Figure 2 shows the predicted deformations experienced by the rectum, the bladder and the prostate when the TRUS probe exerts a force of 30 N on the rectum inner wall. The region where the probe exerts the force, that is, the anterior part of the rectum and the posterior part of the prostate (see Fig. 1a), is the one that experiences the highest deformation. The deformed rectum in turn pushes against the prostate producing its displacement towards the ventral region (-Y ) together with a significant non-uniform deformation of the TZ and PZ geometry. The maximum displacements along the -Y direction for the rectum, TZ and PZ contours in the plane of Fig. 2 were respectively of 13.5 mm, 11 mm and 12 mm. At the same time, the bladder region that was in contact with the prostate was deformed and cranially displaced (Z direction) approximately 9 mm. Note that the high difference in stiffness of bones and muscles contributes to the generation of non uniform deformations of the rectum, the bladder and the prostate. To simulate the displacement of small lesions in the prostate we selected five different nodes, as defined in the two leftmost columns of Table 2 and sketched in Fig. 3. Note that nodes N1, N3, N4 and N5 are located near the outer surface of the PZ whereas the node N2 is located within the TZ.
Figure 4 shows superimposed projections, in the sagittal plane, of the original prostate geometry and the deformed geometry when the TRUS probe exerts a force of 30 N. Comparison of original and deformed surface contours reveals the two main effects of the TRUS probe pressure, namely a motion (a displacement in the absolute frame of reference) and a deformation (a change in volume and shape) of the prostate gland. The displacements of the selected nodes are also portrayed in Fig. 4. For the sake of clarity, we have replicated the same surface contour plot five times showing only one of the nodes in each plot. The detailed information of node displacements along each of the 3-D coordinate-axes, as well as its magnitude, are presented in Table 2. The distance traveled by the nodes ranges between 5.20 and 13.91 mm, being the N1 node the one experiencing by far the highest displacement. This fact is not surprising considering that N1 is the node located closer to the rectum, that is, it lies close to the prostate surface region most directly affected by the rectum motion, which is in turn induced by the probe pressure. On the other hand, the lowest displacement of the N3 node may be attributed to the restraint imposed by the puborectalis and pubococcygeus muscles. Note that the deformation induced by the probe also implies a strong departure from symmetry with respect to the midcoronal plane. In simpler words, the original prostate shape in Fig. 4 still recalls what would be the surface of an idealized ellipsoid whereas the deformed contour features a far more irregular shape.
State-of-the art of MRI-TRUS fusion platforms rely on the procedure known as registration, which consists in the superposition of slices containing the original lesion in the original MRI image set and the corresponding slices in the TRUS image set. Registration is aimed to facilitate the practitioner work during biopsy by removing (or at least greatly reducing) one of the outputs of TRUS, i.e., prostate motion (see Fig. 4). Ideally, the two superimposed slices (from MRI and TRUS) would show similar shapes so that the practitioner conducting the biopsy would estimate with a reasonable degree of accuracy the location of the target lesion in the deformed geometry. Following the particular approach proposed by Igarashi et al. , Fig. 5 shows superimposed slices of the original and deformed prostate in a polar coordinate framework together with the original and displaced locations of the control node N1 in the axial plane. That is, Fig. 5 intends to approximate the type of representation that a MRI-TRUS registration procedure would generate when intending to track the N1 node. The idea behind the polar coordinate framework is to determine the origin of the polar system in the original (undeformed) slice, the corresponding origin in the deformed slice and then to apply a translation of the latter origin into the former one, which results in the superimposition of both images.
During a biopsy, the first question for the practitioner would be what particular slice has to be visualized in the TRUS image. In Fig. 5a we simulate the most obvious choice for an axial slice, i.e., keeping the same vertical location (Z = 0) wherein the lesion was observed in the original MRI images. We see clearly in this figure that even after registration (superimposition of slices) the large deformation experienced by the prostate makes the final slice quite different from the initial one. At first sight, however, it seems that given the initial location of N1 in the axial plane its final location (N1’) would not be difficult to estimate. In this respect, the N1 node appears to be rather favorably placed, as it is very close to the prostate external wall and it lies in the midsagittal (X = 0) plane. Note that, as will be discussed below, we have plotted in Fig. 5a not the real N1’ 3-D location but just its projection in the axial plane. Our biomechanical model predicts a small leftwards displacement of N1 as a result of the deformation, which is consistent with the fact that we have worked with a realistic geometry, that is, a real human body will never be 100% symmetric. The sagittal slices superimposed in Figure 5c show that the biggest source of error in the final N1’ location, when sought in the original (X = 0) axial plane, is in the normal coordinate (Z). Our biomechanical FE simulation predicts that the final N1’ location is not in the original axial location (Z = 0) but in the plane with Z = 5.16mm (see Table 2). This is taken into account in Fig. 5b, where registration is performed using the proper slice for N1’ . Note that both axial polar plots in Figs. 5a and 5b are quite similar. Thus, for the example considered here (for the N1 node) the bright side is that the practitioner would probably produce a good guess of the X and Y coordinates of the lesion in the TRUS image regardless of the particular axial plane being visualized. On the minus side, as clearly shown is Fig. 5c, we have that even with an accurate projection of the lesion in the axial plane a large error could be made in the estimate of its axial location (Z). The example shown in Fig. 5 therefore illustrates the fact that it might be quite difficult to estimate the final lesion location using visual inspection alone. The biomechanical approach presented in this study therefore provides an extra layer of knowledge that might well greatly improve in the future the accuracy in the MRI-TRUS fusion procedures.