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Span of regularization for solution of inverse problems with application to magnetic resonance relaxometry of the brain.

ABSTRACT: We present a new regularization method for the solution of the Fredholm integral equation (FIE) of the first kind, in which we incorporate solutions corresponding to a range of Tikhonov regularizers into the end result. This method identifies solutions within a much larger function space, spanned by this set of regularized solutions, than is available to conventional regularization methods. An additional key development is the use of dictionary functions derived from noise-corrupted inversion of the discretized FIE. In effect, we combine the stability of solutions with greater degrees of regularization with the resolution of those that are less regularized. The span of regularizations (SpanReg) method may be widely applicable throughout the field of inverse problems.

SUBMITTER: Bi C

PROVIDER: S-EPMC9684479 | biostudies-literature | 2022 Nov

REPOSITORIES: biostudies-literature

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Span of regularization for solution of inverse problems with application to magnetic resonance relaxometry of the brain.

Bi Chuan C Ou M Yvonne MY Bouhrara Mustapha M Spencer Richard G RG

Scientific reports 20221123 1

We present a new regularization method for the solution of the Fredholm integral equation (FIE) of the first kind, in which we incorporate solutions corresponding to a range of Tikhonov regularizers into the end result. This method identifies solutions within a much larger function space, spanned by this set of regularized solutions, than is available to conventional regularization methods. An additional key development is the use of dictionary functions derived from noise-corrupted inversion of ...[more]

PMID: 36418516

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Project description:ObjectiveHippocampal sclerosis (HS) is the most common cause of drug-resistant temporal lobe epilepsy, and its accurate detection is important to guide epilepsy surgery. Radiological features of HS include hippocampal volume loss and increased T2 signal, which can both be quantified to help improve detection. In this work, we extend these quantitative methods to generate cross-sectional area and T2 profiles along the hippocampal long axis to improve the localization of hippocampal abnormalities.MethodsT1-weighted and T2 relaxometry data from 69 HS patients (32 left, 32 right, 5 bilateral) and 111 healthy controls were acquired on a 3-T magnetic resonance imaging (MRI) scanner. Automated hippocampal segmentation and T2 relaxometry were performed and used to calculate whole-hippocampal volumes and to estimate quantitative T2 (qT2) values. By generating a group template from the controls, and aligning this so that the hippocampal long axes were along the anterior-posterior axis, we were able to calculate hippocampal cross-sectional area and qT2 by a slicewise method to localize any volume loss or T2 hyperintensity. Individual patient profiles were compared with normative data generated from the healthy controls.ResultsProfiling of hippocampal volumetric and qT2 data could be performed automatically and reproducibly. HS patients commonly showed widespread decreases in volume and increases in T2 along the length of the affected hippocampus, and focal changes may also be identified. Patterns of atrophy and T2 increase in the left hippocampus were similar between left, right, and bilateral HS. These profiles have potential to distinguish between sclerosis affecting volume and qT2 in the whole or parts of the hippocampus, and may aid the radiological diagnosis in uncertain cases or cases with subtle or focal abnormalities where standard whole-hippocampal measurements yield normal values.SignificanceHippocampal profiling of volumetry and qT2 values can help spatially localize hippocampal MRI abnormalities and work toward improved sensitivity of subtle focal lesions.

Dataset Information

Span of regularization for solution of inverse problems with application to magnetic resonance relaxometry of the brain.

Publications

Span of regularization for solution of inverse problems with application to magnetic resonance relaxometry of the brain.

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