Myocardial remodeling: wall stress and the supply-demand ratio

G.C. van den Bos, N. Westerhof
Laboratory for Physiology, Institute for Cardiovascular Research, Free University, Amsterdam, The Netherlands

Correspondence: Dr G.C. van den Bos, Laboratory for Physiology, VU University Medical Center, van der Boechorststraat 7, 1081 BT Amsterdam, The Netherlands. Tel: +31 20 444 8120,fax: +31 20 444 8255, e-mail: vdbos@physiol.vu.nl

Introduction
Cardiac remodeling, characterized by changes in ventricular size, shape, wall thickness, myocardial structure, and ultra structure,[1] is generally interpreted as an adaptation of the heart to myocardial damage, as in myocardial infarction, and to chronic pressure or volume overload. It is triggered by mechanical stress but modified by a variety of other unrelated factors.[2] Although the changes of remodeling are most likely adaptive, the process may become a double-edged sword if pump function is maintained at the cost of increased myocardial oxygen demand while at the same time oxygen delivery is reduced because of the restructured coronary circulation and a reduced capillary-to-myocardial-cell ratio.
In this short review, we describe, in the left ventricle, the factors that determine the supply-demand ratio during remodeling of the pressure-overloaded, the nonfailing volume-overloaded, and the infarcted nonfailing heart.

The supply-demand ratio in the normal heart
Demand
One of the simplest models to examine the relationship between supply and demand is the isolated ventricular trabecula or the papillary muscle. These preparations, like all muscle, generate force when stimulated and consume oxygen and substrates (Figure 1A).


Figure 1. Myocardial muscle mechanics and Laplace’s law in the heart. (A) In isolated contracting papillary muscles, oxygen consumption is approximately linearly related to developed force or the force-time integral (area under the force tracing). (B) Laplace’s law: if an imaginary plane cuts a sphere into two equal halves, the force (tension) in the wall will keep the parts together while the pressure in the sphere will try to separate them. T, wall force or wall stress; P, intraventricular pressure; r, radius; h, wall thickness.

 When oxygen consumption (VO2) during a series of graded contractions is plotted as a function of maximal developed force the relation is approximately linear, with an intercept on the VO2 axis dependent on basal oxygen use. A similar relationship is obtained when the area under the force tracings, approximating mean systolic force, instead of maximal force is used.
In the intact heart during systole the contracting fibers also develop force which is used to raise intraventricular pressure to overcome aortic pressure and to eject stroke volume. This force (T), usually called wall force or wall stress, is difficult to measure but can be calculated using Laplace’s law if intraventricular pressure (P), radius (r) and wall thickness (h) are known: T = Pr/2h
T is the theoretical force that holds the two halves of a sphere intersected by an imaginary plane together when the pressure within this sphere tries to separate them (Figure 1B). The oxygen and substrate consumption of the muscle fibers in the intact heart, like those in isolated papillary muscle, depend on fiber stress and fiber shortening, but the contribution of the former is so much greater that shortening can be neglected.[3]
Laplace’s law, illustrated in the above equation, shows that wall stress increases if intraventricular pressure (P) and/or radius (r)
increase, but it falls if the wall (h) of the ventricle thickens. In other words, a higher pressure and a larger ventricle cause a greater demand. In the normal heart, wall stress thus is a valid index of oxygen and substrate demand.
Although wall force can be calculated, systolic pressure or its time integral, the ‘tension-time index’ (Figure 2), is easier for determining predictors of oxygen demand.[3] Wall force and the tension-time index estimate demand per beat; to arrive at demand in a certain time period these indices have to be multiplied by heart rate, the so-called ‘rate-pressure product’ or ‘double product’.[4]


Figure 2. Factors which determine myocardial oxygen supply and demand: area under the systolic pressure trace is an estimate of demand, area under the diastolic pressure trace is an estimate of supply.

Supply
The myocardial oxygen supply is determined by the product of the arterial oxygen content and the coronary blood flow. Normally, when respiration is adequate, arterial oxygen content is constant and is thus not subject to regulation or adaptation. In the left ventricle, coronary blood flow mainly occurs during diastole when cardiac muscle is relaxed, and thus supply is chiefly dictated by diastolic blood pressure and coronary diastolic resistance. The latter is a function of vascular geometry and vasomotor tone (cardiac muscle itself does not contribute to diastole because intramyocardial pressure is approximately zero).

Supply-demand ratio
In the normal left ventricle, supply and demand are balanced (Figure 2). In most other organs, but not the heart, some compensation for a greater demand or a decreased supply is possible through increased extraction, but in the normal heart, even at rest, extraction is almost maximal so that the only alternative is increased coronary perfusion. The supply-demand ratio per beat can thus best be obtained from the diastolic (supply) and systolic (demand) blood pressure, as shown in Figure 2. When this ratio is 0.7 or more, supply is considered sufficient for even subendocardial layers to function well.[5]

The supply-demand ratio in the stressed heart
Chronic stress to the heart, whether caused by pressure overload, volume overload (Figure 3), or myocardial infarction, will to some extent alter myocardial demand and possibly also supply. Moreover, it may create circumstances in which neither the tension-time index and the double product for demand nor the diastolic pressure-time index for supply may be valid.


Figure 3. Cross-sections of normal, volume-overloaded and pressure-overloaded left ventricles. In the latter two cases the right ventricle is assumed to be normal.

Pressure overload
When pressure overload is instantaneous and short-lasting, wall tension increases according to Laplace’s law even if the ventricular dimensions do not change. Oxygen demand also rises, but in the normal heart, supply will cover this through coronary vasodilatation. When the overload becomes chronic, as in hypertension, the stress causes remodeling and the myocardial cells hypertrophy, leading to increased wall thickness, so that wall tension normalizes. This does not necessarily mean that oxygen demand is also normal: if systolic pressure increases by 50%, wall thickness, ie, the amount of wall tissue, needs to increase also by 50% to normalize wall tension. Therefore, the oxygen demand increases with hypertrophy in spite of the normalized wall stress because the mass of working muscle has increased. The increased demand can no longer be accurately estimated from wall tension because it has been returned to normal, but it will be directly related to the developed pressure because this has not changed in proportion to the tissue mass.
In the heart with concentric hypertrophy, diastolic perfusion still mainly depends on diastolic coronary resistance. Capillarization may not keep pace with myocardial growth so that resistance per gram of tissue may increase. Also, since myocardial cell diameter increases, the diffusion distances rise. Moreover, since remodeling also involves myocardial fibrosis,[2] diastolic stiffness increases so that intramyocardial pressure during diastole may no longer be negligible. Consequently, supply may be limited in the remodeled heart with concentric hypertrophy. The increased resistance and intramyocardial pressure in diastole, together with the decreased amount of oxygen reaching the heart cells by diffusion, may limit the usefulness of the diastolic pressure-time integral as an index of supply.

Volume overload
When volume overload is instantaneous, ventricular diameter increases and wall thickness decreases so that wall tension and thus oxygen demand rise. In chronic volume overload, as in hyperthyroidism and physical training (sports heart), ventricular diameter remains increased while ventricular wall thickness is normal or only slightly increased: wall stress thus remains increased. Under these conditions the use of developed pressure alone is no longer a good index of oxygen demand; instead, wall stress should be calculated from pressure according to Laplace’s law.
Whether supply to the heart with eccentric hypertrophy is changed is at present not entirely clear, but the literature suggests that this is not the case. Diffusion distances will not change, however, because the myocardial cells increase mainly in length.
Thus, in eccentric hypertrophy the systolic developed pressure cannot be used to estimate demand, but the use of the diastolic pressure-time area as an index of supply seems to be appropriate.

The infarcted heart
Whatever the size of the infarct, the altered loading conditions will always result in asymmetric, ie, heterogeneous, increases in wall stress: to keep heart function as near normal as possible, the noninfarcted tissue has to compensate for the noncontractile areas (remodeling). The remodeling which takes place is not only caused by the increased wall force but also by the volume overload hypertrophy in the noninfarcted tissue, and the amount of tissue lost by the ischemia is fully compensated by the hypertrophy through an unknown regulatory mechanism.[2] Local wall stress, which can still be calculated from pressure, local radius, and local wall thickness according to Laplace’s law, is only a predictor of local demand.
Although overall wall stress cannot be used as an index of demand, the systolic pressure and the tension-time index can, but neither will give information about local demand.
The use of the diastolic aortic pressure as an index of supply is even more hazardous because the index indicates overall but not local perfusion. In the normal heart this is not a problem because distribution of coronary flow is to a large extent homogeneous, but in the infarcted heart this is obviously not the case.
If more information is needed about local relationships in the infarcted heart, the methods described by Götte et al[6] should be followed.

Conclusion
We have presented an overview of the pros and cons of the use of mechanical parameters to estimate oxygen supply and demand. The diagram given in Figure 4 summarizes these principles.


Figure 4. Summary of changes in supply and demand in the overloaded heart.

For simplicity we have treated the results of the three forms of remodeling as if they were independent phenomena, but in reality pure concentric or pure eccentric hypertrophy seldom occurs, while the changes in the infarcted heart are even more complex.
There are better but infinitely more complex ways to estimate demand. One of these is the method described by Suga[7] in which demand is calculated from the area under a pressure-volume loop described when pressure is plotted as a function of volume; it is mainly used in experimental studies in animals because the method requires intensive instrumentation. For these reasons we have limited our discussions to the more conventional indices and considered all other methods to be beyond the scope of this brief review.

REFERENCES
 

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Models and remodeling: mechanisms and clinical implications.

Sonnenblick EH, Anversa P.

Department of Medicine, Albert Einstein College of Medicine, Bronx, NY 10461, USA. esonnenbli@aol.com

Ventricular remodeling is a process by which the size, shape and composition of cardiac chambers as well as the thickness and composition of the walls are altered in response to physical loads and/or receptor activation, whether created by loss or overload of cardiac myocytes, or the effects of external hormonal or chemical factors. Involved in this process are hypertrophy, dilation, myocyte loss whether due to necrosis or apoptosis, and myocyte hyperplasia. The present review discusses the dynamic and plastic structure of the heart in its capacity to respond to loading. The mechanisms by which myocyte growth as well as myocyte loss are mediated offer therapeutic opportunities to alter these events.

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Molecular mechanisms of myocardial remodeling.

Swynghedauw B.

Institut National de la Sante et de la Recherche Medicale U. 127, Hopital Lariboisiere, Paris, France.

"Remodeling" implies changes that result in rearrangement of normally existing structures. This review focuses only on permanent modifications in relation to clinical dysfunction in cardiac remodeling (CR) secondary to myocardial infarction (MI) and/or arterial hypertension and includes a special section on the senescent heart, since CR is mainly a disease of the elderly. From a biological point of view, CR is determined by 1 ) the general process of adaptation which allows both the myocyte and the collagen network to adapt to new working conditions; 2) ventricular fibrosis, i.e., increased collagen concentration, which is multifactorial and caused by senescence, ischemia, various hormones, and/or inflammatory processes; 3) cell death, a parameter linked to fibrosis, which is usually due to necrosis and apoptosis and occurs in nearly all models of CR. The process of adaptation is associated with various changes in genetic expression, including a general activation that causes hypertrophy, isogenic shifts which result in the appearance of a slow isomyosin, and a new Na+-K+-ATPase with a low affinity for sodium, reactivation of genes encoding for atrial natriuretic factor and the renin-angiotensin system, and a diminished concentration of sarcoplasmic reticulum Ca2+-ATPase, beta-adrenergic receptors, and the potassium channel responsible for transient outward current. From a clinical point of view, fibrosis is for the moment a major marker for cardiac failure and a crucial determinant of myocardial heterogeneity, increasing diastolic stiffness, and the propensity for reentry arrhythmias. In addition, systolic dysfunction is facilitated by slowing of the calcium transient and the downregulation of the entire adrenergic system. Modifications of intracellular calcium movements are the main determinants of the triggered activity and automaticity that cause arrhythmias and alterations in relaxation.

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The rate-pressure product as an index of myocardial oxygen consumption during exercise in patients with angina pectoris.

Gobel FL, Norstrom LA, Nelson RR, Jorgensen CR, Wang Y.

In order to evaluate hemodynamic predictors of myocardial oxygen consumption (MVO2), 27 normotensive men with angina pectoris were studied at rest and during a steady state at sympton-tolerated maximal exercise (STME). Myocardial blood flow (MBF) was measured by the nitrous oxide method using gas chromatography. MBF increased by 71% from a resting value of 57.4 +/- 10.2 to 98.3 +/- 15.6 ml/100 g LV/min (P less than 0.001) during STME while MVO2 increased by 81% from a resting value of 6.7 +/- 1.3 to 12.1 +/- 2.8 ml O2/100 g LV/min (P less than 0.001). MVO2 correlated well with heart rate (HR) (r = 0.79), with HR x blood pressure (BP) (r = 0.83), and, adding end-diastolic pressure and peak LV dp/dt as independent variables, slightly improved this correlation (r = .86). Including the ejection period (tension-time index) did not improve the correlation (r = 0.80). Thus, HR and HR x BP, both easily measured hemodynamic variables, are good predictors of MVO2 during exercise in normotensive patients with ischemic heart disease. Including variables reflecting the contractile state of the heart and ventricular volume may further improve the predictability.

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The myocardial supply:demand ratio--a critical review.

Hoffman JI, Buckberg GD.

Myocardial ischemia occurs when there is an imbalance between myocardial oxygen demand and supply, and it is usually entirely or predominantly subendocardial. Animal experiments have shown that relative subendocardial ischemia (a reduced inner:outer flow ratio) can be predicted quite accurately from the ratio of two pressure-time areas:DPTI, the area between diastolic aortic and left ventricular pressures, and SPTI, the area beneath the systolic left ventricular pressure curve. Although the importance of relating supply and demand is obvious, care is needed in applying the results of these animal experiments to man. Recent work has shown that the critical DPTI:SPTI ratio below which subendocardial ischemia occurs is about 0.4 to 0.5 rather than 0.7 to 0.8, as originally reported. On the other hand, the critical ratio may be raised to an unknown extent by myocardial edema or hypertrophy, or by thickened or narrowed coronary arteries. Furthermore, the critical ratio is not independent of absolute coronary diastolic pressure: It is much lower than 0.4 when coronary pressures are high, perhaps because intramyocardial diastolic pressures are much higher than once thought. Further work is required to allow an important physiologic concept to be used in making decisions about patients with heart disease.

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Ventricular energetics.

Suga H.

Department of Cardiovascular Dynamics, National Cardiovascular Center Research Institute, Osaka, Japan.

Publication Types:
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