title: Stereological estimation of particle shape and orientation from volume tensors.
abstract: 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.
authors.affiliation: Stereological Research Laboratory, Aarhus University, Aarhus, Denmark.
authors.forename: A H
authors.initials: AH
authors.lastname: Rafati
authors.affiliation: Institute of Mathematical Statistics and Actuarial Science, University of Bern, Bern, Switzerland.
authors.forename: J F
authors.initials: JF
authors.lastname: Ziegel
authors.affiliation: Stereological Research Laboratory, Aarhus University, Aarhus, Denmark.
authors.forename: J R
authors.initials: JR
authors.lastname: Nyengaard
authors.affiliation: Department of Mathematics, Aarhus University, Aarhus, Denmark.
authors.forename: E B Vedel
authors.initials: EB
authors.lastname: Jensen
mesh_terms: D000818:Animals; D048430:Cell Shape; D021621:Imaging, Three-Dimensional; D009474:Neurons; D051381:Rats
keywords: Local stereology; Miles ellipsoid; optical rotator; particle shape; volume tensors