Human Bioenergetic Models
My understanding of what I believe to be current bioenergetic models in Oct. 2010
Motivation for Modeling
There are many reasons for creating a model of the human bioenergetic system. It allows the performance of athletes to be quantified; this allows progression of training to be tracked, prediction performance under different conditions/distances, and comparisons between athletes. For my purposes, I am using it to determine optimal pacing strategies.
I am choosing to classify the bulk of available models into two categories: "Curve Fitting" and "Rate/Capacity" types. The "Curve Fitting" models have come about from observing the variable speed of an athlete, or power output, or energy consumption, etc. and finding a set of equations which provide similar qualitative behavior. The "Rate/Capacity" models are mainly extensions of the critical power model; they add additional rate limiters, introduce other energy sources, etc. They also suffer from some of the same limitations of the original critical power model.
Figure 3. Behavior of curve-fitting model (from Harman 2002)
There are many more curve-fitting models; some are much simpler with power limits described piecewise linearly, others use different parameters which are not based off of the energetic system. These two seem to be the best in category.
All of these curve-fitting models have a few issues though; while the original critical power model described constant power output, and these do not, these simply follow a function's profile; there is no input/output relationship. No effects of an athlete choosing to apply a different power are allowed for. This makes it very difficult to develop an optimal control strategy from one of these models.
Morton in his 2006 review paper goes into great detail in describing this class of models. He visualizes most of them as hydraulic models. There are a number of extensions to the critical power model, as well as more complicated 3-component models. Figure 4 below shows one of the extended models.
Figure 4. Critical Power Model with Aerobic Lag (from Morton 2006)
There also are critical power models which link the maximum available power to the reserve left in the anaerobic tank (closer to how an actual hydraulic system would behave).
One of the more complicated "rate/capacity" models is the Morton-Margaria model, in which there are 3 tanks: 1 unlimited aerobic, 1 anaerobic glycolysis, and 1 anaerobic cp/atp tank. Figure 5 below shows this.
Figure 5. Morton Margaria Hydraulic Model (from Morton 2006)
As shown in the picture, there are many parameters associated with this model. While it can provide a qualitatively good match to the measured data (in terms of respiration/metabolic measurements) it is very difficult to correctly identify all the parameters. No one seems to have done a parameter matching study so far.