Journal of Electromyography and Kinesiology

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1 Accepted Manuscript Empirical modelling of the dynamic response of fatigue during intermittent submaximal contractions of human forearm and calf muscles Simon Green, Brad Stefanovic, Joel Warman, Christopher D. Askew PII: S (14)239-9 DOI: Reference: JJEK 1797 To appear in: Journal of Electromyography and Kinesiology Received Date: 15 September 214 Revised Date: 3 October 214 Accepted Date: 31 October 214 Please cite this article as: S. Green, B. Stefanovic, J. Warman, C.D. Askew, Empirical modelling of the dynamic response of fatigue during intermittent submaximal contractions of human forearm and calf muscles, Journal of Electromyography and Kinesiology (214), doi: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

2 1 Title: Empirical modelling of the dynamic response of fatigue during intermittent submaximal contractions of human forearm and calf muscles Simon Green 1,2, Brad Stefanovic 3, Joel Warman 3, Christopher D. Askew 3. 1 School of Science and Health, University of Western Sydney, Sydney, Australia. 2 Neuroscience Research Australia, Sydney, Australia. 3 School of Health and Sport Sciences, University of the Sunshine Coast, Maroochydore, Australia. Running Head: Fatigue during forearm and calf exercise Address for correspondence: Simon Green, PhD. School of Science and Health University of Western Sydney Sydney, NSW, Australia simon.green@uws.edu.au

3 2 Introduction Fatigue during exercise is reflected in the progressive loss of maximum force (or power) over time. This response is easily observed during sustained maximum contractions, but it is also apparent during intermittent submaximal contractions when the measurements of maximum force (F max ) are interspersed throughout exercise [Fulco et al., 1996]. Since fatigue is a timedependent process, measurement of F max during submaximal exercise has the potential to shed light on the timing and contributions of underlying mechanisms to fatigue [Green et al., 214]. Inherent in the assessment of fatigue during submaximal exercise is the assumption that fatigue is a monophasic, linear response. This is made explicit when investigators fit temporal responses of F max during exercise to a linear function (y = a + bx) and use the slope of this function (b) to assess the rate of fatigue [Egana & Green, 25; 27]. However, nonlinear behaviour is observed in fatigue responses during submaximal exercise [Egana & Green, 25], which becomes more apparent at higher intensities [Egana & Green, 27], and contributes to the curvilinear relationship between exercise intensity and endurance [James & Green, 212]. These observations raise questions about the basic structure of the dynamic response of fatigue, and challenge the assumption that fatigue is a simple linear response. Empirical modelling has helped elucidate the structure of some physiological responses to exercise [Lamarra, 199], including oxygen uptake [Lamarra et al., 1987; Barstow & Mole, 1991] and muscle blood flow [Reeder & Green, 212]. Although physiological responses vary between individuals, empirical modelling helps identify the number, size and timing of underlying phases to reveal a response structure common to most individuals [Reeder & Green, 212]. Essential aspects of empirical modelling include the fitting of a single time series of data to two or more algebraic functions, choosing a best function to describe these data, and using statistics to justify this choice [Motulsky & Ransnas, 1987; Lamarra, 199]. Parameters of the best function can be linked to one or more phases of the response and provide information about the size, timing or rate at which each phase evolves. These parameters are thought to have physiological meaning and, collectively, empirical modelling provides insight into the timing and contribution of mechanisms underlying the overall response. To our knowledge, empirical modelling has not been applied to human fatigue responses during submaximal exercise. Therefore, the aim of the present study was to use it to help

4 3 define the structure of the fatigue response during intermittent, submaximal contractions and address two basic questions. Is fatigue a mono- or biphasic response? Is fatigue a linear or nonlinear response? A narrow range of intensities of submaximal exercise (5-6 %F max ) was selected to induce substantial fatigue but performed to failure to yield a sufficient number of F max measurements for curve fitting. Fatigue was assessed during forearm and calf contractions to establish whether or not its response varied between muscles of the upper and lower limbs. Finally, we compared outcomes of empirical modelling for data obtained from a single versus multiple trials to shed light on recent controversy about this topic [Stirling & Zakynthinaki, 29; Whipp, 29]. Methods Overview Twenty young, healthy males were studied in two experiments. In Experiment 1, ten subjects (age = 25 7 y; height = m; weight = kg) completed single bouts of intermittent, submaximal forearm contractions using both limbs before commencement of a training program. Limbs were assigned as either a control or a training limb - which was subsequently trained in a quasi-random manner to ensure an equal distribution of dominant and non-dominant limbs in these groups. In Experiment 2, ten subjects (age = y; height = m; weight = kg) completed five bouts of submaximal, intermittent calf contractions on separate days using the same limb. During both experiments, fatigue was represented by the loss of peak force (F max ) during exercise, where peak force was measured during brief maximum voluntary efforts interposed between submaximal contractions. Fatigue during forearm contractions was assessed in the control (Arm control ) and training (Arm training ) limbs. Fatigue during calf contractions was assessed during the longest of five exercise trials (Calf single ) and using the averaged F max values from five trials (Calf averaged ). Both experiments yielded 4 sets of fatigue responses, including 2 datasets from the forearm (Experiment 1) and 2 datasets from the calf (Experiment 2). Each fatigue response was fitted to ten empirical functions, and the function which provided the best fit was determined on statistical grounds. To address the primary research questions, best-fit functions were grouped according to whether they were monophasic or biphasic, as well as linear or nonlinear, and probability testing for a dichotomous variable (1 vs 2 phases, linear vs nonlinear) was applied. These experiments were conducted in accordance with the Declaration of Helsinki (28) and approved by the University of the Sunshine Coast Human Research Ethics Committee.

5 4 Forearm Exercise (Experiment 1) Subjects performed single-limb, isometric handgrip exercise while lying supine with the exercising arm abducted to ~9º. Handgrip force was measured using a grip force dynamometer (MLT3/D, AD Instruments, Australia), sampled at 4Hz (PowerLab 16/3 and Chart v 5., AD Instruments) and displayed so that subjects could monitor and control their contractions. Two bouts of exercise were performed by one and then the other arm (Arm control and Arm training ), separated by 15 min rest, in a randomised order. Prior to each bout, subjects completed five maximum voluntary contractions, separated by 6 s rest, and the highest force was taken as F max. Fifteen minutes later, exercise consisting of intermittent contractions (2 s with 4 s rest) was performed at a target force of 5 %F max until it could not be achieved during three consecutive contractions (i.e. task failure). Maximum contractions (2 s duration) were performed 3 s prior to and at 3 s interval throughout exercise, as well as immediately after task failure, for the purpose of describing the fatigue response. Calf Exercise (Experiment 2) Calf exercise was performed in the seated position using a custom-built isometric plantar flexion dynamometer. Subjects sat upright with their hip and knee flexed at 9º. A padded knee-plate connected to a calibrated load cell (S1W, Xtran, Applied Measurement, Australia) was clamped over the thigh of the exercising leg and the foot was centred on an immovable footplate. Attempts to plantar flex resulted in the generation of force which was measured and sampled as described for forearm exercise. F max was determined from the highest force achieved during five maximum voluntary contractions separated by 6 s. Fifteen minutes later, exercise consisting of intermittent contractions (2 s with 3 s rest) was performed at a target force of 6 %F max until task failure (see Forearm Exercise). Maximum contractions (2 s duration) were performed 3 s prior to and at 25 s intervals throughout calf exercise, as well as immediately after task failure, again for the purpose of describing the fatigue response as it evolved during exercise. Calf exercise was repeated on five occasions each separated by 7 days. Fatigue Fatigue during exercise is represented by the temporal response of F max. For single trials (Arm control, Arm training, Calf single ), the number of F max values used to measure fatigue was a function of the frequency of its measurement and duration of exercise (see Results). For Calf averaged, F max values were averaged data obtained at the same times during five exercise trials but the duration of each trial varied and a small number (1-4) of measurements were occasionally excluded from analyses for technical reasons. To limit the distortion of averaged data caused by variation in number of observations between trials, the

6 5 number of F max data used for averaging was limited to 4-5 observations and, consequently, the total number of observations used to assess fatigue during Calf averaged was less than for Calf single. Functions Each fatigue response was fitted to ten algebraic functions and graphical representations of these functions are shown in Figure 1. Functions differed with respect to the number of parameters (2-7), number of phases (1-2), linearity of terms, presence of time delays, and use of conditional arguments. Descriptions of variables, parameters and conditional arguments are provided in Table 1. There are three linear functions, two of which are monophasic (Functions 1, 2) and one which is biphasic (Function 3). There are seven functions containing nonlinear terms and are either monophasic (Functions 4-6) or biphasic (Functions 7-1). Five of these functions contain only nonlinear terms (4, 5, 6, 9 and 1), whereas the remaining two function (7-8) contain linear and nonlinear terms. Curve Fitting and Determining Best Fit The process of fitting fatigue responses and determining the best function was similar to that process described elsewhere [Reeder & Green, 212]. Each fatigue response was fitted to each function. Prior to fitting, starting parameter estimates were adjusted so that the function appeared by visual inspection to provide a good fit without trying to overfit the data. The data were then fitted before parameter estimates were fine-tuned and a second step of fitting was performed. This iterative approach to the adjustment to starting estimates was repeated until there was no change (to 3 significant digits) in the R 2 value. Fitting was done using a weighted least squares nonlinear regression procedure and the Marquardt-Levenberg algorithm (TableCurve 2D, Systat Software Inc). To address which function provided the best fit for each fatigue response, goodness-of-fits of functions were compared on a pairwise basis [Motulsky & Ransnas, 1987]. Judgement about goodness of fit was based ultimately on the significance of difference in residual sums of squares between two functions. Level of significance was established by calculating the F statistic for nested functions using the formula, F = [(RSS 1 RSS 2 )/(p 2 - p 1 )]/[RSS 2 /(n p 2 )], where RSS is the residual sum of squares of the fit of the less complex function (RSS 1 ) and more complex function (RSS 2 ), p is the number of parameters in the function, and n is the number of observations in the time series. If an F-test value exceeded the critical F value (df = p 2 -p 1, n-p 2 ), then the more complex function was chosen as the best function in the pair; otherwise the simpler function was chosen. Comparisons between pairs of functions were

7 6 guided by these principles: 1) parsimony - simpler functions yielding the same or lower RSS than more complex functions were judged to be better and no comparison between them was performed; 2) the best linear function was identified; 3) the best nonlinear function was identified; and 4) the best linear and nonlinear function were only compared if the more complex function yielded a lower RSS. Statistical Analyses To address the main research questions, best-fit functions were grouped according to phase number and linearity. In each condition there were ten independent observations of best-fit function which would yield one of two outcomes (1 or 2 phases, linear or nonlinear) and, thus, were analysed using the probability function for a dichotomous variable following a binomial distribution. A significant difference between outcomes occurred when the ratio of an outcome relative to total outcomes (n = 1) was at least.8 (P =.44, two-tailed test). Results Fatigue Responses During Forearm and Calf Exercise Fatigue responses during forearm exercise (Experiment 1) are shown in Figure 2. For Arm control, exercise times ranged between 33 and 168 s (mean = 771 s) and the number of F max measurements ranged between 11 and 55 (mean = 25). For Arm training, exercise times ranged between 3 and 192 s (mean = 145 s) and the number of F max measurements ranged between 1 and 64 (mean = 34). Fatigue responses during calf exercise of ten subjects (Experiment 2) are shown in Figure 3. For Calf single, exercise times ranged between 225 and 1 s (mean = 573 s) and the number of F max measurements ranged between 9 and 4 (mean = 23). For Calf averaged, exercise times ranged between 15 and 775 s (mean = 45 s) and the number of F max measurements ranged between 6 and 3 (mean = 16). Goodness of Fit Means and SDs of R 2, which provides an overall estimate of the goodness of fit without adjustment for parameter number, for each function in each condition are shown in Table 2. Incidence of Best Fit Since functions 7 and 8, as well as 9 and 1, only differ with respect to the absence or presence of conditional arguments (F1, F2) and occasionally could

8 7 not be distinguished in terms of their goodness of fit, they have been considered to be essentially the same function (i.e. 7/8 and 9/1). For all conditions, five functions provided a best fit to individual fatigue responses: functions 1, 3, 4, 7/8, as well as 9/1. For all fatigue responses (n = 4), the incidence with which these five functions provided the best fit is shown in Table 3. Monophasic versus Biphasic Functions The five functions which provided a best fit (Table 2) are monophasic (Functions 1 and 4) or biphasic (Functions 3, 7/8 and 9/1). For all conditions, the incidence of best fit was numerically higher for biphasic functions. For Arm control, Arm training and Calf averaged, the proportion of best-fits provided by biphasic functions was significant (ratios =.8-1; P<.5); whereas for Calf single this ratio was not significant (.7, P =.12) (Fig. 4). Linear versus Nonlinear Functions which provided a best fit contained only linear terms (Functions 1 and 3) or at least one nonlinear term (Functions 4, 7/8 and 9/1). The contrast between linear and nonlinear functions in terms of proportion of best fit is illustrated in Figure 4. The proportion of best fits for each condition (n = 1) ranged between.4-.6 and were not significant. Discussion Fatigue during submaximal exercise can be attributed to one or more physiological mechanisms involved in the neuromuscular control of muscle force and/or the cardiovascular, respiratory or thermoregulatory support of this contractile effort. Part of the problem in understanding any dynamic physiological response lies in the challenge of quantifying the timing and extent of involvement of a single mechanism when many mechanisms might be involved. Empirical modelling provides unique insight into this problem and, for the first time, has been applied to the responses of muscle fatigue in the present study. Visual inspection of fatigue responses suggested involvement of just one or two phases and so we limited our analysis to mono- and biphasic functions. In addition, linear and nonlinear (exponential) behaviour was apparent in fatigue responses and so functions with linear and/or exponential terms were compared. There were two main findings. First, 35 of 4 fatigue responses were described best by a biphasic function. For three out of four exercise conditions (Arm control, Arm training, Calf averaged ) this higher proportion of best-fit function

9 8 attributed to biphasic functions was significant. This suggests that fatigue at moderate intensities (5-6 %F max ) exhibits a biphasic response. By contrast, similar incidences of best-fit were observed for linear and nonlinear functions, suggesting that fatigue during isolated contractions of forearm and calf muscles exhibits linear and nonlinear behaviour. For reasons outlined below, we conclude that a biphasic function consisting of an exponential (first) and linear (second) term provides an accurate description of fatigue and perhaps best represents the structure of this dynamic response during intermittent submaximal contractions. Choosing a Function Fitting dynamic physiological responses to a function is commonplace, but it is rare to find statistical justification for the choice of function. With respect to fatigue, choosing the most appropriate function is difficult because the basic structure of this response appears to vary between individuals. To account for this variation in response structure, we contrasted a large number of functions (1) compared with previous modelling studies (2-6: [Barstow & Mole, 1991; Reeder & Green, 212]) and then justified the best fit function using an F test (see Methods). The response structure might also be altered by the intensity and mode of exercise, so we restricted the intensity of submaximal contractions to a narrow range and examined responses to forearm and calf exercise. The ability to discern the response structure is also affected by the number of measurements of F max, and so we selected intensities (5-6 % F max ) which induced substantial fatigue but which could be sustained long enough to yield a sufficient density of data for curve fitting and adequate comparison of goodness of fits of competing functions. How many phases define the fatigue response? Visual inspection of fatigue responses in the present (Fig. 2 and 3) and previous studies [Egana & Green, 25; 27] suggests that fatigue during intermittent, submaximal forearm and calf contractions consists of one or two phases. We fitted an equal number of monophasic and biphasic functions to fatigue responses and report consistently higher R 2 values for biphasic functions (Table 2), as expected for functions with more parameters. The F-test adjusts for a difference in parameter number and, when applied in the pairwise comparisons of functions, revealed significantly better fitting for biphasic functions in 7-1 % of responses (Table 3, Fig. 4) during both types of exercise. The proportions of best-fit attributed to biphasic functions were significant for Arm single, Arm training and Calf averaged, but not quite significant for Calf single. This is reasonably consistent evidence of a biphasic response of fatigue during exercise involving upper and lower limb muscles.

10 9 These findings are limited to the intensities studied and should not be easily extrapolated to lower or higher intensities. Visual inspection of fatigue responses during intermittent calf contractions in a previous study [Egana & Green, 27] suggests that biphasic responses were less apparent at lower (3-4 %MVC) and higher intensities (8-9 %MVC) than in the present study (5-6 %MVC). However, the effect of intensity on the structure of the fatigue response needs more careful investigation and must take into account technical and statistical issues which collectively bias the judgement about a best function towards simpler functions (see below). Is fatigue a linear or nonlinear response? Fatigue during intermittent submaximal contractions has been assumed to be a simple, linear process [Egana & Green, 25; 27]. This assumption might not be true and failure to detect nonlinearity in fatigue might occur if, for example, nonlinear behaviour is short-lasting or if there is an insufficient density of data to reveal more subtle features of the response. In the present study, the simplest linear function (1: y = a + bx) provided the best fit to just four out of 4 responses (Table 3). This demonstrates that a linear, monophasic function does not adequately describe the structure of the fatigue response. Moreover, these four fatigue responses were based on a smaller number of measurements (mean = 1) than the average number of measurements for each exercise condition (16-34). In terms of choosing a best function, this highlights a statistical bias towards choosing simpler functions when there are fewer data to fit, and it strengthens the conclusion that fatigue in the present study was not a simple linear response. By contrast, a biphasic linear function (#3: y = a b(x c)f1 + d(x e)f2) provided the best fit to 13 out of 4 responses, the incidence of best fit attributed to this function was similar between conditions (Table 3), and these fatigue responses were based on a larger number of F max measurements (mean = 26). This suggests that linear behaviour is a feature of biphasic fatigue responses during forearm and calf contractions. Linear behaviour was also inherent in another biphasic function (7 and 8), but restricted to the second phase. This function provided the highest incidence of best fit of all functions (16/4 responses) and, together with the linear biphasic function, accounted for more than two thirds of the best fits for all responses. This reinforces the interpretation that linear behaviour is a strong feature of a fatigue response when it is considered to be biphasic.

11 1 In addition to linear behaviour, nonlinear behaviour was apparent in many fatigue responses (Fig. 2 and 3), substantiated by a similar proportion of best fits attributed to linear and nonlinear functions in all four conditions (P >.5; Figure 4). Nonlinear behaviour was particularly evident during the initial phase of a biphasic response and reflected in the higher incidence of best fit attributed to the function containing an exponential (first) and linear term (Functions 7 and 8) compared with a biexponential function for Arm control (P =.3) and Calf averaged (P =.9) conditions. A similar incidence of best fit for these two functions was observed for Arm training and Calf single. These outcomes suggest that nonlinearity is more frequently expressed during the first rather than second phase of a biphasic response, but that there is more uncertainty about nonlinear behaviour in the second phase. These outcomes also raise a question about the linearity of the first phase, particularly given the short period over which this phase occurs and the increased likelihood of bias towards choosing a simpler (linear in this case) term to describe it. Biphasic functions which accounted for most best-fits (3 and 8) differed only with respect to the first phase (i.e. linear versus exponential), and the period over which this phase occurred is reflected in the delay before the second phase begins. The time delay of this second phase was significantly shorter for fatigue responses fitted best by Function 3 compared with Function 8 (median [IQR] = 51.9 [ ] vs [ ] s, Mann-Whitney U = 51, P =.9). Consequently, the average number of measurements fit to the first phase was comparatively less for the linear compared with nonlinear function (2-3 vs 6-8). This again suggests the presence of statistical bias towards choosing a linear rather than nonlinear term to describe the first phase and increases the likelihood that nonlinear behaviour is highly prevalent during this initial phase. Curve Fitting and Parameter Estimation There are technical issues associated with curve fitting which introduce uncertainty into discriminating between functions (as discussed) and affect the accuracy of parameter estimation and utility of curve fitting in experimental studies. For example, the signal to noise ratio influences the fitting of data, accuracy of parameter estimation and confidence in discriminating between functions. The importance of increasing the signal in empirical modelling studies has been emphasised [Lamarra, 199] and, in the present study, a high signal was reflected in the substantial decline in F max (by 4-5 %) for most fatigue responses. A common way of reducing noise has been to average data from multiple trials, and this is considered important for relatively noisy exercise measurements such as ventilation [Lamarra et al., 1987], oxygen uptake

12 11 [Barstow & Mole, 1991] and muscle blood flow [Reeder & Green, 212]. Although fatigue responses appear less noisy than these measurements, the significantly higher R 2 associated with fitting of functions to Calf averaged compared with Calf single responses reflects a lower level of variation ( noise ) in data averaged from multiple trials compared with single trials of data (Fig 3). Whether or not fatigue responses require averaging between multiple trials might depend on the particular parameter of interest, and further investigation into this is required. One criticism of this averaging approach is that it introduces artefacts (e.g., non-existent time delays) and distorts the structure of the response [Stirling & Zakynthinaki, 29], although there was little evidence of this in the present study. Several functions used in the present study differed only with respect to the presence or absence of time delays and/or conditional arguments. The onset of the second phase of fatigue responses is clearly delayed with respect to the first phase and necessitates a time delay in any function which describes it. Conditional arguments are related specifically to time delays (see Methods) and use of them resulted in significant improvement in fit (Functions 8 vs 7 and 1 vs 9; Table 2) and, thus, parameter estimation. Therefore, a biphasic function which captures nonlinear and linear behaviour and incorporates conditional arguments (i.e. Function 8) is perhaps the best function to describe fatigue responses measured in the present study. Limitations This initial, exploratory study was delimited to the testing of a small group of young, healthy men and should not be extrapolated to other members of the general community (e.g., women, elderly) and clinical populations. The structure of the dynamic response of fatigue might be affected by muscle phenotype, sex, age, training status and clinical status, and further studies are required to establish this. In addition, there is now considerable scope for exploring the physiological mechanisms underlying the basic structure of this dynamic response. Conclusion Present findings suggest that fatigue exhibits a biphasic response characterised by nonlinear and linear behaviour. That this was frequently observed during forearm and calf contractions suggests that it might be common to many muscles, but additional studies are required to establish this. The algebraic function and its parameters which best describe this fatigue response can be used to investigate the nature, extent and timing of underlying mechanisms.

13 12 Acknowledgements This study was funded by the University of the Sunshine Coast.

14 13 Table 1. Descriptions and interpretation of parameters and arguments used in the ten functions investigated in this study. Functions Parameter, Constant, Argument Description Interpretation Linear 1-3 a y-intercept MVC at onset of exercise (when x = s). 1-3 b slope Rate of fatigue for either a monophasic response (1,2) or first phase in the biphasic response (3). 2,3 c time delay Onset of fatigue. 3 d slope Difference between parameters d and b is equal to rate of fatigue for second phase in biphasic response. 3 e time delay Onset of second phase of fatigue. Nonlinear 4-1 a y-intercept MVC at onset of exercise (when x = s). 4-1 b amplitude Magnitude of fatigue estimated for either a monoexponential response or the first phase of a biphasic response. 4-1 c time delay Onset of fatigue. 4-1 d time constant Inversely proportional to the rate at which either a monoexponential response or the first phase of a biphasic response is completed. 7-8 e slope Rate of fatigue of the second (linear) phase in a biphasic response. 7-1 f time delay Onset of second phase in a biphasic response. 7-1 e amplitude Magnitude of second (exponential) phase of fatigue in a biphasic response. 7-1 g time constant Inversely proportional to the rate at which second (exponential) phase of biphasic response is completed. Linear and Nonlinear 2,3,6,8, 1 F1 Argument: If x < c then F1 = ; otherwise F1 = 1. 3, 8, 1 F2 Argument: If x < e then F1 = ; otherwise F1 = 1. Limits the fitting of the first phase to and beyond the value of the time delay for that phase. Limits the fitting of the second phase to and beyond the value of the time delay for that phase.

15 14 Table 2. R 2 values (mean and SD) for each of the ten functions in four experimental conditions. Data are based on 1 observations in each condition. Function Arm control Arm training Calf single Calf averaged

16 15 Table 3. Incidence of best fit amongst a select group of functions. Functions 7 and 8, as well as 9 and 1, have been clustered (see text for explanation). Function /8 9/1 Arm control Arm training Calf single Calf averaged Total

17 16 Captions to Figures Figure 1. The equations and their graphical representations compared in this study. Three of the equations are linear, and the remaining equations are nonlinear. Description of the parameters is provided in Methods. The vertical dotted line represents the start of contractions. Functions with time delays are shown to begin after the onset of exercise. Figure 2. Fatigue responses during forearm exercise for both arms (Arm control, Arm averaged ) in ten subjects (#1-1). Figure 3. Fatigue responses during calf exercise for a single trial (Calf single ) and averaged from five trials (Calf averaged ) in ten subjects (#11-2). Figure 4. A: Contrast between proportion of monophasic and biphasic functions which provided the best fit to all fatigue responses. B: Contrast between proportion of linear and nonlinear functions which provided the best fit to all fatigue responses.

18 17

19 Arm control 1 Arm training Time (s) Time (s)

20 Calf single 11 Calf av eraged Time (s) Time (s)

21 2

22 21 References Barstow, T.J. & Mole, P.A. Linear and nonlinear characteristics of oxygen uptake kinetics during heavy exercise. Journal of Applied Physiology 1991; 71: Egana, M. & Green, S. Effect of body tilt on calf muscle performance and blood flow in humans. Journal of Applied Physiology 25; 98: Egana, M. & Green, S. Intensity-dependent effect of body tilt angle on calf muscle fatigue in humans. European Journal of Applied Physiology 27; 99: 1-9. Fulco, C.S., Lewis, S.F., Frykman, P.N., Boushel, R., Smith, S., Harman, E.A., Cymerman, A. & Pandolf, K.B. Muscle fatigue and exhaustion during dynamic leg exercise in normoxia and hypobaric hypoxia. Journal of Applied Physiology 1996; 81: Green, S., Robinson, E. & Wallis, E. Assessment of calf muscle fatigue during submaximal exercise using transcranial magnetic stimulation versus transcutaneous motor nerve stimulation. European Journal of Applied Physiology 214; 114: James, A. & Green, S. A phenomenonological model of muscle fatigue and the power-endurance relationship. Journal of Applied Physiology 212, 113: Lamarra, N. Variables, constants, and parameters: clarifying the system structure. Medicine and Science in Sports and Exercise 199; 22: Lamarra, N., Whipp, B.J., Ward, S.A. & Wasserman, K. Effect of interbreath fluctuations on characterizing exercise gas-exchange kinetics. Journal of Applied Physiology 1987; 62: Motulsky, H.J. & Ransnas, L.A. Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB Journal 1987; 1: Reeder, E. & Green, S. Dynamic response characteristics of muscle hyperaemia: effect of exercise intensity and relation to electromyographic activity. European Journal of Applied Physiology, 212; 112: Stirling, J.R. & Zakynthinaki, M. Counterpoint: the kinetics of oxygen uptake during muscular exercise do not manifest time-delayed phases. Journal of Applied Physiology 29; 17: Whipp, B.J. Point: the kinetics of oxygen uptake during exercise do manifest time-delayed phases. Journal of Applied Physiology 29; 17:

23 Simon Green is Associate Professor in the Schools of Science and Medicine at University of Western Sydney, as well as an honorary senior research officer at Neuroscience Research Australia. His research interests are cardiovascular and neuromuscular control with application to cardiopulmonary diseases. 22

24 23 Associate Professor Chris Askew Dr Chris Askew is an Associate Professor and Senior Research Fellow with the School of Health and Sport Sciences at the University of the Sunshine Coast where he leads the VasoActive research group. He is an accredited exercise physiologist (AEP), and his clinical and research interests focus on exercise intolerance in patients with cardiac, peripheral arterial and cerebrovascular diseases.

25 24 Dr Brad Stefanovic Dr Brad Stefanovic is the Vascular Research Manager at the Royal Brisbane and Women s Hospital (School of Medicine, University of Queensland). His research interests include the effects of conservative and interventional treatment on atherosclerotic and aneurysmal disease and the relationship between blood flow kinetics and muscle function.

26 25 Mr Joel Warman Joel Warman graduated with a degree in Sport and Exercise Science (Honours) from the University of the Sunshine Coast. He is employed as an Accredited Exercise Physiologist at The Sunshine Coast Private Hospital Day Rehabilitation Unit.