On the monolithic and staggered solution of cell contractility and focal adhesion growth.

The mechanical response of cells to stimuli tightly couples biochemical and biomechanical processes, which describe fundamental properties such as cell growth and reorientation. Cells interact continuously with their external surroundings, the extracellular matrix (ECM), by establishing a bond between cell and ECM through the formation of focal adhesions. Focal adhesions are made up of integrins, which are mechanosensitive proteins and responsible for the communication between the cell and the ECM.

Multi-level hp-finite cell method for embedded interface problems with application in biomechanics.

This work presents a numerical discretization technique for solving 3-dimensional material interface problems involving complex geometry without conforming mesh generation. The finite cell method (FCM), which is a high-order fictitious domain approach, is used for the numerical approximation of the solution without a boundary-conforming mesh. Weak discontinuities at material interfaces are resolved by using separate FCM meshes for each material sub-domain and weakly enforcing the interface conditions between the different meshes.

Phase-field boundary conditions for the voxel finite cell method: Surface-free stress analysis of CT-based bone structures.

The voxel finite cell method uses unfitted finite element meshes and voxel quadrature rules to seamlessly transfer computed tomography data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field-based formulation for imposing traction and displacement constraints in a diffuse sense.

Uncertainty quantification for personalized analyses of human proximal femurs.

Computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads, which affect the simulation results. To quantify the influence we developed a probabilistic framework based on polynomial chaos (PC) that propagates stochastic input variables through any computational model. We considered a stochastic E-ρ relationship and a stochastic hip contact force, representing realistic variability of experimental data.

The finite cell method for bone simulations: verification and validation.

Standard methods for predicting bone's mechanical response from quantitative computer tomography (qCT) scans are mainly based on classical h-version finite element methods (FEMs). Due to the low-order polynomial approximation, the need for segmentation and the simplified approach to assign a constant material property to each element in h-FE models, these often compromise the accuracy and efficiency of h-FE solutions. Herein, a non-standard method, the finite cell method (FCM), is proposed for predicting the mechanical response of the human femur.