Originally Posted by
acoggan .
I've discussed the limitations to the impulse-response model in some detail here:
http://home.trainingpeaks.com/articles/cycling/the-science-of-the-performance-manager.aspx
And just to drive those points home (y'all might want to bookmark this post for future reference! /img/vbsmilies/smilies/wink.gif):
1) While the impulse-response model can be used to accurately describe changes in performance over time, it has not been possible to link the structure of the model to specific, training-induced physiological events relevant to fatigue and adaptation, e.g., glycogen resynthesis, mitochondrial biogenesis. In that regard the model must be considered purely descriptive in nature, i.e., largely a “black box†into which it is not possible to see. Although this by no means invalidates the approach, being able to relate the model parameters (in particular, the time constants
Ï„a and
Ï„f (or
Ï„1 and
Ï„2)) to known physiological mechanisms would allow the model to be applied with greater confidence and precision.
2) The impulse-response model essentially assumes that there is no upper limit or upper bound to performance, i.e., a greater amount of training always leads to a higher level of performance, at least once the fatigue due to recent training has dissipated. In reality, of course, there will always be some point at which further training will not result in a further increase in performance, i.e., a plateau will occur. This is true even if the athlete can avoid illness, injury, overtraining, or just mental “burn outâ€. While Busso et al. have proposed a modification to the original model that explicitly recognizes this fact and which results in a slightly improved fit to actual data, this modification further increases the mathematical complexity and requires an even larger amount of data be available to solve the model (see below).
3) To obtain a statistically valid fit of the model parameters to the actual data, it is necessary to have multiple, direct, quantitative measurements of performance. The exact number depends in part on the particular situation in question, but from a purely statistical perspective somewhere between 5 and 50 measurements
per adjustable parameter would generally be required. Since the model has four adjustable parameters, i.e.,
Ï„a and
Ï„f (or
Ï„1 and
Ï„2) and
ka and
kf (or
k1 and
k2), this would mean that performance would have to be directly measured between 20 and 200 times in total. Moreover, since the model parameters themselves can change over time/with training (see more below), these measurements should all be obtained in a fairly short period of time. Indeed, Banister himself has suggested revisting the fit of the model to the data every 60-90 d, which in turn would mean directly measuring an athlete’s maximal performance ability at least every 4th day, if not several times per day. Obviously, this is an unrealistic requirement, at least outside of the setting of a laboratory research study.
4) Even when an adequate number of performance measurements are available, the fit of the model to the data is not always accurate enough for the results to be helpful in projecting
future performance (which is obviously necessary to be able to use the impulse-response model to plan a training program). In other words, even though an adequate R2 might be obtained with a particular combination of parameter estimates, the parameter estimates themselves may not always be sufficiently stable, or certain, to be enable highly reliable prediction of future performance. This seems to be particularly true in cases where the overall training load is relatively low, in which case the addition of the second, negative term to the model often does not result in a statistically significant improvement in the fit to the data, i.e., the model can be said to be
overparameterized. In other studies in the literature, the parameter estimates that provide the best mapping of training (i.e., the input function to the model) to performance (i.e., the output of the model) fall precisely on the constraints imposed when fitting the model, i.e., the model has essentially been forced to fit the data. Again, while this is not necessarily an invalid approach, it suggests that either the model structure is inadequate (even if it the best available choice) to truly describe the data, or that the data themselves are too variable or “noisy†to be readily fit by the model.
5) As illustrated by the data shown in Table 1, the values reported in the literature for
Ï„a (or
Ï„1) are quite consistent across studies, at least when one considers a) the wide variety of sports that have been studied (and hence the wide variety of training programs that have been employed), and b) that the model is relatively insensitive to changes in
Ï„a (or
Ï„1 ) (i.e., increasing or decreasing
Ï„a (or
Ï„1) by 10% changes the output of the model by <5%). Moreover, the interindividual variation in
Ï„a (or
Ï„1) is relatively small, as indicated by the magnitude of the standard deviation compared to the mean value in each case. On the other hand, the values obtained for
Ï„f (or
Ï„2) do vary significantly across studies, and, to a somewhat lesser extent, also within a particular study (i.e., between individuals). However, these variations in
Ï„f (or
Ï„2) appear to be due, in large part, to differences in the overall training load. This effect is especially evident in the study of Busso (2003), in which increasing the training load (by increasing the frequency of training from 3 to 5 d/wk while holding all other aspects constant) resulted in ~33% increase in
Ï„f (or
Ï„2). In addition, the degree to which the training might be expected to result in significant muscle damage also appears to play a role. For example, the value for
Ï„f (or
τ2) obtained in the study of Morton et al. (1990), which involved running, is comparable to that found in the study of swimmers by Iñigo et al. (1996), despite the much smaller total training load in the former study. Indeed, the highest value for
Ï„f (or
τ2) reported in the literature appears to be 22±4 d in a study of elite weight-lifters, with this extreme value presumably reflecting both the nature and magnitude of the training load of such athletes. Thus, although
Ï„f (or
Ï„2) is more variable than
Ï„a (or
Ï„1), this variability appears explainable. In contrast, it is harder to explain the variability obtained in different studies for the gain terms of the impulse-response model, i.e.,
ka and
kf (or
k1 and
k2). In part, this is because these values serve not only to “balance†the two integrals in Eq. 1, but also to quantitatively relate the training load to performance in an absolute sense. In other words, for the same set of data/for the same individual, the values for
ka and
kf (or
k1 and
k2) would be different if performance were, for example, defined as the power that could be maintained for 1 min versus 60 s, or if training were quantified in kilojoules of work accomplished instead of TRIMP. It is clear, however, that this is not the only explanation for the variation in
ka and
kf (or
k1 and
k2) between studies, as even their ratio varies significantly, with this variation seemingly unrelated to factors such as the overall training load. For example, the ratio of
kf to
ka (or
k2 to
k1) in the study of Busso et al. (1997) is comparable to that found by Hellard et al. (2005), despite the large difference type and amount of training. Moreover, as indicated by the standard deviations listed in the last three columns of Table 1, the variability in
kaand
kf (or
k1 and
k2) between individuals in a given study is as large, or even larger, than the variation across studies. Because of this variability, it is difficult, if not impossible, to rely on generic values for
ka and
kf (or
k1and
k2) from the literature to overcome the limitations discussed under points 3 and 4 above. This is especially true given the fact that the impulse-response model is more sensitive to variations in these gain factors than it is to variation in the time constants, especially
Ï„a (or
Ï„1).
Table 1. Representative studies from the literature that have used the impulse-response model.
Note: The time constants
Ï„a and
Ï„f (or
Ï„1 and
Ï„2) are measured in days, whereas the units of the gain factors
ka and
kf (or
k1 and
k2) vary from study to study depending on how training and performance were quantified.