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J Anat. 1991 Oct;178:133-44.

Magnetic resonance imaging (MRI) and model-free estimates of brain volume determined using the Cavalieri principle.

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Department of Human Morphology, Queen's Medical Centre, University of Nottingham, UK.


A complete set of parallel (coronal) slices through a fixed human forebrain was generated by magnetic resonance imaging (MRI) and the Cavalieri principle, combined with point counting, was used to estimate brain volume. Alternative sampling schemes for estimating volume were then assessed by taking systematic and simple random selections of slices. Later, the brain was weighed and its fixed volume determined by fluid displacement. For the complete set of n = 28 MRI slices, the volume (1025 ml) was estimated with a coefficient of error (CE) of less than 1%. Decreasing the number of slices by systematic sampling increased the CE but this was still only 5% when just 5-6 slices were analysed. Estimated volumes varied from 947 ml to 1098 ml. Simple random sampling was less efficient (estimated volumes for 5-6 slices were 644-1187 ml). The forebrain actually weighed 1090 g and displaced 1060 ml of fluid. A set of 14 other brains was physically sliced in order to assess sampling errors in the context of observed brain-to-brain variation. It was found that 5-6 slices per brain is enough to yield efficient estimates of mean brain volume. The findings demonstrate the practicability of using MRI to estimate brain volumes unbiasedly and efficiently. The methods have great potential for noninvasive, longitudinal studies on in vivo brains and other organs.

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