PURPOSE: Recent theory has been developed to estimate volume from a systematic sample of tissue slices of a given thickness and to predict the corresponding error. Our goal was to check the error prediction formulas by resampling and to determine the minimum number of MR slices required to estimate the volumes of the cerebrum and of the compartments of gray matter (GM) and white matter (WM) with prescribed errors. METHOD: Our working data set comprised the GM and WM segmentations obtained from a paradigmatic high signal-to-noise ratio 3D spoiled GRASS MR volume data set for a single healthy human subject. The data were classified using a fuzzy clustering minimum distance algorithm. We thereby obtained a stack of 183 serial coronal slices of 1 mm thickness encompassing the whole cerebrum. Empirical resampling was carried out using the corresponding data vectors, and the theoretical error predictors were thereby checked for slice thicknesses of 1, 3, 9, and 27 mm, with a distance of 45 mm between slice midplanes. RESULTS: Irrespective of slice thickness, a minimum of 3, 5, and 10 slices provided estimates of the true total volume of GM and WM in the cerebrum with coefficients of error (CEs) of 10, 5, and 3%, respectively, where CE(V)% = 100 x SE(V)/V. For the cerebrum, a minimum of two, three, and four slices were required for CEs of the same precision. CONCLUSION: In combination with high signal-to-noise ratio and enhanced tissue contrast, Cavalieri slices are the most appropriate for MRI, they supply unbiased and highly efficient volume estimates of brain compartments. For a given number of slices, CE(V) decreases rapidly when the slices are thicker than the gaps between them; when the slices are thinner than the gaps, then CE(V) is similar to that in the situation when the slice thickness is zero.
PURPOSE: Recent theory has been developed to estimate volume from a systematic sample of tissue slices of a given thickness and to predict the corresponding error. Our goal was to check the error prediction formulas by resampling and to determine the minimum number of MR slices required to estimate the volumes of the cerebrum and of the compartments of gray matter (GM) and white matter (WM) with prescribed errors. METHOD: Our working data set comprised the GM and WM segmentations obtained from a paradigmatic high signal-to-noise ratio 3D spoiled GRASS MR volume data set for a single healthy human subject. The data were classified using a fuzzy clustering minimum distance algorithm. We thereby obtained a stack of 183 serial coronal slices of 1 mm thickness encompassing the whole cerebrum. Empirical resampling was carried out using the corresponding data vectors, and the theoretical error predictors were thereby checked for slice thicknesses of 1, 3, 9, and 27 mm, with a distance of 45 mm between slice midplanes. RESULTS: Irrespective of slice thickness, a minimum of 3, 5, and 10 slices provided estimates of the true total volume of GM and WM in the cerebrum with coefficients of error (CEs) of 10, 5, and 3%, respectively, where CE(V)% = 100 x SE(V)/V. For the cerebrum, a minimum of two, three, and four slices were required for CEs of the same precision. CONCLUSION: In combination with high signal-to-noise ratio and enhanced tissue contrast, Cavalieri slices are the most appropriate for MRI, they supply unbiased and highly efficient volume estimates of brain compartments. For a given number of slices, CE(V) decreases rapidly when the slices are thicker than the gaps between them; when the slices are thinner than the gaps, then CE(V) is similar to that in the situation when the slice thickness is zero.