H. J. Burd

Numerical modelling of the accommodating lens.

Data on geometric and material properties of the human lens derived from various published sources are used to construct axisymmetric, large displacement, finite element models of the accommodating lens of subjects aged 11, 29 and 45 years. The nucleus, cortex, capsule and zonule are modelled as linearly elastic materials. The numerical model of the 45-year lens is found to be significantly less effective in accommodating than the 29-year lens, suggesting that the modelling procedure is capable of capturing at least some of the features of presbyopia. The model of the 11-year lens shows some anomalous behaviour, and reasons for this are explored.

Mechanics of accommodation of the human eye

The classical Helmholtz theory of accommodation has, over the years, not gone unchallenged and most recently has been opposed by Schachar at al. (1993) (Annals of Ophthalmology, 25 (1) 5-9) who suggest that increasing the zonular tension increases rather than decreases the power of the lens. This view is supported by a numerical analysis of the lens based on a linearised form of the governing equations. We propose in this paper an alternative numerical model in which the geometric non-linear behaviour of the lens is explicitly included. Our results differ from those of Schachar et al. (1993) and are consistent with the classical Helmholtz mechanism.

Can reliable values of Young's modulus be deduced from Fisher's (1971) spinning lens measurements?

The current textbook view of the causes of presbyopia rests very largely on a series of experiments reported by R.F. Fisher some three decades ago, and in particular on the values of lens Youngs modulus inferred from the deformation caused by spinning excised lenses about their optical axis (Fisher 1971) We studied the extent to which inferred values of Youngs modulus are influenced by assumptions inherent in the mathematical procedures used by Fisher to interpret the test and we investigated several alternative interpretation methods. The results suggest that modelling assumptions inherent in Fishers original method may have led to systematic errors in the determination of the Youngs modulus of the cortex and nucleus. Fishers conclusion that the cortex is stiffer than the nucleus, particularly in middle age, may be an artefact associated with these systematic errors. Moreover, none of the models we explored are able to account for Fishers claim that the removal of the capsule has only a modest effect on the deformations induced in the spinning lens.

A structural constitutive model for the human lens capsule

Published data on the mechanical performance of the human lens capsule when tested under uniaxial and biaxial conditions are reviewed. It is concluded that two simple phenomenological constitutive models (namely a linear elastic model and a Fung-type hyperelastic model) are unable to provide satisfactory representations of the mechanical behaviour of the capsule for both of these loading conditions. The possibility of resolving these difficulties using a structural constitutive model for the capsule, of a form that is inspired by the network of collagen IV filaments that exist within the lens capsule, is explored. The model is implemented within a rectangular periodic cell. Prescribed stretches are imposed on the periodic cell and the network is allowed to deform in a non-affine manner. The performance of the constitutive model correlates well with previously published test data. One possible application of the model is in the development of a multi-scale analysis of the mechanics of the human lens capsule.

Shear modulus data for the human lens determined from a spinning lens test

The paper describes a program of mechanical testing on donated human eye bank lenses. The principal purpose of the tests was to obtain experimental data on the shear modulus of the lens for use in future computational models of the accommodation process. Testing was conducted using a procedure in which deformations are induced in the lens by spinning it about its polar axis. Shear modulus data were inferred from these observed deformations by means of a finite element inverse analysis procedure in which the spatial variation of the shear modulus within the lens is represented by an appropriate function (see Burd et al., 2011 for a detailed specification of the design of the spinning lens test rig, experimental protocols and associated data analysis procedures that were employed in the tests). Inferred data on lens shear modulus are presented for a set of twenty-nine lenses in the age range 12 years to 58 years. The lenses were tested between 47 h and 110 h from the time of death (average post-mortem time 74 h). Care was taken to exclude any lenses that had been affected by excessive post-mortem swelling, or any lenses that had suffered mechanical damage during storage, transit or the testing process. The experimental data on shear modulus indicate that, for young lenses, the cortex is stiffer than the nucleus. The shear modulus of the nucleus and cortex both increase with increasing age. The shear modulus of the nucleus increases more rapidly than the cortex with the consequence that from an age of about 45 years onwards the nucleus is stiffer than the cortex. The principal shear modulus data presented in the paper were obtained by testing at a rotational speed of 1000 rpm. Supplementary tests were conducted at rotational speeds of 700 rpm and 1400 rpm. The results from these supplementary tests are in good agreement with the data obtained from the principal 1000 rpm tests. Studies on the possible effects of lens drying during the test suggested that this factor is unlikely to have led to significant errors in the experimental determination of the shear modulus. The shear modulus data presented in the paper are used to develop ‘age-stiffness’ models to represent the shear modulus of the lens as a function of age. These models are in a form that may be readily incorporated in a finite element model of the accommodation process. A comparison is attempted between the shear modulus data presented in the current paper and equivalent data published by previous authors. This comparison highlights various limitations and inconsistencies in the data sets.

An improved spinning lens test to determine the stiffness of the human lens

It is widely accepted that age-related changes in lens stiffness are significant for the development of presbyopia. However, precise details on the relative importance of age-related changes in the stiffness of the lens, in comparison with other potential mechanisms for the development of presbyopia, have not yet been established. One contributing factor to this uncertainty is the paucity and variability of experimental data on lens stiffness. The available published data generally indicate that stiffness varies spatially within the lens and that stiffness parameters tend to increase with age. However, considerable differences exist between these published data sets, both qualitatively and quantitatively. The current paper describes new and improved methods, based on the spinning lens approach pioneered by Fisher, R.F. (1971) ‘The elastic constants of the human lens’, Journal of Physiology, 212, 147–180, to make measurements on the stiffness of the human lens. These new procedures have been developed in an attempt to eliminate, or at least substantially reduce, various systematic errors in Fisher’s original experiment. An improved test rig has been constructed and a new modelling procedure for determining lens stiffness parameters from observations made during the test has been devised. The experiment involves mounting a human lens on a vertical rotor so that the lens spins on its optical axis (typically at 1000 rpm). An automatic imaging system is used to capture the outline of the lens, while it is rotating, at pre-determined angular orientations. These images are used to quantify the deformations developed in the lens as a consequence of the centripetal forces induced by the rotation. Lens stiffness is inferred using axisymmetric finite element inverse analysis in which a nearly-incompressible neo-Hookean constitutive model is used to represent the mechanics of the lens. A numerical optimisation procedure is used to determine the stiffness parameters that provide a best fit between the finite element model and the experimental data. Sample results are presented for a human lens of age 33 years.

Enhanced detection of buried assets

This paper reports the design of a new resonator system to enhance the identification of buried underground assets. Results from theoretical calculation, simulation, laboratory measurement, and field test are presented and practical considerations are highlighted. The proposed system has the potential to benefit future civil engineering installations.

Modelling the mechanics of accommodation and presbyopia

Abstract Finite element methods have been used to compute the expected relationship between changes in ciliary body diameter and the change in refractive power implied by the change in geometry of the human ocular lens, using values for the material properties and initial geometry taken from the literature (notably the slit lamp photography of Brown (1973) and the studies by Fisher (1969) of the lens material properties). The results show that if the non‐linearity associated with the changing geometry is taken into account the lens does not respond to ciliary body stretch by an increase in power [as recently claimed by Schachar et al. (1993), but in the conventional way with a decrease in power. The models show a decrease in the amplitude of accommodation between the age of 29 and 45 years (using Browns data, 1973), but using Browns data for the 11‐year‐old eye leads to the paradoxical conclusion that accommodation amplitude in this eye would have been small. In the process of carrying out the modelling, we have examined the consistency of the published measurements and also the validity of the mathematical methods used in interpreting them, and this analysis suggests that further work is needed before one can be confident that the assumptions about geometry and material properties on which the modelling is based are sound.

Field testing of large diameter piles under lateral loading for offshore wind applications

The nature-inspired concept of self-healing materials in construction is relatively new and has recently attracted significant attention as this could bring about substantial savings in maintenance costs as well as enhance the durability and serviceability and improve the safety of our structures and infrastructure. Much of the research and applications to date has focused on concrete, for structural applications, and on asphalt, with significant advances being made. However, to date no attention has been given to the incorporation of self-healing concepts in geotechnical and geo-environmental applications. This includes the use of concrete and other stabilising agents in foundations and other geotechnical structures, grouts, grouted soil systems, soil-cement systems and slurry walls for ground improvement and land remediation applications. The recently established Materials for Life (M4L) project funded by EPSRC has initiated research activities in the UK focussing on those applications. The project involves the development and integration of the use of microcapsules, biological agents, shape memory polymers and vascular networks as healing systems. The authors are exploring development of self-healing systems using mineral admixtures, microencapsulation and bio-cementation applications. The paper presents an overview of those initiatives to date and potential applications and presents some relevant preliminary results.By contrast to studies in petroleum geology and, despite their world-wide occurrence, geotechnical studies of ancient fluvial sediments are rare. This paper introduces the main characteristics of these sediments by reference to a classic UK example. Attention is then drawn to a number of major overseas examples where, although the principal features can be recognised, large differences arise as a result of factors such as the tectonic setting, the volume and mineralogy of the source material and the climate at the time the sediments were deposited. The first, over-riding problem for their engineering evaluation comes during the site investigation phase with the difficulty of deducing the geological structure and distribution of the widely varying lithologies.Strain accumulation in granular soils due to dynamic loading is investigated through long term cyclic triaxial tests and cyclic triaxial tests according to ASTM D 3999-91. Soil parameters, test equipment and loading conditions have a significant influence on strain accumulation, therefore a parameterization of the silica sand and a description of the cyclic triaxial test device are explained. Cyclic triaxial tests are performed and test results are presented illustrating the evolution of Young’s modulus during long term cyclic loading. The influence of the width of the stress-strain loop and the initial void ratio on strain accumulation is investigated and validated with existing accumulation models. The usefulness of Miner’s rule on sand subjected to cyclic loading is demonstrated by two tests with different packages of loading cycles.

Some Experiences of Modelling Tunnelling in Soft Ground Using Three-Dimensional Finite Elements

A three-dimensional finite element model has been developed at Oxford University to study the effects of subsidence from soft ground tunnelling on adjacent surface structures. Simulation of excavation and the ground loss associated with tunnelling are incorporated in the model. Surface buildings are also included, as groups of interconnected two-dimensional facades composed of an elastic no tension material, to model masonry. This paper describes the development, implementation and performance of procedures to model the tunnelling processes. A description is also given of the methods used to generate the finite element meshes and to post-process the data.