Page 16 - The Elegance of the Outer Wall
In previous pages the mathematic model has used the fact that the myocardial volume is constant to make the clear inference that if the mid-wall contracts by 15%, for a given ratio of diastolic short axis dimension and wall thickness, the mean diameter of the systolic epicardial ring is a fixed quantity dictated by the geometry of the situation and not the architecture of the wall. In the “standard” ventricle the model has suggested that 15% shortening at the mid-wall corresponds to 9.6% at the epicardium.
It is logical to assume that these two zones, and the layers between them, will wish to move in harmony and not have one trying to outpace the other. It follows that if the epicardial cells were in the plane of the short axis, i.e. with a zero helical angle, then to match the mid-wall 15% they would only have to contract by 9.6%. As the epicardial myocytes would be capable of 15%, they would seem to under perform, which seems a waste. If they cannot modulate their shortening then they would either continue to try to contract and waste energy going nowhere, or actually achieve 15% and throw stress back on the deeper layers.
From page 2 we see that the outer myocytes actually lie at a helical angle. Can they still match the mid-wall changes when they are not in line? This page will attempt to show how the geometry is arranged to achieve just that.
The diagram above shows two tracts of cells lying in the subepicardial layer, both 100 units long (the actual value is immaterial). One is a hypothetical tract lying in the short axis plane. At any point, systolic movement may occur and I have chosen 10 units an easy number. The other tract lies at 45 degrees helical angle. Because of the angle, if the oblique tract can move by just over 14 units it can still achieve the 10 unit shift in the plane of the short axis. Thus, the outer rim can lie at an angle to the short axis and still move in harmony with the mid-wall.
These numbers represent the ratio of movement between the two tracts, not the absolute. However I think we can take the ratio of contraction percentages as an index of the relative movements, which will represent the cosine of the angle of the oblique tract. Solving this for 9.6% shortening in the short axis plane and 15% in the oblique, the helical angle of the oblique tracts is 50 degrees. Hence, in our "standard" left ventricle, a helical angle of 50 degrees in the subepicardium will allow its cells to move in harmony with the mid-wall.
The grain closer to the mid-wall will have a lesser ratio of freedom, but then it will be at a smaller helical angle. Indeed I do not think it is unreasonable to suggest that, during growth, the grain at any level in the outer half aligns to be at the angle which allows the cells to contract at a full 15% and still keep pace with the mid-wall. In this way, all the cells of the outer half are working in harmony and at the same level of efficiency. If contractility is increased by inotropic stimulation and it affects all cells equally, then all layers will still move in concert.
Importantly, the angle also means that the myocardium can generate a vector of contractile force in the long axis. As most of the myocytes have a helical angle, and assuming that they do follow a helical course, this would explain how the myocardium generates a powerful long axis contraction of up to 15%.
The thicker the wall, the greater is the angulation that the outer rim can achieve. This modelling may well be only possible during growth. This does have an interesting corollary, which is that acquired hypertrophy in adulthood may adversely affect the dynamic architecture of the wall, as the helical angles will cease to be appropriate for the distance of a layer from the mid-wall.
This analysis is a simplification, but it probably captures the major movements involved, and sets the scene within which the repacking and hydraulic forces have to operate.