## Straight to the Heart

1.  This article begins with a REVIEW of expectations for the "Elastance model" of pump function.  In the bioengineering literature this is also known as "compliance pumping" as it has to do with a cardiac chamber that alters its (distending) pressure-volume relationship (PVR) over the course of the cardiac cycle; the native model includes the time-varying compliance (the reciprocal of elastance) of the pump but no resistive or inertial features.  The most basic elastance model assumes a linear relationship between pressure and volume at each instant in time:  $$p(t) = E(t) [V(t)-V_0(t)]$$ where $$p(t)$$ is the chamber distending pressure, $$E(t)$$ is the time-varying elastance, $$V(t)$$ is the instantaneous volume of the chamber, $$V_0(t)$$ is the chamber volume at zero distending pressure (also varies with time).   I'm assuming most cardiologists are familiar with this model and the essential results.  However ....
2. $$\Large \text{Critical Concept:}$$ SIZE MATTERS! The elastance model is of value principly for clarifying cardiac responses to acute changes in preload, afterload, and contractility in a particular LV; it is not directly applicable for comparing hearts that differ in their intrinsic size, shape, or relative wall thickness.
• Although this was clear in the original publications describing the model, the subsequent literature includes comparisons and interpretations for diseased hearts (left ventricular chamber) where remodeling has occurred.  In the absence of an additional conceptual framework, these are not valid comparisons since $$E(t)$$ is entirely dependent on the intrinsic size of the chamber (inversely proportional)   $$E(t)$$ also depends on the amount of muscle tissue, i.e. relative wall thickness, and chamber shape which must be accounted for in comparing one LV to another.
• The compliance of a pressure vessel is proportional to its intrinsic volume; the elastance is inversely proportional.  A great Dane LV, for example, has a lower $$E_{\text{max}}$$ than a Chihuahua LV with the same geometry (shape, relative wall thickness) and muscle characteristics.  These physical attributes are due to the relationship between compliance and vessel size and the relationships are true irrespective of biological characteristics.
• To compare hearts of differing size, we must normalize (transform) both the volume and the elastance for size.  The elastance of each chamber decreases specifically in proportion to intrinsic volume.  So the value of $$E_{\text{max}}$$ is lower for a larger heart irrespective of the "contractility".
• This concept applies also when intrinsic chamber size differences are due to remodelling / disease as opposed to the intrinsic size of the individual.  An LV with DCM likely has a lower $$E_{\text{max}}$$ due to decreased "contractility" (assumed here to be a property of the muscle specifically), but also because the chamber is larger and the relative wall thickness is (likely) decreased; there could also be a geometric contribution due to a change in vessel shape.
• The distending pressure of a vessel (active AND/OR passive) depends on a volume ratio,  $$V/V_s$$ where $$V_s$$ is a scaling volume that represents the intrinsic size of the vessel. Add 1.0 mL of blood to a great Dane heart and the pressure goes up a little; add the same amount to a Chihuahua heart and the pressure goes up a lot.  Increase the volume of either by the same volume fraction ( $$V/V_s$$ ) and pressure increase is the same (relative wall thickness, shape, and muscle/material characteristics being equal).
3. As an aside, the basic model includes elastance only and does not depend on the rate of change volume (first time derivative of volume, i.e. $$dV/dt$$ due to viscous friction or the "ejection effect") or inertial effects (cardiac/fluid mass and accelerations relating to the second time derivative of volume, i.e. $$d^2V/dt^2$$ ).  These are other physical aspects of cardiac function considered in the bioengineering literature.

## Review

Medical cardiology is largely a correlative "science".  We know when we see a reduced ejection fraction (EF) that there's likely a problem, but we've also had to invent a "new" category of heart disease that has a normal EF.  We also know that we'll see individuals with a reduced EF that are in pretty good shape.  So in a nutshell - a reduced EF is a bad thing when it occurs as a result of a disease where a reduced EF is a bad thing.  (You can quote me on that and I'm only being a little bit facetious about this.)  Each/every index/measurement in medicine has a context.   Sure we all know the formula for EF, but we didn't understand that there's a category of heart problems with a normal EF because we don't understand what EF is as it relates to the physics and physiology of the heart.  We didn't invent a new category of heart disease, we just recognized that there's more to the interpretations than originally thought.

We need an expectation of how the EF is likely to behave – how it changes under various circumstances related to remodeling.  This article analyzes these expectations using pencil, paper, and the thing between my ears so you can bet that it's not the whole story.   However I believe there is something to be gained by this approach.  We'll start with a review of the left ventricular pressure volume loop; the elastance model of the left ventricle will be used to "predict" various outcomes.  We'll use a very stylized PV Loop throughout for the discussion as follows:

Obviously this is an oversimplification; I'm using straight lines for the end-systolic (PVRs) and end-diastolic (PVRd) pressure-volume relationships, and the PV Loop is shown as a box just so you can remember where it is (we know the thing is curvier than shown).  (Note: I'm using PVRs and PVRd terminology because that implies the possibility of more realistic functions than straight lines.  Also that way I don't have to fight with anyone over definitions for "elastance" and "compliance".) For simplicity we'll say that the normal end-diastolic pressure is about 10 (Torr) and the end-systolic pressure is about 100 (Torr) as suggested by the figure.  (We will eventually get to a more sophisticated model in Circulation Explorer.)  The slope of the PVRs is called Emax where E refers to an elastance that clearly has units of pressure / volume on the figure.  The elastance model has to do principally with explaining cardiac function under various conditions ( preload, afterload, contractility ) for a specific heart – a specific left ventricle.  By this I mean that the model applies to a heart with fixed intrinsic properties.  It is not allowed to change its muscle mass, size, collagen content, shape, fiber arrangement, etc. etc.; that stipulation doesn't seem to be fully apparent in the literature.

For all PV loops that follow, pressure will be the y-axis and volume the x-axis.  Proceeding with the usual diagrams and thought experiments, here is the behavior we expect to see for this particular heart if we allow the preload to change over a range:

I've arbitrarily assumed a normal EF of 62.5% so the red loop above is considered the baseline with preload varying both above and below the assumed normal of 10 Torr.   Keeping the end-systolic pressure unchanged, an increase in the end diastolic pressure increases the diastolic volume of the heart and increases the ejection volume. The ejection fraction is not a constant of course but increases with increasing preload, i.e. end-diastolic pressure or end-diastolic volume ( the Frank- Starling mechanism).

We should also make note the fact that the slope of the PVRd (Emin ?) tells us something about the sensitivity of the heart to preload.  The slope in the above example happens to be Emin ~0.167 Torr/mL and this heart changes its stroke volume a LOT for a small change in preload (the normal heart is preload dependent).  Other things being equal, (afterload, contractility) we can predict the change in stroke volume resulting from a change in filling pressure as Δp/Emin.  i.e.  1/0.167 mL for each mmHg change in end diastolic pressure in this case (that is if we could somehow magically maintain the same end-systolic pressure despite the increase in cardiac output). Ejection fraction also is highly dependent on the preload in this example; EF is a preload dependent index.

As a counterexample, the figure below is shown at the same scale but has an Emin that is twice the value of the previous example (0.333 Torr/mL, loss of diastolic compliance).   With everything else the same, and allowing the end-systolic pressure to vary over the same range as before, both the stroke volume and ejection fraction are reduced.  This ventricle is less sensitive to preload, by a factor of 2 in comparison with the last example, with a change in stroke volume of 1/0.333 for each mmHg change in end diastolic pressure.  However this LV requires a greater preload to achieve a normal stroke volume or ejection  fraction and so is termed preload dependent  in comparison with the last example.

For the next example, we allow the end-systolic pressure to vary - the afterload.  Obviously we would be talking about some kind of an intervention that causes the aortic pressure to increase such as administration of a pressor or gradually clamping off the aorta in an experimental setting.  We see of course that stroke volume and ejection fraction decrease with increasing end-systolic pressure ( afterload ).  The slope of PVRs (the value of Emax) also tells us something about the ventricle's  sensitivity to afterload.   This relatively normal heart has an Emax value of 363.6 Torr/mL and we'd expect the stroke volume to decrease by 1/363.6 mL for every mmHg increase in end systolic pressure.  A normal heart is not very sensitive to afterload; it is relatively afterload independent.  Once again however, EF changes with afterload.

As a counterexample, consider the loops from the following diseased heart in which Emax is depressed by a factor of 2  (Emax = 181.8).  Both stroke volume and ejection fraction are depressed and the stroke volume decreases by 1/181.8 mL for each mmHg increase in end-systolic pressure i.e. twice as much as the previous example.  This is an afterload dependent heart relative to the last example.

And then of course there are changes in function due to "contractility". In the context of pressure-volume loops, the slope of PVRs, i.e. Emax defines contractility ( although we'll see that it doesn't).  Keeping both preload and afterload unchanged ( end-diastolic and and systolic pressure ), we observe that an increase in Emax (e.g. due to administration of an inotrope, blue loop) increases both stroke volume and ejection fraction (compared to baseline red loop).

The green and yellow loops demonstrate decreasing contractility of course which affects both stroke volume and EF.  Remember again that these are changes or interventions occurring within a particular heart.  This doesn't allow us compare Emax from one heart to another as we will soon see.

## Changes in Cardiac Size

The foregoing was by way of review.  Now we start to work on understanding comparisons between hearts. including comparisons where a particular heart has undergone remodeling, i.e. a change in size and structure.  The original research in this area does not  accommodate these potentialities.  We'll begin with a simple question and ask which of the following 2 PVRs lines portrays the better contractility (Emax) ?

In accordance with the usual application of the elastance model, we would say the blue PVRs curve has a greater slope (Emax) and better contractility.  However, the fact is that there simply isn't enough information on the plot to determine this. Compared with the blue, the red PVRs can occur simply due to a larger heart, e.g. a larger mammal or a larger breed of dog.  The native elastance model of heart function is not normalized for ventricular size.  The slope of the PVRs (Emax) would also decrease due to a decrease in relative wall thickness; we're going to limit the discussion  largely to size-related issues.    The size dependence problem actually is apparent directly from the fact that the x-axis has dimensions of volume which is entirely size-dependent.  The next figure shows stylized PVR relationships, systole and diastole, with associated PV loops, for mammals of differing size.  All the PV relationships and loops are NORMAL.

Now, I haven't found the article that shows this comparison using measured (actual) data and you may suspect that I simply made this up (I did).  However if you work with a wide range of animal sizes you will appreciate that the essential relationships shown could not be otherwise, at least in a general sense.

We can also revert to an analytical approach for a simplified pressure vessel (e.g. a sphere) in terms of the deformations and volume changes resulting from a given distending pressure; we can derive the PVR.  That is done for you HERE  and discussed further within the framework of the cardiac elastance model HERE.  The fact is that the compliance of a pressure vessel is proportional to its intrinsic size (volume specifically); the elastance is inversely proportional.  The comparison applies to pressure vessels of proportionally differing size but of the same material (material properties), shape, and relative wall thickness.  Make sure you understood the last part.  The larger pressure vessel has a proportionally thicker wall than the smaller; the larger is still more compliant.  I'm being categorical about this; the physics is rock solid.  Also note: All the LVs are running the same wall stress -- all the way around the loop.  A larger chamber (radius) does not mean the wall stress increases; it's the wall thickness to radius ratio that matters (relative wall thickness) for wall stress and we're keeping that constant in the comparisons.

So if we look at 2 hearts that are made of the same muscle and have the same shape and relative wall thickness, the physics requires hearts of differing size to exhibit size-dependent changes in compliance (elastance) as suggested in the above figure.  This is common knowledge in the engineering and physical hemodynamics literature and the compliance of pressure vessel can be expressed as a volume distensibility which is the volume-normalized (size independent) version of compliance.

The recognition of the size relationship also affords an even greater appreciation of mammalian cardiac anatomy and function.  It's the same over an extremely wide range of body size.   I don't mean exactly the same of course, but the proportions of the heart are so similar across species that I can just about pass off a cat echo at a human conference by blocking out the size scale and heart rate (and name of course).  Ma Nature seems to have settled on a design that works and simply grows the thing appropriately to suit the size of the beast.  I prefer to believe that the heart probably develops to an appropriate size in response to the demand imposed by the body it sits it (as opposed to, say, genes that determine the heart size apriori for the body in which it will eventually reside).   Also rather obviously, the figure demonstrates that a change in ventricular size is $$\Large \text{THE}$$ mechanism by which the heart can change stroke volume without a change in the other determinants of cardiac performance (preload, afterload, contractility).

To summarize, please note the following about the situation depicted in the above figure:

• The shape, relative wall thickness, and muscle properties are assumed to be the same between the imaginary hearts depicted;  also the same are preload and afterload.  With these stipulations, the differences in PVRd, PVRs, and PV loops are due to a change in size only.
• The LVs all have the same ejection fraction but the stroke volumes are different and obviously depend on the size of the heart.
• The larger hearts have a lower Emax but there is NOTHING wrong with them.  They all have the same contractility  (the muscle is the same) despite the fact that they don't have the same Emax.  To be sure, the larger hearts (with the lower Emax ) are "better" than the  smaller ones (with the higher Emax ) in the sense that they've got more horsepower; the stroke volumes are greater and the area of the work loop is greater by a factor that depends specifically on the size (volume) of the heart.
• Emax does NOT define contractility without some additional work for interpretation.  The slope of PVRs also depends on heart size, shape, and something that tells how much muscle is there (e.g. relative wall thickness).
• This is an analytically valid demonstration regardless of whether it's been shown to occur using data from a range of heart sizes.  This is physics, not biology.

## Scale Transformed Pressure-Volume Loop

The fact that the PV loops are proportional with respect to size on the volume axis allows us to say that the PV loops are scale invariant.  Consequently we can normalize (transform) the PV Loop (and all it's interpretations) for size by rescaling the volume axis.   If we stick with straight lines for systolic and diastolic PV relationships, the form of each is:

$$\large p = E(t) \left[ V(t)-V_0(t) \right]$$

We want to transform this equation by changing the independent variable.  With a little practice and head scratching,  we first rewrite the previous equation as:

$$\large p =\left[ E(t) \;V_s \right] \left[ \frac{V(t)-V_0(t)}{V_s} \right]$$

$$V_s$$ is a scaling volume, a volume that changes the scale of the x-axis as we'll see shortly.  Now make the following definitions:

$$\large \varepsilon(t) \equiv E(t) \; V_s$$

$$\large \upsilon(t) \equiv \frac{V(t)}{V_s}$$

$$\large \upsilon_0(t) \equiv \frac{V_0(t)}{V_s}$$

In terms of the new variables, the original equation now appears as follows:

$$\large p = \varepsilon(t) \left[ \upsilon(t) - \upsilon_0(t) \right]$$

First of all, you can see that the equation still has the exact same form and meaning as it did originally.  However the equation is expressed in terms of new variables and parameters, $$\upsilon$$, $$\varepsilon$$ and $$\upsilon_0$$.  In the figure below the volume axis from several PV Loops of dissimilarly sized hearts (same as above hearts) has been rescaled.  Now we can compare them  --  and they're all the same!  In the first figure below, the volume variable is divided by $$V_0$$; i.e. $$V_s = V_0$$, the undistended diastolic volume.  The plots of the 4 LVs superimpose.  The x-axis is now a nondimensional volume equal to 1.0 when the diastolic distending pressure of the heart is 0.0.

Ignore the math for a moment and recognize that the figure demonstrates something you've probably always known, the proportions of the normal PV loop are essentially the same irrespective of heart (LV) size.  In the next figure a different scaling volume was used (the end diastolic volume defined arbitrarily as the volume at 10 Torr).  The nondimensional volume is now 1.0 at the agreed upon EDP.

The choice of the volume we use to rescale the volume axis may potentially affect the interpretation. We can use the intrinsic body weight to determine $$V_s$$ for example, by which I mean the a body weight that is representative of the individual's intrinsic size (i.e. corrected for body condition).   This would allow us to tell if the measured Emax is appropriate for the size of the individual.  What we're after, however, is whether it's appropriate for the heart.

Note: For those of you who think that you can normalize the ventricular volume by dividing it by body surface area, please see other articles on this website relating to similarity.  The "volume index" approach is nonsense that continues to propagate within the cardiology literature.  Yes I know there's a wealth of literature on this, but it's wrong.  By which I mean, it's wrong.  We're doing physics here, not statistics.

We cannot compare (normal) hearts (Emax, etc.) of differing size without rescaling the volume variable.  We cannot compare  the Emax of a heart that is remodeled (size change) to a normal one.  We cannot compare a heart to itself, before and after remodeling.  If the heart is enlarged, Emax will be a lower value (keeping shape, relative wall thickness, and muscle the same).  We can compare the volume normalized version of Emax:

$$\large \varepsilon_{\text{max}} = V_s E_{\text{max}}$$

where $$V_s$$ is the scaling volume used to nondimensionalize the volume axis.  $$V_s$$ is different for each heart but must be defined in the same way for each to characterize the size of the heart.  $$V_s$$ must characterize the intrinsic size of the pumping chamber; it's not dependent on distending pressure and it's NOT a function of time.  In case there is a doubt as to what's been said here, an LV with DCM will (likely) have a lower Emax partly because it's larger than normal, partly because the relative wall thickness is reduced, (partly because of a change in shape), and partly due to an actual reduction in the "contractility" of the muscle (the material properties of the muscle).  If we want to actually compare muscle function between the hearts, we would also have to normalize further for relative wall thickness (and chamber shape).

In the (bio)engineering literature it's well understood that the compliance of a vessel, $$dV/dp$$, is dependent on it's intrinsic volume.  The volume distensibility is defined as $$\frac{dV}{dp}/V_0$$ so as to  normalize the compliance for vessel size.  Elastance is the reciprocal of compliance, so the corresponding size-normalized expression is $$\frac{dp}{dV} V_0 = E \; V_0$$; in the foregoing I've used the more general $$V_s$$ (scaling volume ) in place of $$V_0$$ since we need to use the same volume value throughout the cardiac cycle (whereas $$V_0(t)$$ is a function of time, changing throughout the cardiac cycle).  I'm not sure whether an English term has been applied in the literature to the quantity $$E \; V_0$$; the term volume elastance is disqualified as it's already been applied in the literature to mean the same as elastance, i.e. not the volume normalized  quantity.  (Anyone know the correct term, please contact me.)

## Interrelationship of Heart Size and Ejection Fraction

We're now in a position to consider heart (LV) size as if it were an additional determinant of cardiac performance, similar to preload, afterload, contractility, heart rate, etc., and see how changes in each affect the others.   Intrinsic heart size cannot change acutely, however, so most would say it is not an attribute of performance.  I began thinking about this as it relates to developing (mathematical) models of the circulation in which the size of the heart might change in response to various disease conditions.   In the examples at the top of the page, we changed one of the determinants of cardiac performance to see what would happen to the others.  In what follows, we repeat the process but LV size is added to the variables.   I think the thought process sheds an interesting light on the ejection fraction.

The EF exhibits an obvious interrelationship with heart size and stroke volume:

$$\large EF = \frac{SV}{EDV}$$

We can consider EDV at a normal/specific EDP as the scaling volume, $$V_s$$ noted above.  If the control systems of the circulation act to maintain stroke volume, but we allow heart size to vary, then EF will change (inversely proportional to the heart size).   Both numerator and denominator of the formula can change, however, due to changes in any of preload, afterload, contractility, and intrinsic heart size.

Consider now the semi-ridiculous notion of installing a NORMAL heart of inappropriate size into an individual.  Also suppose that the heart function is governed by the demands of the circulation; in this case there is a fixed demand for stroke volume and the determinants of cardiac performance will be altered to suit the demand.

In the figure below, we allow the preload to alter to meet the SV requirement.

The PV loops above depict a constant stroke volume for a range of intrinsic heart sizes;  ALL the imaginary hearts are NORMAL, but not necessarily of appropriate size for the individual.  The blue loop is intended as a baseline case with an EF of 0.625 at normal preload and afterload; the largest heart (yellow) is twice the intrinsic size as the blue.  At a fixed afterload, the system has been allowed to regulate the SV by changing preload; in this case, EDP decreases as heart size increases. There is a decrease in EF in this case, but it's not due to reduced preload alone.   Even though preload decreases (EDP), the EDV increases for progressively larger LVs so that the enlarged heart contributes to the lower EF  $$\large \left( EF = \frac{SV}{EDV} \right)$$   Be sure you understand that the differences in Emax and Emin in the above have nothing to do with muscle contractility or material properties.  These LVs are made out of the same stuff, grade A myocardium (on sale at Walmart today only).  The differences in PVRd and PVRs are due to different intrinsic chamber size only and I'm just using graphics to illustrate the result for you.  The size-normalized Emax, ( $$\varepsilon_{\text{max}}$$ ) described above, is the same for all.

Repeating this thought experiment, we now allow the system to adjust by changing Emax ("contractility"), while maintaining a constant SV at the normal preload and afterload.

EF obviously decreases with increasing heart size and the effect is even more pronounced than in the previous example.  Without the context provided, this plot might (would) be interpreted as a demonstration of dilated cardiomyopathy (except that EDP is normal) with the degradation of Emax as the primary problem as opposed to the response of the system to maintain a normal stroke volume.   If stroke volume  (cardiac output) is the controled variable, contractility ( $$\varepsilon_{\text{max}}$$, and Emax) is reduced in the larger heart (at normal preload and afterload) so that normal stroke volume is maintained   In this example, the differences in Emax are due both to intrinsic chamber size and a change in actual contractilty ( $$\varepsilon_{\text{max}}$$  ).

### Reduced EF as a Direct Manifestation of LV Enlargement (Speculation)

Growth and hypertrophy of the heart are quite obviously among the adaptive mechanisms available to the circulation.   In response to pathological circumstances, multiple adaptive mechanisms are invoked in concert to meet the need for blood flow. Install a larger than appropriate heart in an individual?? Hmmmm.... is that really relevant?  In the case of physiologic hypertrophy, the inciting event for adaptation is a direct increase in demand e.g. due to prolonged, vigorous exercise.  The resulting enlargement of the LV can lead to a structural configuration suggestive of disease, i.e. "athletic heart syndrome" with a reduced EF at rest.   Another example, to illustrate a larger than appropriate heart, occurs subsequent to the correction of a PDA where signficant LV remodeling has already taken place.   Late closure of the ductus in dogs often leaves the patient with marked LV enlargement and a dismal EF.  My experience has been that many of these dogs go on to lead an essentially normal life; I don't know if longevity is affected statistically speaking.  In this case again, the EF is not a realistic predictor of the severity of disease. (Does this occur in people with late mitral valve repair?)  So real-life examples corresponding to the above thought experiment do exist.

Despite growing recognition of limitations, EF has been used in the clinical literature as essentially synonymous with "systolic function".  Certainly the most obvious structural manifestations of significant LV dysfunction typically include dilation and a reduced EF.   If  reduced "contractility" is the inciting event (DCM, ICM, valvular disease, etc.),  depressed EF may be initiated a manifestation of systolic myocardial dysfunction with other determinants of performance invoked as compensatory mechanisms.  As elaborated above, however, EF is affected directly by chamber size other determinants being equal.  The problem might originate as an acute or chronic decrease in actual "contractility" ( $$\varepsilon_{\text{max}}$$ described above), but subsequent LV enlargement can result in a further reduction of EF that is not related to a change in myocardial function per se.  Perhaps this "amplification" of EF deterioration, i.e. due to LV enlargement, contributes to its utility as a diagnostic and prognostic marker.  It must be considered, however, that the reduced EF in this setting is due to a combination of LV enlargement / remodeling (growth adaptation ) and an actual reduction in contractility; there may be contributions from reduced relative wall thickness and LV shape changes as well.

Where LV enlargement contributes to reduced EF, the analysis also indicates a static or actually increasing EF where LV enlargement cannot occur.  Functionally speaking, restrictive and hypertrophic myocardial diseases (diastolic dysfunction) might be considered as situations where the option for cardiac enlargement has been denied as an adaptive mechanism.  The circulation must resort to the other available determinants of performance to compensate; there is limited availability of inotropic reserve and a marked increase in preload is typically invoked with CHF the result.  Heart failure with preserved ejection fraction (HFpEF) is a common diagnostic problem said now to account for ~ 50% of CHF in people.  It presents a significant diagnostic challange because of the lack of obvious structural markers (heart size and EF) on routine tests.

#### More of Same Below

The demonstrations are just thought experiments, but I found them useful to get thinking outside the box.

In the figure below, the blue loop (smallest) is the appropriate sized heart for this particular individual and an EF of 0.625 results to deliver the required stroke volume -- the appropriate stroke volume for this individual.  If we install a larger but NORMAL heart (or get off our collective butt and put in some serious exercise so as to grow our own factory installed heart), a lower ejection fraction results to deliver the original stroke volume.  (That's a fact as stated, not a hypothesis!) If we're maintaining fixed preload and afterload, as shown, then the larger heart (orange) must have decreased contractility relative to the smaller (blue). Of course the orange loop represents a heart that might be too large to fit inside the thorax of the individual that started with the blue loop.  But force yourself to recognize that there need not be anything wrong with ANY of the hearts depicted in the figure.  Nothing wrong with them? But where is that information on the figure?? The heart with the red loop is much enlarged (2X), it has an Emax of only half the blue loop's value, and the ejection fraction is much reduced (1/2 X).  Isn't that just about the definition of a sick heart?

See what we're up against now?  The fact is that we can't interpret EF OR Emax without some additional context.  Sure when we see these things in the clinic or the lab, there is a usual interpretation.  You can also cheat by asking the patient some questions (I don't usually get straight answers since I'm a veterinarian).  Also the sick heart is almost certainly going to be operating at an abnormal preload; .  we don't have to do any of this fancy PV loop stuff anyway to figure out that there's a problem.