Optimal control model response using first-principle model to two different workload (blue) demands, approximately square waves of 0–50 W (Lower) and 100–150 W (Upper): 
For each data set (using subject 2’s data), a physiological model with optimal controller is simulated with workload as input (blue) and HR (black) as output, and compared with collected HR data (red). Simulations of blood pressure (Pas, purple) and tissue oxygen saturation ([O2] Respiration was impulsive (perhaps not regulated).
The change in the tradeoff as workload increases is consistent with what we observed using the static model. At low workload and low HR, the main tradeoff is metabolic because both Pas and HR are at safe and sustainable levels. High HR and thus high [O2]2), maintains aerobic muscle metabolism, extending the potential duration of exercise while preserving carbohydrate resources for the brain. At higher workloads, this strategy would produce unsustainably high and potentially damaging Pas and possibly HR, so the optimal controller penalizes these factors more, at the price of reduced [O2]T. HRV (slow time scale) in Fig. 1 (and Pas in Fig. 4) decreases with increasing workload because of the changing tradeoffs between metabolic overhead and Pas, ?O2, and H as their means increase. These explanations in HRV derived from the dynamic aerobic model are richer and more complete but due to the same tradeoffs as in the simpler static model.
Significantly, whilst the mathematics and you will physiology necessary is actually apparently basic together with ensuing cause is actually intuitively obvious and mechanistic, it nevertheless stress the brand new rigor and you can scalability of method. This new simplicity of the fresh black colored-package ties in step 1 and you may Fig. 1 assists introduce causal dating ranging from details and you will indicates emotional mechanisms so you can design in more detail, and you may features has actually regarding indicators which aren’t modeled (i.age., we have perhaps not told me brand new high-frequency of your signals at the low watts into the Fig. step 1, thought in the next parts). The hard homeostatic tradeoffs as well as the actuator effects of Time, venting, and you can vasodilation have been within the anatomy design in 2–5 however the neuroendocrine implementation details were not. As well as, this new feeling regarding mind autoregulatory saturation is actually integrated, although details of execution were not. Nevertheless, this approach allows medically actionable explanations that do not rely toward improperly understood systems peripheral for the parts becoming modeled, while offering a structure to possess systematically refining eg activities playing with good equivalent (however, presumably greatly more complex) combination of black- and you will gray-box models and you can anatomy. Again, if brand new tradeoffs perhaps not sensed listed here are discovered to be extreme, they can be additional privately since additional restrictions try acknowledged and you can selection recomputed. Then, tradeoffs may transform since organ solutions fail, when such patterns try expanded so you can state says.
High-Frequency HRV.
New large-frequency activity in Hours that will be such as for example higher at lowest mean workloads and you will lower Hour can not be informed me because of the easy fits or habits a lot more than, for example most indicators and you can systems must be included that will be causally associated with that it setting. Figs. 5 and six reveal breathing once the a factor in the majority of the new large-regularity HRV. Fig. 5A shows Hour (red) during pure breathing at peace, toward max fixed complement H = h(V) = b·V + c, where V (blue) is counted ventilation disperse cost (inhalation and you will exhalation) from the mouthpiece. The brand new fixed linear complement are often used to level the newest gadgets of V (blue) when you look at the Fig. 5A to imagine an educated fit in order to Time (red) and its error, found inside Table dos. One to Hours and you may venting match so well from inside the regularity are consistent towards observation one to around particular conditions, determination was followed closely by a velocity away from Hour, and expiration by the a great deceleration, a sensation titled breathing sinus arrhythmia (RSA) (16, forty ? ? ? ? ? –46). But not, because the venting and Hr are one another generated by neuroendocrine control, so it match (we.elizabeth., correlation) alone doesn’t highly recommend a specific mechanistic cause of the ensuing ventilation–Hr correlation otherwise HRV.