Radiation Dose Matrix Decomposition for Real-Time Therapy Planning
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Solution Overview
Problem
Conventional radiation therapy treatment planning systems face challenges in efficiently determining and optimizing radiation doses due to the impracticality of storing large fluence matrices and the slowness of dose calculation methods, particularly in particle beam therapy, where millions of voxels and pencil beams result in matrices that exceed conventional memory limits and are not suitable for real-time calculations.
Innovation Solution
The method involves determining an initial approximation of the cumulative voxel radiation dose using parallel processors and graphic processor units (GPUs), decomposing operations into independent linear steps that can be corrected using a set of linear, independent operations with transposes, allowing for efficient calculation and optimization of radiation doses without explicitly constructing the fluence matrix.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the fluence matrix is explicitly constructed to accurately represent the spatial distribution of radiation dose, then the measurement precision is improved, but the device complexity and memory requirements become impractical
Solution Approach 1:
The fluence matrix A is decomposed into a product of three smaller matrices: A = UΣV^T (singular value decomposition) or A = USV^T (truncated SVD). This segmentation transforms a single large 10^12 byte matrix into multiple smaller matrices that can be stored and processed in conventional memory, while preserving the essential information needed for accurate dose calculation.
Solution Approach 2:
Instead of storing the actual large fluence matrix, the patent stores compressed representations (singular vectors and values) that can be used to reconstruct the matrix on-demand or to compute matrix-vector products directly. This copying approach allows the system to work with the essential information without the full data burden.
2Measurement precision
If conventional dose calculation methods are used to ensure accuracy, then the measurement precision is improved, but the productivity and real-time calculation capability deteriorate
Solution Approach 1:
The patent pre-computes and stores the singular value decomposition components (matrices U and V, and singular values Σ) of the fluence matrix before actual dose calculation is needed. This preliminary action allows the system to perform fast matrix-vector multiplications during treatment planning by simply combining the pre-computed components with the current beam weights, rather than performing full Monte Carlo simulations or other computationally intensive calculations in real-time.
3Device complexity
If a sparse approximation of the fluence matrix is used to reduce memory requirements, then the device complexity is reduced, but the measurement precision deteriorates due to neglected small fluence values
Solution Approach 1:
The patent transforms the fluence matrix representation from a dense or sparse format into a singular value decomposition format (A = UΣV^T). This parameter change allows the system to control precision through the number of singular values retained, rather than through spatial sparsification. The singular value decomposition naturally captures the most significant radiation patterns while discarding negligible components, providing a more physically meaningful truncation criterion than simple sparsification.
Data Source
AI summary
A method for planning a radiation therapy treatment of a body represented by a volume of voxels determines a radiation dose matrix representing a spatial distribution of a radiation dose of beams of radiation irradiating the volume with homogeneous stopping power. The beams are collimated and are shifted copies of each other at each depth of the volume, and the spatial distribution is determined by calculating cumulative beam-axial doses in a single matrix-matrix multiplication and redistributing the cumulative beam-axial doses to all voxels in the volume using a convolution. Next, a set of correcting operations is applied to the radiation dose matrix to produce a cumulative voxel radiation dose of the volume. Each correcting operation is linear, independent from another correcting operation and has a transform.