Kiagus Aufa Ibrahim

Sodium-ion (Na ⁺ ) accumulation in the dermis has been increasingly recognized as a functional biomarker associated with various pathological conditions. Non-invasive and accessible methods for localized assessment remain limited. A planar electrical impedance tomography (pEIT) implementing gamma-Jacobian matrix ( γ J -pEIT ) has been proposed to image the sodium-ion concentration c Na within dermis layer. The gamma-Jacobian matrix   γ J establishes a relationship between conductivity distribution σ and the peaks of deconvolved reactance γ ^ associated with c Na within the dermis layer. The   γ J integrates frequency-dependent features derived from deconvolved reactance γ into Jacobian matrix formulation to enhance sensitivity to dermis-associated electrical responses. The γ J -pEIT is applied for c Na imaging within dermis layer in both simulation and ex-vivo experiments across a range of c Na from 5 to 50  mM . As results, the   γ J shows broader spatial sensitivity and higher dermis-related sensitivity than the   Typ J , with 33.8 and 19.32 times increases in the standard deviation ς and mean absolute dermis-related sensitivity | de   J m   | , respectively. Overall, the γ J -pEIT demonstrates enhanced sensitivity and reliable accuracy in visualizing c Na within the dermis layer. In simulation, the γ J -pEIT accurately reconstructed conductivity changes γ sim Δσ across the various c Na within the dermis layer with a strong agreement ( R = 0.982 ) . The   γ J provides an 18-fold increase in sensitivity to c Na relative to   Typ J . Experimental results further demonstrate a strong relationship ( R = 0.997 ) between c Na and ⟨ Δ σ ⟩ . These results demonstrate the potential of the proposed γ J -pEIT for functional imaging of sodium-related processes in the dermis, providing a promising pathway towards non-invasive assessment of tissue ionic microenvironments.

Area of breast cancer tissues has been clustered by newly-proposed electrical impedance tomography (EIT) implemented with Poisson and Gaussian mixture models (EIT-PGMM) for breast cancer identification. EIT-PGMM comprises two distinct methods for comparison: EIT-PMM (Poisson Mixture Model) and EIT-GMM (Gaussian Mixture Model). EIT-PGMM consists of two sections which are 1) reconstruction section by EIT to reconstruct conductivity distribution σ ∈R ^{( F × N )} ( f : frequency 1≤ f ≤ F , n : area resolution 1≤ n ≤ N ) from impedance distribution Z ∈C ^{( F × M )} ( f : frequency 1≤ f ≤ F , m : measurement number 1≤ m ≤ M ) on injection current i between electrodes on measurement boundary and measurement voltages v , and 2) clustering section by PGMM to cluster breast cancer area B with cluster assignment (one-hot vector) s ∈R ^{( N × K )} ( k : cluster number 1≤ k ≤ K ) to sharpen the border between cancerous and normal breast tissues. The s is probabilistically determined through posterior p ( s|σ,Θ ) ( Θ : parameters of Poisson and Gaussian mixture models) assigns each spatial resolution to a specific cluster, which highest mean conductivity distribution 〈 σ _k 〉 among the K clusters is identified as the breast cancer region B . The EIT-PGMM was applied to the mastectomized breast tissues from 5 patients placed inside hemispherical sensor of EIT under the condition of injection current frequencies f ranging from 1 [kHz] to 3 [MHz]. Qualitatively, breast cancer region B remains similar across different values of K and between EIT-PMM and EIT-GMM. In order to quantitatively evaluate B , the results of EIT-PMM and EIT-GMM were compared with the diameter D measured clinically and area A of breast cancer segmented from the coronal plane of CT scan. EIT-GMM provides a more accurate estimation of breast cancer region B with accuracy of 90.2% in diameter D _K ^GMM . and 79.3% in area A _K ^GMM .

The gastric electrical impedance tomography (gEIT) has been assessed by the conventional¹³C-acetate breath test (BT) for gastric retention evaluation. ThegEIT images the conductivity distribution of the gastric volumeVtmin the stomach. ThegEIT was applied to seven healthy subjects during gastric emptying under the experimental conditions which are (i) frequencies of applied current is 30 kHz and 200 ml of 200 kcal liquid meal added with 100 mg sodium acetate- 1-¹³C. During the 90 min of measurement time, thegEIT measured each subject at five-minutes intervals, followed by the BT measurement. ThegEIT calculated the gastric volumeVtm[%] based on the gastric conductivity distributionσobtained from the reconstructed image. Fifty percent completion time of gastric emptyingt50and¹³CO₂-peak exhalation timetmaxwere used as parameters to characterize gastric emptying during the BT. ThegEIT images the conductivity distribution of the gastric volumeVtm[%] in the abdomen. The experimental results show gEIT is strongly correlated with BT between the values oftmaxandt50at frequency of 30 kHz, which indicates a low error in the gastric retention evaluation.gEIT proves to be a reliable, non-radioactive alternative for gastric retention evaluation.

Breast cancer detection and differentiation of breast tissues are critical for accurate diagnosis and treatment planning. This study addresses the challenge of distinguishing between invasive ductal carcinoma (IDC), normal glandular breast tissues (nGBT), and adipose tissue using electrical impedance spectroscopy combined with Gaussian relaxation-time distribution (EIS-GRTD). The primary objective is to investigate the relaxation-time characteristics of these tissues and their potential to differentiate between normal and abnormal breast tissues. We applied a single-point EIS-GRTD measurement to ten mastectomy specimens across a frequency range f = 4 Hz to 5 MHz. The method calculates the differential ratio of the relaxation-time distribution function Δ γ between IDC and nGBT, which is denoted by Δ γ IDC − nGBT , and Δ γ between IDC and adipose tissues, which is denoted by Δ γ IDC − adipose . As a result, the differential ratio of Δ γ between IDC and nGBT Δ γ IDC − nGBT is 0.36, and between IDC and adipose Δ γ IDC − adipose is 0.27, which included in the α -dispersion at τ peak 1 = 0.033 ± 0.001 s . In all specimens, the relaxation-time distribution function γ of IDC γ IDC is higher, and there is no intersection with γ of nGBT γ nGBT and adipose γ adipose . The difference in γ suggests potential variations in relaxation properties at the molecular or structural level within each breast tissue that contribute to the overall relaxation response. The average mean percentage error δ for IDC, nGBT, and adipose tissues are 5.90%, 6.33%, and 8.07%, respectively, demonstrating the model’s accuracy and reliability. This study provides novel insights into the use of relaxation-time characteristic for differentiating breast tissue types, offering potential advancements in diagnosis methods. Future research will focus on correlating EIS-GRTD finding with pathological results from the same test sites to further validate the method’s efficacy.

Invasive ductal carcinoma (IDC) in breast specimens has been detected in the quadrant breast area: (I) upper outer, (II) upper inner, (III) lower inner, and (IV) lower outer areas by electrical impedance tomography implemented with Gaussian relaxation-time distribution (EIT-GRTD). The EIT-GRTD consists of two steps which are (1) the optimum frequency f opt selection and (2) the time constant enhancement of breast imaging reconstruction. f opt is characterized by a peak in the majority measurement pair of the relaxation-time distribution function γ , which indicates the presence of IDC. γ represents the inverse of conductivity and indicates the response of breast tissues to electrical currents across varying frequencies based on the Voigt circuit model. The EIT-GRTD is quantitatively evaluated by multi-physics simulations using a hemisphere container of mimic breast, consisting of IDC and adipose tissues as normal breast tissue under one condition with known IDC in quadrant breast area II. The simulation results show that EIT-GRTD is able to detect the IDC in four layers at f opt = 30, 170 Hz. EIT-GRTD is applied in the real breast by employed six mastectomy specimens from IDC patients. The placement of the mastectomy specimens in a hemisphere container is an important factor in the success of quadrant breast area reconstruction. In order to perform the evaluation, EIT-GRTD reconstruction images are compared to the CT scan images. The experimental results demonstrate that EIS-GRTD exhibits proficiency in the detection of the IDC in quadrant breast areas while compared qualitatively to CT scan images.

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 relaxation times (DRT) with radial base function. To distinguish the relaxation time of the dermis τ _d from the other layers (stratum corneum τ _sc , the epidermis τ _e , and the fat layer τ _f ), the subtracted impedivity was calculated by distant electrode pair z ₁ , and close the electrode pair z ₂ , based on optimum electrode diameter ϕ and distance l . The numerical optimizations were implemented to optimize ϕ 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, ϕ*=1 mm and l *=1 mm, were applied to the skin model under the condition of 1) various sodium-ion concentrations c in the dermis layer, 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 γ and relaxation times τ, were used to evaluate the sodium-ion concentration extraction. Both simulation and experiment results show that the normalized distribution function of the dermis γ* _c (ln τ _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 τ _d =10 ^-2 [s]. TCD-EIS with DSM reveals that the decrease of a normalized distribution function γ* _c (ln τ _d ), correlates with the increased sodium-ion concentration c injected in the dermis layer.

Free and bound sodium in human skin models have been identified by two proposals: skin’s phantom fabrication and skin’s dielectric properties separation algorithm of bioelectrical impedance spectroscopy (spa-BIS). The spa-BIS consist of conductivity-permittivity separation, contact impedance compensation, and a correlation score algorithm based on the vessel with a bipolar electrode. The skin phantom fabrication comprises a recipe combination with temperature-controlled protocol and sodium molarity calculation. In experiments, the human skin models are created to mimic the electrical properties of skin under 1 MHz with several different sodium molarities. Based on five types of human skin models with five samples of each group, the free sodium type conductivity and concentration results R 2 = 0.9903 − following a linear trendline of concentration change in skin tissues theorems with the fRequency range from 1 kHz to 1 MHz , while the bound sodium type results R 2 = 0.9061 − . The spa-BIS compensate 7 − 16 Ω of vessel contact impedance. The dielectric properties of each type have been extracted with less than 10% of the average standard deviation, which is considered an accurate identification method of dermis dielectric properties. The algorithm successfully identifies sodium type: free sodium has a negative, and bound sodium has a positive correlation score trend. As an additional discussion, the different time-dependent effects, the different water content, and different agar content analyses have been provided in this study. As a robust analysis method, the spa-BIS has a prominent performance to replace a ²³Na-MRI in terms of free and bound sodium identification.