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Department of Molecular Physiology and Biological Physics, University of Virginia Health Sciences Center, Charlottesville, Virginia 22906-0011
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ABSTRACT |
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In rat cremasteric
microcirculation, mechanical occlusion of one branch of an arteriolar
bifurcation causes an increase in flow and vasodilation of the
unoccluded daughter branch. This dilation has been attributed to the
operation of a shear stress-dependent mechanism in the
microcirculation. Instead of or in addition to this, we hypothesized
that the dilation observed during occlusion is the result of a
conducted signal originating distal to the occlusion. To test
this hypothesis, we blocked the ascending spread of conducted vasomotor
responses by damaging the smooth muscle and endothelial cells in a
200-µm segment of second- or third-order arterioles. We found that a
conduction blockade eliminated or diminished the occlusion-associated
increase in flow through the unoccluded branch and abolished or
strongly attenuated the vasodilatory response in both vessels at the
branch. We also noted that vasodilations induced by ACh
(10
4 M, 0.6 s) spread to, but not beyond, the area
of damage. Taken together, these data provide strong evidence that
conducted vasomotor responses have an important role in coordinating
blood flow in response to an arteriolar occlusion.
gap junctions; flow dependent; arteriole; acetylcholine; ischemia
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INTRODUCTION |
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THE ROLE PLAYED BY SHEAR STRESS in modulating arteriolar tone in situ has not been fully established. It has been shown that increases in flow (and shear stress) induced in one limb of an arteriolar bifurcation by mechanical occlusion of the sister branch cause dilation of the unoccluded branch (4, 13). This dilation has been attributed to the elevated wall shear stress. However, a more detailed analysis of the parallel occlusion model, including examination of the behavior of both parent and unoccluded daughter vessels, led us to hypothesize that tissue ischemia and/or reduced pressure distal to the site of occlusion may have played a key role in inducing the vasodilation (18). We proposed that the signal for vasodilation spreads upstream from the more distal arteriolar segments exposed to regions of ischemia into both the feed vessel and the sister branch arteriole.
We, along with others, have shown the presence of a conduction process in the wall of an arteriole that is capable of inducing vasodilation in segments far away from a site of application of an agonist. This occurs both in vitro (7, 8) and in vivo (5, 9, 16, 20, 21). The distant mechanical responses observed in the arterioles are preceded by changes in membrane potential (7), supporting the proposal that the signal responsible for the responses is current being conducted between cells of the vessel wall, probably through gap junctions (20, 24, 25).
In the present study, we have investigated a possible role for conducted vasomotion in the dilator responses observed in vessels at a bifurcation. To distinguish between the contributions induced by shear stress and those associated with conduction, we have produced localized blockade of the spread of conducted vasodilation between the sites of stimulation and observation.
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METHODS |
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Animal Preparation
The University of Virginia Animal Care and Use Committee approved the procedures and protocols used in this study. Male Sprague-Dawley rats (181.0 ± 4.7 g, n = 21; Charles River) were prepared for in situ examination of the cremaster microvasculature. Each animal was anesthetized with pentobarbital sodium (80-100 mg/kg ip), and body temperature was maintained at 36.5-37.5°C by radiative and conductive heating. A tracheostomy tube was placed, and the animal breathed room air spontaneously during the course of the experiment. The left femoral vein was cannulated for administration of fluid and anesthesia. The cremaster to be studied was exposed, opened, and cleared of connective tissue (1). Each preparation was then mounted on the stage of a microscope (Nikon), and arterioles were observed with a ×50 objective (Leitz UMK, numerical aperture = 0.6). Intravenous anesthesia (10 mg/ml pentobarbital sodium in normal saline, at 0.5 ml/h) was infused continuously during the remainder of the experiment. The tissue preparation was superfused at 5-6 ml/min with a modified Ringer bicarbonate solution (pH 7.36-7.44) containing (in mM) 132 NaCl, 4.7 KCl, 2.0 CaCl2, 1.2 MgSO4, and 20 NaHCO3. The superfusate was warmed to 33.5-34.5°C and equilibrated by continuous bubbling with 5% CO2-95% N2.Measurements
Second- and third-order arterioles were selected because these have been the subject of prior investigation and they provide the branching structure and length necessary to execute these experiments. The image of a selected arteriolar segment was picked up by a video camera (Dage-MTI 68), displayed on a video monitor (Dage-MTI), and recorded for off-line analysis (Panasonic, PV-S4480). Centerline red blood cell (RBC) velocity in the arterioles was measured using an optical Doppler velocimeter (Microcirculation Research Institute, Texas A&M; see Ref. 2), which was calibrated over the range 1-20 mm/s using a smear of RBCs on a glass disk rotating at known velocities. Measurements of luminal diameter were made off-line using a video caliper (Microcirculation Research Institute, Texas A&M), which was calibrated using a stage micrometer (100 × 0.01 = 1 mm; Graticules). RBC velocity and video caliper voltages were sampled at 6 Hz by an analog-to-digital board, and the data were processed and stored with data acquisition software (DI-190, Dataq). Maximal diameters were determined after application of 10
4 M ACh.
Flow (Q) was calculated using the formula Q = VA, where V is RBC mean velocity [centerline RBC
velocity (mm/s) /1.6] and A is area of the vessel
(cm2). Shear stress (
) was calculated using the formula
= 4
Q/(
r3), where
is viscosity of blood (0.04 dyn · s · cm
2), Q is blood flow (cm3/
), and
r is radius (cm).
Conduction Blockade
A conduction blockade was achieved by producing localized damage to smooth muscle and endothelial cells in a small arteriolar segment (~200 µm). A glass micropipette (fire-polished, 30-µm tip) was pressed on the vessel surface and dragged back and forth until both smooth muscle and endothelial cells over a 200- to 300-µm arteriolar segment were permeabilized. Cell damage and permeability were assessed using circulating propidium iodide (2 µg/ml), a dye that enters damaged cells and fluoresces only when bound to DNA. The pipette application was continued until nuclei of both longitudinally and radially arranged cells within the vessel wall (i.e., endothelial and smooth muscle cells) were clearly labeled. After treatment, a recovery period of 30-60 min was allowed to clear thrombi and allow restoration of arteriolar tone.Arterioles with resting diameters 60-80% of maximal diameter were considered suitable for study. The small, damaged segment of arteriole remained fully dilated and created a bulge that was readily distinguishable from undamaged segments.
Treatments
We utilized two maneuvers to elicit an increase in flow through an arteriole: occlusion of one of a pair of vessels at a branch and microapplication of ACh to a downstream site (Fig. 1, A and B).
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Arteriolar occlusion. Arteriolar occlusion was performed by applying a glass pipette occluder (tip diameter 5-10 µm) to an arteriolar bifurcation to produce an occlusion (18). The occluding pipette was positioned over one arteriole of the branched pair, 100-300 µm distal to the bifurcation (Fig. 1A). Regions were selected with no branches between the bifurcation and occlusion pipette and no large branches for at least 500 µm downstream from the pipette. This selection was implemented to maximize the extent of downstream ischemia during an occlusion. In the unoccluded sister branch, measurements of both RBC velocity and diameter were made at a site 100-200 µm distal to the bifurcation (Fig. 1A, observation area). This distance was chosen because it was close enough to the branch to allow observation of both the occluded and unoccluded branches simultaneously but was far enough away to allow development of a stable flow profile distal to the branch.
To test our hypothesis that the signal for dilation originated from tissue distal to the occlusion, we produced occlusions before and after the conduction blockade in a segment of arteriole distal to the occlusion pipette (Fig. 1A).Downstream dilation.
In an attempt to dissociate the myogenic effects, metabolic-dependent
effects, and flow-dependent effects arising from occlusion of
an arteriole, we devised a method similar to that used by Kurjiaka and
Segal (16) to increase flow through an arteriole. A
conducted vasodilatory response was induced by applying ACh to a short
arteriolar segment 1,000 µm or more downstream from a point of
disrupted conduction. A stimulating micropipette (tip diameter 5 µm)
was positioned within 10 µm of the vessel wall, and ACh
(10
4 M, 0.6 s) was pressure ejected (Picospritzer,
General Valve) onto a small segment of the vessel, causing
bidirectional conducted vasodilation. Changes in hemodynamics were
measured at two sites, 100 µm downstream and 500 µm upstream from
the area of conduction blockade (Fig. 1B, observation
areas). A separate stimulus was applied for measurements at each site.
In these experiments the gas mixture was changed from the control (5%
CO2-95% N2) to 10% O2-5%
CO2-85% N2 to increase tone downstream from
the area of vessel damage.
Statistics
Each data point is the average of two sequential responses at the same arteriolar location. Summary data are presented as means ± SE from the number of animals indicated by n. In each set of experiments, Student's t-test for paired samples was used to compare groups, with P < 0.05 denoting significance. All statistical comparisons were performed with SigmaStat (Jandel Scientific).| |
RESULTS |
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Conduction Blockade
Propidium iodide uptake showed that damage to the arteriole remained focal (~200 µm), and this corresponded to an area without vasomotor tone. No damage to the parenchymal cells was noted. The damaged segment was greater than the length of one endothelial cell and was the width of ~20 smooth muscle cells (11). Thus it must have disrupted the possibility for intercellular connections between undamaged cells. Regions immediately upstream and downstream developed tone in response to elevated superfusion solution PO2, and both regions dilated in response to topically applied ACh (Table 1). The diameters, flows, and shear stresses were similar proximal and distal to the site of blockade (see Table 4). Conduction blockade was confirmed by applying ACh (10
4 M, 0.6 s) downstream
of the damage site. In each experiment, vasodilation spread up to, but
not beyond, the area of blockade (Fig.
2).
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Arteriolar Occlusion
Occlusion of one branch at a bifurcation caused a very rapid vasodilation (within 2 s) in both the feed (data not shown, see Ref. 18) and the unoccluded branch. Flow increased through the unoccluded branch (Fig. 3, control). The increase in flow occurred in the face of reduction in both RBC velocity (Fig. 3, top) and in the estimated shear stress (Fig. 3, bottom). Conduction blockade in the branch that had previously been occluded (Fig. 1A) caused a slight decrease in preocclusion RBC velocity and an increase in diameter in the unoccluded (and undamaged) branch but did not significantly alter resting flow (Table 2). Under these conditions, occlusion of the damaged branch did not lead to dilation in the unoccluded branch, despite a rapid increase in RBC velocity, flow, and shear stress (Fig. 3). In all experiments, resting hemodynamics were restored within 20 s after the occlusion pipette was lifted. It is noteworthy that the feed vessel and occluded branch vessel dilated simultaneously with the unoccluded branch (data not shown, see Ref. 18).
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To establish the nature of the signal causing the vasodilation under
control conditions and to link our findings to previous reports
(15), we used blockers of synthesis of prostaglandin (indomethacin, 10
5 M, Sigma) and nitric oxide
[N
-nitro-L-arginine methyl ester
(L-NAME), 10
5 M, Sigma]. When added to the
superfusate, both blockers increased tone (Table
3), but
neither blocked the dilation in response to arteriolar occlusion,
either when added alone (Fig. 4) or in combination (data not shown). The concentrations of indomethacin and
L-NAME were effective in attenuating arachadonic
acid-mediated vasoconstriction (10
5 M, 0.5 s,
n = 7; Nu-Chek-Prep) and ACh-mediated vasodilation (10
4 M, 0.1 s, n = 4), respectively.
L-NAME had no effect on the vasodilation stimulated by
sodium nitroprusside (10
5 M, 0.1 s,
n = 4; Sigma; data not shown).
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Downstream Dilation
As shown in Fig. 2, ACh initiated a vasodilation that spread up to, but not beyond, the damaged segment of arteriole. The response propagated bidirectionally, and thus the arterioles dilated over at least twice the distance from the stimulating pipette to the region of blockade. The ACh stimulating pipette was located 1,340 ± 411 µm (n = 7) downstream from the site of damage, and, as a result, a total segment of well over 2 mm of arteriole should have dilated (21). The associated fall in arteriolar resistance almost doubled the flow in the arteriole (Fig. 5). After stimulation with ACh, the increase in flow upstream from the site of damage was associated mainly with an increase in RBC velocity rather than an increase in diameter. Both RBC velocity and shear stress rapidly increased by ~35%; however, detectable vasodilation was only observed after 5-10 s of stimulation, much slower than the control, where rapid dilation was observed after 1-2 s of ACh application (Fig. 5, downstream vs. upstream). The magnitude of dilation was markedly attenuated relative to the downstream site (Figs. 2 and 5).
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DISCUSSION |
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Occlusion of one vessel at an arteriolar bifurcation causes a dilation of the unoccluded daughter arteriole. The dilation of the unoccluded vessel is associated with an increase in flow and has been interpreted as being the result of a shear-dependent stimulus (13, 14, 23). Here we report that conducted vasomotor responses make a major contribution to the dilation observed during the parallel occlusion maneuver. By preventing an ascending conducted vasomotor response from reaching the bifurcation, we could severely attenuate or block dilations in the unoccluded daughter, the proximal segment of the occluded branch (Fig. 3), or the parent vessel (data not shown). We also demonstrated a role for ascending vasodilation in modifying wall shear stress and diameter changes, using ACh as an agonist to mimic factors that trigger the ascending dilation during occlusion (Fig. 5).
Previously we proposed (18) that the origin of the vasodilation is distal to the occlusion pipette and that the proximal response occurs very rapidly. In this report, this was tested by selectively preventing the spread of any conducted vasomotor response upstream of a point of focal arteriolar damage. After damage and elimination of conduction, occlusion of the daughter vessel continued to cause an increase in wall shear stress in the unoccluded parallel daughter vessel, but vasodilation was largely abolished (Fig. 3).
Our data show that increases in flow or shear stress do not necessarily cause vasodilation in the microcirculation (Fig. 5). ACh caused an increase in flow through the arteriole (Fig. 5) without significant dilation as previously reported by Kurjiaka and Segal (16). These authors found that ACh stimulated local and conducted vasodilation associated with a decrease in RBC velocity at all observation sites along the arteriole. Here we show that focal damage to the arteriole can largely block the parallel rise in diameter and wall shear stress.
One caveat in the interpretation of our data is that conduction blockade was associated with a substantial reduction in the control wall shear stress (Table 2), a change that may have influenced the contribution of wall shear stress to the vasodilation that we observed. This fact is particularly important to keep in mind, because a recent study has employed increases in plasma viscosity to increase wall shear stress, rather than microvessel occlusion (6). Increases in shear stress were associated with a vasodilation that was sensitive to blockade of NO synthesis and was attributed to changes in wall shear stress (6). It is likely that changes in pressure and flow would have been different in this model from those that occur during occlusion. Furthermore, it is important to note that the effect of an occlusion would depend heavily on the degree to which the ischemic region was supplied by inflow from other vessels, including the unoccluded daughter vessel. These facts make it important to retain the idea that wall shear stress and conduction may act jointly to modulate arteriolar diameter.
The ascending vasodilatation that we observed was likely triggered by reduced intravascular pressure or factors related to tissue ischemia in regions downstream from the point of occlusion (18). Previous microelectrode measurements of periarteriolar PO2 revealed that cessation of blood flow for periods as short as 1-2 s caused vasodilation and a reduction in periarteriolar PO2 at sites distal to the occlusion pipette (17). The dilation was observed both upstream and downstream from the occlusion pipette. As the duration of occlusion was increased, further increases in diameter and decreases in perivascular PO2 were observed, suggesting a metabolic contribution to the dilation (17). In the arteriolar occlusion experiments presented here (Fig. 3), we propose that a similar process occurred. Furthermore, because the dilation spread through the point of occlusion into the bifurcation, a conducted vasomotor response is most likely to have been involved (18).
The identity of the signal for vasodilation has not been established in this study. In contrast to previous reports (15), the contribution by prostaglandins appears to have been small. Both of the blockers we used, indomethacin and L-NAME, caused an increase in tone when applied in the superfusion solution, suggesting a continuous release of nitric oxide and prostaglandins in the rat cremaster. Neither blocker, either alone (Fig. 4) or in combination (data not shown), blocked the dilation in response to arteriolar occlusion. Alternative signaling molecules include the release of a hyperpolarizing factor in response to hypoxia (22) or decreases in the formation of the vasoconstrictor 20-hydroxy-6,8,11,14-eicosatetraenoic acid (12), among others (see Refs. 3 and 10).
It should be noted that the measurement of flow in the microcirculation has several inherent limitations. As previously reported, there is some undetermined inaccuracy in the diameter and/or RBC velocity measurement (19). Because we selected unbranched segments of the arterioles for study, the changes in flow must have been equal at the two upstream and downstream observation sites. This was not measured however (Fig. 5). When faced with similar results, Proctor et al. (19) suggested that the uncertainty lay more with the diameter measurement, especially in constricted vessels. Because the diameters remained relatively constant during arteriolar occlusion after conduction blockade (Fig. 3) and at the upstream site following stimulation with ACh (Fig. 5), the values for percent changes in RBC velocity, flow, and shear stress are likely to be more accurate, and these form the basis of our conclusions.
In summary, we propose that conducted vasomotor responses are important in coordinating blood flow with tissue metabolic demand. Arteriolar occlusion induces a signal downstream from the point of occlusion that is conducted upstream to encompass the unoccluded branch as well as the feed arteriole. This severely compromises one's ability to assess the contribution of wall shear stress to the vasomotor response. The identity of the signal is the subject of ongoing work, but, most likely, altered vascular perfusion or pressure causes hyperpolarization of the arteriole that spreads along the vessel length.
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ACKNOWLEDGEMENTS |
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We thank Dr. Steve S. Segal for loan of the optical Doppler velocimeter. We are grateful to E. D. McGahren for valuable discussions.
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FOOTNOTES |
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The work here was supported by National Heart, Lung, and Blood Institute Grant HL-53318, the American Heart Association, Virginia Affiliate Award 96-F-25, and a C. J. Martin Fellowship from the National Health and Medical Research Council (Australia).
Address for reprint requests and other correspondence: B. R. Duling, Dept. of Molecular Physiology and Biological Physics, Univ. of Virginia Health Sciences Center, PO Box 10011, Charlottesville, VA 22906-0011.
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. §1734 solely to indicate this fact.
Received 10 May 1999; accepted in final form 27 January 2000.
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REFERENCES |
|---|
|
|
|---|
1.
Baez, S.
An open cremaster muscle preparation for the study of blood vessels by in vivo microscopy.
Microvasc Res
5:
384-394,
1973[Web of Science][Medline].
2.
Borders, JL,
and
Granger HJ.
An optical Doppler intravital velocimeter.
Microvasc Res
5:
384-394,
1984.
3.
Brayden, JE.
Potassium channels in vascular smooth muscle.
Clin Exp Pharmacol Physiol
23:
1069-1076,
1996[Web of Science][Medline].
4.
Cabel, M,
Smiesko V,
and
Johnson PC.
Attenuation of blood flow-induced dilation in arterioles after muscle contraction.
Am J Physiol Heart Circ Physiol
266:
H2114-H2121,
1994
5.
Delashaw, JB,
and
Duling B.
Heterogeneity in conducted arteriolar vasomotor response is agonist dependent.
Am J Physiol Heart Circ Physiol
260:
H1276-H1282,
1991
6.
DeWit, C,
Schafer C,
vonBismarck P,
Bolz SS,
and
Pohl U.
Elevation of plasma viscosity induces sustained NO-mediated dilation in the hamster cremaster microcirculation.
Pflügers Arch
434:
354-361,
1997[Web of Science][Medline].
7.
Dora, KA,
and
Duling BR.
Use of fluorescent reporters in the quantitation of microvascular function.
Microcirculation
5:
95-100,
1998[Web of Science][Medline].
8.
Doyle, MP,
and
Duling BR.
Acetylcholine induces conducted vasodilation by nitric oxide-dependent and -independent mechanisms.
Am J Physiol Heart Circ Physiol
272:
H1364-H1711,
1997
9.
Duling, BR,
and
Berne RM.
Propagated vasodilation in the microcirculation of the hamster cheek pouch.
Circ Res
26:
163-170,
1970
10.
Duling, BR,
and
Dora KA.
Control of striated muscle blood flow.
In: The Lung: Scientific Foundations., edited by Crystal RG,
West JB,
Barnes PJ,
and Weibel ER.. Philadelphia, PA: Lippencott-Raven, 1997, p. 1935-1944.
11.
Haas, TL,
and
Duling BR.
Morphology favors an endothelial cell pathway for longitudinal conduction within arterioles.
Microvasc Res
53:
113-120,
1997[Web of Science][Medline].
12.
Harder, DR,
Narayanan J,
Birks EK,
Laird JF,
Imig M,
Lombard JH,
Lange RJ,
Roman RJ,
and
Imig JD.
Identification of a putative microvascular oxygen sensor.
Circ Res
79:
54-61,
1996
13.
Koller, A,
and
Kaley G.
Flow velocity-dependent regulation of microvascular resistance in vivo.
Microcirc Endothelium Lymphatics
5:
519-529,
1989[Web of Science][Medline].
14.
Koller, A,
and
Kaley G.
Endothelium regulates skeletal muscle microcirculation by a blood flow velocity-sensing mechanism.
Am J Physiol Heart Circ Physiol
258:
H916-H920,
1990
15.
Koller, A,
and
Kaley G.
Prostaglandins mediate arteriolar dilation to increased blood flow velocity in skeletal muscle microcirculation.
Circ Res
67:
529-534,
1990
16.
Kurjiaka, DT,
and
Segal SS.
Conducted vasodilation elevates flow in arteriole networks of hamster striated muscle.
Am J Physiol Heart Circ Physiol
269:
H1723-H1728,
1995
17.
Lombard, J,
and
Duling B.
Multiple mechanisms of reactive hyperemia in arterioles of the hamster cheek pouch.
Am J Physiol Heart Circ Physiol
241:
H748-H755,
1981
18.
McGahren, ED,
Dora KA,
Damon DN,
and
Duling BR.
A test of the role of flow-dependent dilation in arteriolar responses to occlusion.
Am J Physiol Heart Circ Physiol
272:
H714-H721,
1997
19.
Proctor, K,
Damon D,
and
Duling B.
Inaccuracies in blood flow estimates in microvessels during arteriolar vasoconstriction.
Microvasc Res
28:
23-36,
1984[Web of Science][Medline].
20.
Segal, SS,
and
Beny JL.
Intracellular recording and dye transfer in arterioles during blood flow control.
Am J Physiol Heart Circ Physiol
263:
H1-H7,
1992
21.
Segal, SS,
Damon DN,
and
Duling BR.
Propagation of vasomotor responses coordinates arteriolar resistances.
Am J Physiol Heart Circ Physiol
256:
H832-H837,
1989
22.
Siegel, G,
Grote J,
Schnalke F,
and
Zimmer K.
The significance of the endothelium for hypoxic vasodilatation.
Z Kardiol
78, Suppl6:
124-131,
1989.
23.
Smiesko, V,
Lang D,
and
Johnson P.
Dilator response of rat mesenteric arcading arterioles to increased blood flow velocity.
Am J Physiol Heart Circ Physiol
257:
H1958-H1965,
1989
24.
Xia, J,
and
Duling BR.
Electromechanical coupling and the conducted vasomotor response.
Am J Physiol Heart Circ Physiol
269:
H2022-H2030,
1995
25.
Xia, J,
Little TL,
and
Duling BR.
Cellular pathways of the conducted electrical response in arterioles of hamster cheek pouch in vitro.
Am J Physiol Heart Circ Physiol
269:
H2031-H2038,
1995
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