Measurement and image-based estimation of dielectric properties of biological tissues —past, present, and future—

Summaries of the 13 papers presenting dielectric measurements of skin and/or the tissues composing skin listed in table 1 are provided below.

Gabriel et al (1996b) measured the dielectric properties of human skin (forearm) in vivo from 10 Hz to 20 GHz. Measurements were conducted using three different coaxial probes to cover this wide frequency range. On the basis of these measurements and their review (Gabriel et al 1996a), parametric models for dry and wet skin were developed using the four-pole Cole–Cole model (Gabriel et al 1996c). Relevant differences in the dispersion characteristics between dry and wet skin were only observed below 100 MHz, which is due to the absence of α- and β-dispersions for dry skin. Moreover, this also indicates that the stratum corneum predominantly determines the measurement results for skin (Gabriel 1997).

Pickwell et al (2004) measured the THz response of human skin in vivo using THz-TDS. THz responses of the palm and/or forearm were measured for 20 volunteers. Dielectric properties of the epidermis were estimated from the obtained mean response from measurements at the forearm of 18 volunteers (24–49 years of age) and a corresponding parametric model was reported using a two-pole Debye model.

Alekseev and Ziskin (2007) measured the dielectric properties of the tissues constituting human skin in vivo from 37 to 74 GHz using open-ended waveguides. The dielectric properties of the stratum corneum and the other skin layers, i.e. the epidermis and dermis without the stratum corneum, were estimated from measurements at the palm and forearm of 12 volunteers (45–60 years of age). Parametric models of each skin layer were reported for the palm and forearm. It was found that the skin water content is the dominant factor for determining the dielectric properties of skin in the considered frequency range.

Alekseev et al (2008) measured murine skin in vivo at frequencies from 37 to 74 GHz. The effect of body hair on the measured dielectric properties was investigated using hairy and hairless mice. Their results showed that the presence of hair led to slightly (5%–14%) lower dielectric properties than those of hairless skin. However, this difference was considered marginal by the authors as the results were within the measurement uncertainty of 10%.

Karacolak et al (2009) measured rat skin in vitro from 200 MHz to 20 GHz at 38 °C for the purpose of designing an implantable antenna. Parametric models using two- and three-pole Cole–Cole models were also presented.

Chahat et al (2011) measured the complex permittivity of human skin in vivo from 10 to 60 GHz using a coaxial probe. The measurements were performed at several body parts, i.e. the palm, wrist, and forearm, for each of seven volunteers. The obtained results for the wrist and forearm were in good agreement, i.e. the observed differences were within the spread expected for this kind of measurement. However, the measurement results obtained at the palm tended to be lower than those at the wrist and forearm, which can be explained by the difference in the thickness of the stratum corneum, which has a low water content. Also, parametric models were reported for the wrist/forearm and palm.

Wilmink et al (2011) reported the optical properties, i.e. refractive index and absorption coefficient, of porcine skin in vitro from 0.13 to 1.6 THz at room temperature using THz-TDS. The presented results were compared with those measured by Pickwell et al (2004), and the discrepancies were within 15% and 40% for the diffraction index and absorption coefficients, respectively.

Sasaki et al (2014a) measured the dielectric properties of skin tissues, i.e. the epidermis and dermis, of porcine skin from 0.5 to 110 GHz at 34 °C–37 °C. Coaxial probe and free-space methods were adopted for the dielectric measurement, and parametric models using the two-pole Cole–Cole model were also reported. Their results for porcine dermis at frequencies up to 20 GHz were in good agreement with the dielectric properties for dry human skin obtained by Gabriel et al (1996c) in vivo. This observation remains interesting, because the data obtained at the surface of dry skin by Gabriel et al (1996b, 1996c) were expected to be predominantly determined by the dermis up to 20 GHz (Gabriel 1997).

Zaytsev et al (2015) investigated the dielectric properties of human skin in vivo from 0.3 to 1 THz using THz-TDS for a purpose of diagnosis application. The dielectric properties of healthy skin and dysplastic and non-dysplastic skin nevi were measured from four patients.

Wake et al (2016) reported conductivities of the porcine epidermis and dermis in vitro at 35 °C from 10 kHz to 1 MHz using a two-electrode method. The conductivities of epidermis were estimated from bulk skin comprising the epidermis and dermis. The measured conductivities of the dermis were almost constant in the considered frequency range, while those of the epidermis showed frequency-dependent characteristics. The authors found that the conductivities of both the epidermis and dermis contribute to the overall conductivity of skin, i.e. both the epidermis and dermis should be considered in numerical models.

Sasaki et al (2017) measured the dielectric properties of porcine dermis in vitro at 35 °C from 0.1 to 1 THz using THz-TDS. The obtained data showed reasonable agreement (within 8% and 25% deviations for permittivity and conductivity, respectively) with the data obtained by Sasaki et al (2014a) at 100 GHz with a different measurement methodology (see above).

Mirbeik-Sabzevari et al (2018) measured human skin in vitro at frequencies from 0.5 to 50 GHz using a coaxial probe. The measurement was conducted at room temperature of 22 °C. Normal and malignant skin were collected by surgery from 41 patients aged 34–89. Single-pole Cole–Cole models for each tissue were reported. The obtained results for normal skin showed agreement within 10% difference from those of wet skin reported by Gabriel et al (1996c). The authors also observed large variability between the patients' subgroups as compared with the samples within each patient subgroup. However, according to the authors, this was expected as the tissues were excised from different body locations for different patients.

Zhekov et al (2019) reported the dielectric properties of human hands obtained in vivo from 5 to 67 GHz using a coaxial probe. Palms and thumbs under dry and moist conditions were measured for 22 volunteers. In addition, parametric models for each part and condition were derived using a single-pole Cole–Cole model. The difference in permittivity between dry thumbs and palm was within 10%. For the conductivity, similar differences of up to approximately 10% were observed in the frequency range up to approximately 20 GHz, which increased to up to 27% difference at higher frequencies. According to the authors, these observations are a consequence of the skin structure. Moreover, the authors noted significant variation in the dielectric properties among the test persons.

Only two papers have reported dielectric measurements of skin frequencies below 500 MHz: Gabriel et al (1996b) reported measurements on the surface of intact dry and wet human skin, and Wake et al (2016) reported the results of in vitro measurements on porcine epidermis and dermis. The conductivity of the dermis obtained by Wake et al (2016) was almost constant at around 0.4 S m⁻¹, while the conductivity of the epidermis increased from 0.0036 to 0.12 S m⁻¹ with increasing frequency from 10 kHz to 1 MHz. Although the frequency trend of epidermal conductivity is different from that of dry or wet skin reported by Gabriel et al (1996b), the values for the conductivity of wet skin reported by Gabriel et al (1996c) are within the range of those for the epidermis and dermis from 10 kHz to 1 MHz reported by Wake et al (2016). Gabriel et al (1996b) measured human skin (forearm) in vivo by contacting a coaxial probe on the skin surface, and thus the measurement results may reflect the differences in dieletric properties of different skin layers such as stratum corneum, epidermis, dermis, and subcutaneous tissue layers (Lahtinen et al 1997, Gabriel 1997). However, the fact that the permittivity data reported by Gabriel et al (1996b, 1996c) for dry skin did not show any α- or β-dispersion but some dispersion became visible after moistening the skin (data for wet skin in Gabriel et al (1996b, 1996c)), strongly suggests that the data for dry skin reported by Gabriel et al (1996b, 1996c) mainly reflect the dielectric properties of the stratum corneum in the low-frequency range. Also, Schmid et al (2013) pointed out the possibility that the stratum corneum, which has extremely low conductivity (Yamamoto and Yamamoto 1976), strongly affected the data for skin reported by Gabriel (1996). Similarly, Wake et al (2016) commented that the conductivity of dry skin reported by Gabriel (1996c) is in good agreement with that of the stratum corneum at 100 kHz, and did not practically represent the values of inner layers, the stratum granulosum layer or the deeper layer of epidermis and dermis.

Figure 2 shows a comparison of the dielectric properties of skin tissues between the measurements above 100 MHz. The authors of several studies in which dielectric measurements of skin were conducted in vivo reported that the considerable variability of the measured data with the body site can be attributed to the variability in skin layer thickness. Therefore, a comparison of the data obtained in vivo from the human forearm and those obtained from the skin/dermis of animal sources is given in figure 2(a), and a comparison of the data of human skin obtained from other sites (including those from reports where no site is mentioned) or those of superfacial layers of skin (stratum corneum and epidermis) is given in figure 2(b). The plots in figure 2 are of the original data or are derived from previously reported empirical equations, while for a few cases, plots were reproduced from figures in the original reference using Engauge Digitizer ver. 12.1. Note that data measured in vitro without the tissue temperature being reported and data measured at room temperature are excluded.

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Figure 2(a) shows that although the source and measurement state were different between Gabriel et al (1996c) and Sasaki et al (2014a, 2017), both the conductivity and permittivity of human skin (forearm) measured in vivo and porcine dermis measured in vitro were in good agreement, with a difference of around 10%. The result of in vitro measurement of the dermis also agreed with the in vitro measurement result of human skin (without the stratum corneum layer) reported by Alekseev and Ziskin (2007). On the other hand, dielectric values for rat skin reported by Karacolak et al (2009) were approximately 30% lower than those reported by Gabriel et al (1996c). This difference is assumed to be acceptable because similar differences were observed between in vivo measurement results of human skin by Gabriel et al (1996c) and Chahat et al (2011).

The measurement results of human skin at several different sites shown in figure 2(b) present larger variations than the difference between the in vivo and in vitro measurements. The dielectric values of skin measured at the palm and thumb were 20%–70% lower than those obtained from porcine dermis by Sasaki et al (2014a). The dielectric properties of the palm and thumb measured in vivo were within the range of those of the epidermis and stratum corneum reported by Sasaki et al (2014a) and Alekseev and Ziskin (2007), respectively, above 40 GHz, but they tended to converge to the dielectric properties of the epidermis as the frequency decreased to 5 GHz. These observations suggest that the sensing depth for the measurement of the human palm was up to the epidermis layer and that the stratum corneum became the dominant layer at high frequencies in their measurements. At frequencies above 300 GHz, the results of in vivo measurements of the conductivity and permittivity of skin by Zaytsev et al (2015) were within 20% and 30% of those of the epidermis measured by Pickwell et al (2004), respectively. Although their target tissues were different, it is difficult to clarify the reason for the difference because Zaytsev et al (2015) did not report the body site of their in vivo measurement of human skin. In particular, at sub-millimeter-wave frequencies, variations in the thicknesses of the skin tissues are expected to strongly impact the measured dielectric properties of skin because of the shallow penetration depth.

Summaries of the 13 papers presenting dielectric measurements of adipose tissue listed in table 2 are provided below.

Gabriel et al (1996b) measured the dielectric properties of adipose tissue in vitro at body temperature using coaxial probes. Their results demonstrated a wide spread of dielectric properties between those obtained from humans and three animal origin, i.e. ovine, bovine, and porcine. They also distinguished between adipose tissue of high fat content (or low water content) and of the higher water content with blood infiltration. On the basis of these findings, two types of parametric models of fat, blood-infiltrated and non-infiltrated, were developed using a four-pole Cole–Cole model (Gabriel et al 1996c).

Lazebnik et al (2007a) measured human breast tissue in vitro between 50 MHz and 20 GHz using a coaxial probe. Tissue samples were obtained from 93 patients (17–65 years of age) by reduction surgery. Tissue temperatures during measurements were approximately from 18 to 26.6 °C. Very large variations (by a factor of 10 or larger) in dielectric properties were observed, and it was found that the dielectric properties were primarily determined by the adipose content of the tissues. Parametric models of the tissue categorized into three groups, i.e. low, middle, and high adipose contents, were also provided. In addition, the parametric models were improved to present better agreement with their measurement results in a later work (Lazebnik et al 2007c).

In a later study by Lazebnik et al (2007b), human breast tissue obtained from 196 patients (19–90 years of age) by cancer surgery were measured in vitro between 50 MHz and 20 GHz using a coaxial probe. Similarly to their previous study (Lazebnik et al 2007a), very large variations were observed between each sample, and it was found that the dielectric properties of tissues with low and high adipose contents obtained by cancer and reduction surgeries were in good agreement.

Stoneman et al (2007) measured the dielectric properties of human adipose tissue in vitro, obtained by surgical mastectomy, from 40 Hz to 100 MHz at approximately 37 °C using a coaxial probe. Tissue samples of normal and cancerous breast tissues were obtained from 34 patients in total by surgical mastectomy. A parametric model proposed by Raicu (1999) was adopted and parametrized.

Bindu and Mathew (2008) reported the dielectric properties of human breast tissue in vitro from 2.4 to 3.0 GHz, measured using a rectangular cavity resonator. Tissue samples were obtained from six patients by an excisional surgical procedure. The bound water contents of the normal adipose tissues ranged from 41% to 49%.

Gabriel et al (2009) reported the conductivities of porcine fat in vivo at approximately 37 °C from 40 Hz to 1 MHz as a supplement of their database (Gabriel et al 1996b;1996c). The dielectric measurement of the tissue was conducted using the four-electrode method. Their conductivities for fat were around twice those of the blood-infiltrated fat measured by Gabriel et al (1996c).

Ashworth et al (2009) measured the dielectric properties of human breast tissue in vitro at room temperature from 0.15 to 2 THz using THz-TDS. Tissue samples collected from 20 patients by breast conserving surgery were histologically separated into healthy adipose and fibrous tissues and breast cancer tissues. Parametric models were reported in a later work by Truong et al (2015).

Wilmink et al (2011) reported the optical properties, i.e. refractive index and absorption coefficient, of porcine adipose tissue in vitro from 0.13 to 1.6 THz at room temperature using THz-TDS. The measured results were compared with those of other groups. Up to 40% larger diffraction indexes were observed, and the absorption coefficients were two to ten times the values previously reported. The authors commented that a possible cause of the disagreement was the difference in the hydration state of the tissue in each study.

Sugitani et al (2014) reported the dielectric properties of human breast tissues (cancer, stroma, and adipose tissues) from 0.5 to 20 GHz in vitro using a coaxial probe for the purpose of microwave diagnostic application. The tissue samples were obtained from cancer surgeries of 35 patients of age 33–88 years. The dielectric measurements were conducted at temperatures of 18 °C–24.1 °C. Parametric models using a two-pole Cole–Cole model were also reported.

Martellosio et al (2015) measured the dielectric properties of human breast tissue in vitro at room temperature of 25 °C from 0.5 to 50 GHz using a coaxial probe. The normal and malignant tissues were obtained by surgery. Parametric models using a single-pole Cole–Cole model were also reported, and the results were in good agreement with those of edible fat.

Wake et al (2016) measured the conductivities of subcutaneous tissue (abdomen) of porcine in vitro at 35 °C from 10 kHz to 1 MHz using the two-electrode method. Their results were almost constant in the considered frequency range. The measured conductivity was six times of that of fat reported by Gabriel et al (1996b, 1996c). Differences in the water contents of the tissue samples measured were reported to be the most likely cause of the difference.

Martellosio et al (2017) measured the dielectric properties of human breast tissue (obtained by cancer surgery) in vitro at 19 °C–22 °C from 0.5 to 50 GHz using a coaxial sensor. Large variations in the dielectric properties of normal breast tissue were reported, which were due to the large variation in tissue density (adipose content). Single-pole Cole–Cole models for different fat contents in three groups, i.e. low (80%–100% adipose contents), medium (20%–80% adipose contents), and high (0%–20% adipose contents) densities, were reported. The effects of the patient age, the sample temperature, and the time between excision and measurements were also discussed (overview were made in section 5).

Sasaki et al (2017) measured the dielectric properties of porcine subcutaneous tissue in vitro at 35 °C from 1 GHz to 1 THz using a coaxial probe and THz-TDS. The obtained results were compared with those of fat reported by Gabriel (1996) for frequencies up to 20 GHz. Their permittivity and conductivity values were up to three and seven times higher than those reported by Gabriel (1996) at frequencies up to 20 GHz, and differences in the water contents of the tissue samples were assumed as the cause of the large difference.

The large spread of data can be attributed to the variation in the composition of adipose tissue as shown by several authors (Lazebnik et al 2007a, Martellosio et al 2017). Figure 3 shows examples of the conductivities of adipose tissues up to (left) and above (right) 100 MHz. The plots in the figure 3 are from the original data or derived from reported empirical equations, while for a few cases, plots were reproduced from figures in the original reference using Engauge Digitizer ver. 12.1.

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At frequencies below 100 MHz, the spread of the conductivity values reported for adipose tissues is within a factor of 30 (maximum to minimum ratio). At frequencies from 100 MHz to 50 GHz, the spreads of the conductivity and permittivity values reported for adipose tissues are within factors of around 30 and 10, respectively. Note that several data were obtained using tissues at temperatures lower than body temperature (approximately 37 °C); however, the observed range of the spread cannot be explained only by temperature differences, as reported in previous investigations (see appendix B). The dielectric properties of fat (not infiltrated) reported by Gabriel et al (1996c) are in good agreement with those of breast tissue with high adipose contents (81%–100%) as reported by Lazebnik et al (2007a), and these values for permittivity and conductivity are considered as lower limits for adipose tissue. The values for tissue with low adipose contents (0%–20%) reported by Martellosio et al (2017) are assumed as the upper limit of the dielectric properties of adipose tissue up to 50 GHz. These observations demonstrated that adipose or water content is dominant factor determining large variations in the dielectric properties of adipose tissues. At frequencies above 50 GHz, the spread of values between the four studies were within factors of around 10 and 3 for conductivity and permittivity, respectively.

Summaries of the 11 papers presenting dielectric measurements of brain tissues listed in table 3 are provided below.

Gabriel et al (1996c) reported parametric models for ovine ⁶ grey and white matter in vitro at 37 °C based on their measurement from 10 Hz to 20 GHz (Gabriel et al 1996b). Authors demonstrated consistency between the frequency trends of the dielectric properties in their results and in previous studies reviewed by Gabriel et al (1996a).

Baumann et al (1997) measured the conductivity of human cerebrospinal fluid in vitro from 10 Hz to 10 kHz at 25 and 37 °C, using a four-electrode method. The measured samples were obtained from seven patients. Their results showed good agreement with those obtained from rabbit at 1 kHz.

Bao et al (1997) measured the dielectric properties of rat white and grey matter in vitro from 45 MHz to 26.5 GHz at 25 °C (or 24 °C) and 37 °C using a coaxial probe. Parametric models based on their measurement results were also reported.

Latikka et al (2001) measured the resistivity of human brain tissues, i.e. white matter, grey matter, and cerebrospinal fluid, in vivo at 50 kHz using a monopolar needle electrode, i.e. equipment usually used for pain treatment. The numbers of patients were five, eight, and two for white matter, grey matter, and cerebrospinal fluid, respectively, and the patients' age ranged from 32 to 87 years. They found that the mean values of conductivity (the inverse of resistivity) of grey matter was approximately 10% larger than that of white matter. In addition, they observed decreasing conductivity for grey matter during the operation.

Tofighi and Daryoush (2002) measured rat white and grey matter in vitro from 15 to 50 GHz at 27 °C using a microstrip line test fixture. Parametric models of tissues using the single-pole Cole–Cole model were also reported.

Schmid et al (2003a) measured the postmortem changes of the dielectric properties of grey matter of porcine brain at 0.9 and 1.8 GHz using a coaxial probe. The number of considered animals was 10, and both in vivo and in vitro measurements of the tissues were conducted. The results demonstrated that in vitro measurements of dielectric properties of brain tissue underestimate in vivo dielectric properties (detail of postmortem effect was summarized in 5.1).

Schmid et al (2003b) reported the dielectric properties of human grey matter in vitro from 0.8 to 2.45 GHz at room temperature (18 °C–25 °C) using a coaxial probe. In total, 20 brains excised less than 10 h postmortem from the bodies of persons who died at ages between 47.5 and 87.5 years were investigated. The dielectric properties of human grey matter showed higher values compared to those reported by Gabriel et al (1996b) for human (24–48 h postmortem) and ovine (2 h postmortem) brain samples in vitro at body temperature. The authors also commented that the discrepancy from the values reported by Gabriel et al (1996b) for around 1 GHz was approximately 10%–30% when the technique used to adjust the tissue temperature from their former work (Schmid et al 2003a) using porcine brain was adopted.

Peyman et al (2007) measured porcine cerebrospinal tissues, i.e. arachnoid, grey matter, white matter, dura mater, and dura spinal cord, in vivo from 50 MHz to 20 GHz using a coaxial probe. In addition, the dielectric properties of these five tissues and cerebrospinal fluid were measured in vitro at 37 °C and their aging effect was also measured and discussed. Details of the comparison between in vivo and in vitro measurements and the aging effect are given in sections 5.1 and 5.3, respectively. The dielectric properties of porcine grey and white matter obtained in vivo showed good agreement with those obtained from ovine in vitro by Gabriel et al (1996b, 1996c), although they were somewhat lower than those reported by Bao et al (1997) and Schmid et al (2003a, 2003b). The authors commented that the differences in the tissue preparation process between the different studies were a possible cause of the discrepancy.

Schmid et al (2007) measured the dielectric properties of human pineal gland in vitro at frequencies ranging from 0.4 to 6 GHz at 18 °C using a coaxial probe. Tissue samples were obtained from 20 patients (26–91 years of age). The obtained data were used for computational simulations of electromagnetic field absorption.

Gabriel et al (2009) measured the conductivities of porcine cerebrospinal fluid in vitro at approximately 37 °C from 40 Hz to 1 MHz using a four-electrode method to supplement their database (Gabriel et al 1996b;1996c).

Mohammed et al (2016) measured the dielectric properties of canine brain tissues, i.e. white matter, grey matter, and cerebrospinal fluid, in vitro at room temperature from 0.3 to 3 GHz using a coaxial probe. The aging effect on the dielectric properties was also investigated and discussed (details are shown in 5.3).

The reported dielectric properties for grey and white matter are compared. Note that data are scarce below 45 MHz and above 50 GHz. Excluding the values reported by Gabriel et al (1996b, 1996c, 2009), the only values for brain tissue conductivity at 50 kHz were reported by Latikka et al (2001). The conductivity values reported by Latikka et al (2001) were 2.2 and 3.3 times those reported by Gabriel et al (1996c) for grey and white matter, respectively. Although the conditions of dielectric measurement, e.g. tissue source, state, and temperature, were different between the two studies, Gabriel et al (1996b) commented that the uncertainty in their measurement may be up to a factor of 2 or 3 due to the effect of electrode polarization below 100 Hz. On the other hand, no special care was taken to supress the electrode poralization for the measurement equipment used by Latikka et al (2001). Hence, the observed differences were clearly in the range of the measurement uncertainty, and the difference in the treatments of electrode poralization is assumed as the main cause.

Figures 4(a) and (b) compare dielectric properties of grey and white matter, respectively, in the frequency range from 10 MHz to 100 GHz. The plots in the figure 4 are from the original data or derived from reported empirical equations, while for a few cases, plots were reproduced from figures in the original reference using Engauge Digitizer ver. 12.1. Most of the data shown in the figures were obtained by in vitro measurements (except those for grey matter reported by Schmid et al (2003a) and Peyman et al (2007)). On the basis of the data reported by Gabriel et al (1996c), which are the most used data, the variabilities of the data were within approximately 30% for both conductivity and permittivity, except for the data reported by Bao et al (1997) and Mohammed et al (2016). These variabilities are larger than the difference between data from in vivo measurements and those reported by Gabriel et al (1996c). One of the possible reasons for the discrepancies between the data of Gabriel et al (1996c) and Mohammed et al (2016) is the different tissue temperatures. Better agreement with the data of Gabriel et al (1996c) can be observed upon adjusting the grey matter conductivity data reported by Mohammed et al (2016) for the temperature using the temperature coefficients for porcine brain obtained by Schmid et al (2003a) (see appendix B). Comparison of the data for grey matter obtained by Gabriel et al (1996c) at 37 °C and the corresponding temperature adjusted data reported by Schmid et al (2003b) revealed that the latter shows 10%–25% higher values. This discrepancy is most likely due to the fact that in Schmid et al (2003b), the measurement probe was placed on the grey matter while keeping the arachnoid intact, whereas the probe was placed on the grey matter after removing the arachnoid in Gabriel et al (1996c).

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Ghanbarzadeh-Daghian et al (2020) measured blood samples from 12 pediatric patients with different types of hematologic cancers at 120 Hz at room temperature using an LCR meter. The relative permittivity ranged from 10.3 × 10⁶ to 16.4 × 10⁶ for patients with cancer and from 5.1 × 10⁶ to 8.8 × 10⁶ for healthy donors, indicating that samples from patients with cancer had approximately two times higher measured relative permittivities than those of healthy individuals.

In Ibrahim et al (2008), the dielectric properties of DNA from blood samples of patients with liver cancer were studied to examine the potential diagnostic ability of such measurements. Three groups were studied: (i) patients with hepatocellular carcinoma (HCC); (ii) patients with chronic hepatitis C (HCV) and (iii) healthy patients as a control. Dielectric measurements were conducted on DNA diluted in sterilized water at 20 °C from 20 Hz to 100 kHz using a precision component analyzer with a conductivity cell. The results indicate that the conductivity of the DNA suspension from HCC patients (and those with chronic HCV) was significantly higher than that of healthy patients. Also, the relative permittivity of the DNA suspension from patients with HCC was significantly higher than that of both patients with HCV and the normal control group below about 100 Hz.

Aiming to investigate the potential for early diagnosis of cancer and monitoring of cancer treatment, Batyuk and Kizilova (2018) obtained the dielectric properties of suspensions of red blood cells (RBCs) and RBC ghosts from patients with breast and lung cancers at 9.2 GHz in the temperature range of 1 °C–46 °C by resonance-based dielectrometry measurement. For the RBCs from cancer patients, the relative permittivity varied from approximately 40 to 60 over the temperature range, whereas for the RBC ghosts from cancer patients, the change was from approximately 40 to 70 over the same range. For the conductivity, a similar trend was observed for both RBCs and RBC ghosts. The relative permittivity was found to be higher in blood from cancer donors than in blood from healthy patients.

O'Rourke et al (2007) measured the dielectric properties of human normal, malignant, and cirrhotic liver tissue in vivo and in vitro from 0.5 to 20 GHz using a coaxial probe. In total, four livers in vitro and five livers in vivo were considered, where the temperature of the in vitro samples varied between 20 °C and 24 °C. The malignant liver tissue category consisted of one primary HCC tumor, five metastatic tumors, one pancreatic tumor, and three colorectal tumors. They reported that there was almost no statistically significant difference between in vivo normal and malignant tissues but a statistically significant difference between in vitro normal and malignant tissues at both 915 MHz and 2.45 GHz. The Cole–Cole parameters for each tissue type were also presented for their in vitro measurements.

Wang et al (2014) conducted in vitro measurements of liver tissues (normal, HCC, hepatic fibrosis, and liver hemangioma) from 10 Hz to 10 MHz using a four-electrode method. It was observed that liver with hemangioma had higher conductivity than the other tissues. Below 1 MHz, the conductivity of hepatic fibrosis tissues was the largest, followed by tissues from normal liver and HCC. The differences among the three tissues gradually decreased with increasing frequency. The changes in permittivity of the four types of liver tissues were similar, with the permittivity rapidly decreasing below 1 kHz. The measured data were also fitted to a two-pole Cole–Cole model, and it was found that the parameters of dispersion in the kHz frequency range can be used to distinguish between normal, HCC, hepatic fibrosis, and hemangioma tissues.

Peyman et al (2015) investigated the variation of dielectric properties due to pathological changes in human liver. Six patients were considered with the following pathological conditions: hemangioma, hepatocellular carcinoma, metastasis of adenocarcinoma of stomach, and colon and a tumour contained in intracellular space. Dielectric measurements were conducted at 25 ± 0.5 °C from 100 MHz to 5 GHz using a coaxial probe and Cole–Cole parameters were reported for each tumour type. For each patient, higher dielectric properties for tumour tissues were observed compared to normal tissue and this was attributed to the fact that tumour cells allow more for the accumulation of higher sodium and water contents than normal cells.

In Halter et al (2009), a four-electrode probe was used to measure the conductivity and permittivity of 50 human prostates in vitro at 20 °C from 0.1 to 100 kHz. It was found that the conductivity of cancer tissues was below those of non-cancerous glandular and stromal tissues across all frequency points above 1 kHz. While, no significant differences were found between the conductivities of cancerous and benign tissues. The permittivity of cancer tissues, on the other hand, was significantly higher than that of all non-malignant tissues at 100 kHz.

Yu et al (2020) reported the dielectric properties of in vitro normal and metastatic intrathoracic lymph nodes. The measured data consisted of dielectric measurements on 41 metastatic lymph nodes and 178 non-metastatic lung thoracic lymph nodes obtained from 74 patients. Measurements were conducted on samples at 24 ± 2.4 °C from 50 MHz to 4 GHz using a coaxial probe. The results showed that the permittivity and conductivity of metastatic thoracic lymph nodes were higher than those of non-metastatic thoracic lymph nodes. The data were also fitted to a two-pole Cole–Cole model.

In Ranade et al (2016), the dielectric properties of saliva samples from oral cancer patients were measured using time-domain reflectometry (10 MHz–20 GHz). The malignant samples had higher average values than the control group for both relaxation time and conductivity. No significant difference was observed for permittivity between the malignant and control groups, while statistically significant difference was observed between the average conductivity of the malignant and control groups. Within the malignant group, both average conductivity and permittivity increased from grade I to grade II and the relaxation time decreased, whereas the trends in all three measured parameters were inconsistent across stages I to IV.

Mayrovitz et al (2018) examined the potential for permittivity to be used to differentiate between skin cancer lesions and non-cancerous skin. In vivo measurements on basal cell carcinoma (BCC) and non-cancerous lesions were performed using a coaxial probe (at a room temperature of 21.6 ± 1.2 °C). The relative permittivity was found to be 22.4 ± 16.2 for BCC lesions and 14.5 ± 9.0 for non-cancerous lesions. Much higher values of 38.1 ± 15.2 and 29.1 ± 9.0 were found for the contralateral (unaffected) skin in the BCC and non-cancerous groups, respectively. However, the permittivity values were not statistically different between BCC lesions and non-cancerous lesions.

In Mirbeik-Sabzevari et al (2018), skin tissue samples (BCC, squamous cell carcinoma (SCC), and normal) were measured at 22 °C from 0.5 to 50 GHz using a coaxial probe. Over the entire frequency band, malignant BCC samples had statistically significantly higher permittivity and conductivity than normal skin tissue. For the malignant SCC samples, statistically significant differences relative to the normal samples were also found across the frequency range, with a higher real part but lower imaginary part over the whole band. Maximum differences of 15 and 111% were found between the dielectric properties of normal and BCC samples and between those of normal and SCC samples, respectively.

In Ibrahim and Ghannam (2012), the dielectric properties of DNA suspensions from human urine samples were examined in the context of investigating such dielectric properties as a potential marker of bladder malignancy in cancer screening. Urine was collected from (i) patients with bladder diseases, (ii) patients with non-malignant (benign) urothelial diseases, and (iii) a control group. Using a loss factor meter, data were collected from 0.1 to 10 MHz (samples at 20 ± 0.1 °C). The relative permittivity was found to decrease from approximately 2400 at 0.1 MHz to approximately 500 at 10 MHz, while the conductivity increased from close to zero to approximately 0.12 S m⁻¹ over the same range. The dielectric properties obtained from the DNA suspension of the malignant group were found to be significantly different from those of both the benign and control groups, with the DNA suspension of the malignant group having higher values. While, the dielectric properties were not found to show a significant positive correlation with the grade of the cancer.

Cheng and Fu (2018b) measured the dielectric properties of normal thyroid samples and papillary thyroid cancer samples in the frequency range of 0.5 to 8 GHz using a coaxial probe. All 236 freshly excised thyroid tissues (138 normal and 98 malignant) from 48 patients were measured within 2 h from excision. Post-excision specimen desiccation was minimized by placing specimens in heated, sealed, and insulated containers for transportation to the measurement area. A pathological examination was also conducted to confirm the histological type of each specimen. They found a statistically significant difference between the two tissue types. The measured data for the mean effective dielectric permittivity varied from 4.03 ± 1.95 to 17.95 ± 1.65 and from 69.78 ± 2.73 to 57.36 ± 1.80 (across the frequency range) for the normal and cancerous tissues, respectively. The obtained mean effective conductivity varied from 0.84 ± 0.20 to 1.87 ± 0.10 S m⁻¹ and from 1.90 ± 0.50 to 9.75 ± 0.94 S m⁻¹ for the normal and cancerous tissues, respectively.

In Gavazzi et al (2018), the dielectric properties of normal, benign, and malignant thyroid tissues obtained from surgery were measured from 200 MHz to 10 GHz using a coaxial probe. Twenty-three excised tissue samples were obtained from 14 patients. Specimens were classified into five groups according to a histological examination, mainly normal, struma (nodular goiter), thyroiditis, adenoma, and cancer, and the data showed that the relative permittivity of the normal thyroid tissue was on average 10% lower than that of cancer tissue and 8% lower than that of goiter tissue over the entire frequency range. The percentage difference in conductivity between normal and malignant tissues varied from 21% to 8% and the percentage difference between normal and goiter tissues varied from 14% to 7% up to 2.45 GHz. However, no statistical difference in the conductivity was observed among the different tissue groups at higher frequencies, with no clear difference between benign and malignant tissues.

In Huang et al (2021) the differences in the dielectric properties of in vitro normal thyroid tissue and benign and malignant thyroid nodules (nodular goiter, follicular adenoma, papillary carcinoma, and follicular carcinoma) were reported. The dielectric properties were measured using a coaxial probe from 1 to 4000 MHz and tissue samples were obtained from 155 patients. Measured data showed that dielectric properties can be correlated to the degree of malignancy, with the 20–70 MHz frequency band giving the most statistically significant difference between the different tissue types. The measured data was also fitted to a two-pole Cole–Cole model.

Gabriel et al (1996b) presented the dielectric properties of human tongue in vivo from 2 MHz to 20 GHz, and compared them with their data measured in vitro for human, ovine, and porcine subjects. They demonstrated that the difference tends to increase with decreasing frequency below 100 MHz, although no significant differences were observed at higher frequencies.

Haemmerich et al (2002) investigated the postmortem effects on the resistivity of swine liver in vivo and in vitro from 10 Hz to 1 MHz. They observed an increase in resistivity (decrease in conductivity) of up to approximately 60% in 10 min after the liver blood supply had occluded (ischemia). Then the change in the resistivity of the liver was measured up to 12 h after excision and compared with the data obtained in vivo. They observed an increase in resistivity of 30%–80% compared with the data obtained in vivo for up to 2 h; the variation tended to exceed 50% below 1 kHz. Authors commented that although the decrease in tissue temperature from 38 °C to around 22 °C was one of the causes of the increase, the ischemia also increased the resistivity. After 2 h, a decrease in the resistivity was observed, which was assumed to be due to cell membrane breakdown of the tissue. The values of resistivity 12 h after from excitation were slightly higher than those obtained in vivo, and the differences were around 10%–20%, thus comparable to the effect of temperature change from 38 °C to 22 °C, as estimated by the authors.

Zurbuchen et al (2010) compared the conductivity of porcine liver obtained by in vivo and in vitro measurements at 470 kHz. They found that the conductivity at 37 °C measured in vivo was approximately 34% higher than that in vitro.

Wang et al (2015) investigated the postmortem effect of human liver in vitro obtained from 20 patients (49 ± 12 years of age) at frequencies from 10 Hz to 100 MHz. Tissues were maintained at 37 °C with humidity of 90% after surgery and the postmortem effect was investigated from 15 min to 24 h after excision. No postmortem change in permittivity was observed, but a significant change in conductivity was observed from 15 min to 24 h after excision at frequencies below 1 MHz. The conductivity tended to decrease up to 1 h after excision, and then increased up to 24 h after excision. The conductivities at 500 Hz and 2 MHz after an excision time of 24 h were 130 and 50% higher than those measured 15 min after excision, respectively. The authors commented that because of the dispersion characteristics, the postmortem effect on the dielectric properties was less sensitive above 1 MHz than at lower frequencies.

Schmid et al (2003a) reported postmortem changes in the dielectric properties of porcine brain grey matter in the frequency range of 800–1900 MHz. The number of subjects was 10 and postmortem changes were observed up to 60 min after sacrificing the animals. The postmortem effect was observed with a tissue temperature of 38 °C by correcting the measured dielectric properties using their temperature dependence based on temperature coefficients obtained by separate in vitro measurements of porcine brain. At frequencies of 0.9 and 1.8 GHz, decreases in permittivity and conductivity of 4% and 8%–12%, respectively, were observed at a postmortem time of 60 min. The obtained postmortem changes were less than twice the maximum combined standard uncertainty of the measurement.

Peyman et al (2007) compared the dielectric properties of porcine brain tissues obtained by in vivo and in vitro measurements from 50 MHz to 20 GHz. The measurements were conducted with an average tissue temperature of approximately 37 °C. For grey matter, little difference in the dielectric properties was observed between the in vivo and in vitro measurements, with the difference within the combined uncertainty of the measurements in the measured frequency range. On the other hand, the differences were within twice the combined uncertainty for white matter; the maximum combined uncertainties were reported to be below 6% and 8% for permittivity and conductivity, respectively, in the measured frequency range. Authors noted that it is difficult to identify the systematic cause of the differences from the comparison between dielectric properties obtained by in vivo and in vitro measurements. They also commented that it is essential to avoid drying of tissue samples and that differences in the dielectric properties may not be observed between in vivo and in vitro measurements at microwave frequencies.

Lazebnik et al (2007a, 2007b) investigated postmortem changes in the dielectric properties of human breast tissues collected by reduction and cancer surgeries from 50 MHz to 20 GHz. The dielectric properties measured up to 50 min and 250–300 min after excision were compared for each category of breast tissue. They observed a statistically significant decrease in the dielectric properties over time after the excision of tissues with high adipose content collected from reduction surgery, but desiccation was considered as the cause of the change. Similarly, Martellosio et al (2017) found no significant differences between those with postmortem times below and more than 90 min for both tumourous and normal human breast tissues in the frequency range from 0.5 to 50 GHz.

O'Rourke et al (2007) compared the dielectric properties of human liver tissues measured in vivo and in vitro at 915 MHz and 2.45 GHz collected from five patients who underwent hepatic resection. The in vitro measurements were conducted approximately 30 min after excision and at tissue temperatures of 20 °C–24 °C. Measured values obtained in vitro showed a decrease in dielectric properties of up to 30% compared with those measured in vivo.

Farrugia et al (2016) compared the dielectric properties of rat liver obtained by in vivo and in vitro measurements from 500 MHz to 40 GHz. Both in vivo and in vitro measurements were conducted at a tissue temperature of around 37 °C. They reported slight changes in the dielectric properties after excision, which were comparable to or smaller than the experimental uncertainty. From the obtained results, they concluded that measurements using excised tissues accurately simulate those of living tissues in the considered frequency range, provided that the tissues are kept well hydrated and at body temperature.

Pollacco et al (2018) compared the dielectric properties of rat muscle and fat measured in vivo and in vitro from 0.5 to 50 GHz. The in vitro measurements were conducted at a tissue temperature of 25 °C. A slight decrease in the dielectric properties from those measured in vivo was observed for the in vitro measurements, and the difference was comparable to the combined uncertainty in the measurements. They also investigated the effect of dehydration on the dielectric properties of the tissue measured in vivo, and a large decrease in the dielectric properties was observed with the dehydration of both muscle and fat tissues. They concluded that excised tissues reliably represent the dielectric parameters of in vivo tissues under certain controlled hydration conditions.

Sabouni et al (2020) compared the dielectric properties of murine colonic tumours obtained by in vivo and in vitro measurements. The measurements were conducted at frequencies from 1 to 5 GHz, and the tissue temperatures ranged from 27 °C to 33 °C and from 20 °C to 25 °C for the in vivo and in vitro measurements, respectively. The dielectric properties obtained in vivo were higher than those obtained in vitro, which was due to the changes in the tissue temperature and water content.

Potential differences between the dielectric properties of human and animal tissues have also been a topic of interest to researchers. However, there are a limited number of studies in which measurements of both human and animal tissues were carried out. Gabriel et al (1996b) compared the dielectric properties of tongue and adipose tissues between humans and other mammals at frequencies from 10 Hz to 20 GHz. In addition, they performed comparisons between animal species for cartilage and cortical bone. Their results demonstrated that the difference between individuals of each species may exceed the variation between species.

Intercomparisons of literature values made in different studies were summarized in section 3 (e.g. figures 2–4), and systematic differences in tissue conditions, such as heterogeneity, temperature, and water contents, were often suggested as the cause of the observed discrepancies, and no indication of a systematic difference between different species according to the data summarized in the previous sections.

Differences in skin permittivity by gender and race were discussed by Mayrovitz et al (2010, 2012, 2015, 2016), who performed in vivo measurement of human skin at 300 MHz. They observed a difference of more than 20% in permittivity with respect to gender for several body parts. A cause of the difference in permittivity was specified as the gender difference in skin thickness, implying that the derived permittivity was affected by adipose tissue below the skin that owing to the sensing depth of the coaxial probe. Regarding race dependence, values of permittivity measured in vivo from skins of 100 volunteers of five different races (10 male and 10 female volunteers for each race) were compared, and a maximum difference of around 20% was observed among the races. However, their reported data showed that the race difference was smaller than the gender difference, which was expected from the greater gender difference than race difference in skin thicknesses. Moreover, the differences were comparable to the standard deviations of the volunteers for each race and gender.

Schmid and Überbacher (2005) investigated the age dependence of dielectric properties for bovine white and grey matter from 0.4 to 18 GHz. The dielectric properties of adult (16–24 months) and young (4–6 months) animals were compared, and decreases in the dielectric properties with age were found for white matter but not for grey matter. The authors explained this by suggesting that aging may change the water content of white matter tissue through a physiological process. Similar observations were made by Peyman et al (2007) and Mohammed et al (2016), who investigated the effect of aging for porcine tissues at frequencies from 50 MHz to 20 GHz and for canine tissues at frequencies from 0.3 to 3 GHz, respectively.

Peyman et al (2007, 2009) reported decreasing dielectric properties with aging for spinal cord and dura from a comparison of porcine tissues aged around 35, 100, and 600 d with masses of 10, 50, and 250 kg, respectively. Similarly to white matter, the effect of aging was explained by the increase in myelination and the decrease in water content. For dura, the aging effect was explained by a decrease in the influence of the surrounding cerebrospinal fluid on the measured dielectric properties due to the increasing dura thickness with age.

In addition to examining white and grey matter, Mohammed et al (2016) compared cerebrospinal fluid at room temperature collected from dogs with ages of 20–81 months, and no significant variation in the dielectric properties with age was observed.

Peyman et al (2009) reported decreasing dielectric properties with age for several bone tissues, i.e. cortical bone, skull, and bone marrow. For bone marrow, the shift of contents from red marrow to yellow marrow with age was considered as the cause of the aging effect. For cortical bone and skull, the reduction in water content and the increase in calcification with age are the cause of the aging effect on the dielectric properties. A similar aging effect was observed for a canine skull by Mohammed et al (2016).

The aging effect on the dielectric properties of the cortical lens was reported by Schmid and Überbacher (2005), and the observed differences were explained as a consequence of the dynamic process in lens development with age. On the other hand, investigations for the cornea and vitreous humor did not show significant age effects on the dielectric properties of the investigated mammalian eye tissues (Schmid and Überbacher 2005, Peyman et al 2009).

Aging effect on the dielectric properties of skin were investigated by Peyman et al (2009) and Mayrovitz et al (2017). Mayrovitz et al (2017) investigated the aging effect on the permittivity of human skin measured in vivo at 300 MHz using several coaxial probes with different sensing depths from 0.5 to 5 mm. Significantly higher values for permittivity (around 20%) were reported for the age group of 62–92 years than for a group of younger individuals (below 56 years of age) when a coaxial probe with a sensing depth of 0.5 mm was used. Considering the fact that no age dependence was observed when the sensing depth was larger than 1.5 mm, the authors stated that the change in skin water from a bound state to a more mobile state for the elder group is the cause of the aging effect on the dielectric properties of skin.

Several studies investigated the aging effect on the dielectric properties of adipose tissues. Peyman et al (2009) focused on porcine fat, and Lazebnik et al (2007a;2007b) and Martellosio et al (2017) focused on normal human breast tissues collected by reduction or cancer surgeries. Only Martellosio et al (2017) reported an aging effect on the dielectric properties: a significant difference was found between the groups with ages below 40 years and above 60 years for the tissues with a high adipose content of above 80%, i.e. tissues with low dielectric properties. However, the effect of age was much smaller than the variation of the dielectric properties with the adipose content observed for normal adipose tissues (see section 3.2).

Peyman et al (2009) also investigated the age dependence of the dielectric properties for intervertebral disc, periosteum, and tongue. No significant effect of age was observed for tongue but decreasing dielectric properties with the age of tissues were observed for intervertebral disc and periosteum, and the decrease in the water content with age was given as an explanation for the age effect.

Lazebnik et al (2007b) discussed the aging effect on the dielectric properties for malignant human breast tissue measured in vitro at 5, 10, and 15 GHz, and no statistical significance was found for the aging effect on the dielectric properties.

A 3D brain mapping that obtained dielectric properties from a standard MRI scan in a few minutes was reported by Voigt et al (2011). Data acquired from six healthy male volunteers were used to validate the dielectric properties of brain tissues at 64 MHz. A large variation was observed in the values obtained for grey matter, white matter, and cerebrospinal fluid (conductivities of 0.69 ± 0.14, 0.39 ± 0.15, and 1.75 ± 0.34 S m⁻¹ and relative permittivities of 103 ± 69, 72 ± 64, and 104 ± 21, respectively), although consistency with the results of simulation studies was obtained from many perspectives.

In another study by van Lier et al (2012), the propagating ${B}_{1}^{+}$ phase was used to measure the electrical properties of human head tissues at 298 MHz. By using the homogenous Helmholtz wave equation, a good estimation of tissue conductivity was possible, and results were confirmed using electromagnetic simulation studies. The measured conductivities of grey matter, white matter, and cerebrospinal fluid were reported to be 0.87 ± 0.21, 0.63 ± 0.27, and 1.93 ± 0.2 S m⁻¹, respectively.

Kim et al (2014) reported that the simultaneous acquisition of electrical conductivity and magnetic susceptibility was possible through a 3D multiecho gradient-echo sequence. Results from phantom and brain imaging with 3 T MRI at 128 MHz demonstrated the feasibility of this approach.

In another clinical application, the electrical conductivity of 90 subjects was measured at 128 MHz for breast cancer diagnosis by Shin et al (2015). The results showed remarkable differences in the measured electrical conductivities of parenchymal tissue (0.43 S m⁻¹) and fat (0.07 S m⁻¹) compared with those in benign (0.56 S m⁻¹) and malignant (0.89 S m⁻¹) regions, which demonstrate efficient usage for breast cancer diagnosis.

Lee et al (2016) developed a multi-receiver coil approach to reconstruct conductivity using MR imaging. The results demonstrated that their method can reduce the variation in conductivity (<15%) and suppress artifacts. The estimated conductivity values were 0.40 ± 0.13 and 2.16 ± 0.32 S m⁻¹ for grey/white matter and cerebrospinal fluid, respectively.

Gho et al (2016) extended the method proposed by Kim et al (2014) by reducing the required time and improve the sensitivity to motion artefacts. In vivo measurements were conducted for of three healthy adult volunteers. The reported conductivities of grey matter, white matter, and cerebrospinal fluid were 0.68 ± 0.06, 0.36 ± 0.05, and 2.20 ± 0.13 S m⁻¹, respectively, at 128 MHz.

Electrical impedance tomography has been known since the work of Henderson and Webster (1978). It was also referred to as applied potential tomography (APT) in early studies (Brown et al 1985). Although the use of the homogenous Helmholtz equation is common for EPT, a method that combines Maxwell's integral equation and high-permittivity materials to improve the estimation quality was proposed by Schmidt and Webb (2016).

Dabek et al (2016) adopted another method based on EIT with electroencephalography and it was used to estimate the electrical conductivity of head tissues of nine subjects at frequencies from 2 to 127 Hz. Data measurements using a 64- electrode electroencephalography layout with consideration of background measurements were performed to estimate the conductivity of the scalp, brain, and skull. The results demonstrated a large inter-subject variability of conductivity from 11 to 127 Hz (skull: 6.7 ± 6.2%, scalp and brain: 1.6 ± 2.0%).

A conductivity tensor is usually used to demonstrate the anisotropic electrical properties of tissues. This explains why conductivity tensor imaging (CTI) is another common name used for MREIT. Diffuse tensor magnetic resonance electrical impedance tomography (DT-MREIT) exhibits values that highly match those measured using invasive methods (Jeong et al 2017). This method enables the direction of water mobility and the ion concentration to be acquired and images of anisotropic tensor conductivity to be generated.

Katoch et al (2019) demonstrated the results of using a 9.4/3 T MRI scanner for electrodeless CTI of a phantom and the human brain of 5 subjects. The human subjects were imaged with 3 T MRI at 128 MHz and the results demonstrated significant inter-subject variabilities. CTI method might be of clinical use as it can be used with a clinical MRI scanner without additional hardware. The reconstructed conductivities were in the ranges of 0.2–0.3, 0.08–0.27, and 1.55–1.82 S m⁻¹ for grey matter, white matter, and cerebrospinal fluid, respectively. The anisotropy ratios of grey matter and white matter were 1.12–1.19 (mean = 1.16) and 1.96–3.25 (mean = 2.43), respectively.

Gavazzi et al (2020a) developed a method named PLANET for the reconstruction of transceiver phase maps, which was validated as a potential method for electrical conductivity mapping using a phantom and volunteer subjects. This method demonstrated efficiency in handling the partial volume effect, and conductivity values of whole brains were reported.

Sun et al (2020) utilized signal processing techniques such as total variation and wavelet regularization which was used to enhance the accuracy of conductivity maps of brain tissues at 128 MHz. The results demonstrated the elimination of the noise effect in conductivity maps, and conductivity values of 0.69 ± 0.09, 0.43 ± 0.05, and 1.82 ± 0.35 S m⁻¹ were obtained for grey matter, white matter, and cerebrospinal fluid, respectively.

Marino et al (2021) calculated CTI maps by combining high frequency conductivity derived from water maps and multiple b-value DTI from the brain data of five subjects. The computed conductivity tensor demonstrated values of 0.55 ± 0.01, 0.3 ± 0.01, and 2.15 ± 0.02 S m⁻¹ for grey matter, white matter, and cerebrospinal fluid, respectively, at 128 MHz. The coefficient of variation was computed from the isotropic conductivity distribution and showed large inter-subject variability even with a small number of subjects. The authors recommended not to use these values as references for further studies.

Lee et al (2021) developed a method based on a two-compartment model to convert the high-frequency conductivity into the extracellular medium conductivity. Results from three subjects and a phantom demonstrated that the proposed method could reconstruct the extracellular electrical properties from the high-frequency conductivity using standard MRI scans. The mean conductivities of grey matter, white matter, and cerebrospinal fluid of the three subjects at 5 MHz were around 0.5–0.6, 0.4, and 1.5 S m⁻¹, and the relative standard deviations from the mean were in the range of 49%–59%, 38%–48%, and 42%–57%, respectively.

Jahng et al (2021) developed a multi-compartment model with the B1 mapping technique to reconstruct the conductivity tensor in phantom, animal, and human studies. A single healthy female subject was used in this study, and the results demonstrated that the proposed model has the potential to estimate the conductivity tensor without external current injection. The conductivities of grey matter, white matter, and cerebrospinal fluid were reported to be 0.59 ± 0.09, 0.42 ± 0.05, and 1.59 ± 0.44 S m⁻¹ at 128 MHz and 0.52 ± 0.08, 0.27 ± 0.05, and 1.56 ± 0.46 S m⁻¹ below 1 kHz, respectively.

Learning-based methods have demonstrated a significant improvement in several data processing/signal analysis applications.

Mandija et al (2019) made it possible to estimate the dielectric properties of human head tissues through a generalized adversarial network (GAN). The results for three subjects demonstrated a remarkable improvement compared with those obtained by conventional MR-EPT methods at 128 MHz. The conductivities were estimated to be 0.53 ± 0.18, 0.37 ± 0.04, and 1.67 ± 0.47 S m⁻¹ for grey matter, white matter, and cerebrospinal fluid, and the corresponding relative permittivities were reported to be 66.0 ± 6.9, 54.4 ± 3.2, and 80.1 ± 4.9, respectively.

Hampe et al (2020) discussed potential extensions of deep learning EPT techniques using a patch-based U-net architecture and their applications. They investigated data obtained from 14 patients and 18 healthy subjects. The validity of deep learning in estimating brain conductivity mapping at 128 MHz was demonstrated.

Gavazzi et al (2020b) adopted deep learning in estimating the conductivity of human pelvic from 42 subjects at 128 MHz. The deep learning conductivity estimation showed high accuracy (average mean error of less than 0.1 S m⁻¹). A 3D patch-based convolutional neural network (CNN) used the transceive phase and ${B}_{1}^{+}$ to estimate electrical conductivity. The highres3dnet architecture was considered as the backbone network for this study, and the results demonstrated high performance compared with conventional methods.

Rashed et al (2020a) presented a deep learning architecture named CondNet as a network architecture that can effectively estimate a non-uniform conductivity map using T1/T2-weighted MRI. The Conductivities of eight tissues, i.e. cerebrospinal fluid, vitreous humor, fat, grey matter, mucous, skin, bone (cortical) and white matter, at 10 kHz obtained from image data of eight subjects were reported. The results demonstrated the efficiency of the proposed method in handling inter- and intra-subject variabilities by estimating the conductivity of whole-head tissues.

Later on, Rashed et al (2020b) extended CondNet to estimate the conductivity, permittivity, and density of 12 head tissues, i.e. blood, cancerous bone, cortical bone, grey matter, white matter, cerebellum, cerebrospinal fluid, dura, fat, mucous, skin, and vitreous humor, of eight subjects at 0.9, 1.8, and 3 GHz in studies on energy absorption by RF exposure. Dielectric properties and those variations (standard deviations) were also reported. They observed large variations (relative standard deviations from mean) for tissues with low dielectric properties, such as bone tissues and fat.

Sajib et al (2021) utilized a machine learning approach to reduce the number of injected current patterns in the DT-MREIT technique to a single pattern. The results of their phantom and human experiments demonstrated a small error of within 15% at 100 Hz.