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European Heart Journal – Cardiovascular Imaging (2016) 17, 633–634
doi:10.1093/ehjci/jew060
EDITORIAL
Global myocardial function, regional myocardial
function, and the Daemon of Laplace
Jens-Uwe Voigt*
Department of Cardiology, University Hospital Gasthuisberg, Catholic University Leuven, Herestraat 49, Leuven 3000, Belgium
Online publish-ahead-of-print 13 April 2016
Pierre-Simon Laplace, the famous 18th century French mathematician, physicist, and astronomer, expressed in his book ‘Essai philosophique sur des Probabilités’ his deterministic view on the world
with the idea that if a hypothetical intellect would be aware of all
laws of nature and the exact condition of all its components at a certain point in time, any past or future state of the universe could be
calculated from that.1 This intellect became later popular as ‘Daemon of Laplace’, and the idea was challenged by both philosophers
and physicists. Not only that in final consequence such a deterministic world spirit would exclude the existence of a free will, it also
causes a logical problem as this intelligence would be part of the system and had to calculate itself. Finally, modern quantum mechanics
tells us that both location and velocity of a particle cannot be measured at the same time.
Determining the regional work performed by the ventricular
myocardium leaves us with a less philosophic problem on a smaller
scale, but with a comparable intellectual challenge. And also here Laplace was involved in laying the foundations. In a joint work with Lavoisier, they confirmed in 1780 that oxygen consumption of an
animal has an energetic equivalent in the body heat that can melt
the ice inside a calorimeter.2
The same principle is nowadays applied when myocardial blood
flow and its oxygen extraction are invasively measured as caloric
equivalent of the energy consumption of the heart which then can
be expressed in J (Joule), Nm (Newton meter), or Ws (Watt second).
On the other side, we can measure the work of the heart which is
performed towards the body. This ‘external work’ is usually described by the pressure–volume loops of the chambers,3 as the product of pressure (N/m2) and volume (m3) equals work (Nm).
However, there is a considerable gap between the consumed energy
and the performed external work which is explained by the ‘potential
work’ which is needed to build up the static pressure in the chamber4
and by the energy demand of the basic cell metabolism. Both ‘external work’ and ‘potential work’, but not the basic metabolism of the
cells, can be determined from invasive haemodynamic measurements
that are displayed in a pressure–volume diagram (Figure 1).
In ventricular dyssynchrony, myocardial contraction is uncoordinated, and the performed myocardial work is partially wasted
by the walls stretching each other. To study such a complicated condition, the assessment of regional myocardial energetics is needed. If
pressure is replaced by the local force created by the myocyte (N)
and volume is substituted by the length change of this myocyte (m),
the resulting force– length loop shows the locally performed work
(Nm). However, we are here in a deterministic dilemma. While the
assessment of length would be even possible by non-invasive imaging, the direct measurement of local force or wall stress is impossible in vivo without the destruction and, consequently, functional
alteration of the tissue. The Daemon of Laplace is back.
Many attempts have been made to estimate the forces inside the
ventricular wall. While some authors make complex assumptions
on a global force distribution modulated by regional deformation
behaviour,5 others use simply the invasively measured LV cavity
pressure as substitute. In the current publication by Vecera and colleagues, not even that is done. The LV pressure curve shape is only
estimated based on the cuff measurement of the systolic blood pressure and cardiac time intervals.6 Earlier work from the same group
had shown that this approach has a negligible error compared with
the use of invasive LV pressure measurements.7 This new concept of
a fully non-invasive assessment of regional myocardial work was
now tested for the first time in the clinical setting of patients undergoing cardiac resynchronization therapy (CRT). The authors confirmed earlier observations from animal experiments8 that
dyssynchronous hearts waste a lot of energy in the early activated
wall (Figure 2). They also demonstrated convincingly that the wasted
work is reduced with resynchronization. In this pilot study with only
21 patients, the value of the ‘wasted work ratio’ for predicting CRT
response was limited, and the additional consideration of myocardial scar extend proved to be indispensable. However, the concept
remains intriguing, and the results from larger, potentially multicentric patient studies can be expected with interest.
It can be discussed that the proposed concept estimates only the
‘external work’ performed by the local myocardium. It ignores the basic metabolism of the cells and the potential work that has to be performed and might therefore exaggerate differences between walls
compared with true measurements of metabolism, e.g. by myocardial
PET scans with Acetate or FDG tracers. Further, both potential work
The opinions expressed in this article are not necessarily those of the Editors of EHJCI, the European Heart Rhythm Association or the European Society of Cardiology.
* Corresponding author. Tel: +32 16 349016. E-mail: [email protected]; [email protected]
Published on behalf of the European Society of Cardiology. All rights reserved. & The Author 2016. For permissions please email: [email protected].
634
Figure 1 Mechanical work performed by the ventricle can be
assessed in the pressure– volume diagram. It consists of the ‘external work’ (EW, green area of the LV pressure volume loop) and the
potential work (PW, yellow area) which is needed to build up the
static pressure in the chamber. ED, ES—end-diastole, end-systole.
The energy needed for the basic metabolism of the cells cannot be
displayed in this way.
and external work depend directly on local wall stress. This, however,
is not measurable in vivo and was therefore substituted with the same
LV pressure curve for all segments. Formally, the multiplication of local strain measurements with a single modelled LV pressure curve results only in weighting the systolic part of the strain curve (during high
LV pressure) 10–20 times higher than the diastolic part (when LV
pressure is very low). It is therefore reassuring that analysing the systolic part of the strain curve only leads to very comparable results as it
had been previously shown by others.9
It must be questioned in all these approaches, however, if the assumption of a uniform wall stress distribution is appropriate for remodelled hearts of LBBB patients at all. Commonly, these patients
have a dilated LV with a thinned septum while the lateral wall is hypertrophied. And here Laplace enters the stage again. He provided us with
a formula that is known by every cardiologist as the ‘Law of Laplace’. It
describes in simple terms the relation of the pressure inside a sphere
and the stress that can be expected in the wall of the sphere for a given
radius and wall thickness. Considering that the lateral wall in remodelled LBBB patient hearts is much thicker than the septum, and that
it further thickens during its systolic contraction, the wasted work
would appear much higher in the septum while the work performed
in the lateral wall would be measured much lower than without wall
thickness correction. So maybe the 18th century ‘Law of Laplace’
could help to overcome the daemon that still inherent in many modern approaches of assessing regional myocardial energetics.
Editorial
Figure 2 In dyssynchronous hearts, the ‘external work’ differs
between regions. Late activated regions (A) perform a lot of external work (green area of the counter-clockwise running loop) while
in early activated regions (B) part of this work is wasted due to
stretching during systole (red area where the loop runs clockwise).
Note that for regional work assessment, LV pressure is only a surrogate for the local force to which the myofibrils are exposed. This
force depends on wall thickness and curvature. Black arrow, direction of loop.
Conflict of interest: None declared.
References
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