Estimating Particle Shape and Orientation Using Volume Tensors

Stereological estimation of particle shape from vertical sections

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.

Stereological estimation of particle shape and orientation from volume tensors

In the present paper, we describe new robust methods of estimating cell shape and orientation in 3D from sections. The descriptors of 3D cell shape and orientation are based on volume tensors which are used to construct an ellipsoid, the Miles ellipsoid, approximating the average cell shape and orientation in 3D. The estimators of volume tensors are based on observations in several optical planes through sampled cells. This type of geometric sampling design is known as the optical rotator. The statistical behaviour of the estimator of the Miles ellipsoid is studied under a flexible model for 3D cell shape and orientation. In a simulation study, the lengths of the axes of the Miles ellipsoid can be estimated with coefficients of variation of about 2% if 100 cells are sampled. Finally, we illustrate the use of the developed methods in an example, involving neurons in the medial prefrontal cortex of rat.