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A coupled polarization-matrix inversion and iteration approach for accelerating the dipole convergence in a polarizable potential function.

ABSTRACT: A coupled polarization-matrix inversion and iteration (CPII) method is described to achieve and accelerate the convergence of induced dipoles for condensed phase systems employing polarizable intermolecular potential functions (PIPF). The present PIPF is based on the Thole interaction dipole model in which all atomic pair interactions are considered, including those that are directly bonded covalently. Although induced dipoles can be obtained both by inverting a 3N x 3N polarization-matrix where N is the number of polarizable sites, or by a direct iterative approach, the latter approach is more efficient computationally for large systems in molecular dynamics simulations. It was found that induced dipole moments failed to converge in the direct iterative approach if 1-2, 1-3, and 1-4 intramolecular interactions are included in the Thole model. However, it is necessary to include all intramolecular interactions in the Thole model to yield the correct molecular anisotropic polarizability tensor. To solve this numerical stability problem, we reformulated the Thole interaction dipole model in terms of molecular block matrices, which naturally leads to a coupled, preconditioning algorithm that involves a polarization-matrix inversion term to account for intramolecular interactions, and an iterative procedure to incorporate the mutual polarization effects between different molecules. The CPII method is illustrated by applying to cubic boxes of water and NMA molecules as well as an alanine pentapeptide configuration, and it was shown that the CPII method can achieve convergence for the dipole induction polarization rapidly in all cases, whereas the direct iterative approach failed to reach convergence in these cases. In addition, the CPII reduces the overall computational costs by decreasing the number of iteration steps in comparison with the direct iteration approach in which intramolecular bonded interactions are excluded to ensure that induced dipole convergence is obtained.

SUBMITTER: Xie W

PROVIDER: S-EPMC2765495 | biostudies-literature | 2009 Mar

REPOSITORIES: biostudies-literature

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A coupled polarization-matrix inversion and iteration approach for accelerating the dipole convergence in a polarizable potential function.

Xie Wangshen W Pu Jingzhi J Gao Jiali J

The journal of physical chemistry. A 20090301 10

A coupled polarization-matrix inversion and iteration (CPII) method is described to achieve and accelerate the convergence of induced dipoles for condensed phase systems employing polarizable intermolecular potential functions (PIPF). The present PIPF is based on the Thole interaction dipole model in which all atomic pair interactions are considered, including those that are directly bonded covalently. Although induced dipoles can be obtained both by inverting a 3N x 3N polarization-matrix where ...[more]

PMID: 19123850

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Project description:BackgroundQuantitative susceptibility mapping (QSM) uses prior information to reconstruct maps, but prior information may not show pathology and introduce inconsistencies with susceptibility maps, degrade image quality and inadvertently smoothing image features.PurposeTo develop a local field data-driven QSM reconstruction that does not depend on spatial edge prior information.Study typeRetrospective.Subjects, animal modelsA dataset from 2016 ISMRM QSM Challenge, 11 patients with glioblastoma, a patient with microbleeds and porcine heart.Sequence/field strength3D gradient echo sequence on 3T and 7T scanners.AssessmentAccuracy was compared to Calculation of Susceptibility through Multiple Orientation Sampling (COSMOS), and several published techniques using region of interest (ROI) measurements, root-mean-squared error (RMSE), structural similarity index metric (SSIM), and high-frequency error norm (HFEN). Numerical ranking and semiquantitative image grading was performed by three expert observers to assess overall image quality (IQ) and image sharpness (IS).Statistical testsBland-Altman, Friedman test, and Conover multiple comparisons.ResultsLoss adaptive dipole inversion (LADI) (β = 0.82, R2 = 0.96), morphology-enabled dipole inversion (MEDI) (β = 0.91, R2 = 0.97), and fast nonlinear susceptibility inversion (FANSI) (β = 0.81, R2 = 0.98) had excellent correlation with COSMOS and no bias was detected (bias = 0.006 ± 0.014, P < 0.05). In glioblastoma patients, LADI showed consistently better performance (IQGrade = 2.6 ± 0.4, ISGrade = 2.6 ± 0.3, IQRank = 3.5 ± 0.4, ISRank = 3.9 ± 0.2) compared with MEDI (IQGrade = 2.1 ± 0.3, ISGrade = 2 ± 0.5, IQRank = 2.4 ± 0.5, ISRank = 2.8 ± 0.2) and FANSI (IQGrade = 2.2 ± 0.5, ISGrade = 2 ± 0.4, IQRank = 2.8 ± 0.3, ISRank = 2.1 ± 0.2). Dark artifact visible near the infarcted region in MEDI (InfMEDI = -0.27 ± 0.06 ppm) was better mitigated by FANSI (InfFANSI-TGV = -0.17 ± 0.05 ppm) and LADI (InfLADI = -0.18 ± 0.05 ppm).ConclusionFor neuroimaging applications, LADI preserved image sharpness and fine features in glioblastoma and microbleed patients. LADI performed better at mitigating artifacts in cardiac QSM.Evidence level4 TECHNICAL EFFICACY STAGE: 1 J. Magn. Reson. Imaging 2020;52:823-835.

Dataset Information

A coupled polarization-matrix inversion and iteration approach for accelerating the dipole convergence in a polarizable potential function.

Publications

A coupled polarization-matrix inversion and iteration approach for accelerating the dipole convergence in a polarizable potential function.

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