Bi-exponential modelling of W' reconstitution kinetics in trained cyclists
About half of W' returns fast (time constant 21.5 s) and half slowly (388 s); after a second exhaustive bout the slow half slows further (716 s)
Participants
n=10 trained cyclists, age 41 ± 10 y, mass 73.4 ± 9.9 kg, VO2max 58.6 ± 7.1 ml/kg/min.
Protocol
Three incremental ramps (20 W/min) to the limit of tolerance per visit, separated by recovery periods of varying length (15-360 s); 5-9 visits per cyclist.
W' reconstitution measured after the first and after the second recovery period.
Mono-exponential and bi-exponential models compared with adjusted R² and bias-corrected AICc.
Key Findings
The bi-exponential model outperformed the mono-exponential one (AICc 30.2 vs 72.2) and fitted group-mean data with adjusted R² = 0.999.
Group-mean parameters, first recovery: fast component amplitude 50.67%, slow component 49.33%; time constants τ-fast = 21.5 s, τ-slow = 388 s.
After the second recovery, W' reconstitution was lower by 9.1 ± 7.3% at 180 s and 8.2 ± 9.8% at 240 s; the modelled τ-slow rose to 716 s with τ-fast unchanged.
Individual models also fitted well (adjusted R² 0.978 ± 0.017) but with large between-rider variation: fast amplitude 47.7 ± 17.8%; first recovery τ-fast 22.0 ± 11.8 s and τ-slow 377 ± 100 s; second recovery τ-fast 16.3 ± 6.6 s in the abstract (printed "16.3.0") and Table 2, 16.6 ± 6.6 s in the Results text (corrected 2026-10-12, full text) and τ-slow 549 ± 226 s.
Authors' conclusion: W' recovers in distinct fast and slow phases; repeated bouts do not change the two amplitudes, but slow the slow phase.
What it means for intervals
Inference from the model, not a tested prescription: with a fast phase of ~21 s, a recovery of 15-30 s returns mostly the fast half of W'; with a slow phase of ~6.5 min (388 s), even 3-4 min of recovery leaves a substantial part of the slow half unrecovered — and after each further exhaustive effort that slow half recovers more slowly still (716 s).
Inference, not tested: recoveries shorter than a few minutes therefore keep the athlete working with a partly depleted W', which is one reason short-recovery formats accumulate fatigue quickly; whether that helps VO2max development was not studied here.
Practical Application
In 10 trained cyclists (41 y, VO2max 58.6) doing three ramps to exhaustion with 15-360 s recoveries, W' recovered along a bi-exponential curve: about half (50.7%) came back fast (time constant 21.5 s) and half slowly (388 s); after a second exhaustive bout the slow half slowed further (time constant 716 s; W' at 180-240 s down by 8-9%) while the fast half was unchanged, and individual time constants varied widely. For an athlete: short rests return only the quick half of your anaerobic reserve, and every successive all-out effort makes full recovery take longer — plan sets, not just intervals.
Limitations
n=10 trained cyclists, one sex composition not given in the abstract; large individual variation in parameters (τ-slow SD 100-226 s).
Ramp-to-exhaustion protocol, not constant-power intervals; the model's transfer to interval sessions is inference.
Group-mean and individual fits both good, but the model was derived in the same data it was fitted to.
How this entry was checked and changed
Why this level
regraded 2026-09-27 from A: within-subject study, n=10
Content correction 2026-09-27
"Optimal recovery for VO2max: 1.5-2.5 min", "shortened recovery from 3 min to 2 min", "at 3-4 min nearly complete W' recovery", "HIDIT perfectly fits" -> not in the abstract (and with τ-slow 388 s the slow half is far from complete at 3-4 min); removed or relabelled as inference.
Added the abstract's second-recovery results (τ-slow 716 s; W' reconstitution −9.1% at 180 s and −8.2% at 240 s) and the individual-variation figures, which the entry lacked.
Level A -> B: within-subject study, n=10. Tier 2-3 -> Tier 2 (VO2max 58.6).
Full text (checked 2026-10-12)
The ten cyclists were 9 male and 1 female amateur competitive cyclists with a training history of 5–14 h week−1 for a minimum of 12 months, tested at the end of their racing seasons (full text).
Each test began with 5 min at 100 W, then a 20 W·min−1 ramp to the limit of tolerance (cadence below 60 r min−1) and a step-down to CP + 30 W until cadence fell below 50 r min−1; recoveries were at 50 W, and later ramps started at CP + 30 W (full text).
Recovery pairs (first/second) were 30 s and 240 s, 60 s and 180 s, 120 s and 120 s, 180 s and 60 s, and 240 s and 60 s, in Latin-square order; three participants did extra sessions at 15 s, 45 s, 5 min and 6 min (full text).
Group CP was 300 ± 37 W and W′ was 9.4 ± 1.8 kJ (full text, Table 1).
Over 30–240 s of recovery, W′ reconstitution ranged from 41.6 ± 10.8% to 73.5 ± 8.3% after the first recovery and from 45.7 ± 14.3% to 65.3 ± 5.8% after the second (full text).
Compared with the first recovery, the second gave a non-significant increase of 4.2 ± 6.6% at 30 s (ES = 0.63) and decreases at 60 s (1.6 ± 9.5%, ES = 0.16), 120 s (3.4 ± 6.7%, ES = 0.51), 180 s (9.1 ± 7.3%, ES = 1.25) and 240 s (8.2 ± 9.8%, ES = 0.84) (full text).
After the first 30 s, W′ reconstitution ranged between 24 and 60% (absolute values: 2.5–4.8 kJ) across individuals; mono-exponential time constants were 125 ± 53 s (first recovery) and 131 ± 69 s (second) (full text).
Correction: the entry gives the individual second-recovery τ-fast as "16.3 ± 6.6 s" (the abstract prints "16.3.0 ± 6.6 s"), while the Results section gives "R2τFC = 16.6 ± 6.6 s" (full text).