Electric Conductivity Reconstruction via Phase Extrapolation

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Solution Overview

Problem

Existing methods for reconstructing spatial distributions of electric conductivity from magnetic resonance image data suffer from severe artifacts, particularly at tissue boundaries, leading to inaccurate results and noise in images of subjects like the head, liver, and prostate.

Innovation Solution

A method that segments magnetic resonance image data into voxels within and outside the volume of interest, extrapolates phase values to reduce boundary artifacts, transforms the numerical kernel into the frequency domain for efficient multiplication, and filters the results to enhance accuracy and reduce noise.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If Fourier transformation is used to accelerate convolution calculation, then processing speed is improved, but boundary artifacts increase due to inability to identify tissue boundaries

Engineering Contradiction:

Improveprocessing speedVSAvoidboundary accuracy

Core Design Contradiction:

ProductivityVSManufacturing precision

Solution Approach 1:

The image is segmented into voxels corresponding to a volume of interest and voxels outside the volume of interest, separated by a segmentation boundary. This allows different processing strategies for different regions, applying the fast Fourier transformation method within the volume of interest while handling boundary regions separately to maintain accuracy.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Phase values are extrapolated for voxels outside the volume of interest before the main reconstruction process. This preliminary action ensures that boundary regions have appropriate phase values ready in advance, preventing artifacts when the Laplacian operation encounters tissue boundaries during the accelerated reconstruction.

Inventive Principle:

Principle #10Preliminary action

2Device complexity

If phase values are directly used at tissue boundaries, then computation is simplified, but severe artifacts occur due to phase discontinuities and noise

Engineering Contradiction:

Improvecomputation complexityVSAvoidreconstruction accuracy

Core Design Contradiction:

Device complexityVSReliability

Solution Approach 1:

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

Extrapolated phase values act as an intermediary between the interior voxels and exterior regions. These interpolated values smooth the transition at boundaries, serving as a mediator that prevents direct contact between contrasting phase regions, thereby eliminating discontinuities and reducing noise at tissue boundaries.

Inventive Principle:

Principle #24Intermediary (Mediator)

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

This approach significantly reduces boundary artifacts and noise, providing a fast and robust method for reconstructing electric conductivity distributions with improved precision, especially in imaging techniques like balanced Fast Field Echo.

Implementation Method 1

The CPU processing time required for calculating the electric conductivity σ can significantly be shortened by a Fourier transformation of the differentiation kernel and the transceive phase φ into the frequency domain, which reduces the convolution to merely a multiplication.

Methodology Applied

Scientific EffectFourier transformation:

Implementation Method 2

The calculation of the Laplacian is realized by a convolution of a differentiation kernel and the transceive phase φ of the acquired magnetic resonance image.

Methodology Applied

Scientific EffectLaplacian operator:

Data Source

PatentUS10185011B2EPT method of electric conductivity reconstruction with enhanced stability and speed

Publication Date: 2019.01.22 KONINKLIJKE PHILIPS NV

AI summary

An electric properties tomography method for reconstructing a spatial distribution of electric conductivity (σ) from magnetic resonance image data representative of a magnetic resonance image of at least a portion of a subject of interest (20), the spatial distribution covering at least a portion of the area of the magnetic resonance image, and the method comprising following steps:—segmenting the magnetic resonance image,—extrapolating acquired phase values, —replacing acquired phase values by the extrapolated phase values,—transforming into the frequency domain,—multiplying a frequency domain-transformed numerical second derivative by the acquired phase values and the frequency domain-transformed numerical second derivative by the extrapolated phase values, respectively, and—transforming the result of the multiplying into the spatial domain. Also covered are a corresponding MRI system and a software module.