Challenge Problems

We expect that the challenge problems in the benchmark can be solved only rarely and after extraordinary effort or additional research and development. We expect almost none of the available computational methods/tools will be able to solve these problems with acceptable accuracy and computational costs.

5. Material Variations

Problem 5 requires the solution of the scattering problems in problems 1-4 when the permittivity and conductivity of the tissues in the models are not fixed but assumed to be within ±10% of the values provided in problems 1-4 with a uniform probability distribution.

5.1a. Uncertain Homogeneous Head-Sized Sphere

Solve the scattering problem and find the mean value of the quantities of interest when the sphere in problem 1a is illuminated by these impressed sources and filled homogeneously with a (frequency-dependent) material whose permittivity and conductivity are within ±10% of the IEEE head tissue-equivalent material [5].

	402 MHz		900 MHz		2.45 GHz
	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)
IEEE head tissue equivalent	44.724±4.472	0.87±0.09	41.5±4.2	0.97±0.10	39.2±3.9	1.80±0.18

5.1b. Uncertain 4-Layered Head-Sized Sphere

Solve the scattering problem and find the mean value of the quantities of interest when the sphere in problem 1b is illuminated by these impressed sources and filled homogeneously with a (frequency-dependent) material whose permittivity and conductivity are within ±10% of the frequency-dependent material properties obtained from [6].

	402 MHz		900 MHz		2.45 GHz
	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)
Skin Dry	46.741±4.674	0.68892±0.06889	41.405±4.141	0.86674±0.08667	38.007±3.801	1.464±0.146
Fat	5.5789±0.5579	0.041151±0.00412	5.462±0.546	0.051043±0.005104	5.2801±0.5280	0.10452±0.01045
Bone Average	9.40725±0.94073	0.0604105±0.0060411	8.97915±0.89792	0.091759±0.009176	8.33895±0.83390	0.2446735±0.0244674
Brain Average	49.721±4.972	0.59178±0.05918	45.8055±4.5806	0.76653±0.07665	42.539±4.254	1.51135±0.15114

5.2a. Uncertain Homogeneous Body-Sized Spheroid

Solve the scattering problem and find the mean value of the quantities of interest when the spheroid in problem 2a is illuminated by these impressed sources and filled homogeneously with a (frequency-dependent) material whose permittivity and conductivity are within ±10% of the equivalent material from [7].

	402 MHz		900 MHz		2.45 GHz
	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)
Equivalent Material	44.724±4.472	0.87±0.09	41.5±4.2	0.97±0.10	39.2±3.9	1.80±0.18

5.2b. Uncertain 3-Layered Body-Sized Spheroid

Solve the scattering problem and find the mean value of the quantities of interest when the spheroid in problem 2b is illuminated by these impressed sources and filled homogeneously with a (frequency-dependent) material whose permittivity and conductivity are within ±10% of the frequency-dependent material properties obtained from [6].

	402 MHz		900 MHz		2.45 GHz
	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)	$\epsr$	$\sigma$ (S/m)
Skin Dry	46.741±4.674	0.68892±0.06889	41.405±4.141	0.86674±0.08667	38.007±3.801	1.464±0.146
Muscle	57.112±5.711	0.79682±0.07968	55.032±5.503	0.94294±0.09429	52.729±5.273	1.7388±0.1739
Bone Average	9.40725±0.94073	0.0604105±0.0060411	8.97915±0.89792	0.091759±0.009176	8.33895±0.83390	0.2446735±0.0244674

5.3a. Uncertain Homogeneous AustinWoman v2.3

Solve the scattering problem and find the mean value of the quantities of interest when the AustinWoman 2.3 model in problem 3a is illuminated by these impressed sources and all voxels are filled homogeneously with a (frequency-dependent) material whose permittivity and conductivity are within ±10% of the equivalent material from [7].

5.3b. Uncertain Inhomogeneous AustinWoman v2.3

Solve the scattering problem and find the mean value of the quantities of interest when the inhomogeneous AustinWoman 2.3 model in problem 3b is illuminated by these impressed sources. Use the four different resolution (8×8×8 mm³, 4×4×4 mm³, 2×2×2 mm³, and 1×1×1 mm³) voxel models available in [8].

Material Properties Table for problem 5.3 is Under Construction
Please refer to AustinMan and AustinWoman website for mean material properties. For problem 5, the permittivity and conductivity of the tissues are not fixed but assumed to be within ±10% of the values provided in problems 1-4 with a uniform probability distribution.

5.4a. Uncertain Homogeneous AustinMan v2.3

Solve the scattering problem and find the mean value of the quantities of interest when the AustinMan 2.3 model in problem 4a is illuminated by these impressed sources and all voxels are filled homogeneously with a (frequency-dependent) material whose permittivity and conductivity are within ±10% of the equivalent material from [7].

5.4b. Uncertain Inhomogeneous AustinMan v2.3

Solve the scattering problem and find the mean value of the quantities of interest when the inhomogeneous AustinMan 2.3 model in problem 4b is illuminated by these impressed sources. Use the four different resolution (8×8×8 mm³, 4×4×4 mm³, 2×2×2 mm³, and 1×1×1 mm³) voxel models available in [8].

Material Properties Table for problem 5.4 is Under Construction
Please refer to AustinMan and AustinWoman website for mean material properties. For problem 5, the permittivity and conductivity of the tissues are not fixed but assumed to be within ±10% of the values provided in problems 1-4 with a uniform probability distribution.