Effect of Afterload on Force-Velocity Relations and Contractile Element Work in the Intact Dog Heart

Transcription

1 Effet of fterload on Fore-Veloity Relations and ontratile Element Work in the ntat Dog Heart By Herbert J. Levine, M.D., Stanley. Forwand, M.D., Kevin M. Mlntyre, M.D., and Eliot Shehter, M.D. n the past few years, an inreasing attempt has been made to interpret the performane of the intat heart in terms of basi musle mehanis. Studies by bbott and Mommaerts 1 and Sonnenblik 2 of fore-veloity relationships in the at papillary musle have provided a firm basis for an analysis of the mehanial behavior of the intat heart. The dependene of fore-veloity relations upon fiber length, previously shown in isolated skeletal musle, 3 has been demonstrated learly in papillary musle as well. 2 s normal systole is ompliated by a onstantly hanging fiber length as well as by omplexities of fiber geometry, it is diffiult both to measure and to interpret mehanial events in a manner analogous to isolated musle. n a study of instantaneous relationships between myoardial fore and veloity in the intat dog heart, Fry et al. 4 sueeded in demonstrating a reiproal relationship between fore and veloity at a given left ventriular fiber length. These authors emphasized that not only the initial but eah sueeding fiber length during systole was important in determining myoardial fore and veloity. Thus, a modifiation of the lassi fore-veloity urve must be derived if one is to apply this type of analysis to the intat heart under its atual working onditions. n a previous paper, 5 an analysis was desribed by whih instantaneous fore and From the New England Medial enter Hospitals and the Department of Mediine, Tufts University Shool of Mediine, Boston, Massahusetts. Supported by Grant HE-7139 from the National Heart nstitute. epted for publiation Deember 13, irulation Researh, Vol. XVlll, June 1966 veloity relations ould be examined in the intat heart throughout the ourse of a single systole. From these data one ould onstrut a single fore-veloity urve for eah beat whih defined the performane of that beat. This method not only provided information on fore-veloity relations at a single fiber length, but permitted an integrated analysis of the full performane of a given systole during fiber shortening. The time ourse of fore-veloity relations studied in this fashion, however, introdues another variable in addition to hanging fiber length; namely, that of the hanging intensity of the ative state of musle. n the earlier study, 5 the effets of hanges in preload (initial fiber length), heart rate and inotropi environment upon these urves were demonstrated and interpreted in light of known mehanis of papillary musle. 1 ' 2 ' t is the purpose of the present report to examine the effet of two other variables, not previously studied, upon fore-veloity urves of single systoles; namely, afterload and the deay of the ative state of musle. t will be seen that abrupt hanges in afterload permit one to distinguish between the effet of fiber shortening and the deay of the maximum ative state on the fore-veloity urve of the left ventrile, and also enables one to explore a rather wide range of the ontratile element work" vs. load urve. n this fashion, some insight may be gained into the means by whih afterload funtions as an important determinant of ventriular performane. Methods ll studies were performed in mongrel dogs 729

2 LEVNE, FORWND, MNTYRE, SHEHTER 73 im Hf/Me FGURE 1 Time ourse of left ventriular pressure, dp/dt and aorti root flow rate. orti resistane was inreased between the seond and third ardia yle (vertial arrow). Time lines are at 2-mse intervals. weighing between 13 and 25 kg, anesthetized with sodium pentobarbital, 25 mg/kg. Respirations were driven by a Harvard pump via a uffed endotraheal tube. Left ventriular pressure was reorded by means of a Statham SF1 atheter-tip miromanometer passed retrograde through the aorti valve. The frequeny response of this system was flat to over 5 yles/ se and there was no phase lag. The miromanometer was alibrated by equating the pressure reorded by the miromanometer to that measured through the lumen of the atheter by means of a Statham P23d strain gauge. The time derivative of pressure was determined eletrially by means of a linear R- differentiating iruit (Eletronis for Mediine) and was alibrated for eah animal study by measuring the maximal slope of the isometri pressure rise. ardia output was determined by the indoyanine dye dilution tehni. End diastoli volume was measured by the thermal dilution tehni. The standard error and reproduibility of this volume method have been presented elsewhere.5 Via a sternal splitting thoraotomy, the root of the aorta was exposed and a square wave eletromagneti flowmeter* was plaed on the proximal aorta as lose to the root as possible. The time ourse of aorti flow rate was reorded and in some studies was integrated eletrially during the ejetion period. Linearity of the flowmeter was demonstrated using alibrated syringes Model 3, arolina Medial Eletronis, Winston-Salem, North arolina. of heparinized blood at varying flow rates. The time onstant of the flowmeter was 3 to 1 mse, and the maximum lag of the flowmeter with referene to the measurement of intraventriular pressure was 2.5 mse, when simultaneous left ventriular and aorta root pressures were reorded using atheter-tip miromanometers to indiate the onset of the ejetion period. ll measurements were reorded simultaneously on an Eletronis for Mediine 8-hannel photographi reorder at paper speeds of 2 mm/se (fig. 1). Thus, as measurements were made at 2 mse (4 mm of paper) intervals of systole, the maximum flow urve delay (.5 mm of paper) was ignored. EXPERMENTL DESGN ardia output and 3 to 5 thermal dilution urves were reorded before and after eah experiment and their average values alulated. When a number of ontrol beats had been reorded, the aorta distal to the flowmeter was abruptly narrowed by manual ompression during a single diastole. With a little pratie a small, moderate or large inrease in afterload ould be ahieved during diastole and maintained throughout the subsequent systole without artifatual distortion of either the pressure or flow urves. n this manner, the end diastoli volume of the ardia yle just before and during the intervention an be assumed equal. To obviate respiratory variations from beat to beat, the Harvard pump was turned off momentarily during eah set of interventions. sovolumi ontrations of the left ventrile were studied in similar fashion, irulation Researh, Vol. XV111, June 1966

3 EFFET OF FTERLOD ON FORE-VELOTY RELTONS 731 but in this ase the aorta was oluded just proximal to the flowmeter by means of an atraumati lamp. The olusion was maintained for one systole only and in eah ase zero flow was reorded by the flowmeter during the period of olusion. Thus, in the analysis of the effet of eah level of afterload, two onseutive ardia yles were examined: one, the normally loaded systole, the seond, the afterloaded systole (fig. 1). t the end of the experiment the left ventrile was disseted from the remainder of the heart and was weighed. SSUMPTONS ND DEFNTONS For the purpose of these analyses, it was assumed that the left ventrile may be represented as a homogeneous, thin-walled sphere and that all portions of the ventrile ontrat simultaneously and equally. s the anine left ventrile more losely resembles a prolate spheroid with a major-minor axis ratio of 2:1, the error introdued in the alulation of wall fore by assuming a spherial shape of equal volume will be approximately 8%. 8 s indiated by Gorlin et al., 8 the hange in axis ratio during systole is suh as to introdue a very small additional error in the alulation of instantaneous wall fore. irumferential fiber length and shortening rate (FSR) refer to the inner irumferene at the equator of a spherial ventrile. Wall fore has been normalized for unit ross-setional area of musle for omparison to the results of others. n this instane, fore was alulated at a point halfway between endoardium and epiardium. n order to provide values of the extension of the series elasti omponent omparable to those obtained in papillary musle, 9 it is assumed for this alulation only that end diastoli fore is supported entirely by the series elasti omponent. F o is defined as the maximum isometri fore and V max as the veloity of the ontratile element at zero load. The duration of systole is defined as the time from the onset of pressure rise to the point when pressure falls to zero, and afterload as the fore enountered by the heart during mehanial systole. The ative state of musle exists whenever the ontratile element eases to be freely extensible and either shortens or develops tension. The intensity of the ative state is defined as the fore developed by the ontratile element when it is neither lengthening nor shortening. n examining the performane of the intat ventrile, it is not possible to measure the intensity of the ative state diretly, nor is it possible to distinguish between asyhronous ontration of portions of the ventrile and a hange in the intensity of the ative state of the musle per se. However, irulation Researh, Vol. XVlll, June 1966 it will be shown that the time ourse of foreveloity relations during systole reflets hanges in the intensity of the ative state of the entire ventrile (vide infra). Thus, while not measured diretly, a major hange in the intensity of the ative state an be inferred from speifi deviations of fore-veloity urves during systole. n this disussion, the expressions "intensity of the ative state" and "maximum ative state" refer to the resultant intensity of the ative state of the entire ventrile. t should be appreiated, however, that this term does not neessarily reflet what is happening to the ontratile apparatus of a given segment of musle. LULTONS nalyses of fore-veloity relations were made at 2-mse intervals through the entire period of systole. With ertain modifiations (vide infra) these analyses were similar to those desribed in a previous paper. 5 The average stroke volume for eah steady state was determined by dividing the ardia output (dye dilution) by the heart rate. The average area under the flow rate urve of 1 to 12 ontrol beats during the steady state was equated to the average stroke volume, 1 and the stroke volume of individual beats was alulated from the ratio of the area under an individual flow urve over the average area. The volume hange (dv/dt) was determined at eah 2-mse interval of systole by either planimetri or eletrial integration of individual flow rate urves. n this manner the instantaneous radius of the ventrile ould be alulated from the volume equation of a sphere, V = 4/37rr. 3 Myoardial tensile fore (F) in dynes was alulated from the equation, F = 7TT 2 P, where P = intraventriular pressure in dynes/m 2 and r = radius of ventrile in m at eah interval of systole. The time derivative of fore (df/dt) was alulated as df/dt TTT 2 dp/dt-27rrp dr/dt or, 77T 2 dp/dt-rp (FSR), and is expressed as dynes/se. Using Hill's series elasti model as a funtional representation of musle ontration, 11 shortening of the ontratile element is expressed both as fiber shortening and as strething of the series elasti omponent (SE). ontratile element veloity (V e ) during ardia systole, therefore, must be derived as the sum of fiber shortening rate and the lengthening veloity of the SE. Thus, V e = FSR + dl/dt, where FSR - irumferential fiber shortening rate in m/se and dl/dt = lengthening veloity of the SE in m/se. FSR was derived from the expression: 3 FSR = flow rate/2r 2. dl/dt was determined from the rate of fore development and the stress-strain harateristis of the SE and this relationship an be expressed as: df/dt =

4 732 LEVNE, FOR WND, MNTYRE, SHEHTER B 4 ontrol o- - -o fterload, mild ontrol o - so volumi ontrol sovolumi 3 V'e 1 m/se 2 \ 1 \ \ X, / fl FORE, 6 dynes FGURE 2 Effet of afterload on fore-veloity relations of single systoles. Eah urve is onstruted from points made at 2-mse intervals of systole. During the early part of systole, foreveloity relations of the ontrol and afterloaded beats are idential and desribe an inverse relationship. s ejetion and fiber shortening proeed, a gradual divergene from the inverse urve ours, onave to the veloity axis, whih is not observed in the isovolumi beats (B and ) and is related to fiber shortening itself. n the ontrol beats, ejetion begins with the fourth point in panels and B, and with the third point in panel. Later in systole a more abrupt divergene from the inverse urve is seen and is assoiated with a simultaneous derease in fore and veloity. n the isovolumi beats, V generally is negative at this point (not shown). This late divergene from the inverse urve is due to deay of the maximum ative state. See text. (df/dl) (dl/dt). The method for determining df/dl appears below. s desribed previously, 7 ontratile element work (EW) was derived as the sum of foregenerating work (FGW), the work performed in strething the series elasti to peak fore, plus fiber shortening work (FSW e ), the work performed by the E in shortening the fiber. FGW was alulated from the equation, FGW = F P /S, where F p = peak fore in dynes and S = the linear slope of the (df/dl)-f relationship" in m" 1. FSW was derived by integrating the time ourse of fiber shortening power per beat. However, sine the SE aids the E in shortening the fiber after peak fore has been ahieved, this work performed by the reoiling SE was subtrated from the total FSW (J F X FSR) in the derivation of FSW e. Thus, FSW e = FSW = FSW se, where FSW se equals the work performed by the reoiling SE in shortening the fiber. Sine the energy expended by the reoiling SE in shortening the fiber was derived by strething the SE to peak fore, it is inluded in the energy balane of the heart as FGW rather than FSW. Diret measurements of intraventriular pressure, aorti root flow rate and dp/dt were made on the original traing and all derived alulations were performed by an BM 162 omputer.* The alulation of FSW e was made by re-plot and planimetry of the E power and fiber shortening power urves. n our earlier experiments the stiffness of the SE (df/dl) was derived by normalization of the linear relationship between df/dl and F found by Sonnenblik in the at papillary musle 2 and extrapolation to the speifi dimensions of eah dog's left ventrile. More reently we have measured the ative stiffness of the intat left ventrile in the dog in the following fashion: the afterload of two adjaent systoles was altered very slightly, suh that the total ontratile element work of the two beats was not hanged signifiantly (vide infra). Thus, EWi = EW 2. Sine EW = FGW + FSW and sine FGW = Fp/S, the above equation may be rewritten as: 'omputation enter, Tufts University, Medford, Massahusetts. irulation Researh, Vol. XV, June 1966

5 EFFET OF FTERLOD ON FORE-VELOTY RELTONS 733 B 4» ontrol» fter load, small &fterlooo', large ontrol oo fterload ontrol o o isovolumi / FORE. 6 dynes FGURE 3 (See legend for fig. 2). Divergene of fore-veloity relations from the inverse urve during the period of maximum fiber shortening is not always observed, partiularly when the afterload of the ontrol beat is large to begin with (B and ). n these instanes, fore-veloity relations move upward along the inverse urve before deay of the maximum ative state is apparent. See text. (F P )JS + FSW 1 - (F p ) 2 /S + FSWo. Solving for S, the ative stiffness of the ventrile at eah level of fore may be derived after normalizing for unit musle length. The normalized value for S found in this fashion was 17.7 ± 4.5 m- 1, while that found by Sonnenblik 9 in the at papillary musle was 32 ± 3.9 m- 1.* The value for S used in our earlier study 5 was 28.8 m" 1 and had been derived from normalization of one of Sonnenblik's first measurements of series elastiity. 2 s it was felt that the in vivo estimation of ative stiffness was more appliable to alulations in the intat dog than values obtained from the at papillary musle, the former was used in the present alulations of dl/dt. The details of the in vivo method form the subjet of a separate report. 32 Per ent extension of the SE was alulated as follows: l se = n %ase = p ^se/'o. where l sw, = hange in length of SE, l = initial fiber length, F p = peak fore in dynes, F^ = end diastoli fore in dynes and *s might have been predited, the ative stiffness of the intat left ventrile is signifiantly lower than that of the at papillary musle, due to the presene of nonontratile tissue in series with homogeneous musle and to nonsynhronous ontration of portions of the left ventrile. irulation Researh, Vol. XV, June 1966 S = slope of the (df/dl)-f relationship. The magnitude of the afterload in eah ardia yle was estimated by omparing the peak fore generated during that beat to the maximum fore (F o ) estimated from an adjaent isovolumi or near isovolumi ontration of the same diastoli fiber length and inotropi environment. Thus F o was derived by extension of the inverse foreveloity urve to the point of zero veloity in an isovolumi or near isovolumi ontration and the ratio of F p /F of both the ontrol and the afterloaded beats provided a measure of the afterload itself. Normalization of F o was derived in the following manner: the average left ventriular weight in grams was added to the average end diastoli volume in ml found in the ontrol studies, and the ross-setional area of musle at the equator of the spherial ventrile alulated. F o was then expressed as g/m 2. Results FORE-VELOTY RELTONS DURNG NORMLLY LODED BETS During the time ourse of a normal ardia systole, an inverse relation between fore and ontratile element veloity (V e ) was observed from early during the isometri period to well into the ejetion period (figs. 2 and 3).

6 734 LEVNE, FORWND, MNTYRE, SHEHTER However, in most instanes as fiber shortening ourred, the time ourse of fore-veloity relations desribed a gradual urve onave to the veloity axis prior to the point at whih peak fore was ahieved (fig. 2). Later in systole, divergene from the inverse urve was more abrupt and zero veloity was assoiated with low values of wall fore. n a smaller number of instanes, and partiularly those ontrol beats in whih the ratio of peak fore to isometri fore was large (large afterload ), fore-veloity relations remained on an inverse urve, onvex to both the fore and veloity axes, until after peak fore was ahieved (fig. 3). These latter urves resemble those reported in an earlier study 5 where the use of an orifie flowmeter resulted in partial aorti obstrution. s with the other ontrol beats, an abrupt divergene from the inverse urve was noted in these beats during the latter half of the ejetion period. Thus, two types of divergene from the harateristi inverse urve were noted during the time ourse of fore-veloity relations of normal ardia systoles. One was gradual, developing early in the ejetion period, and demonstrable only in those beats in whih there was substantial fiber shortening. The seond was more abrupt, ourred later in systole, and was present in all ardia yles examined. The greater the afterload and the less the fiber shortening per beat, the longer fore-veloity relations remained on a urve whih was onvex to both axes. f fore-veloity relations were examined very early in the isometri period (during the first 2 to 4 mse), veloities were often found whih were less than that predited from the entire urve. n the ontrol beats, peak fore was ahieved an average of 17 mse after the onset of pressure rise (38% of the duration of mehanial systole), and at a time when 17% of fiber shortening had ourred (table 1). Late divergene of the F-V e relations from the inverse urve, on the other hand, ourred an average of 164 mse after the onset of pressure rise and was only learly evident after 65% (45 to 81%) of fiber shortening had ourred. The average irumferential fiber shortening during the ontrol beats was 6.8% (5.2 to 11%) of the initial fiber length, while lengthening of the SE was 16.5% (12.1 to 18.4%). The average V max observed in these studies, derived by extrapolation of the inverse urve to the point of zero fore, was 2.5 ±.31 musle lengths/se. F o was more diffiult to estimate from these urves but averaged 4.5 ± 1.5 X 1 u dynes at the endoardial surfae or 343 g/m 2 when normalized for average ross-setional area of musle. f fore was alulated at a point halfway between endoardium and epiardium, the average F o was alulated to be 45 g/m 2. ontratile element work (EW) and power fell to zero at an average of 21 mse or at approximately 71% of the duration of systole. EW (table 2) average 4.75 ±2.1 dyne-m/beat, of whih 52% was devoted to fore generation and 48% to fiber shortening (FSW 1! ). The amount of work performed by the E in shortening the fiber onstituted an average of 76% of the total FSW; the remainder being aounted for by the reoiling SE. n these ontrol beats, the ratio of F p /F averaged 65% (±7.1%). EFFET OF HEGHTENED FTERLOD ON FORE-VELOTY RELTONS The effet of an abrupt inrease in afterload on the fore-veloity urve was suh as to shift the mid and late portion of the urve to positions of higher fore and lesser veloity, and extend the inverse urve towards the projeted F o. n most instanes the instantaneous ontratile element veloity during the ejetion period in the ontrol beat was less for a given wall fore than in the afterloaded beat (fig. 2). When these instantaneous veloities were orreted for hanging fiber length and expressed in musle lengths per seond, this differene in instantaneous veloity at a given fore was still learly apparent (fig- 4). Peak fore was ahieved slightly later in systole in the afterloaded beats (table 1), but at a time when a smaller fration of fiber shortening had ourred (12.7%). n the isovolumi beats peak fore was developed in irulation Researh, Vol. XV, June 1966

7 EFFET OF FTERLOD ON FORE-VELOTY RELTONS mse ompared to 93 mse in their ontrol beats. Late divergene of the fore-veloity relations from the inverse urve ourred at the same time following the onset of pressure rise in the mild to moderately afterloaded beats (161 mse) as in the ontrols (164 mse), but sine there was less fiber shortening, this divergene ourred at a longer fiber length. n the isovolumi beats, too, late divergene was evident at the same TBLE 1 Effet of fterload on Fore-Veloity-Length Relations in Normally Loaded ontrol Beats Dog B D E F G H J Expt verage verage P value t ±SD ±SD lo* F P d l l lo 11.% 9.5% lo d l >.l *l : initial irumferential fiber length, in m. 1 F : fiber length at peak fore. l d : fiber length at point of late divergene from fore-veloity urve. l: total fiber shortening, in m. t r : time of peak fore from onset of pressure rise, in se. p t d : time of late divergene, in se. t EW= : time at whih E veloity reahes zero, in se. %SE: per ent extension of the SE during systole (see text). t: ontrol. : afterload. t F p >.l td >.O7 tew=o >.O5 % SE 18.4% <.O6 irulation Researh, Vol. XV111, June 1966

8 736 LEVNE, FORWND, MNTYRE, SHEHTER time during systole (144 mse) as in the ontrols (142 mse), but ourred only as ontratile element veloity approahed zero (fig. 2B and ). ontratile element work and power fell to zero slightly earlier in the mild to moderate afterloaded beat than in the ontrols (P <.6), and this differene was exaggerated in the isovolumi beats. Thus, despite a prolongation in the duration of systole in the isovolumi beats from 277 to 39 mse, EW fell to zero in 141 mse ompared to 189 mse in the ontrols (P <.1). This may be interpreted as refleting a greater duration of negative work (deremental restraint on the reoiling SE) performed by the ontratile element in the isovolumi beats. The average fiber shortening in the afterloaded group was 4.5% ompared to 6.8% in the ontrols, while the per ent lengthening of the SE was inreased from 16.5 to 17.2% in the afterloaded beats, and to 21.8% in the isometri beats.* EFFET OF HEGHTENED FTERLOD ON ONTRTLE ELEMENT WORK The effet of a sudden inrease in afterload on EW was dependent upon two fators: (1) the magnitude of the afterload itself, and (2) the relationship of peak fore (F,,) of the ontrol beat to maximum isometri fore (Fo). n order to examine eah of these variables separately, the experimental results have been divided into two groups: (1) those studies in whih the ratio of F p /F in the ontrol beat was greater than 5% (table 2), and (2) those in whih the ratio of F p /Fo was less than 5% (table 3). n the former group, whih inluded the majority of interventions examined, a small inrease in afterload produed little if any hange in EW (table 2). When a major afterload was imposed, partiularly in the ase of the isovolumi beats, a large and onsis- *Per ent lengthening of the SE as derived from these alulations does not infer that the SE itself atually lengthened by this amount, sine series elastiity in these dogs was derived as the overall ative stiffness of the entire left ventrile. V e O \ hs/se) V ) ontrol sovolumi X v \, / FORE, 6 dynes FGURE 4 V e for the two heats illustrated in figure 2B is expressed here as instantaneous musle lengths/se. Note that the gradual divergene of the auxotoni ontrol urve during the period of maximum fiber shortening from the inverse urve of the isovolumi beat is still learly apparent. tent derease in total EW was observed. n the group of mild to moderate afterloaded beats the average derease in EW was to 9% of the ontrol levels, while in the isovolumi beats, EW averaged only 8% of the ontrol levels. This relationship between EW and the magnitude of the afterloading intervention is demonstrated in figure 5, where it is shown that as the ratio of F p /F of the afterloaded beat rises, the derease in EW beomes progressively greater. different response to afterload was observed in those experiments in whih the ontrol beat was lightly afterloaded and the ratio of F p /Fo was found to be less than 5%. Under these irumstanes, EW rose rather than fell in the afterloaded beat (table 3, fig. 5). Experiments 7 and 8 performed in the same dog are of interest in that a small afterload produed a rise in EW, while a large afterload resulted in less work performed. These studies indiate that the normal systole funtions near the peak of the E workload urve and that generally any further inrease in afterload dereases total ontratile irulation Researh, Vol. XV, June 1966

9 EFFET OF FTERLOD ON FORE-VELOTY RELTONS s * s ^ ' %of l4 - ontrol EW FGURE 5 Effet of afterload on EW. Per ent hange in EW is plotted against the hange in ratio of F p /F g produed by the afterload intervention. The interrupted lines represent those experiments in whih F p /F fl of the ontrol beat was less than 5%; the solid lines, those in whih F p /F g of the ontrol beat was more than 5%. n the lightly loaded ontrol beats, an inrease in afterload inreased EW in 7 of 8 experiments. When F p /F of the ontrol beat was more than 5%, a fall in EW was generally observed. element work, and that this derease is maximal in the isovolumi beat. Studies of the effet of an abrupt derease in afterload have not been done. However, in a single experiment, an abrupt derease in entral aorti pressure, suffiient to redue F p /Fo from 62 to 4%, produed a fall in EW of 24%. Disussion The interpretation of fore-veloity relations in the intat heart, studied in this fashion, is hampered both by a lak of preision in measurement and by the problem of multiple variables. This beomes partiularly important if one attempts to relate these observations to analogous findings in studies of isolated papillary musle. The method used in this study is based upon a number of assumptions, whih were made to permit reasonably simple estimations of ontratile element fore and veloity. The errors introdued by assuming a spherial ventrile, 8 synhronous musle ontration, 12 a homogenous left ventriular musle mass, 7 and a thin-walled left ventrile 13 have been disussed elsewhere. While it is possible that pathologial variations in these parameters play an important role in the physiology of diseases of the myoardium, there is reason to believe that the data obtained in the present study are in keeping with known physiologial data of the mehanis of normal isolated heart musle. Furthermore, an examination of the mehanis of the intat heart provides an opportunity to observe phenomenon of potential linial importane whih annot be studied in isolated musle. n addition to the problems mentioned above, an important distintion should be made between the time ourse of foreveloity relations onstruted from an auxotoni systole and the lassi fore-veloity urve of isolated musle. n analyzing the former it must be remembered that musle length is shortening ontinually and the in- irulation Researh, Vol. XV, June 1966

10 738 LEVNE, FORWND, MNTYRE, SHEHTER TBLE 2 Effet of fterload on ontratile Element Work in Normally Loaded ontrol Beats Dog Expt. FGW* FSW FSWe EW D H 1 verage t Mild to Moderate fterload Per ent of ontrol EW # FGW: fore-generating work in dyne-m/beat. FSW: total fiber shortening work in dyne-m/beat. FSW : fiber shortening work performed by the ontratile element in dyne-m/beat. EW: ontratile element work in dyne-m/beat. F p /F : ratio of peak fore to projeted isometri fore (see text). f: ontrol. : afterload. : isovolumi. tensity of the ative state is also hanging. While the vagaries of fiber shortening are eliminated in the isovolumi ontrations of the ventrile, the hanging intensity of the ative state still must be rekoned with if measurements are to be made at different times throughout systole. The signifiane of "projeted isometri fore," for example, will F,,Fo be different in these studies from the fore interept of the fore-veloity urve of tetanized skeletal musle, where the intensity of the ative state is onstant. The signifiane of the "projeted isometri fore" derived from sequential fore-veloity points from a single isovolumi systole, is not fully understood, and while omparisons between this value and irulation Researh, Vol. XVlll, June 1966

11 EFFET OF FTERLOD ON FORE-VELOTY RELTONS 739 TBLE 2 ontinued from opposite page* Dog K L M N P Q Expt FGW* FSW sovolumi FSWe fterload EW Per ent of ontrol EW Fp/Fo % verage *For symbols see footnotes of table, opposite page. TBLE 3 Effet of fterload on ontratile Element Work in Lightly Loaded ontrol Beats Dog R T U verage Expt. FGW* FSW* FSWo* EW* See footnote, table 2. irulation Researh, Vol. XV, June Per ent of ontrol EW S Fp/Fo* %

12 74 LEVNE, FORWND, MNTYRE, SHEHTER maximum isometri fore of isolated ardia musle are examined autiously, it must be realized that the two are not analogous. The same aution must be exerised in the examination of other variables; i.e., V mnx, afterload, ative stiffness, et., whih are not diretly omparable to their designated ounterparts in isolated musle. While designations may be used in the present study to onvey a funtional similarity to measurements made in lassi musle physiology, eah should be examined in the ontext of the design of the experiment, identifying whenever possible how the partiular measurement differs from that made in studies of isolated musle. The maximum veloity of the ontratile element of ardia musle has been shown to be dependent upon inotropi environment, 2 ' heart rate, 1 ' 6 and temperature. 14 at papillary musle stimulated at a rate of 3/min at 2 to 23 exhibits maximum veloities of approximately 1. to 1.3 musle lengths per seond. 2 - Ullrik has shown that with a 1 inrease in temperature, V max inreases in the rat heart roughly twofold. 14 nasmuh as the present studies in the intat dog heart were arried out at heart rates of 12 to 18/min at body temperature, the finding of an average V mn x of 2.5 musle lengths/se is not unexpeted. While maximum isometri fore is a funtion of initial fiber length, Sonnenblik found an average F o of 352 g/m 2 in the at papillary musle, although at the apex of the length-tension urve, values as high as 9 g/m 2 were observed. 2 Ullrik found isometri tensions of 5 g/m 2 in rat trabaulae arneae funtioning at optimal length, and further showed that this value was uninfluened by hanges in temperature. 14 n our studies, the average F n was estimated to be 45 g/m. 2 While no diret orrelative measurements of ative state were attempted in these experiments, ertain observations were made whih may shed some light on the time at whih maximum ative state is developed and begins to deay during the normal systole. For example, in most experiments within 4 mse of the onset of pressure rise, fore-veloity relations were suh as to appear to be on the same inverse urve, onvex to both axes, as was desribed by the subsequent fore-veloity points of that beat throughout the first half of systole. This was partiularly true of the isovolumi beats, where an inverse urve ould be onstruted at a single fiber length, whih enabled one to predit the instantaneous veloity whih should be ahieved at a given low value of fore early in systole, if all fibers were ativated equally and maximally. f, for example, the inverse portion of the fore-veloity urve of an isovolumi beat was extended to the veloity axis, the veloity whih should exist at low fores very early in systole an be predited from the extended portion of the urve. That lower veloities were observed during this time may be explained either by asynhrony of left ventriular ativation or by a gradual development of the maximum ative state. Whihever the ase, it may be inferred that in most instanes the ventrile is fully ativated and the intensity of the ative state is lose to maximal within 3 to 5 mse after the onset of pressure rise in these hearts. Furthermore, it would appear that a rapid fall-off in the intensity of the ative state does not generally our earlier than 2 mse before peak fore is ahieved in the isovolumi beats, and that this may our well after peak fore is reahed in normally loaded or mildly afterloaded beats. This is inferred from the observation that the late, generally abrupt divergene of the fore-veloity relations from the inverse urve ours at the same time in systole in the normally loaded and afterloaded beats, and that it is independent of fiber shortening (viz. the isovolumi beats). The only reasonable explanation for this abrupt derease in E veloity in the absene of fiber shortening is a derease in the intensity of the ative state of the ventrile. t is not known whether this is due to the fat that some fibers may ease ontrating earlier than others or that an abrupt derease in the intensity of the ative state of all ventriular fibers ours at this time. t would appear, however, that an irulation Researh, Vol. XV, June 1966

13 EFFET OF FTERLOD ON FORE-VELOTY RELTONS 741 abrupt fall-off in the intensity of the ative state of the ventrile as a whole is manifest by a onspiuous fall in the instantaneous veloity at a given wall fore, and that a sudden inrease in afterload does not seem to alter the duration of the apparent maximum ative state in the next ardia yle. s afterload is inreased, the point at whih ontratile element veloity reahes zero ours earlier and earlier in systole. t the same time, however, the duration of negative E veloity and hene negative E work is prolonged. Of the total ontratile element work done by the normal dog systole, about 5$ was expended as internal or fore-generating work. This is onsiderably more than has been found in the at papillary musle, where internal work at the apex of the E work-load urve was about 36$ of the total work performed, 9 and is due largely to the fat that the value for ative stiffness of the left ventrile used in our alulations of fore-generating work was onsiderably lower than that found by Sonnenblik in isolated papillary musle. This is not to be interpreted as signifying that true series elastiity of the ontratile apparatus is different in the intat heart than it is in isolated musle, but rather that other fators (vide supra) besides series elastiity itself determine the funtional ative stiffness of the entire ventrile. EFFET OF FBER SHORTENNG The effet of afterload on fore-veloity relations during the ourse of a single systole involves not only reiproal hanges in both fore and veloity aording to their hyperboli relationship, but also invokes the effet of hanging instantaneous fiber length upon this relationship. lthough the impliations of the Frank-Starling mehanism have been realized for years, Sonnenblik has shown in the at papillary musle that an inrease in fiber length inreases the maximum isometri fore of musle but does not alter the maximum veloity. 6 n their studies of the intat dog heart, Fry et al. 4 suggested that myoardial funtion be represented by a "three dimensional fore-veloity-length surfae" and irulation Researh, Vol. XV, June 1966 onluded that the work aomplished by the heart must depend on the path traveled on this surfae per beat. While these onlusions were drawn from analyses of single volume points in different systoles, a similar suggestion was made utilizing the present tehni of analyzing fore-veloity points at varying fiber lengths in the same systole. 5 The present results are in keeping with this hypothesis and demonstrate that after ejetion begins, foreveloity relations diverge downwards from the inverse urve of an adjaent afterloaded beat starting from the same initial volume (fig. 4). This divergene is learly evident before the apparent fall-off in maximum ative state and is only demonstrable in those beats in whih afterload is not unusually high. Late divergene of the fore-veloity relations from the inverse urve is related to deay of the intensity of the ative state and has been shown to be independent of fiber shortening per se (vide supra). There is reason to believe that the relatively small amount of fiber shortening observed in the majority of ontrol beats is suffiient to aount for a major fall-off in instantaneous wall fore. The average fiber shortening in the ontrol beats was only 6.8%. However, a derease in fiber length of 6.5$ in the at papillary musle was found to produe a derease in isometri fore to only two-thirds of the initial value,* suggesting that sequential dereases in fiber length during the ourse of a normal systole should be assoiated with a notieable derease in wall fore regardless of hanges in the intensity of the ative state. The failure to demonstrate a derease in projeted isometri fore in some ontrol beats whih already sustain rather high afterloads (fig. 3) is not lear, but probably reflets the limitations of this method to detet the effet of small hanges in instantaneous fiber length. EFFET OF FTERLOD ON ONTRTLE ELEMENT WORK The effet of an abrupt hange in afterload on the total work performed by the ontratile element depends upon the magnitude and Taken from figure 13. 2

14 742 LEVNE, FORWND, MNTYRE, SHEHTER diretion of the hange in afterload and on the afterload of the ontrol beat itself. t is evident from examination of the fore-veloity urve itself that the more time the heart spends funtioning in the middle of this urve, the greater will be the total systoli power and work, and onversely, the more time spent at very high or very low loads, the less work and power will be performed. This essentially is the basis for the observed effet of afterload on E work and is illustrated diagrammatially in figure 6. Unless a ontrol beat was funtioning at a lower than optimal afterload, an inrease in afterload resulted in less E work performed and this derease in work was related to the magnitude of the new load. t should be noted in this ase that two opposing mehanisms are brought to bear by a heightened afterload whih will influene total ontratile element work. By virtue of less fiber shortening, the mean F o of the afterloaded beat (whih represents the average for the omposite fore-veloity urves of that systole) will be greater than in the ontrol beat. Were it not for hanges in afterload, this inrease in mean F o would enable more work to be performed during this beat. However, it would appear that the advantage of an inreased mean F o is outweighed by reiproal hanges in fore and veloity on the new urve suh that less power and work are produed even though isometri fore is extended. The net result is a derease in total ontratile element work. n those ontrol beats in whih the ratio of F p /Fo was low (less than 535), a moderate inrease in afterload permitted the ontratile element to perform a greater amount of work. onversely, in one experiment a redution in afterload from a normal ontrol beat resulted in a marked derease in total work performed. The variable response of external stroke work to a moderate inrease in afterload reported by mperial et al., 15 an probably be explained on this basis. s pointed out by Wilken et al., 1 these workers utilized lightly afterloaded ontrol beats. Thus, a moderate inrease might atually inrease stroke work as well as total ontratile element work, while a major in- VELOTY m / se POWER dyne-m/se FORE, dynes v\ TME, seonds FGURE 6 : Diagram of fore-veloity relations desribed by (1) a lightly loaded beat; (2) a normally loaded beat; (3) a moderately afterloaded beat; and (4) an isovolumi beat. s the afterload is inreased, the mean projeted F of that beat is inreased, and reiproal hanges in fore and veloity are observed suh that more time is spent at positions of greater fore and lesser veloity. Only values of positive V e are shown. B: Power-time plots of the ontratile element for eah of the four urves shown in. The area under eah of the power-time plots represent EW and the relative values of EW for these four beats are 4.64, 6.65, 6.11, and 5.69 respetively. Thus, the seond beat generates maximum EW and lesser or greater loads result in a derease in total work performed. rease onsistently depressed stroke work. n studies of unanesthetized dogs by Wilken and his olleagues, 1 an abrupt inrease or derease in aorti impedane from a normal level resulted in no hange or a fall in external stroke work. t has been shown that the external work done by isolated ardia musle is maximal at 4 to 5% of the isometri load. 6 ' 9 arlson 1 has alulated both the external and internal B irulation Researh, Vol. XVlll, June 1966

15 EFFET OF FTERLOD ON FORE-VELOTY RELTONS 743 work of isolated skeletal musle and found that the ontribution of the latter to the total work of the musle was very small. n his studies, internal work (work performed in strething the series elasti) at isometri load was about 17% of the maximum total work ahieved by that musle. Sonnenblik has made a similar analysis in the at papillary musle and beause of a greater series elastiity in ardia musle, found internal work to omprise a more important fration of the total work of the ontratile element. 9 n his studies, the internal work done at isometri load was approximately 55% of the maximum total work performed at a given fiber length. Beause the addition of internal work to external work assumes greater and greater proportions with inreasing load, the apex of the E work-load urve was observed at 6 to 65% of isometri fore. n the present study, too, the average ratio of peak fore: isometri fore in the ontrol beats was 65%, and assuming that peak fore varies losely with mean fore during a ardia systole,* this would suggest that these ontrol beats are operating near the apex of the E work-load urve. s these dogs were studied under barbiturate anesthesia with heart rates and blood pressures in exess of normal, it is possible that the true apex of the work-load urve may be at a slightly lower load than indiated here. However, from the data in figure 5, it would appear that despite this altered hemodynami state, autoregulatory mehanisms had probably re-established steady state onditions during the ontrol beats and that the apex of the work-load urve lies somewhere near 6% of the isometri load. These studies suggest that the normal systole tends to maintain an optimal relationship between fore and fiber shortening, suh that a maximal amount of ontratile element work is performed within the ditates of a given fore- *The average ratio of F p /mean fore in ontrol beats and isovolumi beats ombined was 1.86 ±.18, although the ratio inreased slightly with inreasing afterload. Based on the average ratio for ontrol beats only, F p in the isovolumi beats overestimated mean fore by an average of 19%. irulation Researh, Vol. XV111, June 1966 veloity urve or omposite of fore-veloity urves. t would seem likely that deviations from this optimal state may play an important role in reruiting mehanisms whih maintain a normal ardia output. Summary The effets of heightened afterload on foreveloity relations and on ontratile element work of single systoles were examined in the intat dog heart. The fore-veloity urve desribed during the ourse of a normal systole represents a omposite of urves, eah with its own projeted isometri fore determined by instantaneous hanges in fiber length. During the first systole following an afterload intervention, reiproal hanges in fore and veloity were observed together with an extension of the projeted isometrifore. The effet of afterload on ontratile element work was determined by: (1) the diretion and magnitude of the afterload, and (2) the afterload of the ontrol beat itself. When the ontrol beat was lightly loaded, an inrease in afterload inreased ontratile element work by two additive mehanisms: (1) an inrease in mean isometri fore, and (2) a shift of fore-veloity relations to positions of greater power and work prodution. n normally loaded ontrol beats, an inrease in afterload resulted in a derease in ontratile element work, despite the fat that mean isometri fore was inreased. n this instane, fore-veloity relations were shifted to positions where less power and work ould be ahieved. Thus, the normal systole appears to funtion at the apex of the ontratile element work-load urve (near 6% of the isometri load). Evidene is presented whih suggests that the apparent maximum ative state of the entire left ventrile is generally ahieved within 3 to 5 mse after the onset of pressure rise, and that its deay is aompanied by abrupt divergene of the fore-veloity relations from the inverse urve of that beat. sudden inrease in afterload does not appear to influene the duration of the maximum

16 744 LEVNE, FORWND, MNTYRE, SHEHTER ative state, although the duration of positive ontratile element work is shortened and that of negative ontratile element work prolonged. knowledgment The authors thank Dr. Rihard Gorlin and Dr. Shapur Naimi for their help in reviewing this manusript and aknowledge the tehnial assistane of Miss Marella zarneki and the seretarial aid of Mrs. Judith Goldberg. Referenes 1. BBOTT, B., ND MOMMEHTS, W. F. H. M.: study of inotropi mehanisms in the papillary musle preparation. J. en. Physiol. 42: 533, SONNENBLK, E. H.: mpliations of musle mehanis in the heart. Federation Pro. 21: 975, BBOTT, B., ND WLKE, D. R.: The relation between veloity of shortening and the tension-length urve of skeletal musle. J. Physiol. 12: 214, FRY, D. L., GRS, D. M., JR., ND GREENFELD, J.., JR.: Myoardial mehanis: tensionveloity-length relationships of heart musle. irulation Res. 14: 73, LEVNE, H. J., NDBRTMN, N..: Fore-veloity relations in the intat dog heart. J. lin. nvest. 43: 1383, SONNENBLK, E. H.: Fore-veloity relations in mammalian heart musle. m. J. Physiol. 22: 931, BRTMN, N.., ND LEVNE, H. J.: ontratile element work: a major determinant of myoardial oxygen onsumption. J. lin. nvest. 43: 1397, GORLN, R., ROLETT, E. L., YURHK, P. M., ND ELLOTT, W..: Left ventriular volume in man measured by thermodilution. J. lin. nvest. 43: 123, SONNENBLK, E. H.: Series elasti and ontratile elements in heart musle: hanges in musle length. m. J. Physiol. 27: 133, WLKEN, D. E. L., HRLEB,.., HOFFMN, J.. E., ND Guz,.: Effets of alterations in aorti impedane on the performane of the ventriles. irulation Res. 14: 283, HLL,. V.: The heat of shortening and the dynami onstants of musle. Pro. Roy. So. London. Ser. B 126: 136, FORWND, S.., MNTYRE, K. M., LPN, J., ND LEVNE, H. J.: tive stiffness of the intat anine left ventrile. n preparation. 13. SNDLER, H., ND DODGE, H. T.: Left ventriular tension and stress in man. irulation Res. 13: 91, ULLRK, W. : harateristi fore-veloity equation of rat heart musle. m. J. Physiol. 26: 1285, MPERL, E. S., LEVY, M. N., ND ZESKE, H.: Outflow resistane as an independent determinant of ardia performane. irulation Res. 9: 1148, RLSON, F. D., HRDY, D. J., ND WLKE, D. R.: Total energy prodution and phosphoreatine hydrolysis in the isotoni twith. J. Gen. Physiol. 46: 851, irulation Researh, Vol. XV, June 1966