The techniques of microPET and microarray are two of the most powerful modalities in the study of molecular gene therapy and gene expression profiles in this century.
The high spatial resolution and sensitivity of microPET make it an ideal modality for in vivo gene imaging. Those images can be employed to monitor the effects of gene therapy inside animal bodies. Recent study [1] shows that the technique of microPET has been developed to trace the gene expression in vivo. Hence, it is very important to enhance the reconstruction and analysis techniques with better precision and fewer artifacts so that the genuine gene expression inside biological objects can be recovered. High-quality image reconstruction is essential in establishing a solid basis for quantitative study of microPET images [2-3].
The conventional methods built-in microPET software (microPET manager V1.6.4), filter backpropagation (FBP) [4] and ordered subsets expectation-maximization approach (OSEM) [5], are used to reconstruct microPET images after applying the Fourier rebinning (FORE) algorithm [6] and random pre-correction. However, the FBP is unable to model the randomness of PET. As the FBP was developed for transmission tomography, it is not accurate when applied to emission tomography which contains randomness in PET. Hence, the FBP reconstruction of microPET
image is typically noisy and inaccurate. Meanwhile, the OSEM can reconstruct more accurate images than the FBP does, but it is basically driven from the inaccurate Poisson model using random pre-correction (that is, applying subtraction on two random variables from two independent Poisson distributions).
On the contrary, iterative algorithms, such as the maximum likelihood expectation-maximization (MLEM) algorithm, are rapidly becoming the standards for image reconstruction in emission tomography. The MLEM reconstruction and related improvements have also been reported in literature [7-10, 14, 16-17, 21-24].
Statistical analysis that supports positron emission tomography (PET) has been discussed as well [9]. The MLEM approach can model randomness in emission tomography with the asymptotic efficiency by applying the row operation and monotonic convergence using the EM algorithm. Furthermore, the EM algorithm can be parallelizable for 3D PET image reconstruction [10].
The generation of quantitative PET images requires that the effects of random coincidences and coincidence efficiencies are corrected [11-12]. One random correction approach applies single count rates to a prompt sinogram [13]. This approach is generally based on geometric and physical characteristics. However, this approach makes many assumptions for approximations that can decrease the accuracy of random correction below that obtained using methods that utilize both prompt and
delay sinograms. An alternate approach applies random pre-correction to sinograms by subtracting the delay sinogram from a prompt sinogram before the processing of images reconstruction. The random pre-correction using various approximations has been applied to correct random (or accidental) coincidental events [14-15]. Different methods have been developed to approximate the distribution of random pre-correction [16-18]. However, random pre-correction increases the variances of estimates [17, 19]. Since the distribution of random pre-correction is no longer Poisson-distributed, the shifted Poisson methods and saddle-point (SD) approximation have been generated to enhance approximation [20]. This study proposes a joint Poisson model of prompt and delay sinograms for random correction with the MLEM reconstruction without using approximations nor increasing variances. This approach is named PDEM. Simulations, physical phantoms and real Mouse studies of the PDEM method using the microPET R4 system were performed. This study analyzed and assessed the reconstruction of 2D data obtained from 3D sinograms after applying the FORE method to verify the proposed approach. The PDEM method can also be utilized in future studies reconstructing 3D images.
Once microPET images have been reconstructed using PDEM, the next step is to segment those regions of interest (ROI) from the reconstructed images. The FBP reconstruction has been applied in tomography due to its power of fast computation.
Wong et al. [26-28] used the method of FBP reconstruction and K-means clustering with Akaike information criterion (AIC) [25] to segment PET images. However, the FBP method is not accurate for reconstructing microPET images. Hence, the PDEM is applied to reconstruct microPET images more accurately instead of the FBP in this study. Due to the variability of variances among different segments of microPET images, we will consider the Gaussian mixture model (GMM) instead of K-means clustering [28-30]. Furthermore, the numbers of cluster and their initialized values used in GMM are determined by the kernel density estimation (KDE).
Similar methods can be adapt to segment spotted microarray images. The microarray is a high throughput technique for exploring the expression profiles for thousands of genes during the studies of genomics in biology and medicine. Although high-density oligonucleotide arrays are currently available, custom-made or spotted cDNA microarrays have also been used, because of their favorable cost, ease of preparation and ease of analysis in the design of co-hybridization experiments [32].
Studies of the functionality of genes in this new era of post-genomics are important [33]. Analyzing the microarray images with high accuracy is essential to measure the gene expression profiles. Advanced analysis for selecting significant genes, clustering, classification, and network reconstruction of gene expression profiles can proceed on a solid foundation following complete accurate measurements [34-35].
The cDNA images, in general, tend to be very noisy. Therefore, various approaches have been proposed to improve the calibration of scanning efficiencies, the alignment and detection of spotting errors, the denoising of background noise from images, the marking of dust, gridding, moving, hybridization and other artifacts [34, 36-37].
Different methods have been proposed for segmenting cDNA microarray images in literature. Markov Random Field (MRF) modeling has been proposed to segment spots in microarray images [32]. This MRF-based approach relies on the prior assumption of class labeling of all pixels [38] and it has a high computational cost.
The alternative approach of region-growing approach relies on the selection of initial seeds that influence its performance [39]. the other approach of Gaussian mixture model (GMM) generally assumed normality when it is applied to this segmentation problem [40]. Accordingly, this study is motivated by the need to investigate the segmentation of cDNA microarray images using the nonparametric method of kernel density estimation (KDE) that does not require the assumption of normality.
In this investigation, the KDE is utilized to classify pixels in a spot into background and foreground that use the estimated density to find the cut-off value. Meanwhile, the approach of initial segmentation using GMM and fine tuning using KDE is proposed to detect feasible boundary between foreground and background in spots.
This approach is named GKDE (that is, GMM + KDE). Empirical studies are
conducted on real microarray data that involve 256 spike genes with known contents.
The segmentation results obtained by the KDE are compared with those obtained using the adaptive irregular segmentation method used in the current version of GenePix Pro software 6.0 (at http://www.moleculardevices.com/pages/software/
gn_genepix_pro.html, with the accompanying User’s Manual).
Microarrays with various sources and experimental designs are needed to monitor the variations of gene expressions. Spike spots of the corresponding spike mRNAs with a range of concentrations are used to monitor the variability of fluorescence intensities and determine the consistency of hybridization among arrays. The spike spots also reveal the variations of pins in an array. Duplicated spots within each array are used to assay the hybridization process of the arrays. Swapped experiments are also used to assay the labeling efficiency of Cy3 and Cy5 fluorescence dyes.
In this application, real microarray images with (1) spike spots with various ratios of Cy5 to Cy3 intensities, (2) duplicated spots in an array and (3) the swapping of microarray experiments, are applied to evaluate the performance and accuracy of the segmentation method.