Modeling oxygen availability to exercising muscle

Physiological determinants of decreased peak leg oxygen uptake in chronic disease: a systematic review and meta-analysis

This systematic review and meta-analysis examined the physiological mechanisms responsible for lower peak exercise leg oxygen uptake (V̇o2) in patients with chronic disease. Studies measuring peak leg V̇o2 (primary outcome) and its physiological determinants during large (cycle) or small muscle mass exercise (single-leg knee extension, SLKE) in patients with chronic disease were included in this meta-analysis. Pooled estimates for each outcome were reported as a weighted mean difference (WMD) between chronic disease and controls. We included 10 studies that measured peak leg V̇o2 in patients with chronic disease (n = 109, mean age: 45 yr; encompassing chronic obstructive pulmonary disease, COPD, heart failure with reduced ejection fraction, HFrEF, or chronic renal failure, RF) and age-matched controls (n = 88). In pooled analysis, peak leg V̇o2 (WMD; -0.23 L/min, 95% CI: -0.32 to -0.13), leg oxygen (O2) delivery (WMD: -0.27 L/min, 95% CI: -0.37 to -0.17), and muscle O2 diffusive conductance (WMD: -5.2 mL/min/mmHg, 95% CI: -7.1 to -3.2) were all significantly lower during cycle and SLKE exercise in chronic disease versus controls. These results highlight that during large and small muscle mass exercise in patients with COPD, HFrEF, or RF, there is no single factor causing peak V̇o2 limitations. Specifically, the lower peak V̇o2 in these pathologies is due to not only the expected impairments in convective O2 delivery but also impairments in muscle oxygen diffusive transport from capillary to mitochondria. Whether impaired muscle O2 transport is caused solely by inactivity or additional muscle pathology remains in question.NEW & NOTEWORTHY Peripheral (skeletal muscle and vasculature) factors contribute significantly to reduced exercise capacity during both large and small muscle mass exercise in chronic diseases such as COPD, HFrEF, or RF and should be important targets of therapy in addition to the primary organs (lungs, heart, and kidneys) affected by disease.

Blood Gas Transport: Implications for O2 and CO2 Exchange in Lungs and Tissues

The well-known ways in which O2 and CO2 (and other gases) are carried in the blood were presented in the preceding chapter. However, what the many available texts about O2 and CO2 transport do not emphasize is why knowing how gases are carried in blood matters, and this second, companion, article specifically addresses that critical aspect of gas exchange physiology. During gas exchange, both at the lungs and in the peripheral tissues, it is the shapes and the slopes of the O2 and CO2 binding curves that explain almost all of the behaviors of each gas and the quantitative differences observed between them. This conclusion is derived from first principle considerations of the gas exchange processes. Dissociation curve shape and slope differences explain most of the differences between O2 and CO2 in both diffusive exchange in the lungs and tissues and convective exchange/transport in, and between, the lungs and tissues. In fact, each of the chapters in this volume describes physiological behavior that depends more or less directly on the dissociation curves of O2 and CO2.

Dynamics of PO2 and VO2 in resting and contracting rat spinotrapezius muscle

This study examined changes in interstitial PO2, which allowed calculation of VO2 during periods of rest, muscle contraction and recovery using an in situ rat spinotrapezius muscle preparation. The PO2 was measured using phosphorescence quenching microscopy and the muscle VO2 was calculated as the rate of O2 disappearance during brief periods of muscle compression to stop blood flow with a supra-systolic pressure. The PO2 and VO2 measurements were made during "5 s compression and 15 s recovery" (CR) cycles. With all three stimulation frequencies, 1, 2 and 4 Hz, the fall in interstitial PO2 and rise in VO2 from resting values occurred within the first 20 s of contraction. The PO2 during contraction became lower as stimulation frequency increased from 1 to 4 Hz. VO2 was higher at 2 Hz than at 1 Hz contraction. With cessation of stimulation, PO2 began increasing exponentially towards baseline values. After 1 and 2 Hz contraction, the fall in muscle VO2 was delayed by one CR cycle and then exponentially decreased towards resting values. After 4 Hz stimulation, VO2 increased for 2 cycles and then decreased. The post-contraction transients of PO2 and VO2 were not synchronous and had different time constants. With further analysis two distinct functional responses were identified across all stimulation frequencies having PO2 during contraction above or below 30 mmHg. The corresponding VO2 responses were different - for "high" PO2, muscle VO2 reached high levels, while for the "low" PO2 data set muscle VO2 remained low. Recovery patterns were similar to those described above. In summary, local microscopic PO2 and VO2 were measured in resting and contracting muscle in situ and the post-contraction transients of PO2 and VO2 were all much slower than the onset transients.

A century of exercise physiology: key concepts on coupling respiratory oxygen flow to muscle energy demand during exercise

After a short historical account, and a discussion of Hill and Meyerhof’s theory of the energetics of muscular exercise, we analyse steady-state rest and exercise as the condition wherein coupling of respiration to metabolism is most perfect. The quantitative relationships show that the homeostatic equilibrium, centred around arterial pH of 7.4 and arterial carbon dioxide partial pressure of 40 mmHg, is attained when the ratio of alveolar ventilation to carbon dioxide flow (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{V}}_{A}/{\dot{V}}_{R}{CO}_{2}$$\end{document}V˙A/V˙RCO2) is − 21.6. Several combinations, exploited during exercise, of pertinent respiratory variables are compatible with this equilibrium, allowing adjustment of oxygen flow to oxygen demand without its alteration. During exercise transients, the balance is broken, but the coupling of respiration to metabolism is preserved when, as during moderate exercise, the respiratory system responds faster than the metabolic pathways. At higher exercise intensities, early blood lactate accumulation suggests that the coupling of respiration to metabolism is transiently broken, to be re-established when, at steady state, blood lactate stabilizes at higher levels than resting. In the severe exercise domain, coupling cannot be re-established, so that anaerobic lactic metabolism also contributes to sustain energy demand, lactate concentration goes up and arterial pH falls continuously. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{V}}_{A}/{\dot{V}}_{R}{CO}_{2}$$\end{document}V˙A/V˙RCO2 decreases below − 21.6, because of ensuing hyperventilation, while lactate keeps being accumulated, so that exercise is rapidly interrupted. The most extreme rupture of the homeostatic equilibrium occurs during breath-holding, because oxygen flow from ambient air to mitochondria is interrupted. No coupling at all is possible between respiration and metabolism in this case.

A Computer Model of Oxygen Dynamics in the Cortex of the Rat Kidney at the Cell-Tissue Level

The renal cortex drives renal function. Hypoxia/reoxygenation are primary factors in ischemia-reperfusion (IR) injuries, but renal oxygenation per se is complex and awaits full elucidation. Few mathematical models address this issue: none captures cortical tissue heterogeneity. Using agent-based modeling, we develop the first model of cortical oxygenation at the cell-tissue level (RCM), based on first principles and careful bibliographical analysis. Entirely parameterized with Rat data, RCM is a morphometrically equivalent 2D-slice of cortical tissue, featuring peritubular capillaries (PTC), tubules and interstitium. It implements hemoglobin/O2 binding-release, oxygen diffusion, and consumption, as well as capillary and tubular flows. Inputs are renal blood flow RBF and PO2 feeds; output is average tissue PO2 (tPO2). After verification and sensitivity analysis, RCM was validated at steady-state (tPO2 37.7 ± 2.2 vs. 36.9 ± 6 mmHg) and under transients (ischemic oxygen half-time: 4.5 ± 2.5 vs. 2.3 ± 0.5 s in situ). Simulations confirm that PO2 is largely independent of RBF, except at low values. They suggest that, at least in the proximal tubule, the luminal flow dominantly contributes to oxygen delivery, while the contribution of capillaries increases under partial ischemia. Before addressing IR-induced injuries, upcoming developments include ATP production, adaptation to minutes-hours scale, and segmental and regional specification.

Oxygen dependence of respiration in rat spinotrapezius muscle contracting at 0.5-8 twitches per second

The oxygen dependence of respiration was obtained in situ in microscopic regions of rat spinotrapezius muscle for different levels of metabolic activity produced by electrical stimulation at rates from 0.5 to 8 Hz. The rate of O₂ consumption (V̇o₂) was measured with phosphorescence quenching microscopy (PQM) as the rate of O₂ disappearance in a muscle with rapid flow arrest. The phosphorescent oxygen probe was loaded into the interstitial space of the muscle to give O₂ tension (Po₂) in the interstitium. A set of sigmoid curves relating the Po₂ dependence of V̇o₂ was obtained with a Po₂-dependent region below a characteristic Po₂ (~30 mmHg) and a Po₂-independent region above this Po₂. The V̇o₂(Po₂) plots were fit by the Hill equation containing O₂ demand (rest to 8 Hz: 216 ± 26 to 636 ± 77 nl O₂/cm³ s) and the Po₂ value corresponding to O₂ demand/2 (rest to 8 Hz: 22 ± 4 to 11 ± 1 mmHg). The initial Po₂ and V̇o₂ pairs of values measured at the moment of flow arrest formed a straight line, determining the rate of oxygen supply. This line had a negative slope, equal to the oxygen conductance for the O₂ supply chain. For each level of tissue blood flow the set of possible values of Po₂ and V̇o₂ consists of the intersection points between this O₂ supply line and the set of V̇o₂ curves. An electrical analogy for the intraorgan O₂ supply and consumption is an inverting transistor amplifier, which allows the use of graphic analysis methods for prediction of the behavior of the oxygen processing system in organs. NEW & NOTEWORTHY The sigmoidal shape of curves describing oxygen dependence of muscle respiration varies from basal to maximal workload and characterizes the oxidative metabolism of muscle. The rate of O₂ supply depends on extracellular O₂ tension and is determined by the overall oxygen conductance in the muscle. The dynamics of oxygen consumption is determined by the supply line that intersects the oxygen demand curves. An electrical analogy for the oxygen supply/consumption system is an inverting transistor amplifier.

Exercise Intolerance in Heart Failure With Preserved Ejection Fraction: Diagnosing and Ranking Its Causes Using Personalized O2 Pathway Analysis

BACKGROUND

Heart failure with preserved ejection fraction (HFpEF) is a common syndrome with a pressing shortage of therapies. Exercise intolerance is a cardinal symptom of HFpEF, yet its pathophysiology remains uncertain.

METHODS

We investigated the mechanism of exercise intolerance in 134 patients referred for cardiopulmonary exercise testing: 79 with HFpEF and 55 controls. We performed cardiopulmonary exercise testing with invasive monitoring to measure hemodynamics, blood gases, and gas exchange during exercise. We used these measurements to quantify 6 steps of oxygen transport and utilization (the O2 pathway) in each patient with HFpEF, identifying the defective steps that impair each one's exercise capacity (peak Vo2). We then quantified the functional significance of each O2 pathway defect by calculating the improvement in exercise capacity a patient could expect from correcting the defect.

RESULTS

Peak Vo2 was reduced by 34±2% (mean±SEM, P<0.001) in HFpEF compared with controls of similar age, sex, and body mass index. The vast majority (97%) of patients with HFpEF harbored defects at multiple steps of the O2 pathway, the identity and magnitude of which varied widely. Two of these steps, cardiac output and skeletal muscle O2 diffusion, were impaired relative to controls by an average of 27±3% and 36±2%, respectively (P<0.001 for both). Due to interactions between a given patient's defects, the predicted benefit of correcting any single one was often minor; on average, correcting a patient's cardiac output led to a 7±0.5% predicted improvement in exercise intolerance, whereas correcting a patient's muscle diffusion capacity led to a 27±1% improvement. At the individual level, the impact of any given O2 pathway defect on a patient's exercise capacity was strongly influenced by comorbid defects.

CONCLUSIONS

Systematic analysis of the O2 pathway in HFpEF showed that exercise capacity was undermined by multiple defects, including reductions in cardiac output and skeletal muscle diffusion capacity. An important source of disease heterogeneity stemmed from variation in each patient's personal profile of defects. Personalized O2 pathway analysis could identify patients most likely to benefit from treating a specific defect; however, the system properties of O2 transport favor treating multiple defects at once, as with exercise training.

Pathophysiological alterations in oxygen delivery to the tissues

This paper reviews co-factors that impact on oxygen delivery and uptake, in the attempt to unravel the mechanisms underlying the correlation between the decrease in oxygen delivery and oxygen consumption. In sequence, the following factors are analyzed that, besides a decrease in haemoglobin concentration, impair tissue metabolism: (1) lung diffusion and perfusion limitation in oxygen transport, (2) decrease in cardiac output, (3) impairment of peripheral microvascular perfusion and (4) reduced ability of cells to extract oxygen. The contribution of the various factors is modeled aiming to present a decisional flow chart for the functional evaluation of the efficiency of the oxygen transport system.

Peripheral oxygen transport and utilization in rats following continued selective breeding for endurance running capacity

Untrained rats selectively bred for either high (HCR) or low (LCR) treadmill running capacity previously demonstrated divergent physiological traits as early as the seventh generation (G7). We asked whether continued selective breeding to generation 15 (G15) would further increase the divergence in skeletal muscle capillarity, morphometry, and oxidative capacity seen previously at G7. At G15, mean body weight was significantly lower (P < 0.001) in the HCR rats (n = 11; 194 +/- 3 g) than in LCR (n = 12; 259 +/- 9 g) while relative medial gastrocnemius muscle mass was not different (0.23 +/- 0.01 vs. 0.22 +/- 0.01% total body weight). Normoxic (Fi(O(2)) = 0.21) Vo(2max) was 50% greater (P < 0.001) in HCR despite the lower absolute muscle mass, and skeletal muscle O(2) conductance (measured in hypoxia; Fi(O(2)) = 0.10) was 49% higher in HCR (P < 0.001). Muscle oxidative enzyme activities were significantly higher in HCR (citrate synthase: 16.4 +/- 0.4 vs. 14.0 +/- 0.6; beta-hydroxyacyl-CoA dehydrogenase: 5.2 +/- 0.2 vs. 4.2 +/- 0.2 mmol.kg(-1).min(-1)). HCR rats had approximately 36% more total muscle fibers and also 36% more capillaries in the medial gastrocnemius. Because average muscle fiber area was 35% smaller, capillary density was 36% higher in HCR, but capillary-to-fiber ratio was the same. Compared with G7, G15 HCR animals showed 38% greater total fiber number with an additional 25% decrease in mean fiber area. These data suggest that many of the skeletal muscle structural and functional adaptations enabling greater O(2) utilization in HCR at G7 continue to progress following additional selective breeding for endurance capacity. However, the largest changes at G15 relate to O(2) delivery to skeletal muscle and not to the capacity of skeletal muscle to use O(2).

Muscle microvascular hemoglobin concentration and oxygenation within the contraction-relaxation cycle

Inability to directly measure microvascular oxygen distribution and extraction in striated muscle during a contraction/relaxation cycle limits our understanding of oxygen transport to and utilization by contracting muscle. We examined muscle microvascular hemoglobin concentration (total [Hb/Mb]) and oxygenation within the contraction-relaxation cycle to determine if microvascular RBC volume would be preserved and if oxygen extraction continued during the actual contraction phase. Eight subjects performed dynamic knee extension exercise (40 contractions/min) at moderate ( approximately 30% of peak work rate) and heavy ( approximately 80% of peak) work rates. Total hemoglobin/myoglobin (total [Hb/Mb]) and deoxy-hemoglobin/myoglobin (deoxy-[Hb/Mb]) were measured in the rectus femoris using NIRS to determine if microvascular total [Hb/Mb] would be preserved during the contraction, and to estimate microvascular oxygen extraction, respectively. Mean values during the relaxation (RP) and contractile phases and the peak values during the contractile phase for both moderate and heavy exercise were calculated. Total [Hb/Mb] increased from rest to steady-state exercise (6.36+/-5.08 microM moderate; 5.72+/-4.46 microM heavy exercise, both P<0.05), but did not change significantly within the contraction/relaxation cycle. Muscle contractions were associated with a significant (1.29+/-0.98 microM moderate; 2.16+/-2.12 microM heavy exercise, P<0.05) increase in deoxy-[Hb/Mb] relative to RP. We conclude that (a) microvascular RBC volume is preserved during muscle contractions (i.e., RBCs are present in the capillaries), and (b) the cyclical pattern of deoxygenation/oxygenation during the respective contraction/relaxation phases of the contraction cycle suggests that oxygen extraction is not restricted to the relaxation phase but continues to occur during muscle contractions.

Blood flow and O2 extraction as a function of O2 uptake in muscles composed of different fiber types

We examined how the greater vasodilatory capacity of slow--(ST) versus fast-twitch (FT) muscles impacts the relationship between blood flow (Q ) and O2 uptake (VO2) and, consequently, the O2 extraction (a-vO2 diff.)-to-VO2 relationship. Q was measured with radiolabelled microspheres, while VO2 was calculated by the Fick principle using measurements of microvascular O2 pressure (phosphorescence quenching) at rest, low--(2.5 V) and high-intensity contractions (4.5 V) for soleus (Sol; ST, n=5), mixed-gastrocnemius (MG; FT, n=7) and white-gastrocnemius (WG; FT, n=7). The slope of the Q-to-VO2 relationship (delta Q/delta VO2] ) was not different among muscles (Sol = 5.5 +/- 0.2, MG = 6.0 +/- 0.11 and WG = 5.8 +/- 0.06; P > 0.05). In contrast, the intercept was greater (P < 0.05) for Sol (16.3 +/- 2.7 ml min(-1) 100 g(-1)) versus MG and WG (in ml min(-1) 100 g(-1): 1.39 +/- 0.26 and 1.45 +/- 0.23, respectively; MG and WG, P > 0.05). In addition, the a-vO2 diff.-to-VO2] relationship for Sol was shifted rightward compared to MG and WG. These data suggest that the increase in Q for a given change in VO2 is similar for slow- and fast-twitch muscles, at least for the range of metabolic rates and muscles studied herein and that a-vO2 diff. differences result from the lower resting Q in FT muscles.

Temporal profile of rat skeletal muscle capillary haemodynamics during recovery from contractions

In skeletal muscle capillaries, red blood cell (RBC) flux (F(RBC)), velocity (V(RBC)) and haematocrit (Hct(CAP)) are key determinants of microvascular O2 exchange. However, the mechanisms leading to the changes in F(RBC), V(RBC) and Hct(CAP) during muscle contractions and recovery thereafter are not fully understood. To address this issue we used intravital microscopy to investigate the temporal profile of the rat spinotrapezius muscle (n = 5) capillary haemodynamics during recovery from 3 min of twitch muscle contractions (1 Hz, 4-6 V). Specifically, we hypothesized that (1) during early recovery F(RBC) and V(RBC) would decrease rapidly and F(RBC) would display a biphasic response (consistent with a muscle pump effect on capillary haemodynamics), and (2) there would be a dynamic relationship between changes (Delta) in V(RBC) and Hct(CAP). The values at rest (R) and end-recovery (ER) were significantly lower (P < 0.05) than at end-contraction (EC) for F(RBC) (in cells s(-1), R = 30.1 +/- 7.8, EC = 46.2 +/- 7.3 and ER = 26.0 +/- 6.1), V(RBC) (in microm s(-1), R = 368 +/- 83, EC = 497 +/- 62 and ER = 334 +/- 59) and Hct(CAP) (R = 0.193 +/- 0.016, EC = 0.214 +/- 0.023 and ER = 0.185 +/- 0.019). The first data point where a significant decrease in F(RBC), Hct(CAP) and V(RBC) occurred was at 5, 5 and 20 s post-contraction, respectively. The decrease in F(RBC) approximated a monoexponential response (half-time of approximately 26 s). The relationship between DeltaV(RBC) and DeltaHct(CAP) was not significant (P > 0.05). Based on the early decrease in F(RBC) (within 5 s), overall dynamic profile of F(RBC) and the approximately 20 s 'delay' to the decrease in V(RBC) we conclude that the muscle pump does not appear to contribute substantially to the steady-state capillary haemodynamics in the contracting rat spinotrapezius muscle. Moreover, our findings suggest that alterations in V(RBC) do not obligate proportional changes in Hct(CAP) within individual capillaries following muscle contractions.

A Mathematical Model of Tissue–Blood Carbon Dioxide Exchange during Hypoxia

A two-compartment mass transport model of tissue CO(2) exchange is developed to examine the relative contributions of blood flow and cellular hypoxia (dysoxia) to increases in tissue and venous blood CO(2) concentration. The model assumes perfectly mixed homogeneous conditions, steady-state equilibrium, and CO(2) production occurring exclusively at the tissues. The behavior of the model is compared with published data derived from an isolated dog hindlimb preparation subjected to either reductions in blood flow (ischemic hypoxia) or decreases in arterial PO(2) (hypoxic hypoxia). The results of the model corroborate the experimental finding of greater venous and tissue CO(2) concentrations with ischemic hypoxia than with hypoxic hypoxia. The model also predicts increases in tissue CO(2) concentration under conditions of adequate O(2) supply if CO(2) transfer from tissue to blood becomes impaired. Consequently, from a theoretical perspective, it appears that increases in the tissue or venous blood CO(2) concentration are neither sensitive nor specific markers of tissue dysoxia. The results of the model support the notion that changes in tissue and venous blood CO(2) concentration during dysoxia reflect primarily alterations in vascular perfusion and not scarcity in cellular energy supply.

A model of vertebrate resting metabolic rate: balancing energetics and O2 transport in system design

In vertebrates, maximal rates of oxygen consumption (V(O(2),max)) exceed resting rates (V(O(2),rest)) by an average factor of ten. This pattern of factorial scope has led to the hypothesis that V(O(2),rest) and V(O(2),max) are causally linked in vertebrates (aerobic capacity model, Bennett and Ruben, Science 206, 649-654, 1979). We propose an alternate theory that vertebrate resting metabolic rates are regulated at levels to optimize metabolic performance during activity, by reducing cardiovascular response times for O(2) transport. First, we argue that circulatory convection has the potential to be rate-limiting to vertebrate aerobic adjustment. We then show mathematically that incremental changes in convection requirements exhibit a nonlinear dependence on initial values. From this, a cost-benefit model is constructed, using energetics and blood-convection requirements, to predict the optimal fractional allocation to V(O(2),rest) in vertebrates as 11% of V(O(2),max). The implications of our results to vertebrate metabolic design and the evolution of endothermy are discussed.