Describing size and shape changes in the human mandible from 9 to 15 years - comparison of elliptical Fourier function and Procrustes methods

HA Statistics

Easton, Valerie J. ; McColl, John

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: HA Statistics;   

Others  :  http://theses.gla.ac.uk/8392/1/2000eastonphd.pdf

来源: University of Glasgow

【 摘 要 】

In the past, there have been many attempts to capture the size and shape information inherent in complex irregular objects by numerical representation. There is much to be gained in a biological sense by numerical description of complex forms, like the craniofacial complex, in the field of dentistry. This thesis aims to review, utilise and build on past research methods in an attempt to describe the size and shape changes of a sample of human mandibles from the age of 9 through to 15 years. Specifically, two methods are considered and contrasted, the elliptical Fourier function and Procrustes analysis (including Bookstein co-ordinates).In chapter 1 the background and motivation for such an investigation is introduced, describing the need for a mathematical description of complex irregular forms with an emphasis on the importance of such models in dentistry with particular reference to the way in which the human mandible grows over time. The methodological and clinical issues of the problem are outlined, including a summary of up to date methods that have been used to capture size and shape information of a growing complex morphological form and an overview of the way in which the mandible grows. Both the so-called landmark dependent and landmark independent (boundary outline) methods are summarised. Whilst all the methods considered are not without constraint in describing the size and shape of complex forms, all have been seen in the past to be beneficial in some way in that they all model 'form' in one way or another at the very least.Chapter 2 then considers in more depth, what is fast becoming a much-promoted method of describing irregular forms, the elliptical Fourier function (EFF). The use of conventional Fourier methods, as well as the newer EFF method in describing size and shape changes is reviewed. A suite of programs that have been specially written to apply the EFF method in the description of complex irregular forms is introduced and an overview of the specific routines available in the package is given.The data sample available for investigation, which consists of a series of lateral headcephalograms (x-rays) from the BC Leighton Growth Study, is described in Chapter 3.The way in which a subset is selected following certain inclusion and exclusion criteriafrom the available x-rays is outlined. The way in which the mandibular data is thenprepared for subsequent use in the EFF suite of programs, as well as with the method ofProcrustes (and Bookstein co-ordinates) is also described in some detail.In Chapter 4, an error study is undertaken to investigate the reproducibility of thetracings of the sample of mandibular outlines prepared in the previous chapter. Both11within- and between-rater studies are looked at. The EFF method is then applied to thesample of tracings collected by one observer to explore any changes in size and shapethat may occur as the mandible grows, concentrating on ages 9, 11, 13 and 15 years. Aswell as producing some very informative plots of the observed and predicted mandibularoutlines, and centroid to boundary outline distances, the usefulness of the harmonicinformation available from the EFF procedure for numerically describing size and shapechanges of a complex irregular form is investigated. Whether or not there are differencesbetween males and females in the data sample, in terms of the size and / or shape of themandible is also explored.Finally, the method of Procrustes analysis (and Bookstein co-ordinates) is described inmore depth in Chapter 5. This particular method is also applied to the same sample ofmandibular outlines in order to investigate its usefulness in describing size and shapechanges of the human mandible from age 9 to 15 years. Shape variability within samplesis also explored by way of principal components analysis. In addition, the method of thinplate splines (TPS) is applied in order to examine shape change between males andfemales.Similar observations were made about mandibular growth in the sample investigatedusing both the EFF and Procrustes (along with Bookstein co-ordinates) procedures.Overall, the mandible was observed to be 'growing' between ages 9 and 15 i.e. changing in both size and shape over a period of time. There was no difference in terms of the sizeand shape of the bone between males and females in the sample, for each age. Further,using Procrustes analysis (and Bookstein co-ordinates) there did not appear to be anyassociation between the size and shape of the mandibular outlines in either the male orfemale samples, for all ages. In addition, investigating shape variability using Procrustesmethods by way of principal components analysis, resulted in broadly similar patterns formales and females, as well as combined samples, and different age groups.It is concluded in Chapter 6 that the methods of elliptical Fourier function and Procrustes(and Bookstein co-ordinates) both provide a very useful framework in which to describethe size and shape of complex irregular forms like the mandible. Although both methodshave their advantages and disadvantages, Procrustes (including the very useful methodusing Bookstein co-ordinates) is preferred for statistical purposes.