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on the gas exchange
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The gas exchange or ventilatory threshold has had a long history in exercise science and cardiorespiratory medicine. It is also a concept that has sparked considerable controversy over the years, particularly when interpreted as an index of the so-called anaerobic threshold or as causally related to the lactate threshold (Meyers & Ashley, 1997). Yet, despite the controversy, the concept has persisted, as it continues to be regarded by many as a useful practical marker of cardiorespiratory fitness and endurance capacity, a more appropriate, individually tailored criterion for exercise prescriptions compared to various arbitrary percentages of maximal capacity, and a meaningful non-invasive clinical measure of cardiorespiratory health.

In fact, it could be argued that the gas exchange threshold would have enjoyed a much greater popularity among scientists and practitioners if it was not for certain difficulties related to its determination. First, the difficulty lies in the fact that the scientific literature contains a wide variety of possible indices of the gas exchange threshold and the comparative evaluations of the validity and reliability of these indices do not always agree. The diversity of approaches is remarkable. The literature includes proposals focused on VCO₂ by VO₂ plots, the ventilatory equivalents, excess CO₂ production, the respiratory exchange ratio, ventilation and ventilatory frequency, and heart rate, among several others (Anderson & Rhodes, 1989; Hughson, 1984). Second, most of the proposed indices rely on subjective criteria for determining a "breakpoint," or change in the slope of plotted ventilatory data. Given the often erratic nature of such data, this subjectivity commonly leads to guesswork, a situation that makes trained scientists feel uncomfortable.

As a solution to the problems associated with the subjective nature of the traditional methods of determination, there have been several attempts to develop computerized methods, based on certain "objective" criteria. Specifically, such attempts have focused on (a) piecewise (2- or 3-phase) linear regression analyses, to identify a piecewise solution that provides a better fit to the data compared to a singular linear solution (e.g., Beaver et al., 1986), (b) time series analyses (combined with various other methods, such as hidden Markov chains), to identify a breakpoint while accounting for serially correlated noise in the data (e.g., Kelly et al., 2001), (c) fitting smoothing spline functions and examining the form of the derivatives (e.g., Sherrill et al., 1990), and others. While these approaches constitute significant advances, most have not found their way into day-to-day practice because (a) some of the mathematical concepts involved are complex and far-from-easy to implement independently and (b) the researchers who proposed these methods have not made any software programs to perform the necessary computations publicly available. Today, some integrated metabolic analysis software packages offer a method for the "automatic" estimation of the gas exchange threshold (usually based on the "V-slope" method proposed by Beaver et al., in 1986 or the "simplified V-slope" method proposed by Sue et al. in 1988), but the exact methods used are poorly documented and the computational details are not disclosed. Furthermore, since all methods can and do fail to produce satisfactory solutions in the cases of certain data sets, relying on a single method of determination leaves users with no recourse in cases of unsatisfactory solutions, other than having to resort to subjective criteria.

WinBreak was developed to address these problems. This is achieved by (a) combining the intuitive appeal of graphical methods with the objectivity of statistical modeling, (b) offering multiple parallel methods of determination as opposed to a single method, and (c) allowing users to experiment with a variety of solutions and visualization options. Specifically, following Gaskill et al. (2001), WinBreak uses the following three graphical methods:

1. The V-slope method: This method consists of plotting CO₂ production over O₂ utilization and identifying a breakpoint in the slope of the relationship between these two variables. The level of exercise intensity corresponding to this breakpoint is considered the gas exchange threshold.

2. The method of the ventilatory equivalents: This method consists of plotting the ventilatory equivalents for O₂ (V_E/VO₂) and CO₂ (V_E/VCO₂) over time or over O₂ utilization and identifying the level of exercise intensity corresponding to the first rise in V_E/VO₂ that occurs without a concurrent rise in V_E/VCO₂.

3. The Excess CO₂ method: This method has been operationalized in various ways. In WinBreak, the operationalization of Excess CO₂ follows that proposed by Gaskill et al. (2001). According to their definition, Excess CO₂ = (VCO₂² / VO₂) - VCO₂. When Excess CO₂ is plotted over time or over O₂ utilization, the gas exchange threshold is thought to occur at the level of exercise intensity corresponding to an increase in Excess CO₂ from steady state.

WinBreak produces the plots required for implementing these three methods with one mouse click, enabling users to obtain a quick graphical representation of the their data. Furthermore, using a feature called the "Visualization Tool", WinBreak applies mathematical algorithms designed to identify a breakpoint in the plotted relationships. Specifically, for the method of the ventilatory equivalents and the Excess CO₂ method, WinBreak uses the standard algorithm proposed by Jones and Molitoris (1984) for identifying the breakpoint of two lines. For the V-slope method, WinBreak uses five algorithms:

1. The Jones and Molitoris (1984) algorithm, as implemented by Schneider et al. (1993). This method considers two regressions, y = b₀ + b₁x and y = b₀+b₁x₀+b₃(x-x₀), and then searches for the value of x₀ that minimizes the residual sum of squares.

2. The "brute force" algorithm proposed by Orr et al. (1982). This method consists of calculating regression lines through all possible divisions of the data into two contiguous groups, and finding the pair of lines yielding the least pooled residual sum of squares.

3. The "V-slope" algorithm proposed by Beaver et al. (1986). This method consists of dividing the VCO₂ by VO₂ curve into two regions, fitting linear regressions through them, and identifying the point at which the ratio of the distance of the intersection point from a single regression line through the data to the mean square error of regression is maximized.

4. The "Dmax" algorithm proposed by Cheng et al. (1992). This method consists of calculating a third-order polynomial regression curve to fit the data and drawing a straight line connecting the first and last data points. The breakpoint is then defined as the point yielding the maximal distance between the curve and the straight line.

5. The "simplified V-slope" algorithm proposed by Sue et al. (1988) and Dickstein et al. (1990). This method again calculates regression lines through all possible divisions of the data into two contiguous groups, and finds a breakpoint at which the first regression has a slope of less than or equal to 1 and the second regression has a slope higher than 1.

In addition, WinBreak allows users to examine the complete computational details of all these methods, to compare the fit of the two-regression solutions to a single-regression solution, and to view and contrast plots of the residuals produced by these solutions. Finally, WinBreak allows users to shift the location of the breakpoint and observe the resultant changes in the slope of the regression lines. This functionality is supplemented by an extensive array of data manipulation tools (e.g., averaging, interpolation, outlier removal, smoothing), ease of use, and the ability to save and print fully customized, presentation-quality graphics.

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