Sj Fahrenholtz

Generalised polynomial chaos-based uncertainty quantification for planning MRgLITT procedures

Abstract 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.

A model evaluation study for treatment planning of laser-induced thermal therapy

Abstract A cross-validation analysis evaluating computer model prediction accuracy for a priori planning magnetic resonance-guided laser-induced thermal therapy (MRgLITT) procedures in treating focal diseased brain tissue is presented. Two mathematical models are considered. (1) A spectral element discretisation of the transient Pennes bioheat transfer equation is implemented to predict the laser-induced heating in perfused tissue. (2) A closed-form algorithm for predicting the steady-state heat transfer from a linear superposition of analytic point source heating functions is also considered. Prediction accuracy is retrospectively evaluated via leave-one-out cross-validation (LOOCV). Modelling predictions are quantitatively evaluated in terms of a Dice similarity coefficient (DSC) between the simulated thermal dose and thermal dose information contained within N = 22 MR thermometry datasets. During LOOCV analysis, the transient model’s DSC mean and median are 0.7323 and 0.8001 respectively, with 15 of 22 DSC values exceeding the success criterion of DSC ≥ 0.7. The steady-state model’s DSC mean and median are 0.6431 and 0.6770 respectively, with 10 of 22 passing. A one-sample, one-sided Wilcoxon signed-rank test indicates that the transient finite element method model achieves the prediction success criteria, DSC ≥ 0.7, at a statistically significant level.

Theoretical model for laser ablation outcome predictions in brain: Calibration and validation on clinical MR thermometry images

Abstract Purpose: Neurosurgical laser ablation is experiencing a renaissance. Computational tools for ablation planning aim to further improve the intervention. Here, global optimisation and inverse problems are demonstrated to train a model that predicts maximum laser ablation extent. Methods: A closed-form steady state model is trained on and then subsequently compared to N = 20 retrospective clinical MR thermometry datasets. Dice similarity coefficient (DSC) is calculated to provide a measure of region overlap between the 57 °C isotherms of the thermometry data and the model-predicted ablation regions; 57 °C is a tissue death surrogate at thermal steady state. A global optimisation scheme samples the dominant model parameter sensitivities, blood perfusion (ω) and optical parameter (μeff) values, throughout a parameter space totalling 11 440 value-pairs. This represents a lookup table of μeff–ω pairs with the corresponding DSC value for each patient dataset. The μeff–ω pair with the maximum DSC calibrates the model parameters, maximising predictive value for each patient. Finally, leave-one-out cross-validation with global optimisation information trains the model on the entire clinical dataset, and compares against the model naïvely using literature values for ω and μeff. Results: When using naïve literature values, the model’s mean DSC is 0.67 whereas the calibrated model produces 0.82 during cross-validation, an improvement of 0.15 in overlap with the patient data. The 95% confidence interval of the mean difference is 0.083–0.23 (p < 0.001). Conclusions: During cross-validation, the calibrated model is superior to the naïve model as measured by DSC, with +22% mean prediction accuracy. Calibration empowers a relatively simple model to become more predictive.

A measurement of the attenuation of radiation from F-18 by a PET/MR scanner

Abstract The attenuation of 511 keV photons by the structure of a PET/MR scanner was measured prior to energizing the magnet. The exposure rate from a source of fluorine‐18 was measured in air and, with the source placed at the isocenter of the instrument, at various points outside of the scanner. In an arc from 45 to 135 degrees relative to the long axis of the scanner and at a distance of 1.5 m from the isocenter, the attenuation by the scanner is at least 5.6 half‐value layers from the MR component alone and at least 6.6 half‐value layers with the PET insert installed. This information could inform better design of the radiation shielding for PET/MR scanners.

A heterogeneous tissue model for treatment planning for magnetic resonance-guided laser interstitial thermal therapy

Abstract We evaluated a physics-based model for planning for magnetic resonance-guided laser interstitial thermal therapy for focal brain lesions. Linear superposition of analytical point source solutions to the steady-state Pennes bioheat transfer equation simulates laser-induced heating in brain tissue. The line integral of the photon attenuation from the laser source enables computation of the laser interaction with heterogeneous tissue. Magnetic resonance thermometry data sets (n = 31) were used to calibrate and retrospectively validate the model’s thermal ablation prediction accuracy, which was quantified by the Dice similarity coefficient (DSC) between model-predicted and measured ablation regions (T > 57 °C). A Gaussian mixture model was used to identify independent tissue labels on pre-treatment anatomical magnetic resonance images. The tissue-dependent optical attenuation coefficients within these labels were calibrated using an interior point method that maximises DSC agreement with thermometry. The distribution of calibrated tissue properties formed a population model for our patient cohort. Model prediction accuracy was cross-validated using the population mean of the calibrated tissue properties. A homogeneous tissue model was used as a reference control. The median DSC values in cross-validation were 0.829 for the homogeneous model and 0.840 for the heterogeneous model. In cross-validation, the heterogeneous model produced a DSC higher than that produced by the homogeneous model in 23 of the 31 brain lesion ablations. Results of a paired, two-tailed Wilcoxon signed-rank test indicated that the performance improvement of the heterogeneous model over that of the homogeneous model was statistically significant (p < 0.01).

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.

SU-F-J-03: Treatment Planning for Laser Ablation Therapy in Presence of Heterogeneous Tissue: A Retrospective Study

PURPOSE MR guided Laser Induced Thermal Therapy (MRgLITT) is an effective technique for cancerous tissue destruction in brain. Precise modeling of the thermal ablation procedure is important for treatment planning for MRgLITT. Physical properties of target tissue such as optical attenuation (µ) highly affect the outcome of thermal ablation modeling. Hence to ensure accuracy of modeling scheme, it is crucial to precisely estimate patient specific heterogeneity in these parameters. METHODS A steady-state Bioheat model is used for simulation of temperature field over the heterogeneous target tissue. Physical properties are assessed from training based on previously recorded MRTI datasets. In detail, a cost function is defined based on the difference between the Bioheat model temperature predictions and MRTI measurements. Minimizing this cost function results in optimal values for physical properties of each tissue type. Optical attenuation coefficients (µ) are the dominant sensitivity and are optimized in this work. Nominal values of other parameters are used. Population averages of the optimal values of µ are then used in Bioheat model for temperature assessment in future patients. Performance of these predictions is then verified using Dice similarity index. RESULTS Results provide a comprehensive analysis of the effect of using heterogeneous tissue segmentations on performance of LITT mathematical simulation. Optimal values of µ coefficients range between 100 m-1 and 200 m-1 . This corresponds with obtained values in literature. The mean and median of Dice similarity index while using optimal values of optical attenuation coefficients is 0.8022 and 0.8225, respectively. CONCLUSION Calibration of mathematical modeling outcomes with clinical MRTI data provides a better understanding about the parameters of the Bioheat equation and consequently provides a more confident thermal dose assessment than either approach alone. Results demonstrate that modeling predictions are accurate in a-priori prediction of thermal dose and may be useful in planning the procedure.

SU‐C‐BRA‐03: Prediction of Laser Induced Thermal Therapy: Results of Model Training and Cross Validation

Purpose: MR-guided laser induced thermal therapy (MRgLITT) is a minimally invasive surgery with applications in the brain, among other sites. In especially precise interventions, like neurosurgery, accurate planning may behoove surgical planning by aiding in the decision of where and how many laser ablations are required. Previous models of tissue heating have relied on literature values extrapolated primarily from normal brain animal research and ex vivo data. In this abstract, an inverse problem provides model parameter data from retrospective analysis of MR temperature imaging data in patient tumor tissue, which represent a training cohort. Within the same cohort, leave-one-out cross validation (LOOCV) estimates the predictive accuracy of the trained model. Methods: The training has three parts: MR temperature datasets (n=20), a relatively simple steady state bioheat model, and a global optimization algorithm maximizing the Dice similarity coefficient (DSC). DSC ranges from 0 to one; >0.7 is considered a ‘successful’ prediction. DSC compares the regions exceeding 57 °C—i.e. ablated tissue regions—and measures accuracy. Blood perfusion and optical parameters are optimized according to DSC, creating a library of 20 pairs of parameters that are used in prediction. The predictive accuracy is estimated by using LOOCV. LOOCV begins by dropping an optimal parameter pair from the library and makes a model prediction, given the average from the remaining 19 pairs. This procedure is permuted so that every dataset is predicted using the other parameter pairs. Results: The distribution of DSC during predictive LOOCV is described by: mean=0.822; median=0.849; standard deviation=0.0872; minimum=0.583; maximum=0.930; 19/20 datasets pass (i.e. DSC>0.7). Best available literature values perform comparably worse: mean=0.668; median=0.656; standard deviation=0.115; minimum=0.455; maximum=0.857; 8/20 pass. Conclusion: Data strongly indicate population-based parameter optimization is potentially useful in treatment planning, as the model far outperforms available literature values in this preliminary study. Research reported in this publication was supported by the National Center for Advancing Translational Sciences of the National Institutes of Health under Award Number TL1TR000369. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

SU-E-J-161: Inverse Problems for Optical Parameters in Laser Induced Thermal Therapy

PURPOSE Magnetic resonance-guided laser-induced thermal therapy (MRgLITT) is investigated as a neurosurgical intervention for oncological applications throughout the body by active post market studies. Real-time MR temperature imaging is used to monitor ablative thermal delivery in the clinic. Additionally, brain MRgLITT could improve through effective planning for laser fibers placement. Mathematical bioheat models have been extensively investigated but require reliable patient specific physical parameter data, e.g. optical parameters. This abstract applies an inverse problem algorithm to characterize optical parameter data obtained from previous MRgLITT interventions. METHODS The implemented inverse problem has three primary components: a parameter-space search algorithm, a physics model, and training data. First, the parameter-space search algorithm uses a gradient-based quasi-Newton method to optimize the effective optical attenuation coefficient, μ_eff. A parameter reduction reduces the amount of optical parameter-space the algorithm must search. Second, the physics model is a simplified bioheat model for homogeneous tissue where closed-form Greens functions represent the exact solution. Third, the training data was temperature imaging data from 23 MRgLITT oncological brain ablations (980 nm wavelength) from seven different patients. RESULTS To three significant figures, the descriptive statistics for μ_eff were 1470 m-1 mean, 1360 m-1 median, 369 m-1 standard deviation, 933 m-1 minimum and 2260 m-1 maximum. The standard deviation normalized by the mean was 25.0%. The inverse problem took <30 minutes to optimize all 23 datasets. CONCLUSION As expected, the inferred average is biased by underlying physics model. However, the standard deviation normalized by the mean is smaller than literature values and indicates an increased precision in the characterization of the optical parameters needed to plan MRgLITT procedures. This investigation demonstrates the potential for the optimization and validation of more sophisticated bioheat models that incorporate the uncertainty of the data into the predictions, e.g. stochastic finite element methods.

WE‐C‐116‐10: Univariate, Multivariate, and Nonlinear Uncertainty Quantification for Magnetic Resonance‐Guided Laser Induced Thermal Therapy

PURPOSE MR-guided laser-induced thermal therapy (MRgLITT) is an emerging minimally invasive neurosurgical tool being explored as a treatment alternative for conditions such as motion disorder, radiation necrosis, and intracranial metastases. The primary goal is to reduce complications and normal tissue morbidity associated with conventional surgery. Computational models are being investigated to aid prospective LITT planning; however, accuracy is undermined by imprecise and non-patient specific knowledge of parameters. This work explores incorporating uncertainty quantification (UQ) of temperature output from the stochastic Pennes bioheat transfer equation (BHT). METHODS A five parameter (perfusion, thermal conductivity, optical absorption, optical scattering) stochastic BHT LITT model was used. Parameters were considered to be uniform distributions with ranges informed by literature values. Generalized polynomial chaos (gPC) was employed to calculate spatio-temporal, voxel-wise functions of the output temperature distributions for UQ. BHT parameter sensitivity in linear and nonlinear models was explored in silico using univariate gPC. Retrospective analysis of MR thermography (MRTI) from both phantom and MRgLITT in normal canine brain in vivo (n=4) was explored using multivariate gPC. Isotherms, temporal and linear profiles were reported. RESULTS Univariate simulations demonstrated that optical parameters explained the majority of model variance (peak standard deviation: anisotropy 3.75 °C, absorption 2.94 °C, scattering 1.84 °C, conductivity 1.42 °C, and perfusion 0.94 °C). Linear model variance enclosed nonlinear model variance. Mean temperature and 95% confidence interval from multivariate simulations correlated well with measured heating even near the applicator. CONCLUSION gPC may provide robust and relatively fast UQ facilitating useful prospective LITT planning in brain tissue despite imprecise knowledge of parameters. The faster linear simulation approximated the nonlinear simulation without excessive variance. Further, the computational burden was reduced with minimal accuracy loss by including only the most sensitive parameters. Subsequent work includes applying stochastic BHT to retrospective human brain tumor LITT.