A fast calculation method for the magnetic field distribution due to (dynamic) changes in susceptibility may allow real-time interventional applications. Here it is shown that a direct relationship can be obtained between the magnetic field perturbation and the susceptibility distribution inside the MR magnet using a first order perturbation approach to Maxwell's magneto-static equations, combined with the Fourier transformation technique to solve partial derivative equations. The mathematical formalism does not involve any limitation with respect to shape or homogeneity of the susceptibility field. A first order approximation is sufficient if the susceptibility range does not exceed 10 Ϫ4 (or 100 ppm). The formalism allows fast numerical calculations using 3D matrices. A few seconds computation time on a PC is sufficient for a 128 ϫ 128 ϫ 128 matrix size. Predicted phase maps fitted both analytical and experimental data within 1% precision.

Respiratory motion introduces substantial uncertainties in abdominal radiotherapy for which traditionally large margins are used. The MR-Linac will open up the opportunity to acquire high resolution MR images just prior to radiation and during treatment. However, volumetric MRI time series are not able to characterize 3D tumor and organ-at-risk motion with sufficient temporal resolution. In this study we propose a method to estimate 3D deformation vector fields (DVFs) with high spatial and temporal resolution based on fast 2D imaging and a subject-specific motion model based on respiratory correlated MRI. In a pre-beam phase, a retrospectively sorted 4D-MRI is acquired, from which the motion is parameterized using a principal component analysis. This motion model is used in combination with fast 2D cine-MR images, which are acquired during radiation, to generate full field-of-view 3D DVFs with a temporal resolution of 476 ms. The geometrical accuracies of the input data (4D-MRI and 2D multi-slice acquisitions) and the fitting procedure were determined using an MR-compatible motion phantom and found to be 1.0-1.5 mm on average. The framework was tested on seven healthy volunteers for both the pancreas and the kidney. The calculated motion was independently validated using one of the 2D slices, with an average error of 1.45 mm. The calculated 3D DVFs can be used retrospectively for treatment simulations, plan evaluations, or to determine the accumulated dose for both the tumor and organs-at-risk on a subject-specific basis in MR-guided radiotherapy.

Focused ultrasound (US) is a unique and noninvasive technique for local deposition of thermal energy deep inside the body. MRI guidance offers the additional benefits of excellent target visualization and continuous temperature mapping. However, treating a moving target poses severe problems because 1) motionrelated thermometry artifacts must be corrected, 2) the US focal point must be relocated according to the target displacement. In this paper a complete MRI-compatible, high-intensity focused US (HIFU) system is described together with adaptive methods that allow continuous MR thermometry and therapeutic US with real-time tracking of a moving target, online motion correction of the thermometry maps, and regional temperature control based on the proportional, integral, and derivative method. The hardware is based on a 256-element phased-array transducer with rapid electronic displacement of the focal point. The exact location of the target during US firing is anticipated using automatic analysis of periodic motions.

The use of proton resonance frequency shift-based magnetic resonance (MR) thermometry for interventional guidance on abdominal organs is hampered by the constant displacement of the target due to the respiratory cycle and the associated thermometry artifacts. Ideally, a suitable MR thermometry method should for this role achieve a subsecond temporal resolution while maintaining a precision comparable to those achieved on static organs while not introducing significant processing latencies. Here, a computationally effective processing pipeline for two-dimensional image registration coupled with a multibaseline phase correction is proposed in conjunction with high-frame-rate MRI as a possible solution. The proposed MR thermometry method was evaluated for 5 min at a frame rate of 10 images/sec in the liver and the kidney of 11 healthy volunteers and achieved a precision of less than 2°C in 70% of the pixels while delivering temperature and thermal dose maps on the fly. The ability to perform MR thermometry and dosimetry in vivo during a real intervention was demonstrated on a porcine kidney during a high-intensity focused ultrasound heating experiment. Magn Reson Med 63:1080-1087, 2010. V C 2010 Wiley-Liss, Inc. Key words: MRI; thermometry; temperature; interventional; imaging; real time system; motion artifacts; proton resonance frequency shift; PRF MR thermometry relying on the water proton resonance frequency is gaining importance for monitoring and guiding thermal therapies such as radiofrequency (1), laser (2), or focused ultrasound thermal ablation (3-5). Typically, proton resonance frequency-based MR thermometry relies on the voxelwise evaluation of phase differences between sequentially acquired gradient echo images. However, for the use on abdominal organs, this renders the method very sensitive to motion artifacts and magnetic field changes. These motion artifacts can be coarsely classed into the two following types: intrascan motion artifacts and interscan motion artifacts. Intrascan motion artifacts are caused by displacement during the MR acquisition process and lead to image blurring and object ghosting. Commonly, this type of artifact is addressed using fast MR acquisition schemes or alternatively with respiratory-gated sequences that reduce the temporal resolution to the respiratory frequency. Interscan motion artifacts are due to organ displacement between the MR acquisitions and lead to a misregistration between subsequent phase images and thus to artifacts in the subtraction process. Furthermore, since any displacement or plastic deformation of the abdominal organs will in general also lead to a modified demagnetization field and thus to a change of the local magnetic field (6-8), additional phase artifacts are introduced.To overcome these problems, several correction strategies have been proposed, such as respiratory gating (9), navigator echoes (10), multibaseline acquisition to sample periodic changes (11,12), and referenceless phase corrections (13). Furthermore, the concept of the equivalent...

Magnetic resonance imaging-guided high intensity focused ultrasound is a promising method for the noninvasive ablation of pathological tissue in abdominal organs such as liver and kidney. Due to the high perfusion rates of these organs, sustained sonications are required to achieve a sufficiently high temperature elevation to induce necrosis. However, the constant displacement of the target due to the respiratory cycle render continuous ablations challenging, since dynamic repositioning of the focal point is required. This study demonstrates subsecond 3D high intensity focused ultrasound-beam steering under magnetic resonance-guidance for the real-time compensation of respiratory motion. The target is observed in 3D space by coupling rapid 2D magnetic resonance-imaging with prospective slice tracking based on pencil-beam navigator echoes. The magnetic resonance-data is processed in real-time by a computationally efficient reconstruction pipeline, which provides the position, the temperature and the thermal dose on-the-fly, and which feeds corrections into the high intensity focused ultrasound-ablator. The effect of the residual update latency is reduced by using a 3D Kalman-predictor for trajectory anticipation. The suggested method is characterized with phantom experiments and verified in vivo on porcine kidney. The results show that for update frequencies of more than 10 Hz and latencies of less then 114 msec, temperature elevations can be achieved, which are comparable to static experiments. Magn Reson Med 64:1704-1712,

Continuous, real-time 3D temperature mapping during a hyperthermic procedure may provide enhanced safety by visualizing temperature maps in and around the treated region, improved efficiency by adapting local energy deposition with feedback coupling algorithms, and therapy endpoints based on the accumulated thermal dose. Noninvasive mapping of temperature changes can be achieved with MRI, and may be based on temperature dependent MRI parameters. The excellent linearity of the temperature dependency of the proton resonance frequency (PRF) and its near-independence with respect to tissue type make the PRF-based methods the preferred choice for many applications, in particular at mid to high field strength (≥ 0.5 T). The PRF methods employ RF-spoiled gradient echo imaging methods, and incorporate fat suppression techniques for most organs. A standard deviation of less than 1 o C, for a temporal resolution below 1 s and a spatial resolution of about 2 mm, is feasible for immobile tissues. Special attention is paid to methods for reduction of artifacts in MR temperature mapping caused by intra-scan and inter-scan motion, and motion and temperature-induced susceptibility effects in mobile tissues. Real-time image processing and visualization techniques, together with accelerated MRI acquisition techniques, are described because of their primary importance for real-time, image guided, therapy guidance.3

Magnetic resonance (MR) guided high intensity focused ultrasound and external beam radiotherapy interventions, which we shall refer to as beam therapies/interventions, are promising techniques for the non-invasive ablation of tumours in abdominal organs. However, therapeutic energy delivery in these areas becomes challenging due to the continuous displacement of the organs with respiration. Previous studies have addressed this problem by coupling high-framerate MR-imaging with a tracking technique based on the algorithm proposed by Horn and Schunck (H and S), which was chosen due to its fast convergence rate and highly parallelisable numerical scheme. Such characteristics were shown to be indispensable for the real-time guidance of beam therapies. In its original form, however, the algorithm is sensitive to local grey-level intensity variations not attributed to motion such as those that occur, for example, in the proximity of pulsating arteries.In this study, an improved motion estimation strategy which reduces the impact of such effects is proposed. Displacements are estimated through the minimisation of a variation of the H and S functional for which the quadratic data fidelity term was replaced with a term based on the linear L(1)norm, resulting in what we have called an L(2)-L(1) functional.The proposed method was tested in the livers and kidneys of two healthy volunteers under free-breathing conditions, on a data set comprising 3000 images equally divided between the volunteers. The results show that, compared to the existing approaches, our method demonstrates a greater robustness to local grey-level intensity variations introduced by arterial pulsations. Additionally, the computational time required by our implementation make it compatible with the work-flow of real-time MR-guided beam interventions.To the best of our knowledge this study was the first to analyse the behaviour of an L(1)-based optical flow functional in an applicative context: real-time MR-guidance of beam therapies in moving organs.

A robust 4D-MRI method, based on clinically available protocols, is presented and successfully applied to characterize the abdominal motion in a small number of pancreatic cancer patients.