Myocardial relaxation and passive diastolic

Transcription

1 PTHOPHYSIOLOGY ND NTURL HISTORY VENTRICULR PERFORMNCE Myocrdil relxtion nd pssive distolic properties in mn. PSIPOULRIDES, M.D., PH.D., ISREL MIRSKY, PH.D., OTro M. HESS, M.D., JOERG GRIMM, PH.D., ND HNs P. KRYENBUEHL, M.D. BSTRCT We hve developed model for ssessing the influence of the decying contrctile systolic tension on distolic wll dynmics nd the pssive properties of left ventriculr muscle. Totl mesured left ventriculr distolic pressure nd stress (T) re determined by two overlpping processes: (1) the decy of ctively developed pressure nd stress (5) nd (2) the buildup of pssive filling pressure nd stress (C*). The decying contrctile stress is formulted in terms of relxtion pressure with time constnt (T) ssessed during the isovolumic relxtion intervl. By subtrcting the contribution of from T we obtin *. With micromnometry, echocrdiogrphy,nd cinengiogrphy, totl nd pssive stress-strin reltions nd strin rtes were evluted over the entire filling period in six norml control subjects nd in seven ptients with ortic stenosis. Elstic stiffness constnts (k), the slopes of the liner pssive stiffness vs * reltions, did not differ in the two groups over common lower stress rnge (6/6 norml, k = ; 7/7 ortic stenosis, k = ). Over higher * rnge, trnsition into much steeper liner region occurred, nd k vlues were much lrger (4/7 ortic stenosis, k = ). When distolic stress levels re elevted, pssive stiffness-stress reltions cn be better described s biliner, with much greter wll stiffness constnt in the higher thn in the lower stress rnge. Dynmic effects of decying systolic contrctile wll stress components re importnt in the rpid filling phse in norml herts s well s in those with ortic stenosis. Circultion 74, No. 5, , NIML nd clinicl investigtions hve demonstrted tht distolic pressure-volume reltions cn be ltered either by cute interventions, such s hypoxi nd ischemi, or by chronic disese sttes such s pressure overlod. 1-3 Mthemticl nlyses-6 hve shown tht the effects of chnges in chmber geometry nd wll mss hve to be distinguished from those of chnges in the elstic properties of the crdic muscle itself. In such nlyticl models it is ssumed tht the ventriculr wll cts s pssive medium nd the models cn be pplied to the beting ventricle only in the ltter prt of distole, time when contrctile stresses hve decyed to negligible levels. In erly distole, fter mitrl vlve opening, left ventriculr pressure continues to fll, lthough the chmber is expnding.7' The erly distolic devition from wht is ex- From the Deprtment of Medicine, Hrvrd Medicl School nd Peter Bent Brighm Hospitl, Boston, nd the Deprtment of Inteml Medicine, Crdiology, University Hospitl, Zurich, Switzerlnd. Supported by USPHS grnts HL nd HL 2552 from the NHLBI nd by the Swiss Ntionl Science Foundtion. ddress for correspondence: res Psipoulrides, M.D., Ph.D., Director of Reserch, Crdiology Service, Deprtment of Medicine, Brooke rmy Medicl Center, Fort Sm Houston, TX Received Dec. 28, 1983; revision ccepted July 31, pected of purely pssively distended elstic chmber hs continued to preclude better understnding of the mechnicl behvior of ventriculr muscle throughout the entire distole. In this study we hve developed model for ssessing the influence of erly incomplete ventriculr relxtion on wll dynmics nd the pssive stiffness of crdic muscle with dt from the entire filling period. Methods Generl considertions. The elstic stiffness of intct pssive ventriculr muscle cn be expressed by n incrementl modulus concept. lthough the overll myocrdil stress-strin response curve is nonliner, it is possible to consider it to be incrementlly liner over smll successive subrnges of stress nd strin. Rther thn remining constnt, the incrementl modulus of pssive muscle increses with incresing stress levels, indicting progressive stiffening of the wll. From the study of Mirsky nd Rnkin,5 the incrementl modulus levels for the wll of pssive elstic chmber re proportionl to the rtio of the increment of stress to the ssocited increment of strin. If the mesured pressure is used to ssess stiffness, this incrementl modulus, s well s ll other heretofore vilble stiffness criteri, ttins implusible negtive vlues with dt from erly distole becuse pssive dynmics re confounded by the decying contrctile wll tension. Definition of pssive stress over the entire filling period. Vol. 74, No. 5, November

2 PSIPOULRIDES et l. W CL) xr~~~~~ TIME FIGURE 1. Schemtic representtion of the instntneous distolic left ventriculr mesured pressure (PM) s the sum of the decying relxtion pressure (PR) nd the incresing pssive filling p pressure (P*). The totl stress computed throughout distole by mens of the mesured pressure (PM) comprises ctive s well s pssive stress components. ccording to our model, its time course is governed by the evolution of two opposing processes: continuing decy of ctive contrctile stress nd grdul buildup of pssive filling stress. Estimtion of pssive muscle stiffness hinges on the ssessment of pssive stress levels in distole. The ctive stress is mnifest in the ugmenttion of mesured ventriculr pressure from levels tht would be expected t ny given stte of filling of the chmber in bsence of persisting ctively developed wll tension. Since wll relxtion does not cese bruptly, nor is it complete t mitrl vlve opening, the net pssive distolic filling pressure (P*) is given by the difference between the totl mesured pressure PM nd the vlues of the relxtion pressure (PR) tht would pply if the ventricle hd continued to relx isovolumiclly (figure 1). Thus, the pssive stress C* needed to ssess pssive stiffness (E*INc) levels over the entire filling period is obtined by using P*, the difference between mesured nd relxtion pressures, insted of the mesured pressure itself in the generl formul for wll stress. To obtin the relxtion pressure PR (t), we mke use of the concept of relxtion time constnt of isovolumic pressure fll described by Weisfeldt's group.9' 1 The relxtion time constnt (T) ws determined from the portion of the isovolumic left Quntities obtined in the beting ventricle by using P* (t) insted of PM (t) s the pressure fctor, re denoted by n sterisk. 992 ventriculr pressure following mximum negtive dp/dt, which cn be dequtely described s n exponentil decy. The lower cutoff pressure dt point used in the regression exceeded the subsequently ttined end-distolic pressure level by t lest 3 mm Hg to llow for the possibility tht the isovolumic relxtion period might be shorter thn is generlly ccepted. From time t =, corresponding to P, the first point on the exponentil portion of the pressure curve, up to the time of mitrl vlve opening, the left ventriculr pressure decy conforms to the generl eqution: PR (t) - P * e-l T + PB where the subscript R identifies the decying vrible s "relxtion pressure" nd PB is n svmptote. In the method developed by Frederiksen et l.9 PB is zero, while in the pproch introduced by Crig nd Murgol it 1 my ssume nonzero vlues nd cn represent n dditive bseline shift. Beginning with mitrl opening, the rte of decline of the pressure tht is ctully mesured, PM, towrd its distolic minimum, flls short of the rte given by the bove eqution. This follows becuse PM vlues in the filling ventricle reflect not only the ongoing relxtion process, but lso the simultneous pssive pressure buildup ssocited with filling. s time of mitrl opening we thus tke the nominl instnt t which the mesured pressure PM begins to diverge from the decying relxtion pressure PR We ssume tht the devition from the relxtion pressure PR in the presence of filling is cused by the development of the pssive filling pressure component. This is in greement with findings obtined by the mitrl inflow occlusion technique in the intct beting ventricle of the dog12: when pressure trces from filling nd nonfilling bets re superimposed, with the onset-of filling the observed erly distolic pressure decy slows down mrkedly compred with its rte in the bsence of filling. Thus the pressure mesured with distolic filling devites from the decying isovolumic relxtion pressure. ssessment of pssive stiffness levels during the entire distolic filling period. Once pssive stress cr* levels re scertined using the net filling pressure P* in the stress formuls, they cn be combined with simultneous geometric dt over the entire filling period to ssess operting levels of n elstic incrementl modulus in the beting ventricle. The formul for the modulus then reduces to E*INC = K */ ln B where In B denotes the nturl logrithm of the midwll minor semixis nd k is geometric fctor5 tht remins pproximtely constnt through distole. In principle, if sttisticl nlysis of pssive stress vs In B dt indictes significnt residul vrition of stress not ssocited with the vrition of In B, investigtion of other components besides the elstic one would be in order. Potentilly, other pssive components might include rte-dependent murl viscous effects. Since our dt showed only smll residul vrition, we did not tke up viscoelstic nlyticl models in this study. Hemodynmic mesurements. Hemodynmic mesurements were obtined fter conventionl dignostic right nd left hert ctheteriztion in dult ptients who hd given informed consent. The ptient popultion studied comprised six control ptients with norml left ventriculr function, ctheterized becuse of typicl chest pin, nd seven ptients with moderteto-severe pure ortic vlvulr stenosis without ssocited regurgittion. Hemodynmic dt nd indexes of systolic function for both groups re provided in tble 1. Selective coronry rteriogrms were norml in ll cses, nd there were no ngiogrphic regionl wll motion bnormlities or synergy. The ptients were premedicted with 1 mg chlordizepoxide hydrochloride CIRCULTION

3 PTHOPHYSIOLOGY ND NTURL HISTORY-VENTRICULR PERFORMNCE TBLE 1 Left ventriculr hemodynmic dt nd systolic functionl indexes (men ± SD) (+ dp/dt)mx LVEDP LVEDV LVSP LVESV EF (+ dp/dt)mx P (-dp/dt)mx (mm Hg) (ml) (mm Hg) (ml) (%) (mm Hg/sec) (sec 1) (mm Hg/sec) Control group ±2 ±26 ±12 ±16 +7 ±295 ±13 ±22 ortic stenosis group ±8 ±49 ±27 ±3 ±9 ±48 ±11 ±289 p vlues (control vs ortic stenosis) <.1 NS <.1 NS NS NS NS NS EF = ejection frction; LVEDP = left ventriculr end-distolic pressure; LVEDV = left ventriculr end-distolic volume; LVESV = left ventriculr end-systolic volume; LVSP = left ventriculr pek systolic pressure; P = pressure; ( + dp/dt)mx = mximl rte of rise of left ventriculr pressure; ( - dp/dt)mx = mximl rte of fll of left ventriculr pressure. (Librium) dministered orlly 1 hr before ctheteriztion. Detils of the mesurement methods nd procedures used in obtining the hemodynmic dt nd in the dignostic ctheteriztion studies hve been presented in previous publiction.'3 Briefly, digitl left ventriculr pressure-dimension dt for complete crdic cycle were obtined from simultneous recordings of high-fidelity pressure nd echocrdiogrphic dimeter. The resonnt frequency of the Millr No. 7F micromnometer, introduced into the left ventricle through No. 11.5F Brockenbrough trnsseptl ctheter, is 25 to 35 khz. The micromnometer ws blnced nd zeroed t 37 C before insertion nd ws clibrted ginst conventionl pressure trcing with fluid-filled ctheter. The frequency response of the recording system, including the tip trnsducer nd the DC mplifier, ws flt to beyond 1 Hz. Single-bem M mode echocrdiogrms (Ekoline 2, Smith-Kline Instruments) were obtined with the ptient in the nteroposterior or slightly right nterior decubitus position. 5/8 inch 2.25 MHz trnsducer, llowing nominl xil resolution of.68 mm ws used, trnsmitting 1 gsec ultrsound pulses t rte of 1/sec. The echocrdiogrphic endocrdil dimension ws ssessed from the septum to the posterior wll just below the mitrl vlve leflets. The crdic cycle for which the simultneous LV pressure-dimension dt were digitized every 5 to 7 msec for nlysis ws selected from bets recorded over one full respirtory cycle. The criterion for selection ws n end-distolic pressure corresponding to the rithmetic men of the highest nd lowest end-distolic pressures of respirtory cycle. The crdic cycles nlyzed occurred pproximtely midwy between the extremes of inspirtion nd expirtion. Left ventriculr cinengiogrphy ws performed with the ptient in the right nterior oblique (RO) position, nd end-distolic mjor nd minor internl xes were mesured ngiogrphiclly ccording to Dodge's re-length method. End-distolic wll thickness ws determined from the left ventriculr silhouette in the RO position or from second contrst dye injection in the nteroposterior projection. Clcultions: left ventriculr dynmic geometry. The left ventricle is ssumed to be n ellipsoid"3 14 with uniform wll thickness. From the end-distolic ngiocrdiogrphic mesurements, we obtined vlues for the wll volume VW, nd for the rtio (R) of the outer mjor Lo to minor Do xis (R = L/DO) t end-distole for ech individul left ventricle studied. We ssumed tht VW nd R remin pproximtely constnt throughout filling. The constncy of the outer rtio R is comptible with substntil chnge in the inner xes rtio becuse of considerble thinning of the thick wll with filling. 14 Precise ntomic mesurements on rrested cnine herts'5 show tht the outer Vol. 74, No. 5, November 1986 rtio (R) chnges by less thn 5% between end-systole nd enddistole; yet, the corresponding chnge of the inner rtio mounts to over 25%. In greement with these findings, under the ssumption of constnt R, the chnge undergone by the inner rtio between end-systole nd end-distole ws substntil (combined verge, % [SD]) nd did not differ significntly between our two groups, rnging from 8% to 35% in both the norml nd the ortic stenosis settings. tfhese vlues re completely comptible with the chnges undergone by the inner rtio, which were mesured by utomted quntittive video ngiocrdiogrphy in norml subjects nd in ptients with ortic stenosis by Heintzen nd Stephn.'6 Using the ngiogrphic R nd VW vlues nd the digitized M mode echocrdiogrphic mesurements of the nominl inner minor xis D(t), we solved for DJ(t) throughout distole ccording to the following cubic eqution: D 2 6 Do3 -[(R- 1) L4 Do - (-6 vw + D3) / R = R FT Using these computed Do(t) nd the corresponding echocrdiogrphic D(t) vlues, we evluted instntneous vlues for wll thickness h(t) nd inner long xis L(t) h = (Do -D) / 2 L = Lo- 2h, where L = R Do The instntneous midwll minor semixis B(t) nd midwll mjor semixis (t) were then computed s B = (D + h)/ 2 = (L + h)/ 2 The B(t) vlues were used to compute the nturl logrithm, ln B, throughout the filling period. Strin rte clcultion. The strin rte dc/dt tht ws used is equivlent to n instntneous normlized midwll circumferentil fiber lengthening velocity evluted in terms of the midwll minor semixis B, nmely: dc/dt = (I/B) * db/dt = d(ln B)/dt Derivtives were obtined digitlly by Lgrngin numericl differentition lgorithm. Generl expressions for stresses. The previously published generl expression for the difference between circumferentil o nd rdil r midwll stresses t the representtive equtoril region is5: CV = Go - Cr = P (B/h) (1 - B2/22-3h2/8B2) With the mesured pressure PM s the pressure fctor, this 993

4 PSIPOULRIDES et l. eqution ws used to ssess the totl stress CT throughout distole. This eqution ws lso dpted to the ssessment in the beting ventricle of the pssive stress c6* throughout the entire filling period. This ws done, s indicted in the section developing the model, by substituting the pssive pressure P* s the pressure fctor P in the bove generl expression t ll dt points throughout the filling period. This point-by-point substitution lso llows evlution of the individul pssive murl stresses (i.e., o*, C *, r*) throughout filling. Sttistics. Differences between group mens for norml subjects nd ptients with ortic stenosis were nlyzed sttisticlly by n unpired, two-tiled Student's t test. When nonprmetric ltemtives to the t test were indicted, becuse no priori ssumption s to the normlity of specific popultion distribution seemed wrrnted, the sign test nd the Wilcoxon signedrnk test for loction of the medin were used. Differences were considered to be sttisticlly significnt t p <.5. Vlues re expressed s men ± SEM unless stted otherwise. stndrd devition of the stress dt points from the three-prmeter modified exponentil lest-squres curve ws clculted ccording to the pproch of Noble et l. 17 The squre of these SD estimtes is prcticlly equl to the sum of squres per dt point used by Rnkin et l. 18 correltion coefficient ws lso estimted by the method of Noble et l.'7 'L 8or 64p Results Net pssive filling pressure. The net pssive filling pressure P*, the difference between totl mesured left ventriculr pressure PM nd relxtion pressure PR, is demonstrted in figure 2. fter the nominl instnt of mitrl vlve opening, the point-by-point difference between PM nd PR is seen to increse continuously throughout the filling period, in contrst to the mesured left ventriculr pressure itself, which first exhibits minimum during erly filling (see lso figure 1). In the cse shown, mitrl opening tkes plce t mesured left ventriculr pressure of bout 12 mm Hg, corresponding to the instnt t which the mesured pressure strts to devite from the decying relxtion pressure. Vlues of the relxtion time constnt T, which enters in the definition of the relxtion pressure PR5 did not differ significntly in the two groups studied (norml, msec; ortic stenosis, msec, p >. 1). The correltion coefficient for the best exponentil fit to the mesured pressure dt during the isovolumic phse of relxtion ws high (r >.99, F > 4), indicting strong, lbeit not necessrily perfect,28 monoexponentil reltionship. When pplied to these bets, midwy between the extremes of inspirtion nd expirtion, the pproch of Crig nd Murgo,"1 llowing for finite symptote in the isovolumic pressure decy, yielded smll nonzero PB vlues (norml, mm Hg; ortic stenosis, -.44 ±.37 mm Hg). These vlues were found not to differ significntly from zero, both by the robust sign test nd the powerful Wilcoxon signedrnk test for loction of the estimted medins of PB PR TIME FIGURE 2. Computer plot of the mesured (PM) nd the relxtion (PR) pressures; the pssive filling pressure (P*) is given by their point-bypoint difference throughout the filling period. The pressure xis is clibrted in mm Hg, the time xis in rbitrry units of time (digitized dt point number). (norml, -.61 mm Hg; ortic stenosis, -.49 mm Hg; both groups combined, -.49 mm Hg). ccordingly, the relxtion pressure estimted by the method of Frederiksen et l.9 could be used in the subsequent steps of the nlysis. The question of how nonzero PB level could modify the dynmic reltionships tht we develop is ddressed in the Discussion (see figures 6 nd 7). Totl nd pssive filling stress vs In B reltions. Simultneous plots of totl, ct, nd pssive filling stress, 6*, vs ln B reltions throughout the filling period re displyed in figure 3. In the representtive norml ventricle (left pnel), the totl stress ct remins prcticlly constnt while considerble frction of the operting stroke volume is being replenished, s indicted by the incresing ln B vlues. In the pttern tht is more common in ptients with ortic stenosis (right pnel), T is found to continue to decline well into the filling phse. In striking contrst to T, the pssive filling stress * is seen to rise continuously beginning with mitrl opening. The "* vs ln B curves exhibit the exponentil form chrcteristic of the elstic response CIRCULTION

5 PTHOPHYSIOLOGY ND NTURL HISTORY-VENTRICULR PERFORMNCE 36 r Norml 72 r ortic Stenosis 32 F 64 F N 1-1 '5 b E in~ CO W 28F 24 F 21F 16 F CO 12 [ 8 4 o r o CMT id o o % N E % - 48 b - 4 k5 () 32 E U 1 U In B I- o o T. 1~~~~~~~~~~~~~~ FIGURE 3. Simultneous plots of totl (OT) nd pssive filling (c*) stresses vs ln B throughout the filling period. Wll stiffness levels, proportionl to the locl slope of such stress-hn B plots, rise continuously with progressive wll distension when the pssive filling stress * is employed. When ssessed by the conventionl method with T, stiffness levels pper to be equl to zero (left) or even negtive (right) during the erly stge of the filling process. In B d of pssive crdic muscle. The "locl slope" of such nonliner digrms is the slope t ny specified In B vlue within the rnge of In B vlues encompssed. The continuous increse in the locl slope of such * vs In B curves should be compred with the peculir behvior during the erly filling stges of the locl slopes of the,t-ln B curves. In prticulr, note how the slope of the T curve in figure 3, right, first chnges from lrge negtive vlues to zero in erly distole. The much higher levels of CT compred with those of * t corresponding In B vlues re lso notble; they expose the dverse effect tht remining contrctile wll stresses exert on ttinble trioventriculr driving pressure differences for erly filling by enhncing the totl left ventriculr pressure. Estimted elstic response digrms. The lest-squres curves fitted to the r* vs In B dt of representtive norml subjects nd ptients with ortic stenosis re displyed in figure 4. s exemplified in the right pnel, in some cses it ws preferble to fit the dt in two distinct lbeit somewht overlpping regions. The regions were identified by numericlly differentiting the rw dt field in every cse to obtin vlues of the locl slope */,ln B nd preliminry plots of E*INc vs *, which disclosed the discontinuity. The discontinuity ws obvious by inspection of these preliminry Vol. 74, No. 5, November 1986 plots despite the noise ttendnt to such tretment of rw dt. The trnsition region lwys corresponded to * level of 35 to 4 g/cm2. Thus only when high distolic stress levels were ttined (four of seven ptients with ortic stenosis) ws it sensible to obtin curve fits to c*-ln B dt in two cs* rnges. s demonstrted by the exmples shown, there ws very little devition of dt points from the elstic three-prmeter modified exponentil form, c* = + feyln B. This ws lso shown sttisticlly by high correltion coefficients (r >.99) nd low stndrd devitions (SD <.8 g/cm2). The goodness of the fits to exponentil forms chrcteristic of n elstic, rther thn rte-dependent viscoelstic pssive response, is noteworthy. Mximum strin rtes ttined during the rpid filling phse were 2.2.2/sec in the norml subjects nd 1.7.2/sec in the ptients with ortic stenosis. Pssive elstic stiffness-stress reltionships. Pssive left ventriculr muscle stiffness E*INC vs stress reltionships re illustrted in figure 5. Pssive incrementl modulus vlues were obtined ccording to the nlyticl expression E*INc = Ky(c* - ). However, rw c* dt vlues were employed, long with the lestsqures estimtors for nd y tht hd been ssessed by nonliner fitting of o*-ln B dt. In ny given 995

6 PSIPOULRIDES et l. 32r 28 V Norml 72 -r l 64 ~ ortic S -ol % 24 N ` 2 bv 16 W C12 s (o.c&cr3) #4 55so b.4~ s s 32, X W > 24 sx 4.6 (occr<38) (36fcr'.cU) * ~~~~~ S~~~~ p 8 _.U * t 1.: In B In B FIGURE 4. Lest-squres fits of pssive stress *-ln B dt points from the entire filling period. ol *OPO 1 < 1 s I 1 ventricle, the vlue of K t end-distole differed by less thn 2% from the vlue found t the onset of filling. Note the bilinerity of pssive stiffness-stress reltionships when distolic stresses ttin high levels. The trnsition region is clerly demrcted t v* 38r Cl E 32 U 28 U z W 24 vi s IL W 12 ;8 W 4 Norml ( C 26) (O cr*c 3) PSSIVE STRESSES Cr*, O* (g/cm2) level of 35 to 4 g/cm2 (figure 5, right). Liner regression correltion coefficients rnged from.99 to 1. in every instnce. When compred t similr stress levels, i.e., over the common lower stress rnge, vlues of the stiffness constnt k, the slope of E*INc vs stress digrms, were not different in the two groups. They Nlo CD14 z W 12 E 1 &L U. W -J W 18Or l JI4 32 ortic Stenois ( q{29 o Q S - (2 o.c Se),o` o cc3rc s7) U ' PSSIVE STRESSES j,, (g/cm2) FIGURE 5. Pssive muscle stiffness vs stress reltionships for the entire distolic filling period. Note the bilinerity of the pssive stiffness-stress plots when high lte-distolic stress levels re ttined (right) CIRCULTION

7 PTHOPHYSIOLOGY ND NTURL HISTORY-VENTRICULR PERFORMNCE were 9.37 ± 1.23 in the norml subjects nd 9.34 ± 1.8 in the ptients with ortic stenosis, for the E*INC vs cs* reltion. However, in the higher stress rnge, such k vlues were gretly ugmented t ± 2.2 for the four ptients with ortic stenosis included. When single liner pssive stiffness-stress reltion corresponding to unique exponentil reltionship between pssive stress nd ln B for both the lower nd the higher stress rnge ws ssumed for ll seven ptients with ortic stenosis, the single k vlue of 12.3 ± 1.22 did not exceed the level found in the norml group (p >.5). End-distolic E*INC levels were similr in the norml nd in the three ventricles ssocited with ortic stenosis tht did not ttin high filling stress levels. They mounted to 317 ± 124 nd 33 ± 85 g/cm2, respectively. In the four ptients with ortic stenosis who hd elevted stress levels, end-distolic E*INC vlues of 945 ± 245 g/cm2 were substntilly higher. Discussion Previously vilble models4-6 for quntitting wll stiffness levels ssume, in ccordnce with pssive elstic dynmic requirements, tht progressive distension of the chmber must be ccompnied by n incresing ventriculr pressure. However, following the nominl instnt of mitrl vlve opening, left ventriculr pressure continues to fll in the rpid filling phse in the fce of substntil increses in chmber dimensions.7 8 Thus such models could not be pplied to distolic mechnics in the beting ventricle. We hve developed new method to ssess in mn pssive properties of left ventriculr muscle nd the influence of relxing contrctile stresses on wll dynmics throughout distole. The proposed model is bsed on the ide tht if the ventricle continued to relx isovolumiclly, its pressure decy would evolve s first-order relxtion process, chrcterized by the time constnt T, s ws shown by Weisfeldt nd collbortors9' 1 nd by Gsch et l. '9 With norml filling, the devition of the mesured left ventriculr pressure from such n exponentilly decying time course reflects the simultneous development of pssive filling stresses. To quntify the net pssive filling pressure, globlly vlid relxtion time constnt must exist to yield the relxtion pressure. Therefore, in its present form the model cnnot be pplied when globl (monoexponentil) estimtes of the isovolumic relxtion time constnt cnnot be obtined or re probbly not pproprite (e.g., crdiomyopthies, segmentl coronry disese of the left ventricle). The elstic incrementl modulus is globlly derived index of ventriculr wll stiffness. The ssumption tht the equtions of liner elsticity pply over infinitesimlly smll intervls of stress nd strin is implicit in its formultion.5 However, lthough constnt over ech stress intervl, the effective modulus vries from one intervl to the next. In this stepwise mnner, n overll exponentil nd thus nonliner elstic response digrm is built out of series of infinitesimlly smll liner segments. The linerity of the corresponding elstic stiffness vs stress reltion over reltively lrge stress nd deformtion rnges is simply mthemticl corollry of the exponentil form of the elstic response of the wll.4 Through most of the filling the totl stress FT exceeds substntilly the corresponding pssive stress cs*. In both the norml subjects nd the ptients with ortic stenosis, the totl nd the pssive filling stress eventully becme indistinguishble from ech other only in the lst prt of the filling process described in stress-ln B digrm. By then, 3.5 to 4 time constnts fter the pproximte time of mximum negtive dp/dt, the ctive muscle stresses hd decyed completely, for prcticl purposes. In the norml ventricle the totl stress cyt tends to remin unchnged erly on despite considerble increses in chmber volume. Here, chmber dimensions increse fst enough in the rpid filling phse so s to just offset the effect of the declining mesured left ventriculr pressure on the totl stress levels. In ventricles with ortic stenosis, strin rtes in the rpid filling phse were reltively low so tht the developing increse in the geometric fctor fell short in offsetting the effect of the simultneous decline of mesured pressure on the totl stress levels. Thus CT could ctully decrese t first in the fce of rising chmber dimensions. 1'12 Other investigtors hve construed declining ventriculr pressure nd wll stresses in the fce of rising chmber dimensions in the rpid filling phse s indicting tht the ventricle consistently contrcts down to end-systolic volumes beyond tht corresponding to its "elstic equilibrium configurtion."22 Subsequently, it ctively sucks up blood in the erly filling period s it recoils bck towrd elstic equilibrium. Hori et l.23 hve provided evidence, using the mitrl occlusion technique, tht isovolumic relxtion cn proceed to negtive pressure in the nesthetized dog, especilly with high experimentl inotropic drive nd smll operting ventriculr volumes. It is unlikely tht such mode of ventriculr function pplies ordinrily in recumbent mn. Indeed, this cnine finding suggests tht in recumbent mn, the blood shift from the cpcious hu- Vol. 74, No. 5, November

8 PSIPOULRIDES et l. w $ qcm Co E 9. Co. z R x o- PRESSURE-LN B PLOTS COMPRISONS WITH & WITHOUT -PB = FIGURE 6. Computer-generted pressure vs In B plots: PM is mesured pressure; PRLN nd PRPB re relxtion pressures with zero nd nonzero symptotes, respectively. The negtive symptote (PB mm Hg) yields n upwrd shift of the pssive filling pressure, reltive to the pssive pressure with zero symptote nd the mesured pressure PM LN B PRLN O PRPB PM-PRLN X PM-PR] tpb mn leg vein reservoirs to the intrthorcic comprtment should yield relxtion pressure symptotes in the bsence of filling tht should not exhibit ny sensible deprture from zero. This is suggested lso by our PB estimtes by the method of Crig nd Murgo,11 which were not sttisticlly different thn zero. The physiologic significnce of nonzero PB nd the nture nd reltive importnce of the vrious fctors tht could ffect it hve not been estblished. We therefore elected to use the relxtion pressure scertined by the method of Frederiksen et l.,9 since in ny event our PB estimtes did not devite significntly from zero. The question of how nonzero PB could modify the dynmic reltionships tht we develop ws ddressed, nd our findings re illustrted in figures 6 CV m COMPRISON OF STRESS-LN B PLOTS PSSIE SESS WI & WITOUT -PO = nd 7. In the pressure-in B plots, the decy of the relxtion pressure towrd negtive PB is ssocited with n upwrd shift of the corresponding pssive filling pressure, reltive to both the pssive filling pressure with zero symptote nd to the mesured pressure. In the pssive stress-ln B plots, there is corresponding upwrd prllel shift of the pssive stress curve computed with negtive PBS reltive to its levels with zero PB. The converse ( downwrd prllel shift) pplies in the cse of positive PB vlue. Such smll prllel shifts ssocited with smll nonzero PB vlues do not influence perceptibly the pssive stiffness-stress reltions nd stiffness constnts obtined by the model developed in this study. By the proposed model, beginning with the nominl FIGURE 7. Computer-generted pssive filling stress, cr*, vs ln B plots corresponding to the pressure-ln B plots in figure 6. There is prllel shift of the pssive stress curve computed with PB --2 mm Hg, reltive to its levels with zero symptote LN B O PB = + PB 998 CIRCULTION

9 PTHOPHYSIOLOGY ND NTURL HISTORY-VENTRICULR PERFORMNCE instnt of mitrl vlve opening, totl stress or pressure vlues reflect the continuously chnging stte of disequilibrium, which involves the opposing dynmic effects of two processes evolving simultneously: (1) the ctive relxtion process of ongoing contrctile wll stress decy nd (2) the pssive process of deformtionl wll stress buildup ssocited with the filling of the chmber. The premise tht totl pressure nd stress re globl dditive mnifesttions of pssive nd ctive wll forces is in greement with clssic (Voigt model) muscle mechnics concepts. Moreover, the dditivity of ctive nd pssive effects is in greement with prllel combintion of ctive nd pssive brnch24 25 elements. The question of lod dependence of relxtion26 must be ddressed in the context of the formultion of the relxtion pressure, PR. In the intct hert, loddependent control could in principle involve hemodynmic loding before ortic vlve closure, during isovolumic relxtion, nd fter mitrl vlve opening. Only loding before ortic closure hs been ctully demonstrted to exert n influence on relxtion in the intct beting left ventricle.27 However, s ws shown by Rff nd Glntz,28 the effect of lod dependence before ortic closure, s well s ny possible effect during isovolumic relxtion, re embodied in the formultion of the relxtion pressure PR nd in the mesurements needed for its determintion: the pressure (P) t the first point on the exponentil portion of the isovolumic pressure decy, nd the time constnt T for isovolumic relxtion. Extrpoltion from interventions on isolted muscle specimens26 to the working ventricle is frught with pitflls,29 nd there is no evidence in the beting ventricle for ny lod-dependent speedup of relxtion fter mitrl opening. Yellin et l.'2 showed by elegnt mitrl occlusion experiments in dogs tht with ordinry mitrl unimpeded inflow the observed erly distolic pressure decy is indeed slowed mrkedly, compred with the decy in bsence of filling. lod-independent relxtion t or fter mitrl opening could be ssocited with the then pplying low rtes of ctivtion decy (clcium sequestrtion), which re reflected in the corresponding low rtes of decline of the relxtion pressure. It should be remembered tht the rte of decy of n exponentil function is proportionl to the instntneously pplying vlues of the exponentil; the vlues of the relxtion pressure t or fter mitrl opening re low nd this leds to correspondingly low rtes of ctivtion decy. Tht lod dependence of relxtion my be bsent or negligible when ctivtion decy rte is low (e.g., fter cffeine ddition) hs been estblished.3 31 Vol. 74, No. 5, November 1986 s is suggested by the work of Poggesi et l.,3 lod dependence of relxtion my be mnifest when elongtion of muscle occurs t or soon fter the pek of the contrction, when the pplying rtes of ctive tension decy re high, nd bsent lte in the course of the twitch, when the pplying ctive tension levels nd their rtes of decy re low. s indicted by the high correltion nd determintion coefficients nd the negligibly smll vlues of the stndrd devitions of the dt points from the exponentil elstic curve, the elstic model ws stisfctory representtion of pssive stress-ln B reltionships throughout the entire filling period. This pplied not only for the ptients with ortic stenosis who did not ttin high strin rtes, but lso for the controls ttining strin rtes in excess of 3/sec during the rpid filling phse. Thus strin rte-dependent simple viscous effects did not cuse ny serious deprture from simple elstic response under bsl hert ctheteriztion conditions. This finding is in hrmony with Noble's conclusion in his recent monogrph32 tht, in the intct beting ventricle, rte-dependent viscous resistnce to stretch is probbly miniml or bsent under quiet resting conditions. Fioretti et l.33 re lso in greement tht left ventriculr viscoelstic properties, such s would be expected to result in incresed pressure in erly distole for n elevted inflow rte, re overshdowed by relxtion processes. The strin-rte indifferent behvior of myocrdil stress-strin reltionships is feture shred by mny living tissues.34 On the other hnd, Rnkin et l.7' 18 found evidence for sensible strin rte-dependent viscous effects in conscious, chroniclly instrumented dogs. The trnsition region is clerly demrcted in plots of the pssive incrementl modulus E*INC vs pssive * nd vs pssive circumferentil muscle stress *. Midwll circumferentil stress t the equtoril region of the left ventricle cn be interpreted s midwll muscle fiber stress, since the fiber direction coincides with the circumferentil direction through the midwll region. Over the common stress rnge, stiffness constnt vlues for the norml nd the ortic stenosis group in this study did not differ. In conventionl nlyses of midnd lte-distolic dt, Peterson et l.3 lso demonstrted norml stiffness constnts in ptients with ortic stenosis. We hve recently suggested tht in clinicl ortic stenosis, muscle stiffness my be norml in contrst to tht observed in short-term experimentl niml pressure overlod studies showing incresed stiffness, probbly cused by incresed fibrosis.4 It is therefore interesting tht the fct tht norml stiffness constnt 999

10 PSIPOULRIDES et l. vlues were found for the ortic stenosis group in the lower (common) stress rnge correltes well with published histochemicl findings in nturlly occurring hypertrophy. It ppers tht in both mn nd nimls with nturlly occurring hypertrophy in the bsence of ssocited coronry hert disese, n increse in collgenous connective tissue components (such s would be expected to rise stiffness constnt vlues over ny given stress rnge) is unusul The bilinerity of the pssive stiffness-stress plots when high lte distolic stress levels re ttined brings forth the need to lwys note the stress rnge over which prticulr elstic stiffness constnt pplies, even in given ventricle. This bilinerity is probbly n expression of the ensuing strong recruitment of very stiff fibrocollgenous composite wll elements t high distolic stress levels. This effect ws not discernible when single stiffness constnt, k, corresponding to unique pssive stiffness-stress reltion ws ssumed to cover both the lower nd the higher filling stress rnges in ll seven ptients with ortic stenosis. Thus, in nlyzing elstic stiffness-stress reltions, different conclusions my be derived if evlution nd comprison of stiffness constnts re mde with due ttention to lrge differences in the pplying filling stress rnges thn if such differences re overlooked. Biliner stiffness-stress reltionships in biomechnics hve been reported by others; for exmple, from his elegnt studies of pssive mechnics nd connective tissue composition of cnine rteries, Cox37 published mple dt exhibiting biliner stiffness-stress reltionships over wide rnge of distending stress. s is true for ll investigtions of crdic mechnics in conscious, closed-chest mn, it ws impossible to mesure pericrdil pressure nd its contribution, long with right ventriculr pressure, to trnsmurl left ventriculr pressure. However, these influences re smll under the conditions of the present study, since the smll positive right ventriculr distolic pressure in these recumbent subjects should offset' the smll negtive penrcrdil pressure. lthough in principle the model is pplicble irrespective of the form of the function to which the relxtion pressure is found to conform, in prctice the relxtion pressure function must be modified ppropritely before the model is pplied to situtions in which the isovolumic pressure decy does not conform to monoexponentil. The pressure fll during isovolumic relxtion does not conform dequtely to monoexponentil decy in number of cliniclly importnt disese sttes, such s regionl ischemi ssocited with segmentl coronry disese nd hypertrophic crdiomyopthy. Evidence tht lck of monoexponentil pressure decy my be directly connected to synchronous relxtion hs been provided both in cnine preprtion,38 nd in ptients undergoing percutneous trnsluminl ngioplsty during trnsient coronry occlusion, when there re striking ptterns of synergic segmentl wll motion during isovolumic relxtion.31 The mthemticl model developed by Brower nd co-workers3941 shows tht biexponentil pressure decy is produced by strongly synchronous left ventriculr relxtion. These investigtors hve shown tht the erly (slower) time constnt of the biexponentil pressure decy chrcterizing synergy results from the combined ction of tht frction of the myocrdium in the process of relxing nd the smller second frction in which relxtion hs not yet been initited. fter the entire myocrdium hs entered the relxtion phse, the mesured pressure conforms to monoexponentil decy with the second (fster) time constnt of the observed biexponentil isovolumic relxtion process.4 Thus, if the two-time constnt model recently described3911 is correct, in the presence of biexponentil isovolumic pressure decy resulting from synchronous left ventriculr relxtion, it is the second (fster) exponentil decy process tht should be used to obtin the relxtion pressure. In conclusion, we hve developed model to ssess in mn the influence of incomplete muscle relxtion on wll dynmics nd the pssive stiffness of left ventriculr muscle. In the rpid filling phse, dynmic globl effects of continuing contrctile wll stress decy re shown to be importnt not only in ptients with ortic stenosis but lso in norml herts. fter subtrcting the decying ctive stress component, pssive stiffness vs stress reltionships nd corresponding elstic stiffness constnts my be scertined. The new method cn be dpted to the study of mechnisms underlying shifts in left ventriculr pressure-volume reltionships such's those observed with vrious phrmcologic interventions. We thnk John Gregg for his skillful computer progrmming. We lso thnk Willim E. Crig, M.D., Brooke rmy Medicl Center, for his helpful suggestions nd criticl review of the mnuscript. We thnk Mrjorie Wilson nd Bettye Jo Hirston, Brooke rmy Medicl Center, for editoril ssistnce. References 1. Plcios 1, Newell JB, Powell WJ Jr: Effect of cute globl ischemi on distolic relxtion in cnine herts. m J Physiol 235: H72, Mnn T, Brodie BR, Grossmn W, McLurin LP: Effect of ngin on the left ventriculr distolic pressure-volume reltionship. Circultion 55: 761, CIRCULTION

11 PTHOPHYSIOLOGY ND NTURL HISTORY-VENTRICULR PERFORMNCE 3. Peterson KL, Tsuji J, Johnson, Di Donn J, Le Winter M: Distolic left ventriculr pressure-volume nd stress-strin reltions in ptients with vlvulr ortic stenosis nd left ventriculr hypertrophy. Circultion 58: 177, Mirsky I, Psipoulrides : Elstic properties of norml nd hypertrophied crdic muscle. Fed Proc 39: 156, Mirsky I, Rnkin JS: The effects of geometry, elsticity, nd externl pressures on the distolic pressure-volume nd stiffness-stress reltions. How importnt is the pericrdium? Circ Res 44: 61, Glntz S, Prmley WW: Fctors which ffect the distolic pressure-volume curve. Circ Res 42: 171, Rnkin JS, rentzen CE, Ring WS, Edwrds CH II, McHle P, nderson RW: The distolic mechnicl properties of the intct left ventricle. Fed Proc 39: 141, Rickrds F, Sebr-Gomes R: Observtions on the effect of ngin on the left ventricle, with specil reference to distolic behvior. Eur J Crdiol 7 (suppl): 213, Frederiksen JW, Weiss JL, Weisfeldt ML: Time constnt of isovolumic pressure fll: determinnts in the working left ventricle. m J Physiol 235: H71, Weisfeldt ML, Frederiksen JW, Yin FCP, Weiss JL: Evidence of incomplete left ventriculr relxtion in the dog: prediction from the time constnt for isovolumic pressure fll. J Clin Invest 62: 1296, Crig WE, Murgo JP: Evlution of isovolumic relxtion in norml mn during rest, exercise, nd isoproterenol infusion. Circultion 62 (suppl II): II-92, Yellin EL, Yorn C, Hori M, Gbby S, Sonnenblick EH, Frter RWM: nlysis of left ventriculr relxtion in the filling nd trnsiently non-filling (completely isovolumic) intct cnine hert. Fed Proc 4: 486, Hess OM, Grimm J, Kryenbuehl HP: Distolic simple elstic nd viscoelstic properties of the left ventricle in mn. Circultion 59: 1178, Dumesnil JG, Shoucri RM, Lwrenceu JL, Turcot J: mthemticl model of the dynmic geometry of the intct left ventricle nd its ppliction to clinicl dt. Circultion 59: 124, Streeter DD Jr, Vishnv RN, Ptel DJ, Spotnitz HM, Ross J Jr, Sonnenblick EH: Stress distribution in the cnine left ventricle during distole nd systole. Biophys J 1: 345, Heintzen PH, Stephn E: Dynmic geometry of the left ventricle in hypertrophy studied by quntittive ngiocrdiogrphy. Bsic Res Crdiol 72: 19, Noble MIM, Milne ENC, Goerke RJ, Crlsson E, Domenech RJ, Sunders KB, Hoffmn JIE: Left ventriculr filling nd distolic pressure-volume reltions in conscious dogs. Circ Res 24: 269, Rnkin JS, rentzen CE, McHle P, Ling D, nderson RW: Viscoelstic properties of the distolic left ventricle in the conscious dog. Circ Res 41: 37, Gsch WH, Blustein S, ndris CW, Donhue RP, vitll B: Myocrdil relxtion. II. Hemodynmic determinnts of rte of left ventriculr isovolumic pressure decline. m J Physiol 239: HI, Pouleur H, Krliner JS, LeWinter MM, Covell JW: Distolic viscous properties of the intct cnine left ventricle. Circ Res 45: 41, Upton MT, Gibson DG: The study of left ventriculr function from digitized echocrdiogrms. Prog Crdiovsc Dis 2: 359, Brecher G: Criticl review of recent work on ventriculr distolic suction. Circ Res 6: 554, Hori M, Yellin EL, Sonnenblick EH: Left ventriculr distolic suction s mechnism of ventriculr filling. Jpn Circ J 46: 124, Loeffler L III, Sgw K: one-dimensionl viscoelstic model of ct hert muscle studied by smll length perturbtions during isometric contrction. Circ Res 36: 498, Seki Y, Sgw K, Sug H: Dynmic stiffness of ct hert muscle in B2+-induced contrcture. Circ Res 42: 324, Brutsert DL, Housmns PR, Goethls M: Dul control of relxtion: its role in the ventriculr function in the mmmlin hert. Circ Res 47: 637, Weber KT, Jnicki JS: Instntneous force-velocity-length reltions in isolted dog hert. m J Physiol 232: H241, Rff GL, Glntz S: Volume loding slows left ventriculr isovolumic relxtion rte: evidence of lod-dependent relxtion in the intct dog hert. Circ Res 48: 813, Seki Y, Sgw K, Sug H: Trnsient tension responses of hert muscle in B2+ contrcture to step length chnges. m J Physiol 238: H34, Poggesi C, Reggini C, Bottinelli R, Riccirdi L, Minelli R: Relxtion in tril nd ventriculr myocrdium: ctivtion decy nd different lod sensitivity. Bsic Res Crdiol 78: 256, Lecrpentier YC, Chuck LHS, Housmns PR, DeClerck NM, Brutsert DL: Nture of lod dependence of relxtion in crdic muscle. m J Physiol 237: H455, Noble MIM: The crdic cycle. Oxford, 1979, Blckwell Scientific Publictions 33. Fioretti P, Brower RW, Meester GT, Serruys PW: Interction of left ventriculr relxtion nd filling during erly distole in humn subjects. m J Crdiol 46: 197, Fung YC: Biomechnics: mechnicl properties of living tissues. New York, 1981, Springer-Verlg 35. Montfort I, Perez-Tomyo R: Muscle: collgen rtio in norml nd hypertrophic humn hert. Lb Invest 11: 463, Sski R, Ymgim H, Ichikw S, Ito, Ymgt S: Histometricl estimtion of scr tissue in hypertrophied humn hert muscle. Tohoku J Exp Med 115: 21, Cox RH: Pssive mechnics nd connective tissue composition of cnine rteries. m J Physiol 234: H533, Crig WE, Psipoulrides : Ventriculr distolic dynmics: effects of wll synchrony on globl relxtion indices. In Proceedings of the 21st nnul Meeting of the ssocition for the dvncement of Medicl Instrumenttion. Chicgo, 1986, p Serruys PW, Wijns W, vn den Brnd M, Meij S, Slger C, Schuurbiers JCH, Hugenholtz PG, Brower RW: Left ventriculr performnce, regionl blood flow, wll motion, nd lctte metbolism during trnsluminl ngioplsty. Circultion 7: 25, Brower RW, Meij S, Serruys PW: model of synchronous left ventriculr relxtion predicting the bi-exponentil pressure decy. Crdiovsc Res 17: 482, Serruys PW, Wijns W, vn den Brnd M, Mey S, Slger C, Schuurbiers JCH, Hugenholtz PG, Brower RW: Left ventriculr function during trnsluminl ngioplsty: hemodynmic nd ngiogrphic study. ct Med Scnd [Suppl] 694: 197, 1984 Vol. 74, No. 5, November