Improving biologic predictors of cycling endurance performance with near‐infrared spectroscopy derived measures of skeletal muscle respiration: E pluribus unum

Abstract The study aim was to compare the predictive validity of the often referenced traditional model of human endurance performance (i.e. oxygen consumption, VO2, or power at maximal effort, fatigue threshold values, and indices of exercise efficiency) versus measures of skeletal muscle oxidative potential in relation to endurance cycling performance. We hypothesized that skeletal muscle oxidative potential would more completely explain endurance performance than the traditional model, which has never been collectively verified with cycling. Accordingly, we obtained nine measures of VO2 or power at maximal efforts, 20 measures reflective of various fatigue threshold values, 14 indices of cycling efficiency, and near‐infrared spectroscopy‐derived measures reflecting in vivo skeletal muscle oxidative potential. Forward regression modeling identified variable combinations that best explained 25‐km time trial time‐to‐completion (TTC) across a group of trained male participants (n = 24). The time constant for skeletal muscle oxygen consumption recovery, a validated measure of maximal skeletal muscle respiration, explained 92.7% of TTC variance by itself (Adj R 2 = .927, F = 294.2, SEE = 71.2, p < .001). Alternatively, the best complete traditional model of performance, including VO2max (L·min−1), %VO2max determined by the ventilatory equivalents method, and cycling economy at 50 W, only explained 76.2% of TTC variance (Adj R 2 = .762, F = 25.6, SEE = 128.7, p < .001). These results confirm our hypothesis by demonstrating that maximal rates of skeletal muscle respiration more completely explain cycling endurance performance than even the best combination of traditional variables long postulated to predict human endurance performance.


| INTRODUCTION
Traditional exercise physiology dogma presents endurance performance aptitude as a biological formulate determined primarily through a combination of: (a) Measures reflecting one's maximal rate of whole-body oxygen (O 2 ) consumption (VO 2max ); (b) A valid fatigue threshold; and (c) An index of bioenergetic efficiency during exercise (Coyle, 1995;Gabriel & Zierath, 2017;Joyner & Coyle, 2008). More specifically, this established and accepted postulate suggests that one must maintain an external workload at a high percentage of their aerobic power (a product of VO 2max and fatigue threshold; "performance VO 2 ") that benefits from comparably higher metabolic (phosphorylative-coupling) and mechanical (contraction coupling) efficiencies (Whipp & Wasserman, 1969) to maximize endurance performance. This premise has never been empirically verified collectively, to the best of our knowledge, and instead relies on implicit assumptions from the aggregation of literature examining human integrative physiology in relation to cycling endurance performance.
The physiologic mechanisms underlying aerobic power, fatigue thresholds, and exercise efficiency are not entirely independent from one another. The common biology shared across these variables relate to bioenergetic properties of skeletal muscle with emphasis on skeletal muscle mitochondria, as have been previously discussed (Gabriel & Zierath, 2017;Jacobs et al., 2011). Thus, a novel and more concise postulate advocates that skeletal muscle respiratory potential directs biological control of endurance performance potential. There is preliminary evidence in support of this theory (Jacobs et al., , 2011. Accordingly, the intent of this study is to empirically scrutinize both postulates regarding the predictive physiology of endurance cycling performance in trained human participants. The aims of the present study are to: (a) Verify that traditional variables commonly used to represent the capacity for exercise at maximal effort, a valid fatigue threshold, and an index of exercise efficiency, as is often discussed across the literature, do collectively account for a high percentage of cycling endurance performance (i.e. >75%); and (b) Demonstrate the close relationship between endurance performance and in vivo measures reflecting maximal skeletal muscle respiratory rates assessed with near-infrared spectroscopy (NIRS), thereby expanding upon the traditional exercise physiology dogma of the physiologic limits of human performance. We hypothesize that the traditionally held formula used to describe endurance performance potential will aptly predict a high percent of endurance performance. However, we anticipate that measures indicative of maximal rates of skeletal muscle respiration will improve the physiological model explaining the potential of human endurance performance when cycling given the biologically based overlap of traditional variables and skeletal muscle respiratory capabilities.

| Participants
Study protocol and consent were approved by the Institutional Review Board at the University of Colorado Colorado Springs (UCCS; IRB 18-122), and all experimental procedures conformed to the standards set by the latest revision of the Declaration of Helsinki. Study participants (male; n = 24) were informed of the experimental purpose, procedures, and risks before providing informed written consent to volunteer in the study. Participants were only considered eligible if they had regularly engaged in at least 3 days of endurance training per week for a minimum of 6 months prior to data collection. All participants were nonsmokers, determined capable of performing maximal exercise as per the recommendations of the American College of Sports Medicine (Riebe et al., 2015), free of any known cardiovascular, metabolic, and neurological diseases, and abstained from alcohol (24 hr), caffeine (12 hr), and exercise (48 hr) prior to data collection. Study participant characteristics are shown in Table 1.  Table 2, included an incremental ramp test to volitional fatigue (exercise test 1), a verification max test 10 min following the end of the initial incremental ramp test (exercise test 2), and then a 25-km time trial (TT 25 ), which commenced 60 min following the verification max test. Measures of power along with absolute ( abs ; l·min −1 ) and relative ( rel ; ml·kg −1 ·min −1 ) rates of whole-body VO 2 collected at maximal efforts from exercise tests 1 and 2 are represented by a superscripted number referencing the exercise test used to derive each measure.
( 1 or 2 , respectively). All other variables do not include a superscripted number, as all other variables were derived from a single exercise test as explained subsequently and in Table 2.

| Exercise tests
Three exercise tests were performed on an electrically braked cycle ergometer (Velotron, Racermate Inc.), which allowed the use of the participant's own cycling shoes, pedal clips, and bike seat. Participants were fitted with a HR monitor (Polar T31, Polar Electro Inc., Bethpage) and continuous-wave NIRS device (Oxymon MKIII, Artinis Medical Systems) for all exercise tests. Participants were also fitted with a head net and face mask combination (Hans Rudolph, Inc) with inspired and expired oxygen and carbon dioxide concentrations continuously measured and analyzed as breath-by-breath values (Ultima CPX, Medgraphics Diagnostics) to assess VO 2 and rates of carbon dioxide production (VCO 2 ) during exercise tests 1 and 2. The gas analyzers and flowmeters were calibrated before each study. Participants were instructed to refrain from interrupted breathing while ventilatory measures were collected. Exercise test 1 consisted of a pre-programmed standardized warm-up and incremental ramp to volitional exhaustion (Velotron Coaching Software). This test was designed to: (a) Collect measures of exercise efficiency at the same absolute workloads during a standardized warm-up; (b) Determine various measures of fatigue threshold during an incremental ramp protocol; and (3) Calculate VO 2max 1 with corresponding averaged measures of maximal power output (W max 1 ), VO 2peak 1 with corresponding average measures of peak power output (W peak 1 ), and peak power output (PPO 1 ), which was the power output at the point of exhaustion (Table 2). A more complete description of these calculations is detailed below. The 15-min standardized warm-up consisted of cycling at two sequential 7.5 min workloads of 50-and-100 W at a set cadence of 80 rpm. Immediately following the 100 W stage, participants were free to pedal at a self-selected cadence as the workload was increased by 18-26 W·min −1 (dependent upon age, BMI, and cycling experience) until achieving volitional exhaustion, which was defined as a drop in cycling cadence < 55 rpm. Participants were verbally encouraged to T A B L E 2 The experimental sequence of study design organizes measured variables with the events/test during which they were derived (read right to left; up to down) Abbreviations: abs, absolute; ATT, adipose tissue thickness; CE, cycling economy; DE, delta efficiency; EC, exercise economy; ExCO 2 , excess CO 2 method; GE, gross efficiency; Isch Calib, ischemic calibration; k, rate constant for the recovering rates of muscle oxygen consumption (mVO 2 ); PPO, the power output at the point of exhaustion; rel, relative; T c , time constant for the recovery of mVO 2 ; TT 25 , 25-km time trial; TTC, time-to-completion; VEQ, ventilatory equivalents method; VO 2max , maximal rate of whole-body oxygen consumption; VO 2peak , peak rate of whole-body oxygen consumption; V-Slope, modified V-Slope method; VT avg , averaged ventilatory threshold (VT) values, including VEQ, ExCO 2 , and V-Slope; W, watt; W max , averaged power output corresponding to VO 2max ; W peak , averaged power output corresponding to VO 2peak . continue cycling to complete exhaustion once a consistent RER > 1.00 was identified. Following cessation of exercise test 1, participants rested on the cycle ergometer for 10 min as PPO 1 was determined and subsequently used to program exercise test 2 (Velotron Coaching Software; RacerMate).
Exercise test 2 was designed to ensure valid measures of VO 2max 1 were collected in exercise test 1 (Poole & Jones, 2017) and to collect measures of exercise efficiency across the same relative constant workloads (Table 2). This test commenced after 10-min of rest and/or light active recovery, as participants completed two sequential 7.5 min workloads set to 15% and 30% PPO 1 , respectively, again at a set cadence of 80 rpm. Immediately following the 30% PPO 1 stage, workload increased to 110% PPO 1 over a 60 s interval. Thereafter, participants continued to pedal at a self-selected cadence at 110% PPO 1 until volitional exhaustion (cadence < 55 rpm). Participants were again verbally encouraged to continue cycling to complete exhaustion throughout the final workload. Following exercise test 2, participants rested for one hour before completing a TT 25 . Fifteen minutes prior to beginning the TT 25 , all participants were provided an isocaloric beverage with a standard carbohydrate load of 36 g (Gatorade, PepsiCo) that had to be consumed prior to beginning the time trial (n = 24) to normalize participant nutrition and provide standardized exogenously available substrate for the TT 25 . After resting for one hour following completion of exercise test 2, participants completed an all-out TT 25 (Racermate One Software, SRAM Inc.) to assess endurance cycling performance. They were instructed to complete the TT 25 as quickly as possible using the same cycle ergometer individually fitted to each participant prior to exercise test 1, with the ability to freely adjust their power output, similar to shifting gears, at any given time throughout the entire test. Participants received restricted temporal feedback during the TT 25 , limited to verbal confirmation for every 5-km completed for the initial 20 km, and then every 1-km for the final 5 km. Our index of cycling endurance performance derived from this test was time-to-completion (TTC).

| Methodology for collecting traditional
physiologic variables relating to human endurance performance 2.2.1 | Determination of VO 2 and power output at maximal effort VO 2 and cycling power were derived at maximal efforts using multiple methods to account for a wide array of concerns regarding measures derived at maximal exercise (Poole & Jones, 2017). Least squares linear regression was used to identify the highest but most stable (flattest slope) average VO 2 across the greatest range of time to determine VO 2max 1 with corresponding measures of W max 1 derived as the average power across that same range of time. Alternatively, VO 2peak 1 & 2 were determined as the highest 30 s average VO 2 throughout each respective exercise test with W peak 1 values reflecting average measures of power output across that same range of time. Given our experimental design: As the verification test was programmed to ramp up to a constant power output equal to 110% of PPO 1 , all measures of power in the verification max test, exercise test 2, are inherently collinear with PPO 1 . Consequently, all measures of cycling power used for statistical analyses were limited to those derived from exercise test 1.

| Determination of fatigue thresholds
Identification of fatigue thresholds using methods to determine ventilatory threshold (VT) have been identified as superior (Amann, Subudhi, & Foster, 2006) or equivalent (Aunola et al., 1988;Cerezuela-Espejo, Courel-Ibáñez, Morán-Navarro, Martínez-Cava, & Pallarés, 2018;Pallarés et al., 2016) to measures and/or surrogates (Black, Durant, Jones, & Vanhatalo, 2014) of lactate threshold (LT). As such, three common methods to determine VT were evaluated, as previously explained (Gaskill et al., 2001). Briefly, the methods evaluated include the following: 1. Ventilatory equivalent method (VEQ): The intensity of activity that causes the first rise in the ventilatory equivalent of oxygen (VE/VO 2 ) without a concurrent rise in the ventilatory equivalent of carbon dioxide (VE/VCO 2 ). 2. Excess carbon dioxide method (ExCO 2 ): The intensity of exercise that causes an increase from steady state to an excess production of CO 2 and is calculated as ((VCO 2 2 / VO 2 )−VCO 2 ). 3. Modified V-slope method (V-slope): The intensity of exercise that, in a plot of the VCO 2 over the VO 2 , shows an increase in the slope from less than 1 to greater than 1. This method was modified from the original method (Beaver, Wasserman, & Whipp, 1986) that used breath-by-breath gas analysis to the use of 5-s gas collection averages.
Corresponding fatigue threshold values of abs VO 2 , rel VO 2 , %VO 2max , workload (W), and %W max were determined using each method. All measures respective to each VT method (methods 1-3 explained above) were also averaged (VT AVG ), because the average of these three methods is postulated to be more resistant to false VT determinations and better reflect one's VT (Gaskill et al., 2001).

| Determination of cycling efficiency
Four common methods to determine cycling efficiency were evaluated, as previously described (Lucía, Hoyos, Pérez, Santalla & Chicharro 2002;Moseley et al., 2004;Moseley & Jeukendrup, 2001). Bioenergetic efficiency of cycling was assessed by determining gross efficiency (GE), exercise economy (EC), and cycling economy (CE) at the same absolute (50and-100 W) and relative (15% and 30% PPO 1 ) steady-state workloads, as well as delta efficiency (DE) across the same absolute and relative steady-state workloads. Calculations of GE, EC, CE, and DE were derived from measures of energy expenditure, VO 2 , and work rate. Energy expended (EE) was calculated from the measures of VCO 2 and VO 2 (Ultima, Medgraphics Diagnostics) and analyzed using the formula: GE was calculated as the mean of the most level portion over the latter portion of each steady-state workload: EC was calculated as the power output divided by the rate of O 2 consumption using the most level portion of the latter portion of each steady-state workload and expressed in kJ·L −1 ; CE was expressed in (W·L −1 ·min −1 ); and both absolute ( abs ) and relative ( rel ) measures of DE were calculated as change in work performed divided by the change in energy expenditure (Jacobs et al., 2011).
Metabolic steady-state is achieved within 3-6 min of exercise at a constant workload, especially at relatively lower submaximal workloads (Gaesser & Brooks, 1975;Wasserman et al., 1973;Whipp & Wasserman, 1972). To ensure that steadystate was reached during all four constant-load stages (Table  2), each stage consisted of cadence-controlled (metronome set to 80 rpm) fixed-effort cycling for 7.5 min stages. To ensure that end-stage averaged values reflected true steadystate conditions, least squares linear regression was used to identify the most level portion (flattest slope) across the end of each constant-load stage for exercise efficiencies derived during all submaximal stages of exercise tests 1 and 2.

| Ultrasound (US)
Thigh adipose tissue thickness (ATT) was measured using B-mode ultrasound (VIVID e; GE HealthCare), as previously described (Müller et al., 2013). Briefly, randomized and counter-balanced measurements were made in a supine position superficial to the left or right m. vastus lateralis ~10 cm superior to the proximal edge of the patella. The US probe was placed, using minimal pressure, parallel to the direction of the m. vastus lateralis with 3-5 mm of US gel (Aquasonic Clear; Parker Laboratories, Inc., Fairfield) between the probe and skin. All measures of ATT were collected by the same research assistant with the US system set to 'default' except for frequency and time-gain compensation. All scans were repeated until image resolution was sufficiently clear for the subcutaneous fat-skeletal muscle interface to be identified. Measures of ATT, in millimeters, were taken to be the average of three points, determined via software calipers, across the image.

| NIRS device
Continuous-wave NIRS (Oxymon MKIII, Artinis Medical Systems) optodes were placed on the skin over the m. vastus lateralis. As previously described (Ryan, Southern, Reynolds, & McCully, 2013), the probe was set to have two source-detector separation distances (between 30 and 45 mm), with the smallest source-detector distance set to approximately twice the ATT. The second source-detector distance was set 1 cm greater than the first. NIRS data were collected at 10 Hz. All statistical analyses included only NIRS-derived measures of deoxygenated hemoglobin and myoglobin (HHbMb). Continuous-wave derived measures of HHbMb are less influenced by skin blood flow immediately below the sensors allowing for a valid estimate of local muscle fractional O 2 extraction (Koga et al., 2015).

| Ischemic/hyperemic calibration
Immediately following exercise test 2, participants were seated on a reclinable chair (Ostrich Deluxe Chair, Detless Corp.) with their feet elevated approximately parallel to the floor, while an ischemic calibration procedure was performed. Blood pressure cuffs (Hokanson SC12D) were placed proximal to the NIRS optodes on the upper thigh of each leg and connected to a rapid-inflation system (Hokanson E20). The blood pressure cuffs were inflated to ~300 mmHg for 5 min (or until the HHbMb signal plateaued). An ischemic/hyperemic occlusion protocol was used to normalize the HHbMb signals to the maximal physiological range of each participant. The highest value obtained represented zero oxygenation in the tissue under the NIRS probe. Upon release of the blood pressure cuff, a hyperemic response causes a re-oxygenation overshoot in the NIRS signal, with the minimum HHbMb identified to represent 100% oxygenation.

| Leg occlusion cuffing protocol
Noninvasive determination of skeletal muscle O 2 consumption (mVO 2 ) recovery rates were determined using a protocol similar to several previously described Ryan et al., 2014;Ryan, Southern, Reynolds, et al., 2013). Immediately following the ischemic/hyperemic calibration, while remaining seated in a recumbent position, participants performed near-maximal to maximal voluntary isometric leg extension contractions for 2 × 10 s contraction/10 s relaxation, followed by one 20 s contraction (60 s in total), which led directly into the occlusion cuffing protocol. Increased measures of mVO 2 between isometric contractions and electrically stimulated contractions have been shown to be similar and independent of exercise intensity . Immediately after completion of the 1 min isometric contraction protocol, the blood pressure cuffs were inflated to ~300 mmHg for a series of 5-15 s occlusions to measure mVO 2 recovery kinetics. The cuffing protocol consisted of 15 cuffs as follows: cuffs 1-5 (5 s on/off), 6-10 (10 s on/ off), 11-15 (15 s on/off). The isometric contractions and leg occlusion cuffing protocols were completed twice for duplicate measures and values determined for each protocol were averaged.

| Rates of skeletal muscle O 2 consumption recovery
Rates of mVO 2 recovery were calculated using simple linear regression across 3 s of each occlusion (30 data points × 15 occlusions). The post exercise repeated measurements of mVO 2 were fit to a monoexponential curve according to the formula below: where y(t) is the relative mVO 2 during the arterial occlusion at time t, end is the mVO 2 immediately following exercise, delta is the change in mVO 2 from rest to end-exercise, and k is the fitting rate constant. According to this first-order metabolic model, the recovery kinetics follow a monoexponential function that is independent of exercise intensity (Crow & Kushmerick, 1982;Mahler, 1985;Meyer, 1988;Paganini et al., 1997;Walter et al., 1997). The rate constant k correlates with maximal rates of skeletal muscle respiration determined via high-resolution respirometry (Ryan et al., 2014). The corresponding time constant (T c ) for the recovery of mVO 2 (1·k −1 ) correlates with PCr recovery kinetics via 31 phosphorus-magnetic resonance spectroscopy ).

| Correction for blood volume
All NIRS data obtained during the ischemic calibration and cuffing occlusion protocol were corrected for blood volume changes as previously described (Ryan et al., 2012). Briefly, it is assumed that oxygenated hemoglobin and myoglobin (O 2 HbMb) and HHbMb change at a 1:1 ratio during arterial occlusions with the resulting signals representative of mVO 2 , and the calculation of a blood volume correction factor (β) takes these changes into account. To correct NIRS signals for changes in blood volume, first the following equation was employed to determine a correction factor for each data point obtained during occlusions: Each data point was then corrected using its corresponding β in the equations shown below. This method for correcting each data point for its corresponding blood volume has been empirically validated (Ryan et al., 2012).
In these equations, O 2 HbMb c and HHbMb c are the corrected O 2 HbMb and HHbMb signals respectively.

| Statistical analyses
Laboratory-based stationary time trial cycling tests do not seamlessly translate to real-world performance, as cyclists with a larger body mass experience greater air resistance, primarily due to increased frontal area, when riding outside of laboratory conditions on flat terrain (Bassett, Kyle, Passfield, Broker, & Burke, 1999;Swain, 1994;Swain et al., 1987). Relative measures of VO 2 consumption and all measures of power output were allometrically controlled for body masssurface area relationships using the mass exponents 0.32 to account for differences across cyclists and improve upon the real-world application of these findings (Swain, 1994).
Comparisons between two parametric or nonparametric variable groups were evaluated using a paired t-test or Mann-Whitney test respectively (GraphPad Prism 8.1.2, GraphPad Software). Comparisons across three or more groups were analyzed using a one-way ANOVA or repeated measurements ANOVA with a Bonferroni correction to control for type I error across multiple comparisons. When appropriate, post hoc tests were conducted using Bonferroni multiple comparison test.
In total, we obtained nine variables at maximal exercise, 20 measures reflective of various fatigue threshold values, 14 indices of cycling efficiency, along with k and T c for examination of variable modeling to best explain TTC variance. The most predictive variable(s) from each tier representing different 'traditional' variable categories (i.e. max exercise, fatigue threshold, & exercise efficiency values) were first identified with linear regression or forward regression analysis (SigmaPlot, Systat). For statistical modeling of cycling endurance performance, there were two objectives: (a) Substantiate that measures of VO 2 or power at maximal efforts, our strongest fatigue threshold value in relation to TTC, and our best measure(s) of exercise efficiency, as often discussed across the literature, do collectively account for a high percent (>75%) of variation of cycling endurance performance, delineated by a TT 25 , across a group of active, well-trained participants; and (b) Examine whether including in vivo rates of skeletal muscle respiration improve upon traditional regression models explaining endurance performance.
Best-fit grouped variables identified through forward stepwise regression analyses were assessed with a correlation matrix (R 2 ≥ .80; Figure 2) and multiple linear regression (variance inflation factor, VIF ≥ 2.0) to further scrutinize variable collinearity. The variable with the stronger/est relation to TTC was retained for further regression model analyses if collinearity was identified, as other collinear variables were removed.
For all statistical evaluations, an α of p < .05 was considered significant and all data are reported as mean ± SD unless specified otherwise.

| Experimental design validation and group comparison analyses
Participant characteristics and indices of TT 25 cycling endurance performance are displayed in Table 1. Neither testing conditions (time of testing, temperature, and humidity) nor subject characteristics (age, height, weight, and BMI) significantly related to TTC (p > .05).

| Identification of best traditional
physiologic variables relating to human endurance performance

| Determination of the best indices of cycling efficiency in relation to human endurance performance
Indices of exercise efficiency significantly related to TTC are shown in Figure 3a. All relative measures of GE, EC, and CE were related to TTC whereas only one absolute measure was significant, GE 50 . Measures of efficiency, such as GE, are known to be positively influence by workload (Gaesser & Brooks, 1975;Moseley & Jeukendrup, 2001). Indeed, relative measures of GE (Figure 3b), EC ( Figure  3c), and CE ( Figure 3d) were influenced by workload such that more 'efficient' measures correlated with higher workloads. Relative efforts during constant-load cycling at 15% and 30% PPO 1 are inherently colinear to PPO 1 as per our study design and thus average power determined at maximal effort, W max , also strongly correlates with power at 15% and 30% (both, R 2 = .9295). Accordingly, these relative measures of exercise efficiency were removed from further grouped regression analyses as the weaker correlates. Instead, absolute indices of exercise efficiency that demonstrated a relationship with TT 25 performance (F > 2.0) were retained for subsequent grouped forward regression analyses. These indices included GE 50 , EC 50 , CE 50 , GE 100 , and EC 100 (Figure 4).

| Determination of best methodology to identify values at fatigue threshold in relation to human endurance performance
There were no significant main effects (all, p < .05) for methodology used to determine corresponding fatigue threshold values of abs VO 2 (F = 3.68), rel VO 2 (F = 3.74), %VO 2max (F = 3.30), W (F = 2.52), and %W max (F = 2.09). Although, comparisons across methods to determine abs VO 2 (p = .057), rel VO 2 (p = .055), and %VO 2max (p = .072) did show trends of difference driven solely by disparities between VEQ and ExCO 2 values (Table 3). Also, fatigue threshold powers did not differ from the average power throughout the TT 25 (F = 2.453, p = .1112; Figure 2a).
All fatigue threshold variables significantly related to TTC are shown in Figure 2b (VO 2 ) & 2C (power). The VEQ method in relation to TTC was identified as superior to all other methods used to determine all respective fatigue threshold values. Accordingly, fatigue threshold values determined by the VEQ method ( abs VO 2 , rel VO 2 , %VO 2max , W, and %W max ) were included in subsequent grouped forward regression analyses.

| Determination of the best indices of cycling efficiency in relation to human endurance performance
At the end of exercise test 1, VO 2max and corresponding W max were determined as the highest stable (slope = 0.00005 ± 0.00811) averaged over the longest (51 ± 23 s) possible range. Secondary VO 2max 1 confirmation criteria included an RER > 1.10 (1.16 ± 0.05) and HR max within 20 bpm of age-predicted (Tanaka et al., 2001) HR max (175 ± 11 vs. 182 ± 8 bpm respectively). Maximal rates of VO 2 were never stable enough at the end of exercise test 2 to utilize least squares linear regression and identify VO 2max 2 , therefore the only measure of VO 2max assessed was derived from exercise test 1.

| Best traditional grouped variable forward regression models in relation to TTC
Traditional variable grouped forward regression analyses limited initial values included in the model as per suggested correlational collinearity (R 2 ≥ .80; Figure 4). Corresponding measures of abs VO 2 , rel VO 2 , and W max were grouped separately for forward regression modeling due to suggested collinearity and to minimize the possibility of overfitting. Note: Fatigue threshold variables consist of absolute ( abs ; l O 2 ·min −1 ) and relative ( rel ; ml O 2 ·min −1 ·kg −0.32 ) measures of oxygen consumption (VO 2 ) or power output (W·kg −0.32 ), as well as % of maximal VO 2 (%VO 2max ) or power (%W max ) determined through different methods: ventilatory equivalent method (VEQ); excess carbon dioxide method (ExCO 2 ); modified V-slope method (V-slope); and the average of VEQ, ExCO 2 , and V-Slope methods (VT avg ). Data reported as mean ± SD. F I G U R E 1 Determination of the best measures for rates of whole-body oxygen consumption (VO 2 ) and power at maximal efforts in relation to endurance performance. The median difference and 95% confidence interval between methods for determining absolute ( abs ; L·min −1 ) VO 2 (a), relative ( rel ; ml·min −1 ·kg −0.32 ) VO 2 (b), and power (W·kg −0.32 ; c) at maximal efforts. The relationship between abs VO 2 (d), rel VO 2 (e), and power (f) in relation to 25-km time trial time-to-completion (TTC). The red lines represent the respective averages of corresponding measures collected during exercise tests 1 ( 1 ) and 2 ( 2 ) and the dotted red line represents 95% confidence interval. Linear regression relationships between traditional variables collected at maximal efforts in relation to TTC (g). The labels within bars reports individual Adj R 2 values representing explained variance and the labels outside of the error bars represents the standard error of the estimate (SEE) as a percent of the averaged group TTC (2,680.9 s). The highest but most stable (flattest slope) average VO 2 across the greatest range of time was used to determine VO 2max

| Best grouped variable forward regression models in relation to TTC including measures of maximal skeletal muscle respiration
Values showing rates of mVO 2 recovery, k, and T c across performance quartiles are shown in Figure 6. Forward regression analyses were assessed with k or T c along with all other top traditional variables excluding those identified as collinear with the NIRS-derived measures of maximal skeletal muscle respiration (Figure 4). The most complete model regarding TT 25 performance included only T c , which, alone, explained 92.7% of TTC variance (Adj R 2 = .927, F = 294.2, SEE = 71.2, p < .001).
Independent variables used for regression modeling were normally distributed (Shapiro-Wilk test) and all regression analyses ( Figure 5) were reported to have sufficient power (all, 1.000) to perform tests with α = .05 (SigmaPlot, Systat).

| DISCUSSION
The present study scrutinized biological predictors of human cycling endurance performance by examining the explained variance of a 25-km time-trial (TT 25 ) time-to-completion (TTC) across a well-defined group of trained adult males (n = 24). Our most important and novel finding is that the time constant for the rate of skeletal muscle oxygen consumption (mVO 2 ) recovery, T c , alone, provided the most complete model of cycling endurance performance by explaining 92.7% of TTC variance across participants. The best model of endurance performance using traditional variables were not as robust. The maximal rate of whole-body oxygen (O 2 ) consumption (l·min −1 ; abs VO 2max ), %VO 2max determined by the ventilatory equivalents method (%VO 2max VEQ ), and cycling economy assessed at 50 W (CE 50 ) collectively explained 76.2% of endurance performance variance. A more complete traditional model that included maximal power output (W max ) and %VO 2max VEQ , which could not be strengthened by any index of exercise efficiency, only explained 81.2% of TTC variance. This is the first study to verify that traditional variables including measures obtained at maximal effort, a valid fatigue threshold value, and an index of exercise efficiency do collectively explain a majority of cycling endurance performance (i.e. >75% variance). Additionally, this is the first study to demonstrate the relationship between NIRS-derived maximal rates of skeletal muscle respiration and cycling endurance performance. These findings expand upon and improve the clarity of how human biology directs cycling endurance performance by highlighting the importance of skeletal muscle respiratory potential over classically held traditional variables in relation to the limits of human performance.
The positive relationship between exercise training, mitochondrial adaption in skeletal muscle, and exercise performance is well-documented. Skeletal muscle mitochondrial protein content (Granata, Jamnick, & Bishop, 2018;Holloszy, 1967;Robinson et al., 2017), volume density (Granata et al., 2018;Hamaoka et al., 1996;Meinild Lundby et al., 2018), and maximal rates of respiration (Granata et al., 2018;Pesta et al., 2011) increase with endurance-type exercise training. These adaptations help facilitate training-induced improvements in endurance capacity Lundby & Jacobs, 2016). Skeletal muscle respiratory potential contributes to the biological mechanisms underlying both VO 2max , as detailed by the Fick equation, and one's fatigue threshold. Skeletal muscle specific capillary density (Hoppeler et al., 1985;Zumstein et al., 1983), mitochondrial volume density (Hoppeler et al., 1985;Hoppeler, Lüthi, Claassen, Weibel, & Howald, 1973;Lundby & Jacobs, 2016), mitochondrial protein content F I G U R E 4 Shown above is a correlation matrix of all this study's best traditional variables typically used to describe human endurance performance along with indices of maximal rates of skeletal muscle respiration. Variables include absolute ( abs ; L·min −1 ) rates of whole-body oxygen consumption (VO 2 ), relative ( rel ; ml·min −1 ·kg −0.32 ) VO 2 , power (W·kg −0.32 ), gross efficiency (GE), exercise economy (EC), cycling economy (CE), rate constant for the recovery of skeletal muscle oxygen consumption (k) or the reciprocal time constant for the recovery of skeletal muscle oxygen consumption (T c ). Traditional measures of VO 2 or power collected at maximal efforts were averaged ( max ). All fatigue thresholds were determined using the ventilatory equivalents (VEQ) method. Indices of exercise efficiency were determined during cadence-controlled cycling (80 rpm) at either 50 or 100 W (Blomstrand, Rådegran, & Saltin, 1997;Jacobs & Lundby, 2011), and measures of maximal cellular respiration (Ivy, Costill, & Maxwell, 1980;Jacobs et al., 2012;Pesta et al., 2011) all correlate with VO 2max . Highintensity interval training can increase maximal rates of skeletal muscle respiration, VO 2peak , and endurance performance independent of changes in maximal cardiac output, blood volumes, and oxygen carrying capacity of the blood . The strong relationships (R 2 > .80) between fatigue thresholds and maximal rates of skeletal muscle respiration (Ivy et al., 1980), which were confirmed in the current study (Figure 4), emphasize the primary role of skeletal muscle bioenergetic oxidative potential in determining one's fatigue threshold during exercise Poole et al., 2016;Vanhatalo et al., 2016). Maximal rates of skeletal muscle respiration obtained via high-resolution respirometry have also been identified as the single best predictor of cycling endurance performance in highly-trainedto-elite level athletes . The biological relationship between VO 2max , fatigue thresholds, and skeletal muscle oxidative potential most likely explain why maximal rates of skeletal muscle respiration more completely describe endurance performance ( Figure 5) when compared to other traditional variables commonly referenced in relation to the limits of human endurance potential across decades of human performance research (Coyle, 1995;Gabriel & Zierath, 2017;Joyner & Coyle, 2008).
Alternatively, abrogating training-induced improvements in skeletal muscle oxidative potential reciprocally blunts improvements in cardiorespiratory fitness, endurance capacity, and, sometimes, measures of whole-body health.
Supplementation of exogenous vitamin C with exercise training can blunt mitochondrial biogenesis in skeletal muscle (Bruns et al., 2018;Gomez-Cabrera et al., 2008) and minimize improvements in VO 2max and/or endurance performance in both humans and rats (Gomez-Cabrera et al., 2008). Diminished skeletal muscle mitochondrial protein is reported to parallel increases in heart rate, ventilation, respiratory exchange ratio, and blood lactate concentrations at the same absolute submaximal exercise intensity following 84 days of detraining (Coyle, Martin, Bloomfield, Lowry, & Holloszy, 1985). Higher VO 2max and lactate threshold values have also been attributed to approximately 50% higher measures of skeletal muscle capillarization and mitochondrial protein in detrained endurance athletes compared to sedentary controls with no history of exercise training (Coyle et al., 1985. More recently, metformin was shown to abolish exercise-induced increases in skeletal muscle respiration and attenuate concomitant improvements to VO 2max and wholebody insulin sensitivity using a randomized double-blind placebo-controlled design. Training-induced changes in skeletal muscle respiration also correlated with changes in whole-body insulin sensitivity (Konopka et al., 2019). The F I G U R E 5 Linear regression models determined via forward regression analyses in relation to 25-km time-to-completion (TTC). The labels within bars reports individual Adj R 2 values representing explained variance and the labels outside of the error bars represents the standard error of the estimate (SEE) as a percent of the averaged group TTC (2,680.9 s). The time constant for the recovery of skeletal muscle oxygen consumption (T c ); Traditional regression models 1, 2, and 3 are defined in the Results section under the section entitled, Regression modeling to explain cycling endurance performance F I G U R E 6 Measures of skeletal muscle respiration. The percent change in rates of skeletal muscle oxygen consumption (mVO 2 ) over time (a) was used to determine the rate (k) and time constants (T c ) for the recovery of mVO 2 (b). Values are separated into quartiles representing the fastest (1st) to the slowest (4th) 25-km times to completion, with an n = 6 in each quartile (total n = 24). The whiskers represent 95% confidence intervals importance of skeletal muscle oxidative potential most likely extends past the relationship with endurance performance, as the whole-body health benefits of exercise training track with improvements in exercise performance (Gabriel & Zierath, 2017). However, until recently, our ability to assess dynamic measures of skeletal muscle mitochondrial function relied primarily on access to an MRI scanner or the more invasive collection of a skeletal muscle via tissue biopsy.
NIRS-derived measures of skeletal muscle oxygenation allow for the direct noninvasive assessment of maximal rates of skeletal muscle respiration (Hamaoka et al., 1996;Ryan et al., 2014;Ryan, Southern, Reynolds, et al., 2013), with a precision capable of differentiating skeletal muscle oxidative potential across human participants with differing levels of fitness (Brizendine, Ryan, Larson, & McCully, 2013;Lagerwaard et al., 2019) and within-subject skeletal muscle respiratory changes contrasting trained and nontrained arms (Ryan, Southern, Brizendine, & McCully, 2013). NIRSderived measures of maximal skeletal muscle respiration have been validated against high-resolution respirometry-derived measures of maximal ADP-stimulated state 3 respiration (Ryan et al., 2014) using an in situ mitochondrial model with permeabilized muscle sample preparations that leave the mitochondrial reticular network intact (Kuznetsov et al., 2008) and in vivo PCr recovery kinetics via 31 phosphorus-magnetic resonance spectroscopy . A benefit of this NIRS methodology is that it allows for maximal rates of skeletal muscle respiration to be assessed without the collection of a skeletal muscle biopsy and away from a costly MRI scanner. This technique, originally tested in 1996 (Hamaoka et al., 1996) and later modified to control for blood volume changes with ischemic limb cuffing in 2012 (Ryan et al., 2012), could greatly improve practical applications of skeletal muscle mitochondrial assessments. Indeed, this study confirms previous findings (Jacobs et al., 2011), which were obtained through skeletal muscle biopsy sampling and high-resolution respirometry, showing that measures reflecting integrative and dynamic rates of maximal skeletal muscle respiration can strongly predict human endurance performance. More research is needed to fully examine the benefit of this procedure as well as general NIRS-derived measures of skeletal muscle oxygenation during exercise to possibly improve the precision with which individualized training can be monitored. NIRS-derived measures of skeletal muscle oxygenation during exercise improved regression modeling to explain 26.15-km (Jacobs et al., 2011) and15-km (van der Zwaard et al., 2018) time trial performances. These data provide the proof-of-concept necessary to further explore the use of skeletal muscle oxygenation assessment similar to, or along with, the use of heart rate during exercise to provide a real-time assessment of biological performance with respect to external measures of performance (i.e. power output, running velocity, etc.).
This study is the first study to completely validate the long-held premise that a combination of traditional variables derived from three separate physiologic tiers representing one's cardiorespiratory fitness, fatigue threshold, and bioenergetic efficiency during exercise, respectively, account for the majority of cycling endurance performance (i.e. >75%). The combination of abs VO 2max , %VO 2max VEQ , and CE 50 accounted for 76.2% of endurance performance variance. Many studies have identified one or two necessary components of the traditional variable postulate as predictive of endurance performance (Amann et al., 2006(Amann et al., , 2004Coyle, Coggan, Hopper, & Walters, 1988;Coyle et al., 1991;Lamberts et al., 2012;van der Zwaard et al., 2018 Measures of cycling power at maximal efforts, which also share a stronger relationship to maximal rates of skeletal muscle respiration (Figure 4), have been reported as more complete than respective measures of VO 2 (Hawley & Noakes, 1992;Lamberts et al., 2012).
Measures of power at maximal effort, however, provide minimal mechanistic insight regarding the biological parameters that are primarily responsible for setting the limits on human endurance performance. Of note, VO 2max more completely explained 15-km time trial performance (R 2 = .79) across a group of cyclists who competed at the national, international, or Olympic levels (van der Zwaard et al., 2018) than in the current study that included recreational-to-highly-trained participants ( Figure  1g). Together these findings highlight the inconsistencies and potential methodological pitfalls when relying on VO 2max to describe endurance performance potential, as is too common across exercise science research. An example of such research includes inappropriately controlled studies testing the live-high train-low model to improve sea level performance with VO 2max as the only measure of performance (Jacobs, 2013).

| Study limitations
The exercise tests conducted in this study were all obtained on the same day within the span of ~4 hr. No familiarization trials were conducted. We do not believe this decision influenced our primary outcome variables, as our data corresponds with previously published literature. For example, Lamberts et al. (2012) examined predictors of 40-km time trial performance across a group of highly trained competitive male cyclists (n = 45) in Cape Town, South Africa (~40 m elevation). Their study participants completed familiarization tests 72 hr prior to an incremental ramp test to collect variables at maximal effort and a 40-km time trial (Lamberts et al., 2012). While we did not conduct familiarization tests, a subsample (n = 14) of participants from our entire sample group (n = 24), consisting of our top cyclists, shared near identical individual characteristics (age, height, weight, VO 2max , PPO, etc.) and measures of performance (average time trial speed and power output) across independent studies (Table 4). Moreover, there was no difference between the ratio of power averaged throughout the TT 25 to W VEQ in those 14 study participants when compared to the additional 10 (Figure 7), which collectively make up the entire sample group for this study. The similarities across independent studies suggest that the lack of familiarization tests in the current study did not greatly influence the results.
Growing evidence suggests that critical power, which was not assessed in the current study, may be the most appropriate fatigue threshold method to assess threshold or functional power output in relation to endurance performance (Jones et al., 2019). Critical power has been shown to relate to cycling endurance performance better than various measures of power at VT (Black et al., 2014;Smith, Dangelmaier & Hill 1999) while measures of power at VT have been reported as superior to respective powers at LT (Amann et al., 2006). Given the complexities, assortment of methodologies, subjective interpretations and/or additional burden of obtaining VT and, especially, LT

T A B L E 4 This table reports study participant characteristics and
indices of cycling endurance performance from a subset (n = 14) of top performers in the current study collected at ~1,950 m alongside published values derived from highly-trained cyclists (Lamberts et al., 2012)  Note: Data reported as mean ± SD.
Abbreviations: NR, not reported; TT, time trial; TTC, time-to-completion; VO 2max , maximal rate of whole-body oxygen consumption.

F I G U R E 7
Comparison of the power ratio, defined as the average 25-km time trial power to individual fatigue threshold power identified using the ventilatory equivalents method, in the fastest (n = 14) versus the slowest (n = 10) study participants. Residuals from the Mann-Whitney test are plotted in a whereas the median difference and 95% confidence interval is shown in b values, we agree, in principal, with the benefit of determining critical power. Consequently, we have implemented a 3-min allout test of critical power (Vanhatalo et al., 2007) in our ongoing research in place of the verification max test utilized in the current study, 110% PPO until volitional fatigue. We cannot, however, rule out that measures of CP may have improved upon some of our 'traditional' regression models of performance. This decision was in part attributed to claims suggesting that the value of critical power is limited to high-intensity exercise efforts lasting under 10 min (Currell & Jeukendrup, 2008) and previous evidence demonstrating the strength of VT values, especially those determined by VEQ, in relation to 40-km time trial cycling performance (Amann et al., 2006). Lastly, all our measures of cycling endurance performance were collected in a controlled environment on a stationary cycle ergometer. While we utilized empirically derived data suggested to improve the translation of stationary laboratory cycling tests to real-world application by allometrically scaling necessary data to account for relationships between body mass, frontal area, and air resistance/drag when cycling outside on flat terrain (Swain, 1994), the results presented here should be reexamined in real-world conditions to validate these findings.

| SUMMARY
This study is the first to verify and validate the traditional predictive theoretical model of endurance performance based on one's VO 2max , a valid fatigue threshold, and an index of exercise efficiency to explain the majority (i.e. >75%) of cycling endurance performance. More importantly, however, this is the first study to demonstrate that one noninvasive NIRS-derived measure reflecting maximal rates of skeletal muscle respiration improves upon the predictive power of the traditional model accounting for 92.7% of endurance performance variance across trained study participants (n = 24). When compared to 43 traditional variables long postulated to predict human endurance performance, measures reflecting maximal rates of skeletal muscle respiration arguably stand alone as the best. E pluribus unum; out of many, one.