On the Laplace-Beltrami operator and brain surface flattening

Angenent, Sigurd; Haker, Steven; Tannenbaum, Allen; Kikinis, Ron

doi:10.1109/42.796283

Cited by 192 publications

(164 citation statements)

References 26 publications

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“…developing parameterizations that are conformal (Angenent et al, 1999;Haker et al, 2000;Hurdal and Stephenson 2004, this volume); in these, the grid lines on the surface intersect at right angles (see grid in Fig. 2, panel 7a), and angular relationships are preserved as data are mapped from one surface to another.…”

Section: Cortical Surface Extraction and Parameterizationmentioning

confidence: 99%

Mapping cortical change in Alzheimer's disease, brain development, and schizophrenia

et al. 2004

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This paper describes algorithms that can identify patterns of brain structure and function associated with Alzheimer's disease, schizophrenia, normal aging, and abnormal brain development based on imaging data collected in large human populations. Extraordinary information can be discovered with these techniques: dynamic brain maps reveal how the brain grows in childhood, how it changes in disease, and how it responds to medication. Genetic brain maps can reveal genetic influences on brain structure, shedding light on the nature-nurture debate, and the mechanisms underlying inherited neurobehavioral disorders. Recently, we created time-lapse movies of brain structure for a variety of diseases. These identify complex, shifting patterns of brain structural deficits, revealing where, and at what rate, the path of brain deterioration in illness deviates from normal. Statistical criteria can then identify situations in which these changes are abnormally accelerated, or when medication or other interventions slow them. In this paper, we focus on describing our approaches to map structural changes in the cortex. These methods have already been used to reveal the profile of brain anomalies in studies of dementia, epilepsy, depression, childhoodand adult-onset schizophrenia, bipolar disorder, attention-deficit/ hyperactivity disorder, fetal alcohol syndrome, Tourette syndrome, Williams syndrome, and in methamphetamine abusers. Specifically, we describe an image analysis pipeline known as cortical pattern matching that helps compare and pool cortical data over time and across subjects. Statistics are then defined to identify brain structural differences between groups, including localized alterations in cortical thickness, gray matter density (GMD), and asymmetries in cortical organization. Subtle features, not seen in individual brain scans, often emerge when population-based brain data are averaged in this way. Illustrative examples are presented to show the profound effects of development and various diseases on the human cortex. Dynamically spreading waves of gray matter loss are tracked in dementia and schizophrenia, and these sequences are related to normally occurring changes in healthy subjects of various ages. D 2004 Published by Elsevier Inc.

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Section: Cortical Surface Extraction and Parameterizationmentioning

confidence: 99%

Mapping cortical change in Alzheimer's disease, brain development, and schizophrenia

et al. 2004

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“…The central surface, in particular, demonstrates accuracy and repeatability in the range of 0.5 and 0.25 mm, respectively. We believe that the central surface is useful for characterization and analysis of the 2-D geometry of the cortex-for example, computation of curvatures (Cachia et al, 2003a;Zeng et al, 1999), geodesic distances (Cachia et al, 2003b;Rettmann et al, 2002), segmenting sulci or gyri (Behnke et al, 2003;Cachia et al, 2003b;Rettmann et al, 2002), surface flattening (Carman et al, 1995;Drury et al, 1996), and spherical mapping (Angenent et al, 1999;Fischl et al, 1999a;Tosun and Prince, 2001).…”

Section: Qualitative Demonstrationsmentioning

confidence: 99%

CRUISE: Cortical reconstruction using implicit surface evolution

et al. 2004

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Segmentation and representation of the human cerebral cortex from magnetic resonance (MR) images play an important role in neuroscience and medicine. A successful segmentation method must be robust to various imaging artifacts and produce anatomically meaningful and consistent cortical representations. A method for the automatic reconstruction of the inner, central, and outer surfaces of the cerebral cortex from T1-weighted MR brain images is presented. The method combines a fuzzy tissue classification method, an efficient topology correction algorithm, and a topology-preserving geometric deformable surface model (TGDM). The algorithm is fast and numerically stable, and yields accurate brain surface reconstructions that are guaranteed to be topologically correct and free from selfintersections. Validation results on real MR data are presented to demonstrate the performance of the method. D 2004 Elsevier Inc. All rights reserved.

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“…For quantitative evaluation, however, it is necessary to establish a coordinate system on the cortex so that features can be identified more rigorously (Angenent et al, 1999;Drury et al, 1996;Fischl et al, 1999;Hurdal et al, 1999;MacDonald et al, 2000;Thompson et al, 2000). Spherical coordinates are appropriate since the topology of the sphere is the same as that of the cortical surface.…”

Section: Spherical Mappingmentioning

confidence: 99%

“…Spherical coordinates are appropriate since the topology of the sphere is the same as that of the cortical surface. Two general approaches have been explored in the past: (1) iterative relaxation followed by radial projection to the sphere (Fischl et al, 1999;Sereno et al, 1996) and (2) conformal mapping (Angenent et al, 1999).…”

Section: Spherical Mappingmentioning

confidence: 99%

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Cortical surface segmentation and mapping

et al. 2004

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Segmentation and mapping of the human cerebral cortex from magnetic resonance (MR) images plays an important role in neuro-science and medicine. This paper describes a comprehensive approach for cortical reconstruction, flattening, and sulcal segmentation. Robustness to imaging artifacts and anatomical consistency are key achievements in an overall approach that is nearly fully automatic and computationally fast. Results demonstrating the application of this approach to a study of cortical thickness changes in aging are presented.

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On the Laplace-Beltrami operator and brain surface flattening

Cited by 192 publications

References 26 publications

Mapping cortical change in Alzheimer's disease, brain development, and schizophrenia

Mapping cortical change in Alzheimer's disease, brain development, and schizophrenia

CRUISE: Cortical reconstruction using implicit surface evolution

Cortical surface segmentation and mapping

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