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Confidence intervals for the volume of brain structures in Cavalieri sampling with local errors

Authors
Journal
Journal of Neuroscience Methods
0165-0270
Publisher
Elsevier
Publication Date
Volume
179
Issue
1
Identifiers
DOI: 10.1016/j.jneumeth.2009.01.026
Keywords
  • Asymptotic Distribution
  • Confidence Intervals
  • Epilepsy
  • Fourier Transform
  • Magnetic Resonance Imaging
  • Systematic Sampling
  • Variance
  • Volume Estimator
Disciplines
  • Mathematics
  • Medicine

Abstract

Abstract The identification and quantification of morphological alterations that occur in the brain due to neurological disease, development and ageing, is of special interest in brain research. Design-based stereological methods have been widely applied in combination with magnetic resonance (MR) imaging to estimate the volume of brain structures. In the Cavalieri method, the volume V is directly estimated from equidistant and parallel MR images of the brain with a uniform random starting position. A second level of sampling is usually required to estimate the section area from each image (e.g., by applying point counting). The mathematical justification and implementation of the methodology is simple and it can be applied to structures of arbitrary shape. However, due to the spatial dependence in the data sample, how to predict the precision of the estimator of V becomes a difficult task. In this paper, we develop a method to construct a confidence interval for V by analysing the variability produced by each level of sampling (i.e., between and within sections’ variability). Simulation from two known analytical measurement functions is carried out to show its validity. Finally, the new approach is applied to investigate the significance of hippocampus volume change in a patient with epilepsy after 2 years of disease.

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