Localised one-dimensional magnetic resonance spatial-frequency spectroscopy
A method of assessing a spatial frequency distribution within a sample comprising subjecting the sample to magnetic resonance excitation, receiving an echo signal from the sample while the sample is subjected to a magnetic field gradient, applying an invertible linear transform to the echo signal, identifying a region of interest in the transformed echo signal and deriving a corresponding window function, applying the window function (in the signal or transform domain) to the echo signal to remove echo signal coming from regions of the sample outside of the region of interest, and analyzing the one dimensional spatial frequency content in the windowed echo signal in order to access a one dimensional spatial frequency distribution within the region of interest within the sample without creating an image.
1. A method that uses a Magnetic Resonance Imaging (MRI) system in generating a spatial frequency distribution from a sample of a structure, wherein the method comprises:
using the MRI system and its associated processors in order to perform the following:
a) subjecting the sample to a magnetic field;
b) subjecting the sample to magnetic resonance excitation;
c) receiving an echo signal from the sample while the sample is subjected to a magnetic field gradient;
d) transforming the echo signal into a corresponding transform domain, using an invertible linear transform while maintaining only linear operations in order to ensure the use of only linear signal processing steps;
e) identifying a region of interest within resulting transform domain of d), and calculating a linear windowing function corresponding to the region of interest;
f) applying the linear windowing function of e) to the echo signal in order to remove echo signal coming from regions of the sample outside of the region of interest;
g) analyzing the complex-valued one dimensional spatial frequency content of the windowed echo signal obtained in f) in order to derive a one dimensional spatial frequency distribution from the region of interest within the sample of the structure without the need to create an image; and
h) displaying a result based on the resulting derived one dimensional spatial frequency distribution.
2. The method of claim 1 wherein applying the linear windowing function comprises:
a) taking a transform of the echo signal;
b) complex multiplying the calculated window function by the echo signal;
c) taking an inverse transform of the result of b).
3. The method of claim 2 wherein the transform and the inverse transform are Fourier transforms.
4. The method of claim 2 wherein the transform and the inverse transform are wavelet transforms.
5. The method of claim 2 wherein the transform and the inverse transform are z-transforms.
6. The method of claim 1 wherein the sample is subjected to a first and second magnetic resonance excitation in order to selectively excite an inner volume.
7. A method that uses a Magnetic Resonance Imaging (MRI) system in generating a spatial frequency distribution from a sample of a structure, wherein the method comprises:
using the MRI system and its associated processors in order to perform the following:
a) subjecting the sample to a magnetic field;
b) subjecting the sample to magnetic resonance excitation;
c) receiving an echo signal from the sample while the sample is subjected to a magnetic field gradient;
d) transforming the echo signal into a corresponding transform domain using an invertible linear transform while maintaining only linear operations in order to ensure the use of only linear signal processing steps;
e) identifying a region of interest within resulting transform domain of d), and calculating a linear windowing function corresponding to the region of interest;
f) applying the linear windowing function of e) to the echo signal in order to remove echo signal coming from regions of the sample outside of the region of interest;
g) analyzing the complex-valued one dimensional spatial frequency content of the windowed echo signal obtained in f) in order to derive a one dimensional spatial frequency distribution from the region of interest within the sample of the structure without the need to create an image;
h) displaying a result based on the resulting derived one dimensional spatial frequency distribution; and
wherein applying the linear windowing function comprises:
i) taking the Fourier transform of the calculated window function; and
j) taking a complex convolution of the echo signal with the transformed window function.