High resolution two-dimensional resistance tomography
Inventors
Grayson, Matthew Allen • Wang, Chulin • Onsager, Claire Cecelia • Aygen, Can Cenap • Costakis, Charles M. • Lang, Lauren E. • Tzavelis, Andreas • Rogers, John Ashley
Assignees
Publication Number
US-12357188-B2
Publication Date
2025-07-15
Expiration Date
2039-11-29
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Abstract
The disclosed 2-D and 3-D tomographic resistance imaging method improves tomographic resistance image resolution by adopting an orthogonal basis with the maximum number of elements N to describe the maximum resolution resistivity map ρ(r), where this number of elements N is set according to the number of electrodes Q; by defining the orthogonal basis according to any known constraints in the problem, thereby enhancing the resolution where it is needed; by positioning electrodes to be sensitive to these basis functions; and by choosing current I and voltage V contact electrode pairs that maximize signal-to-noise ratio.
Core Innovation
The invention pertains to a computer-implemented method for high resolution two-dimensional (2-D) and three-dimensional (3-D) tomographic resistance imaging by adopting an orthogonal basis with the maximum number of elements N to describe the maximum resolution resistivity map ρ(r). The number of elements N is set according to the number of electrodes Q and the orthogonal basis is defined according to any known constraints in the problem to enhance resolution where it is most necessary. The method includes positioning electrodes to be sensitive to these basis functions and selecting current and voltage contact electrode pairs that maximize the signal-to-noise ratio for improved measurement.
The problem solved by the invention arises from the shortcomings of traditional electrical impedance tomography methods that use a high-resolution mesh of thousands of points to estimate resistivity maps. These conventional methods require a large amount of data and intensive computation, often leading to an ill-defined problem where the number of variables exceeds the number of equations, causing non-unique solutions and wasted computing resources. Moreover, these methods rely on poorly placed electrodes and non-optimal measurement pairs that limit achievable resolution and accuracy.
To address these issues, the disclosed method restricts the number of orthogonal basis functions to match the maximum number N of independent tetra-polar resistance measurements, ensuring a well-defined inverse mapping problem with a unique solution. The resistivity map ρ(r) is expressed as a superposition of orthogonal polynomial basis functions ϕi(r), which can be chosen as a priori polynomials (e.g., Zernike polynomials for circular surfaces), constrained polynomials, principal component analysis (PCA)-derived bases, or a combination thereof. Electrode placements and measurement pairs are strategically selected to maximize sensitivity to these basis functions and to optimize the signal-to-noise ratio, thereby enabling enhanced resolution and accuracy in the tomographic image.
Claims Coverage
The patent includes one independent computer implemented claim which covers the method of mapping a tomographic image using orthogonal basis functions and resistance measurements. The main inventive features include the configuration of electrodes, the formulation of the resistivity map, and the methods of measurement and display.
Method for 2-D tomographic image mapping using resistance measurements
Defining a surface area of a resistive sensing membrane with Q peripheral contact electrodes where Q ≥ 5, measuring a maximum number N of independent tetra-polar resistances sequentially using voltage and current electrode pairs, and mapping a 2-D resistance tomographic image by relating the resistivity map ρ(r) to orthogonal basis polynomial functions ϕi(r) with resolution increasing up to the maximum number N of measurements.
Use of Zernike polynomial basis functions for circular surfaces
When the surface area is circular, employing a priori orthogonal polynomial basis functions defined by the Zernike polynomials to represent the resistivity map.
Constrained polynomial basis for improved resolution
Applying constraints to the polynomial basis by disallowing a subset of basis states and indexing remaining allowable basis states from low to high resolution to enhance image quality.
Principal component analysis derived orthogonal basis functions
Deriving orthogonal basis functions by applying PCA to a representative set of likely resistance maps, using covariance matrix diagonalization to obtain eigenvectors representing the most significant variations with an upper limit N matching the independent tetra-polar measurements.
Combination of polynomial and PCA basis functions
Determining orthogonal basis functions by combining a priori polynomial basis, constrained polynomial basis, and PCA basis functions all limited to the maximal number N of independent measurements.
Selection of basis functions focused on constrained regions
Choosing orthogonal basis functions to provide highest resolution within constrained or local regions of interest postulated to improve mapping efficiency.
Restriction of basis functions to local regions under constraints
When constraints exist, restricting orthogonal basis functions to represent features solely within designated local regions of interest.
Optimization of electrode placement for resolution
Selecting the locations of peripheral contact electrodes to maximize resolution by enhancing sensitivity to the defined orthogonal basis functions.
Optimization of current-voltage electrode pair selection
Identifying and selecting pairs of current and voltage electrodes for measurement to derive a maximally independent set of measurements with maximized signal-to-noise ratio.
Determination of measured resistance vector
Calculating a measured resistance vector from the sequentially measured tetra-polar resistances to aid tomographic image reconstruction.
The independent claim encompasses a computer-implemented method that combines a unique electrode arrangement and measurement process with a mathematically defined resistivity map represented by orthogonal basis functions limited by the number of independent measurements, optimizing both resolution and signal quality for accurate 2-D tomographic imaging.
Stated Advantages
Improved tomographic resistance image resolution by matching the number of orthogonal basis functions to the maximum number of independent measurements.
Reduced computational time and complexity compared to traditional mesh-based finite element methods.
Unique and well-defined solution to the inverse problem, avoiding ill-defined and non-unique solutions.
Enhanced sensitivity to regions of interest or known constraints by tailoring the orthogonal basis.
Optimized electrode placement improves measurement sensitivity and resolution.
Selection of current and voltage electrode pairs maximizes signal-to-noise ratio, resulting in higher accuracy.
Documented Applications
Pressure-sensitive polymer pads infused with conductive particles like carbon-nanotubes or carbon-black, where local resistivity changes under applied force enable 2-D pressure pattern imaging.
3-D tomographic imaging of resistive volumes such as human torso tissue to map volume resistivity variations for applications like imaging internal organs.
Sensing and imaging contact pressure or resistivity patterns, exemplified by detection of hand-prints on a resistive elastomeric membrane.
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