogeneous distribution of oxygen tension (PO2) within a volume. Simulated phosphorescence decay data were randomly generated for different distributions and heterogeneity of PO2 inside the excitation/emission volume, consisting of 200 domains, and then fit with equations developed for the four models. Analysis using a monoexponential fit yielded a systematic error (underestimate) in mean PO2 that increased with the degree of heterogeneity. The fitting procedures based on the continuous distribution approach returned more accurate values for parameters of the generated PO2 distribution than did the monoexponential fit. The parameters of the fit (M = mean; sigma = standard deviation) were investigated as a function of signal-to-noise ratio (SNR = maximum signal amplitude/peak-to-peak noise). The best-fit parameter values were stable when SNR > or = 20. All four fitting models returned accurate values of M and sigma for different PO2 distributions. The ability of our procedures to resolve two different heterogeneous compartments was also demonstrated using a bimodal fitting model. An approximate scheme was formulated to allow calculation of the first moments of a spatial distribution of quencher without specifying the distribution. In addition, a procedure for the recovery of a histogram, representing the quencher concentration distribution, was developed and successfully tested.

Application of image analysis for evaluation of red blood cell dynamics in capillaries

We have devised a method to display and directly evaluate red blood cell (rbc) dynamics in capillaries using the same dual camera intravital video microscopy system employed to determine rbc oxygen saturation (Ellis et al., 1990). Capillary images are recorded on videotape and an interactive graphics system is used for analysis. Data are sampled once a frame for 60 sec using a window (one pixel wide (0.93 micron) and 100 pixels high) positioned along the axis of a capillary. The resulting data are displayed as sequential space-time images 100 pixels high by 300 pixels wide (10 sec). The space-time images thus created represent the dynamics of the rbcs in a single comprehensive static image in which the rbcs appear as dark, diagonal bands separated by light bands representing plasma gaps. From these images one can obtain information on velocity of individual rbcs (micron/sec), lineal density of rbcs (rbc/mm), and rbc supply rate (rbc/sec). This information can be used to delineate the temporal and spatial heterogeneity of hemodynamics in capillary networks. These data can then be combined with coincident data on red blood cell oxygenation to provide a complete picture of oxygen transport in capillaries or it can be used alone as a tool for the evaluation of basic in vivo and in vitro rheological questions.

Method for in vivo microscopy of the cutaneous microcirculation of the hairless mouse ear

Abstract The transilluminated, intact ear of the homozygous (hr/hr) hairless mouse was used as an in vivo preparation of the cutaneous microcirculation. The average thickness of the ear is 300 μm. The ear is composed of two full-thickness layers of skin separated by a thin supporting skeleton of elastic cartilage. With the exception of sweat glands, the skin of the hairless mouse ear closely resembles human skin. A subpapillary vascular network contained precapillary arterioles, capillary loops, and postcapillary venules. The remaining vessels were located in a subdermal vascular network. Arteriovenous anastomoses from 10- to 12-μm feeding arterioles were observed with intermittent blood flow. These anastomoses supplied a branching network of capillaries. The hairless mouse ear was easily prepared for study, requiring only light anesthesia and restraints. The observation chamber used was designed for use within the slide holder on a standard laboratory microscope stage. The observed ear was gently outstretched and placed within a well filled with sterile water at room temperature. The skin microcirculation was observed with a water-immersion objective in this manner or the well was sealed by a waterproof putty and a micro-coverglass and observations were made with long-working-distance objectives. The temperature of the water bathing the ear was continuously monitored. A video camera and videotape recorder were used and enable optical methods of blood flow measurement to be performed. Inside-vessel-diameter measurements were made with a video analyzer. The transilluminated hairless mouse ear provided a simple, inexpensive, and reproducible in vivo model to study the microcirculation of intact mammalian skin.

Oxygen gradients in the microcirculation

Early in the last century August Krogh embarked on a series of seminal studies to understand the connection between tissue metabolism and mechanisms by which the cardiovascular system supplied oxygen to meet those needs. Krogh recognized that oxygen was supplied from blood to the tissues by passive diffusion and that the most likely site for oxygen exchange was the capillary network. Studies of tissue oxygen consumption and diffusion coefficient, coupled with anatomical studies of capillarity in various tissues, led him to formulate a model of oxygen diffusion from a single capillary. Fifty years after the publication of this work, new methods were developed which allowed the direct measurement of oxygen in and around microvessels. These direct measurements have confirmed the predictions by Krogh and have led to extensions of his ideas resulting in our current understanding of oxygenation within the microcirculation. Developments during the last 40 years are reviewed, including studies of oxygen gradients in arterioles, capillaries, venules, microvessel wall and surrounding tissue. These measurements were made possible by the development and use of new methods to investigate oxygen in the microcirculation, so mention is made of oxygen microelectrodes, microspectrophotometry of haemoglobin and phosphorescence quenching microscopy. Our understanding of oxygen transport from the perspective of the microcirculation has gone from a consideration of oxygen gradients in capillaries and tissue to the realization that oxygen has the ability to diffuse from any microvessel to another location under the conditions that there exists a large enough PO2 gradient and that the permeability for oxygen along the intervening pathway is sufficient.

Measurement of hemoglobin oxygen saturation using Raman microspectroscopy and 532-nm excitation.

The resonant Raman enhancement of hemoglobin (Hb) in the Q band region allows simultaneous identification of oxy- and deoxy-Hb. The heme vibrational bands are well known at 532 nm, but the technique has never been used to determine microvascular Hb oxygen saturation (So(2)) in vivo. We implemented a system for in vivo noninvasive measurements of So(2). A laser light was focused onto areas of 15-30 microm in diameter. Using a microscope coupled to a spectrometer and a cooled detector, Raman spectra were obtained in backscattering geometry. Calibration was performed in vitro using blood at several Hb concentrations, equilibrated at various oxygen tensions. So(2) was estimated by measuring the intensity of Raman signals (peaks) in the 1,355- to 1,380-cm(-1) range (oxidation state marker band nu(4)), as well as from the nu(19) and nu(10) bands (1,500- to 1,650-cm(-1) range). In vivo observations were made in microvessels of anesthetized rats. Glass capillary path length and Hb concentration did not affect So(2) estimations from Raman spectra. The Hb Raman peaks observed in blood were consistent with earlier Raman studies using Hb solutions and isolated cells. The correlation between Raman-based So(2) estimations and So(2) measured by CO-oximetry was highly significant for nu(4), nu(10), and nu(19) bands. The method allowed So(2) determinations in all microvessel types, while diameter and erythrocyte velocity could be measured in the same vessels. Raman microspectroscopy has advantages over other techniques by providing noninvasive and reliable in vivo So(2) determinations in thin tissues, as well as in solid organs and tissues in which transillumination is not possible.

Estimation of red cell flow in microvessels: Consequences of the Baker-Wayland spatial averaging model

The dual sensor cross-correlation method of H. Wayland and P.C. Johnson [1967), J. Appl. Physiol. 22, 333-337) has become a standard technique for determining the velocity of red blood cells (RBCs) in glass tubes and blood vessels. M. Baker and H. Wayland [1974), Microvasc. Res. 7, 131-143) found that under a variety of conditions the ratio of dual sensor velocity at the centerline of a glass tube to the blood velocity averaged over the lumen was close to 1.6. They provided an explanation of this factor based on spatial averaging of RBC velocity vertically through the tube as well as laterally across the face of the sensor. Their spatial averaging model could also account for the apparent blunting of RBC velocity profiles determined with the dual sensor technique. We used Baker and Waylands spatial averaging model to calculate how the above velocity ratio depends on sensor size. A nonlinear relation between the velocity ratio and sensor size was found such that the velocity ratio varied from 1.6 to 1.33 as the ratio of sensor width to vessel or tube diameter was varied from 0 to 1. These results also hold for vessels or tubes of elliptic cross section. Some investigators have found that the velocity of red cells near the walls of blood vessels can be a substantial fraction of centerline velocity which suggests that RBC velocity distributions can be blunter than a Poiseuille distribution. We repeated the above calculation for blunted parabolic profiles and we found that the velocity ratio ranged from 1 for plug flow to 1.6 for Poiseuille flow. These calculations show that reliable estimates of RBC flow from dual sensor centerline velocity measurements require one to take into account the relative size of the sensor and blood vessel diameter as well as the bluntness of the RBC velocity distribution.