Frictional contact mechanics methods for soft materials: application to tracking breast cancers

Mammography is currently the most widely used screening and diagnostic tool for breast cancer. Because X-ray images are 2D projections of a 3D object, it is not trivial to localise features identified in mammogram pairs within the breast volume. Furthermore, mammograms represent highly deformed configurations of the breast under compression, thus the tumour localisation process relies on the clinician's experience. Biomechanical models of the breast undergoing mammographic compressions have been developed to overcome this limitation. In this study, we present the development of a modelling framework that implements Coulomb's frictional law with a finite element analysis using a C(1)-continuous Hermite mesh. We compared two methods of this contact mechanics implementation: the penalty method, and the augmented Lagrangian method, the latter of which is more accurate but computationally more expensive compared to the former. Simulation results were compared with experimental data from a soft silicon gel phantom in order to evaluate the modelling accuracy of each method. Both methods resulted in surface-deformation root-mean-square errors of less than 2mm, whilst the maximum internal marker prediction error was less than 3mm when simulating two mammographic-like compressions. Simulation results were confirmed using the augmented Lagrangian method, which provided similar accuracy. We conclude that contact mechanics on soft elastic materials using the penalty method with an appropriate choice of the penalty parameters provides sufficient accuracy (with contact constraints suitably enforced), and may thus be useful for tracking breast tumours between clinical images.     

Portable magnetic tweezers device enables visualization of the three-dimensional microscale deformation of soft biological materials

We have designed and built a magnetic tweezers device that enables the application of calibrated stresses to soft materials while simultaneously measuring their microscale deformation using confocal microscopy. Unlike previous magnetic tweezers designs, our device is entirely portable, allowing easy use on microscopes in core imaging facilities or in collaborators' laboratories. The imaging capabilities of the microscope are unimpaired, enabling the 3-D structures of fluorescently labeled materials to be precisely determined under applied load. With this device, we can apply a large range of forces (~1-1200 pN) over micron-scale contact areas to beads that are either embedded within 3-D matrices or attached to the surface of thin slab gels. To demonstrate the usefulness of this instrument, we have studied two important and biologically relevant materials: polyacrylamide-based hydrogel films typical of those used in cell traction force microscopy, and reconstituted networks of microtubules, essential cytoskeletal filaments.     

Ion induced deformation of soft tissue

In this paper the effects of changing the ion concentration in and around a sample of soft tissue are investigated. The triphasic theory developed by Laiet al. (1990,Biomechanics of Diarthrodial Joints, Vol. 1, Berlin, Springer-Verlag) is reduced to two coupled partial differential equations involving fluid ion concentration and tissue solid deformation. These equations are given in general form for Cartesian, cylindrical and spherical geometries. After solving the two equations quantities such as fluid velocity, fluid pressure, chemical potentials and chemical expansion stress may be easily calculated. In the Cartesian geometry comparison is made with the experimental and theoretical work of Myerset al. (1984,ASME J. biomech. Engng,106, 151–158). This dealt with changing the ion concentration of a salt shower on a strip of bovine articular cartilage. Results were obtained in both free swelling and isometric tension states, using an empirical formula to acount for ion induced deformation. The present theory predicts lower ion concentrations inside the tissue than this earlier work. A spherical sample of tissue subjected to a change in salt bath ion concentration is also considered. Numerical results are obtained for both hypertonic and hypotonic bathing solutions. Of particular interest is the finding that tissue may contract internally before reaching a final swollen equilibrium state or swell internally before finally contracting. By considering the relative magnitude, and also variation throughout the time course of terms in the governing equations, an even simpler system is deduced. As well as being linear the concentration equation in the new system is uncoupled. Results obtained from the linear system compare well with those from the spherical section. Thus, biological swelling situations may be modelled by a simple system of equations with the possibility, of approximate analytic solutions in certain cases.     

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time; Application to non-rigid neuroimage registration

Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer.     

Measurement of surface deformation of soft tissue

A method is described for measuring the surface shape and deformations of soft tissue in three dimensions. The method uses close range stereophotogrammetry to record the three-dimensional locations of miniature optical targets applied to the tissue surface. This has been applied to study of human lumbar intervertebral disc. Measurements of the strain along surface annular fibers have been made under varying loads. In this case the maximum expected errors are about 0.15 mm, which corresponds to a strain of less than 1%. Preliminary findings have differed from predictions made in published mathematical models for the disc in that they show very little strain of the annulus in compression loading, but confirm axial torsional loading as liable to produce mechanical disruption of the disc annulus.     

The modelling of fibre reorientation in soft tissue

In this paper, a hyperelastic and thermodynamically consistent model for soft tissue is developed that is able to describe the change of the initial orientation of the collagen fibres. Full numerical implementation is considered as well. The collagen architecture is assumed to reorient driven by a specific thermodynamical force. The anisotropy is described by a strain energy function, which is decomposed into a part related to the matrix and a part related to the fibres. The initial fibre orientation is defined by a structural tensor, while the current orientation is described by a time-dependent structural tensor, which results from the initial one by a rotational transformation. The rotation tensor is obtained via an integration process of a rate tensor, which depends on an adequately defined thermodynamical force. The integration is achieved via an exponential map algorithm, where it is shown that the rotation is necessarily a two-parametric one. Efficiency of the proposed formulation is demonstrated using some numerical examples.     

电场和磁场响应的智能高分子材料

过去的几年里,人们开始对新型智能材料的开发产生了极大的兴趣。这些新型的智能材料包括生物材料、自组装材料、复集合流体材料以及高分子凝胶等;但是人们发现还没有哪种智能材料能像高分子凝胶智能材料那样可以对多重的外场刺激产生响应。这些外场刺激通常包括温度、溶剂、pH值、离子、分子、光、电、磁等。同时这种材料对外场响应时可以产生多种变化,包括体积的膨胀收缩、力学性能的变化、光电性质的变化等。在过去的时间里,人们已经在智能高分子凝胶领域取得了重要的进展。具有电磁响应的胶体粒子能够与高分子凝胶形成复合物。这些胶体粒子可以使高分子凝胶在外场刺激时发生形变。当施加电场或磁场时,高分子凝胶的形状发生变化,当撤去外场时,形状回复原样。基于这些特点,电磁响应的智能材料可以用来设计成新型的驱动器、阀、马达,以及药物输运装置。     

Progress in molecular modelling of DNA materials

The unique molecular recognition properties of DNA molecule, which store genetic information in cells, are responsible for the rise of DNA nanotechnology. In this article, we review the recent advances in atomistic and coarse-grained force fields along with simulations of DNA-based materials, as applied to DNA–nanoparticle assemblies for controlled material morphology, DNA–surface interactions for biosensor development and DNA origami. Evidently, currently available atomistic and coarse-grained representations of DNA are now at the stage of successfully reproducing and explaining experimentally observed phenomena. However, there is a clear need for the development of atomistic force fields which are robust at long timescales and in the improvement of the coarse-grained models.     

Functionalization of soft materials for cardiac repair and regeneration

Coronary artery disease is a leading cause of death in developed nations. As the disease progresses, myocardial infarction can occur leaving areas of dead tissue in the heart. To compensate, the body initiates its own repair/regenerative response in an attempt to restore function to the heart. These efforts serve as inspiration to researchers who attempt to capitalize on the natural regenerative processes to further augment repair. Thus far, researchers are exploiting these repair mechanisms in the functionalization of soft materials using a variety of growth factor-, ligand- and peptide-incorporating approaches. The goal of functionalizing soft materials is to best promote and direct the regenerative responses that are needed to restore the heart. This review summarizes the opportunities for the use of functionalized soft materials for cardiac repair and regeneration, and some of the different strategies being developed.     

GPU-based real-time soft tissue deformation with cutting and haptic feedback

This article describes a series of contributions in the field of real-time simulation of soft tissue biomechanics. These contributions address various requirements for interactive simulation of complex surgical procedures. In particular, this article presents results in the areas of soft tissue deformation, contact modelling, simulation of cutting, and haptic rendering, which are all relevant to a variety of medical interventions. The contributions described in this article share a common underlying model of deformation and rely on GPU implementations to significantly improve computation times. This consistency in the modelling technique and computational approach ensures coherent results as well as efficient, robust and flexible solutions.     

Single-particle tracking: Brownian dynamics of viscoelastic materials

A unifying theoretical framework for analyzing stochastic data from single-particle tracking (SPT) in viscoelastic materials is presented. A generalization of the bead-spring model for linear polymers is developed from a molecular point of view and from the standpoint of phenomenological linear viscoelasticity. The hydrodynamic interaction in the former is identified as the dashpots in the latter. In elementary terms, the intimate correspondence between time-correlation of the fluctuation measurements and transient relaxation kinetics after perturbation is discussed, and the central role of the fluctuation-dissipation relation is emphasized. The work presented here provides a bridge between the microscopic and the macroscopic views of linear viscoelastic biological materials, and is applicable to membrane protein diffusion, linear DNA chain dynamics, and mechanics of intracellular cytoskeletal networks.     

Computational modelling and optimisation of soft tissue outcome in cranio-maxillofacial surgery planning

Cranio-maxillofacial (CMF) surgery operations are associated with rearrangement of facial hard and soft tissues, leading to dramatic changes in facial geometry. Often, correction of the aesthetical patient's appearance is the primary objective of the surgical intervention. Due to the complexity of the facial anatomy and the biomechanical behaviour of soft tissues, the result of the surgical impact cannot always be predicted on the basis of surgeon's intuition and experience alone. Computational modelling of soft tissue outcome using individual tomographic data and consistent numerical simulation of soft tissue mechanics can provide valuable information for surgeons during the planning stage. In this article, we present a general framework for computer-assisted planning of CMF surgery interventions that is based on the reconstruction of patient's anatomy from 3D computer tomography images and finite element analysis of soft tissue deformations. Examples from our clinical case studies that deal with the solution of direct and inverse surgical problems (i.e. soft tissue prediction, inverse implant shape design) demonstrate that the developed approach provides a useful tool for accurate prediction and optimisation of aesthetic surgery outcome.     

Nonlinear machine learning in simulations of soft and biological materials

Abstract

Interpretable parameterisations of free energy landscapes for soft and biological materials calculated from molecular simulation require the availability of ‘good’ collective variables (CVs) capable of discriminating the metastable states of the system and the barriers between them. If these CVs are coincident with the slow collective modes governing the long-time dynamical evolution, then they also furnish good coordinates in which to perform enhanced sampling to surmount high free energy barriers and efficiently explore and recover the landscape. Non-linear manifold learning techniques provide a means to systematically extract such CVs from molecular simulation trajectories by identifying and extracting low-dimensional manifolds lying latent within the high-dimensional coordinate space. We survey recent advances in data-driven CV discovery and enhanced sampling using non-linear manifold learning, describe the mathematical and theoretical underpinnings of these techniques, and present illustrative examples to molecular folding and colloidal self-assembly. We close with our outlook and perspective on future advances in this rapidly evolving field.     

Investigating full-field deformation of planar soft tissue under simple-shear tests

Finite simple shear test characteristics like specimen geometry and boundary conditions could affect the deformation homogeneity during the test. In order to ensure that the parameters of constitutive equations obtained from finite simple shear tests are appropriate, the deformation homogeneity of the specimen during simple-shear test should be examined. The Fourier transform moiré method (FTM) was used to examine the deformation uniformity of a porcine skin specimen in a finite simple shear test. The effects of clamping prestrain (0.15 and 0.3 engineering strain) and specimen geometry (5x5, 5x3.75, and 5x2.5cm) were investigated. These effects include in-plane deformation altered by clamping prestrain, slippage between specimen and clamps, and out-of-plane deformation. The experimental results showed that the wide specimen had more severe deformation alteration by clamping prestrain and was easier to slip out of the clamps when the shear angle is large. Furthermore, in all test configurations, the out-of-plane deformation is significant when the shear angle is large, and a narrow specimen is prone to have out-of-plane deformation. This study may provide guidelines for the selection of specimen aspect ratio and clamping prestrain when studying the material response of soft tissues under simple-shear tests.     

Multiscale modelling and simulation of the deformation and adhesion of a single gecko seta

A 3D multiscale model is presented which describes the adhesion and deformation of a gecko seta. The multiscale approach combines three models at different length scales: at the top level, on the order of several micrometers, a nonlinear finite element beam model is chosen to capture the branched microstructure of the gecko seta. At the intermediate level, on the order of several nanometers, a second finite element model is used to capture the detailed behaviour of the seta tips, the so-called spatulae. At the lowest level, on the order of a few angstroms, a molecular interaction potential is used to describe the van der Waals adhesion forces between spatulae and substrate. Coarse-graining techiques are used to bridge the scale between the model levels. To illustrate and validate the proposed gecko seta model, numerical pull-off simulations are shown and compared to experimental data from the literature.     

Comparison of models for flow induced deformation of soft biological tissue

The behaviour of a deformable porous medium during the flow of fluid under a pressure difference is examined for both infinitesimal and finite deformations. Models for both cases are solved for the problem of steady one-dimensional compression and compared with experimental data from Parker et al. (J. appl. Mech. 54, 794-800, 1987) for a polyurethane sponge. The purpose of this study is to identify a simple model which agrees qualitatively with these published results. To relate the stress relations for biological tissues to the data for polymer sponges (Parker et al., 1987) a translation of 1.1 kPa was introduced. This allows for some structural differences between the two media. It was found that the infinitesimal models were adequate up to 20% strain, but significant divergence occurred for higher strains. A finite deformation model with the permeability depending exponentially on the strain gave the most consistent results and required the fitting of only two parameters.     

Surface facial modelling and allometry in relation to sexual dimorphism

Sexual dimorphism is responsible for a substantial part of human facial variability, the study of which is essential for many scientific fields ranging from evolution to special biomedical topics. Our aim was to analyse the relationship between size variability and shape facial variability of sexual traits in the young adult Central European population and to construct average surface models of adult males and females. The method of geometric morphometrics allowed not only the identification of dimorphic traits, but also the evaluation of static allometry and the visualisation of sexual facial differences.Facial variability in the studied sample was characterised by a strong relationship between facial size and shape of sexual dimorphic traits. Large size of face was associated with facial elongation and vice versa. Regarding shape sexual dimorphic traits, a wide, vaulted and high forehead in combination with a narrow and gracile lower face were typical for females. Variability in shape dimorphic traits was smaller in females compared to males. For female classification, shape sexual dimorphic traits are more important, while for males the stronger association is with face size.Males generally had a closer inter-orbital distance and a deeper position of the eyes in relation to the facial plane, a larger and wider straight nose and nostrils, and more massive lower face. Using pseudo-colour maps to provide a detailed schematic representation of the geometrical differences between the sexes, we attempted to clarify the reasons underlying the development of such differences.     

Engineering soft nanostructured functional materials via orthogonal chemistry

Nanostructured amphiphilic block copolymers, graft copolymers, polymeric thermally responsive molecular brushes and polymer stars are only few examples of macromolecular architectures accessible either via controlled/living radical polymerization (CLRP) techniques or the combination of CLRP mechanisms with efficient post-polymerization routes including click chemistry. Precise control over the composition, molecular weight and functionalities is a prerequisite for soft polymeric materials to self-organize into ordered morphologies. This contribution describes novel orthogonal chemical routes for the synthesis of macromolecular architectures and self-assembly of functional soft polymeric materials. Emerging potential applications of well-defined block and graft copolymers are outlined as well.