Biomedical subjects

H Edwin Romeijn

Publications and source records attributed to H Edwin Romeijn.

5 recordsLinked to original sources

PubMed2006

Fast voxel and polygon ray-tracing algorithms in intensity modulated radiation therapy treatment planning.

We present work on combining three algorithms to improve ray-tracing efficiency in radiation therapy dose computation. The three algorithms include: An improved point-in-polygon algorithm, incremental voxel ray tracing algorithm, and stereographic projection of beamlets for voxel truncation. The point-in-polygon and incremental voxel ray-tracing algorithms have been used in computer graphics and nuclear medicine applications while the stereographic projection algorithm was developed by our group. These algorithms demonstrate significant improvements over the current standard algorithms in peer reviewed literature, i.e., the polygon and voxel ray-tracing algorithms of Siddon for voxel classification (point-in-polygon testing) and dose computation, respectively, and radius testing for voxel truncation. The presented polygon ray-tracing technique was tested on 10 intensity modulated radiation therapy (IMRT) treatment planning cases that required the classification of between 0.58 and 2.0 million voxels on a 2.5 mm isotropic dose grid into 1-4 targets and 5-14 structures represented as extruded polygons (a.k.a. Siddon prisms). Incremental voxel ray tracing and voxel truncation employing virtual stereographic projection was tested on the same IMRT treatment planning cases where voxel dose was required for 230-2400 beamlets using a finite-size pencil-beam algorithm. Between a 100 and 360 fold cpu time improvement over Siddon's method was observed for the polygon ray-tracing algorithm to perform classification of voxels for target and structure membership. Between a 2.6 and 3.1 fold reduction in cpu time over current algorithms was found for the implementation of incremental ray tracing. Additionally, voxel truncation via stereographic projection was observed to be 11-25 times faster than the radial-testing beamlet extent approach and was further improved 1.7-2.0 fold through point-classification using the method of translation over the cross product technique.

Algorithms↗

PubMed2006

A fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation.

We developed an analytical method for determining the maximum acceptable grid size for discrete dose calculation in proton therapy treatment plan optimization, so that the accuracy of the optimized dose distribution is guaranteed in the phase of dose sampling and the superfluous computational work is avoided. The accuracy of dose sampling was judged by the criterion that the continuous dose distribution could be reconstructed from the discrete dose within a 2% error limit. To keep the error caused by the discrete dose sampling under a 2% limit, the dose grid size cannot exceed a maximum acceptable value. The method was based on Fourier analysis and the Shannon-Nyquist sampling theorem as an extension of our previous analysis for photon beam intensity modulated radiation therapy [J. F. Dempsey, H. E. Romeijn, J. G. Li, D. A. Low, and J. R. Palta, Med. Phys. 32, 380-388 (2005)]. The proton beam model used for the analysis was a near monoenergetic (of width about 1% the incident energy) and monodirectional infinitesimal (nonintegrated) pencil beam in water medium. By monodirection, we mean that the proton particles are in the same direction before entering the water medium and the various scattering prior to entrance to water is not taken into account. In intensity modulated proton therapy, the elementary intensity modulation entity for proton therapy is either an infinitesimal or finite sized beamlet. Since a finite sized beamlet is the superposition of infinitesimal pencil beams, the result of the maximum acceptable grid size obtained with infinitesimal pencil beam also applies to finite sized beamlet. The analytic Bragg curve function proposed by Bortfeld [T. Bortfeld, Med. Phys. 24, 2024-2033 (1997)] was employed. The lateral profile was approximated by a depth dependent Gaussian distribution. The model included the spreads of the Bragg peak and the lateral profiles due to multiple Coulomb scattering. The dependence of the maximum acceptable dose grid size on the orientation of the beam with respect to the dose grid was also investigated. The maximum acceptable dose grid size depends on the gradient of dose profile and in turn the range of proton beam. In the case that only the phantom scattering was considered and that the beam was aligned with the dose grid, grid sizes from 0.4 to 6.8 mm were required for proton beams with ranges from 2 to 30 cm for 2% error limit at the Bragg peak point. A near linear relation between the maximum acceptable grid size and beam range was observed. For this analysis model, the resolution requirement was not significantly related to the orientation of the beam with respect to the grid.

Algorithms↗

PubMed2005

A fourier analysis of the dose grid resolution required for accurate IMRT fluence map optimization.

We present a theoretical and empirical analysis of the errors associated with the spatial discretization of the dose grid employed in optimized intensity modulated radiation therapy (IMRT) treatment plans. An information theory based Fourier analysis of the accuracy of discrete representations of three-dimensional dose distributions is presented. When applied to beamlet-based IMRT dose distributions, the theory produces analytic integrals that can bound worst case aliasing errors that can occur regardless of the location and orientation of the dose grid. The predictions of this theory are compared to empirical results obtained by solving a linear-programming based fluence-map optimization model to global optimality. A reasonable agreement between worst case estimates and the empirical results is attributed to the fact that the optimization takes advantage of aliasing to produce an optimal plan. We predicted and empirically demonstrated that an isotropic dose grid with <2.5 mm spacing is sufficient to prevent dose errors larger than a percent. However, we noted that in practice this resolution is mostly needed in high-dose target regions. Finally, a multiresolution 2-4-6 mm spacing model was developed and empirically tested where these spacings were applied to targets, structures, and tissue, respectively.

Algorithms↗

PubMed2004

A unifying framework for multi-criteria fluence map optimization models.

Models for finding treatment plans for intensity modulated radiation therapy are usually based on a number of structure-based treatment plan evaluation criteria, which are often conflicting. Rather than formulating a model that a priori quantifies the trade-offs between these criteria, we consider a multi-criteria optimization approach that aims at finding the so-called undominated treatment plans. We present a unifying framework for studying multi-criteria optimization problems for treatment planning that establishes conditions under which treatment plan evaluation criteria can be transformed into convex criteria while preserving the set of undominated treatment plans. Such transformations are identified for many of the criteria that have been proposed to date, establishing equivalences between these criteria. In addition, it is shown that the use of a nonconvex criterion can often be avoided by transformation to an equivalent convex criterion. In particular, we show that models employing criteria such as tumour control probability, normal tissue complication probability, probability of uncomplicated tumour control, as well as sigmoidal transformations of (generalized) equivalent uniform dose are equivalent to models formulated in terms of separable voxel-based criteria that penalize dose in individual voxels.

Dose-Response Relationship, Radiation↗

PubMed2003

A novel linear programming approach to fluence map optimization for intensity modulated radiation therapy treatment planning.

We present a novel linear programming (LP) based approach for efficiently solving the intensity modulated radiation therapy (IMRT) fluence-map optimization (FMO) problem to global optimality. Our model overcomes the apparent limitations of a linear-programming approach by approximating any convex objective function by a piecewise linear convex function. This approach allows us to retain the flexibility offered by general convex objective functions, while allowing us to formulate the FMO problem as a LP problem. In addition, a novel type of partial-volume constraint that bounds the tail averages of the differential dose-volume histograms of structures is imposed while retaining linearity as an alternative approach to improve dose homogeneity in the target volumes, and to attempt to spare as many critical structures as possible. The goal of this work is to develop a very rapid global optimization approach that finds high quality dose distributions. Implementation of this model has demonstrated excellent results. We found globally optimal solutions for eight 7-beam head-and-neck cases in less than 3 min of computational time on a single processor personal computer without the use of partial-volume constraints. Adding such constraints increased the running times by a factor of 2-3, but improved the sparing of critical structures. All cases demonstrated excellent target coverage (> 95%), target homogeneity (< 10% overdosing and < 7% underdosing) and organ sparing using at least one of the two models.

Algorithms↗