Referenceless proton resonance frequency (PRF) shift thermometry removes the need for baseline phase images by estimating and subtracting the non-temperature background field, and a self-attention-based deep network (C-SANet) has now demonstrated learned referenceless temperature mapping in essentially stationary transcranial focused-ultrasound targets in brain. Whether this learned referenceless paradigm can be extended to highly dynamic, motion-prone organs such as liver and heart — where respiration and cardiac motion continuously change the background field and the heated region's position — and whether explicit temporal modeling across frames improves its stability at low signal-to-noise ratio and under rapidly varying background fields, remains untested. The problem is to develop and validate such a method against referenceless and motion-compensated baselines with an independent temperature ground truth, establishing the accuracy and robustness envelope of learned referenceless thermometry outside the stationary-brain regime.

Background

Magnetic resonance (MR) guided thermal therapy — for example MR-guided focused ultrasound (MRgFUS) tumor ablation or hyperthermia — requires noninvasive temperature monitoring to control energy deposition and protect surrounding tissue. The standard technique is proton resonance frequency (PRF) shift thermometry: the water-proton resonance frequency shifts by about 0.01 ppm per degree Celsius, so temperature change is encoded in the phase of gradient-echo phase images, with the phase difference Δφ=γαB0 TE ΔT\Delta\varphi=\gamma\alpha B_0\,TE\,\Delta T where γ\gamma is the gyromagnetic ratio, α\alpha the PRF-temperature coefficient, B0B_0 the main field, and TETE the echo time; the images are acquired with gradient-echo sequences (the standard rapid MR imaging sequences used for thermometry). Conventional PRF thermometry subtracts a baseline (reference) phase image acquired before heating. This referenced approach fails whenever tissue moves between the baseline and the treatment images — because of respiration, cardiac motion, or drifting anatomy — since the phase difference then mixes temperature change with unrelated background-field changes, which is the central obstacle to MR-guided thermal therapy in abdominal and cardiac targets.

Referenceless PRF thermometry removes the baseline dependence by estimating the non-temperature background phase directly from each image and subtracting it, so that only the focal temperature-induced phase change remains. Classical referenceless methods fit low-order polynomial phase models to the unheated part of each slice (Rieke et al. 2004), use complex field estimation (CFE), which fits the complex image rather than its phase to avoid phase-unwrapping errors (Kuroda et al. 2006), or reconstruct the background phase under a near-harmonic (approximately Laplacian-zero) constraint (Salomir et al. 2012). A five-method comparison (Zou et al. 2017) mapped the accuracy trade-offs among these model-based approaches, which all assume the background field is spatially smooth and the heated region compact. Classical referenceless thermometry has been piloted in the liver under free breathing, on clinical MR-guided laser-ablation data (Kickhefel et al. 2012), and demonstrated on a Thiel-embalmed (soft-fixative-preserved) human cadaver for MRgFUS liver surgery (Karakitsios et al. 2019) — but both are non-learning methods, and no learned referenceless estimator has been validated in living, moving subjects.

Motion-robust thermometry in abdominal organs has instead been pursued through referenced or hybrid strategies: multi-baseline methods that swap in a library of baseline images matched to the current respiratory position, combined with real-time multi-slice acquisition (Kim et al. 2023), and a hybrid multibaseline-plus-referenceless motion-compensation algorithm for MRgFUS hyperthermia (Wong et al. 2024), with the whole family reviewed by Kim et al. (2024). Separately, deep learning (DL) has entered MR thermometry mainly through other bottlenecks: accelerated k-space reconstruction of referenced thermometry (Xu et al. 2025; Khatun et al. 2025), deep correction of breathing-related artifacts in referenced real-time thermometry (de Senneville et al. 2021), and precision improvement via quadratic-phase MR fingerprinting, a sequence-based method that acquires a train of varying echoes and matches the resulting signal evolution to a dictionary (Garrow et al. 2025). None of these is a learned referenceless estimator, and none applies DL referenceless thermometry to moving organs.

Into this gap, Zhao et al. (2026) introduced C-SANet, a referenceless PRF thermometry method built on a deep network with self-attention (the attention mechanism that weighs relationships among spatial features regardless of distance), trained to regress the temperature-related phase change from single frames. It was validated on transcranial focused-ultrasound (FUS) heating in essentially stationary brain targets, where background fields are dominated by slowly varying susceptibility effects from the skull. In its limitations the authors state explicitly that (i) no experiments were performed in highly dynamic organs such as liver or heart, (ii) the network operates frame-by-frame and does not exploit temporal information, with recurrent, temporal-convolutional, or transformer-based temporal modules named as a natural development direction, and (iii) broader validation across orientations, organ systems, and heating strategies is still required.

Problem Statement

Establish whether deep-learning referenceless PRF-shift MR thermometry — demonstrated to date only in essentially stationary transcranial focused-ultrasound targets in brain — can be extended to highly dynamic, motion-prone organs such as liver and heart, and whether explicit temporal modeling across frames (recurrent, temporal-convolutional, or transformer-based modules over the frame sequence) improves its accuracy and stability at low signal-to-noise ratio and under rapidly varying background fields, compared with frame-by-frame estimation.

A complete answer must (1) develop a learned referenceless temperature-estimation method (extending or replacing the frame-by-frame self-attention architecture) that operates on the moving-organ regime, and compare the temporal-modeling variant directly against the frame-by-frame estimator under matched conditions, (2) validate it on motion-realistic data — phantoms under imposed motion, or in vivo abdominal/cardiac focused-ultrasound or hyperthermia settings — against (a) classical referenceless baselines such as polynomial fitting, complex field estimation, or near-harmonic reconstruction, plus at least one motion-compensated baseline such as a multibaseline or hybrid multibaseline-plus-referenceless method, and (b) an independent temperature ground truth that does not itself degrade under the motion being studied (e.g., implanted probe, phantom ground truth, or a carefully justified referenced protocol), and (3) report standard thermometry metrics — temperature accuracy and precision (mean error, limits of agreement, root-mean-square error), heating-region detection quality, and robustness as a function of motion amplitude and SNR — sufficient to delimit the regime in which learned referenceless thermometry is reliable.

References

  1. Zhao, Yueran; Mei, Chang-Sheng; McDannold, Nathan J.; Wang, Meiyun; Shen, Guofeng; Zong, Shenyan. 'Referenceless Proton Resonance Frequency Thermometry Using Deep Learning with Self-Attention.' IEEE Transactions on Biomedical Engineering, 2026. DOI: 10.1109/TBME.2026.3689263, https://doi.org/10.1109/TBME.2026.3689263 (preprint: arXiv:2512.07882, https://arxiv.org/abs/2512.07882)
  2. Rieke, Viola; Vigen, Karl K.; Sommer, Graham; Daniel, Bruce L.; Pauly, John M.; Butts, Kim. 'Referenceless PRF shift thermometry.' Magnetic Resonance in Medicine, 2004. DOI: 10.1002/mrm.20090, https://doi.org/10.1002/mrm.20090
  3. Kuroda, Kagayaki; Kokuryo, Daisuke; Kumamoto, Etsuko; Suzuki, Kyohei; Matsuoka, Yuichiro; Keserci, Bilgin. 'Optimization of self-reference thermometry using complex field estimation.' Magnetic Resonance in Medicine, 2006. DOI: 10.1002/mrm.21016, https://doi.org/10.1002/mrm.21016
  4. Salomir, R.; Viallon, M.; Kickhefel, A.; Roland, J.; Morel, D. R.; Petrusca, L.; Auboiroux, V.; Goget, T.; Terraz, S.; Becker, C. D.; Gross, P. 'Reference-Free PRFS MR-Thermometry Using Near-Harmonic 2-D Reconstruction of the Background Phase.' IEEE Transactions on Medical Imaging, 2012. DOI: 10.1109/TMI.2011.2168421, https://doi.org/10.1109/TMI.2011.2168421
  5. Kickhefel, Antje; Rosenberg, Christian; Roland, Jörg; Viallon, Magalie; Gross, Patrick; Schick, Fritz; Hosten, Norbert; Salomir, Rares. 'A pilot study for clinical feasibility of the near-harmonic 2D referenceless PRFS thermometry in liver under free breathing using MR-guided LITT ablation data.' International Journal of Hyperthermia, 2012. DOI: 10.3109/02656736.2012.670834, https://doi.org/10.3109/02656736.2012.670834
  6. Zou, Chao; Tie, Changjun; Pan, Min; Wan, Qian; Liang, Changhong; Liu, Xin; Chung, Yiu-Cho. 'Referenceless MR thermometry—a comparison of five methods.' Physics in Medicine & Biology, 2017. DOI: 10.1088/1361-6560/62/1/1, https://doi.org/10.1088/1361-6560/62/1/1
  7. Karakitsios, Ioannis; Mihcin, Senay; Melzer, Andreas. 'Reference-less MR thermometry on pre-clinical thiel human cadaver for liver surgery with MRgFUS.' Minimally Invasive Therapy & Allied Technologies, 2019. DOI: 10.1080/13645706.2018.1470985, https://doi.org/10.1080/13645706.2018.1470985
  8. Kim, Kisoo; Diederich, Chris; Narsinh, Kazim; Ozhinsky, Eugene. 'Motion-robust, multi-slice, real-time MR thermometry for MR-guided thermal therapy in abdominal organs.' International Journal of Hyperthermia, 2023. DOI: 10.1080/02656736.2022.2151649, https://doi.org/10.1080/02656736.2022.2151649
  9. Kim, Kisoo; Narsinh, Kazim; Ozhinsky, Eugene. 'Technical advances in motion-robust MR thermometry.' Magnetic Resonance in Medicine, 2024. DOI: 10.1002/mrm.30057, https://doi.org/10.1002/mrm.30057
  10. Wong, Suzanne M.; Akbulatov, Arthur; Macsemchuk, Craig A.; Headrick, Andrew; Luo, Phoebe; Drake, James M.; Waspe, Adam C. 'An augmented hybrid multibaseline and referenceless MR thermometry motion compensation algorithm for MRgHIFU hyperthermia.' Magnetic Resonance in Medicine, 2024. DOI: 10.1002/mrm.29988, https://doi.org/10.1002/mrm.29988
  11. Xu, Sijie; Zong, Shenyan; Mei, Chang-Sheng; Shen, Guofeng; Zhao, Yueran; Wang, He. 'Accelerated proton resonance frequency-based magnetic resonance thermometry by optimized deep learning method.' Medical Physics, 2025. DOI: 10.1002/mp.17909, https://doi.org/10.1002/mp.17909
  12. Khatun, Rupali; Chatterjee, Soumick; Bert, Christoph; Wadepohl, Martin; Ott, Oliver J.; Semrau, Sabine; Fietkau, Rainer; Nürnberger, Andreas; Gaipl, Udo S.; Frey, Benjamin. 'Complex-valued neural networks to speed-up MR thermometry during hyperthermia using Fourier PD and PDUNet.' Scientific Reports, 2025. DOI: 10.1038/s41598-025-96071-x, https://doi.org/10.1038/s41598-025-96071-x
  13. de Senneville, B. Denis; Coupé, P.; Ries, M.; Facq, L.; Moonen, C.T.W. 'Deep correction of breathing-related artifacts in real-time MR-thermometry.' Computerized Medical Imaging and Graphics, 2021. DOI: 10.1016/j.compmedimag.2020.101834, https://doi.org/10.1016/j.compmedimag.2020.101834
  14. Garrow, Sarah J.; Zarcone, Kristen; Keenan, Kathryn E.; Boyacioğlu, Rasim; Griswold, Mark; Grissom, William A. 'MR thermometry with high precision and temporal resolution by quadratic phase MR fingerprinting.' Magnetic Resonance in Medicine, 2025. DOI: 10.1002/mrm.30546, https://doi.org/10.1002/mrm.30546