This study was undertaken in two parts: a primary study in cycling where participants performed four different laboratory-based training sessions, and a validation study where participants performed a single laboratory-based training session using one of three exercise modalities (cycling, running, or kayaking). Conceptually, this study includes a cross-sectional observational study (primary study) as well as a prediction model development and validation study (primary and validation studies). Accordingly, we adhered to the STROBE [22] and TRIPOD + AI [23] reporting guidelines where applicable.

The primary study included 15 participants (ten male, five female), the validation study included 59 participants (41 male, 18 female). Sample size calculations are described in detail in Sect. 2.5. Participant characteristics are shown in Table 1. The study was open to all healthy male or female individuals aged 18–55 years regularly performing ≥ 3 h/week of training in the modality used for testing (cycle, run, or kayak). All interested participants that met the criteria were enrolled, and everyone enrolled completed all sessions. Study protocols and materials were approved by the Auckland University of Technology Ethics Committee (23/143 and 23/258).

Participants reported to the laboratory on five occasions, with 1–7 days between sessions and without performing high-intensity sessions on consecutive days. Participants refrained from intense exercise and alcohol 24 h before each visit and avoided caffeine 16 h before each visit. Exercise was permitted the day before each session, with the duration and sRPE recorded using the Borg CR100® scale [24]. No exercise was allowed on the day of any laboratory visit. Participants were asked to maintain their normal dietary habits and recorded their intake for 1 day prior to each of visits 2–4 using a smartphone-based application that features foods from Australia and New Zealand (Easy Diet Diary, https://xyris.com.au/products/easy-diet-diary). All trials were conducted under standard laboratory conditions (18–20 °C, 40–65% relative humidity), with participants fan-cooled during exercise.

Participants reported to the laboratory in an overnight-fasted state. After obtaining written informed consent and completing a health screening, a graded exercise test was performed to determine ventilatory thresholds and maximal oxygen consumption (\(\dot\)O2max). Participants cycled on an electronically braked cycle ergometer (Excalibur Sport; Lode BV, Groningen, The Netherlands), with expired gas collected and analyzed using a computerized metabolic system with mixing chamber (TrueOne2400; ParvoMedics, Sandy, UT, USA). The test began at 95 W, and power output increased by 35 W every 3 min until identification of the second ventilatory threshold (VT2), where the ventilatory equivalent for oxygen (\(\dot\)E⋅\(\dot\)O2−1) and carbon dioxide (\(\dot\)E⋅\(\dot\)CO2−1) increased alongside a reduction in PetCO2 [17]. Participants then cycled for 10 min at 100 W, followed by a step test starting at 150 W and increasing 30 W/min to task failure to obtain \(\dot\)O2max. Thirty seconds following the test, a 0.3-μL blood sample was collected from the left index fingertip and analyzed immediately using a portable blood lactate analyzer (Lactate Pro 2, Carlton, VIC, Australia). The first ventilatory threshold (VT1) was identified as the work rate at which \(\dot\)E⋅\(\dot\)O2−1 began to increase in the absence of changes in \(\dot\)E⋅\(\dot\)CO2−1. Peak power (Wmax) was determined by the workload in the last completed stage plus the workload relative to the time spent in the last incomplete stage [power of completed stage + (30 × (seconds at uncompleted stage/60)], and \(\dot\)O2max and peak fat oxidation were recorded as the highest 15-s value from a moving average, calculated using the equation of Jeukendrup and Wallis [4] and a 1-s interpolation of breath-by-breath data.

In a randomized and counter-balanced order, participants completed four different training sessions as follows: (1) 90 min continuous cycling at 90% of VT1 power (low-intensity training [LIT] long), (2) 30 min continuous cycling at 90% of VT1 power (LIT-short), (3) 15 min continuous cycling at 90% of VT1 power, followed by two sets of 5 × 3-min intervals with 2 min recovery between intervals and 8 min recovery between sets (high-intensity interval training long, HIIT-long), and (4) 15 min continuous cycling at 90% of VT1 power, followed by two sets of 10 × 30-s intervals with 30-s recovery between intervals and 8-min recovery between sets (HIIT-short). All sessions were performed on the Lode cycle ergometer, with intervals performed using the cadence-dependent linear mode set to produce a workload of 110% VT2 power at their preferred cadence. Participants were instructed to produce their maximal power output across intervals. All recovery intervals were active recovery at 30% Wmax. All sessions were performed at the same time of morning (within 1 h) following an overnight fast. A standardized snack (Frooze balls, 27 g of CHO, 8 g of protein, 19 g of fat; Revive Foods, Auckland, New Zealand) was provided for participants to consume 45 min prior to starting exercise, and ad libitum water intake was allowed before and during the training session.

Music was played during all sessions except the graded exercise test. This was because many cyclists listen to music while training, particularly during extended duration indoor training sessions. Each participant selected their own playlist from a commercial streaming platform, which was repeated for each subsequent visit. Music was standardized based on individual preferences rather than playing the same music for all participants because of the influence of preferred versus non-preferred music on RPE during exercise [25]. An sRPE value was recorded 10–15 min following exercise using the Borg CR100® scale, which offers additional precision compared with the CR10 scale [26]. Participants were familiarized with the CR100 scale in advance of the trials and given the scale for use at home 2 weeks prior to the first testing session.

Expired gas was measured during the last 6 min of every 15-min period during LIT sessions, and from minute 9 onwards during the HIIT sessions, with the exception of a 2-min break during minutes 6–7 of the recovery period between the two sets of intervals. Blood lactate level was measured 30 s before and 30 s after each interval set during the HIIT sessions. A schematic overview of the sessions for the primary and validation arms is shown in Fig. 1.

Schematic overview of the testing sessions. GXT graded exercise test, HIIT high-intensity interval training, LIT low-intensity training, min minutes, RBI rest between intervals, RBS recovery between sets, VO2max maximal oxygen consumption, VTs ventilatory thresholds, VT1 first ventilatory threshold

To validate the prediction equations established in the primary study and to assess their generalizability to other exercise modalities, 59 additional participants were recruited to perform a graded exercise test and a single exercise session using either a cycling ergometer, motorized treadmill (h/p/cosmos, Nussdorf, Germany), or kayak ergometer (Dansprint, Hvidovre, Denmark). The graded exercise test was performed for cyclists as described above, whereas running tests began at 10 km/h and increased in 1-km/h increments, and kayaking tests began at 40 W (female participants) and 60 W (male participants) and increased in 15-W (female participants) and 20-W (male participants) increments. Participants returned to the laboratory 2–7 days later to perform a mixed-intensity exercise session consisting of 30 min of continuous exercise at 95% of VT1 power, followed by a 5-min recovery (5 min active recovery at 100 W for cyclists, or 3 min passive recovery followed by 2 min walking at 4 km/h for runners or 20 W on the kayak ergometer), and 6 × 3-min intervals with 2 min rest between intervals where participants were encouraged to give their best effort across the six intervals (Fig. 1). The cycling intervals were performed as described for the initial HIIT sessions, using the cadence-dependent linear mode. Treadmill intervals were set at 107% VT2 speed based on pilot testing. The intensity for kayak intervals was dictated by the participant. Recovery between intervals was set at 30% peak power output for cycling, 4 km/h for running, and 20% peak power output for kayak sessions.

The validation session was designed to be similar to a typical training session, but different from the sessions in the initial arm of the study. Session rating of perceived exertion was collected 10–15 min following exercise. Expired gas was measured during the last 6 minutesof every 15-min period during the 30-min continuous cycling, and for the remainder of the session. Lactate was measured 30 s before and 30 s after the interval set. A Stryd power meter (Stryd, Boulder, CO, USA) was used to collect running power data [27], and stroke-by-stroke power was collected from the kayak ergometer. To increase generalizability, validation sessions could be performed at any time of day, but subjects refrained from eating in the 4-h pre-exercise window, with the exception of the same standardized snack consumed 45 min prior to exercise.

Carbohydrate utilization and energy expenditure during exercise were determined separately for aerobic and anaerobic energy systems. For each exercise session, breath-by-breath gas exchange data were interpolated into second-by-second values using the whippr R package [28]. To determine the contribution from aerobic energy production, \(\dot\)O2 values were converted to energy equivalents based on respiratory exchange ratio (RER) values using the conversion tables of Elia and Livesey [12]. This allows RER-specific energy conversions to be used. For example, the energy equivalent of 1 L of O2 is 4.687 kcal at an RER of 0.71, and 5.048 kcal at an RER of 1.0 [12]. This approach also allows the calculation of energy equivalents for RER values > 1.0 as CO2 is not needed for calculations [12]. To account for excess (non-oxidative) CO2 excretion, we considered 5.048 kcal/L as the maximum energy equivalent for the aerobic contribution if RER values were > 1.0. Energy equivalents were calculated on a second-by-second basis for the entire session (step 1). The RER value was then used to estimate the percentage of carbohydrate and fat oxidation using the conversions of Elia and Livesey [12]. The percentage carbohydrate contribution was multiplied by the energy equivalent to calculate energy from carbohydrate sources (step 2).

To convert from energy (kcal) to mass (g) of carbohydrate, consideration of exercise intensity is required. This is because the energy yield from carbohydrate varies depending on the source, with a range from 3.719 kcal/g of glucose to 4.187 kcal/g of glycogen [29]. The equations of Jeukendrup and Wallis [4] vary based on exercise intensity, assuming 50% of the carbohydrate oxidation is derived from plasma glucose and 50% from muscle glycogen during low-intensity exercise (40–50% \(\dot\)O2max), and 20% from glucose and 80% from muscle glycogen at moderate-to-high intensity exercise (50–75% \(\dot\)O2max). This results in carbohydrate oxidation yielding 3.95 kcal/g of carbohydrate during low-intensity exercise, and 4.07 kcal/g of carbohydrate during moderate-to-high intensity exercise [4]. It has also been recommended that resting analyses should assume 100% glucose oxidation [4]. With this in mind, we used a scaled approach whereby the percent contribution from glycogen was assumed to be equal to the exercise intensity as a percentage of \(\dot\)O2max, allowing a second-by-second adjustment according to exercise intensity (step 3). The energy yield from glucose and glycogen-derived carbohydrate oxidation was then calculated and summed to get an intensity-adjusted energy yield from carbohydrate (step 4). The value for energy (kcal) from carbohydrate sources was divided by the adjusted energy yield to get a value of carbohydrate in grams for each second (step 5), with these values summed to yield a session total for grams of carbohydrate utilized through the aerobic energy pathways. A step-by-step example is shown in Box 1 for a \(\dot\)O2 of 2.9 L/min and an RER of 0.93, for someone with a \(\dot\)O2max of 3.8 L/min.

Box 1 Example Calculation of Aerobic Energy Production

Step 1: Calculate energy expenditure per second.

RER of 0.93 yields 4.961 kcal/L O2/min

2.9 L × 4.961 kcal/L = 14.39 kcal/min/60 = 0.240 kcal/s

Step 2: Calculate energy expenditure from carbohydrate sources.

RER of 0.93 corresponds to a contribution from carbohydrate of 77.19%

0.240 kcal/s × 0.7719 = 0.185 kcal/s from carbohydrate

Step 3: Calculate percent contribution from glucose and glycogen sources, assuming percentage of glycogen is equivalent to percentage of \(\dot\)O2max.

2.9 L/3.8 L = 76.3% from glycogen

1 − 76.3% = 23.7% from glucose sources

Step 4: Calculate energy yield from glucose-derived and glycogen-derived carbohydrate oxidation, summed for a total intensity-adjusted energy yield.

23.7% × 3.719 = 0.881 kcal/g from glucose

76.3% × 4.187 = 3.195 kcal/g from glycogen

0.881 + 3.195 = 4.076 kcal/g carbohydrate

Step 5: Calculate carbohydrate in grams per second.

0.185 kcal from carbohydrate per second (from step 2)/4.076 kcal/g (from step 4) = 0.045 g carbohydrate per second

Step 6: Calculate the sum of the second-by-second values to get a session total. Expired gas was recorded for the last 6 min of each 15-min block during low-intensity cycling, with the first minute of each collection period discarded. Therefore, values for the 5-min periods were multiplied by 3.

Energy produced from anaerobic lactate metabolism was determined using the net lactate accumulation, body mass, and O2 lactate equivalent method [3, 8], with example calculations shown in Box 2. Lactate was measured before and after the interval sets during the HIIT trials, with the change in lactate (post–pre) multiplied by 3 mL O2⋅kg–1⋅mmol⋅L–1 to create an oxygen equivalent [3], which was then multiplied by 21.1 kJ/L [8], and divided by 4.184 to convert from kJ to kcal (step 1).

To convert from energy (kcal) to mass (g) of carbohydrate, consideration of the ATP yields from anaerobic glycolysis and aerobic oxidation of carbohydrate is required. The net yield of anaerobic glycolysis is 2.9 ATP when starting from glycogen (assuming 90% α-1,4 glycosidic bonds) and 2 ATP when starting from glucose [30]. The complete oxidation of glycogen yields 34.35 ATP, and complete oxidation of glucose yields 33.45 ATP [30]. During high-intensity exercise, we assume the substrate for anaerobic glycolysis is glycogen, implying it would require 11.845 times more carbohydrate (because 34.35/2.9 = 11.845) to produce the same amount of ATP via anaerobic, compared with aerobic, metabolism. Based on the aerobic yield of 4.187 kcal/g of glycogen [12], we calculated grams of carbohydrate from anaerobic sources as kcal from step 1 divided by 4.187, multiplied by 11.845 to account for the inefficiency of ATP production from anaerobic glycolysis (step 2). This process was repeated for both interval sets. Total carbohydrate expenditure was calculated by summing the contributions from the aerobic and anaerobic systems. A step-by-step example of anaerobic energy calculation is shown in Box 2.

Box 2. Example Calculation of Anaerobic Energy Production

Step 1: Calculate kcal from anaerobic energy production.

Delta lactate = 9.3 mmol/L (post) − 1.5 mmol/L (pre) = 7.8 mmol/L

Oxygen equivalent = 3 × 7.8 × 70 kg body mass = 1638 mL O2 = 1.638 L O2.

1.638 L × 21.1 kJ/L = 34.56 kJ.

34.56 kJ/ 4.184 = 8.26 kcal via anaerobic energy production.

Step 2: Convert from kcal to grams of carbohydrate while accounting for the inefficiency of anaerobic energy production.

8.26 kcal/4.187 × 11.845 = 23.4 g carbohydrate

A visual overview of the pathways involved in energy production and rationale for this approach is provided in Fig. 2.

Overview of primary energy producing pathways in skeletal muscle. During glycolysis from glucose, 1 ATP is consumed at hexokinase and 1 ATP is consumed at phosphofructokinase to yield 2 trioses, each of which generates 1 ATP at phosphoglycerate kinase and 1 ATP at pyruvate kinase, for a net yield of 2 ATP/glucose. When starting from glycogen, less ATP is needed for the initial activation at hexokinase (~ 0.1 ATP), resulting in a greater net yield of 2.9 ATP [30]. An additional 31.45 ATP is produced from oxidative reactions, bringing the maximum total yield to 34.35 ATP from glycogen and 33.45 ATP from glucose. Glucose enters the cell via glucose transporters (GLUT)1 and 4. Lactate can be removed from the cell via monocarboxylate transporters (MCT). Fatty acids can enter the cell via fat transport proteins including cluster of differentiation 36 (CD36). Differences in efficiency are highlighted by a comparison of ATP production; to produce 100 ATP requires 34.5 glycogen molecules via anaerobic energy production or 2.9 glycogen molecules via aerobic energy production. Acetyl CoA acetyl coenzyme A, TCA cycle citric acid cycle

In addition to the strong theoretical and mechanistic rationale for this approach, we also tested our method using data from previously published studies that included metabolic tracers and/or muscle glycogen measurements. Calculations are provided in the Electronic Supplementary Material (ESM), showing good agreement (e.g., estimations of total carbohydrate utilization within ~ 1–4 g) when comparing our method with estimates using invasive techniques. For each exercise session, six measures of training load were calculated as shown in Table 2.

To estimate differences in training load across the four sessions for each metric, a series of linear mixed models were fitted using the lme4 R package with training load as the dependent variable, session as a fixed factor, and participant ID as a random intercept. Model-estimated means were calculated using the emmeans R package and contrasts between each session (within each training load metric) were estimated using the Holm correction for multiple comparisons. To examine the bivariate relationship between training load measures and the total carbohydrate and energy cost of exercise, a repeated-measures correlation was performed using the rmcorr R package, which allows analysis of repeated-measures data without violating independence assumptions [32]. To examine day-to-day variation, all four trials began with the same 15-min period of cycling at 90% VT1 power, allowing us to compute the typical error of measurement for VO2, HR, carbohydrate oxidation, and RPE according to the approach of Hopkins [33].

To predict carbohydrate utilization and energy expenditure based on training load and other commonly measured variables known to influence substrate selection such as \(\dot\)O2max, sex, and dietary intake [34], multivariable models were created for each of the six training load measures predicting each of the two dependent variables (energy expenditure and carbohydrate utilization) using generalized estimating equations. Generalized estimating equation models provide population-averaged (e.g., marginal), rather than subject-specific models while accounting for repeated measurements within participants [35]. The Quasi Information Criterion was used for selecting an independence correlation structure as the working correlation matrix [36]. The following variables were considered for the full models: training load, training load2, session duration (minutes), session duration2, prior-day sRPE training load (sRPE-TL), type of session (continuous or interval training), prior day dietary carbohydrate and fat intake (g/kg), \(\dot\)O2 at VT2 (L/min and % \(\dot\)O2max), \(\dot\)O2max (mL/kg/min and L/min), blood lactate at the end of the \(\dot\)O2max test, peak fat oxidation (g/min), and sex. The following pre-specified interactions were also considered in the full model: prior-day sRPE-TL × prior day carbohydrate intake, session duration × training load, type of session × training load, type of session × \(\dot\)O2max, and type of session × \(\dot\)O2 at VT2.

The top candidate models were identified using the glmulti R package [37], which performs a genetic search across possible models specified by a given set of predictors and selects the top models according to the corrected Akaike Information Criterion. From the reduced pool of models, we performed participant-level leave-one-out cross-validation, which fits a series of models on all but one of the participants, whose four sessions are used as a hold-out testing set [38], selecting the model with the lowest mean absolute error (MAE) as the final model for each measure of training load. The fit of each model was checked by visualizing the Q–Q and other residual plots to ensure approximate residual normality and homoscedasticity using the performance R package. Model performance is reported as the coefficient of determination (R2), which represents the proportion of variance explained by the model, and the MAE, which quantifies the average absolute discrepancy between the observed and predicted values. These metrics were calculated using both in-sample data (i.e., the same data used to train the model and evaluate performance) and cross-validation, which offers a more realistic and unbiased (or least biased) estimate of model performance in the population in which the model is intended [39]. Performance metrics for cross-validation are reported as mean [95% confidence intervals]. There were no missing data for models in the primary study.

Data from the validation sessions were analyzed in the same manner as the primary study, with each session analyzed as only the 30-min low-intensity portion, and as the full session (30-min low-intensity and high-intensity intervals). Values of total carbohydrate utilization and energy expenditure for each session were predicted from the previously fit models for each measure of training load. Model performance was assessed using measures of overall fit R2 (proportion of variance in explained in the external validation dataset, calculated using the traditional definition with sum of squares rather than the correlation between predicted and actual values) and MAE, and assessed for calibration, which was quantified as calibration-in-the-large (the difference between mean observed and mean predicted outcome values, with 0 being ideal) and calibration slope (the agreement between predicted and observed values across the range of predicted values, with a slope of 1 being ideal) [39]. Finally, models were recalibrated using the intercept and slope of a linear model regressing the actual values on the predicted values [40], with measures of R2 and MAE reported on the calibrated data. Because of technical issues, data for the low-intensity portion of one kayak trial and the total work done for one running trial were missing. Rather than using imputation, these data points were omitted from the predictions. One other kayaking trial consisted of only three intervals because of an equipment malfunction but data from the first 45 min of the session were included for analysis.

Based on Riley et al. [41], a minimum sample size of 15 was calculated for the primary study. This calculation used an estimated adjusted R2 value of 0.89 and considered a model with up to six predictors. The choice of six predictors was derived from Riley et al. [42], to ensure a shrinkage factor of at least 0.9 and to maintain a difference between adjusted and apparent R2 values below 0.05. However, our sample size is below the minimum size of 240 (using the rule of 234 + number of predictors) needed for precise estimates of the residual standard deviation [41]. This means there will still be some uncertainty in the parameter estimates that can only be solved with very large sample sizes that extend beyond the capacity of this project. The approach of Archer et al. [43] was used to calculate the minimum sample sizes needed in the validation dataset to obtain precise estimates of R2, calibration-in-the-large, and calibration slope, assuming 90% confidence intervals with target widths of 0.2 for R2 and 0.2 for the calibration slope. Calculations were made separately for each model, resulting in a minimum requirement of 7–11 participants (kcal) and 13–19 participants (carbohydrate) in each validation arm depending on the model (Table 1 and R code in the ESM). For the kayaking arm of the validation study, we were only able to recruit 18 athletes, which is sufficient for all energy expenditure models and five of the six carbohydrate models, but just below the target sample size of 19 for sRPE-TL.

To determine the minimum sample size for detecting differences in training load across the four sessions in the primary study, we calculated the means and standard deviations for each session, estimated the pooled standard deviation, and determined the effect size (Cohen’s f). Using these values, we performed a power analysis that indicated that a sample size of six participants was required to achieve 95% power at a 5% significance level. All analyses were carried out with R version 4.3.1 (The R Foundation for Statistical Computing, Vienna, Austria). Descriptive statistics are provided as mean ± standard deviation, statistical significance was accepted at p < 0.05.