Inverse Fourier transformation of combined first order derivative and intensity-curvature functional of magnetic resonance angiography of the human brain.

BACKGROUND AND OBJECTIVE: This paper reports a novel image processing technique based on inverse Fourier transformation and its validation procedure. METHODS: Magnetic Resonance Angiography (MRA) data of the human brain is fitted on a pixel-by-pixel basis with bivariate linear model polynomial function. Polynomial fitting allows the formulation of two measures: the first order derivative (FOD), which is an edge finder, and the intensity-curvature functional (ICF), which is a high pass filter. The calculation of FOD and ICF uses knowledge provided by existing research and is performed through resampling. ICF and FOD are direct Fourier transformed, and their k-space is combined through a nonlinear convolution of terms. The resulting k-space is inverse Fourier transformed so to obtain a novel image called Fourier Convolution Image (FCI). RESULTS: FCI possesses the characteristics of an edge finder (FOD) and a high pass filter (ICF). CONCLUSIONS: FC images yield the following properties versus MRA: 1. Change of the contrast; 2. Increased sharpness in the proximity of human brain vessels; 3. Increased visualization of vessel connectivity. The implication of this study is to provide FCI as another viable option for MRA evaluation.

Intensity-curvature functional based digital high pass filter of the bivariate cubic B-spline model polynomial function.

This research addresses the design of intensity-curvature functional (ICF) based digital high pass filter (HPF). ICF is calculated from bivariate cubic B-spline model polynomial function and is called ICF-based HPF. In order to calculate ICF, the model function needs to be second order differentiable and to have non-null classic-curvature calculated at the origin (0, 0) of the pixel coordinate system. The theoretical basis of this research is called intensity-curvature concept. The concept envisions to replace signal intensity with the product between signal intensity and sum of second order partial derivatives of the model function. Extrapolation of the concept in two-dimensions (2D) makes it possible to calculate the ICF of an image. Theoretical treatise is presented to demonstrate the hypothesis that ICF is HPF signal. Empirical evidence then validates the assumption and also extends the comparison between ICF-based HPF and ten different HPFs among which is traditional HPF and particle swarm optimization (PSO) based HPF. Through comparison of image space and k-space magnitude, results indicate that HPFs behave differently. Traditional HPF filtering and ICF-based filtering are superior to PSO-based filtering. Images filtered with traditional HPF are sharper than images filtered with ICF-based filter. The contribution of this research can be summarized as follows: (1) Math description of the constraints that ICF need to obey to in order to function as HPF; (2) Math of ICF-based HPF of bivariate cubic B-spline; (3) Image space comparisons between HPFs; (4) K-space magnitude comparisons between HPFs. This research provides confirmation on the math procedure to use in order to design 2D HPF from a model bivariate polynomial function.

Intensity-Curvature Measurement Approaches for the Diagnosis of Magnetic Resonance Imaging Brain Tumors.

This research presents signal-image post-processing techniques called Intensity-Curvature Measurement Approaches with application to the diagnosis of human brain tumors detected through Magnetic Resonance Imaging (MRI). Post-processing of the MRI of the human brain encompasses the following model functions: (i) bivariate cubic polynomial, (ii) bivariate cubic Lagrange polynomial, (iii) monovariate sinc, and (iv) bivariate linear. The following Intensity-Curvature Measurement Approaches were used: (i) classic-curvature, (ii) signal resilient to interpolation, (iii) intensity-curvature measure and (iv) intensity-curvature functional. The results revealed that the classic-curvature, the signal resilient to interpolation and the intensity-curvature functional are able to add additional information useful to the diagnosis carried out with MRI. The contribution to the MRI diagnosis of our study are: (i) the enhanced gray level scale of the tumor mass and the well-behaved representation of the tumor provided through the signal resilient to interpolation, and (ii) the visually perceptible third dimension perpendicular to the image plane provided through the classic-curvature and the intensity-curvature functional.

Complex threshold method for identifying pixels that contain predominantly noise in magnetic resonance images.

PURPOSE: To create a robust means to remove noise pixels using complex data. MATERIALS AND METHODS: A receiver operating characteristic (ROC) curve was used to determine the appropriate choice of magnitude and phase thresholds as well as connectivity values to determine what pixels represent noise in the image. To fine-tune the results, a spike removal and hole replacement operator is applied to reduce Type I error and remove small islands of noise. RESULTS: The use of phase information improves the magnitude-only thresholding approach by further recognizing pixels that contain only noise. The performance of the method is enhanced using local connectivity of magnitude and phase data. An ROC analysis on simulated data shows that the Type I and Type II errors are less than 10(-4) and 10(-3), respectively, without connectivity and 0 and 10(-3), respectively, with connectivity for a signal-to-noise ratio (SNR) of 3:1 or higher. CONCLUSION: The joint use of both magnitude and phase images helps to improve the removal of noise points in magnetic resonance images. This can prove useful in automating the visualization of phase images without the highly distractive phase noise in noise regions. Also, it is useful in susceptibility weighted imaging when taking the minimum intensity projections of variably sized regions.

New algorithm for quantifying vascular changes in dynamic contrast-enhanced MRI independent of absolute T1 values.

In this work, we present a new method for predicting changes in tumor vascularity using only one flip angle in dynamic contrast-enhanced (DCE) imaging. The usual DCE approach finds the tissue initial T1 value T1(0) prior to injection of a contrast agent. We propose finding changes in the tissue contrast agent uptake characteristics pre- and postdrug treatment by fixing T1(0). Using both simulations and imaging pre- and postadministration of caffeine, we find that the relative change (NR50) in the median of the cumulative distribution (R50) is almost independent of T1(0). Fixing T1(0) leads to a concentration curve c(t) more robust to the presence of noise than calculating T1(0). Consequently, the NR50 for the tumor remains roughly the same as the ideal NR50 when T1(0) is exactly known. Further, variations in eating habits are shown to create significant changes in the R50 response for both liver and muscle. In conclusion, analyzing data with fixed T1(0) leads to a more stable measure of changes in NR50 and does not require knowledge of T1(0). Both caffeine and eating introduce major changes in blood flow that can significantly modify the NR50 and lead to incorrect conclusions regarding drug treatment.

Establishing a baseline phase behavior in magnetic resonance imaging to determine normal vs. abnormal iron content in the brain.

PURPOSE: To establish a baseline of phase differences between tissues in a number of regions of the human brain as a means of detecting iron abnormalities using magnetic resonance imaging (MRI). MATERIALS AND METHODS: A fully flow-compensated, three-dimensional (3D), high-resolution, gradient-echo (GRE) susceptibility-weighted imaging (SWI) sequence was used to collect magnitude and phase data at 1.5 T. The phase images were high-pass-filtered and processed region by region with hand-drawn areas. The regions evaluated included the motor cortex (MC), putamen (PUT), globus pallidus (GP), caudate nucleus (CN), substantia nigra (SN), and red nucleus (RN). A total of 75 subjects, ranging in age from 55 to 89 years, were analyzed. RESULTS: The phase was found to have a Gaussian-like distribution with a standard deviation (SD) of 0.046 radians on a pixel-by-pixel basis. Most regions of interest (ROIs) contained at least 100 pixels, giving a standard error of the mean (SEM) of 0.0046 radians or less. In the MC, phase differences were found to be roughly 0.273 radians between CSF and gray matter (GM), and 0.083 radians between CSF and white matter (WM). The difference between CSF and the GP was 0.201 radians, and between CSF and the CN (head) it was 0.213 radians. For CSF and the PUT (the lower outer part) the difference was 0.449 radians, and between CSF and the RN (third slice vascularized region) it was 0.353 radians. Finally, the phase difference between CSF and SN was 0.345 radians. CONCLUSION: The Gaussian-like distributions in phase make it possible to predict deviations from normal phase behavior for tissues in the brain. Using phase as an iron marker may be useful for studying absorption of iron in diseases such as Parkinson's, Huntington's, neurodegeneration with brain iron accumulation (NBIA), Alzheimer's, and multiple sclerosis (MS), and other iron-related diseases. The phases quoted here will serve as a baseline for future studies that look for changes in iron content.

Performance assessment of an algorithm for the alignment of fMRI time series.

This paper reports on performance assessment of an algorithm developed to align functional Magnetic Resonance Image (fMRI) time series. The algorithm is based on the assumption that the human brain is subject to rigid-body motion and has been devised by pipelining fiducial markers and tensor based registration methodologies. Feature extraction is performed on each fMRI volume to determine tensors of inertia and gradient image of the brain. A head coordinate system is determined on the basis of three fiducial markers found automatically at the head boundary by means of the tensors and is used to compute a point-based rigid matching transformation. Intensity correction is performed with sub-voxel accuracy by trilinear interpolation. Performance of the algorithm was preliminarily assessed by fMR brain images in which controlled motion has been simulated. Further experimentation has been conducted with real fMRI time series. Rigid-body transformations were retrieved automatically and the value of motion parameters compared to those obtained with the Statistical Parametric Mapping (SPM99) and the Automatic Image Registration (AIR 3.08). Results indicate that the algorithm offers sub-voxel accuracy in performing both misalignment and intensity correction of fMRI time series.