Tensorial biomorphometrics Continuum, discrete and statistical aspects - Publico, Andre Supnet; Dasgupta, Gautam; McAlarney, Mona; ProQuest Dissertations and Thesis (Ann Arbor Columbia University, 2000)
The study of the form and form changes of biological structures is essential to understanding their functions and their adaptation to changing conditions. In the past three decades, developments in geometric morphometrics and in image acquisition and geometrical information extraction technologies have made the investigations of forms in intra- and interpopulation settings increasingly practical. While there are morphometric methodologies for landmark data, outline data or interlandmark distances representation, there is no one method that completely models biological structures. The focus of this dissertation is the development of a methodology for handling, not only the aforementioned form representations, but also the more general cases of multiboundary structures. It consists of a general mean form algorithm and a multiboundary-based tensorial morphometric technique.
For population studies, mean forms are often constructed from the individuals and serve as bases for comparison. The mean form computation developed here, the alternative least squares scaling algorithm (ALESSA), calculates the coordinates of discrete points from their interpoint distances by solving the SSTRESS problem of multidimensional scaling. It enhances the least squares technique based on a novel search scheme.
The tensorial morphometric technique is an extension of the morphometric technique proposed by Dasgupta et al. (1992) for outline forms without landmarks to multiboundary structures with landmarks. It describes the form change of a reference to a final configuration using Green's strains. The kinematics is modeled as a deformation function that satisfies the Laplace equation subject to Dirichlet boundary conditions. This boundary-value problem is then solved using the boundary element method.
This methodology was applied to ventricular function evaluation of normal and abnormal hearts and to the growth analysis of prenatal rat eyes. Excellent results were obtained.
Includes bibliographical references.
Electronic reproduction.
Keywords: Biomedical research; Mechanics