Table 2 Comparison of the human experiment results for the five volunteers and the patient with brain tumor.

From: High frequency conductivity decomposition by solving physically constraint underdetermined inverse problem in human brain

  

(a) \(\sigma _H\) (S/m)

(b) IVF

(c) \(\tilde{\sigma }_{ex, \beta _r}\) (S/m)

(d) \(\tilde{\sigma }_{ex}\) (S/m)

(e) \(\tilde{\sigma }_{in}\) (S/m)

(f) \(\eta (\tilde{\sigma }_{ex,\beta _r})\)

Volunteers

WM-ROI

0.39160

0.38784

0.24975

0.21016

0.18181

–

Patient

WM-ROI

0.60088

0.31107

0.47868

0.44993

0.15268

0.51534

R1-ROI(yellow)

0.78660

0.18676

0.70676

0.67329

0.10352

0.25422

R2-ROI(red)

0.48226

0.34921

0.36963

0.33256

0.15271

0.60880

  1. Mean values of reconstructed results in WM-ROI, R1-ROI (the region designated by the yellow allows in Fig. 5a), and R2-ROI (the region assigned by the red rectangle in Fig. 5a). (a) Mean values of high-frequency conductivity, (b) intra-neurite volume fraction (IVF), (c) recovered apparent extra-neurite conductivity using a reference ratio (\(\beta _r=0.41\)), (d) recovered apparent extra-neurite conductivity by solving the minimization problem Eq. (18), (e) recovered apparent intra-neurite conductivity using the proposed method, and (f) indicator function \(\eta (\tilde{\sigma }_{ex,\beta _r}):={\frac{\nu _{in}\lambda }{(1-\nu _{in}) \tilde{\lambda }^{ext} +\nu _{in} \lambda \beta _r}}\).
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