From Positron to Pattern: A Conceptual and Practical Overview of ¹⁸F-FDG PET Imaging and Spatial Covariance Analysis

Abstract

Imaging of brain glucose metabolism with ¹⁸F-2-fluoro-2-deoxy-d-glucose positron emission tomography (¹⁸F-FDG PET) can give important information regarding disease-related changes in underlying neuronal systems, when combined with appropriate analytical methods. One such method is the scaled subprofile model combined with principal component analysis (SSM PCA). This model takes into account the relationships (covariance) between voxels to identify disease-related patterns. By quantifying disease-related pattern expression on a scan-by-scan basis, this technique allows objective assessment of disease activity in individual subjects. This chapter provides an overview of steps involved in pattern identification in ¹⁸F-FDG PET data and is divided into three sections. Section 1 introduces basic concepts in nuclear imaging and explores the cellular underpinnings of signals measured with ¹⁸F-FDG PET. Section 2 describes relevant basic concepts in ¹⁸F-FDG PET image analysis including anatomical registration, normalization, and analysis of variance and covariance. Section 3 is dedicated to SSM PCA specifically. The goal of this chapter is to make the technique more accessible to readers without a mathematics or neuroimaging background. Although many excellent texts on this topic exist, the current chapter aims to provide a more conceptual overview, including some discussion points that are not always formally described in literature.

Appendix: Effects of Normalization

In this example we demonstrate effects of ratio normalization versus log transformation and subtraction of the mean, as applied in the scaled subprofile model (SSM). In this example, we consider ¹⁸F-FDG uptake in two regions, A and B, in healthy controls and patients. Region B is affected by the disease. Metabolism in this region has changed compared to the control population with ΔB. In our example, region A is unaffected in both groups. For each subject, there is a scaling factor q which accounts for effects due to, for instance, the amount of radioactive label administered. The term q is a subject-specific scaling factor which we need to eliminate from the data.

We introduce another term n, which indicates the relative size of region A.

$$ \mathrm{Mean}\ \mathrm{brain}\ \mathrm{uptake}:\kern0.62em nA+\left(1-n\right)B\kern5.62em 0<n<1 $$

Often, ¹⁸F-FDG uptake is altered in a few areas due to the disease. In such a case, A will contribute much more to the whole-brain average than B. Situations where B contributes only a small proportion to the whole-brain average include, for instance, early Parkinson’s disease, or even its prodromal phases.

One can imagine situations where large parts of the brain are affected by the disease. For instance, in advanced Alzheimer’s disease, we would expect hypometabolism in large parts of the cerebral cortex. In that case, B contributes overwhelmingly to the whole-brain average. As a result, whole-brain and average ¹⁸F-FDG uptake will be lower in patients compared to controls.

As discussed in the main text, a normalization is needed. Two options are discussed. The first method is global mean normalization by proportional scaling, which is commonly applied and entails dividing each voxel value by the subject mean. The second method is the normalization procedure as applied in SSM PCA. In the SSM, data is first log-transformed and subsequently the subject mean is subtracted. In this example we will show that:

• 1. Scaling effects (q) are eliminated in both methods.

• 2. Both normalization techniques can introduce artifacts in (the unaffected) region A.

1.1 Global Mean Normalization

In global mean normalization, ¹⁸F-FDG uptake in each voxel is divided by the mean uptake of the whole brain. For our example, the corrected values are shown in below figure

Although ¹⁸F-FDG uptake in region A is the same in the control and patient population, the values in this area are different after global mean normalization.

Thus, the change in signal in region B due to pathology resulted in an altered signal in region A after global mean normalization (i.e., it produced an artifact).

1.2 Log Transformation and Demean in the SSM

In the SSM, the data are first log-transformed, and next we subtract the mean (see below figure). The fact that factor q can be eliminated in the SSM indicates that any multiplicative effect in the data can be removed, just like it can be eliminated in the global mean normalization. Thus, both methods are invariant to scaling effects (also see Spetsieris and Eidelberg (2011)).

1.3 Practical Examples

We modeled the formulas above in MATLAB, with two values for n (0.9 and 0.1) and variable values for ΔB. For A and B, we chose the same (realistic) fixed values.

Example 1: Changes in a few regions.

In this situation, ¹⁸F-FDG changes are present in a few brain regions. In patients, most of the brain is unchanged, and thus A contributes most to the average (n is close to 1).

We plotted the values for A and B after global mean normalization (“A_mean” and “B_mean”) and after SSM normalization (“A_log” and “B_log”). On the x-axis, we show the values for ΔB, ranging from −1000 (i.e., a decrease in B) to +1000 (i.e., an increase in B). Furthermore, we chose: A = 1001, n = 0.9 and B = 1001. The result is shown in Fig. 4.11a.

Fig. 4.11

The normalized values for region A are plotted for the global mean normalization method (A_mean: black) and for the SSM (A_log: red). The normalized values for region B are also plotted for both regions (B_mean and B_log). In a, the results of example 1 are shown (n = 0.9; A = 1001 and ΔB ranges from −1000 to 1000). In b, the results of example 2 are shown (n = 0.1; A = 1001 and ΔB ranges from −1000 to +1000)

It is clear that there is an offset difference between the two methods. This is inherent to subtracting the mean versus dividing by the mean. When region B becomes hypometabolic, there is a slight (artificial) increase in region A. However, the changes in region A as a function of ΔB, even for extreme values of ΔB, are relatively small. The slope for the new values in A and B after each normalization procedure are almost equal.

Example 2: Changes in most of the brain.

In this situation, most of the cortex of the brain shows altered ¹⁸F-FDG uptake in patients. Only a few brain regions have intact ¹⁸F-FDG uptake (A), and these brain regions only contribute marginally to the whole-brain average. The altered brain areas (B) dominate the whole-brain metabolism, and ΔB is large. To simulate this situation, we repeated the example (A = 1001, B = 1001), but this time we chose n = 0.1. The result is shown in Fig. 4.11b. This example illustrates that both methods can cause an artifactual increase in A, when there is extreme hypometabolism in B.

To summarize, the grand mean normalization and the normalization in the SSM are equivalent methods. We illustrated that normalization to any mean is useful to eliminate subject-specific scaling factors in ¹⁸F-FDG-PET data, but inherently can induce artificial increases and decreases. This is a known issue in any imaging study where absolute values are not available, be it univariate or multivariate. It is therefore important that patients and controls have similar values of average ¹⁸F-FDG brain uptake (i.e., global metabolic rate (GMR)).

This issue has been addressed in several publications concerning the spatial covariance pattern that was identified in Parkinson’s disease (Parkinson’s disease-related pattern, PDRP). This pattern is characterized by relatively increased metabolism in subcortical structures (globus pallidus, putamen, thalamus, cerebellum, and pons), relatively increased metabolism in the sensorimotor cortex, and relatively decreased metabolism in the lateral frontal and parieto-occipital areas (Fig. 4.12). It has been posited that the PDRP reflects normalization artifacts due to GMR differences between controls and patients (Borghammer et al. 2008; Borghammer et al. 2009). Specifically, widespread cortical decreases, rather than subcortical increases, were suggested to be characteristic of the PD disease process (Borghammer et al. 2010). However, both theoretical and empirical evidence is available to support the contention that the PDRP topography holds true pathophysiological meaning and that the “red PDRP nodes” are central to PD pathophysiology.

Fig. 4.12

The Parkinson’s disease-related pattern (PDRP) identified in 17 controls and 19 PD subjects. Stable voxels are displayed, determined after a bootstrap resampling (90% confidence interval not straddling zero). Overlay on a T₁ MRI template. Positive voxel weights are color-coded red (relative hypermetabolism), and negative voxel weights are color-coded blue (relative hypometabolism). L = Left. Coordinates in the axial (Z) and sagittal (X) planes are in Montreal Neurological Institute (MNI) space

Spetsieris et al. showed that GMR reductions in PD patients were not significant relative to healthy controls after 15 years of illness. GMR reductions also did not correlate with symptom duration (in contrast to PDRP scores) (Spetsieris and Eidelberg 2011). Ma et al. analyzed absolute ¹⁸F-FDG uptake (with arterial blood sampling) in 24 patients with early-stage PD (Hoehn and Yahr I–II) and 24 controls. Both absolute (physiological units) and relative (after global mean ratio normalization) scan data was analyzed with a univariate model (SPM). A group contrast of relative count data revealed increased metabolism in the globus pallidus, ventral thalamus, dorsal pons/midbrain, and sensorimotor cortex, but cortical metabolic decreases were not found. There was no significant difference in mean whole-brain CMRglc between patients and controls. When absolute measures (physiological units without global mean normalization) were compared between groups in a similar univariate SPM analysis, no differences were found between controls and patients. This was attributed to the marked reduction in between-subject variability achieved with the normalization step. A similar analysis was also performed in repeat scans of PD patients. Globally normalized values for the “hypermetabolic regions” showed greater reproducibility than the corresponding absolute values (in physiological units). Thus, instead of introducing bias, the authors concluded that, when the global metabolic rate is carefully matched across groups, global normalization enhances the sensitivity of PET to detect meaningful regional differences. The SSM PCA disease-related pattern that was identified in the same data was similar to the SPM pattern but also included some additional regions (Ma et al. 2009).

A PDRP has also been identified by first normalizing the data to the cerebellum (non-log; every voxel divided by average cerebellar uptake), which was very similar to the original PDRP. In addition, the “red” and “blue” parts of the PDRP have also been used as separate vectors to calculate subject scores. Interestingly, both were able to discriminate between controls and PD patients of a new dataset, in which the red pattern performed the best (Spetsieris and Eidelberg 2011). In addition, when the “red” and “blue” vectors were calculated separately in longitudinal FDG PET scans of de novo PD patients and controls (three scans per subject over a 48-month period), the rate of progression of the red regions was the greatest and significantly higher compared to controls. By contrast, the expression of the blue pattern did not differ from controls at any of the three time points (Ma et al. 2009). Moreover, if the “blue” areas in the PDRP define or cause the “red” areas in the PDRP, then the “red” areas should disappear when the PDRP is re-derived in a subspace that excludes the “blue” areas. This was not the case; a PDRP derived in the red voxel subspace was very similar to the “red” vector of the original PDRP, and subject scores for these two patterns were significantly correlated (Spetsieris and Eidelberg 2011). Finally, Dhawan et al. studied a group of healthy participants in whom global metabolic activity was experimentally decreased by sleep induction (with secobarbital). Participants were scanned with ¹⁸F-FDG PET while awake and during stage II sleep (monitored with EEG recordings). Sleep-induced reductions in global metabolic activity did not increase PDRP expression in these controls. In addition, an SSM PCA pattern comparing sleep and wake scans did not disclose any PDRP-like subcortical increases (Dhawan et al. 2012).