Howard Donald Gage

Statistical models of partial volume effect

Statistical models of partial volume effect for systems with various types of noise or pixel value distributions are developed and probability density functions are derived. The models assume either Gaussian system sampling noise or intrinsic material variances with Gaussian or Poisson statistics. In particular, a material can be viewed as having a distinct value that has been corrupted by additive noise either before or after partial volume mixing, or the material could have nondistinct values with a Poisson distribution as might be the case in nuclear medicine images. General forms of the probability density functions are presented for the N material cases and particular forms for two- and three-material cases are derived. These models are incorporated into finite mixture densities in order to more accurately model the distribution of image pixel values. Examples are presented using simulated histograms to demonstrate the efficacy of the models for quantification. Modeling of partial volume effect is shown to be useful when one of the materials is present in images mainly as a pixel component.

Quantification of brain tissue through incorporation of partial volume effects

This research addresses the problem of automatically quantifying the various types of brain tissue, CSF, white matter, and gray matter, using T1-weighted magnetic resonance images. The method employs a statistical model of the noise and partial volume effect and fits the derived probability density function to that of the data. Following this fit, the optimal decision points can be found for the materials and thus they can be quantified. Emphasis is placed on repeatable results for which a confidence in the solution might be measured. Results are presented assuming a single Gaussian noise source and a uniform distribution of partial volume pixels for both simulated and actual data. Thus far results have been mixed, with no clear advantage being shown in taking into account partial volume effects. Due to the fitting problem being ill-conditioned, it is not yet clear whether these results are due to problems with the model or the method of solution.

Evaluation of brain activity in FDG PET studies.

PURPOSE A tool (Gemini) was developed for quantifying regions of interest (ROIs) in registered MR and PET data. Its use was validated through phantom and simulated studies. METHOD Hot spheres were imaged in a phantom (3:1 and 5:1 target-to-nontarget ratios). The computerized 3D Hoffman brain phantom was used to simulate PET studies. Spherical local activity features of two diameters (4 and 10 mm) and five intensities (5, 15, 25, 50, and 100% increase over gray matter) were added to the data in the thalamus and Brodmann area 37. The data were reprojected into sinograms and blurred with a 7 mm kernel. Poisson noise was added, and the sinograms were then reconstructed and analyzed using both SPM96 and Gemini spherical ROIs. RESULTS Based on phantom and simulated data, the 95th percentile of intensity within a Gemini ROI afforded a reasonable joint optimization of variance (reliability) and accuracy (validity). SPM96 and Gemini results were similar for the larger (10 mm) feature, but in this application, Gemini was more sensitive than SPM96 for the small feature (4 mm). CONCLUSION Gemini, a tool for display and measurement of spherical ROIs in registered PET and MR data, is precise and accurate for testing hypotheses of differences in localized brain activity, comparing favorably with SPM96.

Using Probability Densities to Evolve more Secure Software Configurations

The use of Evolutionary Algorithms (EAs) is one method for securing software configurations in a changing environment. Using this approach, configurations are modeled as biological chromosomes, and a continual sequence of selection, recombination, and mutation processes is performed. While this approach can evolve secure configurations based on current conditions, it is also possible to inadvertently lose solutions to previous threats during the evolution process. This paper improves the performance of EA-based configuration management by incorporating parameter-setting history. Over the generations (EA iterations), counts are maintained regarding the parameter-settings and the security of the configuration. Probability densities are then developed and used during mutation to encourage the selection of previously secure settings. As a result, these secure settings are likely to be maintained as attacks alternate between vulnerabilities. Experimental results using configuration parameters from RedHat Linux installed Apache web-servers indicate the addition of parameter history significantly improves the ability to maintain secure settings as an attacker alternates between different threats.

Correction for partial volume effect in PET blood flow images

Current positron emission tomography techniques for the measurement of cerebral blood flow assume that voxels represent pure material regions. In this work, a method is presented which utilizes anatomical information from a high resolution modality such as MRI in conjunction with a multicompartment extension of the Kety model to obtain intravoxel, tissue specific blood flow values. In order to evaluate the proposed method, noisy time activity curves (TACs) were simulated representing different combinations of gray matter, white matter and CSF, and ratios of gray to white matter blood flow. In all experiments it was assumed that registered MR data supplied the number of materials and the fraction of each present. For each TAC, three experiments were run. In the first it was assumed that the fraction of each material determined by MRI was correct, and, in the second two, that the value was either too high or too low. Using the tree annealing method, material flows were determined which gave the best fit of the model to the simulated TAC data. The results indicate that the accuracy of the method is approximately linearly related to the error in material fraction estimated for a voxel.

Quantifying white matter lesions with MRI using finite mixture density and 2D clustering estimation

Research is presented in which white matter lesions are quantified using MRI data on cardiac surgery patients. Various methods of quantification are presented including finite mixture density analysis of various MRI parameters, K-means, and principal components analysis. Pre- and post-operative data sets are studied for each patient to determine the change in lesion load due to surgery. The various methods are compared and the differences are indicated on both registered and unregistered data sets. Agreement among the methods is not good in many instances and at times show an inverse correlation. Images and data showing the gray scale distributions are presented.

Image resolution: the impact on finite mixture density models in medical applications

Finite mixture density (FMD) based approaches to medical image classification or quantification problems have received considerable interest lately. In this paper, we will show through use of computer simulations that as the resolution of the underlying imaging modality decreases (its full width at half maximum (FWHM) increases) the successful application of an FMD approach will become increasingly difficult. A 19 slice computer phantom of the human brain was used. This phantom, generated from MR images of a human brain, is composed of gray matter, white matter, and cerebrospinal fluid regions. Image sets were generated using Gaussian kernels of various sizes and FWHMs. The distributions of single and multiple components pixels were then generated from these image sets. A planar acquisition of a single slice brain phantom is also presented for comparison. It is shown that, with decreasing image resolution, a major weakness of the FMD approach is its inability to incorporate spacial information. Decreasing resolution with respect to object size results in an increasing number of partial volume pixels with resulting effects on its FMD components.