Bi-exponential modeling derives novel parameters for the critical speed concept

All-out exercise testing (AOT) has emerged as a method for quantifying critical speed (CS) and the curvature constant (D'). The AOT method was recently validated for shuttle running yet how that method compares with linear running is unknown. In the present study, we utilized a novel bi-exponential model that derives CS and D' with additional new parameters from the AOT method. Fourteen male athletes (age = 21.6 ± 2.2 years; height = 177 ± 70 cm; weight = 83.0 ± 11.8 kg) completed a graded exercise test (GXT) to derive maximum oxygen uptake ( $$ ) and the average speed between gas exchange threshold and $$ (sΔ50%), a linear AOT, and two shuttle AOTs. Measurement agreement was determined using intraclass correlation coefficient (ICC $$ ), typical error (TE), and coefficient of variation (CV). The y-asymptote ( $$ ) of the speed-time curve (3.52 ± 0.66 m·sec^-1 ) did not differ from sΔ50% (3.49 ± 0.41 m·sec^-1 ) or CS (3.77 ± 0.56 m·sec^-1 ) (P = 0.34). Strong agreement was observed for estimates of CS (ICC $$  = 0.92, TE = 0.18 m·sec^-1 , and CV = 5.7%) and D' (ICC $$  = 0.94, TE = 16.0 m, CV = 7.6%) with significant (P < 0.01) correlations observed between $$ and CS and between $$ and $$ (r values of 0.74 and 0.84, respectively). The time constant of the decay in speed ( $$ ) and the amplitude between maximal speed and $$ ( $$ ) emerged as unique metrics. The $$ and $$ metrics may glean new insights for prescribing and interpreting high-intensity exercise using the AOT method.