US 4,539,640 AGranted

Reconstruction system and methods for impedance imaging

AssigneeTasc Ltd.

InventorsBradley Fry, Alvin Wexler

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Abstract

A method and apparatus for imaging the interior of a structure, such as a mineral or human body, having regions therein which differentially affect particular characteristics of electrical signals transmitted through the body. The method involves injecting a plurality of electrical signals into the body, measuring at least one characteristic of each such signal at a plurality of locations, comparing the measured characteristic with the corresponding characteristic measured at at least one reference point of the structure and generating comparison signals, iteratively reconstructing the impedance spatial relationships between the regions within the structure by utilizing the comparison signals, and providing an image of the interior of the structure from the reconstruction of such impedance spatial relationships.

Claims18

Dependent claims

A method of displaying an image of the interior of a structure having a plurality of surfaces and comprising regions of different conductivities which differentially affect electrical signals transmitted therethrough, said method comprising the steps of:

(a) applying electrical input currents at a plurality of selected current input sites of said structures, each of said electrical input currents flowing within at least one of said regions and exiting from said structure at a selected current output site thereof;
(b) measuring the voltages generated by each of said applied currents at a plurality of selected voltage measuring sites of said structure with respect to a voltage reference point, each of said selected voltage measuring sites being remote from the current input and output sites through which flows the current generating said voltages;
(c) calculating the voltages .phi. at a plurality of locations within said structure, including said selected voltage measuring sites, with respect to said voltage reference point from the equation
-.gradient..multidot..kappa..gradient..phi.=f,
where .kappa. is a value of conductivity assumed for each of said locations and f is the density of each of the electrical input currents at said current input and output sites, the current traversing the surfaces of said structure except at said current input and output sites being assumed equal to zero;
(d) calculating the electrical current flux density J at each of the locations for which the voltage was calculated in step (c) from the equation
J=-.kappa..gradient..phi.;
(e) comparing the voltages calculated in step (c) for each of said selected voltage measuring sites of said structure and the corresponding voltages measured at said selected sites in step (b);
(f) repeating steps (c) and (d) when the difference between the voltages compared in step (e) are greater than a predetermined amount, the voltages measured in step (b) then being substituted at said selected voltage measuring sites for the voltages calculated in step (c);
(g) calculating new values for .kappa. for each of said locations when the squared residual sum R equals ##EQU7## where V is the region over which the imaging is being performed and X represents the excitations over which the sum is taken, by determining the values of .kappa. which minimize R throughout said structure;
(h) repeating steps (f) and (g) until the voltages compared in step (e) do not exceed said predetermined amount;
and
(i) displaying the values of .kappa. calculating in step (h) thereby providing an image of the interior of said structure.

10 more elements

Apparatus for displaying an image of the interior of a structure having a plurality of surfaces and comprising regions of different conductivities which differentially affect electrical signals transmitted therethrough, comprising

a plurality of unguarded electrodes located at selected sites of said structure, a first group of said electrodes functioning as input electrodes during a given interval of time and a second group of said electrodes functioning as output electrodes during said given interval;
means for applying electrical currents during said given interval to said first group of electrodes, said electrical currents flowing within at least one of said regions;
means for withdrawing said electrical currents from said structure during said given interval at said second group of electrodes;
means for selecting during said given interval a plurality of voltages measuring sites of said structure, said voltage measuring sites being remote from the sites selected during said interval for said first and second groups of electrodes;
means for measuring the voltages at said selected plurality of voltages measuring sites with respect to a voltage reference point, said measurements being made during said given interval;
computer means for
(1) calculating the voltages .phi. at a plurality of locations within said structure, including said selected voltage measuring sites, with respect to said voltage reference point from the equation
-.gradient..multidot..kappa..gradient..phi.=f,
where .kappa. is a value of conductivity assumed for each of said locations and f is the density of each of the electrical input currents at said current input and output sites, the current traversing the surfaces of said structure except at said current input and output sites being assumed equal to zero;
(2) calculating the electrical current flux density J at each of the locations for which the voltage was calculated from the equation
J=-.kappa..gradient..phi.;
(3) comparing the calculated voltages with the voltages measured at said plurality of selected voltage measuring sites;
and
(4) iteratively calculating new values of the conductivity .kappa. for each of said locations when the squared residual sum R equals ##EQU8## where V is the region over which the imaging is being performed and X represents the excitations over which the sum is taken, by determining the values of .kappa. which minimize R throughout said structure;
and
display means for displaying the values of conductivity .kappa. thereby producing an image of the interior of said structure.

13 more elements

Dependencies are inferred from the claim text.