Dynamic PET data
Data were used from four arbitrarily chosen AD patients and four HVs recruited for different studies at Uppsala Imanet, GE Healthcare in collaboration with several groups such as Karolinska University Hospital Huddinge, Stockholm, Sweden. The four AD patients were also recruited in a follow-up (FU) study where they were scanned a second time at Uppsala Imanet, GE Healthcare [4]. Data from both the baseline and FU studies were used in this study. Four HVs were selected randomly from a study performed at Uppsala Imanet in collaboration with Karolinska University Hospital Huddinge, Stockholm and University of Pittsburgh School of Medicine, Pittsburgh, USA [2].
Data analysis
Masked Volume Wise Principal Component Analysis
PCA [11, 12] is a data-driven and well-established multivariate analysis technique used to reduce dimensionality of multivariate input datasets such as dynamic PET images. PCA converts the projection of the original images into a new orthogonal coordinate system with lower dimensions in which the new axes explain the variance in the images in decreasing order of importance. This is done by calculating transformation vectors (principal components, i.e. PCs or weight factors), which define the directions of largest variance of the input multi-dimensional dataset in the multidimensional feature space. Each PC is orthogonal to all the others in multi-dimensional space; thus, the first PC (PC1) represents the linear transformation of the original variables which contain the largest variance. The second component, PC2, is the combination that contains the remaining variance as much as possible, orthogonal to the previous one and so on. "PC images" are generated by simply projecting all observations onto the PCs in the new multi-dimensional space. This gives new values along each PC.
If the matrix
X
T= [X
1, X
2, X
3, ..., X
p
]
where X
Tis transpose of the input matrix X, which contains pixel values of a single slice from each frame i, (i = (1, 2, 3, ..., p), as a column vector), has a variance-covariance matrix S with eigenvalues
λ = ⌊λ
1, λ
2, λ
3, ..., λ
p
⌋
and corresponding eigenvectors
e = ⌊e
1, e
2, e
3, ..., e
p
⌋
where
λ
1 ≥ λ
2 ≥ λ
3 ≥ ... ≥ λ
p
≥ 0
and p corresponds to the number of the input column in the matrix X. If q = p in which q refers to number of principal component, then the q
th PC is generated by using Eq. 1:
Y
q
= e'X = e
q1
X
1 + e
q2
X
2 + e
q3
X
3 + ... + e
qp
X
p
The condition Cov(Y
q
, Y
i
) = 0 where i ≠ q is required, i.e. the components are uncorrelated. Principal components should explain the magnitude of variance in decreasing order. Here each element within the eigenvectors is used as weight-factor for creating images.
In a previous work, MVW-PCA was introduced as a new approach of application of PCA on dynamic PET images using various compounds, among others [11C]-PIB [5]. This method is based on using noise prenormalized data that represents whole brain of each time sequence (frame) as a single variable after the background had been removed (masked out) before applying PCA. The result is MVW-PC images, which are separated into different principal components, MVW-PCs. The number of components is equal to the number of PET time frames. In each PET dataset, the whole sequence (all frames) was used to include all information in the dataset. Furthermore, the MVW-PC images can be seen as images representing different kinetic behaviors of the administered tracer and contain more detailed anatomical information with higher precision and quality. They have an improved SNR and visual contrast between the anatomical structures representing both affected and unaffected tissues compared with other methods [13].
However, in this work, only the first three MVW-PCs were explored since higher components contained only noise.
The software used for the application of MVW-PCA on dynamic PET images was developed in-house by one of the authors (PR) using Matlab 7.2 (The Mathworks, Natick, Massachusetts) with installed statistical and image processing toolboxes.
Reference Logan graphical analysis
The reference Logan graphical analysis is a regression method, which is appropriate for tracers with reversible kinetics. The method describes the kinetics of the tracer in a receptor-containing region and in a reference region devoid of specific binding, such that after a certain time there is a linear relationship between the reference Logan variables. The linear slope gives directly the distribution volume ratio (DVR), which corresponds to the ratio of the distribution volume (DV) of a receptor-containing region to the DV of a reference region. The DVR is widely used as a model parameter in PET studies since it is a linear function of the receptor availability. Parametric maps, in which the DVR is calculated for each pixel in the PET image, were generated using 25–60 min (last six frames) for 4 × 2 AD patients (each at both baseline and follow-up) and four HVs.
Eq. 2 is used in the reference Logan graphical analysis is given by:
(2)
where ROI(t) and REF(t) are the radioactivity concentrations in a region of interest and a reference region, respectively. The term int' is the intercept and is the average tissue-to-plasma efflux constant. The slope DVR is obtained from the linear portion of the plot (T > t*), where T and t* are midframe scanning time and equilibrium, respectively. If the ratio ROI(t)/REF(t) is constant, the DVR can be obtained without the use of .
Signal-to-noise ratio
Signal-to-noise ratio, SNR, measures the strength of the signals association to the quantity noise of the data in either sinogram (raw data) or image domain [13]. In this work, signal is defined as the average pixel value, S, and noise as the standard deviation of pixel intensities, N, within the same outlined ROI. SNR is calculated using Eq. 3
(3)
The following four ROIs of similar sizes representing different parts of the brain were drawn, in both AD patients and HVs: frontal cortex sinister (Fsin), frontal cortex dexter (Fdx), parietal cortex sinister (Psin) and parietal cortex dexter (Pdx). According to the study by Klunk [2] the difference in [11C]-PIB retention between AD patients and HVs is largest in these areas. SNR was calculated for all ROIs in images generated by the different methods and the mean results of the SNR were compared and plotted.
Discrimination power
Discrimination power (DP) is a measurement of quantification differences between two independent groups. It is defined as the difference between absolute value of the means, , divided by the square root of the average of the squared standard deviations (σ1 and σ2) [14, 15]. DP was calculated using Eq. 4.
(4)
where
In this study DPs for both images generated by MVW-PCA and reference Logan were calculated using the same ROIs that were used for calculation of SNR (Fsin, Fdx, Psin and Pdx).
In the current study, Graph Pad Prism v. 4.03 (Graph Pad Software, Inc, San Diego, USA) was used to perform all statistical analysis and graphical illustrations.