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Optimal NMR Chemical Shift Imaging With Non-Uniform Fields

IP.com Disclosure Number: IPCOM000060583D
Original Publication Date: 1986-Apr-01
Included in the Prior Art Database: 2005-Mar-08
Document File: 5 page(s) / 68K

Publishing Venue

IBM

Related People

Feig, E: AUTHOR

Abstract

Two recently developed methods of Optimal Nuclear Magnetic Resonance (NMR) imaging (2,3,6) can be combined to yield proton chemical shift images in non-uniform fields whose inhomogeneities are slowly varying, using much fewer scans than do existing methods. Chemical shift imaging involves the determination of a density function d(w,X), where w denotes the chemical-shift variable and X is the space variable. In this article we will only discuss proton chemical shift imaging. In this particular case, the chemical-shift spectrum at each point X in space has a very special form which makes our analysis possible; the spectrum is "essentially" a superposition of two delta functions which are very close together. In n-dimensional imaging X ranges over n-dimensional vector space.

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Optimal NMR Chemical Shift Imaging With Non-Uniform Fields

Two recently developed methods of Optimal Nuclear Magnetic Resonance (NMR) imaging (2,3,6) can be combined to yield proton chemical shift images in non-uniform fields whose inhomogeneities are slowly varying, using much fewer scans than do existing methods. Chemical shift imaging involves the determination of a density function d(w,X), where w denotes the chemical-shift variable and X is the space variable. In this article we will only discuss proton chemical shift imaging. In this particular case, the chemical-shift spectrum at each point X in space has a very special form which makes our analysis possible; the spectrum is "essentially" a superposition of two delta functions which are very close together. In n-dimensional imaging X ranges over n- dimensional vector space. We will only consider here planar imaging (n=2); this case is the practical one because the scanning time is not prohibitively long (it is short enough that we may expect the patient imaged to remain relatively motionless). We will write X = (x,y), and the function d(w,X) = d(w,x,y) will represent the density of excited particles at position (x,y) which are spinning with frequency w. Methods for determining discrete approximations to d(w,x,y) are known [1]. They are very costly. If x and y range over N1 and N2 equally spaced grid values, then the methods call for N1 x N2 scans. Essentially they determine the spectrum of the FID (Function Identification) localized at each of the N1 x N2 distinct spatial coordinates. The support of d-(w,x,y) is in fact very thin because, as was mentioned above, the chemical shift spectrum is essentially two delta functions. Thus, the support of d-(w,x,y) is 2 non-intersecting surfaces. In a homogeneous environment the support of d(w,x,y) would in fact be 2 parallel planes. Let us define a function d(w,x,y) which gives the density of excited particles at position (x,y) which, had they been in a uniform field, would be spinning with frequency w. This function is almost always zero except along the surfaces (wi, x,y), i=1, 2. To us, chemical shift imaging will mean the determination of d(wi,x,y), i=1, 2. In [2], we presented a general chemical shift algorithm that, when applied to proton shift imaging, would yield d(wi,x,y) with only 2N scans, where N=min {N1, N2} . The assumption implicit in the method there is that the main field is uniform. A similar algorithm was proposed by Dixon
[3]. It too requires a uniform magnetic field. In practice, fields are never uniform. Dixon does claim that his method can be used with non-uniform fields provided that one corrects for "the phase error in the image obtained with the modified pulse sequence". He points out that "this phase error results from field inhomogeneities across the image", but he does not mention the possibility of obtaining this phase information from the FID signals themselves. Other enhanced methods for proton chemic...