In vivo simultaneous proton resonance frequency shift thermometry and single reference variable flip angle T₁ measurements

Abstract

Purpose

The single reference variable flip angle sequence with a multi‐echo stack of stars acquisition (SR‐VFA‐SoS) simultaneously measures temperature change using proton resonance frequency (PRF) shift and T₁‐based thermometry methods. This work evaluates SR‐VFA‐SoS thermometry in MR‐guided focused ultrasound in an in vivo rabbit model.

Methods

Simultaneous PRF shift thermometry and T₁‐based thermometry were obtained in a New Zealand white rabbit model (n = 7) during MR‐guided focused ultrasound surgery using the SR‐VFA‐SoS sequence at 3 T. Distinct locations in muscle (n = 16), fat (n = 12), or the interface of both tissues (n = 23) were heated. The T₁‐temperature coefficient of fat was determined using least‐squares fitting of inversion recovery‐based T₁ maps of untreated fat harvested from the animal and was applied to the in vivo measured heat‐induced T₁ changes to create temperature maps.

Results

Using k‐space weighted image contrast reconstruction, temporal resolution of 1.71 s was achieved for simultaneous thermometry at 1.5 × 1.5 × 2 mm voxel resolution. PRF shift thermometry was not sensitive to heating in fat. T₁ changes were observed in fat at the ultrasound focus. The mean T₁‐temperature coefficient for fat was determined to be 1.9%/°C ± 0.2%/°C. Precision was 0.76°C ± 0.18°C for PRF shift thermometry in muscle and 1.93°C ± 0.60°C for T₁‐based thermometry in fat. Sonications in muscle showed an increase in T₁ of 2.4%/°C ± 0.9%/°C.

Conclusion

The SR‐VFA‐SoS sequence was shown to simultaneously measure temperature change using PRF shift and T₁‐based methods in an in vivo model, providing thermometry for both aqueous and fat tissues.

1. INTRODUCTION

MR‐guided focused ultrasound surgery (MRgFUS) is a noninvasive treatment used in numerous clinical applications. ¹ , ² , ³ , ⁴ , ⁵ , ⁶ , ⁷ , ⁸ For thermal applications, a significant advantage of MR‐guidance is the ability to use magnetic resonance temperature imaging (MRTI) to monitor internal temperature change during treatment, providing accurate thermometry without the need for insertion of temperature probes. MRTI can allow for real‐time temperature mapping during thermal procedures. ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ Both 2D ¹⁵ , ¹⁶ , ¹⁷ and 3D ¹⁸ , ¹⁹ , ²⁰ acquisitions have been used in conjunction with focused ultrasound. Necessary spatial and temporal resolutions are dependent on the ultrasound focal size and exposure time, respectively, ²¹ , ²² and are influenced by the sequence parameters, available SNR, and clinical need. ²³ , ²⁴ Generally, spatial resolutions are on the order of a few millimeters ¹⁴ , ²⁵ , ²⁶ , ²⁷ , ²⁸ and temporal resolutions are on the order of seconds ¹⁵ , ¹⁶ , ²⁹ , ³⁰ , ³¹ dependent on application. The ultrasound focus position as well as near‐ and far‐field regions is monitored for heating to maintain patient safety and treatment efficacy. Thermometry for MRgFUS thermal therapy in tissue volumes comprised of both aqueous tissue and fat, however, is challenging, as different thermometry methods are best suited for each tissue type.

Although many MR properties are sensitive to temperature, MRTI is most accurately and precisely achieved using the proton resonance frequency (PRF) shift method. PRF MRTI has been successfully used to monitor thermal changes in aqueous tissues in real time with clinically appropriate spatial and temporal resolution. ³² , ³³ Indeed, all United States Food and Drug Administration‐approved MRgFUS systems use PRF MRTI to monitor the temperature change during treatment. ¹³ , ³⁴ The PRF shift method relies on temperature‐dependent changes in the electronic shielding of the nucleus in hydrogen atoms in water molecules. This change in shielding changes the local magnetic field of the protons, which in turn alters the protons' resonance frequency. This can be described by Eq. (1):

$$B_{\mathrm{loc}}\cong {\mathrm{B}}_0(1-\alpha \mathit{T}),$$ (1)

where B _loc is the local magnetic field of the proton, B₀ is the main magnetic field of the scanner, α is the PRF coefficient in ppm/°C, and T is the tissue temperature. The PRF coefficient has been found to be approximately −0.010 ppm/°C for many aqueous tissues over the range of temperatures of interest in thermal therapies. ³⁵ This temperature‐dependent change in resonance frequency is quantified in MRTI by subtracting phase data acquired from a baseline image from the phase data in images acquired during heating, thereby removing non‐temperature induced phase changes. Because fat tissue does not have the same hydrogen bonding as that experienced by water molecules, the PRF coefficient of fat is negligibly small (approximately −0.00018 ppm/°C ³⁶ ) and the PRF shift method of MRTI is, therefore, mostly insensitive to temperature changes in fat. ³⁷ To date, no MR‐based thermometry method has been universally adopted for fat during thermal therapy treatments.

Other MRTI methods, which can measure temperature change in fat exist, but they are currently not used clinically in thermal therapy treatments. For example, the MR relaxation time constant T₁ has been shown to be dependent on temperature, following Eq. (2):

$${\mathrm{T}}_1(T)\approx T_1\left(T_{\mathrm{ref}}\right)+\frac{{d\mathrm{T}}_1}{\mathit{dT}}\cdot \left(T-T_{\mathrm{ref}}\right),$$ (2)

where T is the dynamic temperature, T _ref is a reference starting temperature, and dT₁/dT is the T₁‐temperature coefficient. Measurements of T₁ over the range 10°C to 70°C have shown a near linear relationship ³⁸ with a temperature dependence on the order of 1%/°C to 3%/°C ³⁹ in many biological tissues, including fat. Several methods exist ⁴⁰ , ⁴¹ , ⁴² , ⁴³ for quantifying T₁, and several T₁‐based MRTI methods have been developed ⁴⁴ , ⁴⁵ , ⁴⁶ allowing for temperature mapping of fat and other non‐aqueous tissues. One significant drawback to T₁‐based MRTI techniques is that the T₁‐temperature coefficient is tissue type specific and must be known for accurate temperature mapping, potentially requiring a priori information, including tissue specific calibration values.

Many hybrid techniques ⁴⁷ , ⁴⁸ , ⁴⁹ , ⁵⁰ , ⁵¹ , ⁵² , ⁵³ that simultaneously measure PRF and T₁ change have been investigated that could be used for MRTI of heterogeneous tissue volumes, but have drawbacks such as low temporal resolution or longer time between T₁ measurements compared to PRF measurements, low spatial resolution, required multiple interleaved baseline images, or could only acquire 2D images. A substantial improvement in temporal resolution of hybrid PRF/T₁ thermometry was introduced with dual‐ and variable‐flip angle (VFA) approaches; however, multiple acquisitions are required for T₁ measurements using these methods. ⁵⁰ , ⁵¹ , ⁵² , ⁵³ , ⁵⁴ As a result, T₁ thermometry measurements were obtained 2 to 4 times less frequently than PRF measurements, limiting the temporal resolution of T₁ to the order of 6 to 15 s for 3D acquisitions. ⁵¹ , ⁵⁴ MRgFUS and other MR‐guided thermal therapies, which generate ablative temperatures within 20 to 40 s ¹⁴ , ⁵⁵ and assess clinical efficacy with time‐dependent dose metrics, require near real‐time monitoring. No hybrid PRF/T₁ MRTI techniques have yet been adopted clinically for thermally ablative focused ultrasound surgery (FUS) therapies.

Svedin et al ⁵⁶ developed a more efficient single reference VFA (SR‐VFA) method with a multi‐echo stack‐of‐stars (SoS, in‐plane radial with through‐plane Cartesian sampling) acquisition and evaluated their simultaneous PRF/T₁ approach during MRgFUS ablations in phantoms and cadaver breasts, and in healthy volunteers under no heating conditions. This method calculates the PRF shift at every time point using the image phase. To calculate ΔT₁, this method uses sets of images, with baseline images acquired at a lower flip angle and dynamic images acquired at a higher flip angle. The change in T₁ is calculated as shown in Eq. (3):

$$T_1+∆T_1=\frac{-\mathrm{TR}}{\ln \left(\frac{1-\gamma }{1-\gamma \cos (\beta )}\right)},$$ (3)

where TR is the repetition time, $\gamma =\frac{1-E_1}{1-E_1\cos (\alpha )}\cdot \frac{1-E_{1\mathrm{est}}\cos (\alpha )}{1-E_{1\mathrm{est}}\cos (\beta )},$ α and β are the lower and higher flip angles, respectively, $E_1=e^{\left(\frac{-\mathrm{TR}}{T_1}\right)}$, and E _1est is an estimated E₁ obtained from baseline and dynamic images and the two flip angles (α and β). The reader is pointed to Svedin et al ³² for the full derivation. Advantages of this method over prior work include that the steady‐state signal remains stable between dynamics because the flip angle is not changed, and therefore, the temporal resolution of the PRF shift and T₁ measurements are the same. The sequence achieves good spatial precision of T₁ measurements in human breast tissue under non‐heating in vivo conditions; however, the temperature precision was not reported because T₁‐temperature coefficient was not determined. Malmberg et al ⁵⁷ assessed the precision and accuracy of the SR‐VFA‐SoS method for T₁‐mapping at various TEs (1.24–7.55 ms) in dynamically variable T₁ phantoms in static and dynamic conditions. Zhang et al ⁵⁴ has reported similar performance of a hybrid VFA sequence using an efficient golden‐angle–ordered 3D SoS technique in vivo in non‐heated human prostate, breast, and brain and ex vivo in FUS ablated porcine fat and muscle.

The purpose of the presented work is to evaluate this hybrid PRF/T₁ sequence in an in vivo MRgFUS ablation treatment setting to demonstrate the ability to simultaneously measure 3D PRF and T₁ changes with spatial and temporal resolution of 1.5 × 1.5 × 2 mm and 1.71 s, respectively. A large animal rabbit model was used to evaluate the sequence. The temperature sensitivity of T₁ from adipose tissues from both the hamstring and dorsum were found from water‐bath calibration experiments and used to convert ΔT₁ to temperature change and assess the temperature precision of this method.

2. METHODS

2.1. In vivo procedure

All animal studies were carried out under the guidance of the local Institutional Animal Care and Use Committee. In vivo experiments were performed in a 3 T MRI scanner (Prisma^FIT, Siemens Healthcare) using a 256 element MRI‐compatible phased‐array transducer, 10 cm radius of curvature, f = 1 MHz, 1.8 × 2.5 × 10.9 mm FWHM of pressure profile as measured in water, (Image Guided Therapy and Imasonic). Female and male New Zealand white rabbits (n = 7) were anesthetized with ketamine and xylazine (25 and 5 mg/kg, intramuscular injection, respectively), intubated, and maintained with isoflurane (1%–3%, inhaled, 100% oxygen). Each animal's leg or back was shaved before treatment and a depilatory agent (Nair, Church and Dwight) was applied to remove any remaining hair.

Initial animals (n = 2) were positioned lateral decubitus with the transducer focus approximately centered in the hamstring; later animals (n = 5), were positioned supine with the transducer geometric focus at the interface of the perirenal fat and paraspinal muscle to treat a larger contiguous volume of fat. The treatment area was acoustically coupled to the transducer with degassed and deionized water (Figure 1). The FUS (22.5–30 s, 45.9–49.6 W acoustic power for animals 3 and 5, 18.0–32.3 W for other animals) was electronically steered to 4 to 11 distinct locations per animal, targeting muscle only (n = 16 total for all subjects), fat only (n = 12), and the fat/muscle interface (n = 23), with the number of sonications in each location for each animal shown in Table 1. Interface sonications were defined to be sonications where the peak T₁ change in the ultrasound focus was located within 4 mm of the muscle/fat interface.

FIGURE 1.

Rabbit MR‐guided focused ultrasound surgery (MRgFUS) system. Experimental structure includes a single‐loop imaging coil (A), focused ultrasound transducer housing (B) with multi‐axis adjustable positioning, water coupling reservoir (C), positioning coils (D), and animal platform (E). White arrows indicate specific locations of identified components. Animals were positioned such that the focal zone of the transducer was located either in the hamstring (lower left) or dorsum (lower right), then electronic steering was used to target specific sites during the MRgFUS ablation procedure. Ultrasound transducer face outlined in green. Focal zone outlined in blue. Approximate single reference‐variable flip angle‐stack of stars (SR‐VFA‐SoS) volume outlined in orange. Muscle and fat indicated by red and yellow arrows, respectively. Purple line indicates approximate slice location for images in Figure 6.

TABLE 1.

Subject‐specific treatment parameters and MR temperature imaging results.

Animal	Sonication location			FUS duration (s)	Successful breath holds	Initial muscle T1 (ms)	Initial fat T1 (ms)	Muscle T1‐temperature coefficient (%/°C)	Fat T1‐temperature coefficient (%/°C)	Precision
	Muscle	Fat	Interface							PRF in muscle (°C)	T1 in fat (°C)
1	0	0	3	30	N/A	779	389	N/A	1.67	0.49 ± 0.10	2.89 ± 0.89
2	2	0	3	22.5	N/A	929	426	2.59	2.25	0.67 ± 0.13	1.64 ± 0.31
3	3	2	4	22.5	9/9	876	377	1.26	1.79	1.19 ± 0.24	1.83 ± 0.33
4	1	3	2	22.5	6/6	918	382	1.91	a	0.87 ± 0.09	1.06 ± 0.19
5	3	0	4	25.0	0/7	875	338	4.14	1.72	0.71 ± 0.30	2.29 ± 0.71
6	4	4	4	22.5	12/12	843	394	2.40	1.84	0.73 ± 0.12	1.86 ± 0.68
7	3	3	3	22.5	6/9	956	364	2.25	a	0.64 ± 0.16	1.98 ± 0.71
Average	N/A	N/A	N/A	N/A	N/A	882	381	2.43	1.85	0.76 ± 0.18	1.93 ± 0.60

Note: Sonications with peak heating within 4 mm of the tissue interface were classified as interface sonications. Number of sonications with successful breath holds relative to the total number of sonications is shown. Subject‐specific measured T₁‐temperature coefficients were used to convert ΔT₁ to temperature change. Initial muscle and fat T₁ values were calculated via inversion recovery images acquired before treatment. A 5 × 5 × 1 voxel region near the heating was selected and the mean T₁ value of the region is reported.

Abbreviations: FUS, focused ultrasound surgery; PRF, proton resonance frequency.

^a T₁‐temperature coefficient not calculated, average value of 1.85%/°C used to determine T₁‐based temperatures.

For temperature imaging, PRF shift and ΔT₁ data were acquired with a custom single‐loop coil during sonications using the SR‐VFA approach with a SoS sequence with a multi‐echo pseudo‐golden angle acquisition with view angle increment of (1–233/377) × 180° and 377 projections per dynamic image (additional parameters found in Table 2). A baseline low flip angle (5°) image and a baseline high flip angle image (15°) were acquired before each sonication. Because a k‐space weighted image contrast (KWIC) algorithm was used in reconstruction as described in Song et al, ⁵⁸ an image at each flip angle was taken before the respective baseline image to “prefill” k‐space. Immediately following the “prefill” and baseline images, 1 to 3 total higher flip angle dynamic acquisitions were acquired in succession, with the focused ultrasound heating beginning at the start of the first dynamic acquisition (Figure 2A). The acquisition time for each image (377 views) was 1 min and tissues were allowed to cool for ˜5.5 min between sonications.

TABLE 2.

MRI sequence parameters.

	TR (ms)	TE (ms)	BW (Hz/pixel)	FA (°)	Matrix size	Slices	Voxel size (mm3)	ETL	Acquisition time (s)
SR‐VFA‐SoS	20	2.46–9.06	1500	5,15	128 × 128	12	1.5 × 1.5 × 2	6	60.3
3D T1‐w VIBE Dixon	13.7	3.7, 9.84	250	15	512 × 384	104	0.5 isotropic	2	99
3D T2‐w SPACE	2000	151	700	120	512 × 344	72	0.5 isotropic	106	282
TurboFLASH	5700	1.72	1184	12	128 × 104	11	1.5 × 1.5 × 4	1	5.4
TSE	8000	7.3	1000	180	256 × 208	11	0.75 × 0.75 × 2	14	104

Abbreviations: TR, repetition time; TE, echo time; BW, bandwidth; ETL, echo train length; FA, flip angle; SPACE, sampling perfection with application optimized contrasts using different flip angle evolution; SR‐VFA‐SoS, single reference‐variable flip angle‐stack of stars; TSE, turbo spin echo; VIBE, volumetric interpolated breath‐hold examination.

FIGURE 2.

Sequence acquisition order [e.g., k‐space weighted image contrast (KWIC) reconstruction and resultant magnitude and phase images]. (A) Two 5° flip angle images (377 full views each) were acquired followed by three 15° flip angle images. Focused ultrasound was applied during the third high flip angle image. Animal breath holds were attempted on the baseline and dynamic acquisitions, dependent on animal tolerance. A KWIC reconstruction algorithm was used to reconstruct a dynamic image sequence with high temporal resolution. The low and high flip angle KWIC images before focused ultrasound surgery (FUS) heating are used as the low flip angle and baseline images for the corresponding images during FUS heating. (B) An example of fully sampled k‐space with radial projections, (C) an example asymmetric KWIC window, and (D) an example of k‐space sampled with three center and 13 total projections after the KWIC window was applied. Actual single reference‐variable flip angle‐stack of stars (SR‐VFA‐SoS) measurements was taken with 13 center and 377 total projections. Representative (E) magnitude (single dynamic averaged across echoes) and (F) phase (single dynamic at the first echo time) images after reconstruction with the KWIC algorithm.

For animals treated in the perirenal fat/paraspinal muscle, 20‐s breath holds were attempted during the 5° and 15° baseline acquisitions and the dynamic acquisition acquired during heating for matching during reconstruction. To avoid excessive CO₂ buildup, breath holds were not implemented if post‐sonication end tidal CO₂ did not return to baseline levels or if irregular respiration patterns were observed before beginning imaging for each sonication. Breath holds, assessed by respiratory monitoring, were implemented and successful for all sonications in three animals, no sonications in one animal, and in six of nine sonications in one animal.

B₁ maps were acquired using a vendor‐supplied TurboFLASH‐based B₁‐mapping sequence before each treatment. Three dimensional T₁‐weighted volumetric interpolated breath‐hold examination Dixon and 3D T₂‐weighted sampling perfection with application optimized contrasts using different flip angle evolution images were captured before and after MRgFUS ablation, with additional contrast‐enhanced T₁‐weighted imaging (gadoteridol, IV 0.1 mmol/kg) post‐ablation.

Animals were euthanized and tissue immediately harvested following post‐ablation imaging.

2.2. SR‐VFA‐SoS reconstruction

All reconstruction was performed using MATLAB 2022b (The MathWorks) on an Intel Xeon Silver 4210 CPU (2.20 GHz). Reconstruction of the SR‐VFA‐SoS images was performed using a KWIC method ⁵⁸ for increased temporal resolution, with 13 central projections and 377 total projections per dynamic using a sliding asymmetric window to leverage oversampling at the center of radial projections (Figure 2B–D), advancing 13 projections between KWIC frames. Echo combination was done by weighting the individual echoes by $\mathrm{TE}\cdot {\left|m\right|}^2$ (where $m$ is the complex MRI signal) for PRF shift ⁵⁹ thermometry and by $\exp \left(-2·\mathrm{TE}/{\mathrm{T}}_2^{*}\right)$ normalized by $\sum _{j=1}^{N_e}\exp \left(-2·{\mathrm{TE}}_j/{\mathrm{T}}_2^{*}\right)$ (where j is the echo number and N _e is the total number of echoes) for ΔT₁‐based ⁵³ thermometry calculations. If available, breath‐held baseline and dynamic acquisitions were paired in the ΔT₁ calculation to reduce motion artifacts. Temporal resolution for both the T₁ and PRF shift temperature data was 1.71 s. Temperature and ΔT₁ data were zero‐filled interpolated to 0.75 × 0.75 × 2 mm voxel spacing to reduce partial volume artifacts. All temperature reconstruction was performed retrospectively.

All VFA approaches, including the SR‐VFA‐SoS sequence, are highly sensitive to inhomogeneities in the B₁ field. In this study, B₁ inhomogeneities were corrected by acquiring a series of 2D B₁ maps before the treatment and interleaving them to have B₁ maps corresponding to all slice locations for the SR‐VFA‐SoS sequence. This B₁ correction was used in all calculations.

2.3. Fat ex vivo T₁ ‐temperature coefficient measurement

The fat T₁‐temperature coefficient was determined ex vivo by measuring the T₁ of excised non‐ablated fat from the contralateral side of the animal at several discrete temperature values between 20°C and 65°C. Immediately after animal euthanasia, untreated fat was excised, sliced into ˜1 cm³ segments, and maintained in saline. Within 24 h of excision, fat was packed into seven vials (ø1.4, length = 5.7 cm) of an MR‐compatible custom circulating water bath apparatus (Figure 3A) containing a single‐loop RF imaging coil. Fiber optic temperature sensors (polytetrafluoroethylene Teflon, range −80°C to 250°C, accuracy = ±0.2°C, Qualitrol) were inserted into the center of four fat‐filled vials for accurate temperature monitoring. The circulating water bath apparatus was placed in a 3 T MRI scanner (Prisma^FIT). Water was brought to a desired temperature by heating in a heated water pump placed outside the scanner suite, then pumped through the circulating water bath apparatus, heating the fat‐filled vials (Figure 3B). The temperature at the center of the fat‐filled vials was monitored using the inserted temperature sensors. After the temperature sensors in the heated fat reported an approximate constant temperature for 5 min, the circulating heated water was diverted through a bypass line, ceasing water flow through the water bath apparatus. Water circulating through the bypass line continued heating to the next desired temperature. This allowed for heating the water during imaging without transferring heat to the fat or incurring excessive water motion artifacts in the images, increasing the efficiency of the process and the quality of the T₁ maps. After a 5‐min waiting period from diverting water flow through the bypass line (to allow for additional temperature equalization of the fat and for water motion inside the apparatus to subside), Turbo spin‐echo (TSE) inversion recovery (IR) images were acquired (TI = 25, 100, 200, 500, 1000, 2000, and 3000 ms) (Table 2) at the center of the vials, with temperature readings from the inserted thermocouples recorded at 1 Hz. After imaging, the bypass line was closed, allowing the fat‐filled vials to be heated to the next temperature. This process was repeated for 5 to 6 increasing temperatures in the 20°C to 65°C range per sample. The ex vivo T₁‐temperature coefficient measurement was only completed for five of the seven rabbits because of inadequate contralateral fat volume (animal 4) and data lost during transfer from the scanner (animal 7).

FIGURE 3.

Experimental setup for ex vivo fat calibration. (A) Seven fat‐packed vials were submerged in a water bath and inserted with thermocouples. A single loop imaging coil encircles the water bath. (B) Water was heated external to the scanner, and then pumped through the water bath until fat reached a specified temperature. Water was diverted through a bypass line during imaging, which allowed for continued heating of water without heating fat or inducing water motion artifacts while inversion recovery images were acquired. This process was repeated for the temperature range 20°C to 65°C.

2.4. T₁ ‐temperature coefficient calculation

The muscle T₁‐temperature coefficient was estimated using the MRgFUS muscle sonications using voxels in a 2.25 × 2.25 × 2 mm³ (3 × 3 × 1 voxel) region of interest centered at each sonication's peak PRF‐shift temperature rise and ΔT₁ for all muscle sonications. Linear regression analysis of PRF‐shift temperature and T₁ changes for each voxel in the region of interest for all time points was used to calculate the estimated muscle T₁‐temperature coefficient.

The fat T₁‐temperature coefficient was determined from the IR images taken during the ex vivo T₁‐temperature coefficient procedure. ⁶⁰ Digital masks were made, which only contained voxels interior to the vials in the reconstructed images (Figure 4A). For each vial, voxels whose T₁ residual values were determined to be outliers via MATLAB's isoutlier function [outliers calculated as values more than three scaled median absolute deviations (MAD) from the median, where $\text{scaled}\mathrm{MAD}=c\times \text{median}\left(\left|A_i-\text{median}(A)\right|\right)$, and where $c=-\frac{1}{\sqrt{2\times {\mathrm{erfc}}^{-1}\left(\frac{3}{2}\right)}}$, $A$ is the residual vector, and erfc⁻¹ is the inverse complementary error function] were also masked out, retaining 80.0% ± 12.3% of voxels. For each rabbit, a T₁‐temperature coefficient was calculated using reduced dimension nonlinear least squares fitting ⁶¹ using the resultant T₁ data and the measured probe temperature.

FIGURE 4.

Ex vivo fat calibration results. Left: Axial view 3D volumetric interpolated breath‐hold examination (VIBE) of interior of fat calibration setup. Approximate masks for vial fat T₁ calculation shown (dashed yellow). Right: Measured fat T₁‐temperature curves derived from inversion recovery data. Average measured T₁ values for vials of fat at indicated temperatures with standard error between vials shown as bars. The average T₁‐temperature coefficient was 7.3 ± 0.7 ms/°C or 1.9%/°C ± 0.2%/°C for the excised fat.

2.5. PRF temperature and T₁ precision measurement

The precision of the measured PRF shift‐based temperature and the measured ΔT₁ by the SR‐VFA‐SoS sequence was determined for each acquired image using an unheated region of tissue. For the PRF‐shift temperature and ΔT₁‐based temperature precision calculations, temperature data from an untreated region of interest in muscle or fat (3.75 × 3.75 × 2 mm³ [5 × 5 × 1 voxels]) was analyzed. For each voxel in the region, the SD of temperature through time was calculated, and then the calculated SD of all voxels in the region was averaged to determine the reported precision value.

To determine if fat may have changed phase during heating, an additional animal was acquired and a slip test ⁶² was performed. Perirenal fat from both sides of the animal was harvested immediately following euthanasia. Fat was then slowly heated at ˜1°C/min in a beaker on a hot plate until melting occurred, then liquid fat was drawn into three capillary pipettes and immediately solidified by cooling in a −7°C freezer for 1 min. The outer edges of the fat were marked, and then the capillary pipettes were submerged in a water bath and heated at 1°C/min. The fat volumes were carefully observed during heating and the temperature of the water bath was recorded the moment the fat slipped beyond the marks.

3. RESULTS

3.1. T₁ ‐temperature coefficient

Fat T₁‐temperature calibration experiments demonstrated an average increase of 7.3 ± 0.7 ms/°C in excised fat or approximately a 1.85% ± 0.23% change in T₁ per (°C) change for the range of 20°C to 65°C. T₁‐temperature curves for each animal are plotted in Figure 4. The error bars represent standard error in mean T₁ values between fat‐filled vials.

The in vivo muscle T₁‐temperature coefficient was calculated to be 2.59, 1.26, 1.91, 4.14, 2.40, and 2.25%/°C for animals 2 to 7, respectively, with an average of 2.43% ± 0.96% increase in T₁ per (°C) above subject body temperature. Correlation between PRF‐shift temperature and ΔT₁ data is shown in Figure 5.

FIGURE 5.

Correlation of proton resonance frequency (PRF) shift temperature and ΔT₁ in muscle. The muscle T₁‐temperature coefficient was estimated for each animal using sonications centered in muscle. The points of maximum heating and maximum T₁ change were identified, and linear regression analysis was performed using a 2.25 × 2.25 × 2 mm³ (3 × 3 × 1 voxel) region of interest centered at those voxels for all time points. The animal‐specific linear fit is shown in orange. The average T₁‐temperature coefficient in muscle was 2.4%/°C ± 0.9%/°C.

3.2. In vivo temperature

Simultaneous PRF and T₁ temperature changes at or near the focal spot were successfully measured for all sonications in muscle. Peak temperature rises from 9°C to 39°C and peak changes of T₁ from 39% to 181% were observed. Peak changes in T₁ for sonications with the focal spot located in fat ranged from 18% to 73%, corresponding to peak temperature rise of 10°C to 41°C. ΔT₁‐based temperatures were calculated with subject‐specific T₁‐temperature coefficients when available and the intersubject mean for rabbits without a subject‐specific measured T₁‐temperature coefficient. Temperature maps at peak‐temperature time points for PRF shift‐based thermometry for a muscle sonication, ΔT₁‐based thermometry for a fat sonication, and PRF shift‐ and ΔT₁‐based thermometry for an interface sonication are shown in Figure 6. Qualitatively, the PRF shift‐based temperatures contained less noise than the ΔT₁‐based temperature maps. These observations are confirmed quantitatively with the measurement precision values detailed in Table 1. The average PRF shift‐based temperature precision was 0.76°C ± 0.18°C (0.60°C ± 0.12°C for hamstring sonications, 0.86°C ± 0.16°C for successful breath‐hold sonications, and 0.72°C ± 0.27°C for sonications in the back without breath holds). The average ΔT₁ precision was 13.5 ± 4.0 ms, resulting in an average ΔT₁‐based temperature precision of 1.93°C ± 0.60°C (2.11°C ± 0.6°C for hamstring sonications, 1.69°C ± 0.54°C for successful breath‐hold sonications, and 2.30°C ± 0.73°C for sonications in the back without breath holds). Figure 7 shows temperature and ΔT₁ versus time plots for the muscle and fat sonications.

FIGURE 6.

Representative single reference‐variable flip angle‐stack of stars (SR‐VFA‐SoS) thermometry maps. (A) Proton resonance frequency (PRF) shift calculated temperature map for focused ultrasound surgery (FUS) sonication in muscle, (B) calculated temperature map from ΔT₁ for FUS sonication in fat, and temperature maps of (C) PRF and (D) ΔT₁ for a single sonication targeting the interface. Partial volume effects and susceptibility artifacts likely lead to inaccuracies in PRF temperatures near the interface. For the interface ΔT₁ image, temperatures are only valid for fat, because the ΔT₁ was scaled by the subject‐specific fat ΔT₁‐temperature coefficient. Voxels at the fat‐muscle interface were noisier than single‐tissue voxels, including some over‐saturated voxels with non‐physiological temperature rises. For inset images, the background image was removed to accurately display the temperature color scale. Arrows denote muscle tissue (red) and fat tissue (yellow). Temperature maps are at the time of maximum focal spot temperature. Thermometry maps are from different sonications of animal 3.

FIGURE 7.

Representative temperature versus time plots for proton resonance frequency (PRF)‐ and ΔT₁‐based thermometry. Temperatures shown are the average temperature of a 3 × 3 in‐plane set of voxels centered at the peak temperature voxel. PRF shift‐based temperature (blue) and ΔT₁ (orange) shown for a sonication centered in muscle (left). PRF shift‐based (blue) and ΔT₁‐based (orange) temperatures shown for a sonication in fat (right). Temperature data taken from the muscle and fat sonications displayed in Figure 6.

Peak temperatures versus applied acoustic powers are shown in Figure 8 for sonications centered in muscle and in fat, with bars showing the precision values for the individual sonication. Peak temperatures normalized by acoustic power averaged 0.57°C/W ± 0.14°C/W in muscle and 0.77°C/W ± 0.28°C/W in fat.

FIGURE 8.

Applied acoustic power versus peak temperature for sonications centered in muscle (left) and fat (right). Bars show measured temperature precision of each sonication as derived from a non‐heated region of tissue. Average peak temperatures normalized by acoustic power were 0.57°C/W ± 0.14°C/W for sonications in muscle and 0.77°C/W ± 0.28°C/W for sonications in fat.

During the slip test for determining melting point, melting occurred at 51°C for all three fat volumes.

4. DISCUSSION

This work demonstrates the feasibility of using the SR‐VFA‐SoS method for simultaneous T₁ and PRF shift MR temperature measurement in vivo. Current United States Food and Drug Administration approved MRgFUS applications acquire MRTI using the PRF method, resulting in no fat thermometry being available. This method of hybrid thermometry allows for the measuring of temperature change across a volume of tissue containing both aqueous tissue and fat, which will be of great value for applications in, for example, the breast and abdomen. The high spatial and temporal resolutions are similar to existing clinical MRgFUS ablation and hyperthermia PRF shift thermometry methods. ³⁴ This work also determined the T₁‐temperature coefficient in rabbit perirenal fat and assessed the variability in the T₁‐temperature coefficient between subjects.

Temperature changes calculated from the PRF shift method were observed in aqueous tissue only, with sonications in muscle showing a clear temperature rise at the ultrasound focal spot. PRF shift thermometry did not show heating in fat sonications, as expected. Relative T₁ changes were observed in the ultrasound focal region in both muscle and fat. The T₁ changes in fat were converted to temperature using an experimentally derived T₁‐temperature coefficient (Figure 4B). When normalized by applied acoustic power, calculated temperatures were higher for sonications in fat (0.77°C/W ± 0.28°C/W) than in muscle (0.57°C/W ± 0.14°C/W), although the acoustic attenuation of fat is lower than in muscle (4.4 vs. 7.1 Np/m at 1 MHz, respectively). ⁶³ Perfusion in muscle is higher than fat ⁶⁴ and has been shown to increase with hyperthermia, ⁶⁵ , ⁶⁶ which can result in lower focal tissue heating, especially at high perfusion values. ⁶⁷

The T₁‐temperature coefficient in muscle was estimated by using PRF shift derived temperatures in conjunction with the measured T₁ change at the focal spot in muscle sonications. The relationship of T₁ changes versus temperature rise for maximum heated voxels in muscle showed increases of 1.26%/°C to 4.14%/°C, in line with the 1.4%/°C value reported in ex vivo bovine muscle at 20°C, ⁶⁸ with the 4.14%/°C coefficient for Animal 5 being an outlier. Additionally, the measured in vivo T₁ for fat without heating for animal 5 was 338 ms, whereas the ex vivo T₁ measurement was 450 ms at 37°C. As shown in Figure 5, animals 3 and 5 had notably higher variance in temperature rise versus ΔT₁ than other animals, which correlates with the higher sonication power used in these animals.

In this study, an increase of 7.3 ± 0.7 ms/°C or 1.85%/°C ± 0.23%/°C was calculated for the T₁ of perirenal rabbit fat using the IR measurements during fat heating, which is higher than the 5.8 ± 1.9 ms/°C and 5.8 ± 2.1 ms/°C reported by Hey et al ⁵⁰ and lower than the 7.78 ± 0.19 ms/°C and 8.11 ± 0.25 reported by Zhang et al ⁵⁴ for ex vivo porcine fat. It is also higher than the average 1.4% increase per (°C) of temperature rise for ex vivo human breast fat reported by Todd et al, ⁵² but still falls within the 1%/°C ³⁹ to 3%/°C ³⁹ seen in many biological tissues. Because of the observed increase in standard error of T₁ at higher temperatures, particularly above 50°C, a slip test ⁶² was used to determine the melting point of perirenal fat in an additional animal, as phase‐changing fat could affect the measured T₁ values. Melting of the fat occurred at 51°C, which may indicate the higher standard error seen at higher temperatures in Figure 4 is because of phase‐changes during the study.

The average calculated precision for the PRF shift‐based temperatures was 0.76°C ± 0.18°C, similar to precision values reported for other PRF methods. In MRgFUS using a porcine model, Quesson et al ⁹ reported a SD of less than 2°C in 75% of voxels in liver, with some voxels exceeding a SD of 4°C, and a SD of less than 2.6°C in 90% of voxels in skin using a multi‐slice gradient‐recalled EPI sequence, with some voxels reaching a maximum SD of 38°C. Odéen and Parker ⁵⁹ compared PRF shift‐based MR thermometry sequences for laser interstitial thermotherapy and reported precision values for 0.94 × 1.88 × 3 mm³ voxels of 0.91°C to 3.33°C for a 3D gradient echo (acquisition time = 5.89 s) sequence and 0.37°C to 1.79°C a 3D EPI (acquisition time = 5.85 s) sequence depending on coil selection for in vivo non‐heating measurements in human brains at 3 T. Adams‐Tew et al ¹⁹ reported precisions of 1.1°C and 2.0°C for a 3D EPI sequence (acquisition time = 4.88 s) with voxel size of 1 × 2 × 3 mm³ in non‐heating measurements in human breast with and without drift correction, ⁶⁹ respectively.

The average calculated precision for the ΔT₁‐based temperatures at 1.93°C ± 0.60°C was slightly worse than PRF precision. Breath holds improved sonication precision measurements over free‐breathing sonications (1.69°C ± 0.54°C and 2.30°C ± 0.73°C, respectively), likely because of reduced animal motion as evidenced by less noise in non‐heated regions of the tissue used to calculate precision. Temperature precision is also dependent on the KWIC window parameters, such as the number and portions of projections included in the window. Additionally, low SNR from the use of a body coil for imaging, as is common clinically, ⁷⁰ may result in poor precision, but SNR can be improved using higher field strengths, specialized coils, ⁷¹ MR ⁷² or ultrasound ⁷³ hardware changes, or optimizing sequence parameters. ⁷⁴

In vivo accuracy of the SR‐VFA‐SoS sequence was not assessed in this work, largely because of technical challenges of the viscous heating artifacts induced by available MR‐compatible temperature sensors. ¹⁹ Using a hybrid VFA SoS sequence, Zhang et al ⁵⁴ reported mean absolute difference between temperature probes and PRF temperatures were 1.89°C and 1.23°C in ex vivo muscle using one transducer and 0.9°C in ex vivo muscle using another. Malmberg et al ⁵⁷ used a novel quantitative rotating phantom to assess the accuracy of T₁ maps acquired using the SR‐VFA‐SoS sequence with and without T₂* correction. ⁷⁵ Correcting for T₂* effects improved both the accuracy and precision of the SR‐VFA‐SoS sequence, with greater improvement seen at longer TEs. Future work will include in vivo validation of both the PRF shift and T₂* corrected T₁‐based temperatures using temperature probes currently undergoing validation for use in focused ultrasound fields.

A significant advantage of the SR‐VFA‐SoS sequence is its ability to produce 3D thermometry maps with both high spatial and temporal resolution. Three dimensional thermometry in MRgFUS allows for better focal spot localization and monitoring of the near‐ and far‐field, as well as reduced partial volume artifacts resulting in, for example, more accurate determination of accumulated thermal dose. It also overcomes FOV and systemic errors seen in Todd et al ⁵² because of the 2D sequence used. The acquired spatial resolution of 1.5 × 1.5 × 2, interpolated to 0.75 × 0.75 × 2 mm spacing, in this study allowed for sufficient determination of the size and position of localized heating and T₁ changes based on the ultrasound transducer FWHM. ²⁷ Increasing acquisition voxel sizes would lead to increased SNR, which can increase the precision of the thermometry, ⁷⁶ but could also negatively impact the peak‐temperature accuracy because of increased partial volume effects. ²⁷

Acquiring both PRF shift and T₁ data with one sequence and using a single reference image eliminates the need for interleaving sequences or alternating flip angles as done in multiple previous studies ⁴⁹ , ⁵⁰ , ⁵¹ , ⁵² and hence, allows for increased temporal resolution. Using KWIC we achieved an in vivo temporal resolution of 1.71 s, higher than in other hybrid techniques. This high temporal resolution provides more accurate treatment monitoring and allows better visualization of the temperature rise and cooling in the treatment volume.

Although we found the T₁‐temperature coefficient varied from animal to animal, Baron et al ⁷⁷ showed that this is not the case for human breast tissue. They measured a mono‐exponential T₁‐temperature relationship for ex vivo human breast fat and found a low deviation, less than 0.5 ms/°C, between intersubject breast fat measurements indicating that a table value T₁‐temperature coefficient for breast fat is likely sufficient for clinical use and subject‐specific T₁‐temperature coefficient measurement may not be necessary. Thermal effects may also include altering tissue characteristics, potentially changing the T₁‐temperature coefficient ⁷⁸ , ⁷⁹ , ⁸⁰ over the course of a MRgFUS treatment.

Another challenge with this method of hybrid thermometry is accurate temperature calculation for mixed‐tissue voxels. Although percent change in T₁ was successfully measured for sonications located at the interface of muscle and fat, accurate T₁‐based thermometry for mixed‐tissue voxels was not possible because of the tissue‐specific nature of the T₁‐temperature coefficients. Additionally, the partial‐volume effects for voxels at the tissue interface can cause under‐ or over‐estimation of the temperature change using the PRF shift method. ⁸¹ The partial‐volume effect at the tissue interface is somewhat mitigated by the small voxel size afforded by the SR‐VFA‐SoS sequence. Susceptibility changes near the interface of fat and aqueous tissues also can cause inaccurate PRF measurements, ⁸² nevertheless, for sonications targeting only aqueous tissues, susceptibility changes are small. ³⁶ , ⁸³

Finally, for clinical use, reconstruction of the SR‐VFA‐SoS sequence needs to take place in real time, with the thermometry available to clinicians during the sonication. For this study, reconstruction of the SR‐VFA‐SoS sequence was done retrospectively, with reconstruction time not considered. Multiple actions can be taken to streamline the reconstruction to reduce the temporal footprint, including parallelizing graphics and/or central processing units for gridding, ⁸⁴ calculating water‐ and fat‐fraction maps before treatment for segmentation (to apply PRF‐based temperature maps for aqueous tissues and T₁‐based maps for fat), and reducing the time required for pre‐ and post‐heating image acquisition. Additionally, the KWIC algorithm can be implemented with an asymmetric or symmetric window. In this case, an asymmetric window was used because a symmetric window (where the central slices of k‐space are located at the center of the window) requires a delay between the acquisition of the center of k‐space and the reconstruction of the temperature maps, although the symmetric window may be more accurate in some cases. ⁸⁵

5. CONCLUSION

This work has provided an in vivo evaluation of the SR‐VFA‐SoS method of simultaneous PRF shift thermometry and T₁ measurement along with the measurement of the T₁‐temperature coefficient in a rabbit model. The SR‐VFA‐SoS method has the capability to measure relative temperature in aqueous tissue and T₁ changes in nonaqueous tissue, which, when combined with a T₁‐temperature calibration curve, allows for the monitoring of relative temperature of fat and aqueous tissues in the treatment area, significantly augmenting thermometry acquired during MRgFUS treatments.

CONFLICT OF INTEREST STATEMENT

The authors report there are no competing interests to declare.

Richards N, Malmberg M, Odéen H, et al. In vivo simultaneous proton resonance frequency shift thermometry and single reference variable flip angle T₁ measurements. Magn Reson Med. 2025;93(5):2070‐2085. doi: 10.1002/mrm.30413