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Am J Physiol Heart Circ Physiol 282: H165-H174, 2002;
0363-6135/02 $5.00
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Vol. 282, Issue 1, H165-H174, January 2002

Force-velocity relationship of myogenically active arterioles

Michael J. Davis and Judy Davidson

Department of Medical Physiology and Cardiovascular Research Institute, Texas A&M University System Health Science Center, College Station, Texas 77843


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

We compared the shortening velocity of smooth muscle in arterioles that had low or high levels of myogenic tone or norepinephrine (NE)-induced tone. We hypothesized that enhanced myogenic tone of arterioles reflects an enhanced maximum velocity of shortening of arteriolar smooth muscle in a way that is different from that produced by NE. These concepts are untested assumptions of arteriolar mechanics. Second-order arterioles from hamster cheek pouch (passive diameter at 40 mmHg = 42 µm) were isolated and cannulated for in vitro study. In the absence of flow, pressure was controlled by hydraulic pumps so that servo control of wall tension could be achieved from measurement of internal diameter and pressure. Isotonic quick-release protocols were used to measure the initial velocity of shortening following release from control wall tension (afterload) to a series of fractional afterloads. After release, the initial rates of shortening were fit to the Hill equation to obtain coefficients for a hyperbolic fit of the velocity-afterload relationship. The maximal unloaded shortening velocity for partially activated arterioles (V'max) was determined from the y-intercept of each plot. Using this procedure, we compared V'max from two groups of arterioles equilibrated at low or high pressure, i.e., with low or high myogenic tone. Arterioles with higher myogenic tone had higher values of V'max than arterioles with lower myogenic tone. V'max for arterioles partially activated with NE at low pressure was comparable to V'max for arterioles with high myogenic tone, but NE produced high velocities at low force, whereas enhanced myogenic tone produced roughly parallel shifts in velocity and force. The results suggest that increased myogenic tone does indeed reflect enhanced activation of arteriolar smooth muscle, and this effect is mechanically different from that produced by NE.

maximal shortening velocity; arteriolar mechanics; isolated arterioles; norepinephrine; agonist-induced tone


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

THE MYOGENIC RESPONSE is an inherent ability of smooth muscle to respond to increased force. In arterial blood vessels, the myogenic response is manifested as a sustained constriction following luminal pressure elevation. The time course of a vascular myogenic constriction occurs in several phases. In most vessels, a rapid elevation in luminal pressure produces an immediate distention. The amount of distension is variable and depends on the level of initial tone (10). After the distension phase, a contraction begins to develop. In large vessels, the delay before vascular smooth muscle (VSM) contraction varies from many seconds in arteries to a fraction of a second in arterioles (17). The amount of constriction is also greater in arterioles (3, 24). In some vessels, the constriction is biphasic, with an exaggerated initial phase that is independent of the rate of pressure rise, followed by a partial relaxation to a steady-state phase (9, 10). The steady-state constriction appears to be maintained almost indefinitely (18) and accounts for the basal tone of resistance vessels in almost every organ.

Implicit in the concept of a myogenic constriction is the assumption that VSM shifts to a higher activation state. Johnson (16) stated this assumption clearly in his landmark chapter in the Handbook of Physiology, basing his conclusion on length-tension analyses of in vivo arterioles from cat mesentery (15). Specifically, enhanced activation associated with myogenic tone was predicted to explain the progressive, leftward shift of calculated arteriolar wall tension with pressure. Whereas Johnson's initial analyses required arteriolar pressures to be extrapolated from measurements of systemic arterial pressure, direct measurements of arteriolar pressure in subsequent experiments confirmed Johnson's predictions (6).

However, analyses of the myogenic response in vivo are subject to concerns about modulation by parenchymal cell metabolites and endothelial cell vasoactive factors because changes in oxygen delivery and flow necessarily accompany changes in perfusion pressure (8). Thus it is important that these protocols be repeated in isolated arterioles where the endothelium is denuded and/or where changes in flow are prevented. Even so, such evidence would only qualitatively support the concept of an increased VSM activation state. A more rigorous test of this idea would be to demonstrate that increased myogenic tone reflects an increase in maximal velocity of shortening (Vmax) of arteriolar smooth muscle. However, measurements of VSM force-velocity relationships have only been possible, to date, on larger blood vessels that lack significant myogenic responsiveness (1, 11, 14, 20, 21).

In this study, we tested the hypothesis that myogenic activation of arterioles is associated with an increase in unloaded shortening velocity of arteriolar smooth muscle. To make these measurements, we performed isotonic release protocols on isolated, cannulated segments of second-order (2A) hamster cheek pouch arterioles using a servo-control system to regulate wall tension. These vessels have been studied extensively in vitro and generate ~50% myogenic tone (relative to maximal passive diameter), which is comparable to 2A tone observed in vivo. Furthermore, maximal length-tension relationships for these vessels have been previously determined (4). As an additional aspect of this study, we compared how enhanced myogenic tone and agonist-induced tone might differentially alter the force-velocity relationship of arteriolar smooth muscle.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Isolated arteriole preparation. Golden Syrian hamsters (120-180 g) were anesthetized with intraperitoneal injections of pentobarbital sodium (60 mg/kg). One cheek pouch from each animal was cleaned, excised, and placed in 4°C physiological saline solution containing 1 g/100 ml albumin. All animal protocols conformed to institutional guidelines.

To perform isotonic release protocols, several substantial modifications were made to our standard isolated arteriole measurement system. To maximize the frequency response of the system and reduce the possibility of cannulation-induced trauma, vessels were studied in a parent-daughter arrangement as previously described (3, 10). After pinning was completed, the avascular connective tissue covering the pouch was removed, and arteriolar segments consisting of a first-order (1A) parent vessel and 2A daughter vessel were selected for study. The segments were carefully cleared of connective tissue with the use of sharpened instruments, excised, and transferred in a Pasteur pipette to a temperature-controlled chamber for cannulation and study (7). At room temperature, both ends of the 1A were cannulated with ~60-µm (external diameter) micropipettes and secured with 12-O suture. Cannulation pipettes contained the following solution (in mM): 145.0 NaCl, 5.0 KCl, 2.0 CaCl2, 1.2 MgSO4, 1.2 NaH2PO4, 0.02 EDTA, 5.0 glucose, 2.0 pyruvate, 2.0 3-(N-morpholino)propanesulfonic acid, and 1 g/100 ml purified bovine serum albumin. The 1A segment was intentionally overstretched in the longitudinal direction to eliminate tone and possible interference with myogenic responses of the daughter vessel through conducted pressure responses (22). The second-order (daughter) side branch (segment length = 400-700 µm) was tied off at its distal end with 12-O suture and stretched to approximately its in vivo length (measured before dissection) using a suction micropipette.

After the chamber and pipette system were transferred to the stage of an inverted microscope, the temperature was slowly raised over 1 h to 36-37°C by a circulating water bath. A roller pump (Gilson Milipuls 3) was used to superfuse (4 ml/min) the vessel segment with a Ringer-bicarbonate solution (RBS) containing (in mM) 131.9 NaCl, 4.7 KCl, 2.0 CaCl2, 1.2 MgSO4, and 18.0 NaHCO3 and bubbled continuously with 95% N2-5% CO2 (pH = 7.35; PO2 approx 50 mmHg). During this time, one end of the vessel segment was pressurized from a reservoir to its normal in vivo pressure while luminal pressure was monitored at the other end using a pressure transducer. Differences between input and output pressures were indicative of leaky vessel segments, and data from leaky segments were not used for further analysis. The amount of myogenic tone was referenced to the passive diameter at 40 mmHg (Lo), which is close the normal in vivo pressure of 2As (4). This value was always measured at 22°C during the initial equilibration period before the vessel gained tone, but in several vessels a complete passive pressure-diameter relationship was obtained at the end of the experiment after equilibration in Ca2+-free RBS containing 10-4 M nitroprusside.

Microscope system. Each vessel segment was transilluminated using a Zeiss IM-35 inverted microscope with a heat-filtered, 100-W tungsten light source, filtered at 515 nm. The 2A branch was visualized at high magnification using a Leitz ×75 oil immersion objective (numerical aperature = 1.0) and bright-field (numerical aperature = 0.63) condenser. The vessel image was displayed on a video monitor using a Newvicon camera, and internal diameter was measured manually with a video micrometer. Pressure and diameter recordings were digitized using a Macintosh 8100/80 computer and MIO-16x data acquisition card (National Instruments; Austin, TX). Experiments were videotaped using a videotimer signal so that arteriolar diameter transients could be measured at high time resolution (1/5 real time) during replay of the videotape. To synchronize diameter and pressure measurements on replay, a video multiplexer was used to record pressure onto the audio track of the videotape. The analog output from the multiplexer was redigitized in synchrony with the replayed diameter signal.

Servo control of pressure and wall tension. To provide computer control over the pressurization system, the following modifications were made. Two static pressure reservoirs used for initial equilibration of the vessels were connected through three-way valves to Ling vibration pumps (model V203; Herts, UK). These pumps were driven by custom-made power amplifiers and allowed servo control of vessel pressure. Pressures at the pumps were measured using Statham P23 Db pressure transducers connected to a custom-built carrier amplifier. Output from this unit was compared with a command pressure from the computer by a custom-built servo amplifier. In initial experiments, tuning low-pass filters on each pressure channel optimized the frequency response and gain of the system. The response was confirmed to be flat to at least 20 Hz by servo-null measurements of pressure at the vessel midpoint.

Protocols. After equilibration and development of spontaneous myogenic tone under pressurization to 44 mmHg from the static reservoir, pressure control was switched over to the computer and set to 40 mmHg. Software programs to control this and subsequent protocols were written using LabView (National Instruments). After verification that the system was working properly, i.e., that there were no leaks and no oscillations in the servo-control system, at least one 2-min pressure step to >= 90 mmHg was performed while recording internal diameter to check for myogenic constrictions. Pressure was then returned to 40 mmHg, and the preparation was allowed to stabilize for 10-15 min. 2As developed ~43% basal tone at 40 mmHg (Table 1), which is greater than that previously reported (see Fig. 3d in Ref. 4). Of 17 arterioles attempted, one was discarded for failing to develop myogenic tone, and one was discarded due to excessive spontaneous vasomotion.

                              
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Table 1.   Baseline parameters for 2As in each group

After these tests, isotonic release protocols were initiated. For this, the computer system was switched from pressure control to tension control mode. The wall tension at the control pressure (either 40 or 90 mmHg) was used as a reference point (i.e., 1.0). Wall tension was calculated from
Tension<IT>=</IT>pressure<IT>·</IT>internal radius (1)
While internal diameter was measured, tension was then "released" to 0.8, 0.6, 0.5, 0.4, 0.3, 0.2, or 0.1 of control tension for a 2- to 15-s period. Any diameter changes during this time resulted in subsequent adjustments in pressure by the computer to maintain constant tension. Tension was then returned to control, the system switched to pressure control mode, and the vessel allowed to regain tone. After this, tension control was switched on again, and the sequence was repeated for the other afterload. Five-minute reequilibration periods were allowed between releases. Between 3 and 12 isotonic releases were performed per vessel, with the sequence of releases being determined pseudo randomly. Attempts were usually made to repeat at least two releases to 0.2 and 0.1, because the velocities of shortening at these values would have the greatest influence over subsequent determinations of maximal shortening velocity.

After a complete series of releases was determined at the first equilibration pressure (40 or 90 mmHg), pressure was set to the other level, and the vessel was allowed to reequilibrate for 20-30 min. In about half of the experiments, the order of these protocols (i.e., 40 or 90 mmHg) was reversed. At 90 mmHg, this group of 2As developed 54% myogenic tone (compare to Fig. 3d in Ref. 4). Further elevations in pressure (e.g., to 118 mmHg) resulted in only 3-5% additional tone and sometimes caused irreversible damage to these vessels (4); therefore, 90 mmHg was considered a safe pressure that would produce nearly maximal myogenic tone. In several arterioles, norepinephrine (NE) was then added to the bath after the vessel had equilibrated at 40 mmHg, and another series of isotonic release protocols was performed. The dose of NE (10-8-10-7 M) was titrated to produce approximately the same level of constriction that would be produced at 90 mmHg (see Table 1). The protocols were terminated if the vessels failed to regain myogenic tone after isotonic releases were performed.

Off-line analysis. The typical diameter response to an isotonic release was a rapid (<200 ms), initial collapse of the arteriole, presumably reflecting recoil of VSM series-elastic elements (23). This was followed by a period of force development (constriction) that lasted 1-10 s. After this, some vessels would begin to myogenically dilate, but at some isotonic release levels, the pressure required to control the desired level of tension was too low (<20 mmHg) to elicit a myogenic response (see Fig. 3d in Ref. 4). Accurate measurements of the diameter changes during the first few seconds following isotonic release were critical for calculation of initial isotonic shortening velocity. Videotapes of the experiment were replayed off-line in slow motion so that the diameters could be remeasured using the video micrometer (several times in some cases) and the computer could subsequently digitize its output. The replayed diameter records were used for subsequent data analysis, whereas the initial (on-line) diameter measurements were necessary for control of wall tension. However, there was almost always very close agreement between the two. Automated diameter tracking devices did not prove sufficiently accurate to track internal diameter because any glitches in tracking led to large spikes in the servo-controlled pressure system. Any errors in the online measurement would obviously generate errors in the pressure servo. However, pressure compensations were typically rather small (a few mmHg, as shown in Fig. 2), and associated errors would not have had a major effect on the shortening velocity measurements.

The diameter data for the first 1-2 s following each isotonic release (and the associated series-elastic recoil) were fit with a first-order polynomial using a least-squares algorithm to estimate isotonic shortening velocity immediately after the release. The data obtained in each release protocol were then compiled and fit to the Hill equation (23, 26). Maximum shortening velocity (V'max) was estimated from the y-intercept of these plots. We use the term "V'max" to indicate that the arterioles in our experiments were not maximally activated nor set to the optimal length for maximal isometric force development. Igor (Wavemetrics; Lake Oswego, OR) macros were used to perform analyses and to construct subsequent force-velocity plots.

Normalization procedures. V'max was expressed as shortening in micrometers per second or in lengths per second. For the later case, the actual change in diameter was normalized to Lo for that vessel.

To compare force-velocity data from the three groups of vessels (P40, P90, NE), the force (tension) values must be normalized to 2A maximal isometric tension. To do this, the peak value of maximal isometric tension (Tmax) for hamster cheek pouch 2As was obtained from previous measurements by Davis and Gore (4), because it was not feasible to perform this measurement on each vessel after isotonic release protocols. This value averaged 680 dyn/cm at Lo = 1.0. The minimal diameter to which 2As can constrict (0.2 of Lo) was estimated from studies by VanBavel et al. (Fig. 2 in Ref. 25) and from Jackson and Duling (Fig. 5 in Ref. 13). Given these parameters, the predicted linear relationship between maximal active tension and Lo for these 2As is shown by the dotted line in Fig. 1, according to the following equation
T<SUB>max</SUB><IT>=</IT>[850 dyn<IT>/</IT>cm<IT>·</IT>(<IT>D</IT><SUB>i</SUB><IT>/L</IT><SUB>o</SUB>)]<IT>−</IT>150 dyn<IT>/</IT>cm (2)
where Tmax is maximal active tension at any length (diameter) and Di is the initial vessel diameter just before isotonic release. To normalize the data for each release, the initial wall tension (Ti) (Fig. 1) was divided by the calculated Tmax at the respective initial diameter. This assumes negligible passive tension, as indicated in Table 1. Force values for each release were normalized in this way and used for the force-velocity determinations in Figs. 7 and 8.


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Fig. 1.   Illustration of a myogenic constriction for a representative second-order arteriole (2A) on a tension-radius plot. Inset: raw pressure (P) and diameter (D) traces. Inverted "Y" shape in the center of the larger graph represents 220 paired diameter (D) and pressure (P) points converted to tension, normalized to passive diameter (Lo), and plotted against L/Lo, where L is diameter at each point in time. Numbers associated with these points indicate the time course of the response and correspond to the numbers in the inset. Open circles, passive tension-diameter plot for this 2A. Dashed line, calculated maximal active tension curve for this vessel as described in METHODS (see Eq. 2). Differences between point 1 and Lo and between point 3 and Lo represent amount of tone at 40 and 90 mmHg, respectively. Ratio of initial tension (Ti) to maximal active tension (Tmax) at each pressure represents "fractional tension" (as summarized in Table 1) of the 2A at the two different levels of myogenic tone.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Myogenic constriction represented on a tension-radius plot. One goal of these experiments was to test whether increased myogenic tone is associated with an enhanced activation of arteriolar smooth muscle. The first indication that this occurs is apparent in the myogenic behavior of a representative 2A as plotted on a length-tension curve (Fig. 1). The raw pressure and diameter data are shown as a function of time following a pressure step from 40 to 90 mmHg (see inset). The open arrows (Fig. 1) in the center of the diagram illustrate the time-dependent sequence of the myogenic constriction. At pressure equalling 40 mmHg, the radius equaled 0.6 Lo (point 1). When pressure was rapidly increased to 90 mmHg, the vessel distended to a radius of 0.68 Lo (point 2), then constricted to a minimum of 0.4 Lo (point 3), and maintained a steady-state constriction at that diameter. For reference purposes, the passive radius-tension relationship for the same 2A is also plotted (open circles) as is the maximal active tension curve (dashed line) calculated from Davis and Gore (4). It is apparent that the myogenic constriction is associated with a leftward shift of the radius-tension relationship for the arteriole. The solid arrows in Fig. 1 indicate the relative degree of myogenic tone, where tone is defined as the difference between the passive diameter at 40 mmHg (Lo) and the normalized steady-state diameter (Di/Lo). Thus this 2A developed ~40% tone at a pressure equalling 40 mmHg and ~60% tone at a pressure equalling 90 mmHg. Also shown in Fig. 1 are vertical lines that project from the two steady-state diameters to denote the intersections with the maximal active tension curve. The ratio of Ti to Tmax at each diameter may perhaps be a superior index of "tone," as defined by VanBavel et al. (25). However, in most previous myogenic studies, the term "tone" refers to a difference in the active versus passive diameter. Therefore to avoid confusion, we employ the term "fractional tension" to refer to the Ti-to-Tmax ratio under different conditions. With the use of this criterion, the 2A shown in Fig. 1 had a fractional tension equalling 0.19 at 40 mmHg and 0.49 at 90 mmHg, respectively. The average values for tone and fractional tension at both pressures and after NE are summarized in Table 1.

A leftward shift in the length-tension relationship in response to pressure elevation suggests increased arteriolar smooth muscle activation during myogenic tone development; however, more rigorous experimental evidence would be provided by demonstration of an increase in Vmax. Vmax can be determined from measurements of isotonic shortening velocity using isotonic release protocols (23) in which the muscle is quickly released from a predetermined afterload to a series of fractional afterloads, during which shortening velocity is measured at each step. This procedure is typically performed on maximally activated muscle, but the resulting force-velocity relationship is also valid for intermediate activation states (2, 19). Because this procedure had never before been performed on myogenically active arterioles, it was first necessary to validate its feasibility.

Isotonic release protocol. Changes in pressure and diameter as a function of tension during two isotonic releases are shown in Fig. 2. The baseline diameter of this arteriole was 24-27 µm at a pressure equalling 40 mmHg. In response to a sudden drop in wall tension from the calculated control value to 20% of control, there was a rapid initial collapse of the vessel (<0.2 s), which presumably represented the recoil of series elastic components (SEC) (26). After the recoil was a 2- to 3-s shortening phase until the arteriole suddenly began to dilate at ~1.8 s after release. The myogenic dilation (induced by the low pressure required to reduce afterload to 0.2) was variable in magnitude and time of onset from vessel to vessel, but never interfered with accurate determinations of the rate of initial shortening. After reequilibration for about 1.5 min at a pressure equalling 40 mmHg, a second release was performed on this vessel, to afterload equalling 0.6. As can be seen from Fig. 2, right, the phase of passive collapse is not clearly discernable, but the initial rate of shortening is lower than for the previous release. Also, the magnitude of the secondary myogenic dilation is greater (dilating above the control diameter; Fig. 2, left) presumably because the vessel is more myogenically active at the pressure required to achieve an afterload of 0.6 (~30 mmHg) compared with the pressure required to achieve an afterload of 0.2 (~15 mmHg).


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Fig. 2.   Example showing two isotonic releases performed on an isolated 2A. Near the beginning of the trace (time ~6 s), the system is switched from pressure control mode (P = 40 mmHg) to tension control mode. Shortly after this switch, tension is suddenly released to 20% of its control value (left) for ~5 s. The sudden drop in pressure and tension is associated with a rapid (<0.2 s) fall in tension that corresponds to recoil of the series elastic component. After this, a shortening phase commences, lasting ~4 s. At time ~11 s, the arteriole begins to dilate, demonstrating that it is myogenically responsive. This dilation is cut short by return of the tension to control. After ~90 s of recovery at P = 40 mmHg, tension is released to 60% of control (right). Same phases are present in the diameter trace, with the series elastic components (SEC) recoil phase being barely discernable. In this case, the secondary myogenic dilation brings diameter above the control level.

Repeatability of diameter changes during identical isotonic releases. To verify that reliable and repeatable changes in diameter could be recorded during isotonic releases, a series of nearly identical release protocols were repeated on a single 2A, as shown in Fig. 3. This arteriole was allowed to develop myogenic tone at a pressure of 40 mmHg. The servo system was switched to tension control mode, and the initial computed wall tension was used as a reference point. Tension was then released to an afterload equivalent to 20% of this value for ~14 s while recording diameter (in slow motion on video playback). The servo system was switched off, pressure was returned to 40 mmHg, and the vessel was allowed to regain myogenic tone. This procedure was repeated two times. The three resulting releases were then superimposed for comparison. The time courses of the diameter changes following isotonic release are remarkably consistent, especially over the first 2-3 s after release (Fig. 3). Note that there are some differences in the baseline tension for each trial due to slight variations in the amount of myogenic tone developed during each recovery period. Also, note that a partial myogenic relaxation occurred (t = 9 s) in one of the trials but that it was inconsequential to the measurement of initial shortening velocity. Importantly, the absolute diameter changes during the isotonic shortening phase (2.0-2.5 µm) were well within the resolution of the microscope system.


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Fig. 3.   Repeatability of diameter shortening phase during isotonic release protocols. This 2A was released three times from control to 20% of control tension. The first two releases were 20 min apart, and the third release was 1 min after that. Traces are superimposed and displayed as the diameter change from control. Magnitude of SEC recoil phase varied from 0.5 to 1.0 µm. Velocities for the first 1 s of the shortening phases were -0.55, -0.91, and -0.76 µm/s. Note slight myogenic dilation that occurs in one protocol at time ~9 s.

Analysis of data from a series of isotonic releases. To assess the force-velocity relationship for each arteriole, tension was released to a series of different afterloads. Each release, upon completion of the force change and SEC recoil, was associated with a shortening phase in which the rate of shortening slowed progressively with time (Figs. 2 and 3). When the logarithm of (1 - fractional shortening) was plotted against time for isotonic releases to various afterloads, the data for the first 2 s of each shortening phase were almost always well fit by a first-order exponential function (not shown).

Figure 4A shows the complete diameter changes for this series of isotonic releases (4 additional releases for this vessel are not shown for clarity). Releases to progressively lower afterloads were associated with progressively greater recoil of the SEC and progressively higher rates of initial shortening. Again, some slight variations occurred in the amount of myogenic tone regained between release protocols, leading to slight variations in the initial tension. Trials in which vessels did not regain sufficient tone to recover to within 15% of their initial wall tension were not included in the analysis; to do so might have skewed the data by combining data from vessels that had significantly different degrees of myogenic tone.


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Fig. 4.   Method of data analysis is illustrated. A: diameter changes for 5 isotonic releases (as recorded on playback of the videotape in slow motion and with corrected time scales). Note progressive increase in magnitude of SEC recoil and progressive increase in initial velocity of shortening as afterload is released to smaller fractions of control tension. Possible exceptions to the latter statement are the very similar initial velocities for releases to 0.1 and 0.3. Myogenic dilations of various magnitudes occur at time ~11 s for three of the releases. Four other releases were performed on the same vessel (data not shown for clarity). B: force-velocity plot of nonnormalized data for all 9 isotonic releases. These data were fit to find the Hill coefficients, a and b (see text for details), and the coefficients were then used to draw a hyperbolic curve through the data and to determine maximal velocity (V'max) from the y-intercept. C: force-velocity plot of same data after normalization of shortening velocity to Lo for this vessel. Lengths/s = (µm · s-1 · L<UP><SUB>o</SUB><SUP>−1</SUP></UP>) · 100.

Shortening velocities were measured from linear fits of the diameter data points over the initial 1-2 s after SEC recoil. The set of calculated shortening velocities for each vessel were then fit, using a nonlinear curve-fitting procedure, to the hyperbolic form of the Hill equation to obtain coefficients for extrapolation of the maximum shortening velocity at zero force on a standard force-velocity plot. The form of the Hill equation used was
(T+<IT>a</IT>) · (<IT>V+b</IT>)=(T<SUB>i</SUB>+<IT>a</IT>) · <IT>b</IT> (3)
where T and V are the relative afterload (tension) and velocity, respectively, and a and b are constants corresponding to the y- and x-intercepts, respectively, of a rectangular hyperbola. V'max for this vessel was determined from the y-intercept of this equation. Figure 4, B and C, shows the force-velocity plot of the data for the vessel in Fig. 4A, expressed in terms of shortening in micrometers per second (Fig. 4B) and lengths per second (Fig. 4C).

Comparison of active and passive tensions. The above procedure is commonly used to determine unloaded shortening velocity on isolated strips of muscle. A possible concern with using it to analyze isotonic shortening data from arterioles, which contain significant amounts of nonforce-generating connective tissue, would be if passive tension made a significant contribution to total wall tension under these conditions and thereby contaminated measurements of active shortening. To address this issue, we compared the range of vessel radius changes that occurred during isotonic releases with the passive tension-radius relationship obtained for each vessel at the end of the experiment, when active tone had been eliminated by calcium-free bath solution containing nitroprusside. An example of this analysis is shown in Fig. 5, where the open circles represent the passive tension-radius relationship and some of the raw isotonic release data for the same vessel are plotted as individual points.


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Fig. 5.   Tension-radius plot to show relationships among active tension, passive tension, tone and fractional tension for a representative 2A subjected to isotonic releases at P = 40 mmHg, 90 mmHg, and after norepinephrine (NE). Open circles, passive tension-radius curve; dotted line, calculated maximal active tension curve (from Eq. 2). Clusters of points are data for single isotonic releases (to different afterloads) from initial tensions associated for the three conditions; each initial release point is enclosed in an open square. Open arrows, release (vertical arrow) and shortening (horizontal arrow) phases for isotonic release after equilibration at 90 mmHg. Solid vertical lines, reference points for illustrating the relative amount of tone associated with the three conditions and also indicate maximum active tension that corresponds to the initial diameter for each condition. Ratio of Ti/Tmax (fractional tension) was used to normalize shortening data for these three trials and other data for the other arterioles as shown in Figs. 7 and 8.

As can be seen from Fig. 5, at each of the initial diameters (denoted by open squares) corresponding to the three conditions (P40, P90, and NE), the contribution of passive tension is quite low compared with the calculated total Ti of the arteriole (average = 5.5%; Table 1). This implies that for isotonic releases from this pressure, only a slight overestimation of active tension may have been made. The average data for each group are summarized in Table 1. Passive wall tension contributed only 5.5% to Ti at a pressure of 40 mmHg and even less (1.8%) at a pressure of 90 mmHg. By extrapolation, the contribution of passive tension for the NE group was intermediate between these two values, but average values for the NE group were not available because complete pressure-diameter curves were not obtained for three of four NE vessels.

Comparison of force-velocity plots for vessels with low and high myogenic tone. Both raw and normalized shortening velocities for each isotonic release protocol from each arteriole were compiled into a spreadsheet for analysis of group data. The first method of analysis is shown in Fig. 6, where the force-velocity relationships were compared for vessels equilibrated at low myogenic tone (pressure = 40 mmHg; n = 12) or high myogenic tone (pressure = 90 mmHg; n = 12). For this analysis, the data were pooled by afterload, the means were calculated, and then Hill coefficients were computed from nonlinear fits of the transformed data. There is clear separation between the data sets, as indicated by comparisons of the group data at each afterload. Shortening velocities at the three lowest afterloads, 0.3, 0.2, and 0.1, were all significantly higher in arterioles with higher initial myogenic tone (ANOVA, P < 0.05). The curves through the data sets represent the best fits of the data to the Hill equation. Determinations of V'max from the y-intercepts suggest that V'max is substantially higher for arterioles with higher myogenic tone.


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Fig. 6.   Comparison of force-velocity relationships for arterioles with low myogenic tone (filled triangles; P = 40 mmHg) and high myogenic tone (open triangles; P = 90 mmHg). For this analysis, data were grouped according to afterload, the means fit to the Hill equation, and values of V'max determined from the y-intercepts for each of the two data sets. Lengths/s = (µm · s-1 · L<UP><SUB>o</SUB><SUP>−1</SUP></UP>) · 100.

Two additional analysis methods were also used to examine this data set, as shown in Table 2. First, raw or normalized (to Lo) shortening velocities for individual vessels were fit to the Hill equation, and V'max for each vessel was estimated from the y-intercepts of the force-velocity plots. These values were then statistically analyzed to obtain an average V'max for each of the groups. Second, all of the data points for each group were fit to the Hill equation, and V'max was estimated from the y-intercept of each force-velocity plot. As shown in Table 2, the two alternative analyses confirmed that V'max was higher in vessels with higher initial myogenic tone.

                              
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Table 2.   Summary of analysis methods to determine V'max

Analysis of data after normalization to maximal isometric force. As mentioned previously, force-velocity data are typically normalized to some force index such as maximal isometric tension. To do this, each data point was normalized to maximal active tension at the respective diameter, as diagrammed in Fig. 5. For example, from the point at which isotonic releases were performed at a pressure of 90 mmHg, this arteriole had 58% initial tone (1.0-0.42), Ti = 78 dyn/cm, an estimated maximal active tension of 135 dyn/cm (from Eq. 2), and therefore a fractional tension of 0.58. The vertical open arrow in Fig. 5 indicates the release phase and the horizontal open arrow indicates the shortening phase when tension was released to 10% of its initial value. Single releases to other afterloads for the pressure at 40 mmHg and NE protocols are also shown to indicate the representative relationships among active and passive tension, tone, and fractional tension relative to the dimensional changes that occurred during the isotonic releases. It should be clear that passive tension is minimal during the isotonic releases.

When all data points for the 40- and 90-mmHg pressure data sets were normalized to maximal tension in this manner, the force-velocity curves appear as shown in Fig. 7. Nonlinear fits of the two data sets to the Hill equation yielded V'max estimates of 4.2 and 8.3 lengths/s for the 40- and 90-mmHg pressure data sets, respectively. The intersection of the 40-mmHg data set with the force axis occurred at a fractional tension of 0.22, whereas the 90-mmHg data set intersected at a fractional tension of 0.56. These values were the average Ti/Tmax values before release for the two groups, and the curve-fitting parameters (Ti in Eq 3) were adjusted to force the x-intercept at these respective values. The approximate twofold higher V'max associated with vessels at higher pressure is consistent with the raw data analyses shown in Fig. 6 and Table 2.


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Fig. 7.   Comparison of force-velocity relationships for arterioles with low myogenic tone (filled triangles; P = 40 mmHg) and high myogenic tone (open triangles; P = 90 mmHg). Shortening velocity was normalized to Lo and force was normalized to Ti/Tmax. Force intercepts were determined by the average initial Ti/Tmax values for each data set: 0.22 for P40 and 0.56 for P90. Lengths/s = (µm · s-1 · L<UP><SUB>o</SUB><SUP>−1</SUP></UP>) · 100.

Comparison of force-velocity plots for vessels with and without NE. To test whether agonist-induced activation of arteriolar smooth muscle would produce a similar shift in the force-velocity relationship, we studied a third group of vessels treated with NE at a pressure of 40 mmHg. The concentration of NE was titrated to produce an additional constriction roughly comparable to the level of myogenic tone seen at a pressure of 90 mmHg. These data, after normalization to maximal active tension, are shown in Fig. 8, along with the data set for arterioles equilibrated at the same pressure in the absence of NE. The curves represent the best fits of the two data sets to the Hill equation. Shortening velocities at almost all afterloads were significantly higher for arterioles constricted with NE, and determinations of V'max from the y-intercepts suggest that V'max was substantially higher for arterioles treated with NE. For the NE data, the average initial Ti/Tmax, and hence the force intercept, was at fractional tension equaling 0.26. 


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Fig. 8.   Comparison of force-velocity relationships for arterioles with low myogenic tone (filled triangles; P = 40 mmHg) and NE-induced tone (open triangles; P = 40 mmHg). Shortening velocity was normalized to Lo and force was normalized to Ti/Tmax. Force intercepts were determined by the average initial Ti/Tmax values for each data set: 0.22 for P40 and 0.26 for NE. Lengths/s = (µm · s-1 · L<UP><SUB>o</SUB><SUP>−1</SUP></UP>) · 100.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The results of our study constitute the first experimental evidence that increases in myogenic tone reflect an enhanced Vmax of VSM. Although previous studies of arteriolar mechanics (13, 15) and of myogenic signaling pathways (5, 25) indicate that arteriolar smooth muscle is indeed activated by pressure, Vmax is perhaps the best quantitative parameter by which to assess the degree of this activation. Vmax has not previously been measured in true arterioles. In addition to a shift in V'max with pressure, NE-induced tone was also associated with an increase in V'max; however, the characteristics of the two respective force-velocity curves were different. Myogenic tone produced roughly parallel increases in velocity and force, whereas NE produced increases in velocity at low force. Therefore, myogenic and NE-induced activation of arteriolar smooth muscle are associated with different mechanical states of arteriolar smooth muscle, which is likely a reflection of different underlying signaling pathways activated by the two stimuli.

Consideration of technical issues. Our conclusions are subject to consideration of several technical issues related to the unique way in which these experiments were performed. One issue is the accuracy of diameter measurements. Because the diameter changes that occur during isotonic releases are only a few microns in magnitude, we chose an objective/condenser system based on the compromise between optical quality and working distance. Given the objective, condenser, and wavelength of light used in our system, the theoretical resolution of this system is 0.38 µm (see Ref. 12, p. 115). Of course, light scattering above and below the focal plane raises this value, an effect that can be rather large when visualizing arterioles in intact tissue (12). However, the use of an isolated arteriole, in the absence of parenchymal tissue and adventitia, minimizes degradation of the image due to light scattering. We estimate that diameter changes of 0.5 µm could clearly be resolved under the conditions of our experiments (4). Moreover, for determination of V'max, the most critical measurements of shortening velocity are those required for isotonic releases to the lowest afterloads, e.g., 0.1 and 0.2, and it is at these afterloads that the absolute magnitude of shortening is greatest, usually well over 0.5 µm and sometimes over 2 µm (Figs. 2-4). Therefore, we have the most confidence in accurate diameter measurements for the most critical protocols.

One problem with estimating V'max is that maximal isometric tension should, ideally, have been determined for each 2A at the end of each experiment to normalize force; however, this was simply not feasible given the complexity of our protocols. Davis and Gore (4) have previously discussed the difficulties involved in determining maximal isometric tension in small arterioles, and their study is the only one of its kind. Given the difference in size between the "2As" (Lo = 58 µm) studied by Davis and Gore (4) and the 2As used for the present study (Lo = 42 µm), our estimate of maximal active tension may be high. Likewise, errors in our estimate of 0.2 L/Lo as the zero active tension intercept on the maximal tension-length curve would alter the normalization of all of the force data in Figs. 7 and 8. However, inaccuracies in our estimates of both of parameters would simply lead to roughly parallel shifts in normalized force values for all three groups (P40, P90, and NE) along the force axis, and thus would not fundamentally alter our conclusions about differences between the groups.

Another potential concern with our analysis relates to possible differences in the initial length of VSM in the two groups (pressure = 40 vs. 90 mmHg). Initial length is an important determinant of Vmax, with Vmax being highest at the optimal length of the muscle, regardless of the level of muscle activation at which the force-velocity relationship is determined (19, 23). For example, in small arteries, Vmax increased by threefold with length increases from 0.4 to 0.7 of maximal length (1). It is obvious from Fig. 5 and Table 1 that the additional myogenic tone associated with equilibration of a 2A at 90 mmHg (compared with 40 mmHg) dictates that the two groups of vessels are at different initial lengths. Thus the larger values of V'max for the group with higher myogenic tone could be explained if, for example, the length was closer to optimal at that diameter (see Fig. 5). However, from the 2A length-tension relationship (4), it is clear that optimal length is about 20% less than the maximal length (4), so that the optimal length for the vessel in Fig. 5 is actually to the right of the 40-mmHg pressure data set. Therefore, both groups of vessels started at initial lengths less than optimal, with the high-tone group being farther away from optimal than the low-tone group. Thus differences in V'max between the two groups of vessels were, if anything, underestimated due to the constraints of our experiments.

Comparison with previous measurements of Vmax. How do our estimates of V'max compare with measurements from other smooth muscle? Comparisons are necessarily limited by the fact that we measured V'max of partially activated arteriolar smooth muscle, whereas most other studies have measured Vmax of maximally activated smooth muscle. We obtain V'max values between 0.04 and 0.08 lengths/s for arterioles with low and high myogenic tone, respectively (Table 2). Estimates of Vmax for other smooth muscles are 0.61 lengths/s in the Bufo stomach (26), 0.51-0.53 lengths/s in the rat portal vein (14, 21), 0.12 lengths/s in the hog carotid (11), and 0.013 lengths/s in the rat caudal vein (20). With the exception of the latter study, our estimates of V'max for arterioles are, predictably, at the low end of the reported range. However, in the most directly relevant study, Boels et al. (1) reported a Vmax of 0.041 lengths/s for coronary "microarteries" (140 µm ID), which is reasonably close to ours (Table 2). However, the unloaded shortening velocity for maximally activated 2As remains to be determined.

Comparison of effects of myogenic- versus agonist-induced tone. Our results show that high levels of myogenic tone and NE produce comparable increases in V'max. However, pressure-induced tone (Fig. 7) is associated with smaller increases in velocity (4.2 to 8.3 lengths/s; ~100% increase) than force (0.22 to 0.56 Ti/Tmax; ~250% increase), whereas NE-induced tone (Fig. 8) is associated with larger increases in velocity (4.2 to 7.5 lengths/s; ~80% increase) than force (0.22 to 0.26 Ti/Tmax; ~20% increase). The differences likely reflect underlying differences in the mechanical states produced by pressure and NE. The classical interpretation of the force-velocity relationship is that an increase in isometric force represents an increase in the number of active cross bridges, whereas an increase in Vmax represents an increase in the cycling rate of active cross bridges (19). Thus the differences in the force-velocity curves produced by pressure and NE lead to the conclusion that myogenic tone is associated with an increase in both the number and cycling rate of active cross bridges.


    ACKNOWLEDGEMENTS

The authors are indebted to Dr. Anthony Goodman for design and construction of the servo amplifier, power amplifiers, carrier amplifier, and data multiplexer required to perform these measurements. Dr. Robert Gore provided the initial inspiration to attempt these experiments. Discussions with Drs. Glenn Bohlen and Richard Meiss were very much appreciated. Dr. David DeFily provided key suggestions for development of LabView algorithms. Editorial suggestions by Dr. Michael Hill were much appreciated. We particularly thank both reviewers of our initial manuscript for extremely valuable insights regarding the data analysis.


    FOOTNOTES

Funding by National Heart, Lung, and Blood Institute Grant HL-46502 and the Texas Heart Association is acknowledged.

Address for reprint requests and other correspondence: M. J. Davis, Dept. of Medical Physiology, Rm. 346 Reynolds Medical Bldg., Texas A&M Univ., College Station, TX 77843 (E-mail: mjd{at}tamu.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.

Received 30 May 2001; accepted in final form 11 September 2001.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

1.   Boels, PJ, Claes VA, and Brutsaert DL. Mechanics of K+-induced isotonic and isometric contractions in isolated canine coronary microarteries. Am J Physiol Cell Physiol 258: C512-C523, 1990[Abstract/Free Full Text].

2.   Brown, IE, Cheng EJ, and Loeb GE. Measured and modeled properties of mammalian skeletal muscle. II. The effects of stimulus frequency on force-length and force-velocity relationships. J Muscle Res Cell Motil 20: 627-643, 1999[ISI][Medline].

3.   Davis, MJ. Myogenic response gradient in an arteriolar network. Am J Physiol Heart Circ Physiol 264: H2168-H2179, 1993[Abstract/Free Full Text].

4.   Davis, MJ, and Gore RW. Length-tension relationship of vascular smooth muscle in single arterioles. Am J Physiol Heart Circ Physiol 256: H630-H640, 1989[Abstract/Free Full Text].

5.   Davis, MJ, and Hill MA. Signaling mechanisms underlying the vascular myogenic response. Physiol Rev 79: 387-423, 1999[Abstract/Free Full Text].

6.   Davis, MJ, Joyner WL, and Gilmore JP. Microvascular pressure distribution and responses of pulmonary allografts and cheek pouch arterioles in the hamster to oxygen. Circ Res 49: 125-132, 1981[Abstract/Free Full Text].

7.   Davis, MJ, Kuo L, Chilian WM, and Muller JM. Isolated, perfused microvessels. In: Clinically Applied Microcirculation Research, edited by Barker JH, Anderson GL, and Menger MD.. Boca Raton, FL: CRC, 1995, p. 435-456.

8.   Davis, MJ, and Meininger GA. The myogenic response in microvascular networks. In: Mechanotransduction by the Vascular Wall, edited by Rubanyi G.. Kisco, NY: Futura, 1993, p. 37-60.

9.   Davis, MJ, and Sikes PJ. A rate-sensitive component to the myogenic response is absent from bat wing arterioles. Am J Physiol Heart Circ Physiol 256: H32-H40, 1989[Abstract/Free Full Text].

10.   Davis, MJ, and Sikes PJ. Myogenic response of isolated arterioles: test for a rate-sensitive mechanism. Am J Physiol Heart Circ Physiol 259: H1890-H1900, 1990[Abstract/Free Full Text].

11.   Herlihy, JT, and Murphy RA. Force-velocity and series elastic characteristics of smooth muscle from the hog carotid artery. Circ Res 34: 461-466, 1974[Abstract/Free Full Text].

12.   Inoué, S. Video Microscopy. New York: Plenum, 1986.

13.   Jackson, PA, and Duling BR. Myogenic response and wall mechanics of arterioles. Am J Physiol Heart Circ Physiol 257: H1147-H1155, 1989[Abstract/Free Full Text].

14.   Johansson, B, Hellstrand P, and Uvelius B. Responses of smooth muscle to quick load change studied at high time resolution. Blood Vessels 15: 65-82, 1978[ISI][Medline].

15.   Johnson, PC. Autoregulatory responses of cat mesenteric arterioles measured in vivo. Circ Res 22: 199-212, 1968[Abstract/Free Full Text].

16.   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, chapt. 15, p. 409-442.

17.   Kirton, CA, and Loutzenhiser R. Alterations in basal protein kinase C activity modulate renal afferent arteriolar myogenic reactivity. Am J Physiol Heart Circ Physiol 275: H467-H475, 1998[Abstract/Free Full Text].

18.   Meininger, GA, Mack CA, Fehr KL, and Bohlen HG. Myogenic vasoregulation overrides local metabolic control in resting rat skeletal muscle. Circ Res 60: 861-870, 1987[Abstract/Free Full Text].

19.   Murphy, RA. Mechanics of vascular smooth muscle. In: Handbook of Physiology. The Cardiovascular System. Vascular Smooth Muscle. Bethesda, MD: Am. Physiol. Soc, 1980, sect. 2, vol. II, chapt. 13, p. 325-351.

20.   Packer, CS, and Stephens NL. Force-velocity relationships in hypertensive arterial smooth muscle. Can J Physiol Pharmacol 63: 669-674, 1985[ISI][Medline].

21.   Peiper, U, Laven R, and Ehl M. Force velocity relationships in vascular smooth muscle. Pflügers Arch 356: 33-45, 1975[ISI][Medline].

22.   Rivers, RJ. Remote effects of pressure changes in arterioles. Am J Physiol Heart Circ Physiol 268: H1379-H1382, 1995[Abstract/Free Full Text].

23.   Simmons, RM, and Jewell BR. Mechanics and models of muscular contraction. Recent Adv Physiol 31: 87-147, 1974.

24.   Sun, D, Kaley G, and Koller A. Characteristics and origin of myogenic response in isolated gracilis muscle arterioles. Am J Physiol Heart Circ Physiol 266: H1177-H1183, 1994[Abstract/Free Full Text].

25.   VanBavel, E, Wesselman JPM, and Spaan JAE Myogenic activation and calcium sensitivity of cannulated rat mesenteric small arteries. Circ Res 82: 210-220, 1998[Abstract/Free Full Text].

26.   Warshaw, DM. Force:velocity relationship in single isolated toad stomach smooth muscle cells. J Gen Physiol 89: 771-789, 1987[Abstract/Free Full Text].


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