$456 Journal of Biomechanics 2006, Vol. 39 (Suppl 1) Oral Presentations

of the L3-L4 and L4-L5 segments were almost within the standard deviation error of the experimental results, independently of the geometrical changes. The numerical study showed that the geometrical update affects the load transfer mechanisms. The computed ranges of motion were in agreement with the experimental results, but no conclusion could be drawn from the experimental data between the two modelled geometries. Therefore, to provide a better understanding of clinical pathologies, the validation of a model should include the load transfer mechanisms as well as the interaction between the geometry and the material properties.

7902 Sa, 15:30-16:00 (P3) Simulation of fracture healing in metaphyseal bone

U. Simon 1 , S.J. Shefelbine 2, P. Augat 3, L. Claes 1 . 1Institute for Orthopaedic Research and Biomechanics, University of UIm, Germany, 2Department of Bioengineering, Imperial College, London, UK, 3 Biomechanics Research Laboratory, Trauma Center Murnau, Germany

Fractures in metaphyseal bone heal primarily through intramembraneous os- sification. This process differs from callus healing in diaphyseal bone, which is based on endochondral ossification. The trabecular marrow in the metaphysis provides a rich vascular supply to the healing bone. Woven bone forms directly without a cartilage intermediary, and is remodeled to form trabecular bone. Previous studies have used numerical methods to simulate diaphyseal fracture healing or bone remodelling. However, trabecular fracture healing, which involves both tissue differentiation and trabecular formation, was not yet modeled. The objective of this study was to simulate trabecular bone fracture healing using Finite Element Method and Fuzzy Logic. We modeled a fracture gap in trabecular bone using an idealized cubic section (600Microns on a side) containing idealized trabeculae spicules at the borders. Load and boundary conditions were enhanced compared with an earlier version of this model to represent the conditions of a transverse metaphyseal fracture in the proximal tibia stabilized by an internal fixator. A constant compressive force of 500 N represented a reduced musculoskeletal load which acted on both the fractured bone and a spring element representing the fixation. The strain state within the gap was determined from the finite element model and used as input to a fuzzy controller which described the biological processes. The model predicted first the formation of woven bone in the gap. After the fracture gap was bridged with woven bone the bone matured, i.e. increasing in stiffness. In the final stage woven bone remodeled to form a trabecular structure. Results demonstrated that metaphyseal fracture healing can be simulated using similar mechanobiological principles to those proposed for endochondral bone formation during diaphyseal fracture healing. A single model that can simulate bone healing and remodelling may prove to be a useful tool in predict- ing musculoskeletal tissue differentiation in different vascular and mechanical environments.

7898 Sa, 16:00-16:30 (P3) The finite element methods in minimal access surgery C. Song. Department of Surgery & Molecular Oncology, Ninewells Hospital and Medical School, University of Dundee, Scotland, UK

Traditionally, the finite element methods (FEM) is an engineering tool for advanced design and optimisation, recently there have been more and more applications of this technology in the field of medicine and biotechnology. Based on our experience of surgical technology during the last decade, this paper will report the novel applications and rapid progress of FEM technology with an emphasis in minimal access surgery. FEM has been used extensively in surgical instrument design, which involves conventional analysis of stress/strain, and CFD, thermal analyses, coupled nonlinear tissue/instrument interaction as well. Many shape memory alloys (SMA) based devices have been developed in our group for minimal access surgery. The nonlinear behaviour of SMA and large deformation were modelled through a special finite element approach. Thermal analysis using FEM has also been carried out to optimise the design to make full use of the shape memory alloys recoverable strain, and to limit the potential heat damages to tissue. Clinical evaluations have been carried out to verify the nonlinear and thermal analysis during the development of various instruments and devices. Biomechanics is another important area for FEM techniques to find broad application at all levels of organ, tissue, cell and molecular, in normal and diseased states, soft and hard samples, flow and solid phases. Finite element models of liver, abdominal wall, breast and other tissues have been developed to investigate the biomechanics for human and animal tissues, different modal- ities of medical imaging (ultrasound, CT and MRI) were used to detect the complex anatomic structures and boundaries, 3D imaging processing software were used into the procedure to develop realistic FE models. Examples of each application will be given with detailed discussion.

New concepts of FEM modelling techniques are emerging in biomedical and biotechnology areas, particularly in the surgical simulation and image-based FEM for biomedical imaging analysis. Issues and areas that need further studies will be discussed.

7904 Sa, 16:30-17:00 (P3) Stress distribution and displacement analysis during an intermaxillary disjunction - A three dimensional fesa study of a human skull

A. Boryor 1 , M. Geiger 1 , A. Hohmann 1 , A. Wunderlich 2, F.G. Sander 1 . 1 Department of Orthodontics, 2 Department of Diagnostic Radiology, University of UIm, Germany

The goal of this study was to help to understand how much expansion force is needed during a maxillary expansion and which bony reaction takes place. A finite element model of a dry human male skull was generated from CT scans. The finite element model which consists of cortical and cancellous bone, teeth and sutures was loaded with the same force magnitudes, directions and working points as in a preceding in vitro experiment with a fresh human head. A three dimensional finite element stress analysis (FESA) of the compressive and tensile forces and the displacement was analysed and compared with the in vitro experiments. The highest stress is observed in the maxilla in the region where the forces were applied and spreads out more or less through almost the whole frontal skull structures. The displacement distribution which causes stress in the skull is highly dependant on the thickness of the bone region and its surrounding supporting structures. All areas with high compressive and tensile stresses are exactly the regions which determine the maximal amount of force to be used during the maxillary expansion and should be examined in case of any complication during a patient's treatment. Regions with significant compressive and tensile stress are the regions observed to have an increase in cellular activity. The displacement and stress distribution also depends on the material properties of the sutures and on their thickness which means that the time of maxillary expansion is highly depending on the individual age, bone growth rate and the state of the bone.

7896 Sa, 17:00-17:30 (P3) Numerical investigation of bone adaptation: A multiscale approach T. Ebinger, S. Diebels, H. Steeb. Chair efApplied Mechanics, Saarland University, Saarbr~cken, Germany

In principle all existing models of bone adaptation can be divided into three classes: microscopic models, e. g. models directly basing on the geometry derived by ~CT, mesoscopic models, approximating the real trabecular mi- crostructure by beam-like and plated structures, and purely macroscopic mod- els, i. e. phenomenological models, basing on continuum theories. Obviously, for a fixed size of a sample, the microscopic model yields the most detailed information. Furthermore, it has the advantage that constitutive equations can be used, which can directly be motivated by the biochemical processes. However, in clinical applications of practical relevance, e. g. studying the influence of screw osteosynthesis on the trabecular microstructure, quite often the detailed information is not necessary leading to unessential computation times due to a large number of Degrees Of Freedom (DOF). Mesoscopic models already reduce the information by approximating the microscopic complexity. However, this requires more sophisticated constitutive equations on the mesoscopic level. The model still includes a lot of information not relevant in clinical applications, e. g. the orientation and thickness of each single mesoscopic element. On the one hand the advantage of the macroscopic models consists of the numerical efficiency due to decoupling of microscopic dimension and the size of macroscopic Boundary Value Problems (BVP). These models are able to predict density distributions and orthotropic material properties. On the other hand it is difficult to formulate macroscopic phenomenological constitutive equations. Thus, quite often macroscopic models are enhanced by including information of the next lower scale via homogenization of a Representative Volume Element (RVE). Generally analytical homogenization techniques are used to formulate the constitutive equations of stress-strain relationships. In the present contribution we formulate the inherent constitutive equations of adaptation on the next lower scale and apply numerical homogenization techniques afterwards. Thereby, we do not use a RVE but a so-called Testing Volume Element (TVE), which does not require periodicity conditions and has only be able to reflect the macroscopic deformation behavior. Thus, the TVE can be much smaller in size than a RVE. However, attention has to be paid to eventual size effects, which means that the effective properties derived on a very small TVE can no longer directly be used on a macroscopic scale neglecting size effects.