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Motion Compensation in Emission Tomography

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Handbook of Particle Detection and Imaging

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Abstract

With the ever-improving spatial resolution available in single photon emission computed tomography (SPECT) and, especially, in positron emission tomography (PET), the unavoidable organ and subject motion is becoming one of the dominant factors limiting the practically achievable spatial resolution in the tomographic images. Moreover, uncorrected subject motion can lead to potentially severe image artifacts and compromise the quantitative integrity of the data. The latter is of special importance in PET where quantitative assessment of tracer concentrations is commonplace both in static investigations via so-called standardized uptake values (SUVs) and in dynamic studies aiming at tracer kinetic modeling and quantification of the corresponding transport constants. Correction of the heart-cycle-related motion in cardiac applications has a long tradition and is covered extensively in the literature. Correction of breathing-related organ motion in emission tomography, however, has drawn considerable interest only in recent years in the context of oncological PET. This is mainly due to the demands of therapy response monitoring and radiation treatment planning. The third important area is high-precision motion correction of random head motion in brain investigations. In this chapter, we give an overview of the methods employed to minimize – and possibly eliminate – the motion influence in emission tomography.

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Notes

  1. 1.

    For a total traveled distance d, the resulting PSF is given by

    $${H}_{t}(x) = \frac{1} {2} \cdot \left (\mathrm{erf}\left ( \frac{x} {{\sigma }_{s}\sqrt{2}}\right ) -\mathrm{erf}\left ( \frac{x - d} {{\sigma }_{s}\sqrt{2}}\right )\right )\,\text{,}$$

    where

    $$\mathrm{erf}(x) = \frac{2} {\sqrt{\pi }}{\int \nolimits }_{0}^{x}\mathrm{{e}}^{-{{\it { s}}}^{2}}d{\it { s}}\,\mathrm{.}$$
  2. 2.

    There also exist high-precision systems such as laser scanners which derive surface models of the monitored object without the need for special target structures. While these techniques are interesting, there are additional complications in deriving the relevant motion information related to the fact that no a priori known landmarks are present in the acquired data leading to the need for image registration in order to derive the actual subject motion. The future will show whether these systems will prove useful in the context of emission tomography.

  3. 3.

    We also include in this notation the case of stroboscopic (gated) acquisitions, where each frame corresponds to a certain phase of a cyclic motion (i.e., heartbeat or breathing cycle).

  4. 4.

    and, contrary to the image correlation coefficient, is applicable to inter-modality registration (e.g. MRI vs. PET) as well

  5. 5.

    Due to the noise and convergence characteristics of iterative image reconstruction, adding up the low-count images after reconstruction would not really solve this problem.

  6. 6.

    Four suitable coordinates unambiguously define a straight line in 3D space. This special choice of coordinates is convenient since α and d are also used in the 2D case. Moreover, the ring coordinates z 1, z 2 are directly provided by the front end electronics and are required anyway in further data processing.

  7. 7.

    The distinction between histograms in LOR space and sinograms is not really important in the present context. Sinograms are generated from the histograms by a so-called re-binning process, i.e., a change to coordinates more suitable for image reconstruction.

  8. 8.

    f in is different for each LOR. Since the number of LORs typically is of the order of 108 and adequate time resolution is required, computation of the f in is the most time-consuming step in the motion correction process.

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Authors and Affiliations

  1. PET Center, Institute of Radiopharmacy, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstrasse 400, 01328, Dresden, Germany

    Jörg van den Hoff & Jens Langner

Authors
  1. Jörg van den Hoff
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  2. Jens Langner
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Editors and Affiliations

  1. Department of Physics, Siegen University, Emmy-Noether-Campus, Walter-Flex-Str. 3, 57072, Siegen, Germany

    Claus Grupen

  2. IMNC-UMR 8165 CNRS, Paris 7 and Paris 11 Universities, Orsay Campus, Building 440, 91406, Orsay Cedex, France

    Irène Buvat

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van den Hoff, J., Langner, J. (2012). Motion Compensation in Emission Tomography. In: Grupen, C., Buvat, I. (eds) Handbook of Particle Detection and Imaging. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13271-1_40

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