Acta Stereologica



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Orlando Guntinas-Lichius & Wolfram F. Neiss

Comparison of empirical and estimated efficiency in neuron counting by the fractionator method and in volume measurement by Cavalieri’s method

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Reconstructing the volume and the nerve cell number of the facial and liypoglossal nucleus of one Wistar rat with Cavalieri’s estimator and a fractionator design we determined the mean empirical error of systematic sampling probes through these nuclei depending on the sample size as reference values. We compared these empirical values of the error to the mean estimated values obtained by error estimators of Gundersen and Jensen (1987; J. Microsc. 147: 229-263) for the Cavalieri and fractionator design and to the error estimator by Cruz—Orive (1990; J. Microsc. 160: 89-95) for the fractionator design. Using the emperical approach, the mean error of the volume determination does not exceed l0%, i.e. the range of interest of most stereological studies, using 4 equidistant sections through the brainstem nuclei. The mean error of the neuron number estimation does not exceed 10% using about 8 sections of the facial or l0 sections of the hypoglossal nucleus in the investigated rat. The error estimator by Gundersen and Jensen (1987) overestimates the error for the volume calculation using small sample sizes ≤ 16 sections, but correlates nearly exact with the empirical error of the nerve cell count using the fractionator design. The error estimator by Cruz—Orive (1990) underestimates the error of the fractionator design for sample sizes ≤ 16 sections in both nuclei. In conclusion, about 2% of the total number of possible 6 µm sections are enough to estimate the volume of cranial nerve nuclei and 5% of the sections to estimate the neuron number with an intra—individual precision less than 10%. In the range of efficient sample sizes the error predictor of Gundersen and Jensen (1987) is very reliable for the neuron number error estimation, but overestimates the error of the neuron number. In our example the error predictor of Cruz—Orive (1990) underestimates the neuron number error in the range of interest.

Keywords : Cavalieri', error estimator, Fractionator, neuron counting, s principle, volume measurement

To cite this article

Orlando Guntinas-Lichius & Wolfram F. Neiss, «Comparison of empirical and estimated efficiency in neuron counting by the fractionator method and in volume measurement by Cavalieri’s method», Acta Stereologica [En ligne], Number 2 - Applications of stereology in life sciences - July 1996, Volume 15 (1996), 131-139 URL :

About: Orlando Guntinas-Lichius

Department of Oto-Rhino-Laryngology, University of Cologne, Lindenthal, D-50924 Köln, Germany

About: Wolfram F. Neiss

Department of Anatomy, University of Cologne, Lindenthal, D-50924 Köln, Germany