Article

Relating pulmonary oxygen uptake to muscle oxygen consumption at exercise onset: In vivo and in silico studies

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Abstract

Assessment of the rate of muscle oxygen consumption, UO2m, in vivo during exercise involving a large muscle mass is critical for investigating mechanisms regulating energy metabolism at exercise onset. While UO2m is technically difficult to obtain under these circumstances, pulmonary oxygen uptake, VO2p, can be readily measured and used as a proxy to UO2m. However, the quantitative relationship between VO2p and UO2m during the nonsteady phase of exercise in humans, needs to be established. A computational model of oxygen transport and utilization—based on dynamic mass balances in blood and tissue cells—was applied to quantify the dynamic relationship between model-simulated UO2m and measured VO2p during moderate (M), heavy (H), and very heavy (V) intensity exercise. In seven human subjects, VO2p and muscle oxygen saturation, StO2m, were measured with indirect calorimetry and near infrared spectroscopy (NIRS), respectively. The dynamic responses of VO2p and StO2m at each intensity were in agreement with previously published data. The response time of muscle oxygen consumption, \(\tau_{{\rm UO}_{{2{\rm m}}}},\) estimated by direct comparison between model results and measurements of StO2m was significantly faster (P < 0.001) than that of pulmonary oxygen uptake, \(\tau_{{\rm VO}_{{2{\rm p}}}},\) (M: 13 ± 4 vs. 65 ± 7 s; H: 13 ± 4 vs. 100 ± 24 s; V: 15 ± 5 vs. 82 ± 31 s). Thus, by taking into account the dynamics of oxygen stores in blood and tissue and determining muscle oxygen consumption from muscle oxygenation measurements, this study demonstrates a significant temporal dissociation between UO2m and VO2p at exercise onset.

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... However, cardiac output (Q ) dynamics can distort the V O 2musc response to V O 2pulm in a nonlinear fashion (10,37,47). In this regard, circulatory models can be applied that account for the time-delaying and distortive effects of venous return (e.g., amount of venous blood volume and Q dynamics) between the exercising musculature and the lungs (2,3,10,19,21,27,37,48). ...
... Consequently, the models are of practical interest for modeling venous return during exercise transients, as has been demonstrated by others (2,5,10,19,21,28,37,48,68). ...
... As demonstrated by the two examples in Fig. 7, V O 2pulm is unpredictable because of the combined and complex influences of venous return and Q dynamics. To sum up, the results are in line with those of others (37,47,48) who have suggested and illustrated significant temporal dissociations between V O 2musc and V O 2pulm kinetics. In this regard, the venous pathway of the nonexercising compartment(s) has the same a-vDO 2 at all times and therefore should have no impact on the resultant V O 2pulm kinetics. ...
Article
Purpose The aim of the present study was to investigate if a single- (SCM) and a multi-compartment venous return model (MCM) will produce significantly different time-delaying and distortive effects on the pulmonary oxygen uptake (V'O2pulm) responses with equal cardiac outputs (Q') and muscle oxygen uptake (V'O2musc) inputs. Methods For each model, 64 data sets were simulated with alternating Q' and V'O2musc kinetics - time constants (τ) ranging from 10 to 80 s - as responses to pseudorandom binary sequence work rate (WR) changes. Kinetic analyses were performed by using cross-correlation functions (CCF) between WR with V'O2pulm and V'O2musc, respectively. Higher maxima of the CCF courses indicate faster system responses - equal to smaller τ values of the variables of interest (e.g., τV'O2musc). Results The models demonstrated a highly significant relationship for the resulting V'O2pulm responses (r=0.976, p<0.001, n=64). Both models showed significant differences between V'O2pulm and V'O2musc kinetics for τV'O2musc ranging from 10 to 30 s (p<0.05 each). In addition, a significant difference in V'O2pulm kinetics (p<0.05) between the models was observed for very fast V'O2musc kinetics (τ=10s). Conclusions The combinations of fast Q' dynamics and slow V'O2musc kinetics yield distinct deviations in the resultant V'O2pulm responses compared to V'O2musc kinetics. Therefore, the venous return models should be used with care and caution if the aim is to infer V'O2musc by means of V'O2pulm kinetics. Finally, the resultant V'O2pulm responses seem to be complex and most likely unpredictable if no cardiodynamic measurements are available in vivo.
... Typically, the VO 2p response has two phases whose slopes are discontinuous: a short (∼20s) cardiac-dependent rise characterized by a circulatory transit time delay (Phase I) followed by a longer exponentialtype increase to a plateau (Phase II) [25] . The relationship between VO 2p and UO 2m dynamics has been studied under a variety of conditions [1,2,9,15] . From dynamic measurements of arterial and femoral venous blood and leg blood flow, Grassi et al. [9] evaluated muscle oxygen uptake (VO 2m ) dynamics, under the assumption its dynamics represents those of UO 2m , and observed that during the transition from light to moderate intensity exercise, the dynamics of VO 2p and VO 2m did not differ significantly. ...
... However, if oxygen stores are considered in a more general mathematical model of oxygen transport and utilization, then simulated exercise responses of VO 2p in Phase II and VO 2m may be different. Indeed, Lai et al. [15,17] used such a model to simulate VO 2m , and UO 2m dynamics in response to exercise. They estimated UO 2m dynamics from muscle oxygen saturation (StO 2m ) measurements performed via near-infrared spectroscopy (NIRS). ...
... The averaged oxy-myoglobin saturation in muscle tissue is S Mb =〈 S tis 〉. The spatially averaged saturations S cap,m 〉and 〈 S tis 〉.are defined as: (13) The oxy-hemoglobin and oxy-myoglobin saturations are related to free O 2 concentrations in blood and tissue [15] . ...
Article
To distinguish mechanisms of impaired muscle oxygen delivery and oxidative metabolism in response to exercise, we need to evaluate how these factors affect muscle oxygen utilization (UO2m), which represents cellular respiration. During human or animal exercise experiments, direct in vivo measurement of UO2m is not feasible. Instead, pulmonary oxygen uptake (VO2p), which represents external respiration, is measured noninvasively at the mouth as an indirect indicator of metabolic processes that control cellular respiration in the working skeletal muscles [1]. Factors that contribute to the differences between the dynamic responses of UO2m and VO2p are circulatory dynamics [2], ventilation, oxygen stored in blood and muscle [3], and oxygen exchange across membranes. Therefore, using VO2p as an indicator of metabolic processes may be misleading in the presence of various disease states. In chronic obstructive pulmonary disease [4], diabetes [5], [6], or chronic heart failure [7], the dynamic response of VO2p to exercise is abnormally slow. In type 2 diabetes, low muscle blood flow may impair oxygen delivery to the working muscle. Clinically, these diseases may impair the mitochondrial oxidative metabolism as well [8].
... To evaluate the effects of extra-vascular volume and blood volume distribution during exercise, a mathematical model was applied to quantify how these factors affect oxygen transport and utilization. 5,6,7 The mathematical model presented here is used to examine the effect of local muscle blood-tissue volume distribution on the responses of muscle oxygen saturation during exercise. Together with NIRS data, optimal estimates can be obtained of maximal metabolic flux (V max ) and blood flow increase (ΔQ) during exercise. ...
... In response to a step increase in work rate from rest, the dynamic response of blood flow Q at exercise is assumed to be exponential: 7 (5) where Q 0 is the steady-state flow before exercise, ΔQ=Q SS -Q 0 is the increase in blood flow between steady states, τ Q is the time constant of muscle blood flow, and t 0 is the time at the onset of exercise. Also, associated with blood flow increase in response to exercise, there is an effective increase in the rate coefficient of capillary-tissue transport: (6) where PS 0 is the steady-state rate coefficient before exercise, ΔPS is the increase in the rate coefficient, Q 0 is the steady-state blood flow, and q C is an arbitrary parameter. ...
... 6 The data, obtained from an experiment with a normal human subject, are typical of responses measured by NIRS for a step response to moderate intensity exercise from a warm-up steady state. 5,6 The transport processes (Eqs. 1 and 2) depend on the muscle blood composition and distribution (f bl ,ω cap ) in which f cap =f bl ωcap and (f tis =1-f bl ). In these equations that relate to the whole muscle, the same parameter values for muscle composition (Table 1) were used for all simulations. ...
Article
Muscle oxygenation measurements by near infrared spectroscopy (NIRS) are frequently obtained in humans to make inferences about mechanisms of metabolic control of respiration in working skeletal muscle. However, these measurements have technical limitations that can mislead the evaluation of tissue processes. In particular, NIRS measurements of working muscle represent oxygenation of a mix of fibers with heterogeneous activation, perfusion and architecture. Specifically, the relative volume distribution of capillaries, small arteries, and venules may affect NIRS data. To determine the effect of spatial volume distribution of components of working muscle on oxygen utilization dynamics and blood flow changes, a mathematical model of oxygen transport and utilization was developed. The model includes blood volume distribution within skeletal muscle and accounts for convective, diffusive, and reactive processes of oxygen transport and metabolism in working muscle. Inputs to the model are arterial O2 concentration, cardiac output and ATP demand. Model simulations were compared to exercise data from human subjects during a rest-to-work transition. Relationships between muscle oxygen consumption, blood flow, and the rate coefficient of capillary-tissue transport are analyzed. Blood volume distribution in muscle has noticeable effects on the optimal estimates of metabolic flux and blood flow in response to an exercise stimulus.
... Skeletal muscle O 2 utilization (V O 2m ) and O 2 delivery (Q O 2m ) are frequently estimated by measurements of pulmonary oxygen uptake (V O 2p ) and cardiac output (Q T), respectively. However, evidence points out that the speed of adjustment of pulmonary oxygen uptake to an exercise transition (V O 2p kinetics) dissociates from V O 2m kinetics because of circulatory and respiratory interactions at exercise onset (13,48,49). Moreover, variability of blood flow redistribution and vasodilatory capacity complicates the approximation of Q O 2m from cardiac output measurements (37,54,69). ...
... As such, these results fail to verify speeding of V O 2m kinetics. However, predictions from computational modeling showed that, in the presence of augmented tissue oxygen availability, speeded V O 2m kinetics would be more likely to increase than to decrease the time constant of phase II V O 2p kinetics (13,49). Hence, the higher resting SmO 2 values preceding the second exercise bout in the present study may indicate a supplementary local oxygen source delaying the increase of oxygen uptake at the lungs. ...
Article
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The extent and speed of transient skeletal muscle deoxygenation during exercise onset in chronic heart failure (CHF) patients is related to impairments of local O2 delivery and utilization. This study examined the physiological background of submaximal exercise performance in 19 moderately impaired CHF patients (Weber class A, B, and C) compared with 19 matched healthy control (HC) subjects by measuring skeletal muscle oxygenation (SmO2) changes during cycling exercise. All subjects performed two subsequent moderate-intensity 6-minute exercise tests (bout 1 and 2) with measurements of pulmonary oxygen uptake kinetics, and SmO2 using near infrared (NIR) spatially resolved spectroscopy (SRS) at the vastus lateralis for determination of absolute oxygenation values, amplitudes, kinetics (mean response time for onset), and deoxygenation overshoot characteristics. In CHF deoxygenation kinetics were slower compared with HC (21.3±5.3 s vs. 16.7±4.4 s, P<0.05, respectively). After priming exercise (i.e. during bout 2) deoxygenation kinetics were accelerated in CHF to values no longer different from HC (16.9±4.6 s vs. 15.4±4.2 s, P=0.35). However, priming did not speed deoxygenation kinetics in CHF subjects with a deoxygenation overshoot, while it did reduce the incidence of the overshoot in this specific group (P<0.05). These results provide evidence for heterogeneity with respect to limitations of O2 delivery and utilization during moderate-intensity exercise in CHF patients, with slowed deoxygenation kinetics indicating a predominant O2 utilization impairment, and the presence of a deoxygenation overshoot, with a reduction after priming in a subgroup, indicating an initial O2 delivery to utilization mismatch.
... Each of these changes appear to coincide with the ventilation threshold (VT) or respiratory compensation threshold (RCT) . Muscle oxygenation via NIRS during incremental exercise has been demonstrated by several studies to be useful for identifying the VT in a non-invasive way (Bhambhani, Buckley, & Susaki, 1997;Grassi et al., 1999;Lai et al., 2006;Xu, Mao, Ye, & Lv, 2011). VT and RCT is determined from metabolic data via the V-slope method (Beaver, Wasserman, & Whipp, 1986). ...
... Regardless, the current data cannot confirm the four characteristic phases as baseline and recovery data was not collected. For the same reason, VT could not be determined with NIRS data as baseline values are required as determined by previous studies (Bhambhani et al., 1997;Grassi et al., 1999;Lai et al., 2006;Xu et al., 2011). However, VT was found by graphing VCO 2 versus VO 2 and confirmed by a calculated slope (VCO 2 /VO 2 ) of ≥ 1 as described by Beaver et al., (1986). ...
Conference Paper
Purpose: The purpose of this study was to examine the effects of hypoxia and pacing strategy on central (brain) and peripheral (muscle) changes in competitive cyclists. Methods: Cyclists (n=10; ages=27 ± 6.3 yrs) performed a maximal aerobic power (VO2max = 53 ± 6.7ml·kg-1·min-1) test prior to two 20km time trials (20TT) in randomly assigned order; one in normoxia (N; 21% O2) and one in acute normobaric hypoxia (H; 15% O2; PB 713mmHg). Participants were blinded to performance variables. Near infrared spectroscopy (NIRS) was used continuously to monitor changes in pre-frontal cortex and vastus lateralis tissues. Rating of perceived exertion (RPE) was recorded every 4kms (subject blinded). Results: There was a significant reduction in time to completion (N = 51.2 ± 9.0mins, H= 57.1 ± 9.6mins) and WattsAVG (N = 237± 10.2W, H= 199±11.5W) during the hypoxic trial, but not RPE at any of the 5 intervals; an ‘endspurt’ was evident in both conditions. There was a significant pre-frontal cortex in HbO2AVG (N = 11.5 ± 6.2, H = 7.1 ± 5.1) and tHbAVG (N = 14.9 ± 7.3, H = 6.8 ± 5.9), and in the vastus lateralis in HbO2AVG (N = -1.2 ± 0.5, H = -2.8 ± 1.6), HHbAVG (N = 7.5 ± 0.7, H = 8.2 ± 0.9), and tHbAVG (N = 6.3 ± 0.9, H = 4.7 ± 1.5). Conclusions: These results suggest that in hypoxia the brain appears to be protected, and in the muscle there is a greater extraction of O2 to complete the same distance. Key Words: Fatigue, Hypoxia, NIRS, Continuous Exercise, Cyclists
... A model was developed that describes the dynamics of O 2 transport and utilization in contracting skeletal muscle during exercise [73]. The model takes into account the dynamics of O 2 stores in blood and tissue and muscle O 2 consumption is estimated from measurements of StO 2m and VO 2p . ...
... Author manuscript; available in PMC 2014 January 11. [68][69][70][71][72][73][74][75][76][77] Drug Discov Today Dis Models. Author manuscript; available in PMC 2014 January 11. ...
Article
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How does skeletal muscle manage to regulate the pathways of ATP synthesis during large-scale changes in work rate while maintaining metabolic homeostasis remains unknown. The classic model of metabolic regulation during muscle contraction states that accelerating ATP utilization leads to increasing concentrations of ADP and Pi, which serve as substrates for oxidative phosphorylation and thus accelerate ATP synthesis. An alternative model states that both the ATP demand and ATP supply pathways are simultaneously activated. Here, we review experimental and computational models of muscle contraction and energetics at various organizational levels and compare them with respect to their pros and cons in facilitating understanding of the regulation of energy metabolism during exercise in the intact organism.
... The development of mathematical models complements the experimental effort to understand the energetics of exercise (Tschakovsky et al., 2006;Lai et al., 2007). With respect to the VO 2 response to exercise, previous mathematical models have focused on the energetic and biochemical processes in skeletal muscle (Vicini and Kushmerick, 2000) and their coupling to whole-body (alveolar) VO 2 (Lai et al., 2006(Lai et al., , 2007. This focus is consistent with the evidence that shows the dynamic response of whole-body VO 2 is determined mainly by contracting skeletal muscles, at least during cycling (Poole et al., 1991;Grassi et al., 1996). ...
... This focus is consistent with the evidence that shows the dynamic response of whole-body VO 2 is determined mainly by contracting skeletal muscles, at least during cycling (Poole et al., 1991;Grassi et al., 1996). A common characteristic of these mathematical models is the simplifying assumption that the contracting skeletal muscle is a single homogeneous entity (Vicini and Kushmerick, 2000;Lai et al., 2006Lai et al., , 2007. The reality is, however, that for common forms of exercise (e.g. ...
Article
Full-text available
The response of oxygen uptake (VO 2 ) to exercise is multiphasic, each phase being exponential and often achieving a plateau before the next phase begins. Although the physiological processes underlying this multiphasic response are unclear, we assume that to some extent they reflect processes within contracting skeletal myocytes. To explore this further, a simple and novel dynamical model of motor unit behaviour during exercise is presented that captures essential features of the exercise VO 2 response.
... To simulate responses to exercise of human subjects, several model variables are related to measured variables. To simulate step changes between steady states at rest (j ϭ R), warm-up (j ϭ W), and moderate exercise (j ϭ E), we assume that OxPhos (32) by assuming that any increase in pulmonary oxygen uptake during exercise is directed to supporting the increased energy demand of working muscles: (10) Muscle blood flow at rest Q m R is 15% of the cardiac output at rest Q R (57). With a step increase in work rate from rest, the blood flow in muscle at the onset of contraction is assumed to immediately increase: ...
... Values of the volume fractions of muscle and blood (Table 4) at resting steady state (t ϭ 0) were applicable to all simulations. Values of the model parameters related to metabolic processes, transport equation, and O 2/Hb and O2/Mb equilibrium relationships (Tables 5 and 6) were the same for all the subjects as described previously (32)(33)(34). ...
Article
Noninvasive, continuous measurements in vivo are commonly used to make inferences about mechanisms controlling internal and external respiration during exercise. In particular, the dynamic response of muscle oxygenation (Sm(O(2))) measured by near-infrared spectroscopy (NIRS) is assumed to be correlated to that of venous oxygen saturation (Sv(O(2))) measured invasively. However, there are situations where the dynamics of Sm(O(2)) and Sv(O(2)) do not follow the same pattern. A quantitative analysis of venous and muscle oxygenation dynamics during exercise is necessary to explain the links between different patterns observed experimentally. For this purpose, a mathematical model of oxygen transport and utilization that accounts for the relative contribution of hemoglobin (Hb) and myoglobin (Mb) to the NIRS signal was developed. This model includes changes in microvascular composition within skeletal muscle during exercise and integrates experimental data in a consistent and mechanistic manner. Three subjects (age 25.6 +/- 0.6 yr) performed square-wave moderate exercise on a cycle ergometer under normoxic and hypoxic conditions while muscle oxygenation (C(oxy)) and deoxygenation (C(deoxy)) were measured by NIRS. Under normoxia, the oxygenated Hb/Mb concentration (C(oxy)) drops rapidly at the onset of exercise and then increases monotonically. Under hypoxia, C(oxy) decreases exponentially to a steady state within approximately 2 min. In contrast, model simulations of venous oxygen concentration show an exponential decrease under both conditions due to the imbalance between oxygen delivery and consumption at the onset of exercise. Also, model simulations that distinguish the dynamic responses of oxy-and deoxygenated Hb (HbO(2), HHb) and Mb (MbO(2), HMb) concentrations (C(oxy) = HbO(2) + MbO(2); C(deoxy) = HHb + HMb) show that Hb and Mb contributions to the NIRS signal are comparable. Analysis of NIRS signal components during exercise with a mechanistic model of oxygen transport and metabolism indicates that changes in oxygenated Hb and Mb are responsible for different patterns of Sm(O(2)) and Sv(O(2)) dynamics observed under normoxia and hypoxia.
... To date, no physiologically-based, whole-organ level model of skeletal muscle cellular metabolism and energetics has been developed that can be applied to analyze available in vivo experimental data and predict dynamic metabolic responses to physiological stimuli in subcellular compartments, such as mitochondria. Previous models have incorporated some aspects of glycolysis, TCA cycle, oxidative phosphorylation, and fatty acid b-oxidation3451112131415161718192021. None of them, however, include sufficient key substrates/metabolites and/or integrate metabolic pathways/reactions that are essential in the regulation of cellular metabolic processes in skeletal muscle in vivo at whole-organ level. ...
... These flux expressions characterize the behavior of saturable enzyme kinetics and in vivo control mechanisms observed experimentally [23,31]. In comparison to the previous models in the literature3451112131415161718192021 , the present model is a selfconsistent , physiologically-based, multi-scale computational model dealing with cellular metabolism and energetics in skeletal muscle in vivo at the whole-organ level. ...
Article
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Control mechanisms of cellular metabolism and energetics in skeletal muscle that may become evident in response to physiological stresses such as reduction in blood flow and oxygen supply to mitochondria can be quantitatively understood using a multi-scale computational model. The analysis of dynamic responses from such a model can provide insights into mechanisms of metabolic regulation that may not be evident from experimental studies. For the purpose, a physiologically-based, multi-scale computational model of skeletal muscle cellular metabolism and energetics was developed to describe dynamic responses of key chemical species and reaction fluxes to muscle ischemia. The model, which incorporates key transport and metabolic processes and subcellular compartmentalization, is based on dynamic mass balances of 30 chemical species in both capillary blood and tissue cells (cytosol and mitochondria) domains. The reaction fluxes in cytosol and mitochondria are expressed in terms of a general phenomenological Michaelis-Menten equation involving the compartmentalized energy controller ratios ATP/ADP and NADH/NAD(+). The unknown transport and reaction parameters in the model are estimated simultaneously by minimizing the differences between available in vivo experimental data on muscle ischemia and corresponding model outputs in coupled with the resting linear flux balance constraints using a robust, nonlinear, constrained-based, reduced gradient optimization algorithm. With the optimal parameter values, the model is able to simulate dynamic responses to reduced blood flow and oxygen supply to mitochondria associated with muscle ischemia of several key metabolite concentrations and metabolic fluxes in the subcellular cytosolic and mitochondrial compartments, some that can be measured and others that can not be measured with the current experimental techniques. The model can be applied to test complex hypotheses involving dynamic regulation of cellular metabolism and energetics in skeletal muscle during physiological stresses such as ischemia, hypoxia, and exercise.
... Em 1999, o mesmo grupo de autores apresentou a análise do metabolismo do lactato em exercício. 20 Lai et al, [21][22][23] do mesmo grupo de investigação, apresentaram versões melhoradas de modelos de transporte e utilização de O_2, incluindo a componente de regulação metabólica e do fluxo, com utilização da monitorização da oximetria do tecido muscular em situação de exercício de intensidade moderada, pesada e severa. ...
Article
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A prescrição do exercício pressupõe que se antecipe a tolerância ao esforço de cada indivíduo. Os erros e imprecisões na determinação da intensidade a prescrever e a complexidade da resposta fisiológica ao exercício comprometem a aplicação das orientações genéricas. A modelação matemática é uma ferramenta para a previsão da resposta fisiológica ao exercício e, por isso, pode tornar-se útil para melhorar a prescrição do exercício. Neste artigo é apresentado o modelo matemático adaptado e desenvolvido pelos autores. É feita referência às perspetivas de aplicação destas metodologias de investigação teórica, tanto no domínio da fisiologia do exercício como no da saúde das populações. Conclui-se ser oportuno a criação de um núcleo de investigação em medicina desportiva com inclusão da modelação matemática em sistemas dinâmicos.
... From there, inferences about aerobic metabolism (mitochondria) using pulmonary oxygen uptake (VO 2pulm ) as a surrogate for V O 2musc kinetics should be made with caution; in particular, if cardio-dynamic impacts are not considered during exercise transients. Thus, appropriate circulatory models are required to distinguish between V O 2pulm and V O 2musc (Barstow and Molé 1987;Barstow et al. 1990;Eßfeld et al. 1991;Cochrane and Hughson 1992;Lai et al. 2006Lai et al. , 2007Zhou et al. 2007Zhou et al. , 2008Zhou et al. , 2009Wagner 2011;Benson et al. 2013). It seems that V O 2pulm kinetics in most instances are not impacted by posture (Hughson et al. 1991(Hughson et al. , 1993Koga et al. 1999;DiMenna et al. 2010;Egaña et al. 2013), but there are also references illustrating that V O 2pulm kinetics are actually affected by body position (e.g., MacDonald et al. 1998). ...
Article
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Purpose The aim of the study was to compare the kinetics responses of heart rate (HR), pulmonary (\(\dot{V}\)O2pulm), and muscular (\(\dot{V}\)O2musc) oxygen uptake during dynamic leg exercise across different body positions (−6°, 45°, and 75°). Methods Ten healthy individuals [six men, four women; age 23.4 ± 2.8 years; height 179.7 ± 8.3 cm; body mass 73 ± 12 kg (mean ± SD)] completed pseudo-random binary sequence (PRBS) work rate (WR) changes between 30 and 80 W in each posture. HR was measured beat-to-beat by echocardiogram and \(\dot{V}\)O2pulm by breath-by-breath gas exchange. \(\dot{V}\)O2musc kinetics were assessed by the procedure of Hoffmann et al. (Eur J Appl Physiol 113:1745–1754, 2013) applying a circulatory model and cross-correlation functions (CCF). Results For \(\dot{V}\)O2pulm kinetics significant differences between −6° (CCF-values: 0.292 ± 0.040) and 45° (0.256 ± 0.034; p < 0.01; n = 10) as well as between −6° and 75° (0.214 ± 0.057; p < 0.05; n = 10) were detected at lag ‘40 s’ of the CCF course as interaction effects (factors: Lag × Posture). HR and \(\dot{V}\)O2musc kinetics yield no significant differences across the postures. Conclusions The analysis of cardio-dynamic and respiratory kinetics, especially with an emphasis on muscular and cellular level, has to consider venous return and cardiac output distortions. Simplified observations of kinetics responses resulting in time constants and time delays only should be replaced by the time-series analysis for a more sophisticated evaluation. The results illustrate that isolated \(\dot{V}\)O2pulm measurements without cardio-dynamic influences may not represent the kinetics responses originally revealed at muscular level.
... The blood supply for skeletal muscle alone is ~20% of cardiac output and O 2 consumption in muscle (UO 2m ) is ~20% of pulmonary O 2 uptake (VO 2p ) (91). During exercise, skeletal muscle accounts for most of the increase in cardiac output and oxygen uptake (81). These changes directly reflect the capacity of metabolic changes in skeletal muscle. ...
... Moreover, decrease in oxidative stress [15] and changes in mitochondrial function [16] have been reported after rhuEPO application in FRDA. Phosphorus 31 magnetic resonance spectroscopy (31P MRS) offers a non invasive investigation of human skeletal muscle bioenergetics by monitoring relative and absolute changes of phosphocreatine (PCr), inorganic phosphate (Pi) and adenosine triphosphate (ATP) during incremental exercise and recovery [17]. ATP production in skeletal muscle tissue relies on three main sources. ...
Article
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Friedreich ataxia (FRDA) is caused by a GAA repeat expansion in the FXN gene leading to reduced expression of the mitochondrial protein frataxin. Recombinant human erythropoietin (rhuEPO) is suggested to increase frataxin levels, alter mitochondrial function and improve clinical scores in FRDA patients. Aim of the present pilot study was to investigate mitochondrial metabolism of skeletal muscle tissue in FRDA patients and examine effects of rhuEPO administration by phosphorus 31 magnetic resonance spectroscopy (31P MRS). Seven genetically confirmed FRDA patients underwent 31P MRS of the calf muscles using a rest-exercise-recovery protocol before and after receiving 3000 IU of rhuEPO for eight weeks. FRDA patients showed more rapid phosphocreatine (PCr) depletion and increased accumulation of inorganic phosphate (Pi) during incremental exercise as compared to controls. After maximal exhaustive exercise prolonged regeneration of PCR and slowed decline in Pi can be seen in FRDA. PCr regeneration as hallmark of mitochondrial ATP production revealed correlation to activity of complex II/III of the respiratory chain and to demographic values. PCr and Pi kinetics were not influenced by rhuEPO administration. Our results confirm mitochondrial dysfunction and exercise intolerance due to impaired oxidative phosphorylation in skeletal muscle tissue of FRDA patients. MRS did not show improved mitochondrial bioenergetics after eight weeks of rhuEPO exposition in skeletal muscle tissue of FRDA patients. EU Clinical Trials Register2008-000040-13.
... However, changes in PS during the transition from rest to contraction are more difficult to assess or alter in vivo. To maintain the physiological partial pressure difference between capillary blood and intracellular O 2 (i.e., O 2 gradient) during the contraction transition from rest to steadystate contraction, PS must increase to deliver enough O 2 to meet metabolic demand (26). However, the rate of this increase has not been measured. ...
Article
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With current techniques, experimental measurements alone cannot characterize the effects of oxygen blood-tissue diffusion on muscle oxygen uptake (VO2) kinetics in contracting skeletal muscle. To complement experimental studies, a computational model is used to quantitatively distinguish the contributions of convective oxygen delivery, diffusion into cells, and oxygen utilization to VO2 kinetics. The model is validated using previously published experimental VO2 kinetics in response to slowed blood flow (Q) on-kinetics in canine muscle (τQ=20s, 46s, and 64s) (Goodwin ML, Hernández A, Lai N, Cabrera ME, Gladden LB. J Appl Physiol. 2012 112(1):9-19). Distinctive effects of permeability-surface area or diffusive conductance (PS) and Q on VO2 kinetics are investigated. Model simulations quantify the relationship between PS and Q, as well as the effects of diffusion associated with PS and Q dynamics on the mean response time of VO2. The model indicates that PS and Q are linearly related and that PS increases more with Q when convective delivery is limited by slower Q dynamics. Simulations predict that neither oxygen convective nor diffusive delivery are limiting VO2 kinetics in the isolated canine gastrocnemius preparation under normal spontaneous conditions during transitions from rest to moderate (submaximal) energy demand, although both operate close to the tipping point.
... The particular application that we consider in this paper is the estimation of the time course of mitochondrial oxygen consumption (nonmeasurable) in muscle tissue during muscle state transitions from rest to contraction and recovery, from the samples of its causally-related measurable effects, such as the dynamics of oxygen concentration in the surrounding medium [2,3]. Quantifying the time course of mitochondrial oxygen consumption during muscle activities is of great importance in the understanding of the dynamic regulation of oxidative phosphorylation and muscle energetics [3,4,5,13,14,15,16,17,18,19]. In a recent paper, Dash et al. [3] developed a computational model of oxygen transport and metabolism in a cylindrically-shaped muscle, immersed in vitro in an oxygenated chamber, and used a recently developed hierarchical Bayesian statistics-based parametric deconvolution algorithm [20] to obtain the estimate of the time course of mitochondrial oxygen consumption from the polarographic measurements of decayed oxygen concentration on the muscle surface (decayed oxygen partial pressure in the chamber) measured before, during and after an isometric twitch contraction of the muscle [19]. ...
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The reconstruction of an unknown input function from noisy measurements in a biological system is an ill-posed inverse problem. Any computational algorithm for its solution must use some kind of regularization technique to neutralize the disastrous effects of amplified noise components on the computed solution. In this paper, following a hierarchical Bayesian statistical inversion approach, we seek estimates for the input function and regularization parameter (hyperparameter) that maximize the posterior probability density function. We solve the maximization problem simultaneously for all unknowns, hyperparameter included, by a suitably chosen quasi-Newton method. The optimization approach is compared to the sampling-based Bayesian approach. We demonstrate the efficiency and robustness of the deconvolution algorithm by applying it to reconstructing the time courses of mitochondrial oxygen consumption during muscle state transitions (e.g., from resting state to contraction and recovery), from the simulated noisy output of oxygen concentration dynamics on the muscle surface. The model of oxygen transport and metabolism in skeletal muscle assumes an in vitro cylindrical structure of the muscle in which the oxygen from the surrounding oxygenated solution diffuses into the muscle and is then consumed by the muscle mitochondria. The algorithm can be applied to other deconvolution problems by suitably replacing the forward model of the system.
... The convection term depends on the difference of total arterial C a,tot and venous C b,tot concentrations of the species, where "total" means that in the oxygen and carbon dioxide concentrations, the oxy-hemoglobin, carbamino-hemoglobin and bicarbonate concentrations are taken into account in addition to the free dissolved concentrations (Dash & Bassingthwaighte, 2006;Lai et al., 2006). The factor Q(t) represents the blood flow, and F is the mixing ratio. ...
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In this article, the steady state condition for the multi-compartment models for cellular metabolism is considered. The problem is to estimate the reaction and transport fluxes, as well as the concentrations in venous blood when the stoichiometry and bound constraints for the fluxes and the concentrations are given. The problem has been addressed previously by a number of authors, and optimization-based approaches as well as extreme pathway analysis have been proposed. These approaches are briefly discussed here. The main emphasis of this work is a Bayesian statistical approach to the flux balance analysis (FBA). We show how the bound constraints and optimality conditions such as maximizing the oxidative phosphorylation flux can be incorporated into the model in the Bayesian framework by proper construction of the prior densities. We propose an effective Markov chain Monte Carlo (MCMC) scheme to explore the posterior densities, and compare the results with those obtained via the previously studied linear programming (LP) approach. The proposed methodology, which is applied here to a two-compartment model for skeletal muscle metabolism, can be extended to more complex models.
... THE OXYGEN CONSUMPTION RESPONSE to a step-like increase in energy demand has been studied extensively over the last few decades at various biological scales and under a variety of conditions (4,26,27,35,40,41,53,64). Indeed, oxygen consumption dynamics in response to various stimuli have been investigated in isolated mitochondria (10,11), isolated myocytes (62), muscle microvasculature (49), and isolated muscle preparations in situ (24), as well as in whole organisms (21,68). ...
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... This association has been experimentally confirmed using the direct Fick technique to determine m _ VO 2 across the contracting thigh muscle during upright cycle ergometry in humans (Grassi et al. 1996). In contrast, a recent computerised simulation found a significant dissociation between the mean response time for m _ VO 2 and p _ VO 2 at the onset of moderate (13 vs. 65 s), heavy (13 vs. 100 s) and very heavy (15 vs. 82 s) cycling exercise in adolescent boys (Lai et al. 2006). However, these results must be interpreted with caution as no attempt was made to characterise the phase II kinetics from the p _ VO 2 response profile, which clearly resulted in the development of the p _ VO 2 slow component during heavy and very heavy exercise. ...
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The energy demand imposed by physical exercise on the components of the oxygen transport and utilization system requires a close link between cellular and external respiration in order to maintain ATP homeostasis. Invasive and non-invasive experimental approaches have been used to elucidate mechanisms regulating the balance between oxygen supply and consumption during exercise. Such approaches suggest that the mechanism controlling the various subsystems coupling internal to external respiration are part of a highly redundant and hierarchical multi-scale system. In this work, we present a "systems biology" framework that integrates experimental and theoretical approaches able to provide simultaneously reliable information on the oxygen transport and utilization processes occurring at the various steps in the pathway of oxygen from air to mitochondria, particularly at the onset of exercise. This multi-disciplinary framework provides insights into the relationship between cellular oxygen consumption derived from measurements of muscle oxygenation during exercise and pulmonary oxygen uptake by indirect calorimetry. With a validated model, muscle oxygen dynamic responses is simulated and quantitatively related to cellular metabolism under a variety of conditions.
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Recent advances in near-infrared spectroscopy (NIRS) allow measurements of absolute tissue oxygen saturation (TOI) using spatially resolved spectroscopy (SRS), while enabling better depth sensitivity. However concerns remain regarding the relative contribution of the extracranial circulation to the cerebral NIRS TOI signal. In this study we investigated this during a period of selective rise in cerebral blood flow (CBF) produced by the administration of acetazolamide (ACZ) in 10 healthy volunteers. A two channel spectrometer (NIRO 300, Hamamatsu Photonics KK) was used to measure absolute cerebral TOI over the frontal cortex using the SRS technique using an optode spacing of 5 cm and 1.5 cm for channel 1 and 2 respectively. After ACZ administration we were able to observe a significant increase in the velocity of middle cerebral artery (V(mca), measured with the transcranial Doppler (TCD)) which was accompanied by an increase in TOI as monitored by the NIRO 300 with an optode spacing of 5 cm but not with an optode spacing of 1.5 cm. Furthermore a direct relationship was seen between the V(mca) and the TOI measured at 5 cm optode spacing. This work suggests that using this commercial NIRS instrument with an optode spacing of 5 cm one is able to detect the intracranial changes.
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Exposure of rats to mild hypoxia initially increases cerebral blood flow (CBF) as much as two-fold which maintains the arterial oxygen delivery rate. Several days after continued hypoxia, CBF decreases toward its baseline level as the blood oxygen carrying capacity is increased through increased hemoglobin content. Evidently, CBF regulation and the oxygen carrying capacity of blood are correlated. To quantitatively analyze the CBF control mechanisms associated with chronic hypoxia, a mathematical model was developed that describes the concentration dynamics of O2 and CO2 transport and metabolic processes in blood and brain tissue. In capillary blood, species transport processes were represented by a one-dimensional convection-dispersion model with diffusion between blood and tissue cells in the cortex and brain stem. Three possible control mechanisms for CBF in response to chronic hypoxia were analyzed: 1) local PO2 change in cerebral tissue; 2) reduced blood flow associated with elevated blood viscosity from increased Hct; 3) neurogenic input from O2 receptors in the brain stem. Our hypothesis is that increased PO2 in the brain stem is the signal for the return of CBF to its baseline condition. This PO2 increase results from an increase in arterial oxygen carrying capacity and a decrease in local energy metabolism. Model simulations quantify the relative contributions of each of these control mechanisms during 4 days of hypoxic exposure. These simulations are consistent with experimental data that show CBF returns to its baseline even though the cerebral cortical tissue remains hypoxic as indicated by increased levels of the transcription factor Hypoxia Inducible Factor-1 (HIF-1).
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Regulation of brain metabolism and cerebral blood flow involves complex control systems with several interacting variables at both cellular and organ levels. Quantitative understanding of the spatially and temporally heterogeneous brain control mechanisms during internal and external stimuli requires the development and validation of a computational (mathematical) model of metabolic processes in brain. This paper describes a computational model of cellular metabolism in blood-perfused brain tissue, which considers the astrocyte-neuron lactate-shuttle (ANLS) hypothesis. The model structure consists of neurons, astrocytes, extra-cellular space, and a surrounding capillary network. Each cell is further compartmentalized into cytosol and mitochondria. Inter-compartment interaction is accounted in the form of passive and carrier-mediated transport. Our model was validated against experimental data reported by Crumrine and LaManna, who studied the effect of ischemia and its recovery on various intra-cellular tissue substrates under standard diet conditions. The effect of ketone bodies on brain metabolism was also examined under ischemic conditions following cardiac resuscitation through our model simulations. The influence of ketone bodies on lactate dynamics on mammalian brain following ischemia is studied incorporating experimental data.
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The binding and buffering of O2 and CO2 in the blood influence their exchange in lung and tissues and their transport through the circulation. To investigate the binding and buffering effects, a model of blood-tissue gas exchange is used. The model accounts for hemoglobin saturation, the simultaneous binding of O2, CO2, H+, 2,3-DPG to hemoglobin, and temperature effects. Invertible Hill-type saturation equations facilitate rapid calculation of respiratory gas redistribution among the plasma, red blood cell and tissue that occur along the concentration gradients in the lung and in the capillary-tissue exchange regions. These equations are well-suited to analysis of transients in tissue metabolism and partial pressures of inhaled gas. The modeling illustrates that because red blood cell velocities in the flowing blood are higher than plasma velocities after a transient there can be prolonged differences between RBC and plasma oxygen partial pressures. The blood-tissue gas exchange model has been incorporated into a higher level model of the circulatory system plus pulmonary mechanics and gas exchange using the RBC and plasma equations to account for pH and CO2 buffering in the blood.
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A novel evanescent-based biosensor (Endotect, ThreeFold Sensors, Inc.) was developed with laser-based fiber optics using fluorescent dye-labeled recombinant human estrogen receptor-alpha (rhERalpha) and hERbeta as probes. A three-tiered approach evaluating various steps in the formation of the estrogen-receptor complex and its subsequent activity was developed for instrument calibration to detect estrogen mimics in biological samples, water and soil. Using this approach, binding affinities and activities of certain known estrogen mimics were determined for their use as calibrator molecules. Results indicated rhERalpha and rhERbeta may be employed as probes to distinguish estrogen mimics with a broad range of affinities. In addition, application of the biosensor for detecting DNA-binding proteins in human tissue extracts was demonstrated. The later studies suggest the biosensor may be used as a clinical laboratory tool for assessing tumor marker proteins.
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A three-tiered approach was developed to determine the influence of a chemically-diverse group of compounds exhibiting estrogen mimicry using recombinant human estrogen receptor (rhER) activity to calibrate a receptor protein-based biosensor. In the initial tier, a ligand competition array was developed to evaluate compounds inhibiting [3H]estradiol-17β binding to rhER. Each of six different concentrations of [3H]estradiol-17β was mixed with increasing concentrations of an unlabeled putative mimic. Each of these mixtures was incubated with a constant amount of rhERα and then receptorbound [[3H]estradiol-17β was measured. This array protocol analyzes ligand binding affinities of hERα with a potential inhibitor over the entire range of receptor protein saturation. When either hERα or hERβ binds to an estrogenic ligand, the receptor monomer forms both homo- and hetero-dimers. Then the ligand-receptor dimer complex activates transcription by associating with an estrogen response element (ERE), which is a specific DNA sequence located upstream of estrogenresponsive genes. The second tier for ligand evaluation utilized an electrophoretic mobility shift assay (EMSA), which was performed with an ERE sequence labeled with [α[32]P]dATP and incubated with rhER in the presence or absence of unlabeled ligand. ERE-hER complexes were separated by electrophoresis and analyzed using phosphor imaging technology. To assess biological effects of an estrogen mimic on expression of an ER-target gene, a yeast cell-based bioassay was constructed with recombinant DNA technology using Saccharomyces cerevisiae. Each of these engineered yeast cells contained a rhERα expression plasmid (YEpE12) and a separate reporter plasmid (YRG2) containing an ERE sequence upstream of a β-galactosidase reporter gene. Incubation of these yeast cells with an estrogenic compound allows formation of ligand-hERα complexes, which recognize the ERE sequence regulating β-galactosidase expression. Estrogenic compounds, which were evaluated as calibrators for ligand-based and EREbased biosensors, elicit varying responses in each of the three tiers of the protocol.
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In the last decade the study of the human brain and muscle energetics underwent a radical change, thanks to the progressive introduction of noninvasive techniques, including near-infrared (NIR) spectroscopy (NIRS). This review summarizes the most recent literature about the principles, techniques, advantages, limitations, and applications of NIRS in exercise physiology and neuroscience. The main NIRS instrumentations and measurable parameters will be reported. NIR light (700-1000 nm) penetrates superficial layers (skin, subcutaneous fat, skull, etc.) and is either absorbed by chromophores (oxy- and deoxyhemoglobin and myoglobin) or scattered within the tissue. NIRS is a noninvasive and relatively low-cost optical technique that is becoming a widely used instrument for measuring tissue O-2 saturation, changes in hemoglobin volume and, indirectly, brain/muscle blood flow and muscle O-2 consumption. Tissue O-2 saturation represents a dynamic balance between O-2 supply and O-2 consumption in the small vessels such as the capillary arteriolar and venular bed. The possibility of measuring the cortical activation in response to different stimuli, and the changes in the cortical cytochrome oxidase redox state upon O-2 delivery changes, will also be mentioned.
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New mathematical model equations for O2 and CO2 saturations of hemoglobin (SHbO2 and SHbCO2) are developed here from the equilibrium binding of O2 and CO2 with hemoglobin inside RBCs. They are in the form of an invertible Hill-type equation with the apparent Hill coefficients KHbO2 and KHbCO2 in the expressions for SHbO2 and SHbCO2 dependent on the levels of O2 and CO2 partial pressures (PO2 and PCO2), pH, 2,3-DPG concentration, and temperature in blood. The invertibility of these new equations allows PO2 and PCO2 to be computed efficiently from SHbO2 and SHbCO2 and vice-versa. The oxyhemoglobin (HbO2) and carbamino-hemoglobin (HbCO2) dissociation curves computed from these equations are in good agreement with the published experimental and theoretical curves in the literature. The model solutions describe that, at standard physiological conditions, the hemoglobin is about 97.2% saturated by O2 and the amino group of hemoglobin is about 13.1% saturated by CO2. The O2 and CO2 content in whole blood are also calculated here from the gas solubilities, hematocrits, and the new formulas for SHbO2 and SHbCO2. Because of the mathematical simplicity and invertibility, these new formulas can be conveniently used in the modeling of simultaneous transport and exchange of O2 and CO2 in the alveoli-blood and blood-tissue exchange systems.
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I.T.B.A.—National Research Council, Via F.lli Cervi 93, I-20090 Segrate (MI), Italy SYNOPSIS. The study of the kinetics of O2 consumption (VO2) at the onset and offset of constant-load submaximal exercise (VO2 on- and off-kinetics) is useful from a practical point of view (a faster adjustment of oxidative metabolism follow- ing an increased metabolic demand reduces the need for substrate level phosphor- ylation, with implications on exercise tolerance and muscle fatigue) and can give valuable insights into the regulation of oxidative metabolism in skeletal muscle. Measurements have been carried out both in man and in animals, at the tissue and at the whole body level. At the tissue level, the VO2 on- and off-kinetics were determined: a) Directly, by dynamic solution of the Fick equation throughout the transients; attempts were also made to obtain similar informations by near-infra- red spectroscopy. b) Indirectly, from the kinetics of phosphocreatine hydrolysis and resynthesis, by chemical methods or by 31P magnetic resonance spectroscopy. At the whole body level, VO2 on- and off-kinetics are determined from breath-by- breath measurements of pulmonary gas exchange. The VO2 5 f(t) function is a complex one, particularly during the on-transient. The so-called ''phase 2'' of the VO2 on-response, as well as the VO2 off-response, yield relevant metabolic infor- mations. In muscle the VO2 on- and off-kinetics are characterized by half-times (t‰) of 15-20 sec. At the whole-body level, t‰ of the VO2 on-kinetics show a wider variability, related to the experimental protocol and to other factors. The VO2 off- phase is more constant, and its kinetic parameters appear closer to those obtained at the tissue level. The study of the VO2 kinetics is valuable for a functional eval- uation of skeletal muscle oxidative metabolism. In ordinary conditions muscle VO2 kinetics appears mainly imposed by intrinsic (metabolic) rather than extrinsic (O 2 delivery) factors.
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New mathematical model equations for O(2) and CO(2) saturations of hemoglobin (S(HbO)(2) and S(HbCO)(2) are developed here from the equilibrium binding of O(2) and CO(2) with hemoglobin inside RBCs. They are in the form of an invertible Hill-type equation with the apparent Hill coefficients KHbO(2) and KHbCO(2) in the expressions for SHbO(2) and SHbCO(2) dependent on the levels of O(2) and CO(2) partial pressures (P(O)(2) and P(CO)(2)), pH, 2,3-DPG concentration, and temperature in blood. The invertibility of these new equations allows PO(2) and PCO(2) to be computed efficiently from S(HbO)(2) and S(HbCO)(2) and vice versa. The oxyhemoglobin (HbO(2)) and carbamino-hemoglobin (HbCO(2)) dissociation curves computed from these equations are in good agreement with the published experimental and theoretical curves in the literature. The model solutions describe that, at standard physiological conditions, the hemoglobin is about 97.2% saturated by O(2) and the amino group of hemoglobin is about 13.1% saturated by CO(2). The O(2) and CO(2) content in whole blood are also calculated here from the gas solubilities, hematocrits, and the new formulas for S(HbO)(2) and S(HbCO)(2). Because of the mathematical simplicity and invertibility, these new formulas can be conveniently used in the modeling of simultaneous transport and exchange of O(2) and CO(2) in the alveoli-blood and blood-tissue exchange systems.
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It is not known whether the asymptotic behavior of whole body O2 consumption (VO2) at maximal work rates (WR) is explained by similar behavior of VO2 in the exercising legs. To resolve this question, simultaneous measurements of body and leg VO2 were made at submaximal and maximal levels of effort breathing normoxic and hypoxic gases in seven trained male cyclists (maximal VO2, 64.7 +/- 2.7 ml O2.min-1.kg-1), each of whom demonstrated a reproducible VO2-WR asymptote during fatiguing incremental cycle ergometry. Left leg blood flow was measured by constant-infusion thermodilution, and total leg VO2 was calculated as the product of twice leg flow and radial arterial-femoral venous O2 concentration difference. The VO2-WR relationships determined at submaximal WR's were extrapolated to maximal WR as a basis for assessing the body and leg VO2 responses. The differences between measured and extrapolated maximal VO2 were 235 +/- 45 (body) and 203 +/- 70 (leg) ml O2/min (not significantly different). Plateauing of leg VO2 was associated with, and explained by, plateauing of both leg blood flow and O2 extraction and hence of leg VO2. We conclude that the asymptotic behavior of whole body VO2 at maximal WRs is a direct reflection of the VO2 profile at the exercising legs.
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Muscle O2 uptake (VO2) kinetics in response to an augmented energetic requirement (on-transition) has never been directly determined in humans. We have developed a constant-infusion thermodilution technique that allowed rapid measurements of leg blood flow (Qleg) and, in conjunction with frequent serial measurement of arteriovenous O2 content difference across the leg [(Ca - Cv)O2leg], permitted the determination of the VO2 of the leg (VO2leg) at 3- to 4-s time intervals. VO2leg kinetics during the on-transition was taken as a close approximation of muscle VO2 (VO2mus) kinetics. Alveolar VO2 (VO2A), Qleg, leg O2 delivery [(Q.CaO2leg)], (Ca - Cv)O2leg, and VO2leg kinetics were determined in six trained subjects [age 22.8 +/- 4.4 (SD) yr; maximal O2 uptake 59.1 +/- 5.3 ml.kg-1.min-1] during the transition from unloaded pedaling to a workload (loaded pedaling; LP) (183 +/- 20 W) well below the previously determined ventilatory threshold. For all variables, two distinct phases were recognized. During the first 10-15 s of loaded pedaling (phase I), VO2A, Qleg, and (Q.CaO2)leg increased rapidly, whereas VO2leg increased only slightly and (Ca - Cv)O2leg actually decreased. After phase I, all variables showed a monoexponential increase (phase II), with similar time courses [slightly faster for (Ca - CV)O2leg]. In a consideration of both phases, the half times of the responses among variables were not significantly different: 25.5 +/- 2.6 s for VO2A, 26.6 +/- 7.6 s for Qleg, 26.9 +/- 8.3 s for (Q.CaO2leg, 23.5 +/- 1.3 s for (Ca - Cv)O2leg, and 27.9 +/- 5.7 s for VO2leg. We conclude that during the on-transition the kinetics of VO2A and VO2leg, as measured by these methods, are similar. The analysis of the early phase (first 10-15 s) of the on-transition indicates that bulk delivery of O2 to the working muscles is not limiting VO2leg kinetics. However, the present results cannot discriminate between maldistribution of blood flow/VO2 vs. inertia the intracellular oxidative machinery as the limiting factor.
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Relations between organs and body size are not linear but rather follow allometric (growth) relations characterized by their powers (exponents). Stroke volume (SV) by M-mode echocardiography was related to height, weight, body surface area (BSA), and ideal BSA (derived from ideal body weight for given height) in 970 normotensive individuals (1 day to 85 years old; 426 < 18 years old; 204 overweight to obese; 426 female). In normal-weight children, adults, and the entire population, SV was related by allometric relations to BSA (power = 0.82 to 1.19), body weight (power = 0.57 to 0.71), and height (power = 1.45 to 2.04) (all P < .0001). Relations of cardiac output to measures of body size had lower allometric powers than those for SV in the entire population (0.41 for body weight, 0.62 for BSA, and 1.16 for height). In overweight adults, observed SVs were 17% greater than predicted for ideal BSA, a difference that was approximated by normalization of SV for height to age-specific allometric powers. Similarly, observed cardiac output was 19% greater than predicted for ideal BSA, a difference that was accurately detected by use of cardiac output/height to age-specific allometric powers but not of BSA to the first power. Indices of SV and cardiac output for BSA are pertinent when the effect of obesity needs to be removed, because these indices obscure the impact of obesity. To detect the effect of obesity on LV pump function, normalization of SV and cardiac output for ideal BSA or for height to its age-specific allometric power should be practiced.
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1H NMR has detected both the deoxygenated proximal histidyl NdeltaH signals of myoglobin (deoxyMb) and deoxygenated Hb (deoxyHb) from human gastrocnemius muscle. Exercising the muscle or pressure cuffing the leg to reduce blood flow elicits the appearance of the deoxyMb signal, which increases in intensity as cellular PO2 decreases. The deoxyMb signal is detected with a 45-s time resolution and reaches a steady-state level within 5 min of pressure cuffing. Its desaturation kinetics match those observed in the near-infrared spectroscopy (NIRS) experiments, implying that the NIRS signals are actually monitoring Mb desaturation. That interpretation is consistent with the signal intensity and desaturation of the deoxyHb proximal histidyl NdeltaH signal from the beta-subunit at 73 parts per million. The experimental results establish the feasibility and methodology to observe the deoxyMb and Hb signals in skeletal muscle, help clarify the origin of the NIRS signal, and set a stage for continuing study of O2 regulation in skeletal muscle.
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In the past, the measurement of O(2) consumption ((2)) by the muscle could be carried out noninvasively by near-infrared spectroscopy from oxyhemoglobin and/or deoxyhemoglobin measurements only at rest or during steady isometric contractions. In the present study, a mathematical model is developed allowing calculation, together with steady-state levels of (2), of the kinetics of (2) readjustment in the muscle from the onset of ischemic but aerobic constant-load isotonic exercises. The model, which is based on the known sequence of exoergonic metabolic pathways involved in muscle energetics, allows simultaneous fitting of batched data obtained during exercises performed at different workloads. A Monte Carlo simulation has been carried out to test the quality of the model and to define the most appropriate experimental approach to obtain the best results. The use of a series of experimental protocols obtained at different levels of mechanical power, rather than repetitions of the same load, appears to be the most suitable procedure.
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Near-infrared spectroscopy (NIRS) was utilized to gain insights into the kinetics of oxidative metabolism during exercise transitions. Ten untrained young men were tested on a cycle ergometer during transitions from unloaded pedaling to 5 min of constant-load exercise below (<VT) or above (>VT) the ventilatory threshold. Vastus lateralis oxygenation was determined by NIRS, and pulmonary O2 uptake (Vo --> Vo2) was determined breath-by-breath. Changes in deoxygenated hemoglobin + myoglobin concentration Delta[deoxy(Hb + Mb)] were taken as a muscle oxygenation index. At the transition, [Delta[deoxy(Hb + Mb)]] was unmodified [time delay (TD)] for 8.9 +/- 0.5 s at <VT or 6.4 +/- 0.9 s at >VT (both significantly different from 0) and then increased, following a monoexponential function [time constant (tau) = 8.5 +/- 0.9 s for <VT and 7.2 +/- 0.7 s for >VT]. For >VT a slow component of Delta[deoxy(Hb + Mb)] on-kinetics was observed in 9 of 10 subjects after 75.0 +/- 14.0 s of exercise. A significant correlation was described between the mean response time (MRT = TD + tau) of the primary component of Delta[deoxy(Hb + Mb)] on-kinetics and the tau of the primary component of the pulmonary Vo2 on-kinetics. The constant muscle oxygenation during the initial phase of the on-transition indicates a tight coupling between increases in O2 delivery and O2 utilization. The lack of a drop in muscle oxygenation at the transition suggests adequacy of O2 availability in relation to needs.
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This review focuses on the theory of oxygen transport to tissue and presents the state of the art in mathematical modeling of transport phenomena. Results obtained with the classic Krogh tissue-cylinder model and recent advances in mathematical modeling of hemoglobin-oxygen kinetics, the role of hemoglobin and myoglobin in facilitating oxygen diffusion, and the role of morphologic and hemodynamic heterogeneities in oxygen transport in the microcirculation are critically discussed. Mathematical models simulate different parts of the pathway of oxygen molecules from the red blood cell, through the plasma, the endothelial cell, other elements of the vascular wall, and the extra- and intracellular space. Special attention in the review is devoted to intracapillary transport, which has been the subject of intensive theoretical research in the last decade. Models of pre- and postcapillary oxygen transport are also discussed. Applications to specific organs and tissues are reviewed, including skeletal muscle, myocardium, brain, lungs, arterial wall, and skin. Unresolved problems and major gaps in our knowledge of the mechanisms of oxygen transport are identified.
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The study of the kinetics of O2 consumption (V&dot;o2) at the onset and offset of constant-load submaximal exercise (V&dot;o2 on- and off-kinetics) is useful from a practical point of view (a faster adjustment of oxidative metabolism following an increased metabolic demand reduces the need for substrate level phosphorylation, with implications on exercise tolerance and muscle fatigue) and can give valuable insights into the regulation of oxidative metabolism in skeletal muscle. Measurements have been carried out both in man and in animals, at the tissue and at the whole body level. At the tissue level, the V&dot;o2 on- and off-kinetics were determined: a) Directly, by dynamic solution of the Fick equation throughout the transients; attempts were also made to obtain similar informations by near-infrared spectroscopy. b) Indirectly, from the kinetics of phosphocreatine hydrolysis and resynthesis, by chemical methods or by 31P magnetic resonance spectroscopy. At the whole body level, V&dot;o2 on- and off-kinetics are determined from breath-by-breath measurements of pulmonary gas exchange. The V&dot;o2 = f(t) function is a complex one, particularly during the on-transient. The so-called “phase 2” of the V&dot;o2 on-response, as well as the V&dot;o2 off-response, yield relevant metabolic informations. In muscle the V&dot;o2 on- and off-kinetics are characterized by half-times (t½) of 15–20 sec. At the whole-body level, t½ of the V&dot;o2 on-kinetics show a wider variability, related to the experimental protocol and to other factors. The V&dot;o2 off-phase is more constant, and its kinetic parameters appear closer to those obtained at the tissue level. The study of the V&dot;o2 kinetics is valuable for a functional evaluation of skeletal muscle oxidative metabolism. In ordinary conditions muscle V&dot;o2 kinetics appears mainly imposed by intrinsic (metabolic) rather than extrinsic (O2 delivery) factors.
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Described is a two-semester, first year graduate level course offered at the University of Notre Dame on mathematical methods in chemical engineering. An unusual characteristic of the course is that the lectures are given on transparencies shown by an overhead projector, the students receiving printed copies of the transparencies. (BT)
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Cardiac performance during bicycle ergometer tests with increasing loads was examined in 12- and 14-year-old boys at different stages of puberty, professionally trained in basketball and swimming, as well as in boys of the same age without regular athletic training. In all these boys, the cardiac chronotropic response grew in intensity with the power and duration of exercise, being maximal in 14-year-old adolescents untrained athletically. During exercise at 0.5 W/kg, the cardiac chronotropic function stabilized within the first ten seconds; at 1.0 and 1.5 W/kg, the heart rate increased more or less monotonically throughout the entire test period. In 12- and 14-year-old swimmers and in untrained boys, the threshold value for an adequate hemodynamic response was found at 0.5 W/kg. The patterns of stroke volume adaptation to increasing loads were shown to be dependent on athletic specialization and independent of age. During the first 30 s of exercise at 0.5 W/kg, cardiac output increased significantly over its basal level. Subsequent load increases to 1.0 and 1.5 W/kg were accompanied by progressive growth of this parameter during the whole period of exercise. Upon transition to a different workload, the increment of cardiac output decreased.
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The dislocation pile‐up avalanche model is used to explain the crystal size dependence for hot spot‐controlled initiation of chemical decomposition in cyclotrimethylenetrinitramine crystals subjected to drop‐weight impact testing. Deformation‐induced temperature rises, hot spot sizes, and lifetimes are related to previously reported values for direct thermal decomposition. A reasonable chemical reaction yield is estimated from available kinetic data.
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The inhomogeneity of tissue structure greatly affects the sensitivity of tissue oxygenation measurement by reflectance near-infrared spectroscopy. In this study, we investigated the influence of a fat layer on muscle oxygenation measurement by in vivo tests and Monte Carlo simulation, and we propose a method for correcting the influence. In the simulation, a three-dimensional model consisting of the epidermis, dermis, fat, and muscle layers was used. In in vivo tests, measurement sensitivity was examined by measuring oxygen consumption of the forearm muscle and the peak-to-peak variation of oxygenation in periodic exercise tests on the vastus lateralis using a newly developed multisensor type of tissue oximeter. Fat layer thickness was also measured by ultrasonography. The correction curve of measurement sensitivity against fat layer thickness was obtained from the results of simulation and in vivo tests. The values of corrected oxygen consumption were almost the same and had less variation between individuals (0.13±0.02  ml 100 g <sup> -1 </sup>  min <sup> -1 </sup>) than did the uncorrected values (0.08±0.04  ml 100 g <sup> -1 </sup>  min <sup> -1 </sup>). © 2000 American Institute of Physics.
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NL2SOL is a modular program for solving nonhnear least-squares problems that incorporates a number of novel features. It maintains a secant approximation S to the second-order part of the leastsquares Hessian and adaptively decides when to use this approximation. S is "sized" before updating, something that is similar to Oren-Luenberger scaling. The step choice algorithm is based on minimizing a local quadratic model of the sum of squares ftmctmn constrained to an elhptmal trust regmn centered at the current approximate minimizer This is accomphshed using ideas chscussed by Mor6, together with a special module for assessing the quahty of the step thus computed. These and other ideas behind NL2SOL are discussed, and its evolution and current implementation are also described briefly.
Article
(1)H-NMR experiments have determined intracellular O(2) consumption (Vo(2)) with oxymyoglobin (MbO(2)) desaturation kinetics in human calf muscle during plantar flexion exercise at 0.75, 0.92, and 1.17 Hz with a constant load. At the onset of muscle contraction, myoglobin (Mb) desaturates rapidly. The desaturation rate constant of approximately 30 s reflects the intracellular Vo(2). Although Mb desaturates quickly with a similar time constant at all workload levels, its final steady-state level differs. As work increases, the final steady-state cellular Po(2) decreases progressively. After Mb desaturation has reached a steady state, however, Vo(2) continues to rise. On the basis of current respiratory control models, the analysis in the present report reveals two distinct Vo(2) phases: an ADP-independent phase at the onset of contraction and an ADP-dependent phase after Mb has reached a steady state. In contrast to the accepted view, the initial intracellular Vo(2) shows that oxidative phosphorylation can support up to 36% of the energy cost, a significantly higher fraction than expected. Partitioning of the energy flux shows that a 31% nonoxidative component exists and responds to the dynamic energy utilization-restoration cycle (which lasts for only milliseconds) as postulated in the glycogen shunt theory. The present study offers perspectives on the regulation of respiration, bioenergetics, and Mb function during muscle contraction.
Article
The halftimes (t1/2) of the VO2 on-and off-responses have been determined on 4 moderately active subjects (1) in arm cranking (VO2 congruent to 1 1/min). (2) in leg pedaling at 4 graded submaximal (VO2 congruent to 0.8 to 2.51/min) work loads, and (3) when superimposing arm cranking on preexisting leg pedaling, both in the supine and in the upright position. In supine experiments the mean t1/2 of the VO2 on-response was longer for arm cranking than for leg pedaling (64 vs 44-49 sec) at equal VO2; however, at the same percentage of arm and leg VO2 max the respective t1/2 were similar. In sitting experiments all t1/2 of the VO2 on-response were shorter than when supine, but the t1/2 for the arms were still slightly longer than those for the legs. When arm cranking was superimposed on preexisting leg pedaling, the t1/4 for arms was reduced both in supine (from 64 to 35-38 sec) and in the sitting position (from 44 to 40 sec). The halftime of the VO2 off-response were much shorter (20-32 sec) than those of the on-response and similar in all experiments. In all conditions the O2 deficits at work onset were considerably larger than the fast component of the corresponding O2 debts during the first minutes of recovery. The difference was totally accounted for by anaerobic glycolysis occurring early during the VO2 on-response, particularly in arm exercise. It is concluded that at submaximal work loads the O2 deficit is accounted for the fast component of the O2 debt plus the O2 equivalent of the early lactate production.
Article
Insights into muscle energetics during exercise (e.g., muscular efficiency) are often inferred from measurements of pulmonary gas exchange. This procedure presupposes that changes of pulmonary O2 (VO2) associated with increases of external work reflect accurately the increased muscle VO2. The present investigation addressed this issue directly by making simultaneous determinations of pulmonary and leg VO2 over a range of work rates calculated to elicit 20-90% of maximum VO2 on the basis of prior incremental (25 or 30 W/min) cycle ergometry. VO2 for both legs was calculated as the product of twice one-leg blood flow (constant-infusion thermodilution) and arteriovenous O2 content difference across the leg. Measurements were made 3-5 min after each work rate imposition to avoid incorporation of the VO2 slow component above the lactate threshold. For all 17 subjects, the slope of pulmonary VO2 (9.9 +/- 0.2 ml O2.W-1.min-1) was not different (P greater than 0.05) from that for leg VO2 (9.2 +/- 0.6 ml O2.W-1.min-1). Estimation of "delta" efficiency (i.e., delta work accomplished divided by delta energy expended, calculated from slope of VO2 vs. work rate and a caloric equivalent for O2 of 4.985 cal/ml) using pulmonary VO2 measurements (29.1 +/- 0.6%) was likewise not significantly different (P greater than 0.05) from that made using leg VO2 measurements (33.7 +/- 2.4%). These data suggest that the net VO2 cost of metabolic "support" processes outside the exercising legs changes little over a relatively broad range of exercise intensities. Thus, under the conditions of this investigation, changes of VO2 measured from expired gas reflected closely those occurring within the exercising legs.
Article
The effect of cardiovascular adjustments on the coupling of cellular to pulmonary gas exchange during unsteady states of exercise remains controversial. Computer simulations were performed to assess these influences on O2 delivery and pulmonary O2 uptake (pVO2). Algorithms were developed representing muscle and "rest-of-body" compartments, connected in parallel by arterial and venous circulations to a pump-and-lungs compartment. Exercise-induced increases in VO2 and cardiac output went to the muscle compartment. Model parameters [e.g., time constants for blood flow and muscle O2 uptake (mVO2)] could be varied independently. Simulation results demonstrated that 1) the rise in pVO2 during exercise contains three phases; 2) the contribution of changes in venous O2 stores to pVO2 kinetics and the O2 deficit occur almost entirely in phase 1; 3) under a wide variety of manipulations, the kinetics of pVO2 in phase 2 were within a couple of seconds of that assigned to mVO2 (i.e., there is not an obligatory slowing of VO2 kinetics at the lungs relative to those at the muscles; 4) by use of available estimates of blood flow adjustment, O2 delivery would not limit mVO2 after exercise onset; and 5) blood flow could limit O2 delivery in recovery, if blood flow returned to base-line levels at rates similar to those during the on-transient phase.
Article
Excess CO2 is generated when lactate is increased during exercise because its [H+] is buffered primarily by HCO-3 (22 ml for each meq of lactic acid). We developed a method to detect the anaerobic threshold (AT), using computerized regression analysis of the slopes of the CO2 uptake (VCO2) vs. O2 uptake (VO2) plot, which detects the beginning of the excess CO2 output generated from the buffering of [H+], termed the V-slope method. From incremental exercise tests on 10 subjects, the point of excess CO2 output (AT) predicted closely the lactate and HCO-3 thresholds. The mean gas exchange AT was found to correspond to a small increment of lactate above the mathematically defined lactate threshold [0.50 +/- 0.34 (SD) meq/l] and not to differ significantly from the estimated HCO-3 threshold. The mean VO2 at AT computed by the V-slope analysis did not differ significantly from the mean value determined by a panel of six experienced reviewers using traditional visual methods, but the AT could be more reliably determined by the V-slope method. The respiratory compensation point, detected separately by examining the minute ventilation vs. VCO2 plot, was consistently higher than the AT (2.51 +/- 0.42 vs. 1.83 +/- 0.30 l/min of VO2). This method for determining the AT has significant advantages over others that depend on regular breathing pattern and respiratory chemosensitivity.
Article
Five subjects exercised with the knee extensor of one limb at work loads ranging from 10 to 60 W. Measurements of pulmonary oxygen uptake, heart rate, leg blood flow, blood pressure and femoral arterial-venous differences for oxygen and lactate were made between 5 and 10 min of the exercise. Flow in the femoral vein was measured using constant infusion of saline near 0 degrees C. Since a cuff was inflated just below the knee during the measurements and because the hamstrings were inactive, the measured flow represented primarily the perfusion of the knee extensors. Blood flow increased linearly with work load right up to an average value of 5.7 l min-1. Mean arterial pressure was unchanged up to a work load of 30 W, but increased thereafter from 100 to 130 mmHg. The femoral arterial-venous oxygen difference at maximum work averaged 14.6% (v/v), resulting in an oxygen uptake of 0.80 l min-1. With a mean estimated weight of the knee extensors of 2.30 kg the perfusion of maximally exercising skeletal muscle of man is thus in the order of 2.5 l kg-1 min-1, and the oxygen uptake 0.35 l kg-1 min-1. Limitations in the methods used previously to determine flow and/or the characteristics of the exercise model used may explain why earlier studies in man have failed to demonstrate the high perfusion of muscle reported here. It is concluded that muscle blood flow is closely related to the oxygen demand of the exercising muscles. The hyperaemia at low work intensities is due to vasodilatation, and an elevated mean arterial blood pressure only contributes to the linear increase in flow at high work rates. The magnitude of perfusion observed during intense exercise indicates that the vascular bed of skeletal muscle is not a limiting factor for oxygen transport.
Article
The oxygen consumption together with lactic acid production and concentration of ATP, ADP, and creatinephosphate was measured during exercise and recovery on an isolated dog gastrocnemius. Oxygen debt contraction and payment follow an exponential path with a half reaction time of about 20 sec. The concentration of ATP and ADP at steady state seem to be unaffected by the intensity of the exercise when this is submaximal and no appreciable production of lactic acid takes place. The concentration of creatinephosphate in muscle at steady state decreases with the intensity of the exercise. The ratio of the oxygen consumption at steady state to the alactic oxygen debt is identified with the speed constant of the resynthesis of phosphagen in muscle; the half reaction time of this process is 17–20 sec. The total alactic oxygen debt amounts to about 50 ml/kg of muscle. These figures are in good agreement with earlier data found in man.
Article
To examine the relationship between body weight in children and aerobic parameters of exercise, we determined the anaerobic threshold (AT), maximum O2 uptake (VO2max), work efficiency, and response time for O2 uptake (RT-VO2) in 109 healthy children (51 girls and 58 boys, range 6-17 yr old) using a cross-sectional study design. Gas exchange during exercise was measured breath by breath. The protocol consisted of cycle ergometry and a linearly increasing work rate (ramp) to the limit of the subject's tolerance. Both AT and VO2max increased systematically with body weight, whereas work efficiency and RT-VO2 were virtually independent of body size. The ratio of AT to VO2max decreased slightly with age, and its mean value was 60%. AT scaled to body weight to the power of 0.92, not significantly different from the power of 1.01 for VO2max. Thus both the AT and the VO2max increase in a highly ordered manner with increasing size, and as judged by AT/VO2max, the onset of anaerobic metabolism during exercise occurred at a relatively constant proportion of the overall limit of the gas transport system. We conclude that in children cardiorespiratory responses to exercise are regulated at optimized values despite overall change in body size during growth.
Article
Single-breath O2 consumption (VO2) at the mouth and heart rate were determined in five healthy male subjects at rest, during 8 min of cycloergometric exercise (50, 100, 125, and 150 W), and in the recovery period following two experimental conditions: air breathing throughout (AA); hypoxic breathing (FIO2 = 0.11) for 6 min of preexercise rest followed by air breathing from the onset of exercise (HA). The O2 deficits and debts as well as the t 1/2 values of the VO2 on- and off-responses were determined and blood lactate concentrations measured at rest and in the recovery after 4 and 8 min of exercise. At all work loads: 1) O2 deficits were on the average 0.39 liter smaller in HA than in AA; 2) VO2 on-responses were faster in HA (t 1/2 approximately equal to 7 s) than in AA (t 1/2 = 20-30 s); and 3) O2 debts and VO2 off-responses were the same in the two conditions. Since the VO2 and heart rate levels at steady state as well as the blood lactate concentrations after 4 and 8 min of exercise were the same in AA and HA, the observed differences of O2 deficit cannot be attributed to changes of energy metabolism in the two conditions; they therefore depend on the reduction of body O2 stores at rest in HA. This, independently measured, was found to be 0.46 liters, not far from the observed O2 deficit difference (0.39 liters). Thus a decrease of O2 stores before exercise is accompanied by a reduction of the O2 deficit and faster VO2 kinetics at the onset of exercise.