Static Matches.

Table 1 lists the minimum root-mean-square (rms) error ||H_data-H_fit|| (where ? x ? = ? t = 1 N ( x t ) 2 / N for a time series x_t of length N) for several static and dynamic fits of increasing complexity for the data in Fig. 1. Not surprisingly, Table 1 shows that the rms error becomes roughly smaller with increased fit complexity (in terms of the number of parameters). Rows 2 and 5 of Table 1 are single global linear fits for all of the data, whereas the remaining rows have different parameters for each cell and https://datingranking.net/de/sapiosexuelles-dating/ are thus piecewise linear when applied to all of the data.

We are going to very first focus on static linear suits (earliest five rows) of one’s function h(W) = b·W + c, in which b and c are constants that prevent the brand new rms error ||H_data-h(W)||, that is available effortlessly from the linear minimum squares. Fixed designs have limited explanatory electricity but they are effortless doing factors in which limitations and you may tradeoffs can be easily identified and you will knew, and we only use measures one to myself generalize to help you active activities (found after) with small boost in complexity. Line 1 away from Desk 1 ‘s the superficial “zero” fit with b = c=0; line 2 is the best around the world linear match (b,c) = (0.35,53) that is used to linearly level the brand new equipment away from W (blue) so you can most readily useful fit brand new Hr research (red) during the Fig. 1A; row step three are a beneficial piecewise ongoing match b = 0 and you will c as being the suggest of each and every analysis set; row cuatro is best piecewise linear fits (black dashed outlines from inside the Fig. 1A) with some more philosophy (b,c) out-of (0.44,49), (0.fourteen,82), and you can (0.04,137) on 0–50, 100–150, and you may 250–300 W. The brand new piecewise linear design from inside the line 4 features quicker mistake than the worldwide linear easily fit in line dos. In the higher workload height, Hr during the Fig. step 1 will not arrived at steady-state into go out level off the fresh studies, the fresh new linear static fit are little much better than lingering match, and therefore such investigation aren’t noticed further getting static matches and you may habits.

Each other Desk 1 and you may Fig. step 1 signify Time responds a bit nonlinearly to different amounts of work stresses. The fresh strong black bend in the Fig. 3A reveals idealized (i.elizabeth., piecewise linear) and you will qualitative however, typical values for h(W) around the world which can be consistent with the fixed piecewise linear fits at the the two all the way down watts account inside Fig. 1A. The alteration in slope from H = h(W) having broadening work ‘s the simplest sign of switching HRV and you will has become all of our initial attention. An excellent proximate lead to is autonomic neurological system harmony, however, we have been finding a deeper “why” when it comes to whole system constraints and you can tradeoffs.

Results

Static analysis of cardiovascular control of aerobic metabolism as workload increases: Static data from Fig. 1A are summarized in A and the physiological model explaining the data is in B and C. The solid black curves in A and B are idealized (i.e., piecewise linear) and qualitatively typical values for H = h(W) that are globally consistent with static piecewise linear fits (black in Fig. 1A) at the two lower workload levels. The dashed line in A shows h(W) from the global static linear fit (blue in Fig. 1A) and in B shows a hypothetical but physiologically implausible linear continuation of increasing HR at the low workload level (solid line). The mesh plot in C depicts P_as–?O₂ (mean arterial blood pressure–tissue oxygen difference) on the plane of the H–W mesh plot in B using the physiological model (P_as, ?O₂) = f(H, W) for generic, plausible values of physiological constants. Thus, any function H = h(w) can be mapped from the H, W plane (B) using model f to the (P, ?O₂) plane (C) to determine the consequences of P_as and ?O₂. The reduction in slope of H = h(W) with increasing workload is the simplest manifestation of changing HRV addressed in this study.