Presented at Muscle Mechanics and Energetics: A Comparative View, Melbourne, October 2002. The papers in these proceedings have been peer reviewed.

# CARDIAC ENERGETICS: FROM E_{MAX} TO PRESSURE–VOLUME AREA

Article first published online: 25 JUL 2003

DOI: 10.1046/j.1440-1681.2003.03879.x

Issue

## Clinical and Experimental Pharmacology and Physiology

Volume 30, Issue 8, pages 580–585, August 2003

Additional Information

#### How to Cite

Suga, H. (2003), CARDIAC ENERGETICS: FROM E_{MAX} TO PRESSURE–VOLUME AREA. Clinical and Experimental Pharmacology and Physiology, 30: 580–585. doi: 10.1046/j.1440-1681.2003.03879.x

#### Publication History

- Issue published online: 25 JUL 2003
- Article first published online: 25 JUL 2003
- Received 13 November 2002; revision 11 February 2003; accepted 16 February 2003.

- Abstract
- Article
- References
- Cited By

### Keywords:

- energetics;
- heart;
- integrative analysis;
- mechanics;
- ventricle

### Summary

- Top of page
- Summary
- Introduction
- E
_{max} - Pressure–volume area
- Ca
^{2+}HANDLING - Cross-bridge cycling
- Conclusions
- Acknowledgements
- References

1. To celebrate this Festschrift for Professor Colin Gibbs, as an invited speaker, I would like to review briefly my 35 year research career in cardiac physiology.

2. My career started in the late 1960s in Tokyo with my serendipitous discovery of E_{max} (ventricular end-systolic maximum elastance) as a load-independent contractility index based on the time-varying elastance (E(t)) model of the ventricle. Professor K Sagawa at the Johns Hopkins University, USA, whom I joined in 1971, encouraged me to go further.

3. The next serendipitous event in my career was the discovery of ventricular pressure–volume area (PVA) as a measure of total mechanical energy of ventricular contraction in the late 1970s. The PVA concept was theoretically deducible from the E(t) and E_{max} concept and correlated surprisingly well with ventricular O_{2} consumption (Vo_{2}).

4. Professor Gibbs' intuitive recognition of the significance of PVA in myocardial energetics in the 1980–1990s greatly encouraged me thereafter. The third serendipitous event in my career occurred in the mid 1990s and was my discovery of a novel integrative analysis method to assess the total amount of Ca^{2+} recruited in each excitation–contraction coupling from the decay rate of postextrasystolic potentiation, taking advantage of the E_{max}–PVA–Vo_{2} framework.

5. I am now hoping to experience one more serendipitous experience by developing an integrative analysis method of cross-bridge cycling in a beating heart using the E_{max} and PVA concepts.

### Introduction

- Top of page
- Summary
- Introduction
- E
_{max} - Pressure–volume area
- Ca
^{2+}HANDLING - Cross-bridge cycling
- Conclusions
- Acknowledgements
- References

When I started my research career in the late 1960s in Tokyo, there were three major cardiac function frameworks: (i) Starling's cardiac function curve or the Law of the Heart at the whole-heart level; (ii) Sarnoff's ventricular function curve at the ventricular level; and (iii) Sonnenblick's force–velocity (V_{max}) curve at the myocardial level. Although Frank first recognized the importance of the ventricular pressure–volume (P-V) diagram in 1895,^{1} it was already incorporated as part of Starling's Law and little attention was paid to the P-V diagram in the 1960s.

Studying these frameworks, I came to the conclusion that none of these could yet satisfactorily account for the cardiac pump performance and started my own experiments. When I transiently clamped the aorta to various extents in canine experiments in 1967, I found that left ventricular pressure increased transiently in synchrony with the dip of the aortic flow measured with an electromagnetic flowmeter and their magnitudes positively correlated with each other.^{2} However, none of the aforementioned cardiac frameworks could quantitatively account for these transient ventricular pressure and flow responses. This greatly strengthened my research interest in cardiac physiology.

### E_{max}

- Top of page
- Summary
- Introduction
- E
_{max} - Pressure–volume area
- Ca
^{2+}HANDLING - Cross-bridge cycling
- Conclusions
- Acknowledgements
- References

In 1968, I experienced the first serendipitous discovery in my cardiac physiology career. The idea was that the left ventricle (LV) could be considered as a time-varying elastance to show the positive correlation between the LV pressure increase and aortic flow dip. Here, my electronics hobby greatly helped me draw the above analogy because the Coulomb law for electricity has a similar inverse relationship between the voltage change of a capacitor and the current out of it when its capacitance changes.

To validate this analogy, I obtained LV P-V loops under various end-diastolic volumes and aortic pressures in anaesthetized, thoracotomized dogs. Left ventricle instantaneous volume was calculated from the electromagnetically measured aortic flow and ejection fraction determined by an indicator dilution method at a stable cardiac contractile state. I found that the left-upper end-systolic corners of the multiple P-V loops drawn in a P-V diagram fell on a straight line (Fig. 1a). I published several papers regarding these observations in Japan over the period 1969-1971^{2–6} and one paper after moving to the US in 1972.^{7}

I also found that the instantaneous P-V line connecting the P-V points at any specific time of contraction was practically linear and increased its slope during contraction and decreased its slope during relaxation (Fig. 1b).^{2–6} I concluded that the LV performance could be characterized as a time-varying elastance, e(t).^{2–7} I then designated the end-systolic slope of the P-V relationship as maximum elastance (e_{max}) in my PhD thesis at the University of Tokyo in 1969.^{3}

I further found that e_{max} increased with an increase in contractility and decreased with its decrease.^{5} Therefore, I proposed e_{max} as a novel contractility index in my PhD thesis. Professor Sagawa at the Johns Hopkins University greatly helped me to establish the e(t) and e_{max} framework with more evidence. He also advised me to capitalize e(t) and e_{max} and use the terms E(t) and E_{max}. We corroborated the E(t) and E_{max} framework in canine experiments after developing better devices to measure ventricular volume and published the confirmed results in *Circulation Research* in 1973 and 1974.^{8,9} After developing a volume servo pump to control and measure LV volume, we more firmly established the E(t) and E_{max} framework, as well as clarifying its limitations, in the *American Journal of Physiology and Circulation Research*.^{12,13}

The strength of the E_{max} concept is that it has dimensions of volume elastance (mmHg/mL) that quantify three-dimensionally a mechanical (i.e. stress–strain) property of the ventricular wall and chamber. This feature of E_{max} is advantageous over the conventional contractility indices, such as peak isovolumic pressure at a given volume, dP/dt_{max}, V_{max} etc., because they are merely phenomenological variables of the LV pump and cannot physically quantify a comprehensive LV mechanical property. Therefore, E_{max} has gained wide popularity as a reliable load-independent contractility index of a beating heart.^{10}

The disadvantages of E_{max} are that: (i) there is some load dependence of E_{max} on LV loading conditions; (ii) it is difficult to obtain E_{max} where there is a non-linear end-systolic P-V relationship; and (iii) there is dependency of E_{max} on the LV size. However, these disadvantages could not outweigh the advantages of E_{max}.

### Pressure–volume area

- Top of page
- Summary
- Introduction
- E
_{max} - Pressure–volume area
- Ca
^{2+}HANDLING - Cross-bridge cycling
- Conclusions
- Acknowledgements
- References

Near the end of my stay at the Johns Hopkins in 1978, I had a second serendipitous insight that came as an extrapolation of the E_{max} concept.^{11} The novel idea was the concept that the total mechanical energy of a contraction could be theoretically deduced from the E(t) model. The total mechanical energy of the ventricle was considered to be analogous to the potential energy stored in a stretched spring and the mechanical work convertible from it (Fig. 1c). The triangular area under the E_{max} line represents the elastic potential energy (PE) stored in the LV (Fig. 1d), whereas the rectangular area within the P-V loop represents the external mechanical work (EW) performed (Fig. 1e).

I then hypothesized that the PVA would be a major determinant of LV O_{2} consumption (Vo_{2}; Fig. 2a). Testing this hypothesis in canine hearts, I found that PVA correlated linearly with Vo_{2} under various pre- and afterload conditions at a stable E_{max} in each heart^{12} (Fig. 2b). An increased E_{max} elevated the linear PVA–Vo_{2} relationship and a decreased E_{max} lowered it (Fig. 2c). Despite changes in the elevation of the PVA–Vo_{2} relationship with E_{max}, the slope of the PVA–Vo_{2} relationship remained unchanged.

We proposed that this slope could identify the O_{2} cost of PVA and its reciprocal could represent the contractile efficiency from Vo_{2} to PVA. We found the O_{2} cost of PVA to be approximately 1.8 × 10^{−5} mL O_{2}/(mmHg·mL) or 2.5 (dimensionless) and the contractile efficiency to be 0.40 (dimensionless). These dimensionless numbers derive from both PVA (mmHg·mL = 1.333 × 10^{−4} J) and Vo_{2} (mL = 20 J) being energy measures with the same dimensions. All these features of PVA indicate that PVA corresponds to the total energy output of contraction that Starling attempted to discover but failed to identify when he proposed the Law of the Heart.

The Vo_{2} intercept of each PVA–Vo_{2} relationship represents the Vo_{2} of an unloaded contraction with zero PVA at each E_{max} (Fig. 2c). The intercept consists of the Vo_{2} of the basal metabolism and the Vo_{2} for excitation–contraction (EC) coupling. We found that the basal metabolic Vo_{2} was little changed by changes in E_{max}. Therefore, it was the Vo_{2} for EC coupling that changed the elevation of the PVA–Vo_{2} relationship.^{12}

We then studied the relationship between E_{max} and the Vo_{2} intercept of the PVA–Vo_{2} relationship under varied E_{max}. We found that the Vo_{2} intercept was linearly dependent on E_{max} and its slope remained relatively constant regardless of E_{max} (Fig. 2d). We designated this slope as the O_{2} cost of E_{max}.

The slope, however, became steeper and, hence, the O_{2} cost of E_{max} greater in failing hearts under conditions such as acidosis, stunning, ryanodine treatment and hypertherma.^{12} The opposite occurred under alkalotic and hypothermic conditions.

The inverse of the O_{2} cost of E_{max} represents the economy of contractility or E_{max}. This cost would increase with various factors related to Ca sensitivity and responsiveness, to cross-bridge cycling and to changes in cytoskeletons, extracellular matrices, ventricular synchrony etc. However, we cannot specify which factor is responsible for a change in the economy in each case.

### Ca^{2+} HANDLING

- Top of page
- Summary
- Introduction
- E
_{max} - Pressure–volume area
- Ca
^{2+}HANDLING - Cross-bridge cycling
- Conclusions
- Acknowledgements
- References

My third serendipitous idea was a novel integrative method to assess total Ca^{2+} handling, which is a major determinant of the O_{2} cost of E_{max} in a beating heart. Most of the released Ca^{2+} is known to be removed by the sarcoplasmic reticulum Ca^{2+} pump with a nominal 2 Ca^{2+} : 1 ATP stoichiometry, whereas residual Ca^{2+} is extruded transsarcolemmally by Na^{+}/Ca^{2+} exchange energetically coupled with the Na^{+}/K^{+} pump with a nominal 1 Ca^{2+} : 1 ATP stoichiometry. Therefore, the fraction of the internally handled Ca^{2+} in the total Ca^{2+} released (i.e. recirculation fraction (RF)) critically determines the O_{2} cost of E_{max}.^{15}

We attempted to obtain RF by the conventional method using the exponential decay of the postextrasystolic potentiation (PESP). However, in the excised canine heart, we found, to our surprise, that the monotonically decaying PESP, which has long been considered representative of normal hearts, was unusual or even exceptional. That is, PESP virtually always decayed in alternans, even under what we considered to be physiological conditions.^{16–18} Although we were disappointed at first by the possibility that the excised cross-circulated heart may not be physiological (e.g. somewhat ischaemic and hypothermic), we soon discovered that, even *in situ*, beating canine hearts show alternans during PESP (H Suga, unpubl. obs., 1993).

I then serendipitously considered that RF could be obtained even from the PESP alternans. Fortunately, we found that the PESP alternans contained an exponential decay component comparable to the conventional monotonic decay reported in earlier studies. We applied a curve-fitting method to extract the exponential decay component needed to calculate RF.^{16}

Once RF is obtained, one can theoretically calculate total Ca^{2+} handled in the EC coupling by the following relationship:

Here, *N* is the number of futile Ca^{2+} cycles relative to one Ca^{2+} cycle of the normal sarcoplasmic reticulum and R is the reactivity of E_{max} to total Ca^{2+} handling.^{16–18} The denominator 2 in the term RF/2 is the ratio of the Ca^{2+} : ATP stoichiometries of the internal and external Ca^{2+} removal processes; the 6 is the molecular P : O_{2} ratio of the atomic 3P : O stoichiometry; 12 is the product of this 2 and 6; 22 400 is the standard molar gas volume to convert O_{2} in mol to O_{2} in mL.

We applied these equations to our experimental Vo_{2} data and obtained total Ca^{2+} handling of 30–110 µmol/kg per beat under various positive and negative inotropic conditions. These values are quite reasonable estimates of the total released and removed Ca^{2+} per beat and are two orders of magnitude greater than the popular peak free Ca^{2+} concentration measured by Ca transient.^{15,17}

The values of *N* and R critically affect the O_{2} cost of E_{max}. We have already assessed changes in *N* and R in various experimental failing hearts, such as hyper- and hypothermia, stunning, ryanodine treatment, 2,3-butanedione monoxime treatment etc.^{15–17} Thus, our method is unique in that it can assess total Ca^{2+} handling in beating hearts compensating for the weakness of the Ca transient methods.

### Cross-bridge cycling

- Top of page
- Summary
- Introduction
- E
_{max} - Pressure–volume area
- Ca
^{2+}HANDLING - Cross-bridge cycling
- Conclusions
- Acknowledgements
- References

The terms E(t), E_{max} and PVA are integrative manifestations of Ca^{2+} handling and cross-bridge (CB) cycling. As for CB cycling, we partly obtained in the late 1970s^{19} and are still obtaining the small-angle X-ray diffraction data of a physiologically contracting myocardium to calculate the electron density changes of the thick and thin filaments. We calculated CB movements between the thick and thin filaments from the changes in (1 : 1)/(1 : 0) diffraction intensity ratio and correlated this ratio with changes in developed force.^{19} We have already found that CB movement towards the thin filaments largely, but not completely, parallels the developed force.^{19} However, the CB movement is slightly in advance of contraction and lags behind in relaxation.

We then attempted to account for the developed force and pressure curves as the difference of a cumulative attached CB curve minus a cumulative detached CB curve. We found that a hybrid logistic model of CB attachment and detachment could serve as a realistic model, consistent with actual cardiac contraction and relaxation.^{20,21} A hybrid Weibull model may be a better model of the actual cardiac contraction.^{22} Unfortunately, the X-ray diffraction study of the myocardium is not yet sufficiently satisfactory to evaluate the appropriateness of these mathematical models.

### Conclusions

- Top of page
- Summary
- Introduction
- E
_{max} - Pressure–volume area
- Ca
^{2+}HANDLING - Cross-bridge cycling
- Conclusions
- Acknowledgements
- References

Over the past 35 years, I have been lucky enough to have experienced multiple serendipitous discoveries in my cardiac function research. My validation of the time-varying elastance E(t) model of the ventricle and proposal of E_{max} as a load-independent index of ventricular contractility were the real start of my career as a scientist. Our two early *Circulation Research* papers on E_{max} in 1973 and 1974 popularized the concept globally. Thereafter, cardiac physiologists and cardiologists preferred it, at least conceptually, in their understanding of cardiac pump function.^{14}

However, skeletal muscle scholars neglected or criticized my E(t) concept because they confused our E(t) model and the already discarded classical cocked-spring model of skeletal muscle. Although the cocked-spring model could not account for the Fenn effect of the skeletal muscle, the E(t) model nicely accounts for the cardiac Fenn effect.^{23} The key difference between the two elastance models is an instant rise of elastance in the cocked-spring model versus a gradual rise in the E(t) model. Once this difference was appreciated, criticism of the E(t) concept ceased.

The concept of E_{max} has made me an internationally well-known scholar for over 30 years and has led me to the above-mentioned PVA concept and the integrative analysis method of assessing Ca handling in a beating heart. These proposals would have been impossible without the E(t) model and E_{max} concept (Fig. 3).

We have a Japanese phrase, *Un-Don-Con* (or luck, focus and endurance), as the important factors needed to succeed in life, at least in Japan. I like this expression very much and believe it has helped me a lot in my career. My greatest luck has been my close acquaintance with Professor Gibbs for nearly 20 years. In particular, his expertise helped PVA, as well as the E(t) model of the ventricle, become established in cardiac mechanoenergetics.

### Acknowledgements

- Top of page
- Summary
- Introduction
- E
_{max} - Pressure–volume area
- Ca
^{2+}HANDLING - Cross-bridge cycling
- Conclusions
- Acknowledgements
- References

I greatly acknowledge all those who encouraged, cooperated and/or understood my research activities on cardiac mechano-energetico-informatics at any time in my career. These names are referenced on the website of the E_{max} PVA Club (http://www5b.biglobe.ne.jp/EMAXPVA/).

### References

- Top of page
- Summary
- Introduction
- E
_{max} - Pressure–volume area
- Ca
^{2+}HANDLING - Cross-bridge cycling
- Conclusions
- Acknowledgements
- References

- 1Die Grundform des Arteriellan Pulses. Z. Biol. 1899; 37: 483–526..
- 2 .
- 3Analysis of left ventricular pumping by its pressure–volume coefficient. Jpn. J. Med. Biol. Eng. 1969; 7: 406–15 (in Japanese with an English abstract)..
- 4 .
- 5 .
- 6Theoretical analysis of a left ventricular pumping model based on the systolic time-varying pressure/volume ratio. IEEE Biomed. Eng. 1971; 18: 47–55..
- 7 , .
- 8 , , .
- 9 , .
- 10Systolic and diastolic function (mechanics) of the intact heart. In: Page E, Fozzard HA, Solaro RJ (eds). Handbook of Physiology. Section 2: The Cardiovascular System, Vol. 1: Heart. Oxford University Press, New York. 2002; Ch. 20., .
- 11 .
- 12 .
- 13Cardiac Contraction and the Pressure–Volume Relationship. Oxford University Press, New York. 1988., , , .
- 14Cardiac function. In: Moller JH, Hoffman JIE (eds). Pediatric Cardiovascular Medicine. Churchill Livingstone, New York. 2000; Ch. 5..
- 15 , , , , .
- 16 , , , , .
- 17 , ,
- 18
*et al.*Postextrasystolic contractile decay independent of extrasystolic interval and compensatory pause in canine heart. Am. J. Physiol. 2000; 279: H225–33. - 19 , , .
- 20 , , , , .
- 21 , , , , .
- 22 , ,
- 23 , , , , .