The Krogh cylinder geometry is not appropriate for modelling O2 transport in contracted skeletal muscle

The V˙O2max Legacy of Hill and Lupton (1923)-100 Years On

PURPOSE

One hundred years ago, Hill and Lupton introduced the concept of maximal oxygen uptake (V˙O2max), which is regarded as "the principal progenitor of sports physiology." We provide a succinct overview of the evolvement of research on V˙O2max, from Hill and Lupton's initial findings to current debates on limiting factors for V˙O2max and the associated role of convective and diffusive components. Furthermore, we update the current use of V˙O2max in elite endurance sport and clinical settings. Practical Applications and Conclusions: V˙O2max is a healthy and active centenarian that remains a very important measure in elite endurance sports and additionally contributes as an important vital sign of cardiovascular function and fitness in clinical settings. Over the past 100 years, guidelines for the test protocols and exhaustion criteria, as well as the understanding of limiting factors for V˙O2max, have improved dramatically. Presently, possibilities of accurate and noninvasive determination of the convective versus diffusive components of V˙O2max by wearable sensors represent an important future application. V˙O2max is not only an indicator of cardiorespiratory function, fitness, and endurance performance but also represents an important biomarker of cardiovascular function and health to be included in routine assessment in clinical practice.

Oxygen flux from capillary to mitochondria: integration of contemporary discoveries

Resting humans transport ~ 100 quintillion (10¹⁸) oxygen (O₂) molecules every second to tissues for consumption. The final, short distance (< 50 µm) from capillary to the most distant mitochondria, in skeletal muscle where exercising O₂ demands may increase 100-fold, challenges our understanding of O₂ transport. To power cellular energetics O₂ reaches its muscle mitochondrial target by dissociating from hemoglobin, crossing the red cell membrane, plasma, endothelial surface layer, endothelial cell, interstitial space, myocyte sarcolemma and a variable expanse of cytoplasm before traversing the mitochondrial outer/inner membranes and reacting with reduced cytochrome c and protons. This past century our understanding of O₂'s passage across the body's final O₂ frontier has been completely revised. This review considers the latest structural and functional data, challenging the following entrenched notions: (1) That O₂ moves freely across blood cell membranes. (2) The Krogh-Erlang model whereby O₂ pressure decreases systematically from capillary to mitochondria. (3) Whether intramyocyte diffusion distances matter. (4) That mitochondria are separate organelles rather than coordinated and highly plastic syncytia. (5) The roles of free versus myoglobin-facilitated O₂ diffusion. (6) That myocytes develop anoxic loci. These questions, and the intriguing notions that (1) cellular membranes, including interconnected mitochondrial membranes, act as low resistance conduits for O₂, lipids and H⁺-electrochemical transport and (2) that myoglobin oxy/deoxygenation state controls mitochondrial oxidative function via nitric oxide, challenge established tenets of muscle metabolic control. These elements redefine muscle O₂ transport models essential for the development of effective therapeutic countermeasures to pathological decrements in O₂ supply and physical performance.

August Krogh: Muscle capillary function and oxygen delivery

The capillary bed constitutes the obligatory pathway for almost all oxygen (O₂) and substrate molecules as they pass from blood to individual cells. As the largest organ, by mass, skeletal muscle contains a prodigious surface area of capillaries that have a critical role in metabolic homeostasis and must support energetic requirements that increase as much as 100-fold from rest to maximal exercise. In 1919 Krogh's 3 papers, published in the Journal of Physiology, brilliantly conflated measurements of muscle capillary function at rest and during contractions with Agner K. Erlang's mathematical model of O₂ diffusion. These papers single-handedly changed the perception of capillaries from passive vessels serving at the mercy of their upstream arterioles into actively contracting vessels that were recruited during exercise to elevate blood-myocyte O₂ flux. Although seminal features of Krogh's model have not withstood the test of time and subsequent technological developments, Krogh is credited with helping found the field of muscle microcirculation and appreciating the role of the capillary bed and muscle O₂ diffusing capacity in facilitating blood-myocyte O₂ flux. Today, thanks in large part to Krogh, it is recognized that comprehending the role of the microcirculation, as it supports perfusive and diffusive O₂ conductances, is fundamental to understanding skeletal muscle plasticity with exercise training and resolving the mechanistic bases by which major pathologies including heart failure and diabetes cripple exercise tolerance and cerebrovascular dysfunction predicates impaired executive function.

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.

Krogh’s capillary recruitment hypothesis, 100 years on: Is the opening of previously closed capillaries necessary to ensure muscle oxygenation during exercise?

In 1919, August Krogh published his seminal work on skeletal muscle oxygenation. Krogh’s observations indicated that muscle capillary diameter is actively regulated, rather than a passive result of arterial blood flow regulation. Indeed, combining a mathematical model with the number of ink-filled capillaries he observed in muscle cross sections taken at different workloads, Krogh was able to account for muscle tissue’s remarkably efficient oxygen extraction during exercise in terms of passive diffusion from nearby capillaries. Krogh was awarded the 1920 Nobel Prize for his account of muscle oxygenation. Today, his observations are engrained in the notion of capillary recruitment: the opening of previously closed capillaries. While the binary distinction between “closed” and “open” was key to Krogh’s model argument, he did in fact report a continuum of capillary diameters, degrees of erythrocyte deformation, and perfusion states. Indeed, modern observations question the presence of closed muscle capillaries. We therefore examined whether changes in capillary flow patterns and hematocrit among open capillaries can account for oxygen extraction in muscle across orders-of-magnitude changes in blood flow. Our four-compartment model of oxygen extraction in muscle confirms this notion and provides a framework for quantifying the impact of changes in microvascular function on muscle oxygenation in health and disease. Our results underscore the importance of capillary function for oxygen extraction in muscle tissue as first proposed by Krogh. While Krogh’s model calculations still hold, our model predictions support that capillary recruitment can be viewed in the context of continuous, rather than binary, erythrocyte distributions among capillaries.

NEW & NOTEWORTHY Oxygen extraction in working muscle is extremely efficient in view of single capillaries properties. The underlying mechanisms have been widely debated. Here, we develop a four-compartment model to quantify the influence of each of the hypothesized mechanisms on muscle oxygenation. Our results show that changes in capillary flow pattern and hematocrit can account for the high oxygen extraction observed in working muscle, while capillary recruitment is not required to account for these extraction properties.

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.

Skeletal muscle capillary function: contemporary observations and novel hypotheses

The capillary bed constitutes a vast surface that facilitates exchange of O2, substrates and metabolites between blood and organs. In contracting skeletal muscle, capillary blood flow and O2 diffusing capacity, as well as O2 flux, may increase two orders of magnitude above resting values. Chronic diseases, such as heart failure and diabetes, and also sepsis impair these processes, leading to compromised energetic, metabolic and, ultimately, contractile function. Among researchers seeking to understand blood-myocyte exchange in health and the basis for dysfunction in disease, there is a fundamental disconnect between microcirculation specialists and many physiologists and physiologist clinicians. While the former observe capillaries and capillary function directly (muscle intravital microscopy), the latter generally use indirect methodologies (e.g. post-mortem tissue analysis, 1-methyl xanthine, contrast-enhanced ultrasound, permeability-surface area product) and interpret their findings based upon August Krogh's observations made nearly a century ago. 'Kroghian' theory holds that only a small fraction of capillaries support red blood cell (RBC) flux in resting muscle, leaving the vast majority to be 'recruited' (i.e. to initiate RBC flux) during contractions, which would constitute the basis for increasing surface area for capillary exchange and reducing capillary-mitochondrial diffusion distances. Experimental techniques each have their strengths and weaknesses, and often the correct or complete answer to a problem emerges from integration across multiple technologies. Today, Krogh's entrenched 'capillary recruitment' hypothesis is challenged by direct observations of capillaries in contracting muscle, which is something that he and his colleagues could not do. Moreover, in the peer-reviewed scientific literature, application of a range of contemporary physiological technologies, including intravital microscopy of contracting muscle, magnetic resonance, near-infrared spectroscopy and phosphorescence quenching, combined with elegant in situ and in vivo models, suggest that the role of the capillary bed, at least in contracting muscle, is subserved without the necessity for de novo capillary recruitment of previously non-flowing capillaries. When viewed within the context of the capillary recruitment hypothesis, this evidence casts serious doubt on the interpretation of those data that are based upon Kroghian theory and indirect methodologies. Thus, today a wealth of evidence calls for a radical revision of blood-muscle exchange theory to one in which most capillaries support RBC flux at rest and, during contractions, capillary surface area is 'recruited' along the length of previously flowing capillaries. This occurs, in part, by elevating capillary haematocrit and extending the length of the capillary available for blood-myocyte exchange (i.e. longitudinal recruitment). Our understanding of blood-myocyte O2 and substrate/metabolite exchange in health and the mechanistic basis for dysfunction in disease demands no less.

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 PO(2) gradient and that the permeability for oxygen along the intervening pathway is sufficient.

Dynamics of muscle microcirculatory and blood-myocyte O(2) flux during contractions

The O(2) requirements of contracting skeletal muscle may increase 100-fold above rest. In 1919, August Krogh's brilliant insights recognized the capillary as the principal site for this increased blood-myocyte O(2) flux. Based on the premise that most capillaries did not sustain RBC flux at rest, Krogh proposed that capillary recruitment [i.e. initiation of red blood cell (RBC) flux in previously non-flowing capillaries] increased the capillary surface area available for O(2) flux and reduced mean capillary-to-mitochondrial diffusion distances. More modern experimental approaches reveal that most muscle capillaries may support RBC flux at rest. Thus, rather than contraction-induced capillary recruitment per se, increased RBC flux and haematocrit within already-flowing capillaries probably elevate perfusive and diffusive O(2) conductances and hence blood-myocyte O(2) flux. Additional surface area for O(2) exchange is recruited but, crucially, this may occur along the length of already-flowing capillaries (i.e. longitudinal recruitment). Today, the capillary is still considered the principal site for O(2) and substrate delivery to contracting skeletal muscle. Indeed, the presence of very low intramyocyte O(2) partial pressures (PO(2)s) and the absence of intramyocyte PO(2) gradients, whilst refuting the relevance of diffusion distances, place an even greater importance on capillary hemodynamics. This emergent picture calls for a paradigm-shift in our understanding of the function of capillaries by de-emphasizing de novo'capillary recruitment'. Diseases such as heart failure impair blood-myocyte O(2) flux, in part, by decreasing the proportion of RBC-flowing capillaries. Knowledge of capillary function in healthy muscle is requisite for identification of pathology and efficient design of therapeutic treatments.

Dynamics of muscle microcirculatory oxygen exchange

PURPOSE

Beyond the initial cardiodynamic "Phase I," pulmonary oxygen uptake (VO(2)) kinetics are dictated largely by, and resemble closely, the VO(2) of the exercising muscles (VO(2)m). Within those muscles, the microcirculation is responsible for affecting almost all blood-myocyte O(2) transfer, and thus, observations at this site may provide key insights into muscle oxidative function in health and dysfunction in disease.

METHODS

Recently, a novel combination of microscopy and phosphorescence quenching techniques has been utilized to understand the dynamics of microvascular O(2) delivery (VO(2)m) and muscle O(2) utilization (VO(2)m) at the onset of muscle contractions.

RESULTS

These experiments have addressed longstanding questions regarding the site of control of VO(2)m kinetics and provide a first look at capillary hemodynamics at exercise onset in healthy muscle and their derangements resulting from chronic diseases such as heart failure and diabetes.

CONCLUSION

This paper will review these novel findings within our current understanding of microcirculatory control and blood-myocyte O(2) transfer.

Remodeling of the vascular bed and progressive loss of capillaries in denervated skeletal muscle

Very little is known regarding structural and functional responses of the vascular bed of skeletal muscle to denervation and about the role of microcirculatory changes in the pathogenesis of post-denervation muscle atrophy. The purpose of the present study was to investigate the changes of the anatomical pattern of vascularization of the extensor digitorum longus muscle in WI/HicksCar rats 1, 2, 4, 7, 12, and 18 months following denervation of the limb. We found that the number of capillaries related to the number of muscle fibers, i.e. the capillary-to-fiber ratio (CFR), decreased by 88%, from 1.55 +/- 0.35 to 0.19 +/- 0.04, during the first 7 months after denervation and then slightly declined at a much lower rate during the next 11 months of observation to 10% of the CFR in normal muscle. Between months 2 and 4 after denervation, the CRF decreased by 2.4 times, from 58% to 24% of the control value. The loss of capillaries during the first 4 months following nerve transection was nearly linear and progressed with an average decrement of 4.16% per week. Electron microscopy demonstrated progressive degeneration of capillaries following nerve transection. In muscle cells close to degenerating capillaries, the loss of subsarcolemmal and intermyofibrillar mitochondria, local disassembly of myofibrils and other manifestations of progressive atrophy were frequently observed. The levels of devascularization and the degree of degenerative changes varied greatly within different topographical areas, resulting in significant heterogeneity of intercapillary distances and local capillary densities within each sample of denervated muscle. Perivascular and interstitial fibrosis that rapidly developed after denervation resulted in the spatial separation of blood vessels from muscle cells and their embedment in a dense lattice of collagen. As a result of this process, diffusion distances between capillaries and the surfaces of muscle fibers increased 10-400 times. Eighteen months after denervation most of the capillaries were heavily cushioned with collagen, and on the average 40% of the muscle cells were completely avascular. Devascularization of the tissue was accompanied by degeneration and death of muscle cells that had become embedded in a dense lattice of collagen. Immunofluorescent staining for the vascular isoform of alpha-actin revealed preservation of major blood vessels and a greater variability in thickness of their medial layer. Hyperplastic growth of the medial layer in some blood vessels resulted in narrowing of their lumens. By the end of month 7 after denervation, large deposits of collagen around arterioles often exceeded their diameters. Identification of oxidative muscle fibers after immunostaining for slow-twitch myosin, as well as using ultrastructural criteria, has shown that after 2 months of denervation oxidative muscle fibers were less susceptible to atrophy than glycolytic fibers. The lower rate of atrophy of type I muscle fibers at early stages of denervation may be explained by their initially better vascularization in normal muscle and their higher capacity to retain capillaries shortly after denervation. Thus, degeneration and loss of capillaries after denervation occurs more rapidly than the loss of muscle fibers, which results in progressive decrease of the CFR in denervated muscle. The change of capillary number in denervated muscle is biphasic: the phase of a rapid decrease of the CFR during the first 7 months after nerve transection is followed by the phase of stabilization. The presence of areas completely devoid of capillaries in denervated muscle and the virtual absence of such areas in normal muscle indicate the development of foci of regional hypoxia during long-term denervation. The anatomical pattern of muscle microvascularization changes dramatically after nerve transection. Each muscle fiber in normal muscle directly contacts on average 3-5 capillaries. (ABSTRACT TRUNCATED)

Morphometric analysis of capillary geometry in pigeon pectoralis muscle

The objective of the study was to examine the relationship(s) between the size and the geometry of the capillary network in the flight muscle of pigeon (Columbia livia). To this end, we used morphometry to analyze the degree of anisotropy (i.e., orientation) of capillaries with respect to the axis of the muscle fibers in perfusion-fixed samples of pigeon pectoralis muscles with large difference in capillary density. Capillary number per fiber cross-sectional area (range, 1,491-5,680 mm-2) depended on fiber size (aerobic fibers, 304-782 microns 2; glycolytic, 1,785-2,444 microns 2), as well as sarcomere length (1.69-2.20 microns), and the relative sectional area of aerobic and glycolytic fibers (aerobic, 42-84% of total fiber area). The degree of tortuosity of capillaries, i.e., their bending or sinuosity relative to the muscle fiber axis, was primarily a function of sarcomere length. In spite of large differences in capillary density, capillary orientation at a given sarcomere length was remarkably similar among samples. In addition to capillaries running parallel to the muscle fiber axis, a unique arrangement of branches running perpendicular to the muscle fiber axis was found in all samples. This arrangement yielded a large circumferential distribution of capillary surface around the muscle fibers. Compared to mammalian limb muscles examined over a 10-fold range of capillary density (range, 450-4,670 mm-2), the degree of anisotropy of capillaries was greater in all samples of pigeon M. pectoralis. In the pigeon, there was no increase in the amount of capillary surface area available for exchange per microvessel as a result of a greater degree of capillary tortuosity in samples with larger capillary density (capillary number per fiber cross-sectional area greater than 4,000 mm-2), as compared to samples with a capillary density less than 4,000 mm-2.

Capillary configuration and fiber shortening in muscles of the rat hindlimb: correlation between corrosion casts and stereological measurements

It has been a matter of discussion whether the dramatic increase in capillary tortuosity visualized in shortened muscles by vascular cast represents in vivo situations. In this study, we combined vascular cast and stereological methods in the same samples, in order to obtain (1) measurements of sarcomere length in the same muscles from which corrosion casts were prepared, and (2) scanning electron micrographs of the three-dimensional arrangement of capillaries in the same muscles where capillary anisotrophy was estimated by morphometry. Various rat skeletal muscles (soleus, gastrocnemius, and gracilis) were examined at lengths ranging from full shortening to full extension. We found a very good correlation between capillary geometry in material prepared for vascular casts and in muscles perfusion-fixed in situ. All muscles, cast and noncast, showed the same progressive curvilinear decrease in capillary anisotropy with decreasing sarcomere length. Capillary tortuosity visualized by corrosion casts in shortened muscles is a consequence of fiber shortening, within physiological sarcomere lengths; it does not represent an artifact related to the casting procedure.

Cross-sectional PO2 distributions in Krogh cylinder and solid cylinder models

Radial profiles, gradients and frequency distributions of PO2 are calculated for two cylindrical tissue models with uniform O2 diffusion properties and O2 consumption: Krogh's cylinder with O2 supplied from a central capillary (model A), and a solid cylinder with O2 supplied from the outer surface (model B). Because the O2 diffusion flux is divergent in model A, and convergent in model B, the PO2 gradient flattens with increasing distance from the supplying surface more rapidly in model A than in model B. In model A, the frequency distribution of PO2 with respect to unit cross-sectional area is highly asymmetric, being skewed to low PO2, whereas it is uniform in model B. Model A is applicable to parallel capillaries uniformly distributed across tissue cross-section. For Model B a large number of capillaries surrounding a cylindrical structure is required. Model A appears to be much more adequate than model B to describe the normal morphometry in skeletal muscle (capillary number/fiber number ratio of about 2, capillary-to-muscle fiber radius ratio of about 0.1). The experimental finding of relatively low PO2 and small PO2 gradients within muscle fiber cross-sections is in agreement with both models, but agrees better with model A than with model B.

Capillary diameter and geometry in cardiac and skeletal muscle studied by means of corrosion casts

Studies of microvascular geometry made from microscope observations of tissues in vivo or after perfusion with a silastic elastomer or india ink are restricted to a two-dimensional field of view. Microvascular corrosion casts, however, if of sufficient rigidity and structural integrity, can yield three-dimensional information when examined under the scanning electron microscope. We have used modified Batson's No. 17 anatomical casting compound (having a shrinkage less than 1% on setting) to prepare casts of the microvasculature of the heart and skeletal muscles in anesthetized rats. In casts from the L. ventricle the capillary network appeared to parallel the arrangement of the muscle fibers, but showed many capillary loops and anastomoses. In skeletal muscles (gastrocnemius and gracilis) held at full extension, in situ, the casts showed long straight capillaries with fewer branchings than in the heart. In shortened skeletal muscle the capillaries exhibited an undulatory configuration. Capillary diameters (mean +/- SD) were 5.14 +/- 1.42 micrometers (N = 202), 5.04 +/- 1.45 micrometers (N = 294) and 4.84 +/- 1.97 micrometers (N = 335) in L. ventricle, gastrocnemius, and gracilis muscles (both shortened), respectively. The mean values for capillary diameter in these three tissues did not differ significantly. Combining our data with those of L. Henquell, P. L. LaCelle, and C. R. Honig on erythrocyte deformability in the rat (Microvasc. Res. 12, 259-274 (1976)) suggests that even when the capillary bed is fully distended the smallest capillaries, amounting to 1-2% of the total number, must be channels for plasma flow alone. In cross-sectional views of the casts from contracted skeletal muscle the capillaries appeared to form a tightly meshed network of convoluted vessels around the fibers, such that in some regions a large fraction of the surface of each fiber was in contact with blood. The Krogh cylinder geometry appears not to be appropriate for modeling O2 transport in maximally shortened skeletal muscle; a more appropriate model may be that of a cylindrical muscle fiber supplied, at any point down its length, by a uniform peripheral O2 supply.