Some comments on coordinate-free and scale-invariant methods in morphometrics

The unusual strategy for comparing biological shapes is to use some kind of superimposition of the two forms under study and then look at the "residuals" as the shape change. In this paper, I take a careful look at this general strategy and point out some subtle but inherent and important pitfalls. Additionally an alternative approach based on Euclidean Distance Matrix representation is presented. It is applicable to two- as well as three-dimensional objects.     

Mineral element content in Ulva lactuca L. with reference to eutrophication in Hong Kong coastal waters

The amounts of tissue nitrogen, phosphorus, potassium, sodium, calcium and iron were estimated in the green alga Ulva lactuca L. collected from 9 rural and 14 urban littoral sites in the waters around Hong Kong Island during 1978 and 1979. The mean levels of tissue nitrogen and phosphorus were respectively 65% and 87% more in urban sites than in rural ones. Very significant correlation (r = 0.920) was found between the logarithmic concentration of seawater inorganic nitrogen and that of tissue nitrogen. The same applied to soluble reactive phosphorus in seawater and tissue phosphorus (r = 0.886). The levels of potassium, sodium and calcium in the alga were relatively uniform. However considerable variation in the level of iron was detected. The potential use of Ulva as an indicator species for eutrophication is discussed.     

Development of a surrogate model based on patient weight,bone mass and geometry to predict femoral neck strains and fracture loads

Osteoporosis and related bone fractures are an increasing global burden in our ageing society. Areal bone mineral density assessed through dual energy X-ray absorptiometry (DEXA), the clinically accepted and most used method, is not sufficient to assess fracture risk individually. Finite element (FE) modelling has shown improvements in prediction of fracture risk, better than aBMD from DEXA, but is not practical for widespread clinical use. The aim of this study was to develop an adaptive neural network (ANN)-based surrogate model to predict femoral neck strains and fracture loads obtained from a previously developed population-based FE model. The surrogate model performance was assessed in simulating two loading conditions: the stance phase of gait and a fall.The surrogate model successfully predicted strains estimated by FE (r² = 0.90–0.98 for level gait load case, r² = 0.92–0.96 for the fall load case). Moreover, an ANN model based on three measurements obtainable in clinics (femoral neck length (level gait) or maximum femoral neck diameter (fall), femoral neck bone mass, body weight) was able to give reasonable predictions (r² = 0.84–0.94) for all of the strain metrics and the estimated femoral neck fracture load. Overall, the surrogate model has potential for clinical applications as they are based on simple measures of geometry and bone mass which can be derived from DEXA images, accurately predicting FE model outcomes, with advantages over FE models as they are quicker and easier to perform.     

Implementation of reflex loops in a biomechanical finite element model

In the field of biomechanics, the offer of models which are more and more realistic requires to integrate a physiological response, in particular, the controlled muscle bracing and the reflexes. The following work aims to suggest a unique methodology which couples together a sensory and motor loop with a finite element model. Our method is applied to the study of the oscillation of the elbow in the case of a biceps brachial stretch reflex. The results obtained are promising in the purpose of the development of reactive human body models.     

Finite element analysis of different loading conditions for implant-supported overdentures supported by conventional or mini implants

The effect of implants’ number on overdenture stability and stress distribution in edentulous mandible, implants and overdenture was numerically investigated for implant-supported overdentures. Three models were constructed. Overdentures were connected to implants by means of ball head abutments and rubber ring. In model 1, the overdenture was retained by two conventional implants; in model 2, by four conventional implants; and in model 3, by five mini implants. The overdenture was subjected to a symmetrical load at an angle of 20 degrees to the overdenture at the canine regions and vertically at the first molars. Four different loading conditions with two total forces (120, 300 N) were considered for the numerical analysis. The overdenture displacement was about 2.2 times higher when five mini implants were used rather than four conventional implants. The lowest stress in bone bed was observed with four conventional implants. Stresses in bone were reduced by 61% in model 2 and by 6% in model 3 in comparison to model 1. The highest stress was observed with five mini implants. Stresses in implants were reduced by 76% in model 2 and 89% increased in model 3 compared to model 1. The highest implant displacement was observed with five mini implants. Implant displacements were reduced by 29% in model 2, and increased by 273% in model 3 compared to model 1. Conventional implants proved better stability for overdenture than mini implants. Regardless the type and number of implants, the stress within the bone and implants are below the critical limits.     

Three-dimensional Orthotropic Viscoelastic Finite Element Model of a Human Ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only.

A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.     

Validation of density–elasticity relationships for finite element modeling of human pelvic bone by modal analysis

In total hip arthroplasty and particularly in revision surgery, computer assisted pre-operative prediction of the best possible anchorage strategy for implant fixation would be a great help to the surgeon. Computer simulation relies on validated numerical models. In the current study, three density–elasticity relationships (No. 1–3) from the literature for inhomogeneous material parameter assignment from CT data in automated finite element (FE) modeling of long bones were evaluated for their suitability for FE modeling of human pelvic bone. Numerical modal analysis was conducted on 10 FE models of hemipelvic bone specimens and compared to the gold standard provided by experimental modal analysis results from a previous in-vitro study on the same specimens. Overall, calculated resonance frequencies came out lower than measured values. Magnitude of mean relative deviation of numerical resonance frequencies with regard to measured values is lowest for the density–elasticity relationship No. 3 (−15.9%) and considerably higher for both density–elasticity relationships No. 1 (−41.1%) and No. 2 (−45.0%). Mean MAC values over all specimens amount to 77.8% (No. 1), 78.5% (No. 2), and 83.0% (No. 3). MAC results show, that mode shapes are only slightly influenced by material distribution. Calculated resonance frequencies are generally lower than measured values, which indicates, that numerical models lack stiffness. Even when using the best suited (No. 3) out of three investigated density–elasticity relationships, in FE modeling of pelvic bone a considerable underestimation of model stiffness has to be taken into account.