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Left ventricular function: time-varying elastance and left ventricular aortic coupling Walley, Keith R Sep 10, 2016

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REVIEW Open AccessLeft ventricular function: time-varyingelastance and left ventricular aorticcouplingKeith R. WalleyAbstractMany aspects of left ventricular function are explainedby considering ventricular pressure–volume characteristics.Contractility is best measured by the slope, Emax, of theend-systolic pressure–volume relationship. Ventricularsystole is usefully characterized by a time-varyingelastance (ΔP/ΔV). An extended area, the pressure–volume area, subtended by the ventricular pressure–volume loop (useful mechanical work) and the ESPVR(energy expended without mechanical work), is linearlyrelated to myocardial oxygen consumption per beat.For energetically efficient systolic ejection ventricularelastance should be, and is, matched to aortic elastance.Without matching, the fraction of energy expendedwithout mechanical work increases and energy is lostduring ejection across the aortic valve. Ventricularfunction curves, derived from ventricular pressure–volume characteristics, interact with venous returncurves to regulate cardiac output. Thus, consideration ofventricular pressure–volume relationships highlightfeatures that allow the heart to efficiently respond toany demand for cardiac output and oxygen delivery.BackgroundThe heart is a muscle pump that delivers blood at a highpressure to drive passive blood flow through a complexarterial and venous circuit. The demand for blood flowis determined by metabolic activity of the tissues. For ex-ample, increased skeletal muscle work leads to increaseddemand for oxygen so blood flow must increase to thisspecific muscle. Since the need for blood flow is deter-mined by peripheral tissue demands, it follows thatblood flow must be regulated by the periphery. So theCorrespondence: Keith.Walley@hli.ubc.caCentre for Heart Lung Innovation, St. Paul’s Hospital, University of BritishColumbia, 1081 Burrard Street, Vancouver, BC V6Z 1Y6, Canadaheart must have special characteristics that allow it torespond appropriately and deliver necessary blood flowand oxygen, even though flow is regulated from outsidethe heart.To understand these special cardiac characteristics westart with ventricular function curves and show howthese curves are generated by underlying ventricularpressure–volume characteristics. Understanding ventricu-lar function from a pressure–volume perspective leads toconsideration of concepts such as time-varying ventricularelastance and the connection between the work of theheart during a cardiac cycle and myocardial oxygen con-sumption. Connection of the heart to the arterial circula-tion is then considered. Diastole and the connection ofthe heart to the venous circulation is considered in an ab-breviated form as these relationships, which define howcardiac output is regulated, stretch the scope of this re-view. Finally, the clinical relevance of this understandingis highlighted by considering, for example, why afterloadreduction is an excellent therapy for systolic heart failurebut fails to help, and instead harms, when systolic heartfailure is not the problem.Ventricular function curvesClassic ventricular function curvesStarling function curves, or ventricular function curves,relate the input of the heart to output (Fig. 1) [1]. Anyinput and any output can be considered. For the heartwe most frequently use right atrial pressure (central ven-ous pressure) or left atrial pressure (pulmonary capillarywedge pressure) as clinically measurable inputs to theheart (preload). Cardiac output (blood flow out of theheart in liters per minute) is a common measure of out-put of the heart. Other inputs and outputs yield differentbut related ventricular function curves.As the preload of the heart increases, cardiac outputincreases—sometimes called Starling’s law of the heartor the Frank–Starling relationship [2]. This relationship© 2016 Walley. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 InternationalLicense (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in anymedium, provided you give appropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.Walley Critical Care  (2016) 20:270 DOI 10.1186/s13054-016-1439-6is curvilinear (Fig. 1) so that, at high preload, furtherincreases in preload yield diminishing increases incardiac output. A specific ventricular function curveapplies to a specific ventricular contractile state, dia-stolic compliance, and afterload. Using cardiac outputas pump output, if ventricular contractility increases(at a constant afterload), then the ventricular functioncurve shifts up and to the left so that, at the sameend-diastolic pressure (preload), a greater stroke vol-ume and cardiac output is achieved [1] (Fig. 1, dashedline). Improved ventricular diastolic compliance anddecreased afterload (aortic pressure) also results in in-creased stroke volume (at a constant contractile state)so these changes also shift the ventricular functioncurve up.Modified ventricular function curvesThe motivation behind early studies of ventricular func-tion curves was the desire to identify intrinsic ventricu-lar contractile function. Classic Starling function curvesshift down with increased afterload [3] without a changein contractility of the heart [4]. Therefore, modificationsto ventricular function curves were considered. In someversions “output” was changed to stroke work or strokework per minute (stroke power) [5]. Stroke work incor-porates afterload since it is pressure afterload × strokevolume. In some versions “input” was changed to end-diastolic volume [6]. This addressed the issue of non-linear diastolic compliance [5]. Probably the zenith ofmodifications to ventricular function curves is theconcept of preload recruitable stroke work [7]. Whenstroke work is plotted against end-diastolic volume therelationship is highly linear and fairly insensitive to load-ing conditions. The slope of this relationship is a meas-ure of ventricular contractility [7]. These modifiedventricular function curves are more specific for intrin-sic ventricular contractile function but fall short ofperfect. Because of different strengths and weaknesses,different variants of ventricular pump function inputsand outputs can be chosen strategically to addressspecific questions. In a clinical context central venouspressure (right ventricular end-diastolic pressure) andcardiac output are readily measurable and are often mostappropriate.Alternative approaches to measurement on intrinsicmyocardial contractility included consideration of therate of change of ventricular chamber pressure duringisovolumic systole—before “afterload” is seen by thecontracting ventricle. The maximum rate of change ofventricular pressure, dP/dtmax, occurs late in isovolumicsystole and increases when contractility is increased [8](for example, by addition of adrenergic agents or cal-cium). While dP/dtmax avoids the problem of afterloadeffect, dP/dtmax is sensitive to changes in preload. Notsurprisingly, when isovolumic contraction starts at agreater end-diastolic volume (VED) then dP/dtmax isgreater. Therefore, empirical corrections have been ap-plied. (dP/dtmax)/VED is another adjusted measure ofventricular contractile function [9]. An interesting exten-sion relates these isovolumic pressure measurements tosarcomere shortening. Vmax [6], the maximum rate ofsarcomere shortening, was calculated by consideringunits of cardiac muscle (sarcomeres) to be made up of acontractile element and a linear series elastic ele-ment—the series elastic element converting contractileelement shortening into pressure. In analogy to cardiacmuscle velocity–length relationships [10], the maximumvelocity of shortening can be extrapolated from a plot ofdP/dt (representing velocity of contractile element short-ening) versus ventricular pressure (representing con-tractile element length). This approach appeared tocircumvent afterload sensitivity and incorporated pre-load. However, these and related computed indices allremain sensitive to changes in preload, afterload, andheart rate to varying degrees.“Curve-fitting” approaches to modifying ventricularfunction curves did not conceptually connect easily withunderlying mechanism—Hill’s sliding filament model ofmuscle contraction. While isovolumic phase measure-ments were linked to underlying mechanism, they re-quired many debatable assumptions. Consideration ofventricular pressure–volume relationships made theconnection to underlying mechanism and incorporatedthe concepts of preload, afterload, diastolic compliance,and contractility [11].Ventricular Function CurveFig. 1 This classic ventricular function curve relates input of theheart (end-diastolic pressure in mmHg) to output of the heart(cardiac output in liters per minute). The ventricular function curveshifts up and to the left when ventricular systolic contractilityincreases. However, increased diastolic compliance and decreasedafterload can also shift the ventricular function curve up and tothe leftWalley Critical Care  (2016) 20:270 Page 2 of 11Ventricular pressure–volume relationshipsUnderlying muscle force–velocity and force–lengthrelationshipsCardiac muscle strips demonstrate length-dependence ofsystolic contractile force (Fig. 2). As the strip of relaxedcardiac muscle is stretched, passive tension rises, but notmuch. That is, the relaxed diastolic muscle strip is verycompliant. When a contraction is elicited by an electricalstimulation the muscle becomes much stiffer so tension(force per area) rises to a maximum systolic value. Whenthe contraction occurs at a greater initial length thenmaximum systolic force increases substantially—an ex-pression of Starling’s law of the heart. This force–lengthrelationship is quite linear but, at extreme musclelengths, the relationship plateaus at a maximum tensionin part because, with increasing stretch, overlap betweenactin and myosin filaments reaches a maximum andthen decreases. Maximum overlap corresponds to amaximum number of actin–myosin cross-bridges and,hence, maximum force. This force–length characteristiccurve describes inherent cardiac muscle properties atone contractile state.Repeat stimulation of the cardiac muscle strip shortlyafter the initial stimulation (potentiated contraction)causes release of further calcium from the sarcoplasmicreticulum into the sarcoplasm, causing increased inter-action of actin and myosin to result in increased con-tractility (Fig. 2). The slope of the potentiated force–length relationship increases. Thus, an increase in theinherent contractility of a cardiac muscle strip results ina shift up and to the left of the force–length relationship,primarily characterized by an increase in slope.Cardiac muscle strips arranged into a three-dimensional,somewhat spherical structure, the heart, then generatepressure due to muscle strip force, at a ventricular chambervolume that relates to underlying muscle strip length. Thus,cardiac muscle force–length relationships underlie ven-tricular pressure–volume relationships and, therefore, sharea number of key features [12].Ventricular pressure–volume loopsTo remove and control the influence of changes in pre-load and afterload, several groups of investigators stud-ied isolated perfused hearts with loading conditionscontrolled using servo systems. Starling’s very early workdemonstrated that increasing end-diastolic pressure andvolume increased stroke volume. The effect of afterloadwas considered next. Weber, Janicki, and colleaguesfound that stroke volume decreased linearly with in-creasing end-systolic pressure [4]. Suga, Sagawa, andcolleagues put these concepts together within a ventricu-lar pressure–volume diagram (Fig. 3) which illustratesthe pressure–volume trajectory of the left ventriclethroughout the cardiac cycle and, in particular, illustratesthe effect of altered preload and altered afterload [13]. Thekey feature is that, at the same contractile state, all con-tractions end on the same end-systolic pressure–volumerelationship (ESPVR).Figure 3 illustrates that during diastole the heart fillsat quite low pressures along the normally compliantdiastolic pressure–volume relationship of the ventricle(labeled “a”). With the onset of isovolumic systole theventricle contracts, raising intraventricular pressure atconstant volume (in the absence of regurgitant valvularheart disease; labeled “b”). When ventricular pressureFig. 2 For an isolated rabbit trabecular muscle strip, force, expressedas force per area = tension, is plotted against starting length. Passivetension during diastole is plotted as open circles. Normal activetension after electrical stimulation is plotted as closed circles.Contractions following a second rapid electrical stimulation, whichincreases the calcium concentration at actin/myosin sliding filamentsand therefore increases contractility (Potentiated), is plotted asopen trianglesVentricular Pressure - Volume Relationships Fig. 3 Left ventricular pressure volume relationships. A cardiac cycleis illustrated by the loop labeled as “a”, “b”, “c”, and “d”. ESPVRend-systolic pressure–volume relationship, LV left ventricularWalley Critical Care  (2016) 20:270 Page 3 of 11exceeds aortic pressure the aortic valve opens andejection occurs (labeled “c”) and continues to an end-systolic pressure–volume point that lies on the ESPVR.Intraventricular pressure decreases during the isovolu-mic relaxation phase (labeled “d”) and the cardiac cyclestarts again.Diastolic filling “a”The diastolic pressure–volume relationship is highlycompliant so that the ventricle fills easily at low diastolicfilling pressures. The relationship is curvilinear, fittedwell with an exponential relationship [14] so that at in-creasing volumes the ventricle becomes increasingly stiff.This curvilinear diastolic pressure–volume relationshipis also fit well with a mathematically similar relationship,P = S × log[(Vm −V)/(Vm −Vo)], where S representsdiastolic myocardial stiffness, Vm is a maximum dia-stolic ventricular volume (set by the pericardium andthe cardiac cytoskeleton [15, 16]), and Vo is diastolicvolume at a pressure of zero [17]. This relationship isasymptotic to the maximum diastolic volume, Vm, sothat maximum volume is reached even if pressure con-tinues to rise; a feature which likely better approximatesthe biological reality that a ventricle can not expand in-definitely [18]. Maximum volume is set by the maximumdimensions of the heart [19] and pericardium [20].Above the maximum volume the ventricle would rup-ture. Either equation conveys the key characteristic ofthe diastolic ventricle—it is highly compliant at low vol-umes and fills easily but becomes much stiffer as it ap-proaches a maximum diastolic volume.Isovolumic contraction “b”Systole starts with active contraction of ventricular muscle.This increase in ventricular wall tension is translated intoan increase in intraventricular pressure via the LaPlace re-lationship. That is, for an approximately spherical ventricleIntraventricular pressure = (Wall tension ×Wall thick-ness × 2)/Radius. In normal hearts, this rise in intraventric-ular pressure closes the mitral valve. Since intraventricularpressure is less than aortic pressure, the aortic valve is alsoclosed. Therefore, during this phase of ventricular contrac-tion, there is no change in ventricular volume. The rate ofrise of pressure during isovolumic systole has been used asa measure of intrinsic ventricular contractile function. Inparticular, the maximum rate of rise of intraventricularpressure, dP/dtmax, (dP/dtmax)/VED, and Vmax are fre-quently used [21].Ejection phase “c”As systolic ventricular contraction continues intraven-tricular pressure rises and then exceeds aortic pressure,which opens the aortic valve and ejection of blood oc-curs. Ejection continues until end-systole. Stroke volume(SV) is the volume of blood ejected with each cardiaccycle and equals end-diastolic volume minus end-systolic volume (SV = VED −VES). Stroke volume islinearly dependent on afterload and, specifically, on end-systolic pressure.It is not surprising that at high afterload (the bloodpressure along segment “c”) the ventricle is not able toeject far whereas at lower afterload the ventricle is ableto eject further. The remarkable finding by Suga andSagawa and others is that end-systolic pressure–volumepoints for differently loaded ejections all fall along anapproximately linear end-systolic pressure–volume rela-tionship (ESPVR in Fig. 3). That is, an increase or de-crease in afterload results in a linearly related decreaseor increase, respectively, in ventricular ejection [4] sothat the end-systolic pressure–volume point lies on thesame ESPVR [13]. Furthermore, if preload is increased(or decreased) so that end-diastolic volume is increased(or decreased) the subsequent stroke volume is in-creased (or decreased) to the same extent so that theend-systolic pressure–volume point still lies on the sameESPVR [22].The end-systolic pressure–volume relationship and EmaxThe ESPVR is approximately a straight line with slopeEmax. The units of this slope are ΔP/ΔV, which is “elas-tance”. (Note that the inverse of elastance is compliance,ΔV/ΔP.) The ESPVR incorporates afterload so that indi-ces of ventricular contractility derived from the ESPVRare independent of afterload [23]. Emax is an excellentmeasure of intrinsic ventricular contractility, which isless load sensitive than other indices of ventricular con-tractility [6] and is insensitive to heart rate within thenormal physiologic range [23]. If Emax increases, it canbe seen (Fig. 3) that the ventricle is able to eject further(to a smaller end-systolic volume) at the same afterload,i.e., it demonstrates increased contractility [22].Time-varying elastanceThe ESPVR is the pressure–volume characteristic curveof the ventricle at end-systole. In an experimental settingthe ESPVR is typically determined by measuring theend-systolic pressure–volume points for several differ-ently loaded cardiac cycles to yield several points along alinear relationship—the ESPVR (Fig. 4) [22]. It is alsopossible to construct pressure–volume characteristiccurves for other time points during the cardiac cycle.For example, pressure–volume points at 50 millisecondsinto the cardiac cycle can just as easily be measured(Fig. 4). Since the slope of each of these lines is ΔP/ΔV(elastance at the specific time point), the cardiac cyclecan be regarded as cyclical changes in elastance of theventricular chamber—time varying elastance [24]. Thus,the muscular ventricular chamber simply cycles fromWalley Critical Care  (2016) 20:270 Page 4 of 11low elastance (high compliance—diastole) to a high elas-tance (low compliance—end-systole) state. The presenceof mitral and aortic valves cause the time-varying elas-tance ventricular chamber to describe a pressure–vol-ume loop. Maximum elastance, Emax, occurs very nearthe end of systole. Because of inertia of blood exiting theaortic valve and aortic impedance, blood flow persistsjust slightly beyond the time of maximum elastance soEmax does not exactly equal ventricular elastance atend-systole, Ees, but these two measures are nearlyequal. The time course of elastance through the cardiaccycle does not change substantially with changes inheart rate [23] but changes markedly with changes incontractility and, indeed by definition, is the full rep-resentation of contractility.During diastole ventricular elastance is at a mini-mum or, said another way, ventricular compliance isat a maximum, to facilitate rapid filling of the ven-tricle at low pressures. The diastolic pressure–volumerelationship is not exactly linear since the diastolicventricle becomes stiffer (less compliant, more ela-stant) as it nears its intrinsic maximum volume andas it impinges upon the constraint provided by themuch stiffer pericardial sac. This points out that pres-sure–volume characteristic curves at any time pointduring the cardiac cycle are not completely linearfrom their diastolic pressure–volume relationship startthrough to their end-systolic pressure–volume rela-tionship maximum [25], but it is impressive that theyare nearly so.Other features of pressure–volume relationshipsThe ESPVR is not completely linear because the systolicventricle has a limit to the maximum pressure that itcan generate [25]. Thus, at high volumes and pressuresthe end-systolic pressure–volume point falls below anexactly linear ESPVR. When the ventricle ejects quicklythe end-systolic pressure–volume point falls slightlybelow an ESPVR generated from slower ejections (orfrom isovolumic contractions). This is due to internalmyocardial viscoelastance. That is, energy is used toovercome viscoelastant characteristics of myocardialmuscle.One perspective is that pressure–volume loops of acardiac cycle are constrained by the diastolic pres-sure–volume relationship below and the ESPVRabove. Thus, a shift up of the diastolic pressure–vol-ume relationship (decreased diastolic compliance) ora shift down of the ESPVR reduces the available oper-ating space for the heart and, ultimately, leads toheart failure. Another perspective of the cardiac cycleillustrated by pressure–volume loops is that theamount of mechanical work performed by the ven-tricle during a cardiac cycle is the integral of pressureand volume, which is simply the area of the interiorof the pressure–volume loop.Pressure–volume relates to metabolic andmechanical functionPressure–volume area and myocardial oxygenconsumptionWork that the ventricle performs must be related to theamount of energy consumed as reflected by myocardialoxygen consumption. However, careful measurementshows the area within a pressure–volume loop (strokework) is not uniformly related to myocardial oxygenconsumption per beat [26]. For example, consider anisovolumic contraction and relaxation with no ejection.There is no area within this vertical line on a ventricularpressure–volume diagram yet the ventricle certainlyconsumes oxygen [26]. Suga and colleagues consideredthat the additional area underneath the ESPVR could beregarded as potential mechanical work [6] (Fig. 5). Thesum of the area within the cardiac cycle pressure–volumeloop plus the additional area under the ESPVR was calledthe pressure–volume area (PVA) [6]. Now the relationshipbetween myocardial oxygen consumption and PVA is lin-ear with a slope of ~30 %, which reflects the efficiency ofthe heart in converting chemical energy into mechanicalenergy [27]. This line intersects the myocardial oxygenconsumption axis so that, even when producing no PVAwork, the heart must consume oxygen to maintain basalcellular function and to recycle calcium back into thesarcoplasmic reticulum with each beat (termed E–Ccoupling) [28].Time varying elastanceFig. 4 Three differently loaded cardiac cycles. The end-systolicpressure–volume points all lie on a line termed the end-systolicpressure–volume relationship (ESPVR). The slope of the ESPVR isEmax, maximum elastance. At any time during systolic contraction(e.g., 50-ms time points are shown as filled circles) a line can be drawnconnecting pressure–volume points from each of the differentlyloaded contractions defining elastance (ΔP/ΔV) at that time point.Ventricular systolic contraction can therefore be regarded as atime-varying elastanceWalley Critical Care  (2016) 20:270 Page 5 of 11An increase in heart rate did not alter the relationshipbetween PVA and myocardial oxygen consumption perbeat [29]. However, an increase in contractility, inducedby increased calcium or by epinephrine, results in a par-allel shift of the relationship [28]. The slope stays thesame, which means that an increment in the chemicalenergy required to produce an increment in PVA workstays the same. However, the myocardial oxygen con-sumption intercept increases, indicating that the heart isconsuming more energy cycling a greater flux of calciumback into the sarcoplasmic reticulum with each beat.An alternative perspective is that myocardial oxygenconsumption is related to the integral of wall tensionover time, the tension–time index [30, 31]. The tension–time index is fundamentally very similar to PVA if con-traction time is approximately related to the theoreticalchange in volume of PVA. PVA leads to a clearer mech-anistic understanding (pressure × volume has units ofwork while tension × time does not) and is, therefore,the focus here.Connection between pressure–volume relationships andventricular function curvesThe pressure–volume loops of a cardiac cycle describedabove are directly related to ventricular function curves(Fig. 6). Stroke volume (determined as the difference be-tween end-diastolic volume and end-systolic volume)multiplied by heart rate yields cardiac output. For aknown systolic contractile state (ESPVR), diastolic pres-sure–volume relationship, and afterload, a unique strokevolume is determined for each end-diastolic pressure.Cardiac output can then be calculated yielding a ven-tricular function curve (Fig. 6). Since stroke volume isinfluenced separately by the ESPVR, the diastolic pres-sure–volume relationship, and afterload, it follows thatventricular function curves are affected by more thanjust changes in systolic contractility. For example, de-creasing afterload results in increased systolic ejection,particularly in the failing heart. This results in increasedstroke volume and cardiac output so that decreasedafterload shifts the ventricular function curve up and tothe left (Fig. 1). Conversely, decreased compliance (in-creased stiffness) of the diastolic left ventricle decreasesstroke volume because end-diastolic volume is decreasedat the same filling pressure. A decrease in contractility(ESPVR), decrease in end-diastolic compliance, orincrease in afterload all decrease stroke volume andtherefore shift the curve downward and cannot be dis-tinguished on a cardiac function curve.Pressure - Volume - Area (PVA)Fig. 5 Pressure–volume area (PVA) is the area within the cardiaccycle pressure–volume (P-V) loop plus the area under the ESPVR.PVA linearly correlates with myocardial oxygen consumption.LV left ventricularFig. 6 Stroke volume, derived from the left-hand panel, multiplied by heart rate yields cardiac output on the right-hand panel. Thus, for a givenESPVR, diastolic pressure–volume relationship, and afterload, a range of end-diastolic pressures on the left-hand panel yield the ventricular functioncurve on the right-hand panel. LV left ventricularWalley Critical Care  (2016) 20:270 Page 6 of 11Interaction with the vasculatureInteraction of ventricular pressure–volume relationshipswith the arterial vasculatureThe left ventricle ejects blood into the aorta so leftventricular elastance interacts with aortic elastanceduring the ejection phase of systole when the aorticvalve is open. Aortic elastance can be estimated fromthe slope of a plot of aortic pressure versus volumeof blood ejected into the aorta (Fig. 7). An optimalratio of stroke work (useful work) to PVA (wastedenergy) of the left ventricle is achieved when leftventricular elastance is approximately equal to aorticelastance. To understand this consider two connectedballoons. Note that elastance equals pressure changeper volume change. If the balloons have equal elas-tance, then they are at equilibrium so the pressure ×volume change in one balloon is exactly counterba-lanced by the pressure × volume change in the otherballoon; transferring volume from one balloon to theother can occur with no external work. Ventricularelastance greater than arterial elastance results in apressure drop from the ventricular balloon to the aor-tic balloon, which results in lost energy [32]. If ven-tricular elastance is less than arterial elastance, thenenergy is wasted as potential mechanical work on aPVA diagram (Fig. 7).Fig. 7 An arterial elastance line can be added to a PVA diagram (Fig. 5) by considering the rise in pressure within the arterial system with anincrease in arterial volume (equals the decrease in ventricular volume). Compared with the healthy state (top panel), a decrease in ventricularelastance and an increase in arterial elastance mean that more energy is wasted on the PVA diagram. LV left ventricular, P-V pressure–volumeWalley Critical Care  (2016) 20:270 Page 7 of 11In health left ventricular end-systolic elastance (end-systolic pressure divided by end-systolic volume) is simi-lar but somewhat less than aortic elastance (slope of theaortic pressure–volume relationship, which is actually a“dynamic” elastance). Over the observed range strokework and efficiency remain close to optimal [33]. Duringthe ejection phase left ventricular elastance increases asdescribed by Suga and Sagawa’s time-varying elastance.Interestingly, elastance of the aorta also increases duringthe ejection phase since the pliable aorta becomes stifferas it fills during the ejection phase. Overall, there is rea-sonable matching of ventricular elastance to aortic elas-tance. This minimizes the amount of work done by theheart in transferring blood from the ventricle to theaorta. Energy due to blood volume stored in the elastantaorta is then available to drive blood flow through per-ipheral arteries during diastole. In a modeling study,Magder et al. [34] also included changes in resistance.They found that aortic compliance and the consequentelastance is only about one-eighth of ventricular end-systolic elastance. They surmised that changes in aorticelastance, as used by Burkhoff and Sagawa [32], may alsoreflect changes in resistance.In disease states ventricular/aortic compliance becomesmismatched. Heart failure due to decreased systolic con-tractility means that ventricular systolic elastance ingreatly decreased. If the cause is related to coronary arterydisease, then it is very common to also find a diseased, stiffaorta. This accentuates the mismatch between ventricularand aortic compliance during systole, which means that agreater fraction of the work done by the ventricle iswasted (a greater fraction of PVA is under the ESPVR andis not stroke work; Fig. 7).Interaction of the heart with venous blood flow returningto the heartThe pressure–volume characteristics of the ventriclemean that if more blood returns to the heart (more dia-stolic filling so a greater VED), then the ventricle will stilleject to the same ESPVR so that stroke volume will in-crease exactly as much as VED increased. This gives theheart the basic characteristic that it will eject anyamount of blood that flows back to it. This allows regu-latory control of cardiac output to move to the periph-eral circulation—a necessary feature because tissuehypoxia is best sensed by the peripheral vasculaturewhere oxygen demand is occurring.The factors governing venous return are illustratedin Fig. 8. When right atrial pressure equals mean sys-temic pressure there is no driving pressure gradientfor blood flow back to the heart; thus, venous returnis zero. As right atrial pressure is reduced the impedi-ment to blood flow back to the heart decreases sothat venous return rises approximately linearly. Theslope of this venous return curve has units that arethe inverse of a resistance—termed “resistance to venousreturn” [35]. When right atrial pressure is reduced to ap-proximately zero the central veins collapse at the level ofthe diaphragm, limiting venous flow.It can be seen that venous return at any right atrialpressure can be increased by increasing mean systemicpressure or by decreasing resistance to venous return.Mean systemic pressure is a vascular compartment pres-sure that arises from venous blood volume distendingthe systemic veins. If the volume of the distensible ven-ous compartment is increased, then mean systemic pres-sure increases. Alternatively, if the capacitance of thevenous compartment decreases, say by catecholamineinfusion or increased sympathetic tone, then the pres-sure within the venous compartment can increase with-out a change in volume.In steady state the amount of blood returning to theheart must equal the amount of blood leaving the heartso that venous return must equal cardiac output. Indeed,stroke volume must, on average, equal “stroke return”.Therefore, as illustrated in Fig. 9, the ventricular func-tion curve and venous return curve can be plotted onthe same set of axes. The intersection of the ventricularfunction curve and venous return curve give the value ofsteady state cardiac output and the value of steady stateright atrial pressure.Implications for treatment of cardiac dysfunctionEffect of inotropic agents and afterload on normal andfailing heart functionIn health, cardiac output is determined almost exclu-sively by the factors governing venous return (meanFactors that govern venous returnFig. 8 Lowering right atrial pressure increases blood flow back tothe heart—venous return. This venous return curve can be shifted,primarily by an increase in the x-axis intercept—mean systemicpressure. RVR resistance to venous returnWalley Critical Care  (2016) 20:270 Page 8 of 11Effects of inotropic agents and afterload reduction on normal and failing hearts Fig. 10 Top: in a normal heart increased contractility does not change the normally steep ventricular function curve so this does not changecardiac output much. In contrast, changes in venous return cause large changes in cardiac output so, in health, cardiac output is primarilycontrolled by the peripheral circulation. Bottom: in a failing heart changes in venous return curves no longer result in substantial changes incardiac output but raise venous pressure (solid circle to open circle on bottom ventricular function curve). Now an increase in contractility resultsin a substantial increase in cardiac output and decrease in end-diastolic pressure (filled circle on lower ventricular function curve to filled circle onupper ventricular function curve)Interaction of venous return curves with ventricular function curves Fig. 9 Ventricular function curves can be plotted on the same set of axes and venous return curves. In steady state cardiac output must equalvenous return so the intersection (filled circle) identifies the cardiac output and end-diastolic pressure of the cardiovascular system. A decrease incardiac function results in a decrease in cardiac output and an increase in end-diastolic pressure (open circle)Walley Critical Care  (2016) 20:270 Page 9 of 11system pressure, resistance to venous return, right atrialpressure). The top panel in Fig. 10 shows that substantialchanges in cardiac output occur with shifts in the ven-ous return curve. In contrast, a shift of the ventricularfunction curve due to either an increase in ventricularcontractility or a decrease in afterload hardly alters car-diac output because, in health, the ESPVR is already verysteep (Fig. 10).When Emax, the slope of the ESPVR, is low thendoubling of Emax or a reduction in afterload leads to avery substantial shift up of the ventricular functioncurve. This results in a large increase in cardiac outputat a decreased end-diastolic pressure and volume. Thus,increasing ventricular contractility is an ineffective strat-egy when the heart is normal but is a highly effectivestrategy to increase cardiac output when systolic con-tractility is reduced in a disease state (Fig. 10, bottompanel). Similarly, arterial vasodilators only reduce arterialpressure in healthy individuals but are very effective inincreasing ventricular function and cardiac output whenEmax is low.ConclusionsMany aspects of left ventricular function are explainedby considering ventricular pressure–volume characteris-tics. Ventricular contractility, diastolic compliance, ac-tual and potential stroke work, and the interaction ofthe heart with the arterial and venous circulations allcan be elucidated from ventricular pressure–volumecharacteristics. Consideration of ventricular pressure–volume relationships highlight features that allow theheart to efficiently respond to any demand for cardiacoutput and oxygen delivery.AbbreviationsdP/dtmax, maximum rate of change of ventricular pressure; Emax, maximumelastance; ESPVR, end-systolic pressure–volume relationship; PVA, pressure–volumearea; SV, stroke volume; VED, ventricular volume at end-diastole; VES, ventricularvolume at end-systole; Vmax, maximum velocity of shortening of the contractileelement; ΔP/ΔV, elastanceFundingCanadian Institutes of Health Research.Competing interestsThe author declares that he has no competing interests.References1. Elzinga G, Westerhof N. How to quantify pump function of the heart. Thevalue of variables derived from measurements on isolated muscle. Circ Res.1979;44(3):303–8.2. Katz AM. Ernest Henry Starling, his predecessors, and the “Law of the Heart”.Circulation. 2002;106(23):2986–92.3. Imperial ES, Levy MN, Zieske H. Outflow resistance as an independentdeterminant of cardiac performance. Circ Res. 1961;9(6):1148–55.4. Weber KT, Janicki JS, Reeves RC, Hefner LL, Reeves TJ. Determinants ofstroke volume in the isolated canine heart. J Appl Physiol. 1974;37(5):742–7.5. Sarnoff SJ, Berglund E. Ventricular function. I. Starling’s law of the heartstudied by means of simultaneous right and left ventricular function curvesin the dog. Circulation. 1954;9(5):706–18.6. Paley HW, McDonald IG, Blumenthal J, Mailhot J. The effects of posture andisoproterenol on the velocity of left ventricular contraction in man. Thereciprocal relationship between left ventricular volume and myocardial wallforce during ejection on mean rate of circumferential shortening. J ClinInvest. 1971;50:2283–94.7. Glower DD, Spratt JA, Snow ND, Kabas JS, Davis JW, Olsen CO, Tyson GS,Sabiston Jr DC, Rankin JS. Linearity of the Frank-Starling relationship in theintact heart: the concept of preload recruitable stroke work. Circulation.1985;71(5):994–1009.8. Noble MI. Problems concerning the application of concepts of musclemechanics to the determination of the contractile state of the heart.Circulation. 1972;45(2):252–5.9. Little WC. The left ventricular dP/dtmax-end-diastolic volume relation inclosed-chest dogs. Circ Res. 1985;56(6):808–15.10. Chiu YC, Walley KR, Ford LE. Comparison of the effects of different inotropicinterventions on force, velocity, and power in rabbit myocardium. Circ Res.1989;65(5):1161–71.11. Sagawa K. End-systolic pressure-volume relationship in retrospect andprospect. Fed Proc. 1984;43(9):2399–401.12. Suga H, Sagawa K. Mathematical interrelationship between instantaneousventricular pressure-volume ratio and myocardial force-velocity relation. AnnBiomed Eng. 1972;1(2):160–81.13. Sagawa K, Suga H, Shoukas AA, Bakalar KM. End-systolic pressure/volumeratio: a new index of ventricular contractility. Am J Cardiol. 1977;40(5):748–53.14. Glantz SA, Kernoff RS. Muscle stiffness determined from canine leftventricular pressure-volume curves. Circ Res. 1975;37(6):787–94.15. Tyberg JV, Smith ER. Ventricular diastole and the role of the pericardium.Herz. 1990;15(6):354–61.16. Holt JP, Rhode EA, Kines H. Pericardial and ventricular pressure. Circ Res.1960;8:1171–81.17. Nikolic S, Yellin EL, Tamura K, Vetter H, Tamura T, Meisner JS, Frater RW.Passive properties of canine left ventricle: diastolic stiffness and restoringforces. Circ Res. 1988;62(6):1210–22.18. Walley KR, Cooper DJ. Diastolic stiffness impairs left ventricular functionduring hypovolemic shock in pigs. Am J Physiol. 1991;260(3 Pt 2):H702–12.19. Glantz SA, Parmley WW. Factors which affect the diastolic pressure-volumecurve. Circ Res. 1978;42(2):171–80.20. Glantz SA, Misbach GA, Moores WY, Mathey DG, Lekven J, Stowe DF,Parmley WW, Tyberg JV. The pericardium substantially affects the leftventricular diastolic pressure-volume relationship in the dog. Circ Res.1978;42(3):433–41.21. Mahler F, Ross Jr J, O'Rourke RA, Covell JW. Effects of changes in preload,afterload and inotropic state on ejection and isovolumic phase measures ofcontractility in the conscious dog. Am J Cardiol. 1975;35(5):626–34.22. Suga H, Sagawa K. Instantaneous pressure-volume relationships andtheir ratio in the excised, supported canine left ventricle. Circ Res.1974;35(1):117–26.23. Suga H, Sagawa K, Shoukas AA. Load independence of the instantaneouspressure-volume ratio of the canine left ventricle and effects of epinephrineand heart rate on the ratio. Circ Res. 1973;32(3):314–22.24. Suga H. Theoretical analysis of a left-ventricular pumping model based onthe systolic time-varying pressure-volume ratio. IEEE Trans Biomed Eng.1971;18(1):47–55.25. Suga H, Yamada O, Goto Y, Igarashi Y. Peak isovolumic pressure-volumerelation of puppy left ventricle. Am J Physiol. 1986;250(2 Pt 2):H167–72.26. Khalafbeigui F, Suga H, Sagawa K. Left ventricular systolic pressure-volumearea correlates with oxygen consumption. Am J Physiol. 1979;237(5):H566–9.27. Suga H, Hayashi T, Shirahata M. Ventricular systolic pressure-volume area aspredictor of cardiac oxygen consumption. Am J Physiol. 1981;240(1):H39–44.28. Suga H, Hisano R, Goto Y, Yamada O, Igarashi Y. Effect of positive inotropicagents on the relation between oxygen consumption and systolic pressurevolume area in canine left ventricle. Circ Res. 1983;53(3):306–18.29. Suga H, Hisano R, Hirata S, Hayashi T, Yamada O, Ninomiya I. Heart rate-independent energetics and systolic pressure-volume area in dog heart. AmJ Physiol. 1983;244(2):H206–14.30. Suga H, Goto Y, Futaki S, Kawaguchi O, Yaku H, Hata K, Takasago T. Systolicpressure-volume area (PVA) as the energy of contraction in Starling’s law ofthe heart. Heart Vessels. 1991;6(2):65–70.Walley Critical Care  (2016) 20:270 Page 10 of 1131. Rooke GA, Feigl EO. Work as a correlate of canine left ventricular oxygenconsumption, and the problem of catecholamine oxygen wasting. Circ Res.1982;50(2):273–86.32. Burkhoff D, Sagawa K. Ventricular efficiency predicted by an analyticalmodel. Am J Physiol. 1986;250(6 Pt 2):R1021–7.33. De Tombe PP, Jones S, Burkhoff D, Hunter WC, Kass DA. Ventricular strokework and efficiency both remain nearly optimal despite altered vascularloading. Am J Physiol. 1993;264(6 Pt 2):H1817–24.34. Magder S, Veerassamy S, Bates JH. A further analysis of why pulmonaryvenous pressure rises after the onset of LV dysfunction. J Appl Physiol(1985). 2009;106(1):81–90.35. Mitzner W, Goldberg H. Effects of epinephrine on resisitive and compliantproperties of the canine vasculature. J Appl Physiol. 1975;39(2):272–80.Walley Critical Care  (2016) 20:270 Page 11 of 11


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