Regular articleComparison of MR imaging against physical sectioning to estimate the volume of human cerebral compartments
Introduction
The estimation of brain volume has been of interest for over a century. Typically, postmortem specimens were fixed in formalin prior to volumetry by fluid displacement, e.g., Bischoff 1880, Marshall 1892, Pearl 1905, or Pakkenberg and Voigt (1964). Miller et al. (1980) applied image analysis to complete series of physical slices of several left cerebral hemispheres to study the variation of total gray and white matter volume with age. However, only by imaging techniques such as MRI is it possible to noninvasively estimate the volume of the internal cerebral hemisphere compartments. Mayhew and Olsen (1991), by using MRI and the Cavalieri method, estimated the total volume of a single formalin-fixed cerebral hemisphere to be 3.3% less than the volume obtained by fluid displacement. The present study is motivated by the increasing interest in applying stereological methods for biomedical research in combination with noninvasive scanning, notably MRI Roberts et al 2000, Doherty et al 2000, Mackay et al 2000, Keller et al 2002. The question has therefore arisen of how reliable MRI is; in this study we have concentrated on its application to human brain. The volumes of three brain compartments were estimated for each of six human specimens by the Cavalieri method using two alternative methods to acquire the section images, namely MRI and physical sectioning.
The compartments considered were (i) cortical gray matter, referred to as “cortex,” (i.e., neocortex plus archicortex; archicortex comprises, in our definition, uncus, hippocampus, dentate gyrus, subicular complex, parahippocampal gyrus, cingulate gyrus, subcallosal area, and amygdala) and (ii) white matter (excluding cerebral ventricles) plus central gray matter nuclei (e.g., thalamus, putamen, caudate nucleus, and basal ganglia), referred to as “subcortex.” The union of both is called “total.”
The material is described in Section 2, the estimation theory in Section 3, and its implementation on the material in Section 4; for didactic purposes a worked numerical example is included in Subsection 4.3. The basic results and their statistical analysis are presented in Section 5. Cursory paired t-tests (Subsection 5.1) revealed no significant differences between MRI and physical section data. Proper graphic displays, however, revealed differences which were confirmed through more appropriate statistical analyses (Subsections 5.2 and 5.3). The analysis adopted in Subsection 5.2 relies upon special error prediction formulae introduced in Subsection 3.2 without empirical verification; the latter is carried out in Section 6 by empirical resampling from the complete MRI data set of one brain. In Section 7 the main conclusions are listed with pertinent comments.
Section snippets
Material and objectives
Six cerebral hemispheres bequeathed by subjects with no history of alcoholism, dementia, or other neurodegenerative disorders were studied; additional details are given in Table 1. The hemispheres were weighed, fixed in 4% formalin (for fixation times see Table 1), and embedded in separate blocks of 6% agarose gel. In the agarose embedding process, the agar was heated and poured over the specimen; the embedded brain specimen was then refrigerated to allow the gel to solidify and provide a
Cavalieri sections
The volume of an object—e.g., a cerebral hemisphere compartment—can be expressed as where A(x), called the area function, denotes the intersection area between the object and a plane normal to a fixed, conveniently oriented sampling axis, at a point of abscissa x (Fig. 2). A(x) is bounded and integrable in a bounded domain [a, b], which represents the orthogonal linear projection of the object on the sampling axis.
To estimate V we intersect the object by a series of parallel
4.1. volume estimation from MRI data
First for each specimen a densely sampled MRI data set was obtained which allowed resampling experiments. After agar embedding, see Section 2, each hemisphere was exhaustively scanned into virtual 1.6-mm-thick coronal slices with a 1.5-T Signa whole-body MR imaging system (General Electric, Milwaukee, WI, USA). A total of 124 coronal T1-weighted images, including the empty ones at the beginning and at the end of the series, were recorded per hemisphere using a 3D spoiled gradient echo (SPGR)
Statistical comparisons between MRI and physical sections
Preliminary paired t tests (Subsection 5.1) revealed no significant mean difference between the volume estimates obtained by either method (MRI and physical sections), although significance was almost reached for the subcortex compartment (P value = 0.06). Nonetheless, significance here would reveal only a departure from zero in the population mean difference, without regard of (a) possible important departures between both methods for individual specimens and (b) the fact that both methods
Verification of the error predictors used in this study
The error prediction formulae given in Subsection 3.2 are based on models for the covariance structure of systematic data, and they are only approximations—as opposed to design unbiased estimators such as (3.2) and (3.3). Since these error predictors were used to construct Fig. 5, we consider it opportune to check them by empirical resampling from a complete data set.
7. conclusions and discussion
As indicated in the Introduction, the main purpose of this study was to analyze the reliability of the MRI technique in the volume estimation of brain compartments using stereological methods (Cavalieri method in combination with point counting). The volume estimates of three brain compartments obtained from MRI sections were compared with those obtained from physical sections for six human specimens. The main conclusions can be summarized as follows.
(1) Let D represent the random difference
Acknowledgements
We are grateful to two anonymous referees for their helpful comments and suggestions. M.G.F. and L.M.C.O. acknowledge financial support from the Spanish Ministry of Science and Technology research project BSA2001-0803-C02. M.G.F. also acknowledges the receipt of a grant from “Secretaría de Estado de Educación y Universidades de España” to visit the University of Liverpool.
References (32)
- et al.
Voxel-Based morphometric comparison of hippocampal and extrahippocampal abnormalities in patients with left and right hippocampal atrophy
NeuroImage
(2002) - et al.
Precision of systematic sampling and transitive methods
J. Statist. Plan. Inf.
(1999) - et al.
Quantitative magnetic resonance in consecutive patients evaluated for surgical treatment of temporal lobe epilepsy
Magn. Reson. Imaging
(2000) - et al.
Quantitative interpretation of magnetization transfer in spoiled gradient echo MRI sequences
J. Magn. Reson.
(2000) - et al.
Handbook of Mathematical Functions
(1965) Human brain
J. Mental Sci.
(1866)Das Hirngewicht des Menschen
(1880)On the precision of systematic samplinga review of Matheron’s transitive methods
J. Microsc.
(1989)Precision of Cavalieri sections and slices with local errors
J. Microsc.
(1999)- et al.
Accuracy and validity of stereology as a quantitative method for assessment of human temporal lobe volumes acquired by magnetic resonance imaging
Magn. Reson. Imaging
(2000)