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] Breathing was natural (not managed).
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.
Importantly, whilst the math and you may structure requisite are apparently elementary additionally the resulting explanation try naturally obvious and you may mechanistic, it still high light this new rigor and you will scalability on the means. The brand new ease of the newest black-field fits in step 1 and you can Fig. step 1 facilitate present causal relationship between details and you may ways physiological mechanisms to help you model in detail, and you may features possess regarding signals which aren’t modeled (we.age., we have perhaps not said the latest high frequency of signals within reduced watts into the Fig. 1, considered next parts). The tough homeostatic tradeoffs and also the actuator negative effects of Hr, ventilation, and you may vasodilation were as part of the physiology design in 2–5 although neuroendocrine execution information were not. Including, new impact of intellectual autoregulatory saturation are included, nevertheless specifics of execution weren’t. However, this approach makes it possible for medically actionable grounds that do not count toward poorly understood mechanisms peripheral on component are modeled, while offering a construction getting methodically polishing instance designs using a great equivalent (but allegedly greatly more complex) mix of black colored- and you will gray-package models and you can anatomy. Once more, in the event the the brand new tradeoffs perhaps not noticed listed below are found to be high, they can be extra privately since even more limitations is actually acknowledged and options recomputed. Further, tradeoffs may changes since the organ possibilities fail, whenever these types of habits is lengthened to problem claims.
The fresh large-regularity action when you look at the Hr which can be such high at the reduced indicate workloads and you may reduced Hr can not be informed me from the effortless fits or habits significantly more than, and therefore extra signals and you can components should be incorporated which can getting causally pertaining to so it mode. Figs. 5 and you may 6 shed light on breathing because a cause of the majority of the brand new higher-volume HRV. Fig. 5A reveals Time (red) during the natural respiration at rest, into optimal static match H = h(V) = b·V + c, in which V (blue) was counted ventilation flow costs (breathing and you can exhalation) within mouthpiece. The fresh new static linear match are often used to size this new systems regarding V (blue) during the Fig. 5A to assume the best fit to help you Hr (red) and its mistake, shown in the Table dos. You envie sport dating revues to Time and you may venting match so well from inside the frequency is actually uniform to the observation one below certain conditions, determination are accompanied by a velocity away from Hours, and you can termination of the good deceleration, a sensation called breathing sinus arrhythmia (RSA) (16, forty ? ? ? ? ? –46). Although not, due to the fact ventilation and you may Hr is actually both generated by neuroendocrine control, this match (i.e., correlation) by itself cannot strongly recommend a specific mechanistic factor of your own resulting venting–Hours relationship or HRV.