Magnetic resonance (MR) guided high intensity focused ultrasound (HIFU) and external beam radiotherapy (EBRT), show great potential for the non-invasive treatment of tumors in abdominal organs. Therapeutic energy delivery delivery in such areas is, however, hampered by the continuous displacement of the organs with respiration ^1,2. One way to overcome this problem is to combine high-frame-rate MR-imaging with real-time image tracking for interventional guidance ^1,3. Previous studies suggested for tracking optical-flow based algorithms such as suggested by Horn&Schunck ⁴. However, this approach is intrinsically also sensitive to gray-level intensity variations from other sources than respiratory motion, such as in-flow enhancement / pulsations due to the cardiac cycle, which frequently leads to tracking errors. In this work, an improved real-time tracking algorithm with increased robustness versus such effects is proposed and experimentally compared to the original Horn&Schunck method in terms of quality of the motion estimate in the presence of arterial pulsations.

The original Horn&Schunck functional shown in equation [1] relies on a signal intensity conservation term and a regularization term, which imposes a smooth differentiable motion.

$$E_{HS}(u,v)=\iint\limits_{\Omega}\!{(I_{x}u+I_{y}v+I_t)^2+\alpha^2(\|\nabla u\|^2+\|\nabla v\|^2)dxdy}\qquad [1]$$

For motion tracking this functional has to be minimized in real-time for each image of the data stream ^1,3. Problematic are hereby intensity variations due to arterial in-flow artifacts, which frequently violate the intensity conservation and thus lead to mis-registration. As consequence, we propose a modified L2-L1 functional (equation [2]), which replaces the quadratic norm of the intensity conservation term by a linear norm:

$$E_{L2L1}(u,v)=\iint\limits_{\Omega}\!{|I_{x}u+I_{y}v+I_t|+\beta^2(\|\nabla u\|^2+\|\nabla v\|^2)dxdy}\qquad [2]$$

The idea is that this functional reduces the confidence in the conservation of signal intensity, relying more on the assumption of an elastic deformation. This leads to a better representation of elastic organ deformation in the vicinity of arterial signal fluctuations.

The experimental validation was performed in the following way: Dynamic MR-imaging of both liver and kidney (Gradient recalled EPI, TR=80 ms, TE=37 ms, bandwidth_readout= 1250 Hz, excitation angle=20^o, resolution=2.5 × 2.5 × 7 mm³, frame-rate 12 images/s) was performed under free-breathing conditions (duration ∼2 min) on the abdomen of two healthy volunteers, resulting in 1500 images for each volunteer. A second dataset was derived by applying retrospective cardiac gating (i.e. while respiratory motion is present, all images represent peak-systole) to serve as a gold standard. Subsequently, the registration error (i.e. registration based on the complete data vs. registration of the cardiac gated images) for both methods is compared.

As shown in figure (1) the proposed tracking algorithm displays a significantly better performance in the upper liver and in particular in the vicinity of larger vessels, such as the hepatic arteries and the portal vein. The robustness of the tracking performance was hereby found comparable to the original algorithm. With respect to the performance, the L2-L1 algorithm converged on average in 25 ms with a typical end-to-end processing latency (since the beginning of the MR-slice acquisition to the output of the motion fields) of under 100 ms. Both the convergence time and the latency are well within the requirements for real-time guidance ^1,3. Note that the proposed functional is no longer differentiable thus, compared to the existing Horn&Schunck approach, substantially more computationally intensive algorithms are required for its minimization. This made an implementation that respects the low-latencies required by real-time applications a particularly challenging task.The presented study proposes an improved MR-based real-time tracking method for respiratory motion. Compared to the previously employed Horn&Schunck algorithm, the proposed method is, by construction, more resilient to gray-level intensity variations from other sources than motion. This was experimentally proven in the current work for the particular case of in-flow enhancement /pulsations due to the cardiac cycle. Additionally, the low end-to-end processing latency renders our method potentially suitable for the real-time MR-guidance of HIFU and EBRT interventions in the abdomen under free-breathing conditions.