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1.
The aim of this study was to test the hypothesis that allopurinol ingestion modifies the slow component of V(.)O(2) kinetics and changes plasma oxidative stress markers during severe intensity exercise. Six recreationally active male subjects were randomly assigned to receive a single dose of allopurinol (300 mg) or a placebo in a double-blind, placebo-controlled crossover design, with at least 7 days washout period between the two conditions. Two hours following allopurinol or placebo intake, subjects completed a 6-min bout of cycle exercise with the power output corresponding to 75 % V(.)O(2)max. Blood samples were taken prior to commencing the exercise and then 5 minutes upon completion. Allopurinol intake caused increase in resting xanthine and hypoxanthine plasma concentrations, however it did not affect the slow component of oxygen uptake during exercise. Exercise elevated plasma inosine, hypoxanthine, and xanthine. Moreover, exercise induced a decrease in total antioxidant status, and sulfhydryl groups. However, no interaction treatment x time has been observed. Short term severe intensity exercise induces oxidative stress, but xanthine oxidase inhibition does not modify either the kinetics of oxygen consumption or reactive oxygen species overproduction.  相似文献   

2.
We hypothesized that the metabolic acidosis resulting from the performance of multiple-sprint exercise would enhance muscle perfusion and result in a speeding of pulmonary oxygen uptake (VO2)kinetics during subsequent perimaximal-intensity constant work rate exercise, if O2 availability represented a limitation to VO2 kinetics in the control (i.e., no prior exercise) condition. On two occasions, seven healthy subjects completed two bouts of exhaustive cycle exercise at a work rate corresponding to approximately 105% of the predetermined Vo2 peak, separated by 3 x 30-s maximal sprint cycling and 15-min recovery (MAX1 and MAX2). Blood lactate concentration (means +/- SD: MAX1: 1.3 +/- 0.4 mM vs. MAX2: 7.7 +/- 0.9 mM; P < 0.01) was significantly greater immediately before, and heart rate was significantly greater both before and during, perimaximal exercise when it was preceded by multiple-sprint exercise. Near-infrared spectroscopy also indicated that muscle blood volume and oxygenation were enhanced when perimaximal exercise was preceded by multiple-sprint exercise. However, the time constant describing the primary component (i.e., phase II) increase in VO2 was not significantly different between the two conditions (MAX1: 33.8 +/- 5.5 s vs. MAX2: 33.2 +/- 7.7 s). Rather, the asymptotic "gain" of the primary Vo2 response was significantly increased by the performance of prior sprint exercise (MAX1: 8.1 +/- 0.9 ml.min(-1).W(-1) vs. MAX2: 9.0 +/- 0.7 ml.min(-1).W(-1); P < 0.05), such that VO2 was projecting to a higher "steady-state" amplitude with the same time constant. These data suggest that priming exercise, which apparently increases muscle O2 availability, does not influence the time constant of the primary-component VO2 response but does increase the amplitude to which VO2 may rise following the onset of perimaximal-intensity cycle exercise.  相似文献   

3.
It has been suggested that the slower O2 uptake (VO2) kinetics observed when exercise is initiated from an elevated baseline metabolic rate are linked to an impairment of muscle O2 delivery. We hypothesized that "priming" exercise would significantly reduce the phase II time constant (tau) during subsequent severe-intensity cycle exercise initiated from an elevated baseline metabolic rate. Seven healthy men completed exercise transitions to 70% of the difference between gas exchange threshold (GET) and peak VO2 from a moderate-intensity baseline (90% GET) on three occasions in each of the "unprimed" and "primed" conditions. Pulmonary gas exchange, heart rate, and the electromyogram of m. vastus lateralis were measured during all tests. The phase II VO2 kinetics were slower when severe exercise was initiated from a baseline of moderate exercise compared with unloaded pedaling (mean+/-SD tau, 42+/-15 vs. 33+/-8 s; P<0.05), but were not accelerated by priming exercise (42+/-17 s; P>0.05). The amplitude of the VO2 slow component and the change in electromyogram from minutes 2 to 6 were both significantly reduced following priming exercise (VO2 slow component: from 0.47+/-0.09 to 0.27+/-0.13 l/min; change in integrated electromyogram between 2 and 6 min: from 51+/-35 to 26+/-43% of baseline; P<0.05 for both comparisons). These results indicate that the slower phase II VO2 kinetics observed during transitions to severe exercise from an elevated baseline are not altered by priming exercise, but that the reduced VO2 slow component may be linked to changes in muscle fiber activation.  相似文献   

4.
The purpose was to examine the adaptation of pulmonary O(2) uptake (Vo(2p)) and deoxygenation of the vastus lateralis muscle at the onset of heavy-intensity, constant-load cycling exercise in young (Y; 24 +/- 4 yr; mean +/- SD; n = 5) and older (O; 68 +/- 3 yr; n = 6) adults. Subjects performed repeated transitions on 4 separate days from 20 W to a work rate corresponding to heavy-intensity exercise. Vo(2p) was measured breath by breath. The concentration changes in oxyhemoglobin, deoxyhemoglobin (HHb), and total hemoglobin/myoglobin were determined by near-infrared spectroscopy (Hamamatsu NIRO-300). Vo(2p) data were filtered, interpolated to 1 s, and averaged to 5-s bins. HHb-near-infrared spectroscopy data were filtered and averaged to 5-s bins. A monoexponential model was used to fit Vo(2p) [phase 2, time constant (tau) of Vo(2p)] and HHb [following the time delay (TD) from exercise onset to the start of an increase in HHb] data. The tauVo(2p) was slower (P < 0.001) in O (49 +/- 8 s) than Y (29 +/- 4 s). The HHb TD was similar in O (8 +/- 3 s) and Y (7 +/- 1 s); however, the tau HHb following TD was faster (P < 0.05) in O (8 +/- 2 s) than Y (14 +/- 2 s). The slower Vo(2p) kinetics and faster muscle deoxygenation in O compared with Y during heavy-intensity exercise imply that the kinetics of muscle perfusion are slowed relatively more than those of Vo(2p) in O. This suggests that the slowed Vo(2p) kinetics in O may be a consequence of a slower adaptation of local muscle blood flow relative to that in Y.  相似文献   

5.
6.
The dependence of O(2) uptake (V(O(2))) kinetics on the muscle mass recruited under conditions when fiber and muscle recruitment patterns are similar following the onset of exercise has not been determined. We developed a motorized cycle ergometer that facilitated one-leg (1L) cycling in which the electromyographic (EMG) profile of the active muscles was not discernibly altered from that during two-leg (2L) cycling. Six subjects performed 1L and 2L exercise transitions from unloaded cycling to moderate [VT) exercise. The 1L condition yielded kinetics that was unchanged from the 2L condition [the phase 2 time constants (tau(1), in s) for 0.05; for >VT: 1L = 26.8 +/- 12.0; 2L = 27.8 +/- 16.1, P > 0.05]. The overall V(O(2)) kinetics (mean response time) was not significantly different for the two exercise conditions. However, the gain of the fast component (the amplitude/work rate) during the 1L exercise was significantly higher than that for the 2L exercise for both moderate and heavy work rates. The slow-component responses evident for heavy exercise were temporally and quantitatively unaffected by the 1L condition. These data demonstrate that, when leg muscle recruitment patterns are unchanged as assessed by EMG analysis, on-transient V(O(2)) kinetics for both moderate and heavy exercise are not dependent on the muscle mass recruited.  相似文献   

7.
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9.
The effects of supplemental carbohydrate (CHO) ingestion on the performance of squats to exhaustion (STE) were investigated with eight resistance-trained men. Subjects participated in a randomized, counterbalanced, double-blind, placebo-controlled protocol with testing separated by 7 days. Subjects consumed 0.3g.kgCHO.bodymass or a placebo (PLC) of equal volume immediately before exercise and after every other successful set of squats. The STE consisted of sets of five repetitions at an intensity of 85% 1 repetition maximum (1RM). Performance measured as total sets (CHO 3.5 +/- 3.2, PLC 3.5 +/- 2.7), repetitions (CHO 20.4 +/-14.9, PLC 19.7 +/- 13.1), volume load (CHO 2928.7 +/- 2219.5 kg, PLC 2772.8 +/- 1951.4 kg), and total work (CHO 29.9 +/- 22.3 kJ, PLC 28.6 +/- 19.5 kJ) was not statistically different between the CHO and PLC treatments. The results suggest that CHO supplementation does not enhance performance of squats performed with 85% 1RM to volitional failure.  相似文献   

10.
Breath-by-breath O2 uptake (VO2) kinetics and increase of blood lactate concentration (delta Lab) were determined at the onset of square-wave stepping (S) or cycling (C) exercise on six male subjects during 1) transition from rest (R) to constant work load, 2) transition from lower to heavier work loads, wherein the baseline VO2 (VO2 s) was randomly chosen between 20 and 65% of the subjects' maximal O2 uptake (VO2 max), and 3) inverse transition from higher to lower work loads and/or to rest. VO2 differences between starting and arriving levels were 20-60% VO2 max. In C, the VO2 on-response became monotonically slower with increasing VO2 s, the half time (t1/2) increasing from approximately 22 s for VO2 s = R to approximately 63 s when VO2 s approximately equal to 50% VO2 max. In S, the fastest VO2 kinetics (t1/2 = 16 s) was attained from VO2 s = 15-30% VO2 max, the t1/2 being approximately 25 s when starting from R or from 50% VO2 max. The slower VO2 kinetics in C were associated with a much larger delta Lab. The VO2 kinetics in recovery were essentially the same in all cases and could be approximated by a double exponential with t1/2 of 21.3 +/- 6 and 93 +/- 45 s for the fast and slow components, respectively. It is concluded that the O2 deficit incurred is the sum of three terms: 1) O2 stores depletion, 2) O2 equivalent of early lactate production, and 3) O2 equivalent of phosphocreatine breakdown.(ABSTRACT TRUNCATED AT 250 WORDS)  相似文献   

11.
Tolerance to high-intensity constant-power (P) exercise is well described by a hyperbola with two parameters: a curvature constant (W') and power asymptote termed "critical power" (CP). Since the ability to sustain exercise is closely related to the ability to meet the ATP demand in a steady state, we reasoned that pulmonary O(2) uptake (Vo(2)) kinetics would relate to the P-tolerable duration (t(lim)) parameters. We hypothesized that 1) the fundamental time constant (τVo(2)) would relate inversely to CP; and 2) the slow-component magnitude (ΔVo(2sc)) would relate directly to W'. Fourteen healthy men performed cycle ergometry protocols to the limit of tolerance: 1) an incremental ramp test; 2) a series of constant-P tests to determine Vo(2max), CP, and W'; and 3) repeated constant-P tests (WR(6)) normalized to a 6 min t(lim) for τVo(2) and ΔVo(2sc) estimation. The WR(6) t(lim) averaged 365 ± 16 s, and Vo(2max) (4.18 ± 0.49 l/min) was achieved in every case. CP (range: 171-294 W) was inversely correlated with τVo(2) (18-38 s; R(2) = 0.90), and W' (12.8-29.9 kJ) was directly correlated with ΔVo(2sc) (0.42-0.96 l/min; R(2) = 0.76). These findings support the notions that 1) rapid Vo(2) adaptation at exercise onset allows a steady state to be achieved at higher work rates compared with when Vo(2) kinetics are slower; and 2) exercise exceeding this limit initiates a "fatigue cascade" linking W' to a progressive increase in the O(2) cost of power production (Vo(2sc)), which, if continued, results in attainment of Vo(2max) and exercise intolerance. Collectively, these data implicate Vo(2) kinetics as a key determinant of high-intensity exercise tolerance in humans.  相似文献   

12.
It is reported that preexercise hyperhydration caused arterial O(2) tension of horses performing submaximal exercise to decrease further by 15 Torr (Sosa-Leon L, Hodgson DR, Evans DL, Ray SP, Carlson GP, and Rose RJ. Equine Vet J Suppl 34: 425-429, 2002). Because hydration status is important to optimal athletic performance and thermoregulation during exercise, the present study examined whether preexercise induction of hypervolemia would similarly accentuate the arterial hypoxemia in Thoroughbreds performing short-term high-intensity exercise. Two sets of experiments (namely, control and hypervolemia studies) were carried out on seven healthy, exercise-trained Thoroughbred horses in random order, 7 days apart. In resting horses, an 18.0 +/- 1.8% increase in plasma volume was induced with NaCl (0.30-0.45 g/kg dissolved in 1,500 ml H(2)O) administered via a nasogastric tube, 285-290 min preexercise. Blood-gas and pH measurements as well as concentrations of plasma protein, hemoglobin, and blood lactate were determined at rest and during incremental exercise leading to maximal exertion (14 m/s on a 3.5% uphill grade) that induced pulmonary hemorrhage in all horses in both treatments. In both treatments, significant arterial hypoxemia, desaturation of hemoglobin, hypercapnia, acidosis, and hyperthermia developed during maximal exercise, but statistically significant differences between treatments were not found. Thus preexercise 18% expansion of plasma volume failed to significantly affect the development and/or severity of arterial hypoxemia in Thoroughbreds performing maximal exercise. Although blood lactate concentration and arterial pH were unaffected, hemodilution caused in this manner resulted in a significant (P < 0.01) attenuation of the exercise-induced expansion of the arterial-to-mixed venous blood O(2) content gradient.  相似文献   

13.
14.
We hypothesized that inhibition of nitric oxide synthase (NOS) by N(G)-nitro-L-arginine methyl ester (L-NAME) would alleviate the inhibition of mitochondrial oxygen uptake (Vo(2)) by nitric oxide and result in a speeding of phase II pulmonary Vo(2) kinetics at the onset of heavy-intensity exercise. Seven men performed square-wave transitions from unloaded cycling to a work rate requiring 40% of the difference between the gas exchange threshold and peak Vo(2) with and without prior intravenous infusion of L-NAME (4 mg/kg in 50 ml saline over 60 min). Pulmonary gas exchange was measured breath by breath, and Vo(2) kinetics were determined from the averaged response to two exercise bouts performed in each condition. There were no significant differences between the control (C) and L-NAME conditions (L) for baseline Vo(2), the duration of phase I, or the amplitude of the primary Vo(2) response. However, the time constant of the Vo(2) response in phase II was significantly smaller (mean +/- SE: C: 25.1 +/- 3.0 s; L: 21.8 +/- 3.3 s; P < 0.05), and the amplitude of the Vo(2) slow component was significantly greater (C: 240 +/- 47 ml/min; L: 363 +/- 24 ml/min; P < 0.05) after L-NAME infusion. These data indicate that inhibition of NOS by L-NAME results in a significant (13%) speeding of Vo(2) kinetics and a significant increase in the amplitude of the Vo(2) slow component in the transition to heavy-intensity cycle exercise in men. The speeding of the primary component Vo(2) kinetics after L-NAME infusion indicates that at least part of the intrinsic inertia to oxidative metabolism at the onset of heavy-intensity exercise may result from inhibition of mitochondrial Vo(2) by nitric oxide. The cause of the larger Vo(2) slow-component amplitude with L-NAME requires further investigation but may be related to differences in muscle blood flow early in the rest-to-exercise transition.  相似文献   

15.
During transitions in work rate, O2 uptake (VO2) kinetics at the working tissue level might be rate limited by O2 transport and/or by O2 utilization. A computer model with parallel working and non-working tissue compartments, connected to an ideal lung by a variable-sized venous blood volume, was developed to study this. The time constant for working tissue O2 demand (tau T) was set by a first-order linear metabolic response. The model attempted to replicate the VO2 response at the alveolar level of a single subject performing step transitions on a cycle ergometer from 25 to 105 W [total lag time (equivalent to 63% increase above baseline) = 40.2 s]. Measured cardiac output kinetics (total lag time = 44.1 s) were used as a model parameter. Blood flow to the nonworking tissue (QNW) was kept constant at 4.5 or 5.0 l/min. A critical PO2 of 20 Torr was set, and the Bohr effect on the O2-hemoglobin dissociation curve was included. The "best" simulation had tau T = 36 s, QNW = 4.5 l/min, and venous blood volume = 2 liters and was not O2 transport limited. The approximation to the real data was good in all but the phase 1 response, where the model underpredicted the measured response. However, when QNW was increased to 5.0 l/min, the model was O2 transport limited; yet the predicted VO2 response at the alveolar level was not notably different from the subject's data.(ABSTRACT TRUNCATED AT 250 WORDS)  相似文献   

16.
The temporal relationship between the kinetics of phase 2 pulmonary O2 uptake (Vo -->Vo2p) and deoxygenation of the vastus lateralis muscle was examined during moderate-intensity leg-cycling exercise. Young adults (5 men, 6 women; 23 +/- 3 yr; mean +/- SD) performed repeated transitions on 3 separate days from 20 W to a constant work rate corresponding to 80% of lactate threshold. Breath-by-breath Vo2p was measured by mass spectrometer and volume turbine. Deoxyhemoglobin (HHb), oxyhemoglobin, and total hemoglobin and myoglobin were sampled each second by near-infrared spectroscopy (Hamamatsu NIRO-300). Vo2p data were filtered, interpolated to 1 s, and averaged to 5-s bins; HHb data were averaged to 5-s bins. Phase 2 Vo2p data were fit with a monoexponential model. For HHb, a time delay (TDHHb) from exercise onset to an increase in HHb was determined, and thereafter data were fit with a monoexponential model. The time constant for Vo2p (30 +/- 8 s) was slower (P < 0.01) than that for HHb (10 +/- 3 s). The TDHHb before an increase in HHb was 13 +/- 2 s. The possible mechanisms of the TDHHb are discussed with reference to metabolic activation and matching of local muscle O2 delivery and O2 utilization. After this initial TDHHb, the kinetics of local muscle deoxygenation were faster than those of phase 2 Vo2p (and presumably muscle O2 consumption), reflecting increased O2 extraction and a mismatch between local muscle O2 consumption and perfusion.  相似文献   

17.
Phase 2 pulmonary O(2) uptake (Vo(2(p))) kinetics are slowed with aging. To examine the effect of aging on the adaptation of Vo(2(p)) and deoxygenation of the vastus lateralis muscle at the onset of moderate-intensity constant-load cycling exercise, young (Y) (n = 6; 25 +/- 3 yr) and older (O) (n = 6; 68 +/- 3 yr) adults performed repeated transitions from 20 W to work rates corresponding to moderate-intensity (80% estimated lactate threshold) exercise. Breath-by-breath Vo(2(p)) was measured by mass spectrometer and volume turbine. Deoxy (HHb)-, oxy-, and total Hb and/or myoglobin were determined by near-infrared spectroscopy (Hamamatsu NIRO-300). Vo(2(p)) data were filtered, interpolated to 1 s, and averaged to 5-s bins. HHb data were filtered and averaged to 5-s bins. Vo(2(p)) data were fit with a monoexponential model for phase 2, and HHb data were analyzed to determine the time delay from exercise onset to the start of an increase in HHb and thereafter were fit with a single-component exponential model. The phase 2 time constant for Vo(2(p)) was slower (P < 0.01) in O (Y: 26 +/- 7 s; O: 42 +/- 9 s), whereas the delay before an increase in HHb (Y: 12 +/- 2 s; O: 11 +/- 1 s) and the time constant for HHb after the time delay (Y: 13 +/- 10 s; O: 9 +/- 3 s) were similar in Y and O. However, the increase in HHb for a given increase in Vo(2(p)) (Y: 7 +/- 2 microM x l(-1) x min(-1); O: 13 +/- 4 microM x l(-1) x min(-1)) was greater (P < 0.01) in O compared with Y. The slower Vo(2(p)) kinetics in O compared with Y adults was accompanied by a slower increase of local muscle blood flow and O(2) delivery discerned from a faster and greater muscle deoxygenation relative to Vo(2(p)) in O.  相似文献   

18.
The effect of prior exercise on pulmonary O(2) uptake (Vo(2)(p)), leg blood flow (LBF), and muscle deoxygenation at the onset of heavy-intensity alternate-leg knee-extension (KE) exercise was examined. Seven subjects [27 (5) yr; mean (SD)] performed step transitions (n = 3; 8 min) from passive KE following no warm-up (HVY 1) and heavy-intensity (Delta50%, 8 min; HVY 2) KE exercise. Vo(2)(p) was measured breath-by-breath; LBF was measured by Doppler ultrasound at the femoral artery; and oxy (O(2)Hb)-, deoxy (HHb)-, and total (Hb(tot)) hemoglobin/myoglobin of the vastus lateralis muscle were measured continuously by near-infrared spectroscopy (NIRS; Hamamatsu NIRO-300). Phase 2 Vo(2)(p), LBF, and HHb data were fit with a monoexponential model. The time delay (TD) from exercise onset to an increase in HHb was also determined and an HHb effective time constant (HHb - MRT = TD + tau) was calculated. Prior heavy-intensity exercise resulted in a speeding (P < 0.05) of phase 2 Vo(2)(p) kinetics [HVY 1: 42 s (6); HVY 2: 37 s (8)], with no change in the phase 2 amplitude [HVY 1: 1.43 l/min (0.21); HVY 2: 1.48 l/min (0.21)] or amplitude of the Vo(2)(p) slow component [HVY 1: 0.18 l/min (0.08); HVY 2: 0.18 l/min (0.09)]. O(2)Hb and Hb(tot) were elevated throughout the on-transient following prior heavy-intensity exercise. The tauLBF [HVY 1: 39 s (7); HVY 2: 47 s (21); P = 0.48] and HHb-MRT [HVY 1: 23 s (4); HVY 2: 21 s (7); P = 0.63] were unaffected by prior exercise. However, the increase in HHb [HVY 1: 21 microM (10); HVY 2: 25 microM (10); P < 0.001] and the HHb-to-Vo(2)(p) ratio [(HHb/Vo(2)(p)) HVY 1: 14 microM x l(-1) x min(-1) (6); HVY 2: 17 microM x l(-1) x min(-1) (5); P < 0.05] were greater following prior heavy-intensity exercise. These results suggest that the speeding of phase 2 tauVo(2)(p) was the result of both elevated local O(2) availability and greater O(2) extraction evidenced by the greater HHb amplitude and HHb/Vo(2)(p) ratio following prior heavy-intensity exercise.  相似文献   

19.
Exercise training increases acetylcholine-induced pulmonary vasorelaxation in pigs with coronary occlusion. The present study tested the hypothesis that chronic exercise training enhances endothelium-mediated vasorelaxation in pulmonary arteries from normal pigs. Yucatan miniswine exercised for 16 wk on a treadmill (Ex); control pigs (Sed) remained in pens. Pulmonary artery rings (2- to 3-mm OD) were studied using standard isometric techniques. Contractile responses to 80 mM KCl and norepinephrine (NE) were determined. Vessels were constricted with levels of NE that resulted in half-maximal contraction to examine endothelium-dependent relaxation to ACh and endothelium-independent relaxation to sodium nitroprusside in the presence and absence of nitric oxide synthase inhibition, cyclooxygenase inhibition, and endothelial denudation. Arteries from Ex pigs developed increased contraction to 80 mM KCl, but the response to NE did not differ between groups. Endothelium-dependent and endothelium-independent responses did not differ between Sed and Ex in the presence or absence of pharmacological inhibitors or denudation. We conclude that chronic exercise training does not alter endothelium-dependent or endothelium-independent vasorelaxation responses of pulmonary arteries from normal pigs.  相似文献   

20.
Modeling in the time domain, the non-steady-state O2 uptake on-kinetics of high-intensity exercises with empirical models is commonly performed with gradient-descent-based methods. However, these procedures may impair the confidence of the parameter estimation when the modeling functions are not continuously differentiable and when the estimation corresponds to an ill-posed problem. To cope with these problems, an implementation of simulated annealing (SA) methods was compared with the GRG2 algorithm (a gradient-descent method known for its robustness). Forty simulated Vo2 on-responses were generated to mimic the real time course for transitions from light- to high-intensity exercises, with a signal-to-noise ratio equal to 20 dB. They were modeled twice with a discontinuous double-exponential function using both estimation methods. GRG2 significantly biased two estimated kinetic parameters of the first exponential (the time delay td1 and the time constant tau1) and impaired the precision (i.e., standard deviation) of the baseline A0, td1, and tau1 compared with SA. SA significantly improved the precision of the three parameters of the second exponential (the asymptotic increment A2, the time delay td2, and the time constant tau2). Nevertheless, td2 was significantly biased by both procedures, and the large confidence intervals of the whole second component parameters limit their interpretation. To compare both algorithms on experimental data, 26 subjects each performed two transitions from 80 W to 80% maximal O2 uptake on a cycle ergometer and O2 uptake was measured breath by breath. More than 88% of the kinetic parameter estimations done with the SA algorithm produced the lowest residual sum of squares between the experimental data points and the model. Repeatability coefficients were better with GRG2 for A1 although better with SA for A2 and tau2. Our results demonstrate that the implementation of SA improves significantly the estimation of most of these kinetic parameters, but a large inaccuracy remains in estimating the parameter values of the second exponential.  相似文献   

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