Strain is a measure of local deformation of a line element
due to tissue motion
and is independent of the rigid motion
of the LV.
To compute the local 2D strain for a given triangle,
correspondence of the 3 vertices with a later time
is sufficient [2].
With such information known, an affine map is completely
determined.
By the polar decomposition theorem,
can be decomposed as
, where
is a rotation matrix, and
is a symmetric
matrix representing the 2D strain.
Under the linear motion assumption,
strain in the direction
of a vector
can be expressed as
Two directions within each such triangle are of particular
interest,
namely, the directions of principal strain, representing the maximum and
minimum stretch within a triangle, and corresponding to the eigenvectors
of . The results of strain analysis done on
images of figure 5
is shown in figure 6 where
the maximum and minimum principal strain directions and values
are shown.
It should be pointed out that
extension of quantities obtained from equations
(8), (9), (10), and (11) to 3D is possible with tagging.
Naturally, there
are three principal strain directions in 3D.