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In previous work, authors have reported measuring
such quantities as torsion, and rotational motion of the tissue. However,
with previous techniques, this
information could only be obtained at a specific set of points within
the myocardium. With the methods
described, we can obtain displacement vectors
on all parts of the myocardium. From this information,
we obtain differential
vector quantities which describe
local rotations and expansions.
Tissue Expansion and Contraction
Expansion or contraction of the myocardium in an
arbitrary area within the LV wall between the endocardial and
epicardial surfaces may be written as:
where the integral on the left is a line integral
computed on a curve 
which bounds
the myocardial mass of interest, 
is the normal to , and 
is
a dense displacement vector field.
The integral on the right is over the area bounded by , and
is the divergence of the
vector
field. This provides an
easy way to compute a quantitative measure of tissue expansion.
The strength of this measure is that it is invariant
to rigid body motion, and so can be used as a measure of
compressibility, of non-rigid deformation, or of
tissue expansion, or contraction.
Circulation
Torsion has been described to be of major significance in the
study of LV. We can evaluate
circulation accurately around
any contour bounding the LV myocardium:
where is a planar contour, 
is the tangent
to such a curve, 
is the
binormal of the curve,
and the integral is evaluated around .
is the component of
curl of
perpendicular to the plane of describing
infinitesimal circulation of the displacement vector
field
at a point.
It is important to note that this information can be evaluated around any
planar contour which passes through the myocardium.