Numerical studies of problems in biophysics, biomechanics and mechanobiology


T. Franz, Cardiovascular Research Unit, Faculty of Health Sciences, University of Cape Town, Private Bag X3, Observatory 7935, Cape Town, South Africa.


The Second African Conference on Computational Mechanics: An International Conference, AfriCOMP2011, was held in Cape Town, South Africa, during 4-7 January 2011. The conference hosted three plenary and keynote lectures, two mini symposia and numerous regular contributions presenting latest research in computational methods applied to problems in biomechanics, mechanobiology, biophysics and related fields. This special issue comprises a selection of invited papers in the areas of biophysics, biomechanics and mechanobiology and on presentations made at AfriCOMP2011.

Hawkins-Daarud et al.[1] present a thermodynamically consistent four-species model of tumour growth on the basis of the continuum theory of mixtures. Unique to this model is the incorporation of nutrient within the mixture as opposed to being modelled with an auxiliary reaction–diffusion equation. The results of an array of numerical experiments demonstrate a wide range of solutions produced by various choices of model parameters. Chen et al.[2] propose a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins involving continuum, atomic and quantum descriptions, assisted with the evolution, formation and visualisation of membrane channel surfaces. The proton channel conductances are studied over a number of applied voltages and reference concentrations, and comparison with experimental data confirms the proposed model.

Nobile et al.[3] propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of cardiac tissue. The underlying mathematical model is based on the active strain assumption with a multiplicative decomposition of the deformation tensor into a passive and an active part. Lafortune et al.[4] introduce a highly parallel coupled electromechanical model of the heart with very good scalability up to several hundreds of processors. This paper focuses on the mechanical part of the problem including the constitutive model, the numerical scheme and the coupling strategy. Marini et al.[5] develop a three-dimensional isotropic finite-strain damage model for abdominal aortic aneurysm wall that considers both the characteristic softening of the material caused by damage and the spatial variation of the material properties. The benefit of this finite-strain damage model is the potential capability to trigger growth and remodel processes in mechanobiological models. El-Baroudi et al.[6] present fluid-structure models towards the analysis of the dynamics of the aorta during a shock loading. The evolution of stresses in the cross section and along the aorta is simulated during a shock loading using different constitutive laws for blood.

Pelteret and Reddy [7] describe a three-dimensional finite element model of the tongue and surrounding soft tissues with potential application to the study of sleep apnoea, linguistics and speech therapy. Hyperelastic constitutive models and an active Hill three-element model were used to describe passive and active material behaviour under consideration of incompressibility. The neural stimulus for various muscle groups was determined through the use of a genetic algorithm-based neural control model.

Sazonov and Nithiarasu [8] provide an overview of surface and volume mesh generation techniques for creating valid meshes to study biomedical flows. The applications of interest are haemodynamics in blood vessels and air flow in upper human respiratory tract. Van Cauter et al.[9] present an automated method for extracting the anatomical axis of the femur and the application to conventional total knee arthroplasty. It was shown that precise measurements can be obtained by using a central and two outer parts with lengths corresponding to 58% of the mean femoral length, allowing partial scanning of the leg. Jansen van Rensburg et al.[10] present a comparison on masticatory induced stress subject to a variation in human skull shape using non-rigid registration. Although magnitudes of the difference are not necessarily obtained, the non-rigid map between subject shapes gives an objective indication on the location of differences.