Functional and structural synergy for resolution recovery and partial volume correction in brain PET
Introduction
Positron emission tomography (PET) has the unmatched ability to image, in absolute quantitative fashion, the distribution of radiolabeled markers with concentrations in the picomolar range. This allows the in-vivo monitoring of functional processes such as perfusion, metabolism, gene and protein expression etc. PET however is hampered by the poor spatial resolution and lack of morphological information, features that are characteristic of CT and MRI. The availability of computational approaches for the between-modalities registration (Woods et al., 1993) but, in particular, the recent availability of combined PET–CT (Beyer et al., 2000) and PET–MRI (Judenhofer et al., 2008, Shao et al., 1997) scanning technology has increased the interest in computational methodologies able to use synergistically multimodal information. In this work we present a statistical model able to combine synergistically PET with morphological data for the resolution recovery of PET data. The model is flexible because the use of structural data is weighted with the relative amount of signal in the functional and morphological images; this allows the preservation of fine functional detail in the absence of matching structural detail. Depending on the quality of structural information that ranges from low (CT) to greater anatomical detail (MRI), the method allows the recovery of the resolution of the PET volume. Moreover, the availability of a registered anatomical image allows the use of standardized morphological information such as, in this case, a probabilistic anatomical atlas. The combined use of the proposed method and the probabilistic anatomical atlas results in an image-based algorithm for the correction of partial volume effects in PET images.
The quantification of small brain structures and the correction of PET signal for underlying morphology may have strong clinical impact (Fazio and Perani, 2000, Leroy et al., 2007). Therefore, accurate quantification via a computational technique that may also be widely and easily applicable is of great relevance in nuclear medicine and neuroscience in general.
Since the finite spatial resolution of PET blurs the distribution of radioligands in images, several authors have proposed resolution recovery (RR) techniques based on the deconvolution of images with the point spread function (PSF) of the scanner (Biemond et al., 1990, Lucy, 1974, Richardson, 1972, Teo et al., 2007). Deconvolution approaches enhance high frequency signal but inevitably increase noise in images and cannot recover anatomical detail that has been lost because of the PSF of the scanner. Alternatively, partial volume correction approaches have been introduced that use PSF and anatomical information derived from segmented MRI images (usually gray and white matter and cerebral spinal fluid relative densities or anatomical segmentation) to correct region of interest (ROI) PET data for the effects of tissue loss (Aston et al., 2002, Labbe et al., 1996, Meltzer et al., 1999, Meltzer et al., 1990, Rousset et al., 2008, Rousset et al., 1998). RR techniques have also been pursued that integrate structural images and position variant PSF into the iterative reconstruction process (Ardekani et al., 1996, Baete et al., 2004, Panin et al., 2006).
The methodology presented here stems from previously proposed ideas for RR based on the wavelet transform (WT) (Boussion et al., 2006, Boussion et al., 2008, Nunez et al., 2005). In particular Boussion et al. (2008) used co-registered CT images to improve the resolution of PET data using a resolution level dependent factor to scale the CT details into the PET image.
The methodology develops previous work (Turkheimer et al., 2008) that used CT/MRI information in a synergistic fashion to denoise functional data. In this instance though, the existing local functional/structural relations are exploited for an accurate and realistic recovery of the resolution of PET images. We labeled the method as “Structural–Functional Synergistic” Resolution Recovery (SFS-RR). SFS-RR uses the WT to decompose the functional (e.g., PET) and the structural reference image (e.g. CT/MRI) into several resolution elements and then replaces the high-resolution component of the functional image with the anatomical image with an appropriate local scaling. Functional and anatomical distributions however may differ (Shidahara et al., 2007, Soret et al., 2007, Teo et al., 2007, Tohka and Reilhac, 2008); to suppress the effects of distribution mismatch, on one hand the proposed methodology handles the substitution of functional with structural details flexibly by evaluating the local ratio between functional and structural signal in the wavelet domain. This however may not be sufficient as no single structural image may provide the anatomical support for the functional study at hand. We therefore developed the synergy concept further and investigated the possibility of using an anatomical frequency-based brain atlas (Hammers et al., 2003) as structural information to inform the SFS-RR. The use of a probabilistic brain atlas, as shown in the following section, makes the SFS-RR into an image-based approach for the partial volume correction of PET images.
In the present study, the performance of SFS-RR was assessed using accurate simulations and clinical brain data for [18F]FDG and [11C]raclopride as representative of the wider range of PET data of relevance for the methodology.
Section snippets
Wavelet transform
The wavelet transform (WT) produces a time/frequency signal decomposition (Mallat, 1999). The WT decomposes the signal f(x) through a high band-pass function Ψ and a low-pass scaling function Φ as:The second term on the right side of Eq. (1) represents low frequency components of the signal. The functions ψj,k are orthonormal basis elements generated by dilated (j) and translated (k) versions of Ψ. The dj(k) in Eq. (1) are the wavelet coefficients which
Results
In all instances, SFS-RR took about 3 min to process a static PET image under Linux OS with Intel Xeon 3G Hz dual CPU and 4 GB memory. Typical parameters for Eq. (3) for atlas-based SFS-RR processing are listed in Table 2.
Discussion
In the present study, we propose a flexible statistical model that uses structural information to recover resolution in functional images. The method is able to accommodate anatomical detail of varying precision by comparing the high frequency content of the PET data with that of the structural reference. The methodology is practical and widely applicable as it can immediately extended to other functional modalities (SPECT/fMRI).
The newly developed method was evaluated in a simulation studies
Conclusion
We have proposed and evaluated the use of the wavelet transform to synergistically link functional and structural information for quantitative resolution recovery (SFS-RR based on wavelet). The technique allows practical and efficient recovery of functional information at high-resolution with MRI but particularly with the use of an anatomical frequency-based atlas.
Acknowledgments
This study was supported in part by a Grant-in-Aid for Young Scientists (B) from the Ministry of Education, Culture, Sports, Science and Technology, (19700395), Japan and by the Medical Research Council under the grant no G78/8306, UK. We wish to thank Dr. Kris Thielemans for guidance during the realistic set-up of the simulation study using the STIR library.
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