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 VCO_{2} by VO_{2} plots,
the ventilatory equivalents, excess CO_{2} 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:

The V-slope method: This method consists of
plotting CO_{2} production over O_{2} 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.

The method of the ventilatory equivalents: This
method consists of plotting the ventilatory equivalents
for O_{2} (V_{E}/VO_{2}) and CO_{2}
(V_{E}/VCO_{2}) over time or over
O_{2} utilization and identifying the level of exercise
intensity corresponding to the first rise in V_{E}/VO_{2}
that occurs without a concurrent rise in V_{E}/VCO_{2}.

The Excess CO_{2} method: This method has been
operationalized in various ways. In WinBreak, the
operationalization of Excess CO_{2} follows that proposed
by Gaskill et al. (2001). According to their definition,
Excess CO_{2} = (VCO_{2}^{2} / VO_{2}) - VCO_{2}.
When Excess CO_{2} is
plotted over time or over O_{2} utilization, the gas exchange
threshold is thought to occur at the level of exercise
intensity corresponding to an increase in Excess CO_{2}
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 CO_{2} 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:

The Jones and Molitoris (1984) algorithm, as implemented
by Schneider et al. (1993). This method considers two
regressions, y = b_{0} + b_{1}x and
y = b_{0}+b_{1}x_{0}+b_{3}(x-x_{0}), and
then searches for the value of x_{0} that minimizes the
residual sum of squares.

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.

The "V-slope" algorithm proposed by Beaver et al.
(1986). This method consists of dividing the VCO_{2} by VO_{2}
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.

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.

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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