A Realistic Computer-Simulated Brain Phantom for Evaluation of PET Charactenstics

Comparison of five cluster validity indices performance in brain [18 F]FET-PET image segmentation using k-means

PURPOSE

Dynamic [¹⁸ F]fluoro-ethyl-L-tyrosine positron emission tomography ([¹⁸ F]FET-PET) is used to identify tumor lesions for radiotherapy treatment planning, to differentiate glioma recurrence from radiation necrosis and to classify gliomas grading. To segment different regions in the brain k-means cluster analysis can be used. The main disadvantage of k-means is that the number of clusters must be pre-defined. In this study, we therefore compared different cluster validity indices for automated and reproducible determination of the optimal number of clusters based on the dynamic PET data.

METHODS

The k-means algorithm was applied to dynamic [¹⁸ F]FET-PET images of 8 patients. Akaike information criterion (AIC), WB, I, modified Dunn's and Silhouette indices were compared on their ability to determine the optimal number of clusters based on requirements for an adequate cluster validity index. To check the reproducibility of k-means, the coefficients of variation CVs of the objective function values OFVs (sum of squared Euclidean distances within each cluster) were calculated using 100 random centroid initialization replications RCI₁₀₀ for 2 to 50 clusters. k-means was performed independently on three neighboring slices containing tumor for each patient to investigate the stability of the optimal number of clusters within them. To check the independence of the validity indices on the number of voxels, cluster analysis was applied after duplication of a slice selected from each patient. CVs of index values were calculated at the optimal number of clusters using RCI₁₀₀ to investigate the reproducibility of the validity indices. To check if the indices have a single extremum, visual inspection was performed on the replication with minimum OFV from RCI₁₀₀ .

RESULTS

The maximum CV of OFVs was 2.7 × 10^-2 from all patients. The optimal number of clusters given by modified Dunn's and Silhouette indices was 2 or 3 leading to a very poor segmentation. WB and I indices suggested in median 5, [range 4-6] and 4, [range 3-6] clusters, respectively. For WB, I, modified Dunn's and Silhouette validity indices the suggested optimal number of clusters was not affected by the number of the voxels. The maximum coefficient of variation of WB, I, modified Dunn's, and Silhouette validity indices were 3 × 10^-2 , 1, 2 × 10^-1 and 3 × 10^-3 , respectively. WB-index showed a single global maximum, whereas the other indices showed also local extrema.

CONCLUSION

From the investigated cluster validity indices, the WB-index is best suited for automated determination of the optimal number of clusters for [¹⁸ F]FET-PET brain images for the investigated image reconstruction algorithm and the used scanner: it yields meaningful results allowing better differentiation of tissues with higher number of clusters, it is simple, reproducible and has an unique global minimum.

Design and construction of a brain phantom to simulate neonatal MR images

This paper presents the design and construction of a 3D digital neonatal neurocranial phantom and its application for the simulation of brain magnetic resonance (MR) images. Commonly used digital brain phantoms (e.g. BrainWeb) are based on the adult brain. With the growing interest in computer-aided methods for neonatal MR image processing, there is a growing demand a digital phantom and brain MR image simulator especially for the neonatal brains. This is due to the pronounced differences between adult and neonatal brains not only in terms of size but also, more importantly, in terms of geometrical proportions and the need to subdivide white matter into two different tissue types in neonates. Therefore the neonatal brain phantom created in the here presented work consists of 9 different tissue types: skin, fat, muscle, skull, dura mater, gray matter, myelinated white matter, nonmyelinated white matter and cerebrospinal fluid. Each voxel has a vector consisting of 9 components, one for each of these nine tissue types. This digital phantom can be used to map simulated magnetic resonance signal intensities resulting in simulated MR images of the newborns head. These images with controlled degradation of the image data present a representative, reproducible data set ideal for development and evaluation of neonatal MRI analysis methods, e.g. segmentation and registration algorithms.

A direct ROI quantification method for inherent PVE correction: accuracy assessment in striatal SPECT measurements

PURPOSE

The clinical potential of striatal imaging with dopamine transporter (DAT) SPECT tracers is hampered by the limited capability to recover activity concentration ratios due to partial volume effects (PVE). We evaluated the accuracy of a least squares method that allows retrieval of activity in regions of interest directly from projections (LS-ROI).

METHODS

An Alderson striatal phantom was filled with striatal to background ratios of 6:1, 9:1 and 28:1; the striatal and background ROIs were drawn on a coregistered X-ray CT of the phantom. The activity ratios of these ROIs were derived both with the LS-ROI method and with conventional SPECT EM reconstruction (EM-SPECT). Moreover, the two methods were compared in seven patients with motor symptoms who were examined with N-3-fluoropropyl-2-beta-carboxymethoxy-3-beta-(4-iodophenyl) (FP-CIT) SPECT, calculating the binding potential (BP).

RESULTS

In the phantom study, the activity ratios obtained with EM-SPECT were 3.5, 5.3 and 17.0, respectively, whereas the LS-ROI method resulted in ratios of 6.2, 9.0 and 27.3, respectively. With the LS-ROI method, the BP in the seven patients was approximately 60% higher than with EM-SPECT; a linear correlation between the LS-ROI and the EM estimates was found (r=0.98, p=0.03).

CONCLUSION

The LS-ROI PVE correction capability is mainly due to the fact that the ill-conditioning of the LS-ROI approach is lower than that of the EM-SPECT one. The LS-ROI seems to be feasible and accurate in the examination of the dopaminergic system. This approach can be fruitful in monitoring of disease progression and in clinical trials of dopaminergic drugs.

Design and construction of a realistic digital brain phantom

After conception and implementation of any new medical image processing algorithm, validation is an important step to ensure that the procedure fulfills all requirements set forth at the initial design stage. Although the algorithm must be evaluated on real data, a comprehensive validation requires the additional use of simulated data since it is impossible to establish ground truth with in vivo data. Experiments with simulated data permit controlled evaluation over a wide range of conditions (e.g., different levels of noise, contrast, intensity artefacts, or geometric distortion). Such considerations have become increasingly important with the rapid growth of neuroimaging, i.e., computational analysis of brain structure and function using brain scanning methods such as positron emission tomography and magnetic resonance imaging. Since simple objects such as ellipsoids or parallelepipedes do not reflect the complexity of natural brain anatomy, we present the design and creation of a realistic, high-resolution, digital, volumetric phantom of the human brain. This three-dimensional digital brain phantom is made up of ten volumetric data sets that define the spatial distribution for different tissues (e.g., grey matter, white matter, muscle, skin, etc.), where voxel intensity is proportional to the fraction of tissue within the voxel. The digital brain phantom can be used to simulate tomographic images of the head. Since the contribution of each tissue type to each voxel in the brain phantom is known, it can be used as the gold standard to test analysis algorithms such as classification procedures which seek to identify the tissue "type" of each image voxel. Furthermore, since the same anatomical phantom may be used to drive simulators for different modalities, it is the ideal tool to test intermodality registration algorithms. The brain phantom and simulated MR images have been made publicly available on the Internet (http://www.bic.mni.mcgill.ca/brainweb).

3D simulation of PET brain images using segmented MRI data and positron tomograph characteristics

A 3D simulation procedure has been developed to generate simulated PET brain images from MRI data. MRI slices were segmented into gray matter, white matter, CSF structures, and assigned with radionuclide distributions. Projections through these regions were generated according to physical characteristics of a positron tomograph, including 3D sampling and resolution, attenuation, scatter, randoms, and counting statistics. The projection data were then reconstructed by filtered backprojection. The procedure was validated with a cold spot phantom. Simulated PET images for cerebral blood flow or metabolism are presented, along with a brief discussion of some applications and limitations.

Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography

A new class of fast maximum-likelihood estimation (MLE) algorithms for emission computed tomography (ECT) is developed. In these cyclic iterative algorithms, vector extrapolation techniques are integrated with the iterations in gradient-based MLE algorithms, with the objective of accelerating the convergence of the base iterations. This results in a substantial reduction in the effective number of base iterations required for obtaining an emission density estimate of specified quality. The mathematical theory behind the minimal polynomial and reduced rank vector extrapolation techniques, in the context of emission tomography, is presented. These extrapolation techniques are implemented in a positron emission tomography system. The new algorithms are evaluated using computer experiments, with measurements taken from simulated phantoms. It is shown that, with minimal additional computations, the proposed approach results in substantial improvement in reconstruction.

Assessment of accuracy of PET utilizing a 3-D phantom to simulate the activity distribution of [18F]fluorodeoxyglucose uptake in the human brain

A three-dimensional brain phantom has been developed to simulate the activity distributions found in human brain studies currently employed in positron emission tomography (PET). The phantom has a single contiguous chamber and utilizes thin layers of lucite to provide apparent relative concentrations of 5, 1, and 0 for gray matter, white matter, and CSF structures, respectively. The phantom and an ideal image set were created from the same set of data. Thus, the user has a basis for comparing measured images with an ideal set that allows a quantitative evaluation of errors in PET studies with an activity distribution similar to that found in patients. The phantom was employed in a study of the effect of deadtime and scatter on accuracy in quantitation on a current PET system. Deadtime correction factors were found to be significant (1.1-2.5) at count rates found in clinical studies. Deadtime correction techniques were found to be accurate to within 5%. Scatter in emission and attenuation correction data consistently caused 5-15% errors in quantitation, whereas correction for scatter in both types of data reduced errors in accuracy to less than 5%.