Technical Note: Harmonic analysis applied to MR image distortion fields specific to arbitrarily shaped volumes.

Area of Science:

• Medical Physics
• Image Analysis
• Radiation Therapy Technology

Background:

• Magnetic resonance imaging (MRI) is increasingly vital in radiation therapy (RT) due to advancements in MR-guided technologies.
• High spatial accuracy of MR images is crucial for RT tasks like treatment planning and in-room guidance.
• System-related distortions in MR images can compromise accuracy, necessitating robust characterization methods.

Purpose of the Study:

• To investigate a novel harmonic analysis method for characterizing complex three-dimensional (3D) distortion fields in MR images.
• To assess the spatial accuracy of MR images for radiation therapy applications.

Main Methods:

• Formulated an interior Dirichlet problem solving the Laplace equation with boundary conditions for 3D distortion fields.
• Employed the finite element method (FEM) to solve the boundary value problem (BVP) for various quadratic and complex geometries.
• Validated the method by comparing harmonic analysis results with experimental reference data from a linearity phantom.

Main Results:

• The harmonic analysis method showed good agreement with experimental data across all tested geometries.
• For quadratic domains, residual distortion values exceeding 1 mm were minimal (0.5% axial, 0.2% vector magnitude).
• For complex fields, the method achieved a maximum residual of 1.4 mm and a mean of 0.25 mm, with only 1.5% of points exceeding 1 mm.

Conclusions:

• Introduced and validated a novel harmonic analysis approach using FEM for MR image distortion characterization.
• The method requires only surface data of the domain, simplifying input requirements.
• This harmonic method can aid in designing new phantoms for MR distortion quantitation and integrating multiple RT imaging tests for quality control.