Using smoothing splines for detecting ventilatory thresholds

A recently developed nonparametric regression technique, called a polynomial smoothing spline, is presented for detecting the ventilatory threshold (VT) and respiratory compensation (RC) points from gas exchange response data taken during an incremental exercise test. This type of curve fitting has the advantage of not requiring investigators to specify, a priori, the form of the underlying model, as is required with all linear regression techniques. This procedure yields a mathematically optimal fitted curve through the O₂ uptake (VO₂) vs CO₂ output (VCO₂) data and estimates of the process’ first and second derivatives. A breakpoint or threshold is indicated by an increase in the value of the derivative and a peak in the second derivative. To evaluate this approach we analyzed gas exchange data collected on nine healthy subjects during a ramp exercise test (15 W·min⁻¹) to the limits of tolerance. Utilizing this procedure we detected VT and RC breakpoints in four subjects and only VT breakpoints in the remaining five subjects. Our results and those obtained using the more conventinoal linear regression method were similar for those subjects whose RC points were detected using the smoothing spline procedure. However, using regression techniques for subjects with low or otherwise undetectable RC breakpoints, the linear regression method yielded less reliable results in our hands.