Underlying muscle force–velocity and force–length relationships
Cardiac muscle strips demonstrate length-dependence of systolic contractile force (Fig. 2). As the strip of relaxed cardiac muscle is stretched, passive tension rises, but not much. That is, the relaxed diastolic muscle strip is very compliant. When a contraction is elicited by an electrical stimulation the muscle becomes much stiffer so tension (force per area) rises to a maximum systolic value. When the contraction occurs at a greater initial length then maximum systolic force increases substantially—an expression of Starling’s law of the heart. This force–length relationship is quite linear but, at extreme muscle lengths, the relationship plateaus at a maximum tension in part because, with increasing stretch, overlap between actin and myosin filaments reaches a maximum and then decreases. Maximum overlap corresponds to a maximum number of actin–myosin cross-bridges and, hence, maximum force. This force–length characteristic curve describes inherent cardiac muscle properties at one contractile state.
Repeat stimulation of the cardiac muscle strip shortly after the initial stimulation (potentiated contraction) causes release of further calcium from the sarcoplasmic reticulum into the sarcoplasm, causing increased interaction of actin and myosin to result in increased contractility (Fig. 2). The slope of the potentiated force–length relationship increases. Thus, an increase in the inherent contractility of a cardiac muscle strip results in a 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 generate pressure due to muscle strip force, at a ventricular chamber volume that relates to underlying muscle strip length. Thus, cardiac muscle force–length relationships underlie ventricular pressure–volume relationships and, therefore, share a number of key features .
Ventricular pressure–volume loops
To remove and control the influence of changes in preload and afterload, several groups of investigators studied isolated perfused hearts with loading conditions controlled using servo systems. Starling’s very early work demonstrated that increasing end-diastolic pressure and volume increased stroke volume. The effect of afterload was considered next. Weber, Janicki, and colleagues found that stroke volume decreased linearly with increasing end-systolic pressure . Suga, Sagawa, and colleagues put these concepts together within a ventricular pressure–volume diagram (Fig. 3) which illustrates the pressure–volume trajectory of the left ventricle throughout the cardiac cycle and, in particular, illustrates the effect of altered preload and altered afterload . The key feature is that, at the same contractile state, all contractions end on the same end-systolic pressure–volume relationship (ESPVR).
Figure 3 illustrates that during diastole the heart fills at quite low pressures along the normally compliant diastolic pressure–volume relationship of the ventricle (labeled “a”). With the onset of isovolumic systole the ventricle contracts, raising intraventricular pressure at constant volume (in the absence of regurgitant valvular heart disease; labeled “b”). When ventricular pressure exceeds aortic pressure the aortic valve opens and ejection occurs (labeled “c”) and continues to an end-systolic pressure–volume point that lies on the ESPVR. Intraventricular pressure decreases during the isovolumic relaxation phase (labeled “d”) and the cardiac cycle starts again.
Diastolic filling “a”
The diastolic pressure–volume relationship is highly compliant so that the ventricle fills easily at low diastolic filling pressures. The relationship is curvilinear, fitted well with an exponential relationship  so that at increasing volumes the ventricle becomes increasingly stiff. This curvilinear diastolic pressure–volume relationship is also fit well with a mathematically similar relationship, P = S × log[(Vm − V)/(Vm − Vo)], where S represents diastolic myocardial stiffness, Vm is a maximum diastolic ventricular volume (set by the pericardium and the cardiac cytoskeleton [15, 16]), and Vo is diastolic volume at a pressure of zero . This relationship is asymptotic to the maximum diastolic volume, Vm, so that maximum volume is reached even if pressure continues to rise; a feature which likely better approximates the biological reality that a ventricle can not expand indefinitely . Maximum volume is set by the maximum dimensions of the heart  and pericardium . Above the maximum volume the ventricle would rupture. Either equation conveys the key characteristic of the diastolic ventricle—it is highly compliant at low volumes and fills easily but becomes much stiffer as it approaches a maximum diastolic volume.
Isovolumic contraction “b”
Systole starts with active contraction of ventricular muscle. This increase in ventricular wall tension is translated into an increase in intraventricular pressure via the LaPlace relationship. That is, for an approximately spherical ventricle Intraventricular pressure = (Wall tension × Wall thickness × 2)/Radius. In normal hearts, this rise in intraventricular pressure closes the mitral valve. Since intraventricular pressure is less than aortic pressure, the aortic valve is also closed. Therefore, during this phase of ventricular contraction, there is no change in ventricular volume. The rate of rise of pressure during isovolumic systole has been used as a measure of intrinsic ventricular contractile function. In particular, the maximum rate of rise of intraventricular pressure, dP/dtmax, (dP/dtmax)/VED, and Vmax are frequently used .
Ejection phase “c”
As systolic ventricular contraction continues intraventricular pressure rises and then exceeds aortic pressure, which opens the aortic valve and ejection of blood occurs. Ejection continues until end-systole. Stroke volume (SV) is the volume of blood ejected with each cardiac cycle and equals end-diastolic volume minus end-systolic volume (SV = VED − VES). Stroke volume is linearly dependent on afterload and, specifically, on end-systolic pressure.
It is not surprising that at high afterload (the blood pressure along segment “c”) the ventricle is not able to eject far whereas at lower afterload the ventricle is able to eject further. The remarkable finding by Suga and Sagawa and others is that end-systolic pressure–volume points for differently loaded ejections all fall along an approximately linear end-systolic pressure–volume relationship (ESPVR in Fig. 3). That is, an increase or decrease in afterload results in a linearly related decrease or increase, respectively, in ventricular ejection  so that the end-systolic pressure–volume point lies on the same ESPVR . Furthermore, if preload is increased (or decreased) so that end-diastolic volume is increased (or decreased) the subsequent stroke volume is increased (or decreased) to the same extent so that the end-systolic pressure–volume point still lies on the same ESPVR .
The end-systolic pressure–volume relationship and Emax
The ESPVR is approximately a straight line with slope Emax. The units of this slope are ΔP/ΔV, which is “elastance”. (Note that the inverse of elastance is compliance, ΔV/ΔP.) The ESPVR incorporates afterload so that indices of ventricular contractility derived from the ESPVR are independent of afterload . Emax is an excellent measure of intrinsic ventricular contractility, which is less load sensitive than other indices of ventricular contractility  and is insensitive to heart rate within the normal physiologic range . If Emax increases, it can be 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 .
The ESPVR is the pressure–volume characteristic curve of the ventricle at end-systole. In an experimental setting the ESPVR is typically determined by measuring the end-systolic pressure–volume points for several differently loaded cardiac cycles to yield several points along a linear relationship—the ESPVR (Fig. 4) . It is also possible to construct pressure–volume characteristic curves for other time points during the cardiac cycle. For example, pressure–volume points at 50 milliseconds into 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 cycle can be regarded as cyclical changes in elastance of the ventricular chamber—time varying elastance . Thus, the muscular ventricular chamber simply cycles from low elastance (high compliance—diastole) to a high elastance (low compliance—end-systole) state. The presence of mitral and aortic valves cause the time-varying elastance ventricular chamber to describe a pressure–volume loop. Maximum elastance, Emax, occurs very near the end of systole. Because of inertia of blood exiting the aortic valve and aortic impedance, blood flow persists just slightly beyond the time of maximum elastance so Emax does not exactly equal ventricular elastance at end-systole, Ees, but these two measures are nearly equal. The time course of elastance through the cardiac cycle does not change substantially with changes in heart rate  but changes markedly with changes in contractility and, indeed by definition, is the full representation of contractility.
During diastole ventricular elastance is at a minimum or, said another way, ventricular compliance is at a maximum, to facilitate rapid filling of the ventricle at low pressures. The diastolic pressure–volume relationship is not exactly linear since the diastolic ventricle becomes stiffer (less compliant, more elastant) as it nears its intrinsic maximum volume and as it impinges upon the constraint provided by the much stiffer pericardial sac. This points out that pressure–volume characteristic curves at any time point during the cardiac cycle are not completely linear from their diastolic pressure–volume relationship start through to their end-systolic pressure–volume relationship maximum , but it is impressive that they are nearly so.
Other features of pressure–volume relationships
The ESPVR is not completely linear because the systolic ventricle has a limit to the maximum pressure that it can generate . Thus, at high volumes and pressures the end-systolic pressure–volume point falls below an exactly linear ESPVR. When the ventricle ejects quickly the end-systolic pressure–volume point falls slightly below an ESPVR generated from slower ejections (or from isovolumic contractions). This is due to internal myocardial viscoelastance. That is, energy is used to overcome viscoelastant characteristics of myocardial muscle.
One perspective is that pressure–volume loops of a cardiac cycle are constrained by the diastolic pressure–volume relationship below and the ESPVR above. Thus, a shift up of the diastolic pressure–volume relationship (decreased diastolic compliance) or a shift down of the ESPVR reduces the available operating space for the heart and, ultimately, leads to heart failure. Another perspective of the cardiac cycle illustrated by pressure–volume loops is that the amount of mechanical work performed by the ventricle during a cardiac cycle is the integral of pressure and volume, which is simply the area of the interior of the pressure–volume loop.