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Polynomial-Based Inverse Planning: General Concepts and a Toy Example

F Li*, J Park , G Yan , University of Florida, Gainesville, FL


(Monday, 7/30/2018) 1:15 PM - 1:45 PM

Room: Exhibit Hall | Forum 7

Purpose: To propose a novel three-stage inverse planning algorithm utilizing orthogonal polynomials, and demonstrate the principle and feasibility with an example in two-dimension (2D) assuming flat PDD and non-diverging beams.

Methods: Conventional IMRT inverse planning adopts an iterative approach that operates on the smallest elements in the system – beamlets and individual voxels. We show that it is possible to work on higher-level mathematical objects such as Chebyshev and Zernike polynomials that spread over many beamlets and voxels. This approach reduces the number of parameters in an optimization problem, resulting in a more efficient inverse planning scheme.

Results: The application of Chebyshev and Zernike Polynomials convert a 2D inverse planning problem into a three-stage process with decreasing computational complexity along the stages. In the first stage, beam profiles and doses are decomposed into Chebyshev and Zernike polynomials, and the optimization problem is mapped into a series of linear equations. The crucial benefit of the first stage is the resulting linear equations have degrees of freedom much smaller than the number of voxels. In the second stage, an approximate solution is obtained by analytically inverting a linear system with small degrees of freedom, which can be efficiently performed in seconds. The result of the second stage is then fed into the third stage where the optimizer refines the intermediate solution to obtain a clinical deliverable plan.

Conclusion: We demonstrated the first and second stage of the proposed inverse planning scheme using a “toy� 2D inverse planning problem assuming flat PDD and non-diverging beams. Inverse planning of a twenty-beam IMRT completed in 10 seconds on a personal computer. The methodology proposed can be extended to three-dimension and non-coplanar optimization problem.


Inverse Planning, Optimization


TH- External beam- photons: IMRT dose optimization algorithms

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