On the modeling, construction, and evaluation of a probabilistic atlas of brain perfusion

Stochastic modeling of the PPG signal: a synthesis-by-analysis approach with applications

In this paper, we propose a stochastic model of photoplethysmographic signals that is able to synthesize an arbitrary number of other statistically equivalent signals to the one under analysis. To that end, we first preprocess the pulse signal to normalize and time-align pulses. In a second stage, we design a single-pulse model, which consists of ten parameters. In the third stage, the time evolution of this ten-parameter vector is approximated by means of two autoregressive moving average models, one for the trend and one for the residue; this model is applied after a decorrelation step which let us to process each vector component in parallel. The experiments carried out show that the model we here propose is able to maintain the main features of the original signal; this is accomplished by means of both a linear spectral analysis and also by comparing two measures obtained from a nonlinear analysis. Finally, we explore the capability of the model to: 1) track physical activity; 2) obtain statistics of clinical parameters by model sampling; and 3) recover corrupted or missing signal epochs by synthesis.

Grouping a few sets of normally distributed voxels of SPECT volumes in discrimination between Alzheimer dementia and controls

It is widely accepted and can be easily verified that any specific voxel in a class of brain single photon emission computed tomography (SPECT) volumes is of a univariate normal distribution. In this research, we conjecture that all the voxels in a class of SPECT volumes are also approximately of a multivariate normal (MVN) distribution from which in terms of the Bayes errors of statistics, an optimal classifier can be designed using quadratic discriminant functions (QDFs). However, the number of training volumes needed for deriving the covariance matrix of an MVN distribution increases quadratically with respect to the number of voxels such that practically the MVN distributions cannot be modeled. To overcome this, we selected a reduced number of voxels and put them into groups based on the P values of two-sided t tests or a greedy algorithm of discrimination between two classes of volumes. We also tried the same approach on the 3D Haar wavelet coefficients which were obtained from the discrete wavelet transform of the voxels. Experiments showed that the accuracies of QDFs, linear discriminant functions (LDFs), and support vector machines (SVMs) were not significantly different in discrimination between Alzheimer's and normal controls verifying that the proposed MVNs effectively model the discrimination information. Moreover, the proposed QDF classifier obtained satisfactory performance.

Optimization of the parameters of a method for computer-aided detection of perfusion deficiencies in brain images

OBJECTIVE

Simulated data from the recent Institute of Physics and Engineering in Medicine audit of quantitative cerebral perfusion were used to optimize the parameters of eigenimage analysis, a method for computer-aided detection.

METHODS

Twenty normal images provided by the audit were registered to the International Consortium for Brain Mapping 452 template using HERMES multimodality software and normalized to total counts. Six normal atlases were formed using the mean image and from zero to five eigenimages. Eight patient images, with computer-simulated lesions at known positions, were similarly registered and normalized. For each atlas, z-score images were formed for each patient. Thresholds of z0 = 2-5 in intervals of 0.5 were applied to the z-score images to form binary images of normal and abnormal voxels. A lesion was defined as a connected group of abnormal voxels with a minimum size of 1 ml. Lesions were assigned to one of 12 regions defined by the template. For eight patients, this gave 96 regions, 19 of which were known to contain an abnormality. Receiver-operating characteristic analysis was performed for the regions using z0 as a variable threshold.

RESULTS

For the receiver-operating characteristic analysis, an optimal area under the curve of approximately 0.90 was found using either one or three eigenimages, whereas good results (sensitivity = 0.75%; specificity = 90%) were obtained for a threshold of z0 approximately equal to 3. When the number of images in the normal dataset was considered, a meta-analysis showed consistency with other studies.

CONCLUSION

Eigenimage analysis was shown to give good diagnostic accuracy for cerebral perfusion images based on objective evaluation using simulated images.

Retrospective evaluation of a topology preserving non-rigid registration method

This paper proposes a comprehensive evaluation of a monomodal B-spline-based non-rigid registration algorithm allowing topology preservation in 3-D. This article is to be considered as the companion of [Noblet, V., Heinrich, C., Heitz, F., Armspach, J.-P., 2005. 3-D deformable image registration: a topology preservation scheme based on hierarchical deformation models and interval analysis optimization. IEEE Transactions on Image Processing, 14 (5), 553-566] where this algorithm, based on the minimization of an objective function, was introduced and detailed. Overall assessment is based on the estimation of synthetic deformation fields, on average brain construction, on atlas-based segmentation and on landmark mapping. The influence of the model parameters is characterized. Comparison between several objective functions is carried out and impact of their symmetrization is pointed out. An original intensity normalization scheme is also introduced, leading to significant improvements of the registration quality. The comparison benchmark is the popular demons algorithm [Thirion, J.-P., 1998. Image matching as a diffusion process: an analogy with Maxwell's demons. Medical Image Analysis, 2 (3), 243-260], that exhibited best results in a recent comparison between several non-rigid 3-D registration methods [Hellier, P., Barillot, C., Corouge, I., Gibaud, B., Le Goualher, G., Collins, D.L., Evans, A., Malandain, G., Ayache, N., Christensen, G.E., Johnson, H.J., 2003. Retrospective evaluation of intersubject brain registration. IEEE Transactions on Medical Imaging, 22 (9), 1120-1130]. The topology preserving B-spline-based method proved to outperform the commonly available ITK implementation of the demons algorithms on many points. Some limits of intensity-based registration methods are also highlighted through this work.

Realistic Simulated MRI and SPECT Databases

This paper describes the construction of simulated SPECT and MRI databases that account for realistic anatomical and functional variability. The data is used as a gold-standard to evaluate four SPECT/MRI similarity-based registration methods. Simulation realism was accounted for using accurate physical models of data generation and acquisition. MRI and SPECT simulations were generated from three subjects to take into account inter-subject anatomical variability. Functional SPECT data were computed from six functional models of brain perfusion. Previous models of normal perfusion and ictal perfusion observed in Mesial Temporal Lobe Epilepsy (MTLE) were considered to generate functional variability. We studied the impact noise and intensity non-uniformity in MRI simulations and SPECT scatter correction may have on registration accuracy. We quantified the amount of registration error caused by anatomical and functional variability. Registration involving ictal data was less accurate than registration involving normal data. MR intensity nonuniformity was the main factor decreasing registration accuracy. The proposed simulated database is promising to evaluate many functional neuroimaging methods, involving MRI and SPECT data.