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
Models and remodeling: mechanisms and clinical
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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
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"Remodeling" implies changes that result in rearrangement of
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In order to evaluate hemodynamic predictors of myocardial oxygen
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maximal exercise (STME). Myocardial blood flow (MBF) was measured
by the nitrous oxide method using gas chromatography. MBF
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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
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independent variables, slightly improved this correlation (r =
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Myocardial ischemia occurs when there is an imbalance between
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