Chapter 10
Characterization of Atherosclerotic
Lesions by Inversion of Eddy-Current
Impedance Data
10.1 The Model
Figure 10.1 shows a planar model of a type Vb lesion that could be situated in the
coronary arteries [122]. This lesion is the largest and most complex stable lesion that
can form, and is characterized by the formation of calcium of the outer cap, which
gives rise to the expression ‘hardening of the arteries.’ Because the vulnerability of
plaque is not closely correlated to plaque size, but rather to the overall composition,
we are interested in determining the amount of fibrous tissue, calcium, lipid core,
and smooth muscle that exists in the lesion, and to do this we return to Fig. 10.1.
We excite Eddy-currents in the layered medium by means of the exciting pancake
coil, and read the impedance of the coil. We then use NLSE, the nonlinear leastsquares parameter estimator in VIC-3D ® to determine the thickness of each layer.
We assume that the conductivity of each layer is known, as shown in the figure.
Figure 10.2 illustrates the ‘standard conductivity model’ for a type Vb lesion. The
problem is to determine the widths, L 1 , · · · , L 5 of each layer, given the conductivity
profile shown. If we assume that the vessel wall’s thickness, L 5 , is fixed at, say,
0.3 mm, then there are only four unknowns to be determined using NLSE.
The data for the standard model of Fig. 10.2 are shown in Table 10.1, which is
taken from [122]. In the model calculations, values for the calcified outer layer were
inferred from cancellous bone values (see Table 10.13). In [122] the conductivity
values for thrombus (fibrous material) and vessel wall were assumed constant up to
1 MHz. Beyond 1 MHz, however, it was assumed that the conductivity of thrombus
and vessel wall increased slightly, and these values were inferred as shown.
Additionally, it was assumed that fibrous tissue had relatively low capacitance due
to an extracellular matrix of various collagens. The capacitance of the vessel wall
was assumed to be mostly due to the smooth muscle, combined with the effects of
fat.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
H. A. Sabbagh et al., Advanced Electromagnetic Models for Materials
Characterization and Nondestructive Evaluation, Scientific Computation,
https://doi.org/10.1007/978-3-030-67956-9_10
249
Characterization of Atherosclerotic
Lesions by Inversion of Eddy-Current
Impedance Data
10.1 The Model
Figure 10.1 shows a planar model of a type Vb lesion that could be situated in the
coronary arteries [122]. This lesion is the largest and most complex stable lesion that
can form, and is characterized by the formation of calcium of the outer cap, which
gives rise to the expression ‘hardening of the arteries.’ Because the vulnerability of
plaque is not closely correlated to plaque size, but rather to the overall composition,
we are interested in determining the amount of fibrous tissue, calcium, lipid core,
and smooth muscle that exists in the lesion, and to do this we return to Fig. 10.1.
We excite Eddy-currents in the layered medium by means of the exciting pancake
coil, and read the impedance of the coil. We then use NLSE, the nonlinear leastsquares parameter estimator in VIC-3D ® to determine the thickness of each layer.
We assume that the conductivity of each layer is known, as shown in the figure.
Figure 10.2 illustrates the ‘standard conductivity model’ for a type Vb lesion. The
problem is to determine the widths, L 1 , · · · , L 5 of each layer, given the conductivity
profile shown. If we assume that the vessel wall’s thickness, L 5 , is fixed at, say,
0.3 mm, then there are only four unknowns to be determined using NLSE.
The data for the standard model of Fig. 10.2 are shown in Table 10.1, which is
taken from [122]. In the model calculations, values for the calcified outer layer were
inferred from cancellous bone values (see Table 10.13). In [122] the conductivity
values for thrombus (fibrous material) and vessel wall were assumed constant up to
1 MHz. Beyond 1 MHz, however, it was assumed that the conductivity of thrombus
and vessel wall increased slightly, and these values were inferred as shown.
Additionally, it was assumed that fibrous tissue had relatively low capacitance due
to an extracellular matrix of various collagens. The capacitance of the vessel wall
was assumed to be mostly due to the smooth muscle, combined with the effects of
fat.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
H. A. Sabbagh et al., Advanced Electromagnetic Models for Materials
Characterization and Nondestructive Evaluation, Scientific Computation,
https://doi.org/10.1007/978-3-030-67956-9_10
249