2, using standard mathematical descriptions of circulation, and with a focus on modeling purely aerobic exercise. That is, we only model blood flow, blood pressure, and O2 in several compartments, and yet the model captures the overall physiologic HR response during moderate exercise in young, fit adults. In standard models of aerobic cardiovascular control (27 ? ? ? –31) the neuroendocrine system controls peripheral vasodilation, minute ventilation, and cardiac output to maintain blood pressure and oxygen saturation within acceptable physiological limits.
Several features of these control systems allow substantial simplification of the model. Minute ventilation V ? E alone can tightly control arterial oxygenation [O2]a, so we assume [O2]a is maintained nearly constant (27). Moreover, peripheral resistance Rs is decreased during exercise and the decrease is determined by local metabolic control. The purpose of decreasing Rs in the arterioles is to increase blood flow and regional delivery of O2, glucose, and other substrates as needed. Because the venous oxygenation [O2]v serves as a good signal for oxygen consumption, we also assume that control of peripheral vascular resistance Rs is a function only of venous oxygenation [O2]v (31).
All c details is actually constants
Combined with those models for blood circulation and oxygen consumption, we have the following physiological model: V a s = c a s ? P a s V v s = c v s ? P v s V a p = c a p ? P a p V v p = c v p ? P v p V t o t = V a site de rencontres adultes kink s + V v s + V a p + V v p [ O 2 ] a = 0.2 Q l = c l ? H ? P v p Q r = c r ? H ? P v s F s = ( P a s ? P v s ) / R s F p = ( P a p ? P v p ) / R p M = ? ? W + M 0 R s = A ? [ O 2 ] v + R s 0 . Here V and P are (subscripts a = arterial, v = venous, s = systemic, P = pulmonary) blood volume and blood pressure, respectively. The main elements of the model are (more details in SI Appendix): (i) arterial and venous compartments of systemic and pulmonary circulations are treated as compliant vessels, modeled in the form V = c·P, with the total blood volume a constant Vtot; (ii) cardiac output of the left (Ql) and right (Qr) ventricles; (iii) blood flow for systemic (Fs) and pulmonary (Fp) circulation; (iv) the metabolic consumption M; (v) [O2]a and Rs are modeled according to the previous description of the control mechanism. Note that we need not model these control systems in detail, but simply extract their most well-known features and use them to constrain the model.
In steady state the follow additional constraints hold: Q r = Q l = F s = F p M = F s ( [ O 2 ] a ? [ O 2 ] v ) The first equation is total blood circulation balance and the second one is based on the oxygen circulation balance, where Fs([O2]a ? [O2]v) is the net change in the arterial and venous blood O2 content. The oxygen drop ?O2 across the muscle bed is defined as ?O2 = [O2]a ? [O2]vbining 2 and 3 plus simple algebra (SI Appendix) gives the steady-state model (Pas, ?O2) = f(H, W) shown in Fig. 3 that constrains the relationship between (Pas, ?O2) and (H, W).