Electricity: measuring and testing – Impedance – admittance or other quantities representative of... – Distributive type parameters
Reexamination Certificate
2000-05-26
2002-09-10
Le, N. (Department: 2858)
Electricity: measuring and testing
Impedance, admittance or other quantities representative of...
Distributive type parameters
C324S639000, C343S853000, C600S407000, C703S002000
Reexamination Certificate
active
06448788
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to electromagnetic imaging of inhomogeneous, lossy targets having arbitrary shape, and in particular, it relates to microwave imaging to reconstruct electrical properties of biological tissue.
2. Statement of the Problem
Active microwave imaging for medical diagnosis is known in the art. U.S. Pat. No. 5,841,288, issued Nov. 24, 1998 to Meaney et al., discloses an apparatus and methods for determining electrical properties of an inhomogeneous target. The electrical property distribution on an arbitrary coarse mesh distribution of the target is first estimated; then corresponding electric field values on a fine mesh distribution of the target are computed. The fine mesh has finer discretization than the coarse mesh and is overlapping with the coarse mesh. Electric field values are then measured at preselected measurement sites within a homogeneous region external to the target. A Jacobian matrix is calculated, which represents a sensitivity calculation relative to a change in the electric field values at selected measurement sites due to a perturbation in the electrical property distribution on the coarse mesh. A difference vector is formed between the computed electric field and the measured electric field values, and an update vector is added to the electrical property distribution as a function of the difference vector and the Jacobian matrix. The electric field values are then re-computed based on the updated electrical property distribution, which is compared with the measured electric field values to produce a least squared error. If this error is not sufficiently small, the steps above, beginning with computing a Jacobian matrix, are repeated until the error is sufficiently small.
The dual mesh scheme reduces the number of points where electrical properties ∈
r
and &sgr; are calculated within a region of interest. The fine mesh is uniformly dense and is used for calculating the electric field values over the region; the coarse mesh is less dense, can be uniform or non-uniform, and is used for representing the k
2
distribution within the region. The term “k
2
” is the complex wavenumber, squared, and includes both electrical properties ∈
r
and &sgr;, (i.e., k
2
=&ohgr;&mgr;∈
o
∈
r
+j&ohgr;&mgr;&sgr;, where ∈
o
is the dielectric constant in a vacuum, ∈
r
is the relative dielectric constant, &sgr; is the conductivity, and &mgr; is the magnetic permeability of free space). The number of nodes on the coarse mesh is less than or equal to the number of individual pieces of measurement data. The dual mesh scheme thus utilizes a practical amount of measurement data and the calculation of the k
2
distribution is performed without compromising the accuracy of the forward solution.
Such known methods and systems provide a calibration routine to convert 3-D measured data to a 2-D format. Such a routine is utilized because microwave antennae radiate into 3-D space; yet, the reconstruction algorithms typically utilize only 2-D radiation characteristics. This is important because of the nature of antennae: in 3-D, the free space loss factor (FSLF) varies proportionally to 1/R
2
from the phase center of a transmitting antenna; while in 2-D, the FSLF varies proportionally to 1/R (R equals the distance from the phase center to the receiver). Thus, this approach substitutes the data's dependency on 1/R
2
with a dependency on 1/R. Specifically, a calibration routine calculates the phase center of each antenna and then modifies the amplitude relative to the 1/R
2
and 1/R dependencies. The phase center is calculated by measuring the electric fields at a number of points within the homogeneous medium. A least squares procedure then determines where the phase center must have been to give such a field distribution.
In calculating the electrical property distribution of a target, the following equation is solved for the electric field vector, {overscore (E)}, at each iteration:
[
A]{{overscore (E)}}={{overscore (b)}},
where [A] is the forward solution matrix, and {{overscore (b)}} is a vector representing the boundary condition. The derivative is then taken with respect to the electrical properties for every coarse mesh node i and every radiating transmitter antenna:
[
∂
A
∂
k
i
2
]
{
E
→
}
=
-
[
A
]
{
∂
E
∂
k
i
2
}
.
Note that {{overscore (b)}} is not a function of the electrical property distribution so its derivative with respect to k
i
2
is zero. This equation is used to solve for
{
∂
E
∂
k
i
2
}
,
since [A], {overscore (E)} are already known. A matrix
[
∂
A
∂
k
i
2
]
is thus formed, in which its coefficients are the derivatives of the individual terms of the matrix [A] used in the forward solution of the electric fields. These coefficients are computed with respect to the electrical properties, k
i
2
, at a single node on the coarse mesh. This new mesh, in combination with the original matrix [A] used in the computation of the electric fields and the most current calculated values of the electric field, {overscore (E)}, is used to compute the variations of the electric fields due to perturbation of the electrical properties, e.g.,
{
∂
E
∂
k
i
2
}
,
at a single coarse mesh node, for a single radiator. The terms
{
∂
E
∂
k
i
2
}
make up the Jacobian matrix. Thus, to build the whole Jacobian matrix, the process is repeated for all of the radiators and all of the nodes. This time-consuming process can be efficiently done in parallel.
Typically, the inhomogeneous target object being analyzed is surrounded by a homogeneous medium contained in an illumination chamber. Transmitter and receiver antennae are disposed in the homogeneous region surrounding the object. Typically, the homogeneous medium is a saline bath or other liquid solution. Measuring the electric field includes irradiating the target with microwave energy having a single operating frequency from a plurality of transmitting antennae that surround the target, and receiving microwave energy at a second plurality of receiving antennae for each of the transmitting antennae. Typically, the antennae are arranged substantially within the same plane about the target. Computing the electric field includes computing, through simulation, the electric field at finite element nodes on the fine mesh. Determining electrical property distributions includes estimating the electrical property values based upon a homogeneous distribution with values identical to the homogeneous medium surrounding the target. Computing an electric field includes computing a two-dimensional field distribution utilizing hybrid element techniques. In such a technique, the electric field values are determined by finite element discretization of the target region and a small portion of the homogeneous region immediately surrounding the target region, in combination with the boundary element method to represent the outer surrounding homogeneous region. The step of discretizing the target with a finite element mesh (that is, the fine mesh) may include minimizing the number of nodes on the fine mesh.
An illumination chamber comprises material that is lossy within the operating frequency range, which is about 300 MHz to 1100 MHz in the prior art. The illumination chamber may have a thick solid wall, for example in a cylindrical or square shape, surrounding the target, and in which the antennae are disposed. Typically, however, the illumination chamber contains a liquid homogeneous medium, in which the target is disposed. Transmitting and receiving antennae are suspended within the liquid homogeneous medium to surround the target. Electrical property distributions are determined through a coarse mesh discretization of the illumination region, which includes the target region and homogeneous region. The fine mesh representing
Fanning Margaret W.
Meaney Paul M.
Paulsen Keith D.
Deb Anjan K.
Lathrop & Gage L.C.
Le N.
Microwave Imaging System Technologies, Inc.
Swenson, Esq. Thomas
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