Citations

World record speeds at different distances for men and women in different age categories are used to develop a model to predict running performance as a function of race distance, age, and sex. This empirical model quantifies the decline in running speed with distance and age in a way that provides insight into the aerobic and anaerobic contributions to running speed and may help with developing training strategies for different age groups at various distances.

Severe impairment of oxygenation in critically ill patients is a major cause of morbidity and mortality, and can occur even with normal alveolar ventilation and cardiac output under conditions of decreased diffusing capacity or increased flow heterogeneity. A theoretical model of pulmonary oxygen uptake under resting conditions is used to simulate decreased diffusing capacity (DL) as well as increased heterogeneity (characterized by an increase in the coefficient of variation [CV] of pulmonary capillary blood flow), with the assumed normal value of CV based on observations of microvascular networks. Under resting conditions with nominal values of DL and CV, the model predicts an oxygen saturation (SO 2 ) of 97% (PO 2 = 94 mmHg). Simulating a 10‐fold reduction in DL leads to an SO 2 of 85% (PO 2 = 51 mmHg), whereas doubling the CV from its normal value leads to an SO 2 of 95% (PO 2 = 78 mmHg); both of these predictions suggest a high degree of reserve in the healthy resting lung. However, simulating these conditions simultaneously leads to a large reduction in SO 2 to 71% (PO 2 = 37 mmHg), exhausting the reserve capacity of the lung and demonstrating the detrimental synergistic effect of heterogeneity in the context of an attenuated diffusing capacity. These results imply that a combination of increased heterogeneity and decreased diffusing capacity can explain the severe impairment in pulmonary oxygen uptake and decreased saturations seen in critical illness. Support or Funding Information Supported by NIH grant HL070657.

AbstractOxygen transport from the lungs to peripheral tissue is dependent on the affinity of hemoglobin for oxygen. Recent experimental data have suggested that the maximum human capacity for oxygen uptake and utilization (V̇O2max) at sea level and altitude (~3000 m) is sensitive to alterations in hemoglobin‐oxygen affinity. However, the effect of such alterations on V̇O2max at extreme altitudes remains largely unknown due to the rarity of mutations affecting hemoglobin‐oxygen affinity. This work uses a mathematical model that couples pulmonary oxygen uptake with systemic oxygen utilization under conditions of high metabolic demand to investigate the effect of hemoglobin‐oxygen affinity on V̇O2max as a function of altitude. The model includes the effects of both diffusive and convective limitations on oxygen transport. Pulmonary oxygen uptake is calculated using a spatially‐distributed model that accounts for the effects of hematocrit and hemoglobin‐oxygen affinity. Systemic oxygen utilization is calculated assuming Michaelis–Menten kinetics. The pulmonary and systemic model components are solved iteratively to compute predicted arterial and venous oxygen levels. Values of V̇O2max are predicted for several values of hemoglobin‐oxygen affinity and hemoglobin concentration based on data from humans with hemoglobin mutations. The model predicts that increased hemoglobin‐oxygen affinity leads to increased V̇O2max at altitudes above ~4500 m.

Background: Hemoglobin, the primary oxygen-carrying protein in humans, provides the intermediate link between pulmonary oxygen uptake and tissue oxygen consumption. Oxygen transport is greatly influenced by the hemoglobin-oxygen affinity, which is commonly characterized by the metric P50 - defined as the oxygen tension at which 50% of hemoglobin is saturated. Humans with rare hemoglobin mutations causing a low P50 (high hemoglobin-oxygen affinity) have demonstrated remarkable preservation of exercise tolerance at high altitude conditions (~3,000m). However, the influence of a low P50 on V̇O2max at extreme altitudes (>5,500m) remains largely unexamined. To examine the dependence of V̇O2max on P50 and altitude, we developed a computational model of oxygen uptake and utilization. We hypothesized that a low P50 would result in a better maintained V̇O2max at extreme altitudes compared to conditions of normal P50 and high P50 (low hemoglobin-oxygen affinity). Methods: We created a model that couples pulmonary oxygen uptake with systemic oxygen utilization to estimate V̇O2max as a function of P50, hemoglobin concentration, and altitude. Fixed values for cardiac output and tissue oxygen demand for V̇O2max at sea level were assigned in accordance with experimental data. The pulmonary oxygen uptake model assumes a single blood compartment exposed to alveolar gas, from which the arterial oxygen tension may be estimated from venous input. Using the alveolar gas equation, we interpolated respiratory parameters from data obtained during human sojourn to the summit of Everest. The systemic oxygen utilization model uses arterial input parameters along with Michaelis-Menten kinetics to compute oxygen consumption. The Fick principle was used to determine the venous oxygen tension, which was assumed to approximate tissue oxygen tension. From these values, systemic oxygen extraction and V̇O2max were determined as a function of P50, hemoglobin concentration, and altitude. Results: We present the results for several cases of P50 (low, normal, and high) and hemoglobin concentrations as a function of altitude. For a low P50, the model demonstrated a greater arterial oxygen saturation, greater oxygen content, and lower systemic extraction at extreme altitudes compared to values determined for cases of normal and high P50. Additionally, a low P50 led to better maintenance of V̇O2max at ~8,850m (~38% decrease from sea-level V̇O2max) compared to values determined for normal P50 and high P50 (~53% and ~67% decrease from sea-level V̇O2max, respectively, P<0.05). Conclusion: This model demonstrates the importance of P50 in the determination of V̇O2max at various altitudes. At low altitudes, a low P50 does not confer an advantage in terms of oxygen utilization, likely due to diffusive oxygen limitations. However, at high and extreme altitudes, a greater convective oxygen transport associated with a low P50 likely outweighs impairments in oxygen diffusivity. This project was supported by the National Institutes of Health R-35-HL139854. This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

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

The ability of the lung to take up oxygen can be characterized by its effective diffusing capacity, which is determined by the transport characteristics of the alveolar‐capillary membrane as well as heterogeneity of pulmonary blood flow. At rest, the healthy lung has a high degree of tolerance for pulmonary flow heterogeneity, but under conditions of physiological stress such as exercise, oxygen uptake may be inadequate to satisfy tissue demand if flow is very heterogeneous. We previously used a mathematical model of pulmonary oxygen uptake to examine the ability of hypoxic pulmonary vasoconstriction (HPV) to mitigate flow heterogeneity. In the model, flow heterogeneity is characterized by the coefficient of variation (CV) of pulmonary capillary blood flow. Assuming an initial lognormal distribution of blood flow with a normal level of heterogeneity (CV = 1.66), we simulate flow regulation over a range of oxygen consumption from rest to maximal exercise by adjusting pulmonary flow resistance in each vessel in accordance with an HPV response curve obtained from previously published experimental data. The effect of HPV on vessel flow resistance is assumed to be characterized by a sigmoidal response dependent on the capillary oxygen tension, which is approximated as the mean of the venous and arterial values in each pulmonary capillary; its maximal sensitivity occurs at a stimulus oxygen tension of approximately 30 torr. The purpose of the present study was to determine whether altering the shape of the HPV response curve would result in an improvement in CV reduction. Altering the HPV by shifting the sigmoidal curve to the right by 10 or 20 torr worsened CV, extraction and total pulmonary vascular resistance (PVR). Similar detrimental results were obtained when the range of oxygen tensions over which HPV varied was expanded by a factor of two, increasing the oxygen tension at which the sensitivity of HPV to oxygen tension was maximal. On the other hand, shrinking the range of variation of the HPV curve by a factor of two neither improved nor significantly worsened the CV or extraction, and resulted in a PVR distribution similar to the case of the normal HPV curve. These results demonstrate that the observed shape of the HPV response tends to minimize heterogeneity of pulmonary flow under conditions of exercise.

A theoretical model of the pulmonary vasculature is used to predict the effects of vasoconstriction over specified ranges of vessel diameters on pulmonary vascular resistance (PVR). The model shows that observed levels of hypoxic vasoconstriction in terminal vessels cannot account for the elevation of PVR associated with hypoxic pulmonary vasoconstriction (HPV). Upstream signaling by conducted responses to engage constriction of arterioles, therefore, plays an essential role in the elevation of PVR during HPV.

Pulmonary oxygen uptake is affected by the transport characteristics of the alveolar‐capillary membrane as well as heterogeneity of pulmonary blood flow, both of which can limit the lung's capacity for oxygen transport as characterized by its effective diffusing capacity. In previous work, we showed that while under resting conditions the healthy lung has a high degree of tolerance for pulmonary flow heterogeneity, under conditions of exercise such flow heterogeneity can preclude the high levels of oxygen uptake necessary to meet tissue demand. The goal of the present study is to test the ability of hypoxic pulmonary vasoconstriction (HPV) to mitigate flow heterogeneity and enable adequate oxygen transport levels in the lung to meet tissue needs under conditions of exercise. A mathematical model of pulmonary oxygen uptake is used, in which flow heterogeneity is characterized by the coefficient of variation (CV) of pulmonary capillary blood flow. Assuming an initial lognormal distribution of blood flow with a high degree of heterogeneity, we simulate flow regulation in the cases of rest and exercise by adjusting pulmonary flow resistance in each vessel in accordance with previously published experimental data. The effect of HPV on vessel flow resistance is assumed to be characterized by a sigmoidal response dependent on the capillary oxygen tension, which is approximated as the mean of the venous and arterial values in each capillary. The results show a reduction in the effective CV from a baseline of 2.73 to 1.83 under resting conditions and to 0.66 in the case of exercise. The stronger reduction in heterogeneity under conditions of exercise corresponds to the need for greater flow regulation to minimize heterogeneity under conditions of physiologic stress. The predicted level of heterogeneity in exercise is in general agreement with our previous prediction of the upper limit of CV consistent with the levels of oxygen uptake in literature data for exercising humans. The results demonstrate the essential role of HPV to regulate flow and minimize heterogeneity under conditions of exercise and highlight the need for a functional pulmonary flow regulation mechanism under stressful or pathophysiological conditions. Support or Funding Information Supported by NIH U01 HL133362. This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal .

Microvascular blood flow regulation has important implications for optimization of metabolism‐perfusion matching in physiological and pathophysiological conditions such as exercise and sepsis. The purpose of this theoretical study is to assess the impact of various regulatory factors on metabolism‐perfusion matching. A microvascular network model including myogenic, shear, and metabolic flow regulation was developed and utilized to obtain estimates of oxygen extraction under control conditions as compared to a 20% global increase in blood flow accompanied by a 50% increase in oxygen consumption. The exercise state was simulated with preserved flow regulation and sepsis was simulated with impaired metabolic flow regulation. For the values of parameters used, overall oxygen extraction was found to be 28% higher in exercise compared to control values as opposed to only 23% higher in sepsis. This study demonstrates the impact of impaired flow regulation on oxygen delivery and highlights microvascular perfusion abnormalities as a putative mechanism for organ failure in critically ill patients.

The rate at which oxygen can be taken up into the bloodstream in the lung is a critical determinant of functional capacity, and can be affected by heterogeneity of pulmonary blood flow (leading to maldistribution and poor ventilation‐perfusion matching) as well as alterations in diffusing capacity. Under resting conditions, the high degree of reserve in the healthy lung leads to adequate oxygen uptake even in the face of increased heterogeneity or decreased diffusing capacity; under conditions of exercise, however, oxygen transport and utilization are contingent upon adequate lung function with relatively little reserve. A mathematical model of pulmonary oxygen uptake is used in this study to investigate the impact of pulmonary flow heterogeneity in exercise, which we characterize by the coefficient of variation (CV) of pulmonary capillary blood flow; under conditions of uniform alveolar ventilation, this is theoretically equivalent to impaired ventilation‐perfusion matching. We have previously demonstrated that any level of pulmonary heterogeneity up to a high degree (CV of approximately 3.0) is consistent with the observed level of arterial oxygen tension under resting conditions. We hypothesize that such high levels of heterogeneity would preclude the high oxygen uptake in the lung observed during exercise. In this study, literature data on humans under normoxic and hypoxic conditions was used to estimate the CV of pulmonary capillary blood flow under conditions of moderate and extreme exercise. With the assumption of a normal diffusing capacity, the best fit overall to aggregated data from five studies was found with a CV of 0.61. These results show that a high degree of pulmonary flow heterogeneity does not limit oxygen uptake at rest, but that in exercise much lower levels of heterogeneity are necessary to achieve observed oxygen fluxes. An important mechanism for reducing heterogeneity is flow regulation via hypoxic pulmonary vasoconstriction (HPV), which is activated at the low levels of venous oxygen tension in exercise. The results suggest that HPV plays an essential role in allowing high levels of pulmonary oxygen uptake in exercise. Support or Funding Information Supported by NIH U01 HL133362 This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal .