Computational Simulation in Biomechanics: Theory and Applications

Benefits of computational biomechanics
The application of computer-based simulation within the medical device sector has made rapid progress in the past decade. The development of a theoretical, visualisation and biological-based framework for biosimulation is advancing rapidly and is now being applied successfully to mimic tissue structures, mechanotransduction, adaptation and tissue and implant interfaces. This continued progress offers the medical device industry a tool that can provide rapid device design assessment, accuracy of solution and three-dimensional (3D) output in the form of highly realistic images that also contain considerable quantifiable data. The success of these systems can be attributed to the development of numerical-based packages such the finite element (FE) method and the rapid development of imaging and data capture techniques that are now successfully employed to scan and produce 3D geometries of the most complex structure of biological tissue, including bone, soft tissue and inserted implant systems and interfaces. Some of the techniques in the area of medical imaging such as magnetic resonance imaging (MRI), computer tomography (CT) and positron emission tomography are now being utilised with great success to capture complex 3D biological structures of hard and soft tissue such as muscle, skin and bone structures. The image data obtained this way can then be utilised to build the 3D FE models needed for the simulation of biological processes of interest.

Technology merger expands capabilities

Figure 1: Bone structure and dental implant geometry prior to mesh generation.

The computer simulation technique described here employs three processes:
■ scanning (MRI, CT µCT)
■ the development of a computer-aided design (CAD) file of the geometry of the 3D system using segmentation software that can generate high quality solid meshes from sterolithography (STL) files
■ the creation of the 3D FE model and the material properties defined.
An important part of this process is the second stage in which the image data is translated into an STL file, which basically describes the surface geometry in a triangulated form that can then be read by many commercial software packages associated with CAD and computer-aided manufacturing (CAM). This has the advantage that it can readily be used within many software systems deployed in the medical sector such as rapid proto-typing and graphic output. The final stage of the process utilises automated mesh generation software that can accurately define the most complex 3D geometry of biological structures, bone and soft tissue layers and in vivo implant systems as well as the material properties. These meshes can consist of more than 800   000 3D solid elements that allow realistic simulation and visual output of the system response. Hence, this process permits the rapid generation of data required for FE analysis, which provides a most powerful computational tool for the solution of large complex structural forms with arbitrary 3D geometries and loading conditions. In this way, problems involving linear and nonlinear tissue deformation, impact analysis, implant–bone contact, performance of biological systems and medical devices response can be evaluated.
 

Figure 2: (a) FE prediction of initial bone remodelling around dental implant; (b) close-up view.

Before considering applications, it should be noted that the FE-based software complies with a thermodynamically consistent constitutive framework and it permits the application of continuum damage-repair mechanics, soft and hard tissue directional properties, remodelling algorithms, apparent density and porosity, mechanical stimulus and controlled anisotrophy.¹ For example, it is well known that strains within the bone mass, associated with medical implants of between 1000 and 3000 micro strain can trigger an increase in bone mass, and strains typically below 50 micro strain are likely to cause disuse atrophy. These strains can be accurately predicted using FE analysis, which provides quantifiable data for medical device assessment prior to manufacture. A variety of application areas can benefit from employing this type of computer simulation.

Dental implants

Figure 3: FE face model showing covering skin layer (transparent), muscles and nasal cartilage.

Dental implants have been a major success story in clinical practice and new designs, implant surface geometries and techniques for insertion are continuing to increasingly provide optimised and cost-effective systems. Computational biomechanics can offer a most powerful tool. It is able to capture the complex 3D geometry of the implant and maxilla and mandible–bone construct and produce a full nonlinear stress analysis of the system (Figure 1). Furthermore, constitutive laws for tissue structure can provide predictions of bone growth(osseointegration), prediction on initial and long-term implant stability, interfacial bone and implant stresses² and invaluable data on how new designs may be introduced to enhance performance (Figure 2). It is also possible to evaluate the relationship between the mechanical parameters obtained by FE simulation and the biological reactions expressed through morphometric parameters measured from scan data.

Other variables such as daily stress stimulus, bone density changes, tissue stress levels, bone remodelling rates, applied loading and load cycles, implant surface activity and threshold density for cortical/cancellous bone and the geometrical and surface structure of the implant can also be quantified. Hence, simulation offers a tool to study new design scenarios and inputs, which can be tested numerically to provide a cost-efficient means of quantifying patient response prior to implant manufacture and costly clinical trials.

Facial reconstruction

Figure 4: Facial expression presurgery of a smile at time zero (left), during facial activation (middle) and fully activated (right).

The human facial construct consists of a complex formation of tissues, which includes the maxilla and mandible, the dentition and more than 40 facial muscles that are associated with facial expression, breathing, eating and communicating. During the past few years, computational techniques have progressed at such a rate that it is now possible to undertake accurate 3D facial simulations that consider the bone structures, musculature, subcutaneous tissue and the overlaying skin. Through the segmentation of imaging files it is possible to build up a facial construct consisting of the underlying bone and soft tissues that after manipulation provides a 3D FE mesh of the 20 most important facial muscles (Figure 3). For the facial analyses the bone structure is modelled as rigid, the subcutaneous and covering skin layer modelled as a Mooney-Rivlin hyperelastic material,³ the muscles as a user defined quasi-incompressible, fibre-enforced, hyperelastic structure and the nose cartilage as linear elastic. The 3D model permits various numerical procedures to be undertaken, which can be used to clinically assess procedures such as a mandibular sagittal split osteotomy, and allow for clinical assessment of the facial construct before and after the procedure. Furthermore, muscular movement facial expressions such as a smile or disgust can now be readily simulated including the complete data of muscle and skin movement within a dynamic time frame (Figure 4). The application of this type of simulation allows assessment of new clinical procedures and prediction of facial growth and expressions.

Further applications
The areas discussed above relate in the main to engineering or physics based computer models and the predictive simulation of solids within a biological system. However, the area of computer simulation in the healthcare sector continues to expand unabated and is now being used to solve problems that were intractable just a few years ago.⁴ This is the result of advances in hardware and software and the vast resources now available to undertake huge computational tasks. Some examples of the successful expansion of computer simulation in the medical field include:
■ computational cell and molecular
biomechanics
■ patient-specific methods and models in cardiovascular biomechanics and pulmonary biomechanics
■ neural IT, modelling and simulation of the brain function and structure
■ mechanobiology, cytoskeletal systems, computational biology and bioinformatics
■ imaging and visualisation, subject-specific models, simulation of near real-time reconstruction in 3D, imaging in robotics, virtual surgery and diagnostics and organ planning routines.
 

These are just some of the areas where novel simulation frameworks (surrogate systems) are being developed for use by a worldwide medical technology sector that is increasingly required to provide advanced solutions for a growing population. The use of computational simulation tools in healthcare is advancing rapidly with more realistic input and biological data becoming available. This advancement is being driven by the use of supercomputers, more accurate biocomputational input data and the need for medical technology to keep pace with an ever-demanding healthcare market. Computational simulation techniques already provide an advanced tool within the medical technology sector, and will continue to expand and provide the advances required by medical and clinical sciences.⁵ 

References
1. M. Doblare and J.M. García, “Anisotropic Bone Remodelling Model Based on a Continuum Damage-Repair Theory,”
J. Biomechanics 35, 1, 1–17 (2002).
2. G. Limbert and J. Middleton, “A Transversely Isotropic Viscohyperelastic Material. Application to the Modelling of Biological Soft Connective Tissues,” Intl. J. Solids and Structures, 41, 15, 4237–4260 (2004).
3. K.J. Bathe, “Finite Element Procedures,” by Prentice Hall Inc., Upper Saddle River, New Jersey, USA (1996).
4. J. Middleton et al. (eds), Computer Methods in Biomechanics and Biomedical Engineering. Proc. of the 8th Intl. Symposium, Porto, Portugal, 2008, published by Arup Consulting, ISBN 978-0-9562121-0-8.
5. www.meditech.cf.ac.uk [5] (medical technology website)

Brian Walker is Associate Director, and Liliana Beldie is Senior Project Engineer, both at Arup UK, The Arup Campus, Blythe Gate Blythe Valley Park, SolihullB90 8AE, UK
tel. +44 1212 133 317,
e-mail: brian.walker@arup.com [6], www.arup.com [7]

Professor John Middleton, DSc, is Director of Biomaterials/Biomechanics Research Centre Cardiff University School of Dentistry, Cardiff Medicentre, Heath Park, Cardiff CF14 4UJ, UK www.meditech.cf.ac.uk [5]

* To whom all correspondence should be sent.