Kalman filtered MR temperature imaging for laser induced thermal therapies

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.

Validating a simulation model for laser-induced thermotherapy using MR thermometry

OBJECTIVES

We want to investigate whether temperature measurements obtained from MR thermometry are accurate and reliable enough to aid the development and validation of simulation models for Laser-induced interstitial thermotherapy (LITT).

METHODS

Laser-induced interstitial thermotherapy (LITT) is applied to ex-vivo porcine livers. An artificial blood vessel is used to study the cooling effect of large blood vessels in proximity to the ablation zone. The experimental setting is simulated using a model based on partial differential equations (PDEs) for temperature, radiation, and tissue damage. The simulated temperature distributions are compared to temperature data obtained from MR thermometry.

RESULTS

The overall agreement between measurement and simulation is good for two of our four test cases, while for the remaining cases drift problems with the thermometry data have been an issue. At higher temperatures local deviations between simulation and measurement occur in close proximity to the laser applicator and the vessel. This suggests that certain aspects of the model may need some refinement.

CONCLUSION

Thermometry data is well-suited for aiding the development of simulations models since it shows where refinements are necessary and enables the validation of such models.

Unscented Kalman Filtering for Real Time Thermometry During Laser Ablation Interventions

We present a data-assimilation Bayesian framework in the context of laser ablation for the treatment of cancer. For solving the nonlinear estimation of the tissue temperature evolving during the therapy, the Unscented Kalman Filter (UKF) predicts the next thermal status and controls the ablation process, based on sparse temperature information. The purpose of this paper is to study the outcome of the prediction model based on UKF and to assess the influence of different model settings on the framework performances. In particular, we analyze the effects of the time resolution of the filter and the number and the location of the observations. Clinical Relevance - The application of a data-assimilation approach based on limited temperature information allows to monitor and predict in real-time the thermal effects induced by thermal therapy for tumors.

Model-Based Thermometry for Laser Ablation Procedure Using Kalman Filters and Sparse Temperature Measurements

In this work, we implement a data-assimilation Bayesian framework for the reconstruction of the spatiotemporal profile of the tissue temperature during laser irradiation. The predictions of a physical model simulating the heat transfer in the tissue are associated with sparse temperature measurements, using an Unscented Kalman Filter. We compare a standard state-estimation filtering procedure with a joint-estimation (state and parameters) approach: whereas in the state-estimation only the temperature is evaluated, in the joint-estimation the filter corrects also uncertain model parameters (i.e., the medium thermal diffusivity, and laser beam properties). We have tested the method on synthetic temperature data, and on the temperature measured on agar-gel phantom and porcine liver with fiber optic sensors. The joint-estimation allows retrieving an accurate estimate of the temperature distribution with a maximal error < 1.5 C in both synthetic and liver 1D data, and < 2 C in phantom 2D data. Our approach allows also suggesting a strategy for optimizing the temperature estimation based on the positions of the sensors. Under the constraint of using only two sensors, optimal temperature estimations are obtained when one sensor is placed in proximity of the source, and the other one is in a non-symmetrical position.

Temperature mapping of exothermic in situ chemistry: imaging of thermoembolization via MR

Purpose: MR temperature imaging (MRTI) was employed for visualizing the spatiotemporal evolution of the exotherm of thermoembolization, an investigative transarterial treatment for solid tumors. Materials and methods: Five explanted kidneys were injected with thermoembolic solutions, and monitored by MRTI. In three nonselective experiments, 5 ml of 4 mol/l dichloroacetyl chloride (DCA-Cl) solution in a hydrocarbon vehicle was injected via the main renal artery. For two of these three, MRTI temperature data were compared to fiber optic thermal probes. Another two kidneys received selective injections, treating only portions of the kidneys with 1 ml of 2 mol/l DCA-Cl. MRTI data were acquired and compared to changes in pre- and post-injection CT. Specimens were bisected and photographed for gross pathology 24 h post-procedure. Results: MRTI temperature estimates were within ±1 °C of the probes. In experiments without probes, MRTI measured increases of 30 °C. Some regions had not reached peak temperature by the end of the >18 min acquisition. MRTI indicated the initial heating occurred in the renal cortex, gradually spreading more proximally toward the main renal artery. Gross pathology showed the nonselective injection denatured the entire kidney whereas in the selective injections, only the treated territory was coagulated. Conclusion: The spatiotemporal evolution of thermoembolization was visualized for the first time using noninvasive MRTI, providing unique insight into the thermodynamics of thermoembolization. Précis Thermoembolization is being investigated as a novel transarterial treatment. In order to begin to characterize delivery of this novel treatment modality and aid translation from the laboratory to patients, we employ MR temperature imaging to visualize the spatiotemporal distribution of temperature from thermoembolization in ex vivo tissue.

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.

Referenceless magnetic resonance temperature imaging using Gaussian process modeling

PURPOSE

During magnetic resonance (MR)-guided thermal therapies, water proton resonance frequency shift (PRFS)-based MR temperature imaging can quantitatively monitor tissue temperature changes. It is widely known that the PRFS technique is easily perturbed by tissue motion, tissue susceptibility changes, magnetic field drift, and modality-dependent applicator-induced artifacts. Here, a referenceless Gaussian process modeling (GPM)-based estimation of the PRFS is investigated as a methodology to mitigate unwanted background field changes. The GPM offers a complementary trade-off between data fitting and smoothing and allows prior information to be used. The end result being the GPM provides a full probabilistic prediction and an estimate of the uncertainty.

METHODS

GPM was employed to estimate the covariance between the spatial position and MR phase measurements. The mean and variance provided by the statistical model extrapolated background phase values from nonheated neighboring voxels used to train the model. MR phase predictions in the heating ROI are computed using the spatial coordinates as the test input. The method is demonstrated in ex vivo rabbit liver tissue during focused ultrasound heating with manually introduced perturbations (n = 6) and in vivo during laser-induced interstitial thermal therapy to treat the human brain (n = 1) and liver (n = 1).

RESULTS

Temperature maps estimated using the GPM referenceless method demonstrated a RMS error of <0.8°C with artifact-induced reference-based MR thermometry during ex vivo heating using focused ultrasound. Nonheated surrounding areas were <0.5°C from the artifact-free MR measurements. The GPM referenceless MR temperature values and thermally damaged regions were within the 95% confidence interval during in vivo laser ablations.

CONCLUSIONS

A new approach to estimation for referenceless PRFS temperature imaging is introduced that allows for an accurate probabilistic extrapolation of the background phase. The technique demonstrated reliable temperature estimates in the presence of the background phase changes and was demonstrated useful in the in vivo brain and liver ablation scenarios presented.

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.

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.

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.

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.

An inverse problem approach to recovery of in vivo nanoparticle concentrations from thermal image monitoring of MR-guided laser induced thermal therapy

Quantification of local variations in the optical properties of tumor tissue introduced by the presence of gold-silica nanoparticles (NP) presents significant opportunities in monitoring and control of NP-mediated laser induced thermal therapy (LITT) procedures. Finite element methods of inverse parameter recovery constrained by a Pennes bioheat transfer model were applied to estimate the optical parameters. Magnetic resonance temperature imaging (MRTI) acquired during a NP-mediated LITT of a canine transmissible venereal tumor in brain was used in the presented statistical inverse problem formulation. The maximum likelihood (ML) value of the optical parameters illustrated a marked change in the periphery of the tumor corresponding with the expected location of NP and area of selective heating observed on MRTI. Parameter recovery information became increasingly difficult to infer in distal regions of tissue where photon fluence had been significantly attenuated. Finite element temperature predictions using the ML parameter values obtained from the solution of the inverse problem are able to reproduce the NP selective heating within 5 °C of measured MRTI estimations along selected temperature profiles. Results indicate the ML solution found is able to sufficiently reproduce the selectivity of the NP mediated laser induced heating and therefore the ML solution is likely to return useful optical parameters within the region of significant laser fluence.