Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Using performance measurement models for benefit realization with enterprise systems: The Queensland Government approach (Case Study)

A range of influences, technical and organizational, has encouraged the wide spread adaption of Enterprise Systems (ES). Nevertheless, there is a growing consensus that Enterprise Systems have in the many cases failed to provide the expected benefits to organizations. This paper presents ongoing research, which analyzes the benefits realization approach of the Queensland Government. This approach applies a modified Balance Scorecard. First, history and background of Queensland Government’s Enterprise Systems initiative is introduced. Second, the most common reasons for ES under performance are related. Third, relevant performance measurement models and the Balanced Scorecard in particular are discussed. Finally, the Queensland Government initiative is evaluated in light of this overview of current work in the area. In the current and future work, the authors aim to use their active involvement in Queensland Government’s benefits realization initiative for an Action Research based project investigating the appropriateness of the Balanced Scorecard for the purposes of Enterprise Systems benefits realization.