US 2002/0057087 A1Published application

Asymmetric radio frequency coils for magnetic resonance

AssigneeNMR Holdings No. 2 Pty Limited

InventorsStuart Crozier, Ben Lawrence, Desmond Yau, Kurt Luescher, Wolfgang Udo Roffman, David Michael Doddrell

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Abstract

Asymmetric radio frequency (RF) coils for magnetic resonance applications are provided. Also provided are time harmonic methods for designing such coils as well as symmetric coils. In addition, methods for converting complex current density functions into discrete capacitive and inductive elements are provided.

Claims46

Dependent claims

Apparatus for use in a magnetic resonance system for transmitting a radio frequency field, receiving a magnetic resonance signal, or transmitting a radio frequency field and receiving a magnetic resonance signal, said apparatus and said magnetic resonance imaging system having a common longitudinal axis, said apparatus comprising:

(a) a support member which defines a bore having first and second open ends which are spaced from one another along the longitudinal axis by a distance L;
and
(b) a plurality of inductive elements and a plurality of capacitive elements associated with the support member;
wherein if used as a transmitter, the apparatus has the following characteristics:
(i) the apparatus produces a radio frequency field which has a radial magnetic component which has a spatially-varying peak magnitude whose average value is Ar-avg;
(ii) the apparatus has a homogenous volume within the bore over which the spatially-varying peak magnitude of the radio frequency field has a maximum deviation from Ar-avg which is less than or equal to 15%;
(iii) the homogeneous volume defines a midpoint M which is on the longitudinal axis, is closer to the first end than to the second end, and is spaced from the first end by a distance D such that the ratio D/L is less than or equal to 0.4;
and
(iv) at least one of said inductive elements comprises a discrete conductor which follows a sinuous path such that during use of the apparatus current flows through a first part of the conductor in a first direction that has both longitudinal and azimuthal components and through a second part of the conductor in a second direction that has both longitudinal and azimuthal components, said first and second directions being different.

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A method for designing apparatus for use in a magnetic resonance system for receiving a magnetic resonance signal having a predetermined radio frequency, said apparatus and said magnetic resonance system having a common longitudinal axis, said method comprising designing the apparatus by treating the apparatus as a transmitter of a radio frequency field having the predetermined radio frequency and then designing said transmitter by:

(a) defining a target region in which the radial magnetic component of the radio frequency field is to have desired values, said target region surrounding said longitudinal axis;
(b) specifying desired values for said radial magnetic component of the radio frequency field at a preselected set of points within the target region;
(c) determining a complex current density function J, having real and imaginary parts, on a specified cylindrical surface by:
(i) defining the complex current density function as a sum of a series of basis functions multiplied by complex amplitude coefficients having real and imaginary parts;
and
(ii) determining values for the complex amplitude coefficients using an iterative minimization technique applied to a residue vector obtained by taking the difference between calculated field values obtained using the complex amplitude coefficients at the preselected points and the desired values at those points;
and
(d) converting said complex current density function J into a set of capacitive elements located on the specified cylindrical surface and a set of inductive elements located on the specified cylindrical surface by:
(i) converting the complex current density function into a curl-free component Jcurl-free and a divergence-free component Jdiv-free using the relationships:
Jcurl-free=∇ψ, and
Jdiv-free=∇×S, where ψ and S are functions obtained from the complex current density function through the equations:
∇2ψ=∇·J −∇2S=∇×J, and −∇2(n·S)=n·∇J,
where n is a vector normal to the specified cylindrical surface;
(ii) calculating locations on the specified cylindrical surface for the set of capacitive elements by contouring the function ψ;
and
(iii) calculating locations on the specified cylindrical surface for the set of inductive elements by contouring the function n·S.

13 more elements

A method for designing apparatus for use in a magnetic resonance system for transmitting a radio frequency field or both transmitting a radio frequency field and receiving a magnetic resonance signal, said apparatus and said magnetic resonance system having a common longitudinal axis, said method comprising:

(a) defining a target region in which the radial magnetic component of the radio frequency field is to have desired values, said target region surrounding said longitudinal axis;
(b) specifying desired values for said radial magnetic component of the radio frequency field at a preselected set of points within the target region;
(c) defining a target surface external to the apparatus on which the magnetic component of the radio frequency field is to have a desired value of zero at a preselected set of points on said target surface;
(d) determining a first complex current density function, having real and imaginary parts, on a first specified cylindrical surface and a second complex current density, having real and imaginary parts, on a second specified cylindrical surface, the radius of the second specified cylindrical surface being greater than the radius of the first specified cylindrical surface by:
(i) defining each of the complex current density functions as a sum of a series of basis functions multiplied by complex amplitude coefficients having real and imaginary parts;
and
(ii) determining values for the complex amplitude coefficients using an iterative minimization technique applied to a first residue vector obtained by taking the difference between calculated field values obtained using the complex amplitude coefficients at the set of preselected points in the target region and the desired values at those points and a second residue vector equal to calculated field values obtained using the complex amplitude coefficients at the preselected set of points on the target surface;
and
(e) converting said first and second complex current density functions into sets of capacitive elements and sets of inductive elements located on the specified cylindrical surfaces by:
(i) converting each of the first and second complex current density functions into a curl-free component Jcurl-free and a divergence-free component Jdiv-free using the relationships:
Jcurl-free=∇ψ, and
Jdiv-free=∇×S, where ψ and S are functions obtained from the respective first and second complex current density functions through the equations:
∇2ψ=∇·J, −∇2S=∇×J, and −∇2(n·S)=n·∇×J,
where n is a vector normal to the respective first and second specified cylindrical surfaces and J is the respective first and second complex current density functions;
(ii) calculating locations on the respective first and second cylindrical surfaces for the respective sets of capacitive elements by contouring the respective functions ψ;
and
(iii) calculating locations on the respective first and second cylindrical surfaces for the respective sets of inductive elements by contouring the respective functions n·S.

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(a) defining a target region in which the radial magnetic component of the radio frequency field is to have desired values, said target region surrounding said longitudinal axis;
(b) specifying desired values for said radial magnetic component of the radio frequency field at a preselected set of points within the target region;
(c) determining a complex current density function J, having real and imaginary parts, on a specified cylindrical surface by:
(i) defining the complex current density function as a sum of a series of basis functions multiplied by complex amplitude coefficients having real and imaginary parts;
and
(ii) determining values for the complex amplitude coefficients by solving a matrix equation of the form:
[A](ac)=B where A is a transformation matrix between current density space and magnetic field space whose components are based on time harmonic Green's functions, ac is a vector of the unknown complex amplitude coefficients, and B is a vector of the desired values for the magnetic field specified in step (b), said equation being solved by:
(1) transforming the equation into a functional that can be solved using a preselected regularization technique, and
(2) solving the functional using said regularization technique to obtain values for the complex amplitude coefficients;
and
(d) converting said complex current density function into a set of capacitive elements located on the specified cylindrical surface and a set of inductive elements located on the specified cylindrical surface.

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(a) defining a target region in which the radial magnetic component of the radio frequency field is to have desired values, said target region surrounding said longitudinal axis;
(b) specifying desired values for said radial magnetic component of the radio frequency field at a preselected set of points within the target region;
(c) defining a target surface external to the apparatus on which the magnetic component of the radio frequency field is to have a desired value of zero;
(d) determining a first complex current density function, having real and imaginary parts, on a first specified cylindrical surface and a second complex current density, having real and imaginary parts, on a second specified cylindrical surface, the radius of the second specified cylindrical surface being greater than the radius of the first specified cylindrical surface by:
(i) defining each of the complex current density functions as a sum of a series of basis functions multiplied by complex amplitude coefficients having real and imaginary parts;
and
(ii) determining values for the complex amplitude coefficients by simultaneously solving matrix equations of the form:
[A1C](aC)+[A1S](aS)=BC
[A2C](aC)+[A2S](aS)=BS
where A1C, A1S, A2C, and A2S are transformation matrices between current density space and magnetic field space whose components are based on time harmonic Green's functions, aC and aS are vectors of the unknown complex amplitude coefficients for the first and second complex current density functions, respectively, BC is a vector of the desired values for the radial magnetic field specified in step (b), and BS is a vector whose values are zero, said equations being solved by:
(1) transforming the equations into functionals that can be solved using a preselected regularization technique, and
(2) solving the functionals using said regularization technique to obtain values for the complex amplitude coefficients;
and
(e) converting said first and second complex current density functions into sets of capacitive elements and sets of inductive elements located on the specified cylindrical surfaces.

11 more elements

Dependencies are inferred from the claim text.

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