Optimized electrical impedance tomography

Patent metadata

Field	Value
Publication number	US-12495985-B2
Application number	US-202218049551-A
Country	US
Kind code	B2
Filing date	Oct 25, 2022
Priority date	Nov 28, 2018
Publication date	Dec 16, 2025
Grant date	Dec 16, 2025

Abstract

The disclosed 2-D resistance tomographic imaging method optimizes computation speed for performing electrical impedance tomography using a model-space with a minimal number of orthonormal polynomial basis functions to describe discernable features in the 2-D resistance tomographic image, determining a minimal number of contacts to take fewer measurements than available information based on the number of basis functions, selecting a subset of rows of a matrix of calculated sensitivity coefficients to form a square Jacobian matrix for a linearized forward problem to be solved and inversion of the linear forward problem, and solving an inverse problem based on the square Jacobian matrix by performing at least one iteration of a Newton's method solve.

First claim

We claim:

1 . A computer implemented method of electrical impedance tomography for preparing a tomographic image to map over a surface of an object, comprising:
defining a surface area of a resistive sensing membrane having Q periphery contact electrodes attached along a periphery of the defined surface area of the resistive sensing membrane, wherein Q comprises an integer higher than or equal to five, wherein a plurality of local area resistances (r ABCD ) i to (r ABCD ) N that vary with an applied contact pressure over the defined surface area of the resistive sensing membrane cause a two-dimensional (2-D) resistance variation; mapping a 2-D resistance tomographic image over the defined surface area of the resistive sensing membrane according to the plurality of local area resistances of the applied contact pressure to the defined surface area of the resistive sensing membrane, wherein the 2-D resistance tomographic image mapping comprises:
measuring the plurality of local area resistances (r ABCD ) i to (r ABCD ) N , wherein i=1 to N, and N represents a maximum number of independent tetra-polar measurements;
determining a reference model to reduce computational steps to converge on a final 2-D resistance tomographic image;
identifying a minimal number M 0 of model-space basis functions to describe features to be discerned in the 2-D resistance tomographic image;
determining a minimal number of contacts C based on M 0 ;
calculating sensitivity coefficients for a D MAX ×M 0 sensitivity matrix;
selecting D 0 rows from the sensitivity matrix to form a Jacobian matrix for a linearized forward problem to be solved, where D 0 is an intended number of tetra-polar measurements to be performed,

D
I

=

C
⁡
(

C
-
3

)

2

,

and

⁢

D
0

<

D
I

,

where D I is a number of independent measurements given a quantity of C contacts;
determining a D 0 -dimensional sensitivity parallelotope volume in model-space based on the selected D 0 rows from the sensitivity matrix;
solving an inverse problem based on the Jacobian matrix to generate the 2-D resistance tomographic image; and
displaying the 2-D resistance tomographic image.

2 . The computer implemented method according to claim 1 , wherein determining the reference model comprises selecting a circular domain model-space with orthonormal polynomials as basis functions.

3 . The computer implemented method according to claim 1 , wherein determining the reference model comprises selecting a circular domain model-space with Zernike polynomial functions Z n k (r, θ) defined over a mesh as a priori conductivity basis functions described by the equations:

Z
n
k

(

r
,
θ

)

=

{

F
n
k

⁢

R
n

❘
"\[LeftBracketingBar]"

k

❘
"\[RightBracketingBar]"

⁢
r
⁢

cos
⁡
(

k
⁢
θ

)

for
⁢

⁢
k

≥
0

-

F
n
k

⁢

R
n

|
k
|

⁢
r
⁢

sin
⁡
(

m
⁢
θ

)

for
⁢

k

<
0

,

R
n

❘
"\[LeftBracketingBar]"

k

❘
"\[RightBracketingBar]"

(
r

Assignees

• Univ Northwestern

Inventors

• Grayson Matthew Allen
• Wang Chulin
• Onsager Claire Cecelia
• Aygen Can Cenap
• Costakis Charles M
• Lang Lauren E
• Tzavelis Andreas
• Rogers John Ashley
• Van Der Lee Suzan

Classifications

• G06T12/00

  Tomographic reconstruction from projections · CPC title

• A61B5/0536 Primary

  Impedance imaging, e.g. by tomography · CPC title

• G06T11/003

  Physics · mapped topic