72 C.A. Sciammarella and L. Lamberti Fig. 10.10 Short-axis (0ı and 90ı) and long-axis MRI images of the right ventricle (RV) and left ventricle (LV). Reference configurations correspond to Fig. 10.9a, c, e (Images were taken from Ref. [7]) 10.7 Processing of the Data Contained in MRI Tagged Images Figure 10.11 illustrates the process of obtaining the displacements of the heart’s left ventricle. In Fig. 10.11, one has the required grid lines patterns Iu that provide horizontal displacements; Iv that corresponds to the vertical displacements and Iw1 that displays the out-of-plane displacements. Figure 10.10 shows the initial configuration. The components of the displacement dp for a point P in the sections A-B and C-D are computed applying the following procedures. The projections of the vector dp illustrated in Fig. 10.7, is the sum of u1, u2 and u3. Each one of these components are obtained from the FTs’ of the patterns Iu, Iv and Iw1 along axes x1, x2 and x3, respectively. Since the heart is contracting, the arrow direction indicates this fact by going towards P. The maps of displacements u1, u2 and u3 experienced by the left ventricle are shown in Fig. 10.12a–c. Values indicated by color maps are consistent with the sketch of Fig. 10.11. 10.8 Computation of the Strains From the recorded images and performing the differentiations in the frequency space utilizing the wrapped phase pattern, the tensor of Eq. (10.30) is computed. The lack of the orthogonal planes in Fig. 10.11e, f implies that some components of the J tensor are unknown, as shown in Eq. (10.34),
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