1. Introduction
The open-ended coaxial probe has become the preferred method for measuring the dielectric properties of biological tissues due to its simplicity, minimal sample handling, and non-destructive nature. It enables both ex vivo and in vivo measurements across a wide frequency spectrum, spanning δ dispersions (between 0.1 and 5 GHz) caused by the dipolar moment of proteins and other large molecules, and γ dispersions (in the GHz range) due to the presence of water and small molecules [
1,
2].
Open-ended probes comprise a truncated section of a coaxial transmission line, along which electromagnetic fields can propagate. The reflections at the probe tip depend on the permittivity of the tissue sample in contact with the tip. A predecessor of this technique was introduced in [
3], where the dielectric in the final segment of a short-circuited coaxial line was replaced by the material under test. This approach has been widely used to characterize dielectric properties of materials [
4]. Various techniques have subsequently evolved and have been adapted to the specifics of biological tissues [
5]. A significant improvement to these techniques was provided by Gabriel et al. [
6], who were able to relate the reflection coefficient at the probe tip with the dielectric properties of the media under test by matching the boundary conditions at the interface between the coaxial line and the semi-infinite media [
7].
The advent of open-ended probes has catalyzed extensive research into the broadband characterization of biological tissues. Gabriel et al. [
1] conducted a comprehensive literature review and supplemented existing data with new measurements to compile a database [
8], which remains a cornerstone among existing databases [
9,
10]. Despite its importance, Gabriel’s data acquisition lacked histological control, which could introduce errors due to histological heterogeneity, even in normal tissues. Consequently, it remains the need to relate permittivity with histological features. Even today, there is a relatively scant amount of data relating both, mostly concerning histological alterations caused by cancer or by other pathologies [
11,
12,
13,
14,
15,
16]. Moreover, histological analysis is often performed in areas much larger than the probe’s sensing region, and the sample processing can alter the sample’s volume and morphology. This complicates the correlation between dielectric properties and histological characteristics, leading to the exclusion of a significant number of samples [
17,
18]. The use of punch biopsies with areas similar to the probe’s footprint could facilitate this correlation and spur the development of comprehensive databases on the complex permittivity of human tissues, incorporating the effects of histological alterations and heterogeneity.
In this article, we address this problem by assembling a measurement workstation adapted to be used in a pathology department. This facilitates access to human tissue samples from surplus diagnostic tissues to combine expert histological analysis with measurements of complex permittivity.
2. Materials and Methods
2.1. Measurement System
The measurement system used in this study has been designed to combine the guidelines provided by La Gioia et al. [
19], to ensure optimal measurement results, and the specific conditions encountered in a pathology department. To address both, we built a complex permittivity workstation cart (
Figure 1) using a modular system [
20] to provide the following essential features: compactness, stable connections between the vector network analyzer (VNA) and the probe, the ability to bring the sample into contact with a fixed probe, and the possibility of adjusting the sample–probe pressure.
The station integrates a VNA (FieldFox N9918A); a PC for data acquisition, instrument control, and measurement validation; a coarse lift platform with a bolted-in precision lab jack (Thorlabs L200/M); a probe stand integrated into the cart’s structure; a 2.2 mm diameter open-ended coaxial probe [
21]; an electronic scale to control the probe-to-sample pressure; and a polytetrafluoroethylene (PTFE) sample holder.
One of the key features required in a broadband complex permittivity system at GHz frequencies is the stability of the electrical properties of the connection between the VNA and the probe. Measurements are highly sensitive to phase and amplitude variations caused by uncontrolled motion of coaxial cables. We addressed this issue by securing the relative positions of the VNA and the probe and using a semi-rigid cable, protected by a plastic tube, between the VNA and the connection point of the probe. The probe stand is built into the cart frame, providing additional mechanical stability and further reducing the risk of uncontrolled cable motion. The VNA is securely mounted to the cart, fitted between two symmetrical, 3D-printed, polylactic acid (PLA) pieces. These pieces can be positioned along an aluminum profile within the modular system to ensure a snug fit for the VNA. The semi-rigid coaxial cable runs between the VNA port, and the upper end of a 3.5 mm female-to-female bulkhead adapter fixed to a horizontal plate on the probe stand. The open-ended probe is connected to the lower part of the bulkhead adapter through a 3.5 to 2.4 mm transition. This setup isolates the cable from probe movements and prevents torque from affecting the connection when attaching the probe to the system.
2.2. Instrument Settings, Calibration, and Validation
Before commissioning the workstation to the pathology department, extensive characterization procedures were conducted to determine the optimal instrument settings, measurement protocol, and associated uncertainties. We employed the standard calibration procedure, which involves measuring three standard loads, where the probe is open-circuited, short-circuited, and immersed in deionized water [
21]. After calibration, we measured a temperature-controlled 0.1 mol/L NaCl solution and compared the results to reference values derived from a Cole–Cole model, whose parameters vary with both temperature and concentration, as described in [
22,
23]. This comparison confirmed that electronic noise was not the main source of discrepancies between the measured permittivity and the reference values. Consequently, variations in the VNA averaging, output power, and intermediate frequency bandwidth (IFBW) had no significant impact when adjusted from the instrument’s default settings.
We investigated the potential effect of the IFBW on measurement time. While low IFBW values, typically used for low-noise measurements, can lead to longer measurement times, our measurements were primarily limited by the instrument’s firmware execution time. Therefore, increasing the IFBW provided no appreciable benefit. Based on these findings, we set the VNA output power to −6 dBm, with no averaging, and an IFBW of 300 Hz. To keep the frequency sweep time within reasonable bounds, we limited the number of points per sweep to 51 and used a logarithmic frequency sweep from 200 MHz to 20 GHz to cover two full frequency decades.
Once the instrument settings were finalized, we established the maximum acceptable difference between the measured and reference permittivity values. VNA calibration was repeated if the validation measurement of the 0.1 mol/L NaCl solution, performed immediately after calibration, exceeded this maximum threshold. Frequency-dependent validation thresholds were determined for both the real and imaginary parts of the permittivity by performing 41 calibration–validation sequences and recording the differences between the measured permittivity and its reference value. The thresholds were set to the 80th percentile of the absolute difference for the real part and the 90th percentile for the imaginary part (
Figure 2).
Once these thresholds had been established, they remained unchanged over 31 months, and proved useful in detecting wear in the short-circuit standard, which could result in defective calibrations or in identifying a lack of instrument stability due to insufficient warm-up time after being powered on. Between one and four VNA calibrations were needed prior to each measurement session.
2.3. Sample Acquisition
All samples used in the study were fresh human diagnostic surplus tissues obtained from surgical specimens or autopsies. Tissue samples were obtained from brain, thyroid, lung, spleen, liver, kidney, salivary gland, fat, skeletal and heart muscle, tongue, and pancreas. Measurements were performed within 30 min of the surgical specimen’s extraction and within 12 h from death for tissues obtained from autopsies. The study was approved by the Ethics Committee of the Hospital Clinic of Barcelona (HCB/2023/920) and conducted in accordance with the Helsinki Declaration. All samples were handled anonymously.
2.4. Tissue Measurements
Permittivity measurements of fresh human tissue samples were conducted in the Pathology Department of Hospital Clinic of Barcelona, Spain. These measurements took about 1 min per sample, required no tissue processing, and did not damage or alter the properties of the samples. Each sample was placed on the PTFE base, and the probe-to-sample pressure was adjusted using the precision jack until a 1 g reading was achieved on the scale (
Figure 3A). The VNA was then used to measure complex permittivity, employing a 51-point logarithmic frequency sweep from 200 MHz to 20 GHz. All facilities and tissues were at room temperature (from 21 to 24 °C).
We performed three consecutive permittivity measurements on every measurement spot using the coaxial probe and recorded their average (
Figure 3A). Then, we performed a 5 mm diameter punch biopsy of the tissue sample, centered on the probe’s footprint area (
Figure 3B). The tissue punch was then fixed in formalin and paraffin-embedded (FFPE) to create a paraffin block. A microtome (Tissue-Tek AutoSection, Sakura, Japan) was used to obtain a 2 µm histological section from the paraffin block containing the FFPE tissue. This tissue section was placed on a glass slide and stained with Hematoxylin–Eosin (HE) (
Figure 3C). We ensured a strong correspondence between the pathological analysis and the permittivity measurements by verifying that the diameter of the punch in the HE-stained tissue slide differed by no more than 0.5 mm from that of the sample prior to FFPE processing.
The HE slides were reviewed by a pathologist (M.C.), using an optical microscope (Olympus BX41, Olympus®, Japan) to identify the tissue type and to evaluate the homogeneity of the measured area within the selected punch area, by identifying features such as fibrous tracts or large vessels, which could affect permittivity measurements and render the sample invalid for our study. All tumoral samples were also discarded. The histological analysis was also utilized to identify samples with fibrosis, necrosis, or fat content, which were then categorized accordingly. All data were annotated in a database to ensure proper correlation between permittivity values and histological features for both normal samples and samples with histological alterations, i.e., fibrosis, necrosis, or fat content.
2.5. Detection of Fat, Necrosis, and Fibrosis Through Permittivity Measurements
To evaluate the potential of complex permittivity for detecting the presence of fibrosis, necrosis, or fat content in samples, we compared the complex permittivity values at 51 frequency points for samples of a given tissue type exhibiting these histological features with the average values of samples of the same tissue type without such features. Detection was possible whenever the real or imaginary parts deviated beyond the expected limits, accounting for instrumental or statistical uncertainties. Statistical uncertainty was defined by the standard deviation of permittivity measurements in samples without the histological feature of interest. Instrumental uncertainty at each frequency was determined through 41 calibration–validation sequences (detailed in
Section 2.1), where the standard deviation of differences between NaCl solution measurements and theoretical values was calculated. The 28th-highest absolute difference (corresponding to the 68th percentile under a normal distribution) was used as the representative value of instrumental uncertainty to mitigate outlier effects.
2.6. Comparison with a Reference Database
For each tissue type, we compared the average permittivity of standard samples with those of the corresponding human tissue types, as published by Gabriel in 1996 [
8], which serves as a reference database (RDB). This database provides permittivity measurements for both animal and human tissues across a broader frequency range than that of our study. Although the maximum frequency in both our dataset and the RDB extends to 20 GHz, the minimum frequency in the RDB varies by tissue type.
Additionally, the RDB data often have sparser frequency sampling for some tissues, with fewer data points distributed over wider frequency ranges (
Table 1). In contrast, our dataset includes 51 frequency points with a uniform logarithmic distribution spanning 200 MHz to 20 GHz for all human tissue types analyzed.
We compared our data with the RDB to evaluate the consistency of measurements over the shared frequency range of 200 MHz to 20 GHz. We evaluated three features: (1) whether the data for that tissue type was present in the RDB; (2) if the distribution of our measurement frequencies was denser than that used in the RDB for the same tissue type; (3) if our measurements of complex permittivity from 200 MHz to 20 GHz were consistent with the RDB data within the same frequency range.
Agreement between complex permittivity values and their RDB counterparts was classified as follows: Good if at least 80% of the measurement points fell within the confidence intervals, Fair if 50% to 80% of the points fell within the intervals, and Poor for values less than 50%. Graphical plots of the RDB data and our measurements for the same tissue type were used to estimate the frequency-dependent edges of the confidence intervals and to count the number of measurement points within these intervals.
3. Results and Discussion
We measured 154 fresh human tissue samples from 14 different tissue types, obtained from surgical surplus specimens or autopsies from 30 patients. The histological analysis (described in
Section 2.4) discarded six samples due to the presence of heterogeneous histological features in the punch area, or for being tumoral. Of the remaining 148 samples, 13 were categorized as necrotic tissue, 9 as fibrotic tissue, and 14 samples had fat content within the tissue.
Table 2 shows the distribution of sample types measured in this study.
Figure 4 displays the measurement results for standard samples. These samples were selected following histopathological evaluation to ensure tissue homogeneity and the absence of morphological features that could interfere with permittivity measurements, such as fibrosis, necrosis, or fat infiltration—except in the case of adipose tissue, where fat is a physiological component. Only samples without such alterations were considered representative of standard tissue architecture. Where applicable, the results were compared with data from [
8], and these comparisons are further elaborated in
Section 3.2.
3.1. Detection of Fat, Necrosis, and Fibrosis Through Permittivity Measurements
The detection of fat, necrosis, and fibrosis in individual samples using complex permittivity is feasible for certain tissue types, as illustrated by the salivary gland example in
Figure 5. In this case, fat content is a normal (non-pathological) condition. Higher fat content in different tissues consistently corresponded to lower permittivity values. A distinct gap is observed between the permittivity values of salivary gland samples without fat and those with fat. This gap is larger than the associated uncertainties, discussed in
Section 2.5, which are primarily influenced by patient-to-patient variability (11 fat-free samples, black trace in
Figure 5).
Complex permittivity measurements enabled the identification of all individual samples having fat in the liver and skeletal muscle. As shown in
Figure 6 and
Figure 7, both real (ε′) and imaginary (ε″) parts of the permittivity decrease in these tissues due to the abnormal fat content. Additionally, all fibrotic lung samples were detected, as fibrosis significantly increased permittivity compared to standard lung samples (
Figure 8). These findings are similar to those found in [
24].
The differences in the permittivity response in tissues with fat content or fibrosis may be attributed to the distinct histological characteristics of each process. Fibrosis leads to an excessive accumulation of extracellular matrix components, particularly collagen, which increases tissue density and structural stiffness. The lung, composed primarily of alveoli, contains a large amount of air, leading to low baseline permittivity. Fibrosis causes the alveoli to collapse or disappear, reducing air content and thus increasing permittivity. In contrast, tissues with fat content had a reduced permittivity probably due to the lower permittivity of lipids present within the adipocytes that infiltrate the tissue.
Necrosis detection proved to be more challenging, as it was identified only in liver samples, with lower permittivity than in both standard liver samples and those with fat content (
Figure 6). No significant changes in permittivity were observed in spleen, kidney, or fat tissues with necrosis. Permittivity remained largely unchanged in these organs, despite the structural damage caused by necrosis.
Necrosis is an irreversible cellular damage resulting from membrane disruption and the release of intracellular components, which contribute to cellular and tissue degradation. The impossibility of the detection of necrosis in all individual necrotic samples in fat, spleen, and kidney tissues may not have been due to the histological process but rather to the composition of the organ (
Figure 9). Fat tissue has a very low nominal permittivity value; therefore, necrosis did not significantly alter its permittivity. In fact, fat necrosis is a specific type of necrosis that releases the cytoplasm content of adipocytes into the interstitium. The cytoplasm content is composed of fat; thus, it could be a plausible explanation for the absence of changes in the measurements. The spleen, a densely packed lymphoid organ, has a naturally high nominal permittivity. The high cellular density of the organ could explain why that permittivity remained largely unaltered, even with necrosis. Similarly, the kidney also maintained relatively stable permittivity with the presence of tubular necrosis. This is probably due to its high density, being mainly composed of a complex extracellular matrix. Tubular necrosis mainly occurs in the epithelial cells of tubules immersed in this dense extracellular matrix, which could have had little influence on the measurements.
Figure 10 shows how the complex permittivity of individual abnormal samples in liver, muscle, and lung tissues compares to the nominal values of normal samples. It also illustrates how the differences in permittivity between normal and abnormal samples exceed the uncertainties, with the most pronounced differences occurring in the real part of the permittivity at low frequencies. These results highlight the potential of complex permittivity as a tool for detecting in situ certain histological features that could be integrated into the workflow of a pathology department for fresh tissue assessment.
3.2. Comparison with Reference Database
Figure 4 presents graphical comparisons of our measurements with those in the RDB, while
Table 3 provides a detailed analysis of the data on human tissues from the RDB and our dataset for each tissue type. Overall, our data align well with the RDB down to 1 MHz, particularly for ε″. Note that the assessments in
Table 3 take into account uncertainties when making comparisons with the RDB, whereas the graphs in
Figure 4 do not. Our data do not align with the standard fat values reported in the RDB, so we instead compared them with RDB breast fat data (
Figure 4).
Table 3.
Summary of comparison features with human measurement data in reference database.
Table 3.
Summary of comparison features with human measurement data in reference database.
Type of Human Tissue | Data in RDB | Improved Freq. Density | In-Band Fit ε′ 1 | In-Band Fit ε″ 1 |
---|
Brain (Grey matter) | Yes | Yes | Poor | Fair |
Brain (White matter) | Yes | Yes | Fair | Fair |
Fat 2 | Yes | No | Good | Good |
Heart | Yes | Yes | Good | Fair |
Kidney | Yes | No | Good | Good |
Liver | Yes | Yes | Poor | Good |
Lung | Yes | No | Poor | Good |
Pancreas | No | NA | NA | NA |
Salivary gland | No | NA | NA | NA |
Skeletal muscle | No | NA | NA | NA |
Spleen | Yes | Yes | Good | Good |
Thyroid | Yes | No | Poor | Poor |
Tongue | Yes | No | Poor | Fair |
In
Table 3, we can observe that, out of the 10 tissue types whose complex permittivity can be compared to the data in the RDB, 5 rate as “good” or “fair” in both ε′ and ε″ (fat, heart, kidney, spleen, and white matter), 4 rate as “good” or “fair” in ε″ and “poor” in ε′ (grey matter, liver, lung, and tongue), and 1 rates as “poor” in both ε′ and ε″ (thyroid).
A key difference between the two datasets lies in the origin and handling of the samples. Except for tongue tissues, all human samples in the RDB were obtained from autopsies performed 24 to 48 h postmortem, without histological analysis to exclude specimens affected by necrosis, fibrosis, or fat content. In contrast, the fresh human tissues used in our study were collected within 12 h postmortem or 30 min after surgical extraction, and measurements were performed at room temperature (21–24 °C), while those in the RDB were obtained at body temperature (37 °C). This temperature difference could account for part of the discrepancies between the RDB and our data, since permittivity in biological tissues is known to be temperature-dependent [
25]. Furthermore, all samples in our study underwent comprehensive histological evaluation to ensure the accuracy and reliability of the permittivity measurements.
Slight modifications to our measurement system could be implemented to conduct measurements at 37 °C, enabling a fair comparison with the reference database and helping to clarify whether differences in sample handling—and the lack of histological control in the RDB—account for discrepancies in complex permittivity values. However, these modifications were not pursued, as they fall outside the scope of our current work, which is focused on assessing the potential of complex permittivity as a tool within pathology workflows.
4. Conclusions
We have assembled a complex permittivity measurement station to be used in a pathology department. Additionally, we have set up a rigorous protocol that ensures correspondence between permittivity measurements and histological analysis. This approach enables a consistent and reliable dataset of human tissue complex permittivity that accurately reflects histological properties, enhancing current best-practice guidelines [
19,
23].
Using this equipment and protocol, we conducted a comprehensive study examining the relationship between complex permittivity and histology in 14 distinct human tissue types. Our findings demonstrate significant variations in complex permittivity associated with specific histological features, whether pathological or not. Fat tissue permittivity levels are normally low, while fat content lowers permittivity in liver, skeletal muscle, and salivary gland. Necrosis reduces permittivity in liver tissue, and fibrosis substantially increases permittivity in lung tissue. These histology-dependent effects are likely the primary contributors to the discrepancies observed between our data and the RDB [
8], which lacks histological control.
Despite differences in measurement protocols and the temperature at which the measurements were taken (37 °C in the RDB), our results show good or fair agreement with the RDB for both ε′ and ε″ in 5 out of 10 comparable tissue types (fat, heart, kidney, spleen, and white matter). However, the agreement is only good or fair for ε″ (and poor for ε′) in four tissue types (grey matter, liver, lung, and tongue), and poor for both ε′ and ε″ in one tissue type (thyroid).
This measurement setup, protocol, and the resulting dataset could spur future updates to the RDB [
8], incorporating histological features.
Our findings further highlight the potential of permittivity-based measurements as a complementary tool in pathology workflows, particularly for the early detection of abnormal tissue conditions—such as fat infiltration, fibrosis, or necrosis—prior to FFPE processing. This approach could aid in prioritizing samples that require immediate diagnosis. Notably, while conventional pathological tissue analysis typically takes at least 12 h, permittivity measurements can be performed on fresh tissue within minutes and without the need for any processing.
Although additional studies with larger sample sizes for each tissue type are needed to achieve a more comprehensive representation, these results highlight the promise of complex permittivity as a valuable parameter for tissue characterization and diagnostic applications in pathology departments. Integrating permittivity measurements into pathology workflows could enable real-time, non-invasive assessment of tissue properties, serving as a rapid intraoperative or prescreening tool. This approach can complement conventional histological and molecular diagnostics, thereby helping to streamline and optimize diagnostic processes. Furthermore, the early detection of tissue abnormalities may support personalized treatment planning—for instance, in diseases where monitoring fibrosis progression is clinically relevant.
Nonetheless, clinical translation will require overcoming specific technical challenges, including standardization of measurement protocols, ensuring sensor stability and reproducibility, and adapting the technology for easy integration within existing pathology infrastructure. With further development, this methodology may contribute to a new generation of biomedical diagnostic strategies based on dielectric tissue properties.