Theoretical model of metabolic blood flow regulation: roles of ATP release by red blood cells and conducted responses

Abstract

A proposed mechanism for metabolic flow regulation involves the saturation-dependent release of ATP by red blood cells, which triggers an upstream conducted response signal and arteriolar vasodilation. To analyze this mechanism, a theoretical model is used to simulate the variation of oxygen and ATP levels along a flow pathway of seven representative segments, including two vasoactive arteriolar segments. The conducted response signal is defined by integrating the ATP concentration along the vascular pathway, assuming exponential decay of the signal in the upstream direction with a length constant of approximately 1 cm. Arteriolar tone depends on the conducted metabolic signal and on local wall shear stress and wall tension. Arteriolar diameters are calculated based on vascular smooth muscle mechanics. The model predicts that conducted responses stimulated by ATP release in venules and propagated to arterioles can account for increases in perfusion in response to increased oxygen demand that are consistent with experimental findings at low to moderate oxygen consumption rates. Myogenic and shear-dependent responses are found to act in opposition to this mechanism of metabolic flow regulation.

Fig. 1.

Representative segment model. The systemic vasculature is represented by 7 regions connected in series. The large and small arterioles are vasoactive, and the remaining segments are fixed resistances.

Fig. 2.

Model predictions along flow pathway for 3 levels of exercise (in cm³ O₂·100 min⁻¹·cm⁻³) at fixed perfusion: oxygen demand M₀ = 1 (rest), M₀ = 8.28 (control, moderate exercise), and M₀ = 20 (heavy exercise). A: saturation. B: ATP concentration. C: conducted response signal (S_CR). Dots indicate ends of segments. A, artery; LA, large arteriole; SA, small arteriole; C, capillary; SV, small venule; LV, large venule; V, vein.

Fig. 3.

A: model predictions of perfusion as a function of oxygen consumption rate at an input arterial pressure of 100 mmHg. Effects of deactivating myogenic (myo), shear-dependent (shear), and metabolic (meta) response mechanisms are shown. Data from canine studies (▴, Ref. ; ▪, Ref. ; •, Ref. 40) are included. The maximum perfusion possible in this model, with arterioles fully dilated, is shown by top horizontal line [activation (A) = 0]. The bottom horizontal line (A = 0.5) indicates no metabolic response active and corresponds to the control state. The diagonal dashed line indicates the perfusion corresponding to 100% oxygen extraction. B: oxygen extraction as a function of oxygen consumption rate in the presence or absence of the 3 regulatory mechanisms, and for A = 0 and A = 0.5. Thin solid line, metabolic response only; dashed line, shear and metabolic responses; dashed-dotted line, myogenic and metabolic responses; thick solid line: myogenic, shear, and metabolic responses.

Fig. 4.

A and B: dependence of activation and diameter on oxygen consumption rate with all regulatory responses present. A: large arteriole. B: small arteriole. C and D: dependence of components of S_tone (wall tension, wall shear stress, and conducted response signal) on oxygen consumption rate. C: large arteriole. D: small arteriole. (+) and (−), Positive and negative contributions to S_tone.

Fig. 5.

Predicted perfusion as a function of oxygen consumption rate for several conducted response signal length constants (L₀). See text for discussion. Data from canine studies as in Fig. 3. A: C_meta = 30 μM⁻¹cm⁻¹. B: C_meta = 10 μM⁻¹cm⁻¹.

Fig. 6.

Predicted perfusion as a function of oxygen consumption rate for input arterial pressures of 70, 100, and 130 mmHg. Data from canine studies as in Fig. 3.

Fig. 7.

Predicted and observed perfusion as a function of oxygen consumption rate. Data from canine studies (29, 40, 57) as in Fig. 3 and from human studies (, , , , –53). Horizontal line, maximum possible perfusion with assumed constant capillary density.

Fig. 8.

Schematic diagram illustrating interactions between factors involved in blood flow regulation. Blunt-ended lines denote negative effects. Heavy lines and arrows show the primary effects in the system. Vertical arrows show the effects of increasing metabolic demand on the indicated quantities in the presence of the metabolic, shear-dependent, and myogenic responses. Pathway a shows the vasodilatory effect of the metabolic response in the presence of increased metabolic demand. Pathway b shows the resulting increase in tone due to decreased shear stress in the system. Pathway c shows the vasoconstriction caused by increased diameter and vessel wall tension. (+) and (−), increase or decrease in tone, respectively, generated by each mechanism as a result of increased metabolic demand.