Continuous Determination of Beat-to-Beat Stroke Volume from Aortic Pressure Pulses in the Dog

Transcription

1 15 Contnuous Determnaton of Beat-to-Beat Stroke Volume from Aortc Pressure Pulses n the Dog MAURICE J. BOURGEOIS, M.D., BARRY K. GILBERT, PH.D., GOETZ VON BERNUTH, M.D., AND EARL H. WOOD, M.D., PH.D. SUMMARY Present methods for measurement of stroke volume from de aortc pressure pulse are not sutable for beat-to-beat determnatons durng non-steady state condtons because these methods assume that each systolc ejecton s equal to the perpheral runoff durng the same beat We bare tested a new method whch allows determnaton of an aortc pressure-volume converson factor over a wde range of pressures durng transent changes n stroke volume and nfusons of vasoactve drugs n 6 dogs wth chroncally mplanted aortc electromagnetc flowmeters. Each aortc dastolc pressure decay s approxmated by an exponental the tme constant of whch s used to calculate the pressure loss durng systole due to blood flow nto the perphery. The total ncrement n aortc pressure due to systolc ejecton, f there were no flow from the aorta durng systole, then s calculated. The total systolc ncrement (AP 3V ) s assumed to descrbe the pressure-volume characterstcs durng systole and s related to stroke volume by a constant multpler that s derved from the ndcator-dluton measurements of cardac output. The values for beat-to-beat varatons that were determned by use of the aortc electromagnetc flowmeter and by ths aortc pressure pulse method were found to be wthn the range of measurement errors of stroke volume determned from ndvdual aortc electromagnetc flow pulses. A FUNDAMENTAL tenet of most methods for estmaton of stroke volume from aortc pressure pulses s that the left ventrcular output nto the arteral tree durng systole s equal quanttatvely to the blood flow nto the perphery durng the same cardac cycle. 1 Ths s equvalent to the assumpton that at end-dastole the pressure falls to the same value as that observed at the begnnng of the pror systole. Although such behavor may be observed durng steady state condtons, t s unlkely durng transent unsteady state condtons and results n a decrease n the accuracy of beat-by-beat calculatons of stroke volume by these methods. 2 It generally s agreed that the ncrease n aortc pressure durng the systolc ejecton phase of the cardac cycle s determned by (1) the stroke volume of that heart beat, (2) the pressure-volume characterstcs of the arteral vessels, and (3) the dranage of blood out of these vessels nto the perphery durng systolc ejecton. 1 "" Of these three factors, the stroke volume can be determned drectly by ndependent methods but the other two can be estmated only ndrectly. 1 However, beat-to-beat estmates of stroke volume from aortc pressure pulses requre a knowledge of these two unknowns throughout each heart beat. We descrbe here a method to crcumvent ths dffculty that s based on the two followng assumptons: (1) that the From the Department of Physology and Bophyscs, Mayo Clnc and Mayo Foundaton and Mayo Medcal and Graduate Schools of Medcne (Unversty of Mnnesota), Rochester, Mnnesota. Supported n part by Grants HL 3532, HL 4664, and RR-7 from the Natonal Insttutes of Health, U.S. Publc Health Servce, and AHA CI-IO from the Amercan Heart Assocaton. Dr. Bourgeos was a Career Investgator Fellow of the Amercan Heart Assocaton and s Head of the Department of Pedatrc Cardology, Unversty Chldren's Clnc, DusseWorf, Germany. Dr. Glbert s an Assocate Consultant n the Department of Physology and Bophyscs. Dr. von Bemuth was a Research Assstant n the Department of Physology and Bophyscs. Dr. Wood s a Career Investgator of the Amercan Heart Assocaton. Address for reprnts. Dr. E.H. Wood, Mayo Foundaton, Rochester, Mnnesota Receved March 24, 1975: accepted for publcaton January 13, 1976 decrement n aortc pressure, or more correctly the pressure ncrement whch fals to occur, due to perpheral dranage of blood durng any gven systole can be estmated from the aortc pressure recorded throughout ths systole and the tme constant (T) of the decrease n aortc pressure durng dastole; and (2) that by addng ths calculated decrement to the pressure ncrease actually observed at end-systole, a corrected end-systolc ncrement n aortc pressure above the precedng end-dastolc pressure can be obtaned whch s proportonal to the total amount of blood ejected nto the aorta by that heart beat,.e., the stroke volume. Theoretcal Consderatons and Hypotheses At the termnaton of systolc ejecton from the ventrcle, the stroke volume of that beat may be thought of as consstng of two portons: (1) a volume of blood that draned nto the perpheral vascular bed durng systole (the "systolc runoff"), and (2) the balance of the stroke volume, that was stored n the large elastc or capactve arteres durng ths systole. The amount of blood draned from these capactve arteres durng dastole depends on the aortc pressure durng dastole, the resstance to blood flow out of the large arteres, and the duraton of dastole. The dastolc runoff nto the perphery thus bears no constant relatonshp to the actual stroke volume of the precedng systole. If the perpheral resstance vessels somehow could be occluded for the duraton of systolc ejecton, the total ventrcular output would be stored wthn the arteral capactance vessels and the pressure wthn these elastc arteres would be ncreased to a hypothetcal value (PHYP) at the end of ejecton (Fg. 1). The rse n pressure from the value at end-dastole (P D ) to the hypothetcal end-systolc level, PHYP, could be consdered as representng a pressure ncrement proportonal to the total stroke volume (SV) of ths beat (Fg. 1); SV cc ( PHYP _ p D). (1) If the stroke volume s the sum of the volume of blood

2 16 CIRCULATION RESEARCH VOL. 39, No. 1, JULY 1976 PRESSURE n whch SA s the area under the systolc porton of the pressure pulse n mllmeters of mercury multpled by tme n seconds. It recently has been demonstrated under a varety of hemodynamc condtons' that the behavor of any gven aortc dastolc decay may be characterzed by a sngle numercal value called the "tme constant" (T). Ths value wll be most accurate f the aortc pressure pulse s recorded from a specfc ste n the lower thoracc aorta, T s the denomnator of Equaton 5. The expermental procedure detaled below was desgned to test the ablty of the formula SV» K A (P ES -P 0 +SA/T) FIGURE 1 Method for determnaton of ndvdual beat-to-beat stroke volume from aortc pressure pulses. The sold curve s a normal pressure pulse from the lower thoracc aorta. The dashed curve above the systolc porton of the pressure pulse represents the hypothetcal aortc pressure contour, resultng n a pressure ncrement, APES, whch would occur f all perpheral vessels were to be closed durng systole, thereby preventng systolc dranage. The pressure equvalent to the daslolc dranage n the steady state case s (PES Pa). The pressure equvalent to the total stroke volume, &P s v, s the sum of these values. K A s a proportonalty factor. dranng nto the perphery durng systole and the volume stored wthn the arteres, also durng systole, these two volumes should be defnable ndependently n terms of the changes n aortc pressure that occur as a result of ther presence. Let dp ES (Fg. 1) represent the hypothetcal ncrement n end-systolc aortc pressure, whch would have occurred f perpheral dranage had been prevented durng aortc ejecton. Then a total pressure equvalent of systolc ejecton (APgv) could be expressed as the sum of these two components,.e., the ncrease n pressure to end-systole (PES - PD) plus the addtonal ncrement n pressure, AP Ea, f no perpheral dranage had occurred. Therefore, the true pressure equvalent of systolc ejecton would be: = (PES - PD) + AP ES. (2) If the foregong assumptons are not too dvergent from realty, and f the AP SV /SV characterstcs of the arteral vessels are reasonably constant,.e., K A = AP 8 v/sv, (3) the stroke volume could be calculated from the relatonshp llustrated n Fgure 1: SV - K^Psv, (4) n whch K A s a pressure-volume proportonalty factor. Snce there are several ndependent methods for measurng the stroke volume,*" 8 the value of K A n ths equaton could be determned f t were possble to determne AP SV drectly from the aortc pressure pulse. Although the term (P ES - P D ) of Equaton 2 can be measured drectly, the AP ES term must be calculated from ndrect measurements. A dervaton for ths latter term s presented n the Appendx: S = SA/r, (5) SV = K A [(P ES - P D ) + SA/r] (6) to yeld values for beat-by-beat stroke volumes n close agreement wth those measured smultaneously by chroncally mplanted aortc electromagnetc flowmeters n a number of dogs. Methods The expermental procedures, as well as the technques for hand and computer processng of the pressure and flow data, have been descrbed.' Sx mongrel dogs wth chroncally mplanted aortc electromagnetc flowmeters (three also had nduced chronc atroventrcular block, 10 ) were studed under morphne (2.5 mg/kg)-pentobarbtal (15 mg/kg' 1 anesthesa wth and wthout control of heart rate and atroventrcular stmulus nterval by means of electroncally coupled rght atral and ventrcular bpolar electrode-tpped cardac catheters. In three of the expermental studes large changes n perpheral resstance and heart rate were nduced by constant-rate nfusons of acetylcholne (0.5 mg/ml) and angotensn II (A II) (2.0 mg/ml) nto the arch of the aorta; the nfuson rates were vared n steps. It was assumed that these vasoactve drugs, partcularly A II, on reachng the large capactve arteres va the vasa vasorum, also would affect the complance of these vessels by ther actons on the vascular smooth muscle, and hence the resstance-capactance (RC) characterstcs of the arteral tree. The tp of a 60-cm, 5-Fr. Lehman catheter, wth the brd's-eye tp postoned n the thoracc aorta a few centmeters cephalad to the dorsal nserton of the daphragm, was used to record aortc pressure pulses usng a stran gauge manometer (Statham P23G). The electrocardogram, atral and ventrcular pacng stmul, flow velocty n the ascendng aorta, pressures (multple aortc, rght atral, rght ventrcular, pulmonary artery, and arway), and the amount and duraton of njecton of ndocyanne green (1.25 mg/ml) were recorded on analog tape and converted on-lne and n real-tme to dgtal form at a rate of 200 samples/second for each channel by a computer-controlled (CDC 3300), multplexed (100,000 ten-bt samples/second) A-D converter. The tme constant, T, used as a measure of the steepness of the ndvdual dastolc decays, was calculated for each pressure pulse by frst samplng the dastolc pressures at 5-msec ntervals. Samplng was not ntated untl 30 msec after the ncsura and was termnated 20 msec pror to the onset of the followng systole n order to mnmze errors due to perturbatons n aortc pressure occurrng near these two

3 STROKE VOLUME FROM AORTIC PRESSURE PULSES/Bourgeos et al. 17 events. Portons of any dastolc decay occurrng later than seconds after the ncsura were not employed n any calculatons, as t has been demonstrated that sgnfcant changes n the r values occur at or after these ntervals, presumably due to reflex changes n perpheral vascular resstance nduced by the decrease n arteral pressure assocated wth asystolc perods of ths duraton." The ndvdual coordnate ponts (t,, P,) were plotted on a semlogarthmc scale, n whch the coordnate values (t,, In P,) followed a nearly straght lne wth a negatve slope. Ths set of semlogarthmc ponts was approxmated by a standard lnear regresson equaton (y = mx + b), n whch m s the slope of the lne and b s the ordnate ntercept. The recprocal of the slope, wth the sgn dsregarded, was defned as the tme constant (T) for the dastolc decay. Photographc paper recordngs also were taken on a suffcently enlarged scale, ether drectly durng each experment or from a playback of the analog tape recordngs, to allow manual analyss. Determnatons of the stroke volumes by ths method then were<:arred out on the records for each dog by a pencl-and-ruler technque, equvalent to that used by the computer, for groups of approxmately 100 pulses selected at regularly spaced ntervals throughout the duraton of each experment. Although t has been demonstrated* that correct placement of the aortc catheter does much to ensure recordngs of smooth monotonc decays of the dastolc portons of the pressure pulses, varable degrees of random beat-to-beat dfferences n shape as well as sporadc pressure dfferences do occur. Consequently, the accuracy of the calculaton of r can be mproved by the followng procedure. METHOD FOR AVERAGING SUCCESSIVE DIASTOLIC DECAYS Begnnng wth the hghest even-valued aortc dastolc pressure after the ncsura, the elapsed tme At, needed for ths pressure to fall 2 mm Hg was measured, as were the addtonal tme segments durng whch the dastolc pressure fell by successve 2-mm Hg steps to the lowest even-valued pressure, or untl a pont seconds after the ncsura, whchever occurred frst. The ndvdually measured duratons for each successve 2-mm Hg decrement n dastolc pressure were stored n the computer memory n assocaton wth the pressure value at whch that change was measured. The subscrpt "" represents the upper pressure of the 2-mm Hg pressure decrement over whch the tme ncrement was measured (e.g., At t = 10 msec ndcates that 10 msec were requred for the dastolc pressure to fall from 98 to 96 mm Hg). The varous At, values from 5-10 consecutve pulses, but assocated wth the same even-valued pressure levels, were averaged to yeld a mean dastolc decay tme (At,) for a decrease of 2 mm Hg to the next lower even-valued pressure level. The analyss procedure descrbed above was carred out by means of a computer program usng as data the dgtzed recordngs of the pressure pulses. However, ths automated method s equvalent to, and was developed on the bass of, a tme-consumng manual method whch requres the drawng of horzontal lnes spaced at even-valued pressure levels on the paper records of greatly enlarged pressure pulse tracngs. Manual measurements of the elapsed At, between the ntersectons of the pressure waveform of each pulse and the horzontal lnes were repeated for each group of 5-10 contguous pulses and, as descrbed above, a set of values for At were computed. Both manually and va the computer method, the successve At, values were used to construct a sngle "averaged" dastolc decay curve represented by a seres of even-pressure values separated from each other by the correspondng AT, values. The resultant average dastolc decay curve then was employed n the manner descrbed earler" for the calculaton of a representatve tme constant value f. Computer analyses of the dluton curves of ndocyanne green for determnatons of cardac output by the Stewart- Hamlton method were carred out usng the technque of Wllams and co-workers. 8 Average stroke volume (SVIG) was calculated by dvdng the cardac output by the average rate n cycles per mnute of the frst 10 heart beats after njecton of the ndcator nto the pulmonary artery. In addton, a sngle n vvo calbraton of the flowmeter aganst the ndcator-dluton method was performed by comparng the sum of the areas under 10 contguous flow pulses recorded durng the duraton of the ndcator-dluton curve wth the sum of the SV^ from the same 10 beats. Thereafter, beat-to-beat stroke volume values were calculated drectly from the flowmeter pulses (SV FM ). Systolc areas under the aortc pressure pulses (SA) were determned ether by hand planmetry of the orgnal tracngs, or by trapezod ntegraton by the computer of the dgtzed (200 sample/second) aortc pressure data. Calbraton of the method was carred out aganst ndcator-dluton measurements of the cardac output, yeldng an aortc pressure-volume converson factor (K A ) to be employed n Equaton 6. The total aortc pressure equvalent (AP SV ) for ndvdual heart beats was determned for each of the 10 pulses mmedately after njecton of ndcator nto the pulmonary artery; these 10 AP S \- values then were summed. The pressure-volume converson factor (K A ) then was determned usng Equaton 3 wth the ndcator-dluton measurement of stroke volumes (SV G ), summed over the same 10 beats, as the ndependent value of cardac output. Results Fgure 2 s an example of the aortc pressure and electromagnetc now pulses and smultaneous beat-to-beat stroke volume values calculated from these two recordngs. The converson factor K A requred for the pressure pulse technque was determned for each succeedng ndcatordluton curve n order to test ts consstency under the nfluence of the large changes n cardac rate and rhythm plus large changes n perpheral vascular resstance nduced durng observaton perods rangng n duraton from 3 to 6 hours. Table 1 shows a summary of the average values (K A ) and lsts the range and percent of standard devaton (SD) of the K A values for each dog. The values of K A from dfferent dogs vared, although n several cases K A values for the ndvdual dogs were wthn 1 SD of one another. In an addtonal seres of tests, only the sngle calbraton of K A and SV FM based on the frst ndcator-dluton

4 18 CIRCULATION RESEARCH VOL. 39, No. 1, JULY 1976 SVru U.a I ml FIGURE 2 A seres of aortc pressure pulses recorded from a 12-kg dog wth chronc atrovenlrcular block durng large beat-to-beat varatons n stroke volume caused by a successon of spontaneous escape ventrcular beats, ndcated by (*) n the ECG trace. These beats rendered the heart refractory to the atral and ventrcular pacng pulses that mmedately followed them (these pulses ndcated by A and V n the ECG). The numercal data below the curves are the related stroke volume values determned by the pressure pulse method, SVAp, and aortc flowmeter, SV F y The anesthetcs were morphne and penlobarblal. measurement of cardac output performed at the begnnng of an experment was used for all subsequent determnatons of stroke volume by these two methods. The successve determnatons of cardac output by the dluton method at ntervals throughout the experment were used only for the estmate of S~V G and not for recalbraton of the flowmeter or the pressure pulse method; hence, all succeedng SV IG, SVAP, and SV FM represented values based on converson factors determned from the frst dluton curve. The seres of stroke volume values extendng over observaton perods of 3-6 hours n sx dogs are plotted n Fgure 3. Regresson analyses of the sets of smultaneous values for all sx dogs shown n Fgure 3 were carred out for the three methods, wth the values determned by the more accepted method for each set of pared values plotted on the abscssa as the ndependent varable. The statstcs from the regresson data obtaned for these sx dogs are summarzed n Table 2. The ranges of aortc systolc, dastolc, and pulse pressures and the heart rates encountered durng the perods of observaton n each of the dogs are gven n Table I. Wth reference to the results of Table 2: (1) The correlaton coeffcents were, n general, greatest n the comparsons between SVA P = SV F M (P < 0.001). (2) An equalty relatonshp of the form SV A = SV B, where A and B ndcate any two of the methods, was often not best exemplfed by the SV G vs. SV FM methods, but rather n half of all cases, by SV AP vs. SV FM (dogs 2, 3, and 5). (3) The Y-ntercepts of the regresson lnes were, n general, not zero, wth the smallest magntudes appearng n the relaton between SV FM and SV IC. (4) The SD (e., SYX) values were approxmately the same for all methods, wth a value of ±2 ml about the lne. Comparsons of varablty between pars of smultaneous stroke volume values determned by ndcator-dluton, aortc flowmeter, or pressure pulse technques reveal no clear-cut dfferences between the three methods. The best correlatons generally were observed when the flowmeter technque was one of the methods ncluded as a member of the par. Because SV IC s by nature a mean value, t was necessary (Fg. 3) to average the ndvdual bea.t-to-beat stroke volume values obtaned by the SV FM and SVAP methods over the 10 heart beats after each njecton of ndcator nto the pulmonary artery n order to allow all three sets of values to be compared. However, every one of the pared smultaneous beat-by-beat stroke volume values determned by the pressure pulse and electromagnetc flowmeter technques are compared n Fgures 4 and 5. In each fgure, the aortc pressure pulse method was calbrated only once aganst an ndcator-dluton measurement of cardac output at the begnnng of the experment. The varatons n the stroke volumes shown n Fgure 4 were nduced wthout the nfuson of vasoactve agents. The statstcal data suggest the exstence of an equalty relatonshp between the two methods [slope of 1.07, Y-ntercept of 0.3, SD (.e., SYX) of 2.8 ml]. Smlar relatonshps, whch became more evdent as the number of observatons ncreased, were noted for the TABLE 1 Range of K A Values and Hemodynamc Parameters Induced n Sx Dogs by Inra-aortc Infusons of Acetylcholne and Angotensn II and by Cardac Pacng (Morphne-Pentobarbtal Anesthesa) Values Experment duraton, ntal through fnal dye curve (hr) Number of dluton curvesf Heart rate (beats/mn)t Cardac output (ml/kg) Stroke volume (ml){ Aortc systolc pressure (mm Hg) Aortc dastolc pressure (mm Hg) Aortc pulse pressure (mm Hg) Perpheral resstance (mm Hg-sec/ml) K A (mean) (ml/mm Hg) K A (range) (ml/mm Hg) K A (% SD of mean) Dog 1 (16 kg) ( ) 10.4 Dog 2 (15 kg) ( ) 14.3 Dog 3' (13 kg) ( ) 10.5 Dog 4* (14 kg) ^* ^* ( ) 12.1 Dog 5* (12kg) ' ( ) 16.6 Dog6 (17kg) ( ) 16.2 * Dogs wth chronc atrovcntrcular block. t Total number or dluton curves throughout experment duraton. J Heart rates, pressure, stroke volumes, and resstance values are averages of frst 10 beats after each njecton of ndocyanne green nto pulmonary artery. Range of cardac output values determned by arteral-dluton curves of ndocyanne green dye.

5 STROKE VOLUME FROM AORTIC PRESSURE PULSES/Bourgeos e al. 19 e Ul" 3 / 40 - Dog 20 a I - \[*^ D->-* \ 1! 1 METHOD o o Indcator -Dluton - Flowmeter X --x Pressure r Dog n - Dog 3 Angotensn Acetyl- cho lne! t v r$ < * I I 40 - Dog 5 40 r Dog HOURS HOURS HOURS FIGURE 3 Comparson of stroke volumes determned smultaneously from ndcator-dluton curves, an aorttc electromagnetc flowmeter, and aortc pressure pulse Intra-aortc nfusons of acetylcholne and angotensn II were carred out n dogs 3, 4, and 5. two addtonal dogs n whch vasoactve substances were not employed. Fgure 5 dsplays data from one of three dogs n whch large changes n perpheral vascular resstance and cardac output were nduced by ntra-aortc nfusons of acetylcholne and A II (see Fg. 3, dog 4). A sngle regresson lne, plotted on all three panels, s based on all of the 1,900 pars of smultaneous values obtaned durng ths experment, wthout regard to heart rate or the drug nfused. The fact that ths same sngle regresson lne satsfactorly represents the three dfferent sets of data supports the exstence of an equalty relatonshp between the SVA P and SV FM values (slope of 1.02) under a wde range of hemodynamc condtons; ths result also suggests that the value of K A n Equaton 6 s not sgnfcantly altered by these changes n hemodynamc status, ncludng alteratons of the complance of the large elastc arteres. The nclusve percent standard devaton between the two technques s 11 % about the mean value. These results suggested that even durng major changes n the hemodynamc status, beat-to-beat calculatons of stroke volume by ths aortc pressure method compare favorably wth more "drect" methods such as electromagnetc flow measurement. Fgure 2 depcts a seres of beats n whch the stroke volumes vared consderably, accompaned by alteratons n TABLE 2 Comparson n Sx Dogs of Mean Stroke Volumes (ml) Calculated for Same Beats from Indcator-Dluton Measurements of Cardac Output, Aortc Electromagnetc Flowmeter, and Aortc Pressure Pulse Method Ordnate: SV^p Abscssa: SV rm Ordnate: SV A f Abscssa: SV O Slope Intercept r SD{ Slope Intercept r SD{ Dogl (I3)t Dog 2 (16)t Dog 3* (6)t Dog 4* (28)t Dog 5* (22)t Dog6 (I2)t Ordnate: SV rm Abscssa: 3V, C Slope Intercept r SDt % Dogs wth chronc alroventrcular block. t Number of observatons. In each observaton the values of mean stroke volume calculated by the three methods were based on the frst 10 beats after njecton of ndocyanne green nto the pulmonary artery. J Standard devatons (ml) computed wth respect to the regresson lnes (SYX)

6 20 CIRCULATION RESEARCH VOL. 39, No. 1, JULY 1976 SV FM and AP S v were performed by a sngle ndcator-dluton curve, carred out more than 3 hours pror to the recordng of ths arrhythmc burst. Dscusson o X Q O * It 3 t 0. It o ^*v N y r SD ± 693 / 07X ELECTROMAGNETIC 2.8 FLOWMETER (ml). SV FU FIGURE 4 Comparson of 693 pars of smultaneous stroke volume values determned by aortc flowmeter and pressure pulse technques from ndvdual heart beats recorded at ntervals over more than 3 hours. No vasoaclve substances were nfused. Morphnepentobarbtal anesthesa was used (dog 6). the mean aortc pressure, pulse pressure ampltude, and maxmal blood flow n the ascendng aorta (represented by the maxmal deflecton of the flow pulse). The dfferences n flow pulse areas are drectly proportonal to the large beat-to-beat changes n stroke volume. These varatons are especally large between the sxth and seventh pulses from the left, n whch the flowmeter-calculated stroke volume decreases from 26.7 ml to 2.9 ml, wth comparable values computed va the SVAP technque. The calbratons of UJ 40 a. n m cc so a. a o < to CONTROL 10 to ANGIOTENSIN 10 to ACETYLCHOLINE 10 to 30 N = y = 1.02 X T = 0.98 SD ±2.2 The lnearty of the relatonshp between SV A P and Sv FM was demonstrated for sx dogs n whch large hemodynamc varatons were provoked contnuously over perods of 3-6 hours. The relatve nvarablty of the K A value over these duratons and under the condtons of these experments s mpled by the numercal smlarty of the standard devatons calculated from the entre set of data measured durng short experments as well as from those of extended duraton. Further, n the sequental comparsons of the three methods wth each other throughout the duratons of the experments (Fg. 3), the SVA P values dsplayed a close correlaton to the other stroke volumes n all nstances, although some offset was apparent n at least one dog. Snce both the flowmeter and the pressure pulse methods were calbrated on the bass of a sngle ndcator-dluton measurement of cardac output at the begnnng of the experment, small errors durng ths sngle calbraton could result n the parallel shfts observed. Fnally, graphs of the pared values (SVA P, SV FM ) usng every heart beat recorded throughout an experment (Fgs. 4 and 5) dsplayed a very close approxmaton to an equalty relatonshp for each of the sx dogs, wth a Y-ntercept approxmately at the orgn. The standard devatons about the lne (SYX) n these fgures had a maxmal value of ±20% over hours of unnterrupted observaton, durng whch large varatons were nduced n the hemodynamc status of each dog and n the beat-to-beat stroke volume wthout subsequent recalbraton. FIGURE 5 Comparson of 1,900 pars of stroke volume values determned va flowmeter and pressure pulse from ndvdual heart beats recorded from a 14-kg dog wth chronc atrovenlrcular heart block: study duraton exceeded 4 hours and ncluded nfusons of acetylcholne and angotensn. Sold lne n each panel s the same regresson lne calculated from all 1,900 pars, not a lne of dentty. Morphne-pentobarbtal anesthesa was used. ELECTROMAGNETIC FLOWMETER (ml). SV FU

7 STROKE VOLUME FROM AORTIC PRESSURE PULSES/Bourgeos el al. 21 Ths pressure pulse method thus appears to be an acceptable alternatve to electromagnetc flowmetry for those cases n whch nstantaneous determnatons of the beat-to-beat stroke volume s desred and n whch condtons prevent use of an aortc flowmeter. There s no ntent to mply that the fndngs reported heren ndcate the exstence of a strctly lnear pressurevolume relatonshp n the arteral tree over a wde range of pressures. The concept of the pressure equvalent to stroke volume, AP S v, although supported by the data of these experments, s an artfcal construct that was derved by a plausblty argument for applcaton n the rather crcumscrbed manner prevously dscussed. The major sources of error n ths pressure pulse method are as follows: (1) An error n the automated recognton of the ntaton and termnaton of systole whch occurs most often when a computer program does not determne accurately the onset and termnaton of systole. The resultant errors n the calculaton of systolc area degrade the accuracy of AP ES derved from Equaton 5. (2) Errors n the determnaton of the tme constant affect the accuracy of the rght-most term n Equaton 6 for the calculated stroke volume. As r s used for the calculaton of AP ES only (Eq. 5), errors n the determnaton of ts numercal value wll be mnmzed n the fnal value of stroke volume by the rato of APES to AP SV. For example, n one case examned for the nfluence of these errors on the calculated value of stroke volume, AP E s accounted for an average of 40% to 50% of the total AP S v, and thereby of the total stroke volume (range, 20-80%). Calculatons of stroke volume durng non-steady state rregular heart beats have been found to be rather senstve to errors n T, partcularly f the pressure pulses are recorded from other than the optmum locaton n the thoracc aorta 9 or f the computaton was performed usng tme constants based on the dastolc decays of ndvdual heart beats. In these nstances, but also n general, the accuracy of the stroke volume could be mproved substantally f r were determned from an average of consecutve dastolc decays (see Methods) rather than from sngle beats. Ths s llustrated n Fgure 6, for whch the pressure pulse values ml/ nc mm Hg 200 too Aorta SO Flowmeter ECG SV FU 10.0 SV^p(Arg) SV. P ml FIGURE 6 Comparson of ndvdual stroke volume values determned by aortc flowmeler and two varatons of pressure pulse technque durng transent changes n stroke volume caused by an extrasyslole. A closer correlaton wth flowmeter values was obtaned from the SV^P (avg) value for stroke volume. The dog {16 kg) had chronc alrovenlrcular heart block: morphne-pentobarblal anesthesa was used. ml ml were calculated usng two dfferent values of T based on (1) the same heart beat for whch the stroke volume s calculated (SVA P ), and (2) an average of the dastolc decays of the fve heart beats shown n the llustraton [SVjp (avg)]. The SVA P values calculated from the "average" method agree well wth the SV FM, but an addtonal varaton of -3% to +8%, referenced to the ndvdual SV FM values, s present between the stroke volume determned from the "averaged" r and from the sngle-pulse r values, respectvely. An addtonal mprovement occurs when the dogs are allowed to breathe durng the recordng perod. In most dastolc decay waveforms, even f recorded from the "optmum" locaton n the thoracc aorta, one or more random pressure varatons of small ampltude and short duraton are frequently observed, whch result n a degradaton of the accuracy of calculaton of r from the dastolc decay. The alteratons n aortc pressure levels assocated wth changes n ntrathoracc pressure durng the respratory cycle cause these small varatons to be dstrbuted more unformly over the entre pressure range of the "averaged" dastolc decay. Another beneft accrued from these cyclcal varatons n ntrathoracc pressure, and thereby n the baselne of the aortc pressure curve, s the cancellaton of small ampltude perturbatons caused by reflected pressure waves wthn the arteral tree.'- " Snce the relatve tmng of these reflected waves durng the cardac cycle s unrelated to alteratons n baselne pressure, the resultng short duraton ncreases and decreases n aortc pressure occur at a varety of absolute pressure levels n consecutve dastoles. The technque descrbed earler of segmental averagng of ndvdual successve dastoles mnmzes the effects of these pressure varatons on the calculated average dastolc decays. The averaged r, therefore, s less senstve to pressure varatons than the T values calculated from the ndvdual dastolc decays. Clncal applcatons of ths (or any other) aortc pressure pulse technque may be more restrcted than n the research laboratory because of the necessty of ntroducng an aortc catheter retrogradely va a perpheral vessel. The technques requste for mantenance of ndwellng aortc catheters over extended duratons, for example, n postoperatve recovery envronments, have become hghly developed." In those nstances n whch aortc catheters are already n routne use, ths new method may allow smultaneous montorng of mnute-by-mnute cardac output, beat-by-beat stroke volume, systemc perpheral resstance, and effectve beat-bybeat stroke work, ether quanttatvely or, f a calbraton aganst an ndependent method s not avalable, qualtatvely. As a test of the dagnostc value of the avalablty of such nformaton n a real-tme envronment, an on-lne computer program has been wrtten for the CDC 3500 computer and s presently undergong evaluaton. Appendx Ths secton demonstrates that AP E s n Equaton 2 may be represented by Equaton 5, whch may be appled drectly to the calculaton of stroke volume as demonstrated by Equaton 6. The organsm s consdered to be n a hemodynamc steady state for the duraton of one heart cycle f no asystolc perod exceeds seconds, snce t has been demon-

8 22 CIRCULATION RESEARCH VOL. 39, No. 1, JULY 1976 strated that the reflex control mechansms do not nduce major alteratons n perpheral resstance wthn a shorter tme." The blood flow rate nto the perphery (Q) at the same levels of arteral pressure (P,) s assumed to be the same, ndependent of the phase of the cardac cycle; that s, Q., = Q dl, (7) where the subscrpts s and d refer to events n systole and dastole, respectvely, and the subscrpt refers to events occurrng at or near a gven pressure, P,. The magntudes of the flows n Equaton 7 are governed by the drvng force P va the Ohm's law analogy for lquds. Snce the hysteress factor wthn the large elastc arteres s small," only the magntudes of pressure changes, and not ther sgns, need to be consdered. The tme ncrement At s the duraton requred for the aortc pressure to change by a measurable amount AP,, e.g., from P, to P, +,. The defntons of AP, and At, wll be refned below. It s assumed further that the volume flowng from the large arteres nto the perphery s a functon only of the duraton At, over whch P, s the drvng force, whether durng systole or dastole. The small amount of blood runoff at each P, durng systole and dastole may then be representedos- Systolc runoff, = AV., = Q,,At,, (8) Dastolc runoff, - AV d, = Q d,at d, (9) where the At,, and At d, are the short duratons n whch P, s the drvng pressure. Dvdng Equaton 8 by Equaton 9 and nvokng Equaton 7 yelds: AV., At. (10) If t s now postulated that whether n systole or dastole, a small change n stored blood volume n the arteral tree may be approxmated by a proportonal small change n arteral pressure: AV, - k,ap,, (11) and ths equaton s appled to events n dastole, t s possble to defne a small "nstantaneous pressure change equvalent to dastolc runoff, AP d," nto the perphery for each P,. Durng dastole, when the change n volume of the arteral tree s due only to perpheral runoff, the AP d, are observable values easly measured from the dastolc decay curve. Snce the magntudes of the AP d, should be small to preserve the accuracy of Equatons 8-11, but are otherwse arbtrary, t s reasonable to defne all AP d, to be the same magntude. The assocated At,,, are then the duratons requred for the dastolc pressure to change by amounts AP dl = AP,,.e., by successve small steps durng whch small volumes of blood AV d, dran nto the perphery. Although perpheral dranage also occurs durng systole, the effects of ths outflow on systolc pressure are masked by the nflow of blood nto the arteral tree, whch rases arteral pressure more per unt of tme than the systolc dranage decreases ths pressure. Thus, unlke n dastole, the pressure decrements A P.,, the "nstantaneous pressure changes equvalent to systolc runoff," are not measurable drectly from the systolc curves but must be calculated from values measurable durng dastole and a reformulaton of Equaton 10. Durng the tme At,, requred for P, to ncrease by AP,, a volume AV B, drans nto the perphery. If the AP, n systole arc chosen to be of the same magntude as the AP d,, and the same absolute pressure levels P, are consdered n systole and dastole, the AV,, and AV d, wll be n proporton to the duratons requred for the pressure to change by AP d, va Equaton 10. In general, At,, = At,,, as n most cases the nstantaneous rate of systolc pressure rse s unequal to the rate of dastolc decay at each P,. The small pressure rse whch would have occurred durng systole for each small change AP, = AP d,, f no dranage had occurred, can be derved from Equatons 10 and 11:.AP., = AP d,- 111!. (12) Equaton 12 allows a calculaton of AP,,, an artfcal construct not measurable from the aortc pressure pulse, from real values of At^,, At,,, and AP dl, whch can be measured from the pulse. The constants of proportonalty, k, n Equaton 11 do not appear n Equaton 12 snce for any P they are assumed to be equal n systole and dastole (assumpton of mnmal hysteress), hence would appear n both numerator and denomnator of Equaton 12. As a hypothetcal example, suppose that a pressure change A P, of 5 mm Hgwas consdered over the same range n systole and dastole. The lmtng values P, = 105 mm Hg, and P mm Hg, mght correspond to the tmes At, = 2 msec on the systolc segment and At^ = 10 msec on the dastolc segment of the aortc pressure pulse. The pressure loss resultng from the dranage from the arteres dufng the At,,, s the dastolc decay from the upper pressure level down to the lower level, that s, AP d, = 5 mm Hg durng the A^, = 10 msec. Employng Equaton 12, the hypothetcal pressure equvalent to systolc runoff durng the systolc pressure rse from 100 mm Hg to 105 mm Hg, as n the foregong example, s calculated to be 1 mm Hg. That s, f perpheral dranage were prevented durng systole, the pressure wthn the aorta would have rsen from 100 mm Hg, not to 105 mm Hg, but to 106 mm Hg. Although Equaton 12 s an approxmaton, the systematc error would be reduced sgnfcantly f a smaller pressure dfference than AP, = AP d, = 5 mm Hg had been chosen. The determnaton of the ndvdual AP I values from Equaton 12 for the successve P, values may be carred out from the onset of aortc systole, PD, up to the peak systolc pressure. Extrapolaton on semlog scale of the dastolc decay curves to the range of pressures up to the peak systolc pressure would be requred for those values of P, greater than P KS - Snce t s assumed that the drecton of pressure change has no effect on the arteral elastc characterstcs, the calculaton may be contnued from the peak systolc pressure down to the pressure at end-systole, PES- Summaton of all nstantaneous pressure equvalents AP,, for the successve P, throughout the duraton of systole yelds APES. defned as the pressure equvalent to the total dranage of

9 STROKE VOLUME FROM AORTIC PRESSURE PULSES/Bourgeos el al. 23 blood from the arteral tree nto the perphery durng systole (Fg. 1). From Equaton 12: 2 AP., = 2 AP dl - PD t D \ (13) Although Equaton 13 represents the ratonale for the nterpretaton of AP ES, t s too cumbersome for drect applcaton, partcularly because of the necessty of extrapolatng the dastolc decay curve up to the peak systolc pressure. A smplfed expresson for AP E s results from the dervaton of an alternate form and substtuton for AP d, on the rght sde of Equaton 13. On the bass of the Ohm's law analogy, t s assumed that perpheral dranage out of the elastc arteral tree at any gven nstant s proportonal to the pressure n the arteral tree: Flow, - - ^ dt = K..P, (14) If a small change n stored blood volume n the arteral tree may be approxmated by a proportonal small change n arteral pressure, then: and n the lmt, -AV, = K b,(-ap,) dv, dp, (15) (16) Assumng that stored blood volume and arteral pressure are related to one another, from Equaton 16 and the chan rule for dfferentaton, we have: _dv, = /dv, dpa _ dp,_ dt \dp, dt / dt Substtute -dv, from Equaton 17 nto Equaton 14, dt yeldng: = N. t, Nj dt K b, Form a fnte dfference approxmaton of Equaton 18: (18) AP, - -K,P,At,. (19) If ths formulaton s appled to the events that occur durng dastole by recognzng that Equaton 19 becomes AP, = AP dl ; At, = At«,, AP d, = -K.PAtd,. (20) Subttute Equaton 20 for AP d,, dsregardng the sgn, nto the rght sde of Equaton 13: tea/ At, \ 1 ES AP ES = 2 AP d, ^-1 = 2 (K,P,At.,X (21) t D \ ^td/ t D The rght-most expresson of Equaton 21 s recognzed to be a sum of small rectangles of heght P, and wdth At., under the systolc porton of the curve, each multpled by a dfferent weghtng factor, K,. An mmedate smplfcaton results f all K, are assumed to be the same, that s, f K, = K for all. Equaton 21 can then be rewrtten as t E s AP ES = K 2 (P.At.,) (22) to The rght-most term s now the rectangular ntegral approxmaton to the area (SA) under the systolc porton of the pressure curve; hence: AP B8 = K(SA), (23) where K s stll to be evaluated. The assumpton that all K, = IC mposes specal constrants on the characterstcs of the dastolc pressure decay. In partcular, ths defnton n effect converts Equaton 18 nto a lnear frst-order dfferental equaton whose soluton n terms of P, s: P, = Ae- K " - Ae" 1 '"-. (24) Equaton 24 s a decreasng exponental n whch K s the recprocal of T and A represents the ntal pressure of the dastolc decay at tme-zero (ths s the pressure P ES n Fg. 1). Equaton 24 results drectly from the assumpton that K, = K and can only be consdered vald f the actual aortc dastolc pressure decay characterstcs support such an assumpton. It has been demonstrated (9) that ths approxmaton may be made wth a hgh degree of correlaton: hence, Equaton 23 becomes Equaton 5: APES = Va Equatons 2 and 5, Equaton 4 thus becomes Equaton 6: SV = K A [(P ES - P D ) + AP E9 ] SA [(P E3 - PD) + I As descrbed earler, oscllatons provoked by aortc valve moton durng the ntal perod of dastole are n part responsble for the characterstc shape of the ncsura, ncludng both the negatve notch and thereafter the postve peak of the dcrotc wave. It s also probable that pulse wave reflectons wthn the aorta and ts major branches contrbute as well to the conformaton of the notch and subsequent postve wave phase. These characterstc contours, whch are present even at the optmal aortc segment,* cause an underestmaton of the pressure ncrease wthn the aorta at end-systole f the lowest porton of the ncsura s equated to P ES ; t s possble to mnmze errors from ths source by choosng a mean value between the ncsura and the followng dcrotc peak, P DP, called "P E M," whch s used n place of P ES n Equaton 6: D ^ T PDP + PES (25) Acknowledgments We thank Juljs Zanns and Donald Hcgland for ther techncal assstance durng the experments, Sharon K. Zahn and Wlls Van Norman for ther

10 24 CIRCULATION RESEARCH VOL. 39, No. 1, JULY 1976 computer programmng, and Jean Frank and her assstants for preparaton of the fgures and typng of the manuscrpt. Paul Perkns asssted the authors wth the preparaton of the text. References 1. Warner HR, Swan HJC, Connolly DC, Tompkns RG, Wood EH- Quanttaton of beat-to-beat changes n stroke volume from the aortc pulse contour n man. J Appl Physol 5: , Starmer CF, McHale PA, Cobb FR, Greenfeld JC Jr Evaluaton of several methods of computng stroke volume from central aortc pressure. Crc Res 33: , Broemser PH, Ranke OF: Ueber de Messung des Schlagvolumeru des Herzens auf unblutgem Wegc. Z Bol 90: , Frank O: Schatzung des Schlagvolumens des menschlchen Herzens auf Grund der Wellen- und Wndkesjcltheone. Bol 90: , Hamlton WF, Remngton JW: The measurement of the stroke volume from the pressure pulse. Am J Physol 148: 14-24, Denson AB Jr, Spencer MP, Green HD A square wave electromagnetc flowmeter for applcaton to ntact blood vessels. Crc Res 3: 39-46, Ferguson DJ, Wells HS: Frequences n pulsatle flow and response of magnetc meter. Crc Res 7: , Wllams JCP, O'Donovan TPB, Wood EH- A method for the calculaton of areas under ndcator-dluton curves. J Appl Physol 21: , Bourgeos MJ, Glbert BK, Donald DE, Wood EH- Characterstcs of aortc dastolc pressure decay wth applcaton to the contnuous montorng of changes n perpheral vascular resstance. Crc Res 35: 56-66, Wllams JCP, Lambert EH, Ttus JL' Use of ntracardac A-V nodal potentals n producng complete heart block n dogs. J Appl Physol 27: , Hamlton WF, Dow P: Expermental study of the standng wave n the pulse propagated through the aorta. Am J Physol 125: 48-59, Gardner RM, Warner HR, Toronto AF, Gasford WD: Catheter-flush system for contnuous montorng of central arteral pulse wave form. J Appl Physol 2* , 1970 External Detecton and Vsualzaton of Myocardal Ischema wth x ^-Substrates n Vtro and n Vvo EDWARD S. WEISS, M.D.,* EDWARD J. HOFFMAN, PH.D., MICHAEL E. PHELPS, PH.D., MICHAEL J. WELCH, PH.D., PHILIP D. HENRY, M.D., MICHEL M. TER-POGOSSIAN, PH.D. AND BURTON E. SOBEL, M.D. SUMMARY To characterze externally detectable changes n myocardal metabolsm of free fatty acds (FFA) and glucose assocated wth schema, sovolumcally beatng rabbt hearts were perfused under condtons of selected flows wth cyclotron-produced, short-lved (t H = 20.4 mnutes), I1 C-labeled sotopes of glucose and FFA. Tenson-tme ndex decreased 83% and lactate producton ncreased from 0.5 ± 1.9 (SE) to 5.3 ± 2.1 ^mol/mn per g of dry weght reflectng myocardal schema after flow was reduced from 20 to 5 ml/mn. After 30 mnutes of low flow the myocardal accumulaton of "C-octanoate, expressed as the extracton fracton, declned from 56 ± 15% to 30 ± 3%, reflectng metabolc suppresson of FFA extracton durng low flow. Effects attrbutable exclusvely to THE NEED to detect and estmate the mass of schemc myocardum n vvo has gven mpetus to the development of several approaches. The presence and extent of mpared contractlty, altered ventrcular dastolc complance, and ventrcular dyskness have been used as ndrect ndces of the severty of schemc nsults. l Electrophysologcal alteratons have proved useful dagnostcally but suffer from quanttatve lmtatons. 2 Although schema can be nferred from analyss of coronary artery anatomy or detected n From the Cardovascular Dvson and Dvson of Radaton Scences, Washngton Unversty School of Medcne, St. Lous, Mssour. Supported n part by NIH SCOR n Ischemc Heart Dseases I PI7 HL , and NIH Grant 5 P01 HL , Washngton Unversty, St. Lous, Mssour. Fellow, Esther & Morton Wohlgemuth Foundaton, Inc. Address for reprnts- Edward S. Wess, M.D., Cardovascular Dvson, Washngton Unversty School of Medcne, 660 South Eucld Avenue, St. Lous, Mssour Receved August 11, 1975, accepted for publcaton March g, prolonged resdence tme were excluded. Smlar results were obtaned wth "C-palmtate. The myocardal ardty for "C-palmtate was demonstrable by rectlnear whole body scannng n dogs gven 5 mc of the agent ntravenously. Dmnshed "C-palmtate uptake n zones of myocardum rendered scbemc for 20 mnutes pror to reflow n ntact dogs was delneated by elettrocardographcally gated postron-emsson traasaxal computer reconstructon tomography. Thus, dmnshed "C-FFA extracton, externally detectable, accompanes decreased perfuson n solated perfused hearts, and decreased "C-FFA uptake reflectng myocardal schema n vvo can be evaluated nonnvasvely by postron-emsson traasaxal tomography. studes of regonal myocardal perfuson, the local metabolc consequences cannot be evaluated wth avalable methods. 3 Release of consttuents such as potassum, lactate, or enzymes from myocardum, and ther detecton n coronary snus or perpheral blood, provde only gross ndces of altered metabolsm or tssue ntegrty and do not localze or quantfy reversble or rreversble njury. 4 Durng the past two decades the metabolc characterstcs of normal and schemc myocardum have been clarfed substantally. Data have been gathered prmarly n studes of coronary arterovenous dfferences and n nvestgatons of substrate utlzaton n solated perfused hearts subjected to selected physologcal condtons.'" In general, aerobc myocardum preferentally utlzes free fatty acd (FFA) for energy producton. In contrast, FFA oxdaton ceases n anoxc or severely schemc tssue and glycolytc flux ncreases at least transently. However, the effect of tran-