Strain

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.