Clinical and Experimental Pharmacology and Physiology (2003) 30, 580–585

Muscle Mechanics and Energetics: A Comparative View

CARDIAC ENERGETICS: FROM EMAX TO PRESSURE–VOLUME AREA Hiroyuki Suga National Cardiovascular Center Research Institute, Osaka, Japan

SUMMARY

INTRODUCTION

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 Emax (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 Emax concept and correlated surprisingly well with ventricular O2 consumption (VO2). 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 Ca2+ recruited in each excitation–contraction coupling from the decay rate of postextrasystolic potentiation, taking advantage of the Emax–PVA–VO2 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 Emax and PVA concepts. Key words: energetics, heart, integrative analysis, mechanics, ventricle.

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 (Vmax) 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.

Correspondence: Dr Hiroyuki Suga, Director General, Research Institute, National Cardiovascular Center, 5-7-1 Fujishirodai, Suita, Osaka 565-8565, Japan. Email: [email protected] Presented at Muscle Mechanics and Energetics: A Comparative View, Melbourne, October 2002. The papers in these proceedings have been peer reviewed. Received 13 November 2002; revision 11 February 2003; accepted 16 February 2003.

E MAX 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 endsystolic 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 1969-19712–6 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

Cardiac energetics: from Emax to PVA 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 (emax) in my PhD thesis at the University of Tokyo in 1969.3 I further found that emax increased with an increase in contractility and decreased with its decrease.5 Therefore, I proposed emax 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 emax framework with more evidence. He also advised me to capitalize e(t) and emax and use the terms E(t) and Emax. We corroborated the E(t) and Emax 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 Emax framework, as well as clarifying its limitations, in the American Journal of Physiology and Circulation Research.12,13 The strength of the Emax concept is that it has dimensions of volume elastance (mmHg/mL) that quantify three-dimensionally a

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mechanical (i.e. stress–strain) property of the ventricular wall and chamber. This feature of Emax is advantageous over the conventional contractility indices, such as peak isovolumic pressure at a given volume, dP/dtmax, Vmax etc., because they are merely phenomenological variables of the LV pump and cannot physically quantify a comprehensive LV mechanical property. Therefore, Emax has gained wide popularity as a reliable load-independent contractility index of a beating heart.10 The disadvantages of Emax are that: (i) there is some load dependence of Emax on LV loading conditions; (ii) it is difficult to obtain Emax where there is a non-linear end-systolic P-V relationship; and (iii) there is dependency of Emax on the LV size. However, these disadvantages could not outweigh the advantages of Emax.

PRESSURE–VOLUME AREA 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 Emax concept.11 The novel idea was the concept that the total

Fig. 1 (a,b) Schematic illustration of the ventricular pressure–volume (P-V) loops and relationships in a P-V diagram and Emax (maximum elastance). (c) Time-varying elastance (E(t)) model of the ventricle in systole and diastole and its energy changes. Systolic P-V area represents total mechanical energy of contraction in isovolumic contraction (d) and ejecting contraction (e). ES, ED, end-systole and end-diastole, respectively; PVA, pressure–volume area; PE, potential energy; EW, external mechanical work.

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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 Emax 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 O2 consumption (VO2; Fig. 2a). Testing this hypothesis in canine hearts, I found that PVA correlated linearly with VO2 under various pre- and afterload conditions at a stable Emax in each heart12 (Fig. 2b). An increased Emax elevated the linear PVA–VO2 relationship and a decreased Emax lowered it (Fig. 2c). Despite changes in the elevation of the PVA–VO2 relationship with Emax, the slope of the PVA–VO2 relationship remained unchanged. We proposed that this slope could identify the O2 cost of PVA and its reciprocal could represent the contractile efficiency from VO2 to PVA. We found the O2 cost of PVA to be approximately

1.8  10–5 mL O2/(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 VO2 (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 VO2 intercept of each PVA–VO2 relationship represents the VO2 of an unloaded contraction with zero PVA at each Emax (Fig. 2c). The intercept consists of the VO2 of the basal metabolism and the VO2 for excitation–contraction (EC) coupling. We found that the basal metabolic VO2 was little changed by changes in Emax. Therefore, it was the VO2 for EC coupling that changed the elevation of the PVA–VO2 relationship.12 We then studied the relationship between Emax and the VO2 intercept of the PVA–VO2 relationship under varied Emax. We found that the VO2 intercept was linearly dependent on Emax and its slope remained relatively constant regardless of Emax (Fig. 2d). We designated this slope as the O2 cost of Emax.

Fig. 2 Schematic illustrations of ventricular Emax (maximum elastance) and PVA (total mechanical energy) in a pressure–volume (P-V) diagram (a), the VO2 (ventricular O2 consumption)–PVA relationship at (b) control and (c) different levels of contractility (Emax) and (d) the PVA-independent VO2–Emax relationship. PVA, pressure–volume area; PE, potential energy; EW, external mechanical work; ESPVR, end-systolic P-V relationsip.

Cardiac energetics: from Emax to PVA The slope, however, became steeper and, hence, the O2 cost of Emax 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 O2 cost of Emax represents the economy of contractility or Emax. 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. All these Emax- and PVA-related studies were reviewed in my 1990 Physiological Review paper12 and have been summarized in two books.13,14

CA

2+

HANDLING

My third serendipitous idea was a novel integrative method to assess total Ca2+ handling, which is a major determinant of the O2 cost of Emax in a beating heart. Most of the released Ca2+ is known to be removed by the sarcoplasmic reticulum Ca2+ pump with a nominal 2 Ca2+ : 1 ATP stoichiometry, whereas residual Ca2+ is extruded transsarcolemmally by Na+/Ca2+ exchange energetically coupled with the Na+/K+ pump with a nominal 1 Ca2+ : 1 ATP stoichiometry. Therefore, the fraction of the internally handled Ca2+ in the total Ca2+ released (i.e. recirculation fraction (RF)) critically determines the O2 cost of Emax.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,

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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 Ca2+ handled in the EC coupling by the following relationship: Total Ca2 + handling = 6  107  ((total Ca2 + handling VO2)/ 22 400)/(RF/2 + (1 – RF) + N  RF/2) N = (12  107/22 400)((O2 cost of Emax)/RF)  R + 1 – 2/RF Here, N is the number of futile Ca2+ cycles relative to one Ca2+ cycle of the normal sarcoplasmic reticulum and R is the reactivity of Emax to total Ca2+ handling.16–18 The denominator 2 in the term RF/2 is the ratio of the Ca2+ : ATP stoichiometries of the internal and external Ca2+ removal processes; the 6 is the molecular P : O2 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 O2 in mol to O2 in mL. We applied these equations to our experimental VO2 data and obtained total Ca2+ handling of 30–110 mol/kg per beat under various positive and negative inotropic conditions. These values are quite reasonable estimates of the total released and removed Ca2+ per beat and are two orders of magnitude greater than the popular peak free Ca2+ concentration measured by Ca transient.15,17 The values of N and R critically affect the O2 cost of Emax. 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 Ca2+ handling in beating hearts compensating for the weakness of the Ca transient methods.

Fig. 3 Three-storied framework of cardiac mechano-energetic-informatics. The bottom line lists the number of papers on these topics, total number of IF (impact factors of journals) and total number of citations. CB, cross-bridges; PVA, pressure–volume area; Emax, ventricular end-systolic maximum elastance.

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CROSS-BRIDGE CYCLING

ACKNOWLEDGEMENTS

The terms E(t), Emax and PVA are integrative manifestations of Ca2+ handling and cross-bridge (CB) cycling. As for CB cycling, we partly obtained in the late 1970s19 and are still obtaining the smallangle 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.

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

CONCLUSIONS 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 Emax 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 Emax 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 Emax has made me an internationally wellknown scholar for over 30 years and has led me to the abovementioned 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 Emax 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.

REFERENCES 1. Frank O. Die Grundform des Arteriellan Pulses. Z. Biol. 1899; 37: 483–526. 2. Suga H. Time course of left ventricular pressure–volume relationship under various extents of aortic occlusion. Jpn. Heart J. 1970; 11: 373–8. 3. Suga H. Analysis 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. Suga H. Time course of left ventricular pressure–volume relationship under various enddiastolic volume. Jpn. Heart J. 1969; 10: 509–15. 5. Suga H. Left ventricular time-varying pressure/volume ratio in systole as an index of myocardial inotropism. Jpn. Heart J. 1971; 12: 153–60. 6. Suga H. Theoretical analysis of a left ventricular pumping model based on the systolic time-varying pressure/volume ratio. IEEE Biomed. Eng. 1971; 18: 47–55. 7. Suga H, Sagawa K. Mathematical interrelationship between instantaneous ventricular pressure–volume ratio and myocardial force– velocity relation. Ann. Biomed. Eng. 1972; 1: 160–81. 8. Suga H, Sagawa K, Shoukas AA. Load independence of the instantaneous pressure–volume ratio of the canine left ventricle and effects of epinephrine and heart rate on the ratio. Circ. Res. 1973; 32: 314–22. 9. Suga H, Sagawa K. Instantaneous pressure–volume relationships and their ratio in the excised, supported canine left ventricle. Circ. Res. 1974; 35: 117–26. 10. Covell JW, Ross J. Systolic 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. Suga H. Total mechanical energy of a ventricle model and cardiac oxygen consumption. Am. J. Physiol. 1979; 236: H498–505. 12. Suga H. Ventricular energetics. Physiol. Rev. 1990; 70: 247–77. 13. Sagawa K, Maughan WL, Suga H, Sunagawa K. Cardiac Contraction and the Pressure–Volume Relationship. Oxford University Press, New York. 1988. 14. Suga H. Cardiac function. In: Moller JH, Hoffman JIE (eds). Pediatric Cardiovascular Medicine. Churchill Livingstone, New York. 2000; Ch. 5. 15. Araki J, Mohri S, Iribe G, Shimizu J, Suga H. Total Ca2+ handling for E-C coupling in whole heart: Integrative analysis. Can. J. Physiol. Pharmacol. 2001; 79: 87–92. 16. Araki J, Takaki M, Matsushita T, Matsubara H, Suga H. Postextrasystolic transient contractile alternans in canine hearts. Heart Vessels 1994; 9: 241–8. 17. Shimizu J, Araki J, Mizuno J et al. A new integrative method to quantify total Ca2+ handling and futile Ca2+ cycling in failing hearts. Am. J. Physiol. 1998; 275: H2325–33. 18. Shimizu J, Araki J, Iribe G et al. Postextrasystolic contractile decay independent of extrasystolic interval and compensatory pause in canine heart. Am. J. Physiol. 2000; 279: H225–33. 19. Matsubara I, Suga H, Yagi N. An X-ray diffraction study of the crosscirculated canine heart. J. Physiol. 1977; 270: 311–20. 20. Matsubara H, Araki J, Takaki M, Nakagawa ST, Suga H. Logistic characterization of left ventricular isovolumic pressure–time curve. Jpn. J. Physiol. 1995; 45: 535–52.

Cardiac energetics: from Emax to PVA 21. Matsubara H, Takaki M, Yasuhara S, Araki J, Suga H. Logistic time constant of isovolumic relaxation pressure–time curve in the canine left ventricle: Better alternative to exponential time constant. Circulation 1995; 92: 2318–26. 22. Araki J, Matsubara H, Shimizu J et al. Weibull distribution function for cardiac contraction: Integrative analysis. Am. J. Physiol. 1999; 277: H1940–5.

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23. Nozawa T, Yasumura Y, Futaki S, Tanaka N, Suga H. The linear relation between oxygen consumption and pressure–volume area in left ventricle can be reconciled with the Fenn effect. Circ. Res. 1989; 65: 1380–9.