Fig. 2: In-silico testbed results: visualization of the reconstruction error for two target maps and two different catheter configurations. | Nature Communications

Fig. 2: In-silico testbed results: visualization of the reconstruction error for two target maps and two different catheter configurations.

From: Real-time 3D temperature reconstruction in microwave cancer hyperthermia from scarce temperature measurements

Fig. 2

a Fully anthropomorphic human phantom Duke V3.0 employed to simulate an HT treatment, using a phased array applicator made of eight patch antennas immersed in the water bolus; the inset shows the tumor target position (highlighted in green). b The temperature values \(\widetilde{T}({{{{\bf{q}}}}}_{{{{\mathcal{l}}}}},t_{ST})\) used to perform the reconstruction are acquired in the spatial points \({{{{\bf{q}}}}}_{{{{\mathcal{l}}}}}\), \({{{\mathcal{l}}}}=1,\ldots,L,\) (black dots) distributed along the direction of a fiber-optic thermometer inserted on the transversal (\({xy}\)) plane passing through the tumor at its centroid; from top to bottom the number of points considered are: \(L=\) 20 (case 1) and 7 (case 2). c, d Boxplots showing the minimum, maximum, median and interval between the 25th and the 75th percentiles of the set of thermal parameters (\(k\) and \(\omega\)) corresponding to key tissues in the ROI (M = muscle, F = fat + SAT, S = skin, T = tumor) when a Sobol sequence is used to sample the parameters space; superimposed dots represent the combinations of parameters \({{{{\boldsymbol{\xi }}}}}_{a}\) of two target maps \({{{\mathcal{F}}}}\left({{{\bf{r}}}},{t}_{{{{\rm{ST}}}}};{{{{\boldsymbol{\xi }}}}}_{a}\right),\) \(a=1\) (c), \(a=2\) (d). e Goodness function \(g(\chi )\), Eq. (1): rows refer to the catheter cases (b), and columns represent the target maps (c, d). The blue-dot line corresponds to the reconstruction of the target map without noise; the blue-shadow region includes 2000 realizations of a Gaussian distribution function (\(\mu=\pm 0.1\,\)°C and \(\sigma=0.2\,\)°C) used to introduce an error on the target map, with the blue dashed line denoting the average and the dash-dotted line indicating the 95th percentile; the red-dot line expresses the discrepancy between the target field and the baseline map (SoA simulation approach). Source data are provided as a Source Data file.

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