## Validating the Numerical Simulation by in Vitro Experiments

To validate the numerical simulation, the postprocessing method for thickness determination was used to measure real MR images of two different objects, an acrylic plate phantom.

A phantom of sheet-like objects with known thickness was used. It consisted of four acrylic plates of 80 x 80 (mm2) with thickness t = 1.0,1.5,2.0, and 3.0 (mm), placed parallel to each other with an interval of 30 mm (Fig. 10.21(a)).

Figure 10.21: Acrylic plate phantom and its MR images. (a) Physical appearance. (b) MR images. The horizontal and vertical axes of the images correspond to the x-axis and z-axis, respectively. The voxel size was Axy = 0.625 mm and Az = 1.5 mm. As can be easily observed by naked eye, the acrylic plate with t = 1 mm appears to be imaged slightly thicker in 0 = 45° and \$ = 0° than 0 = 0° and \$ = 0°. (© 2004 IEEE)

The phantom was submerged in a water bath so that the background (water) showed higher intensity as contrasted to low intensity objects (acrylic plates). Three-dimensional MR images (TR/TE/flip angle/matrix/FOV/slice thickness: 12.8 ms/5.6 ms/5/256x256/160 mm/1.5 mm) of the phantom were obtained using a fast spoiled gradient-echo sequence (FSPGR). The voxel size was Axy = 0.625(= 260) (mm) and Az = 1.5 (mm). Thus, voxel anisotropy =

0.625

Thirteen datasets of 3D MR images were acquired with different normal positions of the phantom plates, eight with variable 0 (0 = 0, 15, 25, 35, 45, 60, 75, and 90 degrees) and fixed \$ (\$ = 0), and five with variable \$ (\$ = 0, 15, 25, 35, and 45 degrees) and fixed 0 (0 = 0). In the obtained MR images, we observed L _ = L + = 40 and L 0 = 0. Figure 10.21(b) shows examples of the MR images. We compared actually measured thickness from the real MR data with the computational thickness calculated by the numerical simulations.

Figure 10.22 shows the averages and the SDs of the actually measured (in vitro) thickness from the MR data of the phantom imaged with different

0 15 30 45 60 75 90 Sheet normal orientation 0 (deg)

0 15 30 45 60 75 90 Sheet normal orientation 0 (deg)

0 15 30 45 60 75 90 Sheet normal orientation § (deg)

Figure 10.22: Comparison of simulated thickness and in vitro thickness determined from MR images of acrylic plate phantom. Axy = 0.625 mm, Az = 1.5 mm,

and a = 2- Axy. For in vitro thickness, its average and SD values are indicated by symbols and error bars. (a) Dependences on sheet normal orientation 0. (b) Dependences on sheet normal orientation 0. Note that the dependence on 0 is theoretically equivalent to the dependence on 0 when the anisotropy is A = 1. (© 2004 IEEE)

z xy

e and \$ and the plots of the simulated thickness representing the dependences on sheet normal orientation e and \$. Figures 10.22(a) and 10.22(b) show the plots of the dependences of e and \$ with a = ^ Axy, respectively. Good agreement between the simulated and the in vitro thicknesses was observed in both cases although the in vitro thicknesses was slightly greater than the simulated thickness. The biases, i.e., the difference between the simulated thickness and the average of in vitro thickness, were predominantly around 0.1 mm or less (except for e = 75° of t = 3 mm), and the SDs of the in vitro thickness were mostly within 0.1 mm (except for e = 45° of t = 2 mm and e > 35° of t = 3 mm). It should be noted that the dependence on \$ is theoretically equivalent to the dependence on e when the anisotropy is = 1.