Model predictive filtering for improved temporal resolution in MRI temperature imaging

Technical advances in motion-robust MR thermometry

Proton resonance frequency shift (PRFS) MR thermometry is the most common method used in clinical thermal treatments because of its fast acquisition and high sensitivity to temperature. However, motion is the biggest obstacle in PRFS MR thermometry for monitoring thermal treatment in moving organs. This challenge arises because of the introduction of phase errors into the PRFS calculation through multiple methods, such as image misregistration, susceptibility changes in the magnetic field, and intraframe motion during MRI acquisition. Various approaches for motion correction have been developed for real-time, motion-robust, and volumetric MR thermometry. However, current technologies have inherent trade-offs among volume coverage, processing time, and temperature accuracy. These tradeoffs should be considered and chosen according to the thermal treatment application. In hyperthermia treatment, precise temperature measurements are of increased importance rather than the requirement for exceedingly high temporal resolution. In contrast, ablation procedures require robust temporal resolution to accurately capture a rapid temperature rise. This paper presents a comprehensive review of current cutting-edge MRI techniques for motion-robust MR thermometry, and recommends which techniques are better suited for each thermal treatment. We expect that this study will help discern the selection of motion-robust MR thermometry strategies and inspire the development of motion-robust volumetric MR thermometry for practical use in clinics.

Evaluation of acoustic-thermal simulations of in vivo magnetic resonance guided focused ultrasound ablative therapy

PURPOSE

To evaluate numerical simulations of focused ultrasound (FUS) with a rabbit model, comparing simulated heating characteristics with magnetic resonance temperature imaging (MRTI) data collected during in vivo treatment.

METHODS

A rabbit model was treated with FUS sonications in the biceps femoris with 3D MRTI collected. Acoustic and thermal properties of the rabbit muscle were determined experimentally. Numerical models of the rabbits were created, and tissue-type-specific properties were assigned. FUS simulations were performed using both the hybrid angular spectrum (HAS) method and k-Wave. Simulated power deposition patterns were converted to temperature maps using a Pennes' bioheat equation-based thermal solver. Agreement of pressure between the simulation techniques and temperature between the simulation and experimental heating was evaluated. Contributions of scattering and absorption attenuation were considered.

RESULTS

Simulated peak pressures derived using the HAS method exceeded the simulated peak pressures from k-Wave by 1.6 ± 2.7%. The location and FWHM of the peak pressure calculated from HAS and k-Wave showed good agreement. When muscle acoustic absorption value in the simulations was adjusted to approximately 54% of the measured attenuation, the average root-mean-squared error between simulated and experimental spatial-average temperature profiles was 0.046 ± 0.019 °C/W. Mean distance between simulated and experimental COTMs was 3.25 ± 1.37 mm. Transverse FWHMs of simulated sonications were smaller than in in vivo sonications. Longitudinal FWHMs were similar.

CONCLUSIONS

Presented results demonstrate agreement between HAS and k-Wave simulations and that FUS simulations can accurately predict focal position and heating for in vivo applications in soft tissue.

Validation of a drift-corrected 3D MR temperature imaging sequence for breast MR-guided focused ultrasound treatments

Real-time temperature monitoring is critical to the success of thermally ablative therapies. This work validates a 3D thermometry sequence with k-space field drift correction designed for use in magnetic resonance-guided focused ultrasound treatments for breast cancer. Fiberoptic probes were embedded in tissue-mimicking phantoms, and temperature change measurements from the probes were compared with the magnetic resonance temperature imaging measurements following heating with focused ultrasound. Precision and accuracy of measurements were also evaluated in free-breathing healthy volunteers (N = 3) under a non-heating condition. MR temperature measurements agreed closely with those of fiberoptic probes, with a 95% confidence interval of measurement difference from -2.0 °C to 1.4 °C. Field drift-corrected measurements in vivo had a precision of 1.1 ± 0.7 °C and were accurate within 1.3 ± 0.9 °C across the three volunteers. The field drift correction method improved precision and accuracy by an average of 46 and 42%, respectively, when compared to the uncorrected data. This temperature imaging sequence can provide accurate measurements of temperature change in aqueous tissues in the breast and support the use of this sequence in clinical investigations of focused ultrasound treatments for breast cancer.

Adaptive simulation of 3D thermometry maps for interventional MR-guided tumor ablation using Pennes' bioheat equation and isotherms

Minimally-invasive thermal ablation procedures have become clinically accepted treatment options for tumors and metastases. Continuous and reliable monitoring of volumetric heat distribution promises to be an important condition for successful outcomes. In this work, an adaptive bioheat transfer simulation of 3D thermometry maps is presented. Pennes' equation model is updated according to temperature maps generated by uniformly distributed 2D MR phase images rotated around the main axis of the applicator. The volumetric heat diffusion and the resulting shape of the ablation zone can be modelled accurately without introducing a specific heat source term. Filtering the temperature maps by extracting isotherms reduces artefacts and noise, compresses information of the measured data and adds physical a priori knowledge. The inverse heat transfer for estimating values of the simulated tissue and heating parameters is done by reducing the sum squared error between these isotherms and the 3D simulation. The approach is evaluated on data sets consisting of 13 ex vivo bio protein phantoms, including six perfusion phantoms with simulated heat sink effects. Results show an overall average Dice score of 0.89 ± 0.04 (SEM < 0.01). The optimization of the parameters takes 1.05 ± 0.26 s for each acquired image. Future steps should consider the local optimization of the simulation parameters instead of a global one to better detect heat sinks without a priori knowledge. In addition, the use of a proper Kalman filter might increase robustness and accuracy if combined with our method.

Temperature estimation for MR-guided microwave hyperthermia using block-based compressed sensing. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2020;2020:5057-5060. [PMID: 33019123 DOI: 10.1109/embc44109.2020.9176206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Mild hyperthermia has been clinically employed as an adjuvant for radiation/chemotherapy and is under investigation for precise thermally-mediated delivery of cancer therapeutic agents. Magnetic Resonance Imaging (MRI) facilitates non-invasive, real-time spatial thermometry for monitoring and guiding hyperthermia procedures. Long image acquisition time during MR-guided hyperthermia may fail to capture rapid changes in temperature. This may lead to unwanted heating of healthy tissue and/or temperature rise above hyperthermic range. We have developed a block-based compressed sensing approach to reconstruct volumetric MR-derived microwave hyperthermia temperature profiles using a subset of measured data. This algorithm exploits the sparsity of MR images due to the presence of inter- and intra-slice correlation of hyperthermic MR-derived temperature profiles. We have evaluated the performance of our developed algorithm on a phantom and in vivo in mice using previously implemented microwave applicators. This algorithm reconstructs 3D temperature profiles with PSNR of 33 dB - 49 dB in comparison to the original profiles. In summary, this study suggests that microwave hyperthermia induced temperature profiles can be reconstructed using subsamples to reduce MR image acquisition time.

Reducing temperature errors in transcranial MR-guided focused ultrasound using a reduced-field-of-view sequence

PURPOSE

To reduce temperature errors due to water motion in transcranial MR-guided focused ultrasound (tcMRgFUS) ablation.

THEORY AND METHODS

In tcMRgFUS, water is circulated in the transducer bowl around the patient's head for acoustic coupling and heat removal. The water moves during sonications that are monitored by MR thermometry, which causes it to alias into the brain and create temperature errors. To reduce these errors, a two-dimensional excitation pulse was implemented in a gradient-recalled echo thermometry sequence. The pulse suppresses water signal by selectively exciting the brain only, which reduces the imaging FOV. Improvements in temperature precision compared to the conventional full-FOV scan were evaluated in healthy subject scans outside the tcMRgFUS system, gel phantom scans in the system with heating, and in 2×-accelerated head phantom scans in the system without heating.

RESULTS

In vivo temperature precision (standard deviation of temperature errors) outside the tcMRgFUS system was improved 43% on average, due to the longer TR and TE of the reduced-FOV sequence. In the phantom heating experiments, the hot spot was less distorted in the reduced-FOV scans, and background temperature precision was improved 59% on average. In the accelerated head phantom temperature reconstructions, temperature precision was improved 89% using the reduced-FOV sequence.

CONCLUSIONS

Reduced-FOV temperature imaging alleviates temperature errors due to water bath motion in tcMRgFUS, and enables accelerated temperature mapping with greater precision.

Simultaneous multislice MRI thermometry with a single coil using incoherent blipped-controlled aliasing

PURPOSE

To increase volume coverage in real-time MR thermometry for transcranial MR-guided focused ultrasound (tcMRgFUS) ablation, without multiple receive coils.

THEORY AND METHODS

Multiband excitation and incoherent blipped-controlled aliasing were implemented in a 2DFT pulse sequence used clinically for tcMRgFUS, and an extended k-space hybrid reconstruction was developed that recovers slice-separated temperature maps assuming that heating is focal, given slice-separated pretreatment images. Simulations were performed to characterize slice leakage, the number of slices that can be simultaneously imaged with low-temperature error, and robustness across random slice-phase k-space permutations. In vivo experiments were performed using a single receive coil without heating to measure temperature precision, and gel phantom FUS experiments were performed to test the method with heating and with a water bath.

RESULTS

Simulations showed that with large hot spots and identical magnitude images on each slice, up to three slices can be simultaneously imaged with less than 1 ∘ C temperature root-mean-square error. They also showed that hot spots do not alias coherently between slices, and that an average 86% of random slice-phase k-space permutations yielded less than 1 ∘ C temperature error. Temperature precision was not degraded compared to single-slice imaging in the in vivo SMS scans, and the gel phantom SMS temperature maps closely tracked single-slice temperature in the hot spot, with no coherent aliasing to other slices.

CONCLUSIONS

Incoherent controlled aliasing SMS enables accurate reconstruction of focal heating maps from two or three slices simultaneously, using a single receive coil and a sparsity-promoting temperature reconstruction.

Magnetic resonance thermometry and its biological applications - Physical principles and practical considerations

Most parameters that influence the magnetic resonance imaging (MRI) signal experience a temperature dependence. The fact that MRI can be used for non-invasive measurements of temperature and temperature change deep inside the human body has been known for over 30 years. Today, MR temperature imaging is widely used to monitor and evaluate thermal therapies such as radio frequency, microwave, laser, and focused ultrasound therapy. In this paper we cover the physical principles underlying the biological applications of MR temperature imaging and discuss practical considerations and remaining challenges. For biological tissue, the MR signal of interest comes mostly from hydrogen protons of water molecules but also from protons in, e.g., adipose tissue and various metabolites. Most of the discussed methods, such as those using the proton resonance frequency (PRF) shift, T₁, T₂, and diffusion only measure temperature change, but measurements of absolute temperatures are also possible using spectroscopic imaging methods (taking advantage of various metabolite signals as internal references) or various types of contrast agents. Currently, the PRF method is the most used clinically due to good sensitivity, excellent linearity with temperature, and because it is largely independent of tissue type. Because the PRF method does not work in adipose tissues, T₁- and T₂-based methods have recently gained interest for monitoring temperature change in areas with high fat content such as the breast and abdomen. Absolute temperature measurement methods using spectroscopic imaging and contrast agents often offer too low spatial and temporal resolution for accurate monitoring of ablative thermal procedures, but have shown great promise in monitoring the slower and usually less spatially localized temperature change observed during hyperthermia procedures. Much of the current research effort for ablative procedures is aimed at providing faster measurements, larger field-of-view coverage, simultaneous monitoring in aqueous and adipose tissues, and more motion-insensitive acquisitions for better precision measurements in organs such as the heart, liver, and kidneys. For hyperthermia applications, larger coverage, motion insensitivity, and simultaneous aqueous and adipose monitoring are also important, but great effort is also aimed at solving the problem of long-term field drift which gets interpreted as temperature change when using the PRF method.

Improved MR thermometry for laser interstitial thermotherapy

OBJECTIVES

To develop, test and evaluate improved 2D and 3D protocols for proton resonance frequency shift magnetic resonance temperature imaging (MRTI) of laser interstitial thermal therapy (LITT). The objective was to develop improved MRTI protocols in terms of temperature measurement precision and volume coverage compared to the 2D MRTI protocol currently used with a commercially available LITT system.

METHODS

Four different 2D protocols and four different 3D protocols were investigated. The 2D protocols used multi-echo readouts to prolong the total MR sampling time and hence the MRTI precision, without prolonging the total acquisition time. The 3D protocols provided volumetric thermometry by acquiring a slab of 12 contiguous slices in the same acquisition time as the 2D protocols. The study only considered readily available pulse sequences (Cartesian 2D and 3D gradient recalled echo and echo planar imaging [EPI]) and methods (partial Fourier and parallel imaging) to ensure wide availability and rapid clinical implementation across vendors and field strengths. In vivo volunteer studies were performed to investigate and compare MRTI precision and image quality. Phantom experiments with LITT heating were performed to investigate and compare MRTI precision and accuracy. Different coil setups were used in the in vivo studies to assess precision differences between using local (such as flex and head coils) and non-local (i.e., body coil) receive coils. Studies were performed at both 1.5 T and 3 T.

RESULTS

The improved 2D protocols provide up to a factor of two improvement in the MRTI precision in the same acquisition time, compared to the currently used clinical protocol. The 3D echo planar imaging protocols provide comparable precision as the currently used 2D clinical protocol, but over a substantially larger field of view, without increasing the acquisition time. As expected, local receive coils perform substantially better than the body coil, and 3 T provides better MRTI accuracy and precision than 1.5 T. 3D data can be zero-filled interpolated in all three dimensions (as opposed to just two dimensions for 2D data), reducing partial volume effects and measuring higher maximum temperature rises.

CONCLUSIONS

With the presented protocols substantially improved MRTI precision (for 2D imaging) or greatly improved field of view coverage (for 3D imaging) can be achieved in the same acquisition time as the currently used protocol. Only widely available pulse sequences and acquisition methods were investigated, which should ensure quick translation to the clinic. Lasers Surg. Med. 51:286-300, 2019. © 2019 Wiley Periodicals, Inc.

Validation of hybrid angular spectrum acoustic and thermal modelling in phantoms

In focused ultrasound (FUS) thermal ablation of diseased tissue, acoustic beam and thermal simulations enable treatment planning and optimization. In this study, a treatment-planning methodology that uses the hybrid angular spectrum (HAS) method and the Pennes' bioheat equation (PBHE) is experimentally validated in homogeneous tissue-mimicking phantoms. Simulated three-dimensional temperature profiles are compared to volumetric MR thermometry imaging (MRTI) of FUS sonications in the phantoms, whose acoustic and thermal properties are independently measured. Additionally, Monte Carlo (MC) uncertainty analysis is performed to quantify the effect of tissue property uncertainties on simulation results. The mean error between simulated and experimental spatiotemporal peak temperature rise was +0.33°C (+6.9%). Despite this error, the experimental temperature rise fell within the expected uncertainty of the simulation, as determined by the MC analysis. The average errors of the simulated transverse and longitudinal full width half maximum (FWHM) of the profiles were -1.9% and 7.5%, respectively. A linear regression and local sensitivity analysis revealed that simulated temperature amplitude is more sensitive to uncertainties in simulation inputs than in the profile width and shape. Acoustic power, acoustic attenuation and thermal conductivity had the greatest impact on peak temperature rise uncertainty; thermal conductivity and volumetric heat capacity had the greatest impact on FWHM uncertainty. This study validates that using the HAS and PBHE method can adequately predict temperature profiles from single sonications in homogeneous media. Further, it informs the need to accurately measure or predict patient-specific properties for improved treatment planning of ablative FUS surgeries.

Effect of k-space-weighted image contrast and ultrasound focus size on the accuracy of proton resonance frequency thermometry

PURPOSE

To construct a predictive model that describes how the duration and symmetry of a k-space-weighted image contrast (KWIC) window affects the temporal resolution of differently sized ultrasound foci when using a pseudo-golden angle stack-of-stars acquisition.

METHODS

We performed a modulation analysis of proton resonance frequency temperature measurements to create the temporal modulation transfer function for KWIC windows of different symmetry and temporal duration. We reconstructed simulated ultrasound heating trajectories and stack-of-stars k-space data as well as experimental phantom data using the same trajectories. Images were reconstructed using symmetric and asymmetric KWIC windows of 3 different temporal durations. Simulated results were compared against temporal modulation transfer function predictions, experimental results, and the original simulated temperatures.

RESULTS

The temporal modulation transfer function shows that temporal resolution with KWIC reconstructions depend on the object size. The KWIC window duration affected SNR and severity of undersampling artifacts. Accuracy and response delay improved as the KWIC window duration decreased or the size of the heated region within the KWIC plane increased. Precision worsened as the window duration decreased. Using a symmetric window eliminated the response delay to heated region size but introduced a large reconstruction delay.

CONCLUSION

The accuracy and precision of proton resonance frequency temperature measurements from a stack-of-stars acquisition using a sliding KWIC window reconstruction are dependent on the size of the KWIC window and the size and shape of the heated region. The temporal modulation transfer function of KWIC reconstructions for any object size can predict the temporal response to changes in signal being acquired, such as temperature and contrast enhancement.

Motion Correction in Proton Resonance Frequency-based Thermometry in the Liver

The unique ability of magnetic resonance imaging to measure temperature noninvasively, in vivo, makes it an attractive tool for monitoring interventional procedures, such as radiofrequency or microwave ablation in real-time. The most frequently used approach for magnetic resonance-based temperature measurement is proton resonance frequency (PRF) thermometry. Although it has many advantages, including tissue-independence and real-time capability, the main drawback is its motion sensitivity. This is likely the reason PRF thermometry in moving organs, such as the liver, is not commonly used in the clinical arena. In recent years, however, several developments suggest that motion-corrected thermometry in the liver is achievable. The present article summarizes the diverse attempts to correct thermometry in the liver. Therefore, the physical principle of PRF is introduced, with additional references for necrosis zone estimation and how to deal with fat phase modulation, and main magnetic field drifts. The primary categories of motion correction are presented, including general methods for motion compensation and library-based approaches, and referenceless thermometry and hybrid methods. Practical validation of the described methods in larger patient groups will be necessary to establish accurate motion-corrected thermometry in the clinical arena, with the goal of complete liver tumor ablation.

A spiral-based volumetric acquisition for MR temperature imaging

PURPOSE

To develop a rapid pulse sequence for volumetric MR thermometry.

METHODS

Simulations were carried out to assess temperature deviation, focal spot distortion/blurring, and focal spot shift across a range of readout durations and maximum temperatures for Cartesian, spiral-out, and retraced spiral-in/out (RIO) trajectories. The RIO trajectory was applied for stack-of-spirals 3D imaging on a real-time imaging platform and preliminary evaluation was carried out compared to a standard 2D sequence in vivo using a swine brain model, comparing maximum and mean temperatures measured between the two methods, as well as the temporal standard deviation measured by the two methods.

RESULTS

In simulations, low-bandwidth Cartesian trajectories showed substantial shift of the focal spot, whereas both spiral trajectories showed no shift while maintaining focal spot geometry. In vivo, the 3D sequence achieved real-time 4D monitoring of thermometry, with an update time of 2.9-3.3 s.

CONCLUSION

Spiral imaging, and RIO imaging in particular, is an effective way to speed up volumetric MR thermometry. Magn Reson Med 79:3122-3127, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Volumetric MRI thermometry using a three-dimensional stack-of-stars echo-planar imaging pulse sequence

PURPOSE

To measure temperature over a large brain volume with fine spatiotemporal resolution.

METHODS

A three-dimensional stack-of-stars echo-planar imaging sequence combining echo-planar imaging and radial sampling with golden angle spacing was implemented at 3T for proton resonance frequency-shift temperature imaging. The sequence acquires a 188x188x43 image matrix with 1.5x1.5x2.75 mm3 spatial resolution. Temperature maps were reconstructed using sensitivity encoding (SENSE) image reconstruction followed by the image domain hybrid method, and using the k-space hybrid method. In vivo temperature maps were acquired without heating to measure temperature precision in the brain, and in a phantom during high-intensity focused ultrasound sonication.

RESULTS

In vivo temperature standard deviation was less than 1°C at dynamic scan times down to 0.75 s. For a given frame rate, scanning at a minimum repetition time (TR) with minimum acceleration yielded the lowest standard deviation. With frame rates around 3 s, the scan was tolerant to a small number of receive coils, and temperature standard deviation was 48% higher than a standard two-dimensional Fourier transform temperature mapping scan, but provided whole-brain coverage. Phantom temperature maps with no visible aliasing were produced for dynamic scan times as short as 0.38 s. k-Space hybrid reconstructions were more tolerant to acceleration.

CONCLUSION

Three-dimensional stack-of-stars echo-planar imaging temperature mapping provides volumetric brain coverage and fine spatiotemporal resolution. Magn Reson Med 79:2003-2013, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Simultaneous MR thermometry and acoustic radiation force imaging using interleaved acquisition

PURPOSE

A novel and practical method for simultaneously performing MR acoustic radiation force imaging (ARFI) and proton resonance frequency (PRF)-shift thermometry has been developed and tested. This could be an important tool for evaluating the success of MR-guided focused ultrasound procedures for which MR-thermometry measures temperature and thermal dose and MR-ARFI detects changes in tissue mechanical properties.

METHODS

MR imaging was performed using a gradient recalled echo segmented echo-planar imaging pulse sequence with bipolar motion encoding gradients (MEG). Images with ultrasound pulses (ON) and without ultrasound pulses (OFF) during the MEG were interleaved at the repetition time (TR) level. ARFI displacements were calculated by complex subtraction of ON-OFF images, and PRF temperature maps were calculated by baseline subtraction. Evaluations in tissue-mimicking phantoms and ex vivo porcine brain tissue were performed. Constrained reconstruction improved the temporal resolution of dynamic measurements.

RESULTS

Simultaneous maps of displacement and temperature were acquired in 2D and 3D while keeping tissue heating < 1°C. Accuracy of the temperature maps was comparable to the standard PRF sequence. Using constrained reconstruction and subsampled k-space (R = 4.33), 3D simultaneous temperature and displacement maps can be acquired every 4.7 s.

CONCLUSION

This new sequence acquires simultaneous temperature and displacement maps with minimal tissue heating, and can be applied dynamically for monitoring tissue mechanical properties during ablation procedures. Magn Reson Med 79:1515-1524, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Multiecho pseudo-golden angle stack of stars thermometry with high spatial and temporal resolution using k-space weighted image contrast

PURPOSE

Implement and evaluate a 3D MRI method to measure temperature changes with high spatial and temporal resolution and large field of view.

METHODS

A multiecho pseudo-golden angle stack-of-stars (SOS) sequence with k-space weighted image contrast (KWIC) reconstruction was implemented to simultaneously measure multiple quantities, including temperature, initial signal magnitude M(0), transverse relaxation time ( T2*), and water/fat images. Respiration artifacts were corrected using self-navigation. KWIC artifacts were removed using a multi-baseline library. The phases of the multiple echo images were combined to improve proton resonance frequency precision. Temperature precision was tested through in vivo breast imaging (N = 5 healthy volunteers) using both coronal and sagittal orientations and with focused ultrasound (FUS) heating in a pork phantom using a breast specific MR-guided FUS system.

RESULTS

Temperature measurement precision was significantly improved after echo combination when compared with the no echo combination case (spatial average of the standard deviation through time of 0.3-1.0 and 0.7-1.9°C, respectively). Temperature measurement accuracy during heating was comparable to a 3D seg-EPI sequence. M(0) and T2* values showed temperature dependence during heating in pork adipose tissue.

CONCLUSION

A self-navigated 3D multiecho SOS sequence with dynamic KWIC reconstruction is a promising thermometry method that provides multiple temperature sensitive quantitative values. Magn Reson Med 79:1407-1419, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Accelerated magnetic resonance thermometry in the presence of uncertainties

A model-based information theoretic approach is presented to perform the task of magnetic resonance (MR) thermal image reconstruction from a limited number of observed samples on k-space. The key idea of the proposed approach is to optimally detect samples of k-space that are information-rich with respect to a model of the thermal data acquisition. These highly informative k-space samples can then be used to refine the mathematical model and efficiently reconstruct the image. The information theoretic reconstruction was demonstrated retrospectively in data acquired during MR-guided laser induced thermal therapy (MRgLITT) procedures. The approach demonstrates that locations with high-information content with respect to a model-based reconstruction of MR thermometry may be quantitatively identified. These information-rich k-space locations are demonstrated to be useful as a guide for k-space undersampling techniques. The effect of interactively increasing the predicted number of data points used in the subsampled model-based reconstruction was quantified using the L2-norm of the distance between the subsampled and fully sampled reconstruction. Performance of the proposed approach was also compared with uniform rectilinear subsampling and variable-density Poisson disk subsampling techniques. The proposed subsampling scheme resulted in accurate reconstructions using a small fraction of k-space points, suggesting that the reconstruction technique may be useful in improving the efficiency of thermometry data temporal resolution.

Kalman Filtered Bio Heat Transfer Model Based Self-adaptive Hybrid Magnetic Resonance Thermometry

To develop a self-adaptive and fast thermometry method by combining the original hybrid magnetic resonance thermometry method and the bio heat transfer equation (BHTE) model. The proposed Kalman filtered Bio Heat Transfer Model Based Self-adaptive Hybrid Magnetic Resonance Thermometry, abbreviated as KalBHT hybrid method, introduced the BHTE model to synthesize a window on the regularization term of the hybrid algorithm, which leads to a self-adaptive regularization both spatially and temporally with change of temperature. Further, to decrease the sensitivity to accuracy of the BHTE model, Kalman filter is utilized to update the window at each iteration time. To investigate the effect of the proposed model, computer heating simulation, phantom microwave heating experiment and dynamic in-vivo model validation of liver and thoracic tumor were conducted in this study. The heating simulation indicates that the KalBHT hybrid algorithm achieves more accurate results without adjusting λ to a proper value in comparison to the hybrid algorithm. The results of the phantom heating experiment illustrate that the proposed model is able to follow temperature changes in the presence of motion and the temperature estimated also shows less noise in the background and surrounding the hot spot. The dynamic in-vivo model validation with heating simulation demonstrates that the proposed model has a higher convergence rate, more robustness to susceptibility problem surrounding the hot spot and more accuracy of temperature estimation. In the healthy liver experiment with heating simulation, the RMSE of the hot spot of the proposed model is reduced to about 50% compared to the RMSE of the original hybrid model and the convergence time becomes only about one fifth of the hybrid model. The proposed model is able to improve the accuracy of the original hybrid algorithm and accelerate the convergence rate of MR temperature estimation.

Specialized volumetric thermometry for improved guidance of MRgFUS in brain

PURPOSE

MR thermometry is critical for safe and effective transcranial focused ultrasound. The current single-slice MR thermometry sequence cannot achieve all desired treatment monitoring requirements. We propose an approach in which the imaging requirements of different aspects of treatment monitoring are met by optimizing multiple sequences.

METHODS

Imaging requirements were determined for three stages of MR-guided focused ultrasound brain treatment: 1) focal spot localization, 2) focal spot monitoring, and 3) background monitoring. Multiple-echo spiral thermometry sequences were optimized for each set of requirements and then validated with in vivo signal-to-noise ratio measurements and with phantom heating experiments.

RESULTS

Each of the proposed sequences obtained better precision than the current two-dimensional Fourier transform (2DFT) thermometry sequence. Five-slice focal spot localization achieved two-fold better resolution with 1.9-fold better precision but two-fold longer acquisition compared to 2DFT. Five-slice focal monitoring achieved 2.1-fold better precision with similar speed but 12% larger voxels than 2DFT. Full-brain background monitoring was demonstrated in both axial (7.1 s) and sagittal (11.4 s) orientations. Phantom heating time curves were consistent across all sequences after correcting for resolution.

CONCLUSION

Multiple-echo spiral imaging significantly improves MR thermometry efficiency, enabling multiple-slice monitoring. Optimizing multiple specialized sequences provides better performance than can be achieved by any single sequence. Magn Reson Med 78:508-517, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

MR thermometry for focused ultrasound monitoring utilizing model predictive filtering and ultrasound beam modeling

Background

A major challenge in using magnetic resonance temperature imaging (MRTI) to monitor focused ultrasound (FUS) applications is achieving high spatio-temporal resolution over a large field of view (FOV). This is important to accurately monitor all ultrasound (US) power depositions. Magnetic resonance (MR) subsampling in conjunction with thermal model-based reconstruction of the MRTI utilizing Pennes bioheat transfer equation (PBTE) is one promising approach. The thermal properties used in the thermal model are often estimated from a pre-treatment, low-power sonication.

Methods

In this proof-of-concept study we investigate the use of US simulations computed using the hybrid angular spectrum (HAS) method to estimate the US power deposition density Q, thereby avoiding the pre-treatment sonication and any potential tissue damage. MRTI reconstructions are performed using a thermal model-based reconstruction method called model predictive filtering (MPF). Experiments are performed in a homogeneous gelatin phantom and in a gelatin phantom with embedded plastic skull. MPF reconstructions are compared to separate sonications imaged with fully sampled data over a smaller FOV. Temperature root-mean-square errors (RMSE) and focal spot positions and shapes are evaluated.

Results

HAS simulations accurately predict the location of the focal spot (to within 1 mm) in both phantoms. Accurate temperature maps (RMSE below 1 °C), where the location of the focal spot agrees well with fully sampled “truth” (to within 1 mm), are also achieved in both phantoms.

Conclusions

HAS simulations can be used to accurately predict the focal spot location in homogeneous media and when focusing through an aberrating plastic skull. The HAS simulated power deposition (Q) patterns can be used in the MPF thermal model-based reconstruction to obtain accurate temperature maps with high spatio-temporal resolution over large FOVs.

Fast temperature estimation from undersampled k-space with fully-sampled center for MR guided microwave ablation

PURPOSE

This study aims to accelerate MR temperature imaging using the proton resonance frequency (PRF) shift method for real time temperature monitoring during thermal ablation.

MATERIALS AND METHODS

The proposed method estimates temperature changes from undersampled k-space with a fully sampled center. This proposed algorithm is based on the hybrid multi-baseline and referenceless treatment image model and can be seen as an extension of the conventional k-space-based hybrid thermometry. The parameters of hybrid model are acquired by utilizing information from low resolution images which are obtained from fully-sampled centers of k-space. Registration is used to correct temperature errors due to the displacement of the subject. Phantom heating simulations, motion simulations, phantom heating and in-vivo experiments were performed to investigate the efficiency of the proposed method. SPIRiT and the conventional k-space estimation reconstruction thermometry were implemented for comparison using the same sampling pattern.

RESULTS

The phantom heating simulations showed that the proposed method results in lower RMSEs than the conventional k-space hybrid thermometry and SPIRiT at various reduction factors tested. The motion simulations indicated the robustness of the proposed method to displacement of the subject. Phantom heating experiment further demonstrated the ability of the method to reconstruct temperature maps with less computation time and higher accuracy (RMSEs lower than 0.4°C) at a net reduction factor of 3.5 in the presence of large noise caused by a microwave needle. In-vivo experiments validated the feasibility of the proposed method to estimate temperature changes from undersampled k-space (net reduction factor 4.3) in presence of respiratory motion and complicated anatomical structure, while reducing computation time as much as 10-fold compared with the conventional k-space method.

CONCLUSION

The proposed method accelerates the PRF-shift MR thermometry and provides more accurate temperature maps in presence of motion with relatively short computation time, which may make real time imaging for MR-guided microwave ablation possible.

Analytical estimation of ultrasound properties, thermal diffusivity, and perfusion using magnetic resonance-guided focused ultrasound temperature data

For thermal modeling to play a significant role in treatment planning, monitoring, and control of magnetic resonance-guided focused ultrasound (MRgFUS) thermal therapies, accurate knowledge of ultrasound and thermal properties is essential. This study develops a new analytical solution for the temperature change observed in MRgFUS which can be used with experimental MR temperature data to provide estimates of the ultrasound initial heating rate, Gaussian beam variance, tissue thermal diffusivity, and Pennes perfusion parameter. Simulations demonstrate that this technique provides accurate and robust property estimates that are independent of the beam size, thermal diffusivity, and perfusion levels in the presence of realistic MR noise. The technique is also demonstrated in vivo using MRgFUS heating data in rabbit back muscle. Errors in property estimates are kept less than 5% by applying a third order Taylor series approximation of the perfusion term and ensuring the ratio of the fitting time (the duration of experimental data utilized for optimization) to the perfusion time constant remains less than one.

Prior image based temporally constrained reconstruction algorithm for magnetic resonance guided high intensity focused ultrasound

PURPOSE

A prior image based temporally constrained reconstruction (PITCR) algorithm was developed for obtaining accurate temperature maps having better volume coverage, and spatial, and temporal resolution than other algorithms for highly undersampled data in magnetic resonance (MR) thermometry.

METHODS

The proposed PITCR approach is an algorithm that gives weight to the prior image and performs accurate reconstruction in a dynamic imaging environment. The PITCR method is compared with the temporally constrained reconstruction (TCR) algorithm using pork muscle data.

RESULTS

The PITCR method provides superior performance compared to the TCR approach with highly undersampled data. The proposed approach is computationally expensive compared to the TCR approach, but this could be overcome by the advantage of reconstructing with fewer measurements. In the case of reconstruction of temperature maps from 16% of fully sampled data, the PITCR approach was 1.57× slower compared to the TCR approach, while the root mean square error using PITCR is 0.784 compared to 2.815 with the TCR scheme.

CONCLUSIONS

The PITCR approach is able to perform more accurate reconstructions of temperature maps compared to the TCR approach with highly undersampled data in MR guided high intensity focused ultrasound.

Respiration artifact correction in three-dimensional proton resonance frequency MR thermometry using phase navigators

PURPOSE

To develop reliable three-dimensional (3D) segmented echo planar imaging (seg-EPI) proton resonance frequency (PRF) temperature monitoring in the presence of respiration-induced B0 variation.

METHODS

A free induction decay (FID) phase navigator was inserted into a 3D seg-EPI sequence before and after EPI readout to monitor B0 field variations. Using the field change estimates, the phase of each k-space line was adjusted to remove the additional phase from the respiratory induced off-resonance. This correction technique was evaluated while heating with MR-guided focused ultrasound (MRgFUS) in phantoms with simulated breathing and during nonheating conditions in healthy in vivo breasts.

RESULTS

With k-space phase correction, the standard deviation of magnitude images and PRF temperature measurements in breast from five volunteers improved by an average factor of 1.5 and 2.1, respectively. Improved accuracy of temperature estimates was observed after correction while heating with MRgFUS in phantoms.

CONCLUSION

Phase correction based on two FID navigators placed before and after the echo train provides promising results for implementing 3D monitoring of thermal therapy treatments in the presence of field variations due to respiration. Magn Reson Med 76:206-213, 2016. © 2015 Wiley Periodicals, Inc.

Sampling strategies for subsampled segmented EPI PRF thermometry in MR guided high intensity focused ultrasound

PURPOSE

To investigate k-space subsampling strategies to achieve fast, large field-of-view (FOV) temperature monitoring using segmented echo planar imaging (EPI) proton resonance frequency shift thermometry for MR guided high intensity focused ultrasound (MRgHIFU) applications.

METHODS

Five different k-space sampling approaches were investigated, varying sample spacing (equally vs nonequally spaced within the echo train), sampling density (variable sampling density in zero, one, and two dimensions), and utilizing sequential or centric sampling. Three of the schemes utilized sequential sampling with the sampling density varied in zero, one, and two dimensions, to investigate sampling the k-space center more frequently. Two of the schemes utilized centric sampling to acquire the k-space center with a longer echo time for improved phase measurements, and vary the sampling density in zero and two dimensions, respectively. Phantom experiments and a theoretical point spread function analysis were performed to investigate their performance. Variable density sampling in zero and two dimensions was also implemented in a non-EPI GRE pulse sequence for comparison. All subsampled data were reconstructed with a previously described temporally constrained reconstruction (TCR) algorithm.

RESULTS

The accuracy of each sampling strategy in measuring the temperature rise in the HIFU focal spot was measured in terms of the root-mean-square-error (RMSE) compared to fully sampled "truth." For the schemes utilizing sequential sampling, the accuracy was found to improve with the dimensionality of the variable density sampling, giving values of 0.65 °C, 0.49 °C, and 0.35 °C for density variation in zero, one, and two dimensions, respectively. The schemes utilizing centric sampling were found to underestimate the temperature rise, with RMSE values of 1.05 °C and 1.31 °C, for variable density sampling in zero and two dimensions, respectively. Similar subsampling schemes with variable density sampling implemented in zero and two dimensions in a non-EPI GRE pulse sequence both resulted in accurate temperature measurements (RMSE of 0.70 °C and 0.63 °C, respectively). With sequential sampling in the described EPI implementation, temperature monitoring over a 192×144×135 mm3 FOV with a temporal resolution of 3.6 s was achieved, while keeping the RMSE compared to fully sampled "truth" below 0.35 °C.

CONCLUSIONS

When segmented EPI readouts are used in conjunction with k-space subsampling for MR thermometry applications, sampling schemes with sequential sampling, with or without variable density sampling, obtain accurate phase and temperature measurements when using a TCR reconstruction algorithm. Improved temperature measurement accuracy can be achieved with variable density sampling. Centric sampling leads to phase bias, resulting in temperature underestimations.

Spatio-temporal quantitative thermography of pre-focal interactions between high intensity focused ultrasound and the rib cage

OBJECTIVE

The aim of this paper is to quantitatively investigate the thermal effects generated by the pre-focal interactions of a HIFU beam with a rib cage, in the context of minimally invasive transcostal therapy of liver malignancies.

MATERIALS AND METHODS

HIFU sonications were produced by a phased-array MR-compatible transducer on Turkey muscle placed on a sheep thoracic cage specimen. The thoracic wall was positioned in the pre-focal zone 3.5 to 6.5 cm below the focus. Thermal monitoring was simultaneously performed using fluoroptic sensors inserted into the medullar cavity of the ribs and high resolution MR-thermometry (voxel: 1 × 1 × 5 mm3, four multi-planar slices).

RESULTS

MR-thermometry data indicated nearly isotropic distribution of the thermal energy at the ribs' surface. The temperature elevation at the focus was comparable with the pericostal temperature elevation around unprotected ribs, while being systematically inferior, by more than a factor of four on average, to the intra-medullar values. The spatial profiles of the pericostal and intra-medullar thermal build-up measurements could be smoothly connected using a Gaussian function. The dynamics of the post-sonication thermal relaxation as determined by fluoroptic measurements was demonstrated to be theoretically coherent with the experimental observations.

CONCLUSION

The experimental findings motivate further efforts for the transfer towards clinical routine of effective rib-sparing strategies for hepatic HIFU.

Model predictive filtering MR thermometry: Effects of model inaccuracies, k-space reduction factor, and temperature increase rate

PURPOSE

Evaluate effects of model parameter inaccuracies (thermal conductivity, k, and ultrasound power deposition density, Q), k-space reduction factor (R), and rate of temperature increase ( T˙) in a thermal model-based reconstruction for MR-thermometry during focused-ultrasound heating.

METHODS

Simulations and ex vivo experiments were performed to investigate the accuracy of the thermal model and the model predictive filtering (MPF) algorithm for varying R and T˙, and their sensitivity to errors in k and Q. Ex vivo data was acquired with a segmented EPI pulse sequence to achieve large field-of-view (192 × 162 × 96 mm) four-dimensional temperature maps with high spatiotemporal resolution (1.5 × 1.5 × 2.0 mm, 1.7 s).

RESULTS

In the simulations, 50% errors in k and Q resulted in maximum temperature root mean square errors (RMSE) of 6 °C for model only and 3 °C for MPF. Using recently developed methods, estimates of k and Q were accurate to within 3%. The RMSE between MPF and true temperature increased with R and T˙. In the ex vivo study the RMSE remained below 0.7 °C for R ranging from 4 to 12 and T˙ of 0.28-0.75 °C/s.

CONCLUSION

Errors in MPF temperatures occur due to errors in k and Q. These MPF temperature errors increase with increase in R and T˙, but are smaller than those obtained using the thermal model alone.

Accelerated MRI thermometry by direct estimation of temperature from undersampled k-space data

PURPOSE

Acceleration of magnetic resonance (MR) thermometry is desirable for several applications of MR-guided focused ultrasound, such as those requiring greater volume coverage, higher spatial resolution, or higher frame rates.

METHODS

We propose and validate a constrained reconstruction method that estimates focal temperature changes directly from k-space without spatial or temporal regularization. A model comprising fully-sampled baseline images is fit to undersampled k-space data, which removes aliased temperature maps from the solution space. Reconstructed temperature maps are compared to maps reconstructed using parallel imaging (iterative self-consistent parallel imaging reconstruction [SPIRiT]) and conventional hybrid thermometry, and temporally constrained reconstruction thermometry.

RESULTS

Temporal step response simulations demonstrate finer temporal resolution and lower error in 4×-undersampled radial k-space reconstructions compared to temporally constrained reconstruction. Simulations show that the k-space method can achieve higher accelerations with multiple receive coils. Phantom heating experiments further demonstrate the algorithm's advantage over reconstructions relying on parallel imaging alone to overcome undersampling artifacts. In vivo model error comparisons show the algorithm achieves low temperature error at higher acceleration factors (up to 32× with a radial trajectory) than compared reconstructions.

CONCLUSION

High acceleration factors can be achieved using the proposed temperature reconstruction algorithm, without sacrificing temporal resolution or accuracy.

Generalised polynomial chaos-based uncertainty quantification for planning MRgLITT procedures

PURPOSE

A generalised polynomial chaos (gPC) method is used to incorporate constitutive parameter uncertainties within the Pennes representation of bioheat transfer phenomena. The stochastic temperature predictions of the mathematical model are critically evaluated against MR thermometry data for planning MR-guided laser-induced thermal therapies (MRgLITT).

METHODS

The Pennes bioheat transfer model coupled with a diffusion theory approximation of laser tissue interaction was implemented as the underlying deterministic kernel. A probabilistic sensitivity study was used to identify parameters that provide the most variance in temperature output. Confidence intervals of the temperature predictions are compared to MR temperature imaging (MRTI) obtained during phantom and in vivo canine (n = 4) MRgLITT experiments. The gPC predictions were quantitatively compared to MRTI data using probabilistic linear and temporal profiles as well as 2-D 60 °C isotherms.

RESULTS

Optical parameters provided the highest variance in the model output (peak standard deviation: anisotropy 3.51 °C, absorption 2.94 °C, scattering 1.84 °C, conductivity 1.43 °C, and perfusion 0.94 °C). Further, within the statistical sense considered, a non-linear model of the temperature and damage-dependent perfusion, absorption, and scattering is captured within the confidence intervals of the linear gPC method. Multivariate stochastic model predictions using parameters with the dominant sensitivities show good agreement with experimental MRTI data.

CONCLUSIONS

Given parameter uncertainties and mathematical modelling approximations of the Pennes bioheat model, the statistical framework demonstrates conservative estimates of the therapeutic heating and has potential for use as a computational prediction tool for thermal therapy planning.

Extended Kalman filtering for continuous volumetric MR-temperature imaging

Real time magnetic resonance (MR) thermometry has evolved into the method of choice for the guidance of high-intensity focused ultrasound (HIFU) interventions. For this role, MR-thermometry should preferably have a high temporal and spatial resolution and allow observing the temperature over the entire targeted area and its vicinity with a high accuracy. In addition, the precision of real time MR-thermometry for therapy guidance is generally limited by the available signal-to-noise ratio (SNR) and the influence of physiological noise. MR-guided HIFU would benefit of the large coverage volumetric temperature maps, including characterization of volumetric heating trajectories as well as near- and far-field heating. In this paper, continuous volumetric MR-temperature monitoring was obtained as follows. The targeted area was continuously scanned during the heating process by a multi-slice sequence. Measured data and a priori knowledge of 3-D data derived from a forecast based on a physical model were combined using an extended Kalman filter (EKF). The proposed reconstruction improved the temperature measurement resolution and precision while maintaining guaranteed output accuracy. The method was evaluated experimentally ex vivo on a phantom, and in vivo on a porcine kidney, using HIFU heating. On the in vivo experiment, it allowed the reconstruction from a spatio-temporally under-sampled data set (with an update rate for each voxel of 1.143 s) to a 3-D dataset covering a field of view of 142.5×285×54 mm(3) with a voxel size of 3×3×6 mm(3) and a temporal resolution of 0.127 s. The method also provided noise reduction, while having a minimal impact on accuracy and latency.

An analytical solution for improved HIFU SAR estimation

Accurate determination of the specific absorption rates (SARs) present during high intensity focused ultrasound (HIFU) experiments and treatments provides a solid physical basis for scientific comparison of results among HIFU studies and is necessary to validate and improve SAR predictive software, which will improve patient treatment planning, control and evaluation. This study develops and tests an analytical solution that significantly improves the accuracy of SAR values obtained from HIFU temperature data. SAR estimates are obtained by fitting the analytical temperature solution for a one-dimensional radial Gaussian heating pattern to the temperature versus time data following a step in applied power and evaluating the initial slope of the analytical solution. The analytical method is evaluated in multiple parametric simulations for which it consistently (except at high perfusions) yields maximum errors of less than 10% at the center of the focal zone compared with errors up to 90% and 55% for the commonly used linear method and an exponential method, respectively. For high perfusion, an extension of the analytical method estimates SAR with less than 10% error. The analytical method is validated experimentally by showing that the temperature elevations predicted using the analytical method's SAR values determined for the entire 3D focal region agree well with the experimental temperature elevations in a HIFU-heated tissue-mimicking phantom.

Kalman filtered MR temperature imaging for laser induced thermal therapies

The feasibility of using a stochastic form of Pennes bioheat model within a 3-D finite element based Kalman filter (KF) algorithm is critically evaluated for the ability to provide temperature field estimates in the event of magnetic resonance temperature imaging (MRTI) data loss during laser induced thermal therapy (LITT). The ability to recover missing MRTI data was analyzed by systematically removing spatiotemporal information from a clinical MR-guided LITT procedure in human brain and comparing predictions in these regions to the original measurements. Performance was quantitatively evaluated in terms of a dimensionless L(2) (RMS) norm of the temperature error weighted by acquisition uncertainty. During periods of no data corruption, observed error histories demonstrate that the Kalman algorithm does not alter the high quality temperature measurement provided by MR thermal imaging. The KF-MRTI implementation considered is seen to predict the bioheat transfer with RMS error < 4 for a short period of time, ∆t < 10 s, until the data corruption subsides. In its present form, the KF-MRTI method currently fails to compensate for consecutive for consecutive time periods of data loss ∆t > 10 sec.

Robust adaptive extended Kalman filtering for real time MR-thermometry guided HIFU interventions

Real time magnetic resonance (MR) thermometry is gaining clinical importance for monitoring and guiding high intensity focused ultrasound (HIFU) ablations of tumorous tissue. The temperature information can be employed to adjust the position and the power of the HIFU system in real time and to determine the therapy endpoint. The requirement to resolve both physiological motion of mobile organs and the rapid temperature variations induced by state-of-the-art high-power HIFU systems require fast MRI-acquisition schemes, which are generally hampered by low signal-to-noise ratios (SNRs). This directly limits the precision of real time MR-thermometry and thus in many cases the feasibility of sophisticated control algorithms. To overcome these limitations, temporal filtering of the temperature has been suggested in the past, which has generally an adverse impact on the accuracy and latency of the filtered data. Here, we propose a novel filter that aims to improve the precision of MR-thermometry while monitoring and adapting its impact on the accuracy. For this, an adaptive extended Kalman filter using a model describing the heat transfer for acoustic heating in biological tissues was employed together with an additional outlier rejection to address the problem of sparse artifacted temperature points. The filter was compared to an efficient matched FIR filter and outperformed the latter in all tested cases. The filter was first evaluated on simulated data and provided in the worst case (with an approximate configuration of the model) a substantial improvement of the accuracy by a factor 3 and 15 during heat up and cool down periods, respectively. The robustness of the filter was then evaluated during HIFU experiments on a phantom and in vivo in porcine kidney. The presence of strong temperature artifacts did not affect the thermal dose measurement using our filter whereas a high measurement variation of 70% was observed with the FIR filter.