Brand new “best” piecewise linear activities balancing mistake with complexity try after that emphasized inside purple in the Table 1

Fixed Suits.

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 are thus piecewise linear when applied to all of the data.

We shall initially work with static linear matches (very first five rows) of setting h(W) = b·W + c, where b and c are constants you to definitely minimize new rms mistake ||H_data-h(W)||, that’s available effortlessly because of the linear minimum squares. Fixed models don’t have a lot of explanatory electricity but are easy performing circumstances in which limitations and you can tradeoffs can easily be recognized and you can realized, and now we use only steps that really generalize in order to vibrant designs (found later) having smaller boost in difficulty. Row 1 away from Table step 1 is the trivial “zero” match b = c=0; row 2 is the best global linear match (b,c) = (0.35,53) that is used so you can linearly scale the fresh new systems of W (blue) in order to finest match the fresh new Hours studies (red) within the Fig. 1A; row step 3 is actually a great piecewise constant match b = 0 and c as being the imply each and every studies lay; row 4 is the greatest piecewise linear suits (black dashed contours inside Fig. 1A) that have slightly additional opinions (b,c) out-of (0.49,49), (0.14,82), and (0.04,137) from the 0–fifty, 100–150, and you will 250–3 hundred W. The newest piecewise linear model into the row 4 has actually faster error than simply the worldwide linear fit in row dos. From the higher work level, Hr for the Fig. step 1 will not arrived at steady-state toward big date measure away from new studies, this new linear fixed match is little much better than ongoing fit, and therefore these types of data aren’t believed further to possess static suits and you will habits.

Each other Table step 1 and Fig. step one imply that Hr responds somewhat nonlinearly to several amounts of workload stressors. The new good black colored curve inside the Fig. 3A shows idealized (i.age., piecewise linear) and qualitative however, normal opinions to own h(W) in the world that will be similar to the static piecewise linear suits in the the 2 straight down watts profile for the Fig. 1A. The change in slope out-of H = h(W) with growing work is the easiest sign of altering HRV and you will is now our very own 1st notice. An excellent proximate lead to was autonomic nervous system balance, but we are finding a much deeper “why” when it comes to whole system restrictions and you can tradeoffs.

Overall performance

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 incontri milf nere 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.