Modeling a Sheet Structure

A 3-D sheet structure orthogonal to the x-axis is modeled as s0(x; t) = Bar(x; t), (10.41)

Figure 10.16: Modeling 3-D sheet structures. (a) Bar profile of MR values along sheet normal direction with thickness t. L0, L_, and L + denote sheet object, left-side, and right-side background levels, respectively. (b) 3-D sheet structures with thickness t and normal orientation (© 2004 IEEE)

Figure 10.16: Modeling 3-D sheet structures. (a) Bar profile of MR values along sheet normal direction with thickness t. L0, L_, and L + denote sheet object, left-side, and right-side background levels, respectively. (b) 3-D sheet structures with thickness t and normal orientation (© 2004 IEEE)

in which t represents the thickness (width) of the sheet. L 0, L _, and L + are the MR signal intensities of the sheet and both sides of backgrounds, respectively (Fig. 10.16(a)). Let (0, 0) be a pair of latitude and longitude which represents the normal orientation of the sheet given by r0= (cos 0 cos 0, cos 0 sin 0, sin 0)T. (10.43)

The 3-D sheet structure with orientation r0^ is written as s(x ; t, 7ro,0) = S0(X; t), (10.44)

where s = R0^r, in which R0^ denotes a 3 x 3 matrix representing rotation which enables the normal orientation of the sheet s0(r ; t), i.e. the x-axis, correspond to ro0 (Fig. 10.16(b)).

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