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Am J Physiol Heart Circ Physiol 295: H1562-H1571, 2008. First published August 8, 2008; doi:10.1152/ajpheart.00261.2008
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Theoretical model of metabolic blood flow regulation: roles of ATP release by red blood cells and conducted responses

Julia C. Arciero,1 Brian E. Carlson,2 and Timothy W. Secomb1,3

1Program in Applied Mathematics, University of Arizona, Tucson, Arizona; 2Biotechnology and Bioengineering Center, Medical College of Wisconsin, Milwaukee, Wisconsin; and 3Department of Physiology, University of Arizona, Tucson, Arizona

Submitted 11 March 2008 ; accepted in final form 6 August 2008


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
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 ~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.

microcirculation; myogenic response; shear-dependent response

THE CIRCULATORY SYSTEM is responsible for supplying every tissue in the body with sufficient oxygen and nutrients. Tissue demand varies according to factors such as metabolism, growth, injury, and infection. Small arteries and arterioles regulate the amount of blood flow supplied to tissue by changing their diameters. The capability of vascular supply to match tissue demand implies the existence of mechanisms for information transfer within the vascular system (4, 56).

Studies of flow regulation have shown the presence of control mechanisms that act both locally and remotely in microvascular networks. Arterioles dilate or constrict in response to changing intravascular pressure (myogenic response) (31). Changes in luminal wall shear stress trigger endothelial release of nitric oxide (NO), which initiates coordinated dilation of local and feed arterioles (shear-dependent response) (43). Stimuli acting at a particular location in a network can elicit remote responses via cell-to-cell communication along the vessel wall (conducted response). For example, application of acetylcholine (ACh) to terminal arterioles in a tissue preparation leads to both local and ascending vasodilation of arterioles and feed arteries (13). Subsequent studies have shown that several different mechanisms are involved in conducted responses (6, 22, 61, 64) and that conducted responses are transmitted both upstream and downstream along vessel walls (3). These and other observations indicate that myogenic responses, flow-dependent vasodilation, local metabolic effects, and propagated effects all contribute to blood flow regulation.

Primarily responsible for carrying oxygen in blood, red blood cells (RBCs) may also act as oxygen sensors and thus play a role in communicating metabolic demand (16). RBCs respond to oxygen level by releasing ATP at a rate that depends on their oxyhemoglobin saturation level (5). This ATP release may initiate a conducted response that travels upstream and triggers arteriolar vasodilation (36). Ellsworth (17) established three points that support this proposed role of the RBC. First, RBCs released an increased amount of ATP when exposed to low PO2 (with pH and PCO2 held constant). Second, ATP applied intraluminally to collecting venules resulted in an increase in vessel diameter of upstream arterioles (11). Third, when arteriolar diameter and ATP levels from venule effluent were measured as PO2 was reduced, increases in diameter and ATP concentration occurred only in vessels containing RBCs. The conducted response occurred within seconds, supporting the physiological relevance of this possible regulatory mechanism. These observations imply that RBCs release ATP at higher rates when depleted of oxygen, initiating upstream conducted responses that increase flow (17).

Several studies have examined the mechanisms for release of ATP from the RBC in response to lowered oxygen saturation (7, 30). Jagger et al. (30) quantified the ATP release at low O2 levels in the presence and absence of CO to demonstrate that the release of ATP from RBCs may be linked to the conformational change of the hemoglobin molecule from its relaxed state (R state, fully liganded) to its deoxygenated state (T state). Once released from the RBC, ATP binds to P2Y purinergic receptors on the luminal surface of the endothelium, initiating the conducted response (26, 41, 49). Alternatively, ATP may be degraded into AMP or adenosine, which may bind to P1 receptors and initiate the vasodilatory response (15, 26). Conducted responses initiated by either of these mechanisms may contribute to metabolic regulation of blood flow.

The overall goal of the present study was to gain insight into the roles of several mechanisms contributing to metabolic blood flow regulation. A previous model for myogenic control of arteriolar diameter (9) was extended to include effects of metabolic and shear-dependent responses on blood flow as oxygen demand is varied. The model was used to test the hypothesis that saturation-dependent ATP release by RBCs, triggering a conducted response and upstream vasodilation, provides a mechanism for metabolic flow regulation. The effects of varying model parameters and input arterial pressure were assessed, and model predictions were compared with experimental data.


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Representative segment model. A flow pathway through the vascular system is represented by several compartments connected in series, each comprising a set of identical, parallel-arranged segments that are assumed to experience the same hemodynamic and metabolic conditions. The number of compartments is chosen according to the level of detail desired in the model and the amount of experimental data available. This model includes seven representative segments (Fig. 1) : upstream artery (A), large arteriole (LA), small arteriole (SA), capillary (C), small venule (SV), large venule (LV), and downstream vein (V). Arterioles are divided into two compartments (LA and SA) according to diameter to permit different reactions to changes in pressure and shear stress (12, 60). LA and SA segments are assumed to be vasoactive, while the remaining segments are considered fixed resistances. Inclusion of vessel types spanning the entire circulatory pathway allows simulation of conducted responses involving a signal originating in the capillaries or venules and upstream effector sites located in the arterioles.


Figure 1
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  		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.

 
Geometric and hemodynamic parameters are defined for each compartment. The subscript i denotes compartment type, where i = A, LA, SA, C, SV, LV, or V. Li is the length of segments, ni is the number of segments, {tau}i is the shear stress, Di is the diameter of vessels, and Qi is the flow in compartment i. Since total blood flow must be the same in each compartment, the following relationships hold:

Formula 1(1)
where Qtot is the total flow. The pathway is assumed symmetrical with respect to the lengths and numbers of corresponding arterial and venous segments, i.e., nA = nV, LA = LV; nLA = nLV, LLA = LLV; and nSA = nSV, LSA = LSV. For convenience, nLA = 1. The flow resistance of each compartment is calculated with Poiseuille's law: Ri = (128Liµi)/({pi}niDi4). Blood viscosity, µi, is assigned to each compartment according to an experimental in vivo relationship (48). The pressure drop across the entire pathway, {Delta}Ptot, is held constant. The total flow is Qtot = {Delta}Ptot/Rtot, where Rtot = {sum}Ri, and the flow in an individual segment is Qi = Qtot/ni. The wall shear stress and the pressure drop in each segment are {tau}i = (32µiQi)/({pi}Di3) and {Delta}Pi = QtotRi.

Oxygen saturation. The model assumes that oxygen is delivered to surrounding tissue by the upstream artery, large arterioles, small arterioles, and capillaries. Oxygen exchange by venules and veins is neglected. A Krogh-type cylinder model is used in which each oxygen-delivering vessel runs along the axis of a cylinder representing a tissue region to which it is exclusively responsible for supplying oxygen. The width of the tissue region, d, is assumed to be the same for each oxygen-delivering vessel, and so the radius of the tissue cylinder (rt,j) and the radius of the vessel (rj) satisfy rt,j – rj = d, where j = A, LA, SA, and C. The oxygen demand is assumed to be constant, M0.

By conservation of mass, the decline in oxygen flux must equal the rate of oxygen consumption, giving the following equation for the change in oxygen saturation, S(x), with distance, x, along each segment:

Formula 2(2)
where Q is volume flow rate in an individual vessel, c0 is the carrying capacity of RBCs at 100% saturation, HD is the discharge hematocrit, and q = {pi}M0(rt,j2 – rj2) is oxygen consumption per vessel length. Equation 2 is solved to give

Formula 3(3)
Saturation at the start of the vascular pathway, S(0), is assumed to be 0.97, corresponding to an initial blood PO2 of 100 mmHg. The Hill equation S(Pb) = PbnH/(P50nH + PbnH), where nH is the Hill coefficient and P50 is half-maximal Hb saturation, gives the relationship between saturation and blood PO2 (denoted Pb). Values of the parameters are given in Table 1.


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  		Table 1. Parameter values describing oxygen transport and saturation-dependent ATP release by red blood cells

 
ATP concentration. The release rate of ATP from an RBC, R[S(x)], is defined by a decreasing linear function of oxyhemoglobin saturation based on experimental data. ATP release from human erythrocytes in response to normoxia and hypoxia was observed in in vitro experiments (5). Erythrocyte suspensions were exposed to 50 s of hypoxia and then assayed for ATP. The procedure was also conducted under control conditions (i.e., normoxia). At a saturation of 0.33, 0.985 nmol·s–1·cm–3 of ATP was released. Under normoxic conditions (saturation of 0.97), 0.166 nmol·s–1·cm–3 of ATP was released (5). A linear fit of these experimental values defines the ATP release function of saturation:

Formula 4(4)
Values of R0 and R1 are listed in Table 1. Ectonucleotidases on the endothelial cell surface of the vessel wall degrade ATP (14, 39). The rate of change in plasma ATP concentration, C(x), is given by the difference between the rates of ATP release and degradation:

Formula 5(5)
where HT is tube hematocrit. The degradation reaction at the endothelial surface is described by Michaelis-Menten kinetics with maximum rate Vmax = 22 nmol·min–1·10–6 cells and Michaelis constant Km = 249 µM for cultured porcine aortic endothelial cells (14). Here, ATP degradation is assumed first order in plasma ATP concentration with rate constant kd. The surface area of endothelial cells ranges from 400 to 900 µm2 (2), giving a rate constant between 1.63 x 10–4 and 3.68 x 10–4 cm/s. Here, kd is assumed to be 2 x 10–4 cm/s, yielding model predictions of venous ATP concentrations consistent with experimental data (25).

Equation 5 can be solved for ATP concentration:

Formula 6(6)
where {alpha}, β, and {gamma} are functions of diameter, hematocrit, oxygen consumption, flow, degradation rate, and initial conditions:

Formula 7(7)

Formula 7
Equation 5 is solved separately for each compartment to account for different diameters and flows. Therefore, in Eq. 6, x0 denotes the initial position and C0 refers to the initial ATP concentration in the compartment being considered. At the start of the vascular pathway (x0 = 0), C0 = 0.5 µM for consistency with measured arterial ATP levels (25).

Conducted response signal. Metabolic control of LA and SA diameters is assumed to occur via a conducted response that is generated throughout the vascular pathway and transmitted upstream. Multiple mechanisms have been identified that contribute to conducted responses, which may decay with distance traveled (64) or travel without significant decay (23). For simplicity, exponential decay is assumed here with a length constant L0. Effects of varying L0 are examined. At each point in the network, a signal is generated at the vessel wall in proportion to the local concentration of ATP in the plasma. This signal is summed from the end of the LV to the midpoints of the LA and SA in order to obtain the conducted response signal, SCR(x), that reaches the large and small arterioles, respectively. The summation is represented by the integral of the ATP concentration along the vascular pathway, including exponential decay of the signal in the upstream direction:

Formula 8(8)
In Eq. 8, xmp,k is the midpoint of compartment k, for k = LA or SA, and xend is the end point of the LV. Parameter values are given in Table 1.

Arteriolar activation and diameter. Circumferential wall tension (T) is related to pressure and diameter by the law of Laplace, T = PD/2, assuming that vessel wall thickness is much less than vessel diameter. A theoretical model (8, 9) describes the vascular effects of the myogenic response based on active and passive length-tension characteristics of vascular smooth muscle (VSM) and defines the total tension in a vessel wall by:

Formula 9(9)
Tpass represents the passive tension in a vessel wall and is given by an exponential function of diameter. The product of smooth muscle activation, A, and maximal active tension, Tactmax, defined by a Gaussian function of diameter, represents the contractile tension generated by VSM cells. Activation is given by a sigmoidal function that varies between 0 and 1:

Formula 10(10)
Stone is defined as the stimulus that dictates the level of VSM tone:

Formula 11(11)
where Cmyo = 0.0101 cm/dyn (LA), 0.0359 cm/dyn (SA) and Cshear = 0.0258 cm2/dyn (LA and SA) (8). Cmeta is unknown, and a range of values is considered. In the model simulations presented here, Cmeta = 30 µM–1cm–1 in the LA and SA. The calculation of C''tone = 10.11 (LA), 10.66 (SA) is described below (Control state). The equation for Stone is analogous to the previous definition (9), with additional terms for metabolic and shear signals.

Determination of steady-state diameters and activation levels. If pressure is altered, a vessel shows a rapid passive change in diameter followed by an active smooth muscle contraction or dilation to a new equilibrium diameter. This behavior can be represented by the system of equations:

Formula 12(12)

Formula 12
Here, Dc and Tc are the values of diameter and tension in the control state (see below), Ttotal and Atotal are the calculated steady-state values of vessel wall tension and smooth muscle activation for given levels of pressure and oxygen demand, and {tau}d and {tau}a are time constants governing the rates of passive diameter and VSM activation change, respectively. When arteriolar diameters were measured after step changes in arterial pressure in the range of 7.35–125 mmHg, the time to approach a new equilibrium was typically ~1 min (20). Therefore, {tau}a = 60 s is used in this model. The initial passive response to changes in intraluminal pressure occurs within seconds (31), and thus {tau}d = 1 s is assumed. Steady-state values of D and A are determined by integrating Eq. 12 until equilibrium is reached. The assumed values of {tau}a and {tau}d do not affect the eventual steady-state condition.

Control state. A control (or reference) state is defined to represent conditions in skeletal muscle at a level of oxygen consumption corresponding to moderate exercise. Several experiments show that wall shear stress is approximately uniform in the arteriolar tree but has lower values in the venous circulation (27, 35, 45). Here, control values of {tau}A = {tau}LA = {tau}SA = {tau}C = 55 dyn/cm2 and {tau}V = {tau}LV = {tau}SV = 10 dyn/cm2 are assumed, consistent with experimental data (45). In addition, an input arterial pressure of 100 mmHg is assumed. Pressure drops of 10, 15, 40, and 15 mmHg are chosen in A, LA, SA, and C so that the midpoint control pressures of LA and SA, 82.5 and 55 mmHg, lie in the middle of the ranges of pressures observed in those vessel types (45). It is assumed that the level of activation of LA and SA in the control state is 50%, i.e., ALA = 0.5 and ASA = 0.5. Then, from Eq. 10, Stone = 0 in both segments.

From these assumptions and the symmetry of the vascular pathway, the remaining values of vessel diameter, flow, length, pressure drop, and number are calculated. Control diameters of the large and small arterioles, DLA = 65.2 µm and DSA = 14.8 µm, are obtained by solving Eq. 12 for its steady state. Capillary diameter is set to DC = 6 µm, consistent with experimental values from rat skeletal muscle (32). DA and DV are not specified, and these segments are considered to act as fixed resistances. DLV is computed from DLA:

Formula 13(13)
and similarly for DSV. Given the control diameters, the control values of flow in each segment are calculated. Vessel lengths are deduced from the assumed pressure drops with Poiseuille's law. Substituting these values into the length symmetry condition (LA = LV, LLA = LLV, and LSA = LSV) gives an equation for the remaining pressure drops along the pathway:

Formula 14(14)
and similarly for {Delta}PSV and {Delta}PV. Since nLA = 1, the number of vessels in each compartment is ni = QLA/Qi. The capillary density, N, is given by

Formula 15(15)
where rt,i = ri + d in arterial vessels and capillaries, and rt,i = ri in venous vessels. The value N = 500 capillaries/mm2 is chosen because it is the typical measured value of capillary density in human skeletal muscle (38). This choice for N corresponds to a tissue region of width d = 18.8 µm around each arteriole and capillary.

Perfusion in the control state depends on the total flow through the pathway and the volume of the tissue

Formula 16(16)
and is 70.9 cm3 O2·100 cm–3·min–1. The corresponding oxygen consumption rate, M0 = 8.28 cm3 O2·100 cm–3·min–1, is estimated by linear interpolation of experimental data (25). Control values of segment diameter, length, shear stress, pressure drop, resistance, number, velocity, transit time, viscosity, and volume fraction are listed in Table 2. C''tone is chosen to satisfy the condition that Stone = 0 in the control state.


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  		Table 2. Control state values for representative segments

 

   RESULTS
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 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 GRANTS
 REFERENCES
 
Conducted response signal. Figure 2 shows the changes in saturation, ATP concentration, and conducted response signal with distance along the vascular pathway for three levels of oxygen demand: 1, 8.28, and 20 cm3 O2·100 cm–3·min–1, representing rest, moderate exercise, and heavy exercise, respectively. Perfusion is held fixed at its control level. In each case, the greatest drop in oxygen saturation occurs across the capillaries. Saturation remains constant in the SV, LV, and V since oxygen exchange by these segments is neglected. ATP concentration declines slightly in the resistance vessels, where saturation is high and ATP degradation exceeds ATP release. The greatest ATP concentration occurs in the venules and veins, which are characterized by low oxygen saturation, decreased blood velocity, and long blood transit times. At rest, only slight changes in oxygen saturation and ATP concentration are predicted. Increasing oxygen demand to 20 cm3 O2·100 cm–3·min–1 at this perfusion level results in complete extraction of oxygen from the capillaries. ATP levels approach 2 µM at the venous end, resulting in the generation of a stronger vasodilatory conducted response signal. ATP levels return to lower levels in arterial blood after traveling through the lungs, where a significant amount of ATP is taken up (24). In Fig. 2C, the conducted response signal is plotted as a function of distance along the vascular pathway. The majority of the signal originates in the venules. Arrows at the midpoints of the small and large arterioles indicate the locations at which the conducted response signal is evaluated in Eq. 8.


Figure 2
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  		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 (SCR). Dots indicate ends of segments. A, artery; LA, large arteriole; SA, small arteriole; C, capillary; SV, small venule; LV, large venule; V, vein.

 
Metabolic regulation of flow. Figure 3 shows model results for levels of oxygen demand ranging from 1 to 25 cm3 O2·100 cm–3·min–1, with the various regulatory mechanisms activated or deactivated. The predicted tissue perfusion and oxygen extraction are plotted as functions of oxygen consumption rate, which may be lower than demand. With all mechanisms activated, the model predicts a strong increase in perfusion with increasing consumption (Fig. 3A, heavy line). Myogenic and shear stress responses are deactivated by holding values of wall tension and shear stress, respectively, constant at control levels for the purpose of calculating Stone. For low and moderate levels of oxygen consumption (0–10 cm3 O2·100 cm–3·min–1), deactivation of the myogenic or shear stress responses has little effect on the predicted perfusion. At higher rates of oxygen consumption, deactivating the myogenic and/or shear-dependent responses leads to increased perfusion, implying that these responses tend to weaken metabolic regulation. The upper horizontal line in Fig. 3A shows the maximum supply of blood available when both arterioles are fully dilated. Figure 3B shows the predicted oxygen extraction under corresponding conditions. In the presence of all three mechanisms, extraction varies from ~25% under resting conditions to 90% under heavy exercise.


Figure 3
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  		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 ({blacktriangleup}, Ref. 29; {blacksquare}, Ref. 57; bullet, 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.

 
Figure 4, A and B, show the dependence of activation and diameter of the large and small arterioles on oxygen consumption rate when all three responses are activated. Diameters increase with increasing consumption. Figure 4, C and D, show the dependence of the components of Stone on oxygen consumption rate. The metabolic term (CmetaSCR) increases with consumption, causing vasodilation. The myogenic term (CmyoT) increases with consumption, because wall tension increases with diameter. The resulting myogenic constriction tends to oppose the metabolic dilation. The shear-dependent response term (Cshear{tau}) increases very slightly in the large arteriole and decreases in the small arteriole. Thus the shear-dependent response also tends to oppose the dilation induced by the metabolic response.


Figure 4
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  		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 Stone (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 Stone.

 
The effects on perfusion of the assumed conducted response length constant, L0, and metabolic sensitivity parameter, Cmeta, are examined in Fig. 5. With Cmeta = 30 µM–1cm–1, a length constant of 1 cm yields an increase in perfusion for low to moderate exercise levels consistent with experiment (Fig. 5A). Increasing L0 above 1 cm has little effect on perfusion. Decreasing L0 to 0.2 or 0.5 cm reduces the amount of perfusion attained for M0 = 25 cm3 O2·100 cm–3·min–1. This effect can be reversed by increasing Cmeta to much larger values (data not shown). In this case, only the SA would participate significantly in flow regulation since very little metabolic signal would reach the LA. If a smaller value of Cmeta is assumed, perfusion is decreased for a given value of L0 (Fig. 5B). In this case, large increases in L0 yield only slight changes in perfusion. The available data do not uniquely determine the values of Cmeta and L0. In the following, it is assumed that L0 = 1 cm and Cmeta = 30 µM–1cm–1.


Figure 5
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  		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: Cmeta = 30 µM–1cm–1. B: Cmeta = 10 µM–1cm–1.

 
In Fig. 6, the effect of varying input arterial pressure (70, 100, and 130 mmHg) on model predictions of perfusion is examined. The assumed mechanism of metabolic flow regulation operates effectively at all three pressure levels, but the maximum consumption rate that can be achieved decreases with decreasing pressure. Higher perfusion values are obtained as input arterial pressure increases. The effect of the myogenic response is evident in that perfusion does not increase linearly with pressure.


Figure 6
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  		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.

 
Figure 7 compares the model predictions with data collected from both canine and human studies (1, 25, 29, 33, 40, 42, 50–53, 57) over a wide range of exercise levels. With the present assumptions and parameter values, particularly the assumed capillary density of 500 mm–2, the model does not predict the very high rates of oxygen consumption and perfusion observed in some human studies. This apparent discrepancy is discussed below.


Figure 7
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  		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 (1, 25, 33, 42, 50–53). Horizontal line, maximum possible perfusion with assumed constant capillary density.

 

   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
GRANTS
 REFERENCES
 
Model predictions. The results of this model support the concept that the saturation-dependent ATP release by RBCs can act as a mechanism for metabolic flow regulation by triggering a conducted response and upstream vasodilation. In Fig. 2, the effects of increasing M0 are examined in the absence of flow regulation, i.e., at constant blood flow. With increasing M0, venous saturation declines and ATP concentration increases significantly in the venules but not in the arterioles or capillaries. The ATP levels predicted by the model lie within a physiologically realistic range and are obtained from independent data on ATP degradation and release rates (5, 14). Ellsworth et al. (11, 16, 36) showed that these ATP levels are sufficient to cause arteriolar vasodilation. The model assumes that the conducted response signal is generated along the vascular pathway in proportion to ATP level. For a conducted response with L0 = 1 cm, the signal reaching large and small arterioles varies significantly with M0 (Fig. 2C). Together, these model predictions confirm the potential of this mechanism to provide metabolic flow regulation.

As shown in Fig. 3A, the model predicts an increase in flow consistent with experimental observations (29, 40, 57) as oxygen demand increases from low to moderate levels in the presence of the metabolic, myogenic, and shear-dependent response mechanisms. The shear-dependent response has been considered an important contributor to flow regulation (43) since it provides a potential mechanism for vessel diameters to increase in response to increased flow rate through a vascular network (56). However, the present model predicts that the shear-dependent response has limited effect on metabolic flow regulation. Moreover, the shear-dependent response is predicted to act in opposition to the metabolic mechanism, contrary to previous concepts. This unexpected behavior can be explained as follows. With increasing oxygen consumption rate, the metabolic response triggers vasodilation of the small and large arterioles, such that wall shear stress decreases despite the increase in flow (Fig. 4D). This decrease in wall shear stress reduces the overall vasodilatory stimulus. The myogenic response causes vasoconstriction due to increased wall tension as vessels dilate (Fig. 4, C and D). This increase in wall tension also reduces the vasodilatory stimulus. According to this model, both the myogenic and shear-dependent mechanisms cause a reduction in perfusion from the levels that would be attained at high consumption rates with only the metabolic response active.

These effects are shown schematically in Fig. 8, with the primary effect in the system highlighted by bold lines and arrows. Increased metabolic demand yields an increased metabolic signal, which decreases vascular tone (pathway a). This decrease in tone, resulting in increased diameter, is represented schematically by (–). The increase in diameter causes both decreased shear stress and increased wall tension, yielding an increase in vascular tone, represented by (+), according to the shear-dependent and myogenic responses (pathways b and c). Thus myogenic and shear-dependent responses act in opposition to metabolic flow regulation.


Figure 8
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  		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.

 
Figure 5 shows the effect of the conducted response length constant on predicted perfusion levels. These results imply that a length constant of ~1 cm is required to trigger arteriolar vasodilation consistent with experimental values. The distance the signal must travel from the venule to the arterioles is ~1 cm. Increasing L0 above this value does not lead to a significant increase in perfusion. Some studies have suggested that conducted responses travel only 0.5–2 mm (11, 36), although these values may be more indicative of limitations on the field of view in intravital microscopy than of actual conduction lengths (4). More importantly, experimental studies have shown that applying ATP to venules leads to a significant increase in diameter of upstream arterioles (17). In Ref. 18, segments were observed to dilate when ACh was applied 750 µm downstream, and the conduction through the segment was not attenuated. Pries et al. (44) used a length constant of 1.73 cm in a model that simulates structural diameter changes in response to shear stress, intravascular pressure, and a conducted metabolic response. The conducted response is assumed to decay in the upstream direction with a single L0. As mentioned above, multiple mechanisms may contribute to the conducted response. The assumed length constant represents an effective decay rate taking into account the combined effects of the mechanisms involved.

The model predicts that metabolic flow regulation is achieved over a range of pressures. An approximately fourfold range of perfusion is predicted at each pressure level considered (Fig. 6). The predictions of the model with regard to autoregulation of blood flow are considered in a separate study (8).

Other regulatory mechanisms. In the present model, the metabolic signal is assumed to result only from ATP release by RBCs, which occurs mainly in the venules. The effects of ATP from other sources, such as nerves and muscles, and of other vasoactive substances, such as adenosine, NO, and potassium, that are produced in response to muscle contraction are not included in the present model. These substances may diffuse into and relax the smooth muscle cells of arterioles, leading to local vasodilation. Stamler et al. (59) described a mechanism that involves the binding of NO to hemoglobin and the release of NO from S-nitrosohemoglobin after a change in oxygenation state. It was hypothesized that the released NO may then act on the endothelium to cause vasodilation. However, theoretical models (34) show that strictly local responses of arterioles in skeletal muscle provide poor matching of blood supply with local demand. At high perfusion rates, the extraction from arterioles is small, and therefore arteriolar oxygen level does not provide a sensitive indication of tissue oxygen levels. Mechanisms based on local responses do not appear capable of accounting for local metabolic regulation of blood flow over a wide range of consumption rates.

Diffusion of vasoactive substances between paired venules and arterioles can cause arteriolar vasodilation (28). Known as the countercurrent exchange of metabolites or venular-arteriolar communication, this diffusion typically occurs between larger arterioles and venules since vessels of these sizes often exist in close alignment (in pairs) in vivo. Increased venular levels of ATP were found to cause an endothelium-dependent dilation of adjacent arterioles that could be blocked by disrupting the venular endothelium (28).

The effects of the autonomic nervous system should also be considered when modeling the control of blood flow. Increased muscle activity is accompanied by recruitment of motor units and vasodilation. Simultaneously, the sympathetic nervous system is stimulated and causes smooth muscle contraction primarily through the release of norepinephrine (62). However, blood flow increases with exercise despite activation of sympathetic nerve activity (63). Several explanations for the decreased sensitivity of active muscles to nerve activity compared with inactive muscles have been offered and may play a role in blood flow regulation (62). These regulatory mechanisms could in principle be integrated into the present model by including additional terms in Stone.

Limitations of the model. The present model includes several simplifications. Oxygen and ATP concentration levels are estimated in a flow pathway consisting of seven representative segments. This highly simplified network system excludes some characteristics of real networks. For example, it neglects the role of diffusive exchange between capillaries and arterioles in oxygen delivery (54), the effects of heterogeneity in pathway length and transit time (47), and the effects of arcading structures of arterioles (19). A Krogh-type model is used to simulate oxygen transport from vessels to tissue, leading to the possibility of 100% extraction of oxygen from blood. In reality, oxygen extraction is restricted by several factors including diffusive and convective limitations of oxygen transport, as evidenced by substantial oxygen saturation (15–30%) remaining in venous blood (37). The present approach could be extended to overcome these limitations by introducing dependence of oxygen consumption on the partial pressure of oxygen with Michaelis-Menten kinetics, and, further, by introducing detailed three-dimensional simulations of the oxygen field (55).

As shown in Fig. 7, perfusion levels attained in some studies on humans exceed the maximum level that this model can predict (1, 25, 33, 42, 50–53). The present model assumes a constant capillary density, 500 capillaries/mm2, although actual capillary density has been shown to be higher (38). Increased exercise rates are accompanied by capillary recruitment, which is not considered in this model. Capillary recruitment may occur independently of arteriolar dilation (10). The present results support the established concept that capillary recruitment, working in conjunction with arteriolar dilation, is necessary to generate the very wide range of perfusion levels between rest and maximal exercise (58).

In the present model, parameter values and comparisons with experimental data are based on observations of skeletal muscle. The model could in principle be applied to other tissues in which ATP release by RBCs is a major mechanism of metabolic flow regulation. For example, Farias et al. (21) have provided evidence for a role of plasma ATP in regulation of cardiac blood flow.

Conclusion. This study supports the concept that upstream conducted responses stimulated by ATP release from RBCs can account for increases in perfusion observed for moderate increases in oxygen consumption rates. It provides a quantitative assessment of the roles of myogenic, shear-dependent, and metabolic responses in flow regulation and confirms that the metabolic response is the primary mechanism contributing to the increase in perfusion with increasing demand, overcoming the opposing effects of the myogenic and shear-dependent responses.


   GRANTS
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 ABSTRACT
 METHODS
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 DISCUSSION
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REFERENCES
 
This work was supported by National Institutes of Health Grants HL-070657 and T32-EB-001650.


   FOOTNOTES
 

Address for reprint requests and other correspondence: T. W. Secomb, Dept. of Physiology, Univ. of Arizona, Tucson, AZ 85724-5051 (e-mail: secomb{at}u.arizona.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


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  1. Andersen P, Saltin B. Maximal perfusion of skeletal muscle in man. J Physiol 366: 233–249, 1985.[Abstract/Free Full Text]
  2. Baldwin AL, Thurston G, al Naemi H. Inhibition of nitric oxide synthesis increases venular permeability and alters endothelial actin cytoskeleton. Am J Physiol Heart Circ Physiol 274: H1776–H1784, 1998.[Abstract/Free Full Text]
  3. Beach JM, McGahren ED, Duling BR. Capillaries and arterioles are electrically coupled in hamster cheek pouch. Am J Physiol Heart Circ Physiol 275: H1489–H1496, 1998.[Abstract/Free Full Text]
  4. Berg BR, Cohen KD, Sarelius IH. Direct coupling between blood flow and metabolism at the capillary level in striated muscle. Am J Physiol Heart Circ Physiol 272: H2693–H2700, 1997.[Abstract/Free Full Text]
  5. Bergfeld GR, Forrester T. Release of ATP from human erythrocytes in response to a brief period of hypoxia and hypercapnia. Cardiovasc Res 26: 40–47, 1992.[Abstract/Free Full Text]
  6. Budel S, Bartlett IS, Segal SS. Homocellular conduction along endothelium and smooth muscle of arterioles in hamster cheek pouch: unmasking an NO wave. Circ Res 93: 61–68, 2003.[Abstract/Free Full Text]
  7. Buehler PW, Alayash AI. Oxygen sensing in the circulation: "cross talk" between red blood cells and the vasculature. Antioxid Redox Signal 6: 1000–1010, 2004.[Web of Science][Medline]
  8. Carlson BE, Arciero JC, Secomb TW. Theoretical model of blood flow autoregulation: roles of myogenic, shear-dependent, and metabolic responses. Am J Physiol Heart Circ Physiol (August 22, 2008). doi: 10.1152/ajpheart.00262.2008.[Abstract/Free Full Text]
  9. Carlson BE, Secomb TW. A theoretical model for the myogenic response based on the length-tension characteristics of vascular smooth muscle. Microcirculation 12: 327–338, 2005.[CrossRef][Web of Science][Medline]
  10. Cohen KD, Berg BR, Sarelius IH. Remote arteriolar dilations in response to muscle contraction under capillaries. Am J Physiol Heart Circ Physiol 278: H1916–H1923, 2000.[Abstract/Free Full Text]
  11. Collins DM, McCullough WT, Ellsworth ML. Conducted vascular responses: communication across the capillary bed. Microvasc Res 56: 43–53, 1998.[CrossRef][Web of Science][Medline]
  12. Davis MJ, Sikes PJ. Myogenic responses of isolated arterioles: test for a rate-sensitive mechanism. Am J Physiol Heart Circ Physiol 259: H1890–H1900, 1990.[Abstract/Free Full Text]
  13. Duling BR, Hogan RD, Langille BL, Lelkes P, Segal SS, Vatner SF, Weigelt H, Young MA. Vasomotor control: functional hyperemia and beyond. Fed Proc 46: 251–263, 1987.[Web of Science][Medline]
  14. Dull RO, Tarbell JM, Davies PF. Mechanisms of flow-mediated signal transduction in endothelial cells: kinetics of ATP surface concentrations. J Vasc Res 29: 410–419, 1992.[Web of Science][Medline]
  15. Duza T, Sarelius IH. Conducted dilations initiated by purines in arterioles are endothelium dependent and require endothelial Ca2+. Am J Physiol Heart Circ Physiol 285: H26–H37, 2003.[Abstract/Free Full Text]
  16. Ellsworth ML. The red blood cell as an oxygen sensor: what is the evidence? Acta Physiol Scand 168: 551–559, 2000.[CrossRef][Web of Science][Medline]
  17. Ellsworth ML. Red blood cell-derived ATP as a regulator of skeletal muscle perfusion. Med Sci Sports Exerc 36: 35–41, 2004.[Web of Science][Medline]
  18. Emerson GG, Segal SS. Endothelial cell pathway for conduction of hyperpolarization and vasodilation along hamster feed artery. Circ Res 86: 94–100, 2000.[Abstract/Free Full Text]
  19. Engelson ET, Schmid-Schonbein GW, Zweifach BW. The microvasculature in skeletal muscle. II. Arteriolar network anatomy in normotensive and spontaneously hypertensive rats. Microvasc Res 31: 356–374, 1986.[CrossRef][Web of Science][Medline]
  20. Falcone JC, Davis MJ, Meininger GA. Endothelial independence of myogenic response in isolated skeletal muscle arterioles. Am J Physiol Heart Circ Physiol 260: H130–H135, 1991.[Abstract/Free Full Text]
  21. Farias M III, Gorman MW, Savage MV, Feigl EO. Plasma ATP during exercise: possible role in regulation of coronary blood flow. Am J Physiol Heart Circ Physiol 288: H1586–H1590, 2005.[Abstract/Free Full Text]
  22. Figueroa XF, Chen CC, Campbell KP, Damon DN, Day KH, Ramos S, Duling BR. Are voltage-dependent ion channels involved in the endothelial cell control of vasomotor tone? Am J Physiol Heart Circ Physiol 293: H1371–H1383, 2007.[Abstract/Free Full Text]
  23. Figueroa XF, Paul DL, Simon AM, Goodenough DA, Day KH, Damon DN, Duling BR. Central role of connexin40 in the propagation of electrically activated vasodilation in mouse cremasteric arterioles in vivo. Circ Res 92: 793–800, 2003.[Abstract/Free Full Text]
  24. Folkow B. A critical study of some methods used in investigations on the blood circulation. Acta Physiol Scand 27: 118–129, 1952.[Web of Science][Medline]
  25. Gonzalez-Alonso J, Olsen DB, Saltin B. Erythrocyte and the regulation of human skeletal muscle blood flow and oxygen delivery: role of circulating ATP. Circ Res 91: 1046–1055, 2002.[Abstract/Free Full Text]
  26. Gorman MW, Ogimoto K, Savage MV, Jacobson KA, Feigl EO. Nucleotide coronary vasodilation in guinea pig hearts. Am J Physiol Heart Circ Physiol 285: H1040–H1047, 2003.[Abstract/Free Full Text]
  27. Hacking WJ, VanBavel E, Spaan JA. Shear stress is not sufficient to control growth of vascular networks: a model study. Am J Physiol Heart Circ Physiol 270: H364–H375, 1996.[Abstract/Free Full Text]
  28. Hester RL, Hammer LW. Venular-arteriolar communication in the regulation of blood flow. Am J Physiol Regul Integr Comp Physiol 282: R1280–R1285, 2002.[Abstract/Free Full Text]
  29. Horstman DH, Gleser M, Delehunt J. Effects of altering O2 delivery on Formula 16O2 of isolated, working muscle. Am J Physiol 230: 327–334, 1976.[Abstract/Free Full Text]
  30. Jagger JE, Bateman RM, Ellsworth ML, Ellis CG. Role of erythrocyte in regulating local O2 delivery mediated by hemoglobin oxygenation. Am J Physiol Heart Circ Physiol 280: H2833–H2839, 2001.[Abstract/Free Full Text]
  31. Johnson PC. The myogenic response. In: Handbook of Physiology. The Cardiovascular System. Vascular Smooth Muscle. Bethesda, MD: Am. Physiol. Soc., 1980, sect. 2, vol. II, p. 409–442.
  32. Kindig CA, Richardson TE, Poole DC. Skeletal muscle capillary hemodynamics from rest to contractions: implications for oxygen transfer. J Appl Physiol 92: 2513–2520, 2002.[Abstract/Free Full Text]
  33. Knight DR, Poole DC, Schaffartzik W, Guy HJ, Prediletto R, Hogan MC, Wagner PD. Relationship between body and leg Formula 16O2 during maximal cycle ergometry. J Appl Physiol 73: 1114–1121, 1992.[Abstract/Free Full Text]
  34. Lo A, Fuglevand AJ, Secomb TW. Oxygen delivery to skeletal muscle fibers: effects of microvascular unit structure and control mechanisms. Am J Physiol Heart Circ Physiol 285: H955–H963, 2003.[Abstract/Free Full Text]
  35. Mayrovitz HN, Roy J. Microvascular blood flow: evidence indicating a cubic dependence on arteriolar diameter. Am J Physiol Heart Circ Physiol 245: H1031–H1038, 1983.[Abstract/Free Full Text]
  36. McCullough WT, Collins DM, Ellsworth ML. Arteriolar responses to extracellular ATP in striated muscle. Am J Physiol Heart Circ Physiol 272: H1886–H1891, 1997.[Abstract/Free Full Text]
  37. McGuire BJ, Secomb TW. A theoretical model for oxygen transport in skeletal muscle under conditions of high oxygen demand. J Appl Physiol 91: 2255–2265, 2001.[Abstract/Free Full Text]
  38. McGuire BJ, Secomb TW. Estimation of capillary density in human skeletal muscle based on maximal oxygen consumption rates. Am J Physiol Heart Circ Physiol 285: H2382–H2391, 2003.[Abstract/Free Full Text]
  39. Meghji P, Pearson JD, Slakey LL. Kinetics of extracellular ATP hydrolysis by microvascular endothelial cells from rat heart. Biochem J 308: 725–731, 1995.[Web of Science][Medline]
  40. Mohrman DE, Regal RR. Relation of blood flow to Formula 16O2, PO2, and PCO2 in dog gastrocnemius muscle. Am J Physiol Heart Circ Physiol 255: H1004–H1010, 1988.[Abstract/Free Full Text]
  41. Olearczyk JJ, Stephenson AH, Lonigro AJ, Sprague RS. Heterotrimeric G protein Gi is involved in a signal transduction pathway for ATP release from erythrocytes. Am J Physiol Heart Circ Physiol 286: H940–H945, 2004.[Abstract/Free Full Text]
  42. Pedersen PK, Kiens B, Saltin B. Hyperoxia does not increase peak muscle oxygen uptake in small muscle group exercise. Acta Physiol Scand 166: 309–318, 1999.[CrossRef][Web of Science][Medline]
  43. Pohl U, de Wit C, Gloe T. Large arterioles in the control of blood flow: role of endothelium-dependent dilation. Acta Physiol Scand 168: 505–510, 2000.[CrossRef][Web of Science][Medline]
  44. Pries AR, Reglin B, Secomb TW. Structural adaptation of microvascular networks: functional roles of adaptive responses. Am J Physiol Heart Circ Physiol 281: H1015–H1025, 2001.[Abstract/Free Full Text]
  45. Pries AR, Secomb TW, Gaehtgens P. Design principles of vascular beds. Circ Res 77: 1017–1023, 1995.[Abstract/Free Full Text]
  46. Pries AR, Secomb TW, Gaehtgens P. Biophysical aspects of blood flow in the microvasculature. Cardiovasc Res 32: 654–667, 1996.[Abstract/Free Full Text]
  47. Pries AR, Secomb TW, Gaehtgens P. Relationship between structural and hemodynamic heterogeneity in microvascular networks. Am J Physiol Heart Circ Physiol 270: H545–H553, 1996.[Abstract/Free Full Text]
  48. Pries AR, Secomb TW, Gessner T, Sperandio MB, Gross JF, Gaehtgens P. Resistance to blood flow in microvessels in vivo. Circ Res 75: 904–915, 1994.[Abstract/Free Full Text]
  49. Ralevic V, Burnstock G. Receptors for purines and pyrimidines. Pharmacol Rev 50: 413–492, 1998.[Abstract/Free Full Text]
  50. Richardson RS, Grassi B, Gavin TP, Haseler LJ, Tagore K, Roca J, Wagner PD. Evidence of O2 supply-dependent Formula 16O2 max in the exercise-trained human quadriceps. J Appl Physiol 86: 1048–1053, 1999.[Abstract/Free Full Text]
  51. Richardson RS, Leigh JS, Wagner PD, Noyszewski EA. Cellular PO2 as a determinant of maximal mitochondrial O2 consumption in trained human skeletal muscle. J Appl Physiol 87: 325–331, 1999.[Abstract/Free Full Text]
  52. Roca J, Agusti AG, Alonso A, Poole DC, Viegas C, Barbera JA, Rodriguez-Roisin R, Ferrer A, Wagner PD. Effects of training on muscle O2 transport at Formula 16O2 max. J Appl Physiol 73: 1067–1076, 1992.[Abstract/Free Full Text]
  53. Schaffartzik W, Barton ED, Poole DC, Tsukimoto K, Hogan MC, Bebout DE, Wagner PD. Effect of reduced hemoglobin concentration on leg oxygen uptake during maximal exercise in humans. J Appl Physiol 75: 491–498, 1993.[Abstract/Free Full Text]
  54. Secomb TW, Hsu R. Simulation of O2 transport in skeletal muscle: diffusive exchange between arterioles and capillaries. Am J Physiol Heart Circ Physiol 267: H1214–H1221, 1994.[Abstract/Free Full Text]
  55. Secomb TW, Hsu R, Park EY, Dewhirst MW. Green's function methods for analysis of oxygen delivery to tissue by microvascular networks. Ann Biomed Eng 32: 1519–1529, 2004.[CrossRef][Web of Science][Medline]
  56. Secomb TW, Pries AR. Information transfer in microvascular networks. Microcirculation 9: 377–387, 2002.[CrossRef][Web of Science][Medline]
  57. Sparks HV. Effects of local metabolic factors on vascular smooth muscle. In: Handbook of Physiology. The Cardiovascular System. Vascular Smooth Muscle. Bethesda, MD: Am. Physiol. Soc., 1980, sect. 2, vol. II, p. 475–513.
  58. Stainsby WN, Otis AB. Blood flow, blood oxygen tension, oxygen uptake, and oxygen transport in skeletal muscle. Am J Physiol 206: 858–866, 1964.[Abstract/Free Full Text]
  59. Stamler JS, Jia L, Eu JP, McMahon TJ, Demchenko IT, Bonaventura J, Gernert K, Piantadosi CA. Blood flow regulation by S-nitrosohemoglobin in the physiological oxygen gradient. Science 276: 2034–2037, 1997.[Abstract/Free Full Text]
  60. Sun D, Huang A, Koller A, Kaley G. Flow-dependent dilation and myogenic constriction interact to establish the resistance of skeletal muscle arterioles. Microcirculation 2: 289–295, 1995.[Medline]
  61. Tallini YN, Brekke JF, Shui B, Doran R, Hwang SM, Nakai J, Salama G, Segal SS, Kotlikoff MI. Propagated endothelial Ca2+ waves and arteriolar dilation in vivo: measurements in Cx40BAC GCaMP2 transgenic mice. Circ Res 101: 1300–1309, 2007.[Abstract/Free Full Text]
  62. Thomas GD, Segal SS. Neural control of muscle blood flow during exercise. J Appl Physiol 97: 731–738, 2004.[Abstract/Free Full Text]
  63. VanTeeffelen JW, Segal SS. Interaction between sympathetic nerve activation and muscle fibre contraction in resistance vessels of hamster retractor muscle. J Physiol 550: 563–574, 2003.[Abstract/Free Full Text]
  64. Xia J, Duling BR. Electromechanical coupling and the conducted vasomotor response. Am J Physiol Heart Circ Physiol 269: H2022–H2030, 1995.[Abstract/Free Full Text]



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