Researchers interested in identifying and quantifying the optimal k-space locations for model-based reconstruction of MR thermometry data.

Compressive sensing and sparse image reconstruction has received significant attention and has demonstrated potential in reduction of acquisition times. However, in many methods, under-sampling strategies are heuristically chosen and empirically validated. This often leads to a relatively larger number of k-space samples than needed for a particular application. The presented work develops a mathematically rigorous and quantitative methodology for k-space under-sampling with respect to model-based reconstruction of MR thermometry. Hence, the key question here is that whether there exist optimal locations in k-space such that they provide maximum information regarding the image? And if they exist, how one can develop a general framework to find these locations on k-space?An accelerated model-based information theoretic approach is developed to perform the task of image reconstruction from observed k-space samples. The key idea of the proposed approach is to optimally detect the useful samples of k-space in order to refine the model, and then the refined mathematical model is utilized to reconstruct the image¹. Uncertainty quantification techniques² along with information theoretic concepts, i.e, entropy, are used to locate k-space regions that demonstrate the highest sensitivity with respect to a composite heat transfer and MR physics. The key contribution of this method is to optimally select the samples on k-space such that they result in the best estimate of the corresponding temperature map. Optimally selected observations on k-space are utilized to refine the mathematical model and the refined model is then used to generate the temperature field corresponding to the observations. Fig.1 illustrates schematic view for implementation of the proposed algorithm for brain tumor laser ablation. Note that only small fraction of lines in k-space are used for data acquisition (bottom left). Acquired measurement data is then merged with model prediction data (top left) in a minimum variance framework to estimate the temperature filed over the tissue (top right). Corresponding error between the estimated and the true temperature field is also shown in Fig.1 (bottom right).An in-silico simulation is compared to MR temperature imaging from a human brain ablation. Fig.2 shows the position of the tumor in brain. Performance of the proposed technique is retrospectively validated in fully sampled planar temperature imaging acquired during the thermal ablation process. Fully sampled k-space data acquired in-vivo³ are used as a control for the computed sub-sampling strategies. MR temperature imaging was performed on a 1.5 T MRI (ExciteHD®, General Electric, Milwaukee, WI) GE scanner at every Δt =15 seconds (TR/FA = 38 ms/30º, frequency × phase = 256 × 128, FOV = 26 cm × 26 cm, BW = 100 Hz/pixel, slice thickness 5 mm). Fig.3 represents acquired k-space data points based on the proposed technique and other conventional sampling methods. The error in temperature estimate, while using different k-space data acquisition techniques, is also shown in Fig. 4. As expected, proposed approach results in minimum error in comparison with other subsampling schemes.The novelty of the proposed approach demonstrates that locations of high-information content with respect to a model based reconstruction of MR thermometry may be quantitatively identified. The information locations identified are a consequence of the physics based modeling of the laser induced heating and an intelligent characterization of the measurement uncertainties of the acquisition system. In particular, efficient k-space points are selected by variance maximization of model-based prediction of the MR signal. Our mathematical model of the MR thermometry acquisition is refined using this set of judiciously selected data observations to reconstruct the thermal image. Intuitively, the precision and confidence of the thermal image reconstruction depends on multiple factors like accuracy, information content, and the number of data observations. Optimally selected k-space samples allow reconstruction of high quality MR thermometry images with significantly less data compared to the fully sampled control data.