Theoretical evaluation of the cataract extraction-refraction-implantation techniques for intraocular lens power calculation

PURPOSE: To evaluate theoretically three previously published formulae that use intra-operative aphakic refractive error to calculate intraocular lens (IOL) power, not necessitating pre-operative biometry. The formulae are as follows: IOL power (D) = Aphakic refraction x 2.01 [Ianchulev et al., J. Cataract Refract. Surg.31 (2005) 1530]; IOL power (D) = Aphakic refraction x 1.75 [Mackool et al., J. Cataract Refract. Surg.32 (2006) 435]; IOL power (D) = 0.07x(2) + 1.27x + 1.22, where x = aphakic refraction [Leccisotti, Graefes Arch. Clin. Exp. Ophthalmol.246 (2008) 729]. METHODS: Gaussian first order calculations were used to determine the relationship between intra-operative aphakic refractive error and the IOL power required for emmetropia in a series of schematic eyes incorporating varying corneal powers, pre-operative crystalline lens powers, axial lengths and post-operative IOL positions. The three previously published formulae, based on empirical data, were then compared in terms of IOL power errors that arose in the same schematic eye variants. RESULTS: An inverse relationship exists between theoretical ratio and axial length. Corneal power and initial lens power have little effect on calculated ratios, whilst final IOL position has a significant impact. None of the three empirically derived formulae are universally accurate but each is able to predict IOL power precisely in certain theoretical scenarios. The formulae derived by Ianchulev et al. and Leccisotti are most accurate for posterior IOL positions, whereas the Mackool et al. formula is most reliable when the IOL is located more anteriorly. CONCLUSION: Final IOL position was found to be the chief determinant of IOL power errors. Although the A-constants of IOLs are known and may be accurate, a variety of factors can still influence the final IOL position and lead to undesirable refractive errors. Optimum results using these novel formulae would be achieved in myopic eyes.

Asymmetric price transmission in EU petroleum markets

This research investigates the determinants of asymmetric price transmission (APT) in European petroleum markets. APT is the faster response of retail prices to cost increases than to cost decreases; resulting in a welfare transfer from consumers to fuel retailers. I investigate APT at 3 different levels: the EU, the UK and at the Birmingham level. First, I examine the incidence of asymmetries in the retail markets of six major EU countries; significant asymmetries are found in all countries except from the UK. The market share data suggest that asymmetries are more important in more concentrated markets; this finding supports the collusion theory. I extend the investigation to 12 EU countries and note that APT is greater in diesel markets. The cross-country analysis suggests that vertical and horizontal concentration at least partly explains the degree of asymmetry. I provide evidence justifying scrutiny over retail markets’ pricing and structure. Second daily data unveil the presence of APT in the UK fuel markets. I use break tests to identify segments with different pricing regimes. Two main types of periods are identified: periods of rising oil price exhibit significant asymmetries whilst periods of recession do not. Our results suggest that oligopolistic coordination between retailers generate excess rents during periods of rising oil price whilst the coordination fails due to price wars when oil prices are going downwards. Finally I investigate the pricing behaviour of petroleum retailers in the Birmingham (UK) area for 2008. Whilst the market structure data reveals that the horizontal concentration is higher than the national UK average, I find no evidence of APT. In contrast, I find that retail prices are sticky upwards and downwards and that firms with market power (majors and supermarkets) adjust their prices slower than other firms.