Objective. Conventional computed tomography (CT) imaging does not provide quantitative information on local thermal changes during percutaneous ablative therapy of cancerous and benign tumors, aside from few qualitative, visual cues. In this study, we have investigated changes in CT signal across a wide range of temperatures and two physical phases for two different tissue mimicking materials, each. Approach. A series of experiments were conducted using an anthropomorphic phantom filled with water-based gel and olive oil, respectively. Multiple, clinically used ablation devices were applied to locally cool or heat the phantom material and were arranged in a configuration that produced thermal changes in regions with inconsequential amounts of metal artifact. Eight fiber optic thermal sensors were positioned in the region absent of metal artifact and were used to record local temperatures throughout the experiments. A spectral CT scanner was used to periodically acquire and generate electron density weighted images. Average electron density weighted values in 1 mm3 volumes of interest near the temperature sensors were computed and these data were then used to calculate thermal volumetric expansion coefficients for each material and phase. Main results. The experimentally determined expansion coefficients well-matched existing published values and variations with temperature—maximally differing by 5% of the known value. As a proof of concept, a CT-generated temperature map was produced during a heating time point of the water-based gel phantom, demonstrating the capability to map changes in electron density weighted signal to temperature. Significance. This study has demonstrated that spectral CT can be used to estimate local temperature changes for different materials and phases across temperature ranges produced by thermal ablations.

Computed tomography (CT) has been shown to be a useful imaging modality to guide thermal ablations. However, conventional CT is limited in monitoring and visualizing treatment zones during ablation. The periphery of frozen volumes formed during cryoablations are typically observable, especially in soft tissue; however, lethal sub-zero isotherms are not. Moreover, visual cues from hyperthermal ablations are limited primarily to faint hypoattenuating signal and gas bubble formation in the hottest regions near the probe only. Although these soft surrogate temperature inferences provide some information, thermal-ablation procedures are typically characterized by very steep and anisotropic temperature gradients, with temperatures upwards of ±100 °C near the tip of the applicator, and normal body temperatures as close as 2–3 cm from the tip. Thus, it is important to accurately estimate temperature locally throughout the treatment volume, or at least at the treatment margins.

Few strategies can be deployed clinically to monitor local temperature changes during image-guided interventional oncology procedures. One possibility is to rely on external temperature sensors percutaneously inserted at critical locations in the treated volume. However, those will provide individual reference points only, and extrapolation to obtain isotherms of lethally treated volumes is challenging. Another option is to use MR-Thermometry, a well-established technique that leverages changes in phase with temperature. However, there are few commercially available ablation systems that are MR-Safe or MR-Conditional for interventional oncology procedures. Additionally, MR-Thermometry is currently limited to hyperthermal ablations owing to the challenges in generating MR signal from frozen tissue. Moreover, current MR-guided interventional oncology procedures represent a small fraction of all image-guided procedures, primarily due to the associated complexity of safely introducing large, partially ferrous objects in the MR environment(Thompson et al 2021).

The dependence of x-ray attenuation on temperature has been discussed since the early days of x-ray CT (Bydder and Kreel 1979). Changes in temperature cause tissues to expand or contract, thusmodifying their physical density, which will in turn be reflected in changes to the recorded CT-signal. CT-based thermometry estimates have been explored since the very beginning of CT (Fallone et al 1982). However, to date the clinical requirements for intraprocedural temperature mapping—specifically the combination of 1–2 mm spatial resolution, <5 °C temperature accuracy and clinically acceptable radiation dose—have been very challenging to achieve. Recent advances in spectral CT, combined with the introduction of advanced reconstruction and postprocessing algorithms to reduce noise without sacrificing quantitative accuracy, offer the opportunity to break this barrier and have renewed the interest in CT-based thermometry for clinical applications (Hübner et al 2020, Heinrich et al 2022, Shapira et al 2022, Liu et al 2023, Wang et al 2023).

In this work, we first investigated the theoretical relationship of signal and temperature for both conventional x-ray CT images from a polychromatic beam and electron density weighted images. We subsequently designed an experimental setup that enabled the acquisition of data spanning a large range of temperatures—with a goal to cover from −100 °C to +100 °C. Finally, we used this experimental setup to perform a series of controlled experiments to generate spectral CT data to empirically characterize the thermal expansion coefficient of soft tissue and fat-mimicking materials in temperature ranges of clinical relevance for both hypo and hyper-thermal ablation procedures. This process was designed to validate the relationship between CT signal and temperature by using external benchmarks for the thermal expansion coefficient.

2.1. Theoretical relationship of thermal volumetric expansion coefficient with CT signal

Spectral CT scanners offer the ability to generate electron density-weighted (EDW) material maps, expressed in terms of a percentage of the value for water (at room temperature). This in turn results in a direct relationship with physical density, and therefore, with temperature:

where is the material electron density at temperature relative to the electron density of water at a fixed temperature. Note, manipulating equation (1) into its final form relies on an approximation that is contingent on small fractional changes in volume only. Consequently, the coefficient of volumetric thermal expansion, for a given material (and physical state) can be extracted from a direct fit of repeated empirical measurements of EDW across a range of temperatures of interest that does not include phase transitions. If is constant then the integral in equation (1) simplifies to the more common expression, However, it is widely reported in the literature that volumetric expansion coefficients vary with temperature, typically expressed as a low order polynomial function of temperature. (Powell 1958, Rabin et al 1998) Consequently, we can rewrite equation (1) as follows:

where expansion coefficient's dependence on temperature has been formulated as a second order polynomial, and is a constant value corresponding to the extrapolated value of from a specific physical phase. Notably, this approach does not rely on simulation or estimation of an attenuation coefficient, nor any proprietary knowledge of the CT scanner x-ray beam filtration and energy distribution.

2.2. Experimental setup

Percutaneous tumor ablation procedures performed clinically use a variety of local applicators and thermal techniques (liquid N2 or Joule–Thompson effect for cryoablations, microwave, laser, high intensity focused ultrasound or radiofrequency energy for hyperthermal ablations) to obtain lethal temperatures within the tumor margins and with very sharp gradients to minimize damage to surrounding tissues. These temperatures span a range of approximately −100 °C to 100 °C. In order to collect the experimental data required to obtain over this wide temperature range, applicators used in clinical practice were applied to locally modify the temperature of our tissue-mimicking materials and generate the required data. These applicators typically consist of a metal shaft to provide rigidity, resulting in significant artifacts in CT images, which would otherwise confound the relationship between CT data and local temperature. To overcome this limitation, we designed and built a custom 3D-printed holder with a rectangular array of openings 5 mm apart in orthogonal directions. This set-up enabled accurate and repeatable positioning of thermal applicators in a 2 × 2 configuration, 2 cm apart, to achieve the desired temperature range in the midplane between the probes where metal artifacts were negligible to non-existent. Eight fiber optic temperature sensors (OmniFlex, Neoptix) were arranged linearly at approximately 5 mm intervals and used to locally record the temperature in the midplane. To further reduce artifacts from the temperature sensors and support structures, the temperature sensors were placed at a ∼30° angle relative to the midplane. Figure 1 provides illustrative representations of the thermometry experiment setup and a photograph of the phantom.

Figure 1. Diagram (A) and photograph (B) of the experimental setup designed to generate profiles of CT signal as a function of temperature for different materials and conditions, including close-up views of the thermal applicators and optical temperature sensors (C)–(D).

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To mimic the thermal properties of soft tissue, a water-based gel consisting of 3% HEC, 0.15% NaCl, and 96.85% distilled water was created and used to fill an anthropomorphic phantom. In a second set of experiments, olive oil was investigated due to its similarity to fat tissue properties, its relatively simple chemical composition and critically, the availability of reference in the literature (in liquid form The Engineering ToolBox 2009). Gel and olive oil were placed in a 25 cm anthropomorphic phantom with the aforementioned, 3D-printed holder placed on top.

To explore freezing and heating temperature ranges, we performed a total of 4 individual sets of measurements. In the first two experiments, 4 IceForce cryoprobes (Boston Scientific) were used to freeze the gel- and oil-filled phantoms, respectively. In the third experiment, 3 microwave probes (PRX, Johnson and Johnson MedTech, Neuwave) were used to locally heat the gel-filled phantom. We intentionally and carefully adjusted the cooling (duty cycle on cryoprobes) and heating (microwave power) rates throughout the experiments to slow the rate of temperature change and enable data acquisition throughout the temperature range of interest. This approach could not be used to locally heat olive oil due to its different thermophysical properties, e.g. convective heat transfer coefficient. Consequently, olive oil was separately heated to above 80 °C, transferred to an insulated container, and allowed to slowly cool to near room temperature, while measurements were taken. Across all 4 experiments, the eight embedded temperature sensors recorded temperature values at 1-second intervals, while periodic CT scans (parameters described below) captured phantom images.

2.3. Data acquisition and analysis

A Spectral CT7500 scanner (Philips Healthcare) was used to collect spectral CT data and generate EDW images. The objective of this investigation was to obtain the highest quality CT data (i.e. minimal signal variation due to image noise) for temperature characterization and benchmarking. Using an acquisition protocol consisting of 5 consecutive axial scans over the same volume (16 × 0.625 mm collimation, 1 s rotation, 120 kV, 350 mA) enabled a ∼200 mGy radiation dose (CTDIvol) per acquisition while keeping the x-ray tube at an operational temperature throughout the experiment. To further reduce image noise as much as possible, an aggressive iterative reconstruction setting (iDose-6) and the smoothest convolution filter available for reconstruction (A, cutoff MTF value of 8 lp cm−1) were used to reconstruct the images (200 mm field-of view, 1 mm slice thickness, 1 mm increment). CT data were collected approximately every one minute, starting at room temperature and throughout heating/cooling (∼60–90 min each).

For each imaging timepoint, one volume-of-interest (VOI) measuring 1 mm3 was identified adjacent to each temperature sensor, for a total of 8 VOIs. The average EDW within each VOI was matched to the average temperature reading from the corresponding channel during that acquisition timepoint. If a sensor's recorded temperature varied by more than 1 °C during the CT acquisition (approximately 8 s), that datapoint was discarded. Each acquisition timepoint therefore generated up to 8 valid datapoints, as shown in figure 2, which depicts recorded temperatures for the frozen gel experiment, as well as a CT image showing the location of the volumes of interest for each sensor for a representative timepoint. All sensor and corresponding VOI measurements, spanning the required wide range of temperatures, were combined into signal-versus-temperature scatter plots. From the fitted scatter plots, we computed the coefficient of thermal volumetric expansions as a function of temperature using equation (2) and compared it to existing values in the literature, when available, to validate the accuracy of our data. Adjusted R2 was used as the regularization parameter to determine the optimal polynomial order for

Figure 2. Recorded temperatures (A) and CT image showing the location of the volumes of interest for each sensor for a representative timepoint (B) during the frozen gel experiment. The colors used for each temperature channel were kept consistent in subsequent figures to reflect the relative location of the temperature sensors.

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With our experimental setup and the use of thermal applicators, we were able to record artifact-free EDW values for temperatures as cold as −100 °C and −70 °C for frozen gel and olive oil, respectively. Conversely, in the heating experiments we were able to collect data at temperatures as high as 93 °C and 80 °C for gel and oil, respectively. The individual EDW versus temperature plots for each experiment are shown in figures 3–6 .

Figure 3. EDW(T) for the frozen-gel experiment. (A) all collected datapoints, including measurements over the phase transition. (B) data fitted to equation (2) and used to extract an expression for the thermal expansion coefficient.

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For the freezing experiments, data were collected over the phase transition for the investigated materials. In the case of water-based gel (figure 3(A)), the transition is very sharp: below approximately −15 °C the changes in physical density due to the phase change appear complete and a EDW data below this temperature were used in the fit to equation (2) (figure 3(B)). On the other hand, a phase transition from liquid oil to solid state was discernible starting at −5 °C until as low as −40 °C, accompanied by a wide variance in the relationship between EDW and temperature (figure 4(A)). As a result, only data below −40 °C could be reliably fitted to estimate the volume expansion coefficient for frozen oil (figure 4(B)). This wide phase transition of olive oil during cooling is consistent with the literature (Vecchio Ciprioti et al 2017).

Figure 4. EDW(T) for the frozen-gel experiment. (A): all collected datapoints, including measurements over the phase transition. (B): data fitted to equation (2) and used to extract an expression for the thermal expansion coefficient.

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Figure 5. EDW(T) for the heated-gel experiment. All datapoints were fitted to equation (2) and used to extract an expression for the thermal expansion coefficient.

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Figure 6. EDW(T) for the heated-oil experiment. All datapoints were fitted to equation (2) and used to extract an expression for the thermal expansion coefficient.

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From the experimental data and using equation (2), we extracted the thermal volumetric expansion coefficients as a function of temperature for gel and olive oil in the freezing and heating temperature ranges, respectively. Significantly different thermal expansion coefficient values were extracted for the different materials. In the case of frozen gel, a linear expression of was found to best fit the data and provided an excellent match with the values provided in the literature for ice across the temperature range of interest. (Powell 1958, Rabin et al 1998) At T = −40 °C, this corresponded to For frozen oil, the resulting coefficient of thermal volumetric expansion was a very weakly quadratic function of temperature, with a value of at T = −40 °C, not known to be documented. In the case of heated gel, a quadratic relationship of with temperature was found to best fit the experiment data for EDW(T) (figure 5), and it provided an excellent match with the data reported in the literature across the temperature range of interest (The Engineering ToolBox 2009). At T = 40 °C, this functional form corresponded to 2.5 times higher than for the same material in the solid phase. Finally, the heated oil experiment yielded a quadratic relationship for albeit with a lower dependency on temperature than water (figure 6). At T = 40 °C, this functional form corresponded to twice the value for water-based gel and an excellent match with the reported value (non-temperature specific) () (The Engineering ToolBox 2009). The coefficients of thermal volumetric expansion as a function of temperature for all the investigated configurations are summarized in figure 7.

Figure 7. Plots of calculated volumetric thermal expansion coefficients for oil and gel in both solid and liquid phases across the temperature ranges investigated in this study. Reference thermal expansion coefficients provided in the plots are for ice (Powell 1958), liquid oil (The Engineering ToolBox 2009), and water (The Engineering ToolBox 2009).

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Employing the empirically determined expansion coefficients, we identified a separate CT scan—i.e. not included in the fitted EDW(T) data—near the peak of the heating gel experiment and generated a temperature map by inverting the EDW(T) relationship described in equation (2) using our coefficients of thermal volumetric expansion (figure 8). In table 1, we report the 8 measured temperature values and the correspondent CT-based temperature estimates for this timepoint. The error between the measured and CT-based temperature estimates was <5 °C for each of the 8 datapoints. Of note, the validation CT data was obtained using a single axial acquisition, thus 20% the radiation dose used to generate the EDW(T) data.

Figure 8. Left: conventional single-energy CT image during localized heating of water-based gel. The temperature sensors are visible as bright spots near the center of the image. Right: magnified view of spectral CT-based temperature mapping, demonstrating a range of temperatures up to 100 °C, with sharp, irregular temperature gradients. The voxels corresponding to the temperature sensors are displayed as artificially low temperature, i.e. dark regions. Temperature readings are compared to adjacent T(EDW) measurements in table 1.

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Table 1. Measured and CT-derived temperatures for the location adjacent to the 8 fiber optics sensors. This timepoint was acquired near the peak of the heating gel experiment, using 20% of the radiation dose of the main datapoints, and was not included in the data used to fit a functional form to for heated gel.

 Temperature sensors Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Measured (°C)47.557.565.675.784.578.862.453.6CT-derived (°C)4957617984815952Error3%−1%−7%4%−1%3%−5%−3%

In this work, we designed and built an experimental setup that allows us to investigate the thermal properties and dependence of CT signal on temperature for a variety of materials and a wide range of temperatures. Then, we leveraged this setup to validate the accuracy of spectral CT data by estimating the volumetric thermal expansion coefficient for both a water-based gel and olive oil, in both their non-frozen and frozen states. Finally, we demonstrated the potential of these data to generate accurate temperature maps in the presence of sharp gradients and irregular distributions. The congruency of the measurements in the temperature map shown in figure 8 at the location of the sensors corroborates the accuracy of our thermal expansion coefficient estimates and is promising for their use to generate CT-based temperature mapping in CT-guided thermal procedures.

A goal of this work was to validate the accuracy of our data by benchmarking them against independent references, such as the thermal volumetric expansion coefficient. This was best performed by using EDW data, as their dependence on the volume expansion coefficient is not affected by the proprietary energy spectra of a given CT scanner, nor does it require an accurate empirical estimate of photoelectric and Compton weighting coefficients, unlike conventional CT data expressed in HU. A CT image reconstructed from projection data obtained from a conventional polychromatic x-ray beam will display the following relationship of signal (expressed as CT Number in Hounsfield units) with temperature:

where ρ is the physical density of the material; Z and A are its effective atomic number and mass, respectively; α is its thermal volumetric expansion coefficient; FKN is the Klein–Nishina equation describing Compton-scatter interaction (Klein and Nishina 1928) and the subscript w refers to water. k1 , k2 , and n are empirically determined coefficients describing the relative contribution of photoelectric absorption and Compton scattering. To estimate the thermal expansion coefficient of a given material from CT measurements obtained at different temperatures, accurate knowledge of these empirical coefficients, as well as the polychromatic distribution of energies in the x-ray beam used by the vendor is required.

We can rewrite equation (3) to express the sensitivity of conventional single-energy (or virtual monoenergetic) CT signal to temperature variations as a function of EDW(T) that could be derived from spectral CT data:

Equation (4) shows that the higher the effective atomic number (Z) of the material, the higher the numerator in the parentheses, i.e. the term that scales EDW(T). When Z for a given material is larger than that of water, the term in the parentheses is larger than 1 and thus the CT number will be more sensitive to temperature changes than EDW. This is due to the relatively higher contribution of the photoelectric interaction to those images compared to EDW. However, virtually all clinical applications of CT-based thermometry will involve materials with an effective atomic number less than 20 (Calcium), so this is unlikely to be a significant disadvantage. Additionally, spectral CT offers the key advantage of enabling material decomposition, thus allowing to characterize and separate the contribution of different tissues, e.g. fatty deposits in the liver. Given the up to 5-fold variation in thermal expansion coefficient for soft tissue and fat-mimicking materials demonstrated in this work, and confirmed by the available literature, properly identifying and separating the contribution of different materials prior to converting the CT signal to temperature is an essential step for accurate CT-based thermometry in clinical conditions. Spectral CT-based accurate material decomposition remains challenging, particularly in the liver, and further work will be necessary.

The data included in this work was acquired at high radiation dose, to minimize noise contribution to signal variation and improve accuracy in extracting temperature dependent relationships for different experiments. These relationships are expected to be applicable to in vivo data acquired at routine radiation dose, which is supported by our validation test. An investigation of the required radiation dose needed to achieve specific accuracy in temperature estimates, which would be dependent on spectral CT detector performance, patient size, tissue type, as well as desired spatial resolution of temperature maps, was beyond the scope of this investigation.

Key aspects of our work complement and differ from those published in literature. Liu and colleagues have recently reported on the use of spectral CT for non-invasive temperature quantification (Liu et al 2023). In their approach, first a series of parametrized models are derived that output physical density at a reference temperature from input data derived from a variety of spectral results (virtual monoenergetic images at 70 keV, effective atomic number and electron density maps). From this step, relative temperature changes can be derived by taking the ratio of the physical density at two temperatures, and assuming a known (and static) thermal volumetric expansion coefficient. On the other hand, our data directly extracted and validated the thermal expansion coefficient by comparing it to values reported in the literature. Moreover, our data span both frozen and heated materials over a wide range of temperatures that fully encompass the range of interest in thermal tumor ablations.

Our study has certain limitations. Only one spectral CT scanner was investigated. Future work to extend this approach to include different platforms for spectral CT, including photon-counting, is ongoing. Additionally, only one phantom size was used in this work. The dependency of the EDW(T) mapping on the size of the phantom or the tube potential was not tested; however, neither is expected to be a significant factor. Finally, the two materials investigated in this study, while sharing several similarities with soft tissue and adipose human tissue, respectively, they are non-ideal surrogates. Characterization of the thermal properties of actual human tissues is needed prior to exploration of clinical CT-based thermometry in vivo.

This study provided the first validation of spectral CT-thermometry in the clinically realistic scenario of rapidly varying temperature gradients (range −100 °C–100 °C) in soft tissue and fat-mimicking materials, respectively. The customized 3D-printed experimental setup enables investigations of a variety of materials and is flexible to phantom size, type and number of thermal applicators. The reported thermal expansion coefficients and their dependence on temperature well matches the reported values in the literature. Furthermore, to our knowledge, this work provides the first reported thermal expansion coefficient for frozen olive oil in the literature. Incorporation of these material-specific temperature maps with spectral CT-based tissue decomposition promises to be a viable pathway to clinical, intraprocedural thermometry during CT-guided thermal tumor ablations.

All data that support the findings of this study are included within the article (and any supplementary information files).