Dataset Information

BRAIN 2.0: time and memory complexity improvements in the algorithm for calculating the isotope distribution.

ABSTRACT: Recently, an elegant iterative algorithm called BRAIN (Baffling Recursive Algorithm for Isotopic distributioN calculations) was presented. The algorithm is based on the classic polynomial method for calculating aggregated isotope distributions, and it introduces algebraic identities using Newton-Girard and Viète's formulae to solve the problem of polynomial expansion. Due to the iterative nature of the BRAIN method, it is a requirement that the calculations start from the lightest isotope variant. As such, the complexity of BRAIN scales quadratically with the mass of the putative molecule, since it depends on the number of aggregated peaks that need to be calculated. In this manuscript, we suggest two improvements of the algorithm to decrease both time and memory complexity in obtaining the aggregated isotope distribution. We also illustrate a concept to represent the element isotope distribution in a generic manner. This representation allows for omitting the root calculation of the element polynomial required in the original BRAIN method. A generic formulation for the roots is of special interest for higher order element polynomials such that root finding algorithms and its inaccuracies can be avoided.

SUBMITTER: Dittwald P

PROVIDER: S-EPMC3953541 | biostudies-literature | 2014 Apr

REPOSITORIES: biostudies-literature

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Publications

BRAIN 2.0: time and memory complexity improvements in the algorithm for calculating the isotope distribution.

Dittwald Piotr P Valkenborg Dirk D

Journal of the American Society for Mass Spectrometry 20140212 4

Recently, an elegant iterative algorithm called BRAIN (Baffling Recursive Algorithm for Isotopic distributioN calculations) was presented. The algorithm is based on the classic polynomial method for calculating aggregated isotope distributions, and it introduces algebraic identities using Newton-Girard and Viète's formulae to solve the problem of polynomial expansion. Due to the iterative nature of the BRAIN method, it is a requirement that the calculations start from the lightest isotope varian ...[more]

PMID: 24519333

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Project description:In the present work, we investigated the accuracy of the electron pencil-beam redefinition algorithm (PBRA) in calculating central-axis percent depth dose in water for rectangular fields. The PBRA energy correction factor C(E) was determined so that PBRA-calculated percent depth dose best matched the percent depth dose measured in water. The hypothesis tested was that a method can be implemented into the PBRA that will enable the algorithm to calculate central-axis percent depth dose in water at a 100-cm source-to-surface distance (SSD) with an accuracy of 2% or 1-mm distance to agreement for rectangular field sizes > or = 2 x 2 cm. Preliminary investigations showed that C(E), determined using a single percent depth dose for a large field (that is, having side-scatter equilibrium), was insufficient for the PBRA to accurately calculate percent depth dose for all square fields > or = 2 x 2 cm. Therefore, two alternative methods for determining C(E) were investigated. In Method 1, C(E), modeled as a polynomial in energy, was determined by fitting the PBRA calculations to individual rectangular-field percent depth doses. In Method 2, C(E) for square fields, described by a polynomial in both energy and side of square W [that is, C = C(E,W)], was determined by fitting the PBRA calculations to measured percent depth dose for a small number of square fields. Using the function C(E,W), C(E) for other square fields was determined, and C(E) for rectangular field sizes was determined using the geometric mean of C(E) for the two measured square fields of the dimension of the rectangle (square root method). Using both methods, PBRA calculations were evaluated by comparison with measured square-field and derived rectangular-field percent depth doses at 100-cm SSD for the Siemens Primus radiotherapy accelerator equipped with a 25 x 25-cm applicator at 10 MeV and 15 MeV. To improve the fit of C(E) and C(E,W) to the electron component of percent depth dose, it was necessary to modify the PBRA's photon depth dose model to include dose buildup. Results showed that, using both methods, the PBRA was able to predict percent depth dose within criteria for all square and rectangular fields. Results showed that second- or third-order polynomials in energy (Methods 1 and 2) and in field size (Method 2) were typically required. Although the time for dose calculation using Method 1 is approximately twice that using Method 2, we recommend that Method 1 be used for clinical implementation of the PBRA because it is more accurate (most measured depth doses predicted within approximately 1%) and simpler to implement.

Dataset Information

BRAIN 2.0: time and memory complexity improvements in the algorithm for calculating the isotope distribution.

Publications

BRAIN 2.0: time and memory complexity improvements in the algorithm for calculating the isotope distribution.

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