Sodium concentration imaging in dermis layer by square-wave open electrical impedance tomography (SW-<i>o</i>EIT) with spatial voltage thresholding (SVT)

Abstract

Abstract In this study, sodium concentration in the dermis layer is imaged by the square wave open electrical impedance tomography (SW- o EIT) with spatial voltage thresholding (SVT). The SW- o EIT with SVT consists of three steps which are (1) voltage measurement, (2) spatial voltage thresholding, and (3) sodium concentration imaging. In the 1st step, the root mean square voltage <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mo>̃</mml:mo> </mml:mover> </mml:math> is calculated based on the measured voltage <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>v</mml:mi> </mml:math> under the square wave current <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>I</mml:mi> </mml:math> through the planar electrodes on the skin domain Ω. In the 2nd step, the m -th measured voltage <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>v</mml:mi> </mml:math> is converted to a compensated voltage v * based on the voltage electrodes distance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">v</mml:mi> </mml:mrow> </mml:msup> </mml:math> and threshold distance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Γ</mml:mi> </mml:mrow> </mml:msup> </mml:math> in order to highlight the region of interest of the dermis layer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">Ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> </mml:msup> <mml:mo>.</mml:mo> </mml:math> In the 3rd step, sodium concentration is imaged by the Gauss-Newton reconstruction method. The SW- o EIT with SVT was applied to multi-layer skin simulation and ex-vivo experiments under various dermis sodium concentrations c in the range of 5–50 mM. As an image evaluation result, the spatial mean conductivity distribution <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close="〉" open="〈"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">Ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> </mml:msup> </mml:math> is successfully determined as increasing c on both simulations and experiments. The relationship between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">〈</mml:mo> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mo>*</mml:mo> </mml:msup> </mml:mrow> <mml:mo stretchy="false">〉</mml:mo> </mml:math> and c was evaluated by the determination coefficient R 2 and the normalized sensitivity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">〈</mml:mo> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mo stretchy="false">〉</mml:mo> <mml:mo>.</mml:mo> </mml:math> The optimized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mi mathvariant="normal">Γ</mml:mi> </mml:msup> </mml:math> with the highest evaluation values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mspace width="0.25em"/> <mml:mo>=</mml:mo> </mml:math> 0.84 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">〈</mml:mo> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mo stretchy="false">〉</mml:mo> </mml:mrow> <mml:mspace width="0.25em"/> <mml:mo>=</mml:mo> </mml:math> 0.83 is under the condition of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml

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