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.

Determination of the Poisson's ratio of the cell: recovery properties of chondrocytes after release from complete micropipette aspiration.

Chondrocytes in articular cartilage are regularly subjected to compression and recovery due to dynamic loading of the joint. Previous studies have investigated the elastic and viscoelastic properties of chondrocytes using micropipette aspiration techniques, but in order to calculate cell properties, these studies have generally assumed that cells are incompressible with a Poisson's ratio of 0.5. The goal of this study was to measure the Poisson's ratio and recovery properties of the chondrocyte by combining theoretical modeling with experimental measures of complete cellular aspiration and release from a micropipette. Chondrocytes isolated from non-osteoarthritic and osteoarthritic cartilage were fully aspirated into a micropipette and allowed to reach mechanical equilibrium. Cells were then extruded from the micropipette and cell volume and morphology were measured throughout the experiment. This experimental procedure was simulated with finite element analysis, modeling the chondrocyte as either a compressible two-mode viscoelastic solid, or as a biphasic viscoelastic material. By fitting the experimental data to the theoretically predicted cell response, the Poisson's ratio and the viscoelastic recovery properties of the cell were determined. The Poisson's ratio of chondrocytes was found to be 0.38 for non-osteoarthritic cartilage and 0.36 for osteoarthritic chondrocytes (no significant difference). Osteoarthritic chondrocytes showed an increased recovery time following full aspiration. In contrast to previous assumptions, these findings suggest that chondrocytes are compressible, consistent with previous studies showing cell volume changes with compression of the extracellular matrix.

Finite element modeling predictions of region-specific cell-matrix mechanics in the meniscus.

The knee meniscus exhibits significant spatial variations in biochemical composition and cell morphology that reflect distinct phenotypes of cells located in the radial inner and outer regions. Associated with these cell phenotypes is a spatially heterogeneous microstructure and mechanical environment with the innermost regions experiencing higher fluid pressures and lower tensile strains than the outer regions. It is presently unknown, however, how meniscus tissue mechanics correlate with the local micromechanical environment of cells. In this study, theoretical models were developed to study mechanics of inner and outer meniscus cells with varying geometries. The results for an applied biaxial strain predict significant regional differences in the cellular mechanical environment with evidence of tensile strains along the collagen fiber direction of approximately 0.07 for the rounded inner cells, as compared to levels of 0.02-0.04 for the elongated outer meniscus cells. The results demonstrate an important mechanical role of extracellular matrix anisotropy and cell morphology in regulating the region-specific micromechanics of meniscus cells, that may further play a role in modulating cellular responses to mechanical stimuli.

Large deformation finite element analysis of micropipette aspiration to determine the mechanical properties of the chondrocyte.

Chondrocytes, the cells in articular cartilage, exhibit solid-like viscoelastic behavior in response to mechanical stress. In modeling the creep response of these cells during micropipette aspiration, previous studies have attributed the viscoelastic behavior of chondrocytes to either intrinsic viscoelasticity of the cytoplasm or to biphasic effects arising from fluid-solid interactions within the cell. However, the mechanisms responsible for the viscoelastic behavior of chondrocytes are not fully understood and may involve one or both of these phenomena. In this study, the micropipette aspiration experiment was modeled using a large strain finite element simulation that incorporated contact boundary conditions. The cell was modeled using finite strain incompressible and compressible elastic models, a two-mode compressible viscoelastic model, or a biphasic elastic or viscoelastic model. Comparison of the model to the experimentally measured response of chondrocytes to a step increase in aspiration pressure showed that a two-mode compressible viscoelastic formulation accurately captured the creep response of chondrocytes during micropipette aspiration. Similarly, a biphasic two-mode viscoelastic analysis could predict all aspects of the cell's creep response to a step aspiration. In contrast, a biphasic elastic formulation was not capable of predicting the complete creep response, suggesting that the creep response of the chondrocytes under micropipette aspiration is predominantly due to intrinsic viscoelastic phenomena and is not due to the biphasic behavior.

The micromechanical environment of intervertebral disc cells determined by a finite deformation, anisotropic, and biphasic finite element model.

Cellular response to mechanical loading varies between the anatomic zones of the intervertebral disc. This difference may be related to differences in the structure and mechanics of both cells and extracellular matrix, which are expected to cause differences in the physical stimuli (such as pressure, stress, and strain) in the cellular micromechanical environment. In this study, a finite element model was developed that was capable of describing the cell micromechanical environment in the intervertebral disc. The model was capable of describing a number of important mechanical phenomena: flow-dependent viscoelasticity using the biphasic theory for soft tissues; finite deformation effects using a hyperelastic constitutive law for the solid phase; and material anisotropy by including a fiber-reinforced continuum law in the hyperelastic strain energy function. To construct accurate finite element meshes, the in situ geometry of IVD cells were measured experimentally using laser scanning confocal microscopy and three-dimensional reconstruction techniques. The model predicted that the cellular micromechanical environment varies dramatically between the anatomic zones, with larger cellular strains predicted in the anisotropic anulus fibrosus and transition zone compared to the isotropic nucleus pulposus. These results suggest that deformation related stimuli may dominate for anulus fibrosus and transition zone cells, while hydrostatic pressurization may dominate in the nucleus pulposus. Furthermore, the model predicted that micromechanical environment is strongly influenced by cell geometry, suggesting that the geometry of IVD cells in situ may be an adaptation to reduce cellular strains during tissue loading.