Validation of a novel noninvasive cardiac index of left ventricular contractility in patients

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1 Am J Physol Heart Crc Physol 292: H2764 H2772, Frst publshed January 19, 2007; do: /ajpheart Valdaton of a novel nonnvasve cardac ndex of left ventrcular contractlty n patents Lang Zhong, 1 Ru-San Tan, 1 Dhanjoo N. Ghsta, 2 Edde Yn-Kwee Ng, Leok-Poh Chua, and Ghassan S. Kassab 4,5,6 1 Department of Cardology, Natonal Heart Centre, 2 Dvson of Engneerng, Scence, and Technology, Unversty of New South Wales-Asa, and College of Engneerng, School of Mechancal and Aerospace Engneerng, Nanyang Technologcal Unversty, Sngapore; and Departments of 4 Bomedcal Engneerng, 5 Surgery, and 6 Cellular and Integratve Physology, Indana Unversty-Purdue Unversty Indanapols, Indanapols, Indana Submtted 25 May 2006; accepted n fnal form 15 January 2007 Zhong L, Tan R-S, Ghsta DN, Ng EY, Chua L-P, Kassab GS. Valdaton of a novel nonnvasve cardac ndex of left ventrcular contractlty n patents. Am J Physol Heart Crc Physol 292: H2764 H2772, Frst publshed January 19, 2007; do: /ajpheart Although there are several excellent ndexes of myocardal contractlty, they requre accurate measurement of pressure va left ventrcular (LV) catheterzaton. Here we valdate a novel nonnvasve contractlty ndex that s dependent only on lumen and wall volume of the LV chamber n patents wth normal and compromsed LV ejecton fracton (LVEF). By analyss of the myocardal chamber as a thck-walled sphere, LV contractlty ndex can be expressed as maxmum rate of change of pressure-normalzed stress (d*/dt max, where * /P and and P are crcumferental stress and pressure, respectvely). To valdate ths parameter, d*/dt max was determned from contrast cne-ventrculography-assessed LV cavty and myocardal volumes and compared wth LVEF, dp/dt max, maxmum actve elastance (E a,max ), and snglebeat end-systolc elastance [E es(sb) ] n 0 patents undergong clncally ndcated LV catheterzaton. Patents wth dfferent tertles of LVEF exhbt statstcally sgnfcant dfferences n d*/dt max. There was a sgnfcant correlaton between d*/dt max and dp/dt max (d*/ dt max dP/dt max 4.70, r 0.88, P 0.01), E a,max (d*/dt max 1.20E a,max 1.40, r 0.89, P 0.01), and E es(sb) [d*/dt max 1.60E es(sb) 1.20, r 0.88, P 0.01]. In 0 addtonal ndvduals, we determned senstvty of the parameter to changes n preload (ntravenous salne nfuson, n 10 subjects), afterload (sublngual glyceryl trntrate, n 10 subjects), and ncreased contractlty (ntravenous dobutamne, n 10 patents). We confrmed that the ndex s not dependent on load but s senstve to changes n contractlty. In concluson, d*/dt max s equvalent to dp/dt max, E a,max, and E es(sb) as an ndex of myocardal contractlty and appears to be load ndependent. In contrast to other measures of contractlty, d*/dt max can be assessed wth nonnvasve cardac magng and, thereby, should have more routne clncal applcablty. cardac mechancs; ventrcular elastance; ventrculography; wall stress THE QUEST TO DELINEATE and quantfy myocardal notropc functon n humans, ndependent of ventrcular loadng condtons, s an ongong preoccupaton of researchers and clncans (15 17, 19, 29, 45 47). In the left ventrcle (LV), the peak frst tme dervatve of LV ntracavty pressure (dp/dt max ), whch s reached just before aortc valve openng, s arguably the most senstve cardac ndex of notropcty and s the gold standard (15, 16). Accurate determnaton of dp/dt max requres measurement of ntraventrcular LV pressure by nvasve cardac catheterzaton. In some ndvduals wth mtral regurgtaton, dp/dt max may be approxmated from tme-resolved mtral regurgtaton veloctes, whch are acqured nonnvasvely usng contnuous-wave Doppler echocardography (1). In general, however, accurate nonnvasve assessment of ventrcular pressure s very dffcult. An addtonal dffculty wth LV dp/dt max s that t s not preload ndependent (2). Concevably, the LV pressure-volume relaton and elastance reflect LV contractle functon more accurately (22, 1, 2, 40, 42, 4). Suga and Sagawa (42) formalzed ths concept as the tme-varyng elastance of the ventrcle by defnng elastance (E) as follows: E(t) P(t)/ [V(t) V d ], where P(t) and V(t) represent ventrcular pressure and volume, respectvely, whch vary wth tme t, and V d s the LV volume correspondng to zero LV pressure obtaned by drawng a tangent to the pressure-volume curves at end ejecton. The end-systolc pressure-volume (ESPV) relaton, whch s the locus of pressure and volume ponts at end systole, has been shown to be nsenstve to varatons of the end-dastolc volume (preload) and the mean arteral pressure (afterload). The ESPV relaton s usually a straght lne wth a slope of E es (.e., elastance at end systole). It has been found that E es remans essentally constant f the preload and afterload are allowed to vary wthn the physologcal range but s senstve to notropc agents and schema. Hence, E es has been proposed as a load-ndependent ndex of contractlty of the ventrcle (2,, 7). The loadng condtons do affect E es, however, f ventrcular pressure and volume are made to vary over a wder range (4, 25). Under these condtons, the ESPV relaton becomes curvlnear, concave toward the volume axs, and load dependent. Hence, ndexes such as E es and the ESPV relaton lose ther clncal applcablty (2). Elastance measures also requre cardac catheterzaton for measurement of pressure, whch further reduces ther clncal utlty. An addtonal lmtaton of E es s the dffculty of changng afterload and obtanng multple pressure-volume data ponts n a gven subject whle mantanng a constant contractlty. Hence, t s mpractcal to use E es clncally for patent-specfc LV catheterzaton-ventrculography data. Recently, several approaches, generally referred to as the sngle-beat method [E es(sb) ], have been proposed for estmat- Downloaded from by on December 4, 2017 Address for reprnt requests and other correspondence: G. S. Kassab, Dept. of Bomedcal Engneerng, Indana-Purdue Unv., Indanapols, IN (e-mal: gkassab@upu.edu). The costs of publcaton of ths artcle were defrayed n part by the payment of page charges. The artcle must therefore be hereby marked advertsement n accordance wth 18 U.S.C. Secton 174 solely to ndcate ths fact. H /07 $8.00 Copyrght 2007 the Amercan Physologcal Socety

2 ng E es wthout loadng nterventons (7, 8, 44). Senzak et al. (7) descrbed a method for estmatng E es(sb) that s based on normalzed tme-varyng elastance curves. In subsequent studes, ths method was mproved by adjustment of the normalzed elastance curve to compensate for load dependences and contractlty (8). Zhong et al. (46) ntroduced the formulaton of an actve LV elastance term, E a,max, derved from LV pressure-volume data. E a represents LV myocardal sarcomere actvaton; hence, the peak E a (E a,max ) s hypotheszed to represent LV contractle functon. Nevertheless, the use of E a,max as an ntrnsc LV contractlty ndex s tempered by the need for nvasve LV pressure measurement and complex and tme-consumng computatons (see APPENDIX A). The dp/dt max s based on LV ntracavty pressure, whch s generated by an actve myocardal stress. Hence, t s more approprate to formulate an LV contractlty ndex on the bass of LV wall stress (5, 9, 24). Numerous methods have been devsed to measure LV wall stress (1) or to approxmate t by use of geometrc models (8, 19, 6). Measurement of transmural wall stress (wth mplantable stran gauges) s hampered, however, by the degree of couplng between the transducer and the ventrcular wall (5). We prevously hypotheszed that LV contractlty s the capacty of the LV to develop ntramyocardal stress to eject blood volume as rapdly as possble (45). On the bass of ths concept, we developed an LV contractlty ndex based on wall stress n a sphercal LV model. The LV contractlty ndex s formulated as follows: d(/p)/dt max or d*/dt max, where * /P. In contrast to dp/dt max, E a,max, and E es(sb), ths novel ndex s derved solely from LV ntracavty and myocardal wall volume data, whch can be determned nonnvasvely. Snce ths approach obvates the need for nvasve pressure measurement, t has the potental to become a clncal routne wth nonnvasve magng of ventrcular volume and myocardal mass. In the present study, we descrbe a proof of concept for ths novel stress-based LV contractlty ndex by valdatng t aganst dp/dt max, E a,max, and E es(sb) n 0 ndvduals wth dsparate ventrcular functon. Furthermore, we verfed the load ndependence of the ndex under dfferent preload and afterload condtons. METHODS Experment I: comparson of d*/dt max wth dp/dt max, E a,max, and E es(sb) determned from nvasve cardac catheterzaton. Thrty patents wth dverse cardac condtons undergong clncally ndcated nvasve cardac catheterzaton were enrolled n the study, whch was approved by the Local Research Ethcs Commttee. Informed consent was obtaned from each patent. The catheterzaton laboratory employs a Phlp Integrs Allura 9 wth the Dynamc Flat Detector (Phlps Medcal Systems, Best, The Netherlands) X-ray magng system. Standard technques used to advance catheters n retrograde fashon across the aortc valve allowed contnuous measurement of LV chamber pressure. The LV pressure was then dfferentated wth respect to tme for determnaton of maxmal rate of ncrease durng systole (LV dp/dt max). The peak ECG R wave was used as an end-dastolc tmng marker. Straght or angled sx-sde-hole pgtal catheters (5-F or 6-F) were used at the dscreton of the operator. Each patent underwent rapd bolus nfuson of 0 6 ml of nononc radopaque contrast soluton nto the LV through the pgtal catheter at ml/s. H2765 Ventrculograms were obtaned n the standard 0 rght anteror oblque projecton wth a 9-n. mage ntensfer at a speed of 50 frames per second. Ventrculography and hemodynamc data analyses were performed offlne. Planmetry of sngle-plane LV endocardal and epcardal areas (aded by automated border detecton) and LV long-axs length determnaton allowed calculaton of frame-to-frame varaton n LV ntracavty volumes as well as LV myocardal volumes usng the correspondng Vewstaton (Phlps Medcal Systems; Fg. 1) (, 0, 4). ECGs were recorded contnuously wth the ventrculograms. The mages chosen for planmetry were from the frst snus beat wth adequate opacfcaton. LV ejecton fracton (LVEF) was easly calculated from LV end-dastolc volume (LVEDV) and LV end-systolc volume (LVESV) as follows: LVEF (LVEDV LVESV)/LVEDV. The dp/dt max was calculated, usng Matlab software, as the maxmum frst tme dervatve of the LV pressure-tme plot (Fg. 2). The formulaton for calculaton of actve elastance s descrbed n APPENDIX A, and that of the proposed wall stress-based LV contractlty ndex s brefly descrbed below and n more detal n APPENDIX B. Experment II: load ndependence of echocardographcally derved d*/dt max. An addtonal 0 volunteers were subsequently recruted for studes n whch echocardographc examnatons were performed, and d*/dt max was derved from nonnvasvely determned LV cavty and myocardal volumes at baselne and after physologcal manpulatons of preload, afterload, or myocardal contractlty. The study was approved by the Local Research Ethcs Commttee, and nformed consent was obtaned from each ndvdual. There were three groups of volunteers: 10 healthy subjects were gven sublngual glyceryl trntrate (500 1,000 g) to decrease afterload, wth a target decrease n systolc blood pressure of 10% (group A), 10 healthy subjects receved ntravenous normal salne soluton (500 ml) over 20 0 mn to ncrease preload (group B), and 10 consecutve patents were scheduled to undergo clncally ndcated dobutamne stress echocardography (group C). In all subjects, echocardography was performed at baselne, as well as after alteratons of afterload, preload, and myocardal contractlty. In group C, echocardographc measurements were made durng ntravenous dobutamne nfuson at 5.0 gkg 1 mn 1, a dose that ncreases myocardal contractlty but does not have sgnfcant cardac chronotropc or volume effects. Fg. 1. ECG-trggered contrast cne left ventrculography at the rght anteror oblque projecton depctng opacfed left ventrcular (LV) cavty at the enddastolc phase of the cardac cycle. End-dastolc and end-systolc endocardal contours are outlned. An 4-cm segment of LV free wall epcardum at the juncton of the apcal and mddle thrds s also depcted. Average LV wall thckness s obtaned from the quotent of ths segmental area and segmental length. From ths, myocardal wall volume can be estmated (0, 4). Downloaded from by on December 4, 2017

3 H2766 Fg. 2. Top: LV pressure (P) and volume (V) throughout the cardac cycle [tme (n seconds) from start of sovolumc contracton] n 1 representatve subject (subject x). Measurements have been corrected for geometrc dstorton from the respectve recordng systems. Bottom: pressure-volume relaton n subject x. Ascendng numbers ndcate frame number (each frame lasts 20 ms) from begnnng of sovolumc contracton (frame 1). Frames 1 5, sovolumc contracton; frames 5 17, ejecton; frames 17 21, sovolumc relaxaton; frames 21 6, ventrcular fllng. All echocardograms were acqured usng Vvd 7 (General Electrc). M-mode measurements of the LV were obtaned, and LV mass was calculated usng standardzed methodology (6, 18). Myocardal volume was calculated by dvdng LV mass by myocardal densty (assumed to be 1.05 g/ml). Furthermore, two-dmensonal apcal fourand two-chamber vews of the LV were acqured, and end-dastolc and end-systolc endocardal contours were manually outlned. The correspondng LVEDV and LVESV were then automatcally determned usng Smpson s bplane method. Pulse-wave echocardographc Doppler nterrogaton of the LV outflow tract (LVOT) allowed, n the absence of sgnfcant mtral regurgtaton or aortc valve dysfuncton, calculaton of the maxmal LV volume rate (dv/dt max) durng ejecton: dv/dt max V peak AVA, where V peak s the peak velocty sampled at the LVOT and AVA s the aortc valve area (AVA D 2 /4, where D s the LVOT dameter measured n the 2-dmensonal parasternal long-axs mage of the heart). Substtuton of values of myocardal volume and dv/dt max nto Eq. 7 (see below) yelds d*/dt max. E es(sb) estmaton usng blnearly approxmated tme-varyng elastance. The algorthm s based on the elastance curve derved from the pressure-volume loop (8). It s prmarly focused on the shape of the curve, wth the assumpton of a dependence on contractlty and loadng condtons. The tme-varyng elastance s approxmated by a blnear functon: one for the sovolumc contracton phase and another for the ejecton phase. E es(sb) s then gven by E es(sb) [P ad (P ad P ed )/PEP ET P es ]/SV (1) where P ad s pressure at the end of sovolumc contracton, P ed s end-dastolc pressure, P es s end-systolc pressure, PEP s preejecton perod, ET s ejecton tme, s the rato of the slope n the ejecton phase to the slope n the sovolumc contracton phase, and SV s stroke volume. The bvarate model of Shshdo et al. (8) was used to estmate : EF 0.682PEP/(PEP ET), where EF s LV ejecton fracton. Dervaton of a novel wall stress-dependent LV contractlty ndex. For smplcty, we approxmate the LV as a thck-walled sphercal shell consstng of ncompressble, homogeneous, sotropc, elastc materal. The nner and outer rad of the shell are denoted r and r e, respectvely. The epcardal (outer) surface s consdered load free, whereas the endocardal surface s subjected to LV ntracavty pressure P(t), where t s tme. The crcumferental wall stress ( ) can be expressed at any transmural radal poston n the wall (r) as r P r r e r 1 r P r 1 r e e 2r r e 2r 1 r r e P r r r e 2r 1 r r e (see APPENDIX B for dervaton). In ths model, the maxmum wall stress occurs at the endocardum, r r, and s gven by () r P r /r e 1/2 1 r /r e The geometrc relaton between wall volume (V m), LV cavty volume (V), r, and r e can be expressed as (2) V m 4r e r / and V 4r / (4) If we combne Eqs. and 4, we obtan the desred result 1 V/(V m P V V m V) r P [V/(V m V) 1/2] 2V m P V 2V m 1 2 (5) By normalzng wall stress to LV ntracavty pressure (P), an ndex of LV contractle functon may result as /P V 2V m 1 2 (6) Ths noton s based on the premse that LV wall stress (due to LV myocardal sarcomere contracton) s responsble for the development of LV pressure. Hence, t s more ratonal to base LV contractlty ndex on LV wall stress per pressure, rather than on stress or pressure alone. Analogous to dp/dt max, we propose an LV contractlty ndex as the maxmal rate of change of pressure-normalzed wall stress d*/dt max d /P dt 2V max m dv dtmax Obvously, ths ndex s ndependent of pressure by defnton. (7) Downloaded from by on December 4, 2017

4 H2767 Data analyss. Mathematcal modelng and curve fttng were performed usng Matlab 6.5 software. Statstcal analyss was performed usng Medcalc statstcal software. All parametrc data are means SD. Statstcal sgnfcance was defned at P In experment I, the patents were dvded nto tertles accordng to ther LVEF for analyss. For multple-group comparsons, ANOVA was followed by Student-Newman-Keuls test for parwse comparsons f ANOVA revealed sgnfcant ntergroup dfferences. Lnear regresson analyss was employed to quantfy the correlaton between d*/dt max and other ndexes of LV contractlty [dp/dt max, E a,max, and E es(sb)]. In experment II, pared Student s t-test was used to compare parameters measured at baselne and after physologcal manpulaton. RESULTS Correlaton of d*/dt max wth dp/dt max,e a,max, and E es(sb). Thrty volunteers [mean 58.1 (range 48 77) yr of age, 1:2 male-to-female rato] wth dverse cardac condtons were recruted for experment I. Sample LV pressure-volume data from one patent are shown n Fg. 2. LVEF and dp/dt max were computed drectly from these traces. E a at varous tmes was also computed from the pressure-volume loops (Table 1), as descrbed n APPENDIX A. E a,max was extrapolated from the peak of the E a -tme curve (Fg. ). E es(sb) was also computed from the pressure-volume loop usng Eq. 1. Ages, heart rates, ejecton fractons, and derved LV contractlty parameters of the patents are shown n Table 2. The patents were dvded nto three groups on the bass of tertles of LVEF, wth 10 ndvduals n each group. Intergroup comparsons show sgnfcant dfferences (P 0.05) between the mean values of dp/dt max, E a,max, E es(sb), and d*/dt max n those n the hghest tertle compared wth those n lowest and mddle tertles. There s agreement n regard to the proposed ndex d*/ dt max wth dp/dt max, E a,max, and E es(sb) across the three tertles of ascendng LVEF values, wth statstcally sgnfcant dfferences n LV contractlty ndexes among the three groups. The average values of dp/dt max, E a,max, E es(sb), and d*/dt max for the hghest tertle were 1,60 97 mmhg/s, mmhg/ml, mmhg/ml, and s 1, respectvely. Values of dp/dt max, E es(sb), and d*/dt max were Table 1. E a at dscrete tme ponts durng sovolumc contracton and relaxaton n subject Frame No. () t, s P, mmhg V, ml Ea, mmhg/ml Isovolumc contracton Isovolumc relaxaton , Tme-n cardac cycle (frame no. from end dastole); t, tme from start of sovolumc contracton; P, measured left ventrcular (LV) ntracavty pressure; V, measured LV ntracavty volume. For sovolumc contracton, actve elastance (E a) at tme s calculated; for sovolumc relaxaton, E a,17 wll be determned from curve ft of Fg. 2. Fg.. Actve elastance (E a) values durng sovolumc contracton and relaxaton vs. tme from start of sovolumc contracton n subject x. Curve ft to Eq. A2 yelds E a, mmhg/ml, C s, Z C 1.61, d 0.28 s, R s, and E a, mmhg/ml (root mean square error mmhg/ml). statstcally sgnfcantly lower n patents n the lowest and mddle tertles had than those n the hghest tertle. Fgure 4 summarzes the correlaton between d*/dt max, dp/dt max, and E a,max, as well as E es(sb). Lnear regresson analyss revealed good correlaton between d*/dt max and dp/dt max, E a,max, and E es(sb), wth sgnfcant correlaton coeffcents of 0.9 n each case: d*/dt max dP/dt max 4.70 (r 0.88, P 0.01), d*/dt max 1.20E a,max 1.40 (r 0.89, P 0.01), and d*/dt max 1.60E es(sb) 1.20 (r 0.88, P 0.01). In contrast, the correlaton between d*/dt max and LVEF s less strong (r 0.71), as s the correlaton between E es(sb) and LVEF (r 0.78), underscorng the lack of specfcty of LVEF as an ndex of myocardal contractlty. Load ndependence of d*/dt max. In experment II, we studed alteratons n d*/dt max under varous loadng condtons. We nduced a sgnfcant decrease n blood pressure and ncrease n LVEDV n groups A and B, respectvely (Table ). There was no sgnfcant change n d*/dt max n response to Table 2. LV contractlty ndexes classfed nto tertles of LVEF Tertle Lowest Mddle Hghest EF * * Age, yr Heart rate, beats/mn dp/dt max, mmhg/s * 1,12111* 1,6097 E a,max, mmhg/ml * * E es(sb), mmhg/ml * * d*/dt max, s * * Values are means SD. EF, ejecton fracton; dp/dt max, peak frst tme dervatve of ventrcular pressure; d*/dt max, LV contractlty ndex; E a,max, maxmum LV elastance; E es(sb), sngle-beat LV end-systolc elastance. *Sgnfcantly dfferent from hghest tertle (P 0.05). Downloaded from by on December 4, 2017

5 H2768 afterload reducton or preload ncrease. In contrast, there was a sgnfcant ncrease n d*/dt max durng dobutamne nfuson (5 gkg 1 mn 1 ) compared wth baselne d*/dt max ( vs s 1, P 0.0) n group C. Fg. 4. Lnear regresson analyss demonstrates good correlaton between d*/ dt max and dp/dt max (d*/dt max dP/dt max 4.70, r 0.88; A), between d*/dt max and E a,max (d*/dt max 1.20E a,max 1.40, r 0.89; B), and between d*/dt max and E es(sb) [d*/dt max 1.60E es(sb) 1.20, r 0.88; C]. DISCUSSION Any ndex of contractlty n the ntact heart may be crtczed as somewhat arbtrary because of lack of an deal descrptor of the ntrnsc LV contractle state. Despte ts establshed acceptablty, LV dp/dt max s an extrnsc measure of LV contractlty that has been shown to be load dependent (2). It s therefore mportant to represent LV contractlty by means of an ntrnsc property of the LV that s ndependent of the preload and afterload. In ths regard, E es and E a,max are effectve contractlty ndexes (2,, 46). Smlar to dp/dt max, however, ther determnaton requres nvasve catheterzaton for measurement of LV pressure. Durng LV systole, LV wall stress s generated ntrnscally by sarcomere contracton and results n the development of extrnsc LV pressure. LV wall stress s dependent on wall thckness, LV geometry, and chamber pressure and sarcomere contracton. Hence, t s ratonal to quantfy the LV wall stress as an ntrnsc measure of myocardal contractlty. For example, Hood et al. (12) evaluated stress as an ndex of the approprateness of the anatomc and functonal response to any gven pressure or volume load, but they were unable to provde a formulaton for the normalzed LV stress. A smlar noton has been suggested by several nvestgators (5, 12, 24). Here, we present the frst valdated formulaton of a stressdependent contractlty ndex d*/dt max. The LV wall stress also has a bearng on the myocardal oxygen supply-and-demand, whch potentally nfluences contractle functon. As wall stress ncreases, stran energy and myocardal oxygen demand ncrease n tandem (41). Increased wall stress can also reduce myocardal oxygen supply by compresson of ntramural arteral blood flow, whch augments flow resstance (11). Hence, LV wall stress s only one determnant of LV myocardal perfuson. Other factors nclude pressure n the coronary vessels and coronary vasculature and LV myocardal porosty. The latter s n part nfluenced by LV wall stress. We have valdated a new LV contractlty ndex, d*/dt max, based on the maxmum rate of development of LV wall stress wth respect to LV pressure. From the rght-hand sde of Eq. 7, ths ndex s also seen to represent the maxmal flow rate from the ventrcle (cardac output) normalzed to myocardal volume (or mass). The cardac output has been used as a measure of myocardal contractlty n rats, provded that the nfluences of afterload are taken nto account (7). Furthermore, normalzaton of ventrcular measurements to the myocardal volume or mass has been used to standardze pressure-volume relatons (2, 10). The present model formalzes these features analytcally. The peak rates of myocardal stress (d/dt) and LV pressure (dp/dt) development typcally occur durng the sovolumc contracton phase (Fg. 5, B and D, respectvely). The rate of development of pressure-normalzed wall stress (* /P) durng sovolumc contracton, however, s nearly zero because of the small changes of LV geometry durng sovolumc contracton (Fg. 5F). In Eq. 7, the peak rate of normalzed wall Downloaded from by on December 4, 2017

6 Table. Hemodynamc varables at baselne and after physologcal manpulaton wth glyceryl trntrate, salne, and dobutamne H2769 GTN Salne Dobutamne Baselne After Baselne After Baselne After MAP, mmhg * SV, ml * LVEDV, ml * d*/dt max, s * Values are means SD. (n 10). GTN, glyceryl trntrate; LVEDV, left ventrcular end-dastolc volume; MAP, mean arteral pressure; SV, stroke volume. *Sgnfcantly dfferent from baselne (P 0.05). Note sgnfcant decrease n MAP and LVEDV after glyceryl trntrate admnstraton and sgnfcant ncrease n LVEDV after salne nfuson. stress d*/dt (left-hand sde of Eq. 7) occurs durng the ejecton phase (Fg. 5F), consstent wth the peak cardac output durng the ejecton phase (rght-hand sde of Eq. 7). Hence, there s synchronzaton between the novel contractlty ndex and the rate of ejecton, as suggested by Eq. 7. In the 0 patents studed n experment I, d*/dt max correlated very well wth the tradtonal and nvasvely determned dp/dt max and E a,max, as well as wth the computed end-systolc elastance E es(sb) (Fg. 4). These data valdate the proposed contractlty ndex. Addtonally, d*/dt max has the dual advantage of requrng relatvely smple computatons wth no requrement for nvasve LV pressure measurement. In Fg. 4, there exsts a nonzero ntercept for d*/dt max, whch mples a resdual d*/dt max, even n an LV wth an mpared sarcomere and, hence, zero values of dp/dt max, E a,max,ore es(sb). In the 0 addtonal subjects/patents studed n experment II, d*/dt max s nsenstve to preload changes nduced by ntravenous salne nfuson and afterload changes nduced by glyceryl trntrate but s senstve to changes n contractlty provoked by an nfuson of dobutamne. The use of ntroglycern to vary afterload results n a declne n preload (a decrease n EDV, albet not statstcally sgnfcant). In future studes, the afterload resstance or mpedance must be measured to ensure the desred effect on afterload;.e., the ndex needs to be further tested n the settng of acute changes n vascular mpedance load. Downloaded from by on December 4, 2017 Fg. 5. Plot of wall stress (; A), rate of wall stress (d/dt; B), LV pressure (P; C), rate of LV pressure (dp/dt; D), pressure-normalzed wall stress (* /P; E), and rate of * (d*/dt; F) vs. tme. Data were obtaned from 1 typcal subject.

7 H2770 Tradtonal axsymmetrc models of LV determne wall stress at the equator of a thck-walled sphere. For the formulaton of the new ndex, the LV was modeled as a pressurzed thck-walled sphere. Smlar geometrc assumptons had been made by nvestgators studyng LV pressure-volume dynamcs n small anmal models (14, 26). Ths was done to reduce the mathematcal complexty of calculaton, whch s especally pertnent n clncal cases. Regardless of the smplfed LV sphercal model, the present results ndcate that d*/dt max can dstngush between mpared and normal LVEF and correlates well wth dp/dt max, E a,max, and E es(sb). Future studes must consder more realstc geometres, such as an ellpsod or patent-specfc fnte-element model of the heart. Those mprovements n model must be weghed aganst the ncurred computatonal cost. Angocardography s frequently used for determnaton of heart dmensons n humans. Numerous studes have shown that, when used properly, such measurements are relable and reasonably accurate (, 20, 4, 5). There s no doubt that MR magng technques are more accurate and reproducble. The development and refnement of three-dmensonal cne-mr magng technques have enabled reconstructon of the ventrcle by the nterleavng of multple long- and short-axs mages. Smlarly, three-dmensonal echocardography has also developed to a level of sophstcaton that permts expedtous and accurate determnaton of LV volumes and mass (27, 28). These magng modaltes can thus provde very accurate geometrc models of the heart that can yeld relable estmates of myocardal contractlty. In concluson, we valdate a novel ndex of LV contractlty that can dscrmnate between patents wth dfferent LVEF values. Ths ndex can be determned nonnvasvely from LV cavty and wall volume measurements and can become a routne clncal adjunct to echocardographc or cardac MR magng for assessment of LV contractlty and functon. Our data demonstrate that d*/dt max correlates well wth dp/dt max, E a,max, and E es(sb), s ndependent of changes n preload and afterload, and s senstve to changes n myocardal contractlty. APPENDIX A Calculaton of E a from LV pressure and volume data. The governng dfferental equaton relatng LV ntracavty pressure (P) and volume (V) s gven by Zhong et al. (46) dp M(dV ) dev MdV VdE EdV (A1) where M s the nerta term and E s the sum of LV passve and actve elastance (E p and E a). E p governs the pressure response to volume change and can be expressed as a monoexponental functon, and E a characterzes ntrnsc LV stffness attrbutable to actvaton of the myocardal sarcomere durng actve contracton and relaxaton. The relaxaton can also be deemed to be an actve process requrng actve decouplng of Ca 2 from myocardal contractle protens. An E a term was prevously formulated as (46) E a E a,01 e t C Z ce td R Z R (A2) where t represents tme from the start of sovolumc contracton, E a,0 s the E a coeffcent, C s the tme coeffcent of the rate of elastance rse durng LV contracton, R s the tme coeffcent of the rate of elastance fall durng LV relaxaton, and d s a tme constant. The exponents Z C and Z R were ntroduced to smooth out the E a curve durng sovolumc contracton and relaxaton. It was proposed that E a,max may be adopted as an ntrnsc measure of LV contractlty. The parameter d s a tme constant durng the ejecton phase; the term u(t d) s the unt step functon: u(t d) 0 for t d. Durng sovolumc contracton, when u(t d) 0, Eq. A2 reduces to E a E a,01 e t C Z c (A) Durng sovolumc contracton and sovolumc relaxaton, LV volume and E p are constant. Wth dv 0 and dv 0, Eq. A1 becomes VdE dp, whch can be dscretzed for any tme durng the sovolumc contracton as V E E 1 V E a, E p, E a,1 E p,1 (A4) V E a, E p,ed E a,1 E p,ed dp and, for tme durng the sovolumc relaxaton, as V E a, E p, E a,1 E p,1 (A5) V E a, E p,es E a,1 E p,es dp where V and P are LV volume and pressure measured at tme, E p,es s passve elastance at end dastole, and E p,es s passve elastance at end systole. Applyng Eqs. A4 and A5 to study measured LV pressure and volume data allows calculaton of E a durng sovolumc contracton and relaxaton for varous patents (Table 1). In each patent, E a,0, C, and Z C n Eq. A can be determned from a curve ft of LV pressure and volume data durng sovolumc contracton. Substtutng the values of these parameters nto the more general E a of Eq. A2, the remanng parameters d, R, and Z R can be determned smlarly to ft LV pressure and volume data durng sovolumc relaxaton. The resultant smooth curve ft functon of Eq. A2 represents E a at all tmes and enables determnaton of E a,max (Fg. 2). APPENDIX B Analyss of wall stress n a thck-walled sphercal LV model based on the theory of elastcty (9). The LV was modeled as a pressurzed thck-walled sphercal shell. If u r represents the radal dsplacement of a sphercal surface element n the LV wall at radus r, then, at the outer surface of radus r r, the correspondng radal dsplacement can be expressed as u r (u r/r)dr. Stran n the radal drecton ( r) s then gven by u r u r r dr r dr u r u r r (B1) Sphercal symmetry mples that strans n the orthogonal crcumferental axes ( and ) are dentcal. Therefore, stran n the crcumferental drecton ( )s 2r u r 2r u r 2r r Strans along the three orthogonal axes are r u r r, u r r, and u r r (B2) (B) Smlarly,. For equlbrum n the radal drecton, we have r 2r2r r r r r2r r2 2r r 22r sn 2r r 22r sn 0 Snce,d r ( r/r)r, and Eq. B4 reduces to (B4) Downloaded from by on December 4, 2017

8 H d r 2 dr r2 r 2 r (B5) On the bass of Hooke s law, we can express the consttutve equaton as r 1 E r u r r or du r dr 1 E r 2 (B6) where E s the elastc modulus and v s the Posson s rato. Smlarly, from Eq. B2 1 E r u r r or u r r 1 E 1 r Dfferentatng Eq. B7 wth respect to r, we obtan (B7) du r dr E1 1 r r r (B8) r r Equatons B6 and B8 can be combned as 1 dr dr dr r r 2 0 dr If we combne (Eq. A5) nto Eq. A9, we obtan 1 d 2 r 2 r dr r 2 dr 2 r dr 2 r 0 dr r dr If we substtute r 2 r y, Eq. B10 becomes d2 y dr 2 r dy dr y r y 2 r dy 2 r dr 0 or d2 y dr 2 2y r 2 0 Ths yelds a homogeneous lnear equaton wth the soluton y Ar 2 B r and r y r 2 A B r where A and B are constants. From Eqs. B5 and B12, wefnd A B 2r (B9) (B10) (B11) (B12) (B1) For a thck-walled sphercal shell subjected to nternal pressure (P ) and zero external pressure, the boundary condtons are r P when r r and r 0 when r r e. From Eq. B12, we obtan A B r P and A B 0 (B14) r e Hence, we can determne the constants of ntegraton as A r P r and B r e r P e r r e r (B15) From Eqs. B12 B14, expressons for radal and crcumferental stresses are r r P r e r 1 r e r r P r e r 1 r e 2r (B16) (B17) The present formulaton wll focus on the crcumferental stress, whch s sgnfcantly larger n magntude than and opposte n sgn (tensle) from the radal (compressve) stress. ACKNOWLEDGMENTS We are grateful to Drs. Lm Soo-Tek and K. Gunasegaran (Natonal Heart Centre) for professonal and techncal assstance n cne ventrculography and stress echocardography. GRANTS Ths study was supported by Sngapore A*STAR Research Grant and Natonal Heart, Lung, and Blood Insttute Grant 2 R01 HL REFERENCES 1. Barggga GS, Bertucc C, Recusan F, Rasaro A, de Serv S, Valdes- Cruz LM, Sahn DJ, Troncon L. A new method for estmatng left ventrcular dp/dt by contnuous-wave Doppler echocardography. Valdaton studes at cardac catheterzaton. Crculaton 80: , Belcher P, Boerboom LE, Olnger GN. Standardzaton of end-systolc pressure-volume relaton n the dog. Am J Physol Heart Crc Physol 249: H547 H55, Brower PW, Meester GT, Hugenholtz PG. Quantfcaton of ventrcular performance: a computer-based system for the analyss of angographc data. Cathet Cardovasc Dagn 1: 1 155, Burkhoff D, de Tombe PP, Hunter WC. Impact of ejecton on magntude and tme course of ventrcular pressure-generaton capacty. Am J Physol Heart Crc Physol 265: H899 H90, DeAnda A Jr, Komeda M, Moon MR, Green GR, Bolger AF, Nkolc SD, Daughters GT, Mller DC. Estmaton of regonal left ventrcular wall stresses n ntact canne hearts. Am J Physol Heart Crc Physol 275: H1879 H1885, Devereux RB, Alonso DR, Lutas EM, Gottleb GJ, Campo E, Sachs I, Rechek N. Echocardographc assessment of left ventrcular hypertrophy: comparson to necropsy fndngs. Am J Cardol 57: , De Wldet DJ, Sangster B. An evaluaton of derved aortc blood flow parameters as ndces of myocardal contractlty n rats. J Pharmacol Methods 10: 55 64, Falsett HL, Mates RE, Grant C, Greene DG, Bunnell IL. Left ventrcular wall stress calculated from one-plane cneangography. Crc Res 26: 71 8, Ffer MA, Gunther S, Grossman W, Mrsky I, Carabello B, Barry W. Myocardal contractle functon n aortc stenoss as determned from the rate of stress development durng sovolumc systole. Am J Cardol 44: , Goto T, Slnker BK, LeWnter MM. Smlar normalzed E max and O 2 consumpton pressure-volume area relaton n rabbt and dog. Am J Physol Heart Crc Physol 255: H66 H74, Hoffman JIE, Baer RW, Hanley FL, Messna LM. Regulaton of transmural myocardal blood flow. J Bomech Eng 107: 2 9, Hood WP, Rackley CE, Rolett EL. Wall stress n the normal and hypertrophed human left ventrcle. Am J Cardol 22: , Husman RM, Elznga G, Westerhof N, Spkema P. Measurement of left ventrcular wall stress. Cardovasc Res 14: , Janz RF, Kubert BR, Mrsky I, Korecky B, Tachman GC. Effect of age on passve elastc stffness of rat heart muscle. Bophys J 16: , Kass DA, Beyar R. Evaluaton of contractle state by maxmal ventrcular power dvded by the square of end-dastolc volume. Crculaton 84: , Kass DA, Maughan WL, Guo ZM, Kono A, Sunagawa K, Sagawa K. Comparatve nfluence of load versus notropc states on ndces of ventrcular contractlty: expermental and theoretcal analyss based on pressure-volume relatonshps. Crculaton 76: , Lambert CR, Nchols WW, Pepne CJ. Indces of ventrcular contractle state: comparatve senstvty and specfcty. Am Heart J 106: , Lang RM, Berg M, Devereux RB, Flachskampf FA, Foster E. Recommendatons for chamber quantfcaton. J Am Soc Echocardogr 18: , Mason DT, Braunwald E, Covell JW, Sonnenblck EH, Ross J. Assessment of cardac contractlty. Crculaton 44: 47 58, Masquet C, Slama MS, Dbe A, Sheehan FH, Lenard J. Normal left ventrcular volume and ejecton fracton: assessment wth quanttatve dgtal cardoangography. Int J Card Imagng 14: 27 6, Mrsky I. Elastc propertes of the myocardum: a quanttatve approach wth physologcal and clncal applcatons. In: Handbook of Physology. Downloaded from by on December 4, 2017

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