Cortical surface-based analysis reduces bias and variance in kinetic modeling of brain PET data

Highlights

• This is a study of the effects of preprocessing on exploratory PET analysis.

• Volumetric 3D smoothing of PET data exacerbates the partial volume effect.

• Volumetric smoothing and partial volume correction combine to increase variability.

• Cortical surface-based smoothing does not exacerbate the partial volume effect.

• Surface-based kinetic analysis reduces intersubject variance by a factor of 4.

Abstract

Exploratory (i.e., voxelwise) spatial methods are commonly used in neuroimaging to identify areas that show an effect when a region-of-interest (ROI) analysis cannot be performed because no strong a priori anatomical hypothesis exists. However, noise at a single voxel is much higher than noise in a ROI making noise management critical to successful exploratory analysis. This work explores how preprocessing choices affect the bias and variability of voxelwise kinetic modeling analysis of brain positron emission tomography (PET) data. These choices include the use of volume- or cortical surface-based smoothing, level of smoothing, use of voxelwise partial volume correction (PVC), and PVC masking threshold. PVC was implemented using the Muller-Gartner method with the masking out of voxels with low gray matter (GM) partial volume fraction. Dynamic PET scans of an antagonist serotonin-4 receptor radioligand ([¹¹C]SB207145) were collected on sixteen healthy subjects using a Siemens HRRT PET scanner. Kinetic modeling was used to compute maps of non-displaceable binding potential (BP_ND) after preprocessing. The results showed a complicated interaction between smoothing, PVC, and masking on BP_ND estimates. Volume-based smoothing resulted in large bias and intersubject variance because it smears signal across tissue types. In some cases, PVC with volume smoothing paradoxically caused the estimated BP_ND to be less than when no PVC was used at all. When applied in the absence of PVC, cortical surface-based smoothing resulted in dramatically less bias and the least variance of the methods tested for smoothing levels 5 mm and higher. When used in combination with PVC, surface-based smoothing minimized the bias without significantly increasing the variance. Surface-based smoothing resulted in 2–4 times less intersubject variance than when volume smoothing was used. This translates into more than 4 times fewer subjects needed in a group analysis to achieve similarly powered statistical tests. Surface-based smoothing has less bias and variance because it respects cortical geometry by smoothing the PET data only along the cortical ribbon and so does not contaminate the GM signal with that of white matter and cerebrospinal fluid. The use of surface-based analysis in PET should result in substantial improvements in the reliability and detectability of effects in exploratory PET analysis, with or without PVC.

Introduction

Exploratory spatial methods are used in neuroimaging to find areas that show an effect of diagnosis, demographics, treatment, etc., where no strong a priori anatomical hypothesis exists. To do this, a parametric map of some neuroimaging measure is acquired for each subject. This map is then transformed into a common space where subjects can be compared independently at each voxel. Based on this test, each voxel is assigned a statistic to create a statistical parametric map (SPM). The effect under study can be declared significant only after correcting the SPM for multiple spatial comparisons, usually by creating clusters of contiguous voxels whose statistic exceeds a threshold (Friston et al., 1993). These clusters need not have well-defined anatomical boundaries and so might not be found with region-of-interest (ROI) analysis. Exploratory analysis has been applied extensively in PET neuroimaging (e.g., Becker et al., 2011, Haahr et al., 2012b, Kochunov et al., 2009, Kraus et al., 2012, Park et al., 2006, Protas et al., 2010; see also references in Table 1).

A disadvantage with exploratory analysis is that the measurement at a single voxel is often quite noisy which reduces the statistical power and makes it difficult to find clusters. To compensate, spatial smoothing is widely applied in exploratory analysis (Worsley et al., 1996). Spatial smoothing is the process of replacing the value at a voxel by a distance-weighted average of neighboring voxels. If the signal is more similar over the neighborhood than the noise, then the averaging process yields a boost in the signal-to-noise ratio (SNR). Spatial smoothing can profoundly affect the results of an exploratory spatial analysis by increasing the statistical power at individual voxels (Strother et al., 2004). The weight of a neighbor is determined by the distance to the center voxel and choice of full-width/half-maximum (FWHM) of the Gaussian weighting kernel. In volumetric smoothing, the neighborhood is defined in three-dimensional space, encompassing all voxels within a surrounding sphere irrespective of whether a given voxel within that sphere is of the same tissue type as the central voxel. For example, if the central voxel is within cortical gray matter (GM), then voxels within the smoothing kernel may be white matter (WM), cerebrospinal fluid (CSF), subcortical GM, or cortical GM from a neighboring gyrus. In contrast, surface-based smoothing defines a neighborhood to be only along the cortical surface (i.e., within the “cortical ribbon”) with distances computed along the ribbon. This prevents blurring effects of neighboring WM, CSF, and subcortical GM with cortical GM and also prevents blurring between two cortical areas that are close in Euclidian space but far apart along the surface (e.g., precentral and superior temporal gyri). Thus, surface-based smoothing should be used instead of volume-based smoothing for the analysis of cortical structures.

PET imaging is susceptible to partial volume effects (PVE) for reasons involving the finite size of detector crystals, detector principles, traveling distance before annihilation, Poisson count statistics, and reconstruction methods. The reconstructed image can be approximated by assuming that the true underlying PET image has been volume-smoothed with a Gaussian of a known FWHM (the point spread function of the scanner). This implicit smoothing is distinct from the explicit smoothing performed in an exploratory analysis as mentioned above. The PVE causes the radiotracer signal to spill over between tissue types. Typically this results in an underestimation of radiotracer concentration in GM. The amount of underestimation at a location depends on the volume of GM near that area. When studying diseases where GM volume is changing (such as Alzheimer's disease), PVEs can create uncertainty as to whether a change in radiotracer concentration is due to a change in tissue uptake or simply a change in GM volume (Thomas et al., 2012). Either can change the measured radiotracer concentration.

Post-reconstruction methods have been developed to correct for PVEs (PVC) on a voxel-wise basis given a coregistered tissue segmentation from CT or MRI and the FWHM of the PET point spread function. The most common of these is the Muller-Gartner (MG) method (Muller-Gartner et al., 1992) but others have also been proposed (Meltzer et al., 1990, Meltzer et al., 1996, Thomas et al., 2012). The principle is that the PET signal spilling into one tissue type from an adjacent tissue type is estimated and subtracted and, subsequently, each voxel is divided by the partial volume fraction (PVF) for its tissue type. The resulting image is then transformed to common space, spatially smoothed, and compared across subject; some examples of studies that have taken this approach are shown in Table 1.

Evaluation of voxelwise PVC performance has been limited to how accurately the PET signal can be recovered inside of a ROI (Hutton et al., 2013, Meltzer et al., 1990, Muller-Gartner et al., 1992, Thomas et al., 2012, Yanase et al., 2005). The performance of PVC has not been evaluated after the explicit spatial smoothing operation ubiquitously performed in exploratory analysis. This is a critical omission because MG PVC can cause noise amplification (Rousset et al., 2007) due to the division by the PVF, a number always less than 1 (sometimes much less). If the spill-in subtraction is inaccurate, then this inaccuracy will also be amplified. The more distant a voxel is from GM, the smaller the GM PVF and the more the noise amplification. When the data are volume-smoothed, problematic voxels (i.e., those with low PVF) will be smoothed into, and in so doing contaminate, the high PVF voxels.

PET time series data are often analyzed using kinetic or graphical models to determine the binding potential (BP_ND) of a radioligand (Ichise et al., 1996, Ichise et al., 2003, Lammertsma and Hume, 1996, Lammertsma et al., 1996, Logan et al., 1990). Ichise et al. (2003) demonstrated that BP_ND estimates computed from kinetic models are subject to noise-dependent bias. This means that as the noise level increases, not only does the variance of the estimated BP_ND increase, but it systematically deviates from the true underlying BP_ND. The noise-dependent bias can be expected to be much worse in an exploratory analysis where the voxel-wise noise level is much greater than that in a ROI. If the noise level is different across subjects, then the bias will increase the intersubject variability. If the noise level is different across groups, then noise-dependent bias can contribute to inter-group bias. This emphasizes the need to properly manage time series noise in exploratory kinetic modeling applications.

To summarize, (1) exploratory analysis is needed to find effects for which there is no spatial a priori hypothesis, (2) spatial smoothing is needed in exploratory analysis to improve voxel-wise SNR, and (3) volume-based spatial smoothing can interact with MG PVC to cause an increase in noise and bias. As a result, exploratory analysis with PVC of brain PET data is problematic. The purpose of this study is to document the noise and bias amplification that results from the interaction of MG-style PVC and volume-based smoothing and to show that these problems are greatly reduced when cortical surface-based smoothing is used instead. We also demonstrate that the bias and noise properties of surface-based smoothing are superior to that of volume-based even when PVC is not used. The demonstration uses a kinetic modeling application, which is particularly sensitive to noise and so has the most to gain from the new surface-based technique.