Jens Randel Nyengaard

In the present paper, we describe a new simple stereological method of estimating volume tensors in 3D from vertical sections. The volume tensors provide information about particle shape in 3D. In a model-based setting, the method requires that the particle distribution is invariant under rotations around the vertical axis. In a design-based approach, where the vertical section is uniformly rotated around the vertical axis, the method provides information about an index of elongation of the particles in the direction of the vertical axis. The method has been implemented on human brain tissue for the analysis of neurons in layer III of the medial frontal gyrus of Brodmann Area 46. In the actual implementation, the new estimator shows similar precision as an earlier estimator, based on an optical rotator design, but it is a factor 3 faster to collect the measurements for the new estimator. Furthermore, the calculations needed for determining the new estimator are much simpler. Lay Description A new method is described for estimating volume tensors in 3 dimensions based on the stereological method: planar rotator. In general, volume tensors may provide information about particle volume, shape and direction. The new estimator was implemented on human brain tissue for the analysis of neurons in layer III of the medial frontal gyrus on Brodmann Area 46 and compared to a previous published method, based on an optical rotator design. The new estimator shows similar precision as the earlier estimator, but it is a factor 3 faster to collect the measurements. Besides, the calculations behind the new estimator are simpler and easier to implement to a software program.