Sodium-Ion Concentration Extraction in Dermis Layer by Time-Constant-Domain Electrical Impedance Spectroscopy (TCD-EIS) With Dermis Separation Model (DSM)

Sodium-ion concentration
$c$
in the dermis layer has been extracted by time-constant-domain electrical impedance spectroscopy (TCD-EIS) with the dermis separation model (DSM). The TCD-EIS with DSM consists of the dermis separation formulation, ridge regression optimization, and distribution of relaxation times (DRTs) with radial basis function. To distinguish the relaxation time of the dermis
$\tau _{d}$
from the other layers (stratum corneum
$\tau _{\text {sc}}$
, the epidermis
$\tau _{e}$
, and the fat layer
$\tau _{f}$
), the subtracted impedivity was calculated by distant electrode pair
$z_{1}$
, and close the electrode pair
$z_{2}$
, based on optimum electrode diameter
$\phi $
and distance
$l$
. The numerical optimizations were implemented to optimize
$\phi $
from 0.5 to 3 mm and
$l$
from 2 to 8 mm, regarded as DSM sensor parameters. In the simulation, the optimized DSM sensor parameters,
$\phi ^{\ast }$
= 1 mm and
$l^{\ast }$
= 1 mm, were applied to the skin model under the condition of: 1) various sodium-ion concentrations
$c$
in the dermis layer and 2) frequencies
$f$
from 100 Hz to 1 MHz. In the experiments, the optimized TCD-EIS with DSM was applied to porcine skin under the condition following the simulations. The relation between the distribution function
$\widehat {\gamma }$
and relaxation times
$\tau $
was used to evaluate the sodium-ion concentration extraction. Both simulation and experiment results show that the normalized distribution function of the dermis
$\widehat {\gamma _{c}^{\ast }}(\ln {\tau _{d})}$
decreases with the increase of sodium-ion concentration
$c$
. The sodium-ion concentration
$c$
in the dermis layer was distinguished properly at dermis relaxation times
$\tau _{d}={10}^{-2}$
s. TCD-EIS with DSM reveals that the decrease of a normalized distribution function
$\widehat {\gamma _{c}^{\ast }}(\ln {\tau _{d})}$
correlates with the increased sodium-ion concentration
$c$
injected in the dermis layer.