Assessment and statistics of surgically induced astigmatism

The aim of the thesis (Næser 2008) was to develop methods for the assessment of surgically induced astigmatism (SIA) in individual eyes, and in groups of eyes. The thesis is based on 12 peer-reviewed publications published over a period of 16 years. Both contemporary and older literature was reviewed (Næser 2001). A new method of analysing SIA was developed: the polar system. Multivariate statistical analysis of refractive data was described (Næser 1997; Næser & Hjortdal 1999, 2001a, 2001b). Clinical validation studies were performed. The description of a cylinder surface with polar values and differential geometry was compared. The main results were that refractive data (in the form of sphere, cylinder and axis) may define an individual patient or data set, but are unsuited for mathematical and statistical analyses (Næser 2001). The polar-value system converts net astigmatisms to orthonormal components in dioptric space. A polar value is the difference in meridional power between two orthogonal meridians (Næser 1990; Næser et al. 1994). Any pair of polar values, separated by an arch of 45°, characterizes a net astigmatism completely (Næser & Behrens 1997). The two polar values represent the net curvital and net torsional power over the chosen meridian (Næser & Hjortdal 2006). The spherical component is described by the spherical equivalent power. Several clinical studies demonstrated the efficiency of multivariate statistical analysis of refractive data (Næser & Guo 2000; Næser & Hjortdal 2001a, 2001b; Næser et al. 2002). Polar values and formal differential geometry describe astigmatic surfaces with similar concepts and mathematical functions (Næser & Hjortdal 2006). Other contemporary methods, such as Long’s power matrix, Holladay’s and Alpins’ methods, Zernike (Næser & Hjortdal 2004) and Fourier analyses (Næser & Hjortdal 2006), are correlated to the polar-value system. In conclusion, the analysis of SIA should be performed with polar values or other contemporary component systems. This PhD thesis is published as an electronic supplement, see:Næser K (2008): Assessment and statistics of surgically induced astigmatism. Acta Ophthalmol86 (Suppl.): 5–28 This study was supported by Statens Sundhedsvidenskabeligt Forskningsråd, Cykelhandler P. Th. Rasmussen og Hustrus Mindelegat, Hotelejer Carl Larsen og Hustru Nicoline Larsens Mindelegat, Landsforeningen til Værn om Synet, Forskningsinitiativet for Århus Amt, Alcon Denmark, and Desirée and Niels Ydes Fond.