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Paper Review Arunesh Mittal

Lung Motion Correction on Respiratory Gated 3-D PET/CT Images Mohammad Dawood, Norbert Lang, Xiaoyi Jiang, and Klaus P. Schafers

Dawood et al. in their paper present a novel optical-flow based method for motion correction in positron emission tomography (PET)/computed tomography (CT) imaging. For imaging studies such as those done using 18FDG, the PET images are often acquired over a long duration of time (~5mins) during which breathing causes displacement of several organs within the thorax such as lungs, heart, ribs etc. This motion leads to two artifacts in the reconstructed image 1) incorrect tissue attenuation and 2) image blurring. These artifacts may lead to wrong staging of tumors. This is observed in tumors such as those near the base of the lung; these tumors would be expected to have pronounced motion due to breathing.

Due to the attenuation properties of different tissues such as lungs and bones, once, the PET data is acquired, the data is rescaled to account for the differences in tissue attenuation properties, that is, a correction is made by rescaling the number of (PET) photons registered at the detectors in accordance with the density of tissues. In PET/CT, the CT scan is used to measure the densities of the different tissues. Since CT images are acquired over a much shorter time window than PET images, CT images represent a snapshot of the breathing tissue over a very small duration during the breathing cycle. In contrast, the PET signal is acquired over a much longer duration of time. As the PET signal may correspond to a time window longer in duration than that of the CT imaging time window, the tissues might have been displaced to a different location relative to their position during the CT scan. This causes the PET data to be incorrectly attenuated in a non-motion-corrected PET scan. For example: activity from heart may be attenuated with lung density. The second artifact in of PET images that are not motion corrected is motion blur. Since the source of radioactive emission is in constant motion, the information on the ungated PET images is dispersed over an area proportional to the magnitude of the motion. This leads to loss of contrast in presence of high noise. This presents itself as blurring in the PET image.

The paper by Dawood et al. discusses a few techniques that had been tried to resolve the motion artifacts discussed above. Most of these techniques were based on external monitoring of patient motion with the help of external markers and video cameras. Using the video data the images were sorted in accordance with the motion of the external markers. Other methods have involved the use of deformable elastic membranes as a model. However, both such procedures have practical limitations and cannot be applied

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to all tissues within the thoracic cavity to yield promising results. The limitations are described in specific detail in the Dawood et al. paper.

To overcome the limitations of previous methods, Dawood et al., in their paper propose the use of respiratory gating for obtaining relatively motion free images of the lungs. Following this step, motion is minimized using optical-flow based transformations to a target (template) image. Since gating the PET data leads to a much lower SNR than the SNR of an un-gated PET image, the PET image data from the individual gates is transformed to a single position corresponding to the breathing cycle and then added up to achieve an image set with minimum motion and containing all information (Fig 3).

The first step in the motion correction scheme is respiratory gating. The breathing signal is recorded during imaging with a pressure transducer. The acquisition is then divided into eight parts using the respiratory signal (See Fig. 2). The PET data is divided into smaller parts and then sorted into these eight gates where each gate represents only a fraction of the total respiratory motion, thus, reducing the motion within each gate, relative to the image acquired over an entire respiratory cycle.

The second step of this scheme is the computation of optical flow. Lucas-Kanade algorithm is considered one of the best methods for calculating optical flow fields under different aspects and especially in presence of noise and hence was chosen. Computation of optical flow requires an assumption of the following four conditions 1) intensity similarity 2) incremental transformation 3) smoothness and 4) error minimization. Since the intensity (pixel values) between images is assumed to be the same but shifted, the following relationship holds true:

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Where I is the intensity function. Given the intensity similarity assumption the Taylor series can be written as:

Since the shift in position of pixels is assumed to be small the higher order terms (H.O.T.) are small enough and can be ignored. This gives us the following equation:

This can be written as:

However, this is an equation in two unknowns and cannot be solved as such. This is known as the aperture problem. To solve this equation Dawood et al. use the Lucas and Kanade non-iterative method, which assumes a locally constant flow within a volume. That is, for all pixels within a volume Vx , Vy and Vz remains constant. We get the following over determined system of equations:

This over determined system of equations can be solved using the least squared method. In addition, matched smoothing and derivative filters can also be applied prior to flow computation to help suppress the effects of noise.

The last step in the motion correction scheme is the projection of the data to a target position. A specified target gate in the breathing cycle is selected to which all other gates are projected. The optical flow algorithm is used to compute transformation matrices between all of gated acquisitions and the target gate i.e. the motion between the gates is calculated with the help of optical flow algorithm. During the taylor expansion, we made the assumption that change in position of pixels was relatively small, as this allowed us to disregard the higher order terms. Therefore, the optical flow algorithm calculates the transformation matrices with smaller motion much more precisely than those with large motion. Hence, it is a better to calculate the optical flow between the adjacent gates rather than to calculate it for every gate directly with the target gate. To get the best results, individual gates are projected to the target gate successively.

The following figure illustrates the advantages of motion correction in PET/CT images.

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The work by Dawood et al. was cited by several studies that extended their work by using more advanced optical flow algorithms [2] and several other groups that used variants of optical flow algorithms for motion correction and gating. Their method has also been used in a few tumor quantification studies [3][4].

References

[1] Dawood, Mohammad, et al. "Lung motion correction on respiratory gated 3-D PET/CT images." Medical Imaging, IEEE Transactions on 25.4 (2006): 476-485. [2] Dawood, Mohammad, et al. "Respiratory motion correction in 3-D PET data with advanced optical flow algorithms." Medical Imaging, IEEE Transactions on 27.8 (2008): 1164-1175. [3] Liu, Chi, et al. "The impact of respiratory motion on tumor quantification and delineation in static PET/CT imaging." Physics in medicine and biology 54.24 (2009): 7345. [4] Papathanassiou, Dimitri, et al. "Positron Emission Tomography in oncology: present and future of PET and PET/CT." Critical reviews in oncology/hematology 72.3 (2009): 239-254.