Efficient computation of volume of hexahedral cells

Grandy, J.

doi:10.2172/632793

Cited by 23 publications

(21 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The merit function by design will have a minimum when the displacement field induces a good match between the images. The displacement field in general will turn cubic voxels into displaced, irregular hexahedra whose volumes (53) give the volume-change field. The merit function is minimized efficiently using standard numerical methods.…”

Section: Data Acquisition and Preparation Raw Digital Imaging And Comentioning

confidence: 99%

Subregional neuroanatomical change as a biomarker for Alzheimer's disease

Holland¹,

Brewer²,

Hagler³

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

207

192

View full text Add to dashboard Cite

Regions of the temporal and parietal lobes are particularly damaged in Alzheimer's disease (AD), and this leads to a predictable pattern of brain atrophy. In vivo quantification of subregional atrophy, such as changes in cortical thickness or structure volume, could lead to improved diagnosis and better assessment of the neuroprotective effects of a therapy. Toward this end, we have developed a fast and robust method for accurately quantifying cerebral structural changes in several cortical and subcortical regions using serial MRI scans. In 169 healthy controls, 299 subjects with mild cognitive impairment (MCI), and 129 subjects with AD, we measured rates of subregional cerebral volume change for each cohort and performed power calculations to identify regions that would provide the most sensitive outcome measures in clinical trials of disease-modifying agents. Consistent with regional specificity of AD, temporal-lobe cortical regions showed the greatest disease-related changes and significantly outperformed any of the clinical or cognitive measures examined for both AD and MCI. Global measures of change in brain structure, including whole-brain and ventricular volumes, were also elevated in AD and MCI, but were less salient when compared to changes in normal subjects. Therefore, these biomarkers are less powerful for quantifying disease-modifying effects of compounds that target AD pathology. The findings indicate that regional temporal lobe cortical changes would have great utility as outcome measures in clinical trials and may also have utility in clinical practice for aiding early diagnosis of neurodegenerative disease.

show abstract

Section: Data Acquisition and Preparation Raw Digital Imaging And Comentioning

confidence: 99%

Subregional neuroanatomical change as a biomarker for Alzheimer's disease

Holland¹,

Brewer²,

Hagler³

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

207

192

View full text Add to dashboard Cite

show abstract

“…Coplanarity is assumed in area calculations making them trivial, while for volume calculations we use a very efficient method described in Grandy (1997). Critical elements with small individual step sizes have crucial impact on solution time as they dictate overall usable time-step size.…”

mentioning

confidence: 99%

Rupture risk in abdominal aortic aneurysms: A realistic assessment of the explicit GPU approach

Štrbac

Pierce

Rodríguez-Vila

et al. 2017

Journal of Biomechanics

View full text Add to dashboard Cite

Accurate estimation of peak wall stress (PWS) is the crux of biomechanically motivated rupture risk assessment for abdominal aortic aneurysms aimed to improve clinical outcomes. Such assessments often use the finite element (FE) method to obtain PWS, albeit at a high computational cost, motivating simplifications in material or element formulations. These simplifications, while useful, come at a cost of reliability and accuracy. We achieve research-standard accuracy and maintain clinically applicable speeds by using novel computational technologies. We present a solution using our custom finite element code based on graphics processing unit (GPU) technology that is able to account for added complexities involved with more physiologically relevant solutions, e.g. strong anisotropy and heterogeneity. We present solutions up to 17x faster relative to an established finite element code using state-of-the-art nonlinear, anisotropic and nearly-incompressible material descriptions. We show a realistic assessment of the explicit GPU FE approach by using complex problem geometry, biofidelic material law, doubleprecision floating point computation and full element integration. Due to the increased solution speed without loss of accuracy, shown on five clinical cases of abdominal aortic aneurysms, the method shows promise for clinical use in determining rupture risk of abdominal aortic aneurysms.

show abstract

“…(5) and for all three meshes the error is found to decrease linearly with 5 the number of points for all three types of meshes. Although the volume of the hexahedra could have been computed directly with the formula of Grandy (1997), with GHOST the Gauss quadrature is used since it is also needed in the next section. The total volume of the spherical mesh is given by: where Ω stands for the volume inside the spherical shell, Ω c is the volume of a cell.…”

Section: Areas and Volume Measurementsmentioning

confidence: 99%

GHOST: Geoscientific Hollow Sphere Tesselation

Thieulot¹

2018

Preprint

View full text Add to dashboard Cite

Abstract. I present in this work the GHOST (Geoscientific HOllow Sphere Tesselation) software which allows for the fast generation of computational meshes in hollow sphere geometries counting up to a hundred millions of cells. Each mesh is composed of concentric spherical shells which are built out of quadrilaterals or triangles. I focus here on three commonly used meshes used in geodynamics/geophysics and demonstrate the accuracy of shell surfaces and mesh volume measurements as a function of resolution. I further benchmark the built-in gravity and gravitational potential procedures in the simple case of a 5 constant density geometry and finally show how the produced meshes can be used to visualise the S40RTS mantle tomography model. The code is open source and is available on the GitHub sharing platform.

show abstract

Efficient computation of volume of hexahedral cells

Abstract: We describe an e cient method to compute the volume of hexahedral cells used in three-dimensional hydrodynamics simulations. We consider two common methods for treating the hexahedron using triangular boundaries.Motivation

Cited by 23 publications

References 0 publications

Subregional neuroanatomical change as a biomarker for Alzheimer's disease

Subregional neuroanatomical change as a biomarker for Alzheimer's disease

Rupture risk in abdominal aortic aneurysms: A realistic assessment of the explicit GPU approach

GHOST: Geoscientific Hollow Sphere Tesselation

Contact Info

Product

Resources

About