An improved tracking technique for real-time MR-guided beam therapies in moving organs

Cornel Zachiu^{1}, Nicolas Papadakis^{2}, Mario Ries^{1}, Chrit Moonen^{1}, and Baudouin Denis de Senneville^{1,2}

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 mm^{3}, 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.

1. Ries M et al. Real-time 3D target-tracking in MRI-guided focused ultrasound ablations in moving tissues, Mag Res Med 2010, 64:1704-12.

2. Langen K and Jones D. Organ motion and its management, Int J Radiation Oncology Biol Phys 2001, 50: 265–278.

3. Roujol S et al. Real-time MR-thermometry and dosimetry for interventional guidance on abdominal organs, Mag Res Med 2010, 63:1080-87.

4. Horn B and Schunck B. Determining optical flow, Artificial Intelligence 1981, 17: 185 – 203.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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