The step response: a method to characterize mechanisms of renal blood flow autor - 《American Journal of Physiology》美国生理学杂志干细胞之家



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发表于 2009-4-21 13:45 |只看该作者 |倒序浏览 |打印

作者：T. Wronski, E. Seeliger, P. B. Persson, C. Forner, C. Fichtner, J. Scheller,  B. Flemming作者单位：Johannes Müller Institut für Physiologie,Humboldt-Universität (Charité), 10117 Berlin, Germany " b7 F. `8 E& Y% b$ C! @


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      【摘要】$ _3 h3 P6 N2 o8 k
   Response of renal vasculature to changes in renal perfusion pressure (RPP)involves mechanisms with different frequency characteristics. Autoregulationof renal blood flow (RBF) is mediated by the rapid myogenic response, by theslower tubuloglomerular feedback (TGF) mechanism, and, possibly, by an evenslower third mechanism. To evaluate the individual contribution of thesemechanisms to RBF autoregulation, we analyzed the response of RBF to a stepincrease in RPP. In anesthetized rats, the suprarenal aorta was occluded for30 s, and then the occlusion was released to induce a step increase in RPP.Three dampened oscillations were observed; their oscillation periods ranged from 9.5 to 13 s, from 34.2 to 38.6 s, and from 100.5 to 132.2 s,respectively. The two faster oscillations correspond with previously reporteddata on the myogenic mechanism and the TGF. In accordance, after furosemide,the amplitude of the intermediate oscillation was significantly reduced.Inhibition of nitric oxide synthesis by N -nitro- L -arginine methyl ester significantly increased the amplitude of the 10-s oscillation. It is concludedthat the parameters of the dampened oscillations induced by the step increasein RPP reflect properties of autoregulatory mechanisms. The oscillation periodcharacterizes the individual mechanism, the dampening is a measure for thestability of the regulation, and the square of the amplitudes characterizes the power of the respective mechanism. In addition to the myogenic responseand the TGF, a third rather slow mechanism of RBF autoregulation exists. ; d2 m4 w' _! M# A/ q/ r5 C7 z( f( v
      【关键词】 myogenic reaction tubuloglomerular feedback furosemide N nitro L arginine methyl ester
   VARIOUS STUDIES ARE AIMED at determining the pressure range andthe efficiency of renal blood flow (RBF) autoregulation under variousconditions ( 3, 7, 25 ). Typically, in these studies, renal perfusion pressure (RPP) is changed according to astaircase-shaped or a rampshaped function to obtain pressure-flow relationships ( 7, 8, 22 ). Although thisexperimental approach allows us to determine the autoregulatory pressure rangeand to compare the autoregulatory efficiency under different conditions, itdoes not allow us to determine the individual contribution of the underlyingmechanisms to the overall response.
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Our understanding of the relative importance of the myogenic response andthe tubuloglomerular feedback (TGF) mechanism stems mainly from studies inwhich vascular diameters of isolated vessels, isolated nephrons, orhydronephrotic kidneys were measured( 1, 26 ). In these studies, stepchanges in perfusion pressure were used as a stimulus, and the time constantof the vascular response was used to assess the contribution of themechanisms. This was also done in preparations, which lack the TGF[hydronephrotic kidney, isolated nephron without distal tubule( 4 )].3 Z0 a$ T$ S8 f4 ~9 t
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Other experimental approaches, which were applied in whole animal preparations, employed simultaneous recordings of spontaneous variations inarterial pressure and RBF for several hours ( 2, 5, 6, 15 ) or broadband forcings( 9 ), followed by the calculation of transfer functions. In these studies, extreme values of thegain of transfer function were observed at distinct frequencies, i.e., themyogenic response was found to operate at frequencies of 0.1 to 0.2 Hz and theTGF at frequencies of 0.03 to 0.05 Hz. This approach, however, is very timeconsuming, and, in addition, it requires the long-term stability of the biological system, a condition that is hard to fulfil in vivo.* T* m) G; N! c8 @1 @2 }6 j5 E* o

Here, we present a new approach to study the mechanisms contributing to RBFautoregulation in whole animal preparations. The frequency response of RBF toa step increase of RPP, as induced by release of a 30-s occlusion of thesuprarenal aorta, is analyzed. This allows to calculate the contribution ofoscillations of different frequencies and thus of different autoregulatorymechanisms. As with the transfer-function method, this procedure does not allow determination of the autoregulatory pressure range and theautoregulatory efficiency.- P; |9 y& |0 }$ @$ \$ _$ j

The mathematical analysis of the step response is based on procedures widely used in technical control theory. The application of control theory tophysiological systems has recently been described by Rosengarten et al.( 24 ). If mathematical modelsof second order are sufficient to represent the experimentally obtained timecourse, the calculation yields two time constants (frequency and dampening),which allow an unequivocal interpretation ( 24 ). If models of higherorder are required to represent the time course (i.e., the time course is morecomplicated), then the number of time constants corresponds with the order of the model. Again, these time constants unequivocally characterize the controlsystem ( 21 ), but a directphysiological interpretation of these time constants is impossible.) @: ^* \8 F" X/ a9 [% f/ F
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To validate the new method, we tested whether it is able to reproducewell-known physiological results originally obtained by use of differentmethodical approaches. To this end, we used established experimentalinterventions to alter autoregulatory mechanisms. The TGF was abolished byfurosemide ( 4, 12, 20 ). The myogenic response wasenhanced by inhibition of nitric oxide synthesis( 10, 13, 16, 25, 27, 28 ).8 Z" I+ @: {5 T0 l4 {  p( ^

MATERIALS AND METHODS# J/ {7 p# N) o! G
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The experiments were performed on 18 male, adult, 3- to 4-mo-old Wistarrats and 10 male Sprague-Dawley rats of the same age (Charles River). Bodyweight ranged from 300 to 400 g. The experimental procedures used to verifythe method [administration of furosemide and N -nitro- L -arginine methyl ester( L -NAME), respectively] were part of more extensive protocolsperformed in separate series of experiments in Wistar and Sprague-Dawley rats,respectively. The rats received a standard rat diet. One day before thepreparatory surgery, the animals were deprived of food but allowed free accessto tap water. The investigation conformed with the Guide for the Care andUse of Laboratory Animals published by the National Institutes of Health(NIH) (NIH Publication No. 85-23, revised 1996).
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Surgical procedures and measurements. The rats were anesthetized by an intraperitoneal injection of urethane solution (2% in water; 6 ml/kgbody wt; Sigma, Steinheim, Germany). During the surgery and experiment, therats were positioned on a heated table (39°C). A tracheal cannula wasinserted, and the rats breathed spontaneously. A catheter was advanced into a jugular vein, which was later on used to administer furosemide or L -NAME. Then, the abdominal cavity was opened by a midventral incision. An inflatable cuff was placed around the suprarenal aorta just belowthe junction of the superior mesenteric artery. A catheter was inserted intothe infrarenal aorta and then connected to a pressure transducer and anamplifier (Gould, Valley View, OH). Finally, an ultrasound transit time flow probe (Type 1RB, Transonic Systems, Ithaca, NY) was positioned around the leftrenal artery by use of a micromanipulator. During the surgery and experiment,the abdominal cavity was continuously flushed with isotonic salinethermostatized at 37°C. RPP (infrarenal aortic pressure) and RBF (leftkidney) were recorded continuously. Following analog-to-digital conversion, the data were stored on-line with a sampling rate of 100 Hz.; }5 b7 l; G( i) I

Experimental protocols. Each experiment started with astabilization period of 10 min, after which baseline values of RPP and RBF were obtained.
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The first set of experiments was performed in Wistar rats ( n =18). After baseline recordings, the aortic occluder cuff was rapidly filledsuch that RPP and RBF took on values of approximately zero. The occlusion wasmaintained for 30 s. Then, the occlusion was rapidly released, i.e., a stepincrease of RPP was induced to obtain the time course of RBF restoration (stepresponse). Then, L -NAME was intravenously administered (Sigma;bolus injection of 1 mg followed by continuous infusion ofa1mM solution), and,after a period of 15 min, the procedure was repeated.

The second set of experiments was performed in Sprague-Dawley rats( n = 10). After baseline recordings, the step-response procedure wasperformed as described above. Then, furosemide was intravenously administered(Lasix, Hoechst, Germany; bolus injection of 20 mg in 2 ml), and, after aperiod of 15 min, the step-response procedure was repeated.. r: q1 w+ d0 l" [$ r/ c/ ~
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Data analysis. The original data were averaged by sliding average with a window size of 1 s. Relative values of RPP and RBF were obtained byrelating the absolute data to the absolute baseline values measuredimmediately before the start of the protocol. Relative conductance values werecalculated by dividing the relative RBF values by the respective relative RPPvalues.: D* x) ~4 \& a( q4 ^1 B, i$ V

Analysis of the step response and theoretical background. The rapid release of the aortic occluder results in an immediate increase in RPPand, in turn, in an increase in RBF. Thus, in terms of control theory, thestep increase in RPP constitutes the input signal, and RBF the output signal,of the physiological system. According to the literature( 12 ), RBF autoregulation ismediated by the rapid myogenic response, by the slower TGF, and, possibly, byan even slower third mechanism. Thus we presume that RBF autoregulationconsists of three parallel subsystems. Each of the subsystems is exposed tothe same input signal, and the individual output signals of the subsystemsoverlap one another, thus a lumped overall output signal is formed.
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The original RBF recordings of the step response revealed that the timecourse of the RBF increase roughly followed an exponential function( y = l - e - x ),which gradually approaches a steady state at RBF values comparable topreocclusion values. In most cases, visible oscillations were superimposed onthis exponential time course. In accordance with technical systems, we thuspresumed that each autoregulatory mechanism is best described by a lag elementof second order [low-pass element (PT 2 )]( 21 ). The step response of asingle PT 2 element is described by

( 1 )

where u a is output signal, u e is input signal, k isamplitude, t is time, is angular frequency, isdampening, and is phase angle.

At time 0, this function yields a u a value of zero,and, with increasing time, u a increases exponentially to approach asteady state. The values of and, respectively, determine thetime course of the transient. If, then oscillationsoverlay the exponential time course; if, then thetransient is aperiodic.- |0 m7 G) p- s5 c/ I* R3 k# H
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In case of three parallel PT 2 elements, the overall output signal is the sum of the three individual output signals  s3 f# \0 ~5 R) [& I  h+ L
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u a and u e are measured variables (in our case, RBFand RPP). The aim of the mathematical procedure is to determine the unknown variables, i.e., phase angles i, angular frequencies i, dampenings i, andamplitudes k i by means of a least-square fitting(Levenberg-Marquardt algorithm).

As three oscillations were presumed to be involved, 12 unknown parametershad to be determined according to equation 2. These 12 parameterswere not determined simultaneously but by three subsequent fitting procedures,each yielding the four unknown parameters of one of the involved oscillations,as described by Mautz ( 19 ). Figure 1 depicts the threesubsequent fitting procedures as applied to a typical individual step response following the administration of L -NAME.' k% a" d+ K0 H2 H

Fig. 1. Mathematical procedure to analyze the renal blood flow (RBF) step responseas illustrated by use of an original data example. For details, please referto MATERIALS AND METHODS.
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It is well known that the adequate choice of starting values is pivotal forthe success of any iterative fitting procedure. Because the step responsepresumably contains oscillations of different frequencies, the fittingprocedure can yield different results dependent on the starting values chosenfor the angular frequency and the dampening. Therefore, withineach of the three subsequent fitting procedures, the fitting was done 18 timesusing six different starting values for (0.96, 0.48, 0.24, 0.12, 0.06,and 0.03 s) and, for each, three different values of the dampening,i.e., = /10 (mild dampening), = /2 (strongdampening), and = 2 (aperiodic). These ranges of startingvalues of the frequency were chosen in accordance with the literature on theindividual mechanisms of RBF autoregulation, which are reported to haveoscillation periods of 10, 30, and 100 s, respectively. Of course, the valuesfor and listed above were only used as starting points to runthe respective fitting, yet the starting values, as all other parameters, were free to change during the following iterations. From the 18 runs, themathematical function that fit best to the original RBF step response wastaken as the result of the respective fitting procedure.
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In Fig. 1 A, theresults of the first fitting procedure are depicted alongside the originalstep response of flow (thin line). In this individual step response, anoscillation with a high frequency dominates. By the first fitting procedure, this dampened oscillation (see inset ) was extracted according to equation 1. The four parameters 1, 1, 1, and k 1 were used toreconstruct the time course (bold line). This first approximation yielded r 2 = 0.830.6 ?' o6 i! U/ q( `: P

In the second fitting procedure, the remaining difference between theoriginal step response of flow (thin line in Fig. 1 A ) and the firstapproximation (bold line in Fig.1 A ), i.e., the residuum, was used to extract a secondoscillation according to equation 1. This dampened oscillation isdepicted in Fig. 1 B, inset. The eight parameters 1, 1, 1, k 1 (from the first fitting procedure), and 2, 2, 2, k 2 (from the second fitting procedure) were used to reconstruct a new time course(bold line in Fig.1 B ). The inclusion of the second oscillation improved theapproximation considerably ( r 2 = 0.953). As shown in Fig. 1 C, the thirdfitting procedure, which was done in analogy to the second, yielded a thirddampened oscillation (see inset ). The time course was reconstructedfrom the 12 parameters calculated in all three fitting procedures, i.e., thethird approximation (bold line) fits very well with the original step response ( r 2 = 0.978).! ?# ]8 b! a8 J% J) Z+ ~1 i: n/ J
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As a result of the three subsequent fitting procedures, three separateeigenoscillations are detected, each of which is characterized by certainvalues of angular frequency, amplitude, dampening, and phase angle. By use ofthe parameter angular frequency (or oscillation period, respectively), theobserved oscillation can be ascribed to one of the known autoregulatorymechanisms, as long as the observed frequency closely corresponds with the frequency or oscillation period values reported for the individual mechanismin the literature. By use of the parameter "square of the individualamplitudes," the distribution of energy among the autoregulatorymechanisms is characterized." q7 \$ @( L% K- e
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L -NAME administration resulted in a marked increase of arterial blood pressure. Higher preocclusion RPP values result in a greater height ofthe RPP step, which would increase the absolute amplitude of RBF oscillations.Therefore, the parameter square of amplitudes was normalized, i.e., it wasdivided by the individual preocclusion RPP (p 0 ). In addition, therelative contributions of the individual mechanisms were determined. Theparameter dampening characterizes the stability of regulation, i.e., thelarger the absolute amount of the negative dampening constant, the faster thesystem approaches a steady state. The parameter phase angle was left unconsidered in this study." z5 j/ y+ J* W* m. R, s
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Statistical analysis. Statistical comparisons were made by Kruskall-Wallis test for unpaired data. The probability level was set at P depicted as means± SE.

RESULTS

Resting values averaged 106 ± 1 mmHg for arterial pressure and 5.9± 0.1 ml/min for RBF in Wistar rats and 91 ± 3 mmHg and 6.2± 0.8 ml/min, respectively, in Sprague-Dawley rats. To verify the newmethodical approach, established procedures to alter autoregulatory mechanismswere used, i.e., the step response was studied with and without L -NAME and with and without furosemide. Administration of L -NAME, as expected, decreased the resting value (before startingthe RPP reduction) of RBF from 5.9 ± 0.1 to 2.4 ± 0.3 ml/min andincreased arterial pressure from 106 ± 1to 154 ± 1 mmHg./ |) B% D/ M1 s: Q8 d- O

In Fig. 2 A, therelative changes in RBF as induced by the step increase in RPP following a30-s occlusion of the suprarenal aorta are depicted. L -NAMEamplified the initial RBF oscillation markedly. For quantitative comparisonbetween control conditions and L -NAME, the square values of thecalculated oscillatory amplitudes (normalized by preocclusion RPP,p 0 ) are depicted as a function of their respective oscillationperiods (in classes with a class width of 4 s). Under control conditions( Fig. 2 B ), oscillationperiods between 5 and 20 s are frequently found. There is a secondaccumulation at oscillation periods between 20 and 60 s, whereas several smalloscillations are widely scattered over the range beyond 60 s. After L -NAME ( Fig. 2 C ), the square amplitudes of fastest oscillationsincreased by about one order of magnitude.
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Fig. 2. A : step response of relative RBF values during control conditionsand during N -nitro- L -arginine methylester ( L -NAME) administration. B and C : average(means ± SE) of normalized (division by preocclusion pressure;p 0 ) square amplitudes of eigenoscillations vs. oscillationperiod.

The three ranges of oscillation periods observed, i.e., 5-20, 20-60, and 60-200 s, were each summarized to three classes ofoscillations, named OP1, OP2, and OP3. As shown by Fig. 3 A, the averageperiod durations of these three classes of oscillations were unaffected by L -NAME. Figure3 B depicts the respective dampening coefficients. L -NAME did not alter the dampening significantly. In Fig. 3 C, the squareamplitudes (normalized by p 0 ) of the classes are depicted on alogarithmic scale. L -NAME dramatically increased the amplitude ofthe fastest oscillation (OP1), whereas it did not significantly alter the amplitudes of the slower oscillations (OP2 and OP3). The square value of anoscillatory amplitude is a proportional measurement of the oscillations'energy content. To evaluate the relative contribution of the individualoscillations to the overall response, the portion of the individualoscillations' energy content to the overall energy content was calculated. Tothis end, the square amplitudes of the individual classes of oscillation wererelated to the sum of square amplitudes of all classes ( Fig. 3 D ). Therelative contribution (or power) of the individual oscillations is markedlychanged by L -NAME: the relative power of the fastest oscillation(OP1) increased to reach almost 100%.
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Fig. 3. Average values (means ± SE) of oscillation period (OP; A ),absolute amount of dampening ( B ), normalized square amplitudes( C ), and relative contribution of the individual eigenoscillation'senergy content to the sum of the energy content ( D ) during controlconditions and during L 60 s. *Significant difference ( P  D) f1 C! f9 a- Z. J
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Figure 4 summarizes theeffects of furosemide on the step response. Furosemide did not significantlychange the absolute resting values of RBF and arterial pressure. With regardto the RBF step response ( Fig.4 A ), differences between control conditions andfurosemide appear rather small. However, depicting the square amplitudes(normalized by p 0 ) as a function of oscillation period( Fig. 4, B and C ) reveals a marked difference. After furosemide,oscillations in the range between 20 and 60 s are diminished or almostcompletely abolished.
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Fig. 4. A : step response of relative RBF values during control conditionsand during furosemide administration. B and C : average(means ± SE) of normalized square amplitudes of eigenoscillations vs.oscillation period.; J7 @/ B' E3 R  E
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In accordance, the square amplitude( Fig. 5 C ) and therelative contribution or power ( Fig.5 D ) of the medium frequency oscillations (OP2) aresignificantly reduced after furosemide compared with control conditions. Theaverage period durations ( Fig.5 A ) and the dampening( Fig. 5 B ) were notsignificantly altered.

Fig. 5. Average values (means ± SE) of oscillation period ( A ),absolute amount of dampening ( B ), normalized square amplitudes( C ), and relative contribution of the individual eigenoscillation'senergy content to the sum of the energy content ( D ) during controlconditions and during furosemide. *Significant difference ( P

DISCUSSION$ d& |1 v& x( K2 y* d' U  V
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In this study, we present a new experimental approach to elucidate theindividual contribution of autoregulatory mechanisms to the overall responsein whole animal preparations. With the use of established interventions toalter autoregulatory mechanisms to verify the new method, we could corroborateearlier results obtained by different methodical approaches.
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In Fig. 1 A, thestep increase in RPP that was used as input signal is depicted alongside thestep response of RBF, i.e., the output signal. Although the output signal RBFcontains marked oscillation, the input signal RPP does not. Thus possible oscillations in RPP are excluded as a reason behind the observed RBFoscillations. Rather, these RBF oscillations reflect eigenoscillations ofintrarenal systems capable of oscillating, which are triggered by the stepchange of the input signal RPP.; o) {: m  U0 n2 V
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Theoretically, dampened oscillations that superimpose an exponential stepresponse could also occur in passive elastic systems, particularly, if themass inertia of blood in conjunction with the elastic properties of thevasculature plays a significant role. However, the finding that the observedoscillations are significantly altered, when autoregulatory mechanisms arealtered, strongly supports the assumption that these oscillations are broughtabout by active regulation. Administration of L -NAME andfurosemide, respectively, i.e., experimental interventions that alterindividual autoregulatory mechanisms, resulted in significant changes of theamplitude of distinct oscillations, i.e., oscillations within a certain rangeof period duration.2 H% A! k& v" C/ t/ k

The average oscillation periods in the classes OP1 and OP2 (see Table 1 ) correspondquantitatively with the time constants of the myogenic mechanism and the TGF,respectively, as reported in the literature( 2, 5, 6, 9, 18 ). Furthermore, Just et al.( 11 - 14 )recently observed that renal vascular resistance increases very slowlyfollowing a 60-s incomplete aortic occlusion. The authors postulated that athird mechanism contributes to RBF autoregulation. This mechanism's timeconstant was 100 s. The time constant of the slow oscillations (OP3)observed in our study come close to this time constant. One may speculate thatthese slow oscillations represent an intrarenal mechanism related to metabolicchanges, i.e., the accumulation of metabolites brought about by the ischemiaassociated with aortic occlusion could impinge on the vasculature.
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Table 1. OPs of eigenoscillations during control conditions, during L -NAME administration, and during furosemideadministration1 c0 K: Y" X/ O/ A) w% Q% x

In this context, it should be noted that the duration and degree of theprior occlusion could influence the RBF step response. Our experimentalprotocol was based on a study by Pflueger et al.( 23 ), who used a 30-s completeaortic occlusion. Given the usual duration of (warm) kidney ischemia duringtransplantation surgery, it seems unlikely that a 30-s ischemia would result in cellular damage, which would compromise autoregulatory mechanisms. However,even within this short period, some metabolites would be accumulated that mayinfluence the vascular response to the pressure step. In line with thisnotion, Just et al. ( 12 ) reported that the step response following a 60-s complete occlusion differedfrom that observed after reducing RPP to 50 mmHg only.
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Because the calculated oscillation periods correspond closely to the timeconstants of the autoregulatory mechanisms as reported in the literature, theassumption seems justified that these oscillations reflect theeigenoscillations of the autoregulatory mechanisms. Comparison of the stepresponse between control conditions and L -NAME reveals thatinhibition of nitric oxide (NO) synthesis increased the amplitude of thefastest oscillation (OP1) markedly ( Fig.2 ). The average oscillation period (9.5 ± 1.2 s duringcontrol conditions; 11.5 ± 1.1 s during L -NAME) and thedampening were unchanged.

It is generally accepted that the rapid (stepwise) increase in RPP asexerted by release of the aortic occluder induces a myogenic response, i.e.,the vessels contract. Under control conditions, this is counteracted by thedilating effect of NO. Accordingly, the myogenic response becomes morepronounced following inhibition of NO synthesis, and the relative contribution of the myogenic mechanism to the overall reaction increases. This is in linewith several recent reports on the effect of NO on the myogenic mechanism( 10, 13, 16, 17, 25, 27, 28 ).5 v; D* x, a9 [: P6 v0 d
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Furosemide is well known to abolish TGF, beside its other renal effects.This has been observed, among others, in isolated nephron preparations( 4, 20 ) and recently confirmed byJust et al. ( 12 ), who analyzedthe time course of renovascular resistance changes following an incomplete60-s aortic occlusion. Comparison of the step response between controlconditions and furosemide ( Fig.2 ) reveals a marked reduction of oscillatory amplitudes within therange of oscillation periods from 20 to 60 s following furosemide. Therelative contribution of these oscillations to the step response is strikinglydiminished. We conclude that the mechanism responsible for theeigenoscillations in OP2, i.e., the TGF, is almost completely abolished. Thisresult clearly demonstrates that this new method reliably describes thealteration of autoregulatory mechanisms.

Taken together, the oscillation period allows us to ascribe the individualeigenoscillation to one of the autoregulatory mechanisms, i.e., myogenicresponse, TGF, and a third mechanism possibly related to metabolisms.Futhermore, the distribution of the portions of energy contents among theindividual eigenoscillations, as measured by the square values of amplitudes,allows the estimation of the relative contribution of these individual mechanisms to the overall autoregulatory response. The dampening, which wouldcharacterize the stability of regulation, was not significantly changed by theexperimental interventions used in this study.: z( p: P- i4 Y6 G. }- w

The present study did not aim at new physiological insights but at amethodical progress that seems warranted with regard to further physiologicalanalysis of RBF autoregulatory mechanisms, as mentioned previously. Moreover,the simple manipulation to occlude a vessel and to analyze the step responseinduced by release of the occlusion in terms of eigenoscillations should easily be applicable to other vascular beds as well.  _, u( V& E% R1 G" ^2 _
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