The connEulor:​ unbiased estimation of connectivity using physical disectors under projection

Gundersen, H. J. G.; Boyce, R. W.; Nyengaard, J. R.; Odgaard, A.

Affiliations

¹Stereological Research Laboratory, University Institute of Pathology and 2nd University Clinic of Internal Medicine, Biomechanics Laboratory, Institute of Experimental Clinical Research, University of Aarhus, Denmark

²Rhône-Poulenc Rorer Central Research, Collegeville, Pa., USA

Abstract

The Euler number and the connectivity of an arbitrary object is defined, and it is illustrated why the connectivity of an n-dimensional object cannot be estimated in an (n − 1)-dimensional section. The disector-principle for 3-D counting of the Euler-events is illustrated in cancellous bone. The correct handling for unbiased counting of events at artificial edges is outlined. A nomogram for predicting the precision of an estimate is provided.

Links

DOI: 10.1016/8756-3282(93)90144-Y

PubMed: 8363860

WoS: A1993LD83300007

Cited Works (3)

Year	Entry
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Cited By (22)

Year	Entry
2010	Parkinson IH, Forbes D, Sutton-Smith P, Fazzalari NL. Model-independent 3D descriptors of vertebral cancellous bone architecture. J Osteopor. 2010;2010:641578.
2001	Odgaard A. Quantification of cancellous bone architecture. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:14-1–14-19.
2000	Ding M. Age variations in the properties of human tibial trabecular bone and cartilage. Acta Orthop Scand. 2000;71(suppl 292):1-45.
1996	Amling M, Pösl M, Ritzel H, Hahn M, Vogel M, Wening VJ, Delling G. Architecture and distribution of cancellous bone yield vertebral fracture clues: a histomorphometric analysis of the complete spinal column from 40 autopsy specimens. Arch Orthop Trauma Surg. July 1996;115(5):262-269.
1994	Compston JE. Connectivity of cancellous bone: assessment and mechanical implications. Bone. September–October 1994;15(5):463-466.
1995	Boyce RW, Wronski TJ, Ebert DC, Stevens ML, Paddock CL, Youngs TA, Gundersen HJG. Direct stereological estimation of three-dimensional connectivity in rat vertebrae: effect of estrogen, etidronate and risedronate following ovariectomy. Bone. February 1995;16(2):209-213.
1995	Boyce RW, Ebert DC, Youngs TA, Paddock CL, Mosekilde L, Stevens ML, Gundersen HJG. Unbiased estimation of vertebral trabecular connectivity in calcium-restricted ovariectomized minipigs. Bone. June 1995;16(6):637-642.
1997	Odgaard A. Three-dimensional methods for quantification of cancellous bone architecture. Bone. 1997;20(4):315-328.
1998	Thomsen JS, Ebbesen EN, Mosekilde L. Relationships between static histomorphometry and bone strength measurements in human iliac crest bone biopsies author links open overlay panel. Bone. February 1998;22(2):153-163.
1999	Kabel J, Odgaard A, van Rietbergen B, Huiskes R. Connectivity and the elastic properties of cancellous bone. Bone. 1999;24(2):115-120.
2002	Thomsen JS, Ebbesen EN, Mosekilde L. Predicting human vertebral bone strength by vertebral static histomorphometry. Bone. March 2002;30(3):502-508.
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2020	Ryan MK, Oliviero S, Costa MC, Wilkinson JM, Dall’Ara E. Heterogeneous strain distribution in the subchondral bone of human osteoarthritic femoral heads, measured with digital volume correlation. Materials. 2020;13(20):4619.
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2009	Moesen M. Modeling of the Geometry and Mechanical Behavior of Bone Scaffolds [PhD thesis]. Katholieke Universiteit Leuven; June 2009.
2001	Boyd SK. Microstructural Bone Adaptation in an Experimental Model of Osteoarthritis [PhD thesis]. Calgary, AB: University of Calgary; January 2001.
2006	Lau AG. Development of a Microstructural Homogenization Model for Calcifying Cartilage Using the Generalized Method of Cells [PhD thesis]. Charlottesville, VA: University of Virginia; January 2006.