title: The spatial rotator.
abstract: This paper presents a new local volume estimator, the spatial rotator, which is based on measurements on a virtual 3D probe, using computer assisted microscopy. The basic design of the probe builds upon the rotator principle which requires only a few manual intersection markings, thus making the spatial rotator fast to use. Since a 3D probe is involved, it is expected that the spatial rotator will be more efficient than the the nucleator and the planar rotator, which are based on measurements in a single plane. An extensive simulation study shows that the spatial rotator may be more efficient than the traditional local volume estimators. Furthermore, the spatial rotator can be seen as a further development of the Cavalieri estimator, which does not require randomization of sectioning or viewing direction. The tissue may thus be sectioned in any arbitrary direction, making it easy to identify the specific tissue region under study. In order to use the spatial rotator in practice, however, it is necessary to be able to identify intersection points between cell boundaries and test rays in a series of parallel focal planes, also at the peripheral parts of the cell boundaries. In cases where over- and underprojection phenomena are not negligible, they should therefore be corrected for if the spatial rotator is to be applied. If such a correction is not possible, it is needed to avoid these phenomena by using microscopy with increased resolution in the focal plane.
authors.affiliation: Stereology and Electron Microscopy Laboratory, Aarhus University Hospital, Aarhus, Denmark.|Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University, Aarhus, Denmark.|Department of Computer Science, Aarhus University, Aarhus, Denmark.
authors.forename: A
authors.initials: A
authors.lastname: Rasmusson
authors.affiliation: Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University, Aarhus, Denmark.|Department of Mathematics, Aarhus University, Aarhus, Denmark.
authors.forename: U
authors.initials: U
authors.lastname: Hahn
authors.affiliation: Stereology and Electron Microscopy Laboratory, Aarhus University Hospital, Aarhus, Denmark.|Department of Neuroscience and Pharmacology, University of Copenhagen, Copenhagen, Denmark.
authors.forename: J O
authors.initials: JO
authors.lastname: Larsen
authors.affiliation: Stereology and Electron Microscopy Laboratory, Aarhus University Hospital, Aarhus, Denmark.
authors.forename: H J G
authors.initials: HJG
authors.lastname: Gundersen
authors.affiliation: Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University, Aarhus, Denmark.|Department of Mathematics, Aarhus University, Aarhus, Denmark.
authors.forename: E B Vedel
authors.initials: EBV
authors.lastname: Jensen
authors.affiliation: Stereology and Electron Microscopy Laboratory, Aarhus University Hospital, Aarhus, Denmark.|Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University, Aarhus, Denmark.
authors.forename: J R
authors.initials: JR
authors.lastname: Nyengaard
mesh_terms: D000818:Animals; D002466:Cell Nucleolus / Q000648:ultrastructure; D048430:Cell Shape; D048429:Cell Size; D005057:Eukaryotic Cells / Q000166:cytology* / Q000648:ultrastructure; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods* / Q000706:statistics & numerical data; D008853:Microscopy / Q000295:instrumentation / Q000379:methods*