Application of the Cavalieri principle in volume estimation using laser confocal microscopy.

The Cavalieri principle, a well-established stereological technique, uses interpolation between samples to estimate volume of three-dimensional (3D) objects. Serial optical sectioning with the confocal microscope resembles certain aspects of the Cavalieri principle, albeit with no interpolation. However, reconstruction and analysis of finely spaced optical sections can be cumbersome and time consuming. Application of the Cavalieri principle to confocal sections may be advantageous in reducing the size of the data set required to obtain reliable estimates of volume. In the present study, somal volumes of phrenic motoneurons were estimated by applying the Cavalieri principle to confocal images. These estimates were compared to measurements of somal volume using on interpolation of confocal sections. Phrenic motoneurons in adult rats were retrogradely labeled with a fluorescent rhodamine dye. Confocal optical sections of 0.6 micron thickness were then obtained from 150-micron-thick spinal cord slices containing labeled neurons. These image sets were reoriented to represent transverse sections. The Cavalieri principle was applied to these confocal image sets at selected sampling intervals from 1.2 to 3.0 microns. Planimetric measurements of motoneuron somal cross-sectional area in the selected sections were made using a point-counting method. At sampling intervals less than 2.4 microns, individuals motoneuron somal volume estimates were similar for the noninterpolated confocal and the interpolated Cavalieri methods. At these sampling intervals, the distributions of motoneuron somal volumes were also similar for the two methods. At a sampling interval of 2.4 microns or greater, there was a greater variability in individual motoneuron somal volume estimates, although the population mean and median were similar to the noninterpolated confocal measurements. Therefore, a satisfactory agreement between noninterpolated confocal measurements and the Cavalieri estimates suggests that less-stringent optical sectioning parameters may suffice for individual cell volume measurements when using confocal microscopy, thus making it significantly more efficient.