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.

An Integrated Design, Material, and Fabrication Platform for Engineering Biomechanically and Biologically Functional Soft Tissues.

We present a design rationale for stretchable soft network composites for engineering tissues that predominantly function under high tensile loads. The convergence of 3D-printed fibers selected from a design library and biodegradable interpenetrating polymer networks (IPNs) result in biomimetic tissue engineered constructs (bTECs) with fully tunable properties that can match specific tissue requirements. We present our technology platform using an exemplary soft network composite model that is characterized to be flexible, yet ∼125 times stronger (E = 3.

Biofabricated soft network composites for cartilage tissue engineering.

Articular cartilage from a material science point of view is a soft network composite that plays a critical role in load-bearing joints during dynamic loading. Its composite structure, consisting of a collagen fiber network and a hydrated proteoglycan matrix, gives rise to the complex mechanical properties of the tissue including viscoelasticity and stress relaxation. Melt electrospinning writing allows the design and fabrication of medical grade polycaprolactone (mPCL) fibrous networks for the reinforcement of soft hydrogel matrices for cartilage tissue engineering.

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.

Stochastic description of the peak hip contact force during walking free and going upstairs.

Uncertainty quantification for the response of a patient specific femur is mandatory when advocating finite element (FE) models in clinical applications. Reliable stochastic descriptions of physiological hip contact forces are an essential prerequisite for such an endeavor. We therefore analyze the in-vivo available data of seven individuals from HIP98 and OrthoLoad with the objective of characterizing the variability of the peak hip contact force magnitude and two corresponding spatial angles (in sagittal and frontal plane) during walking free and going upstairs.

Prediction of the mechanical response of the femur with uncertain elastic properties.

A mandatory requirement for any reliable prediction of the mechanical response of bones, based on quantitative computer tomography, is an accurate relationship between material properties (usually Young's modulus E) and bone density ρ. Many such E-ρ relationships are available based on different experiments on femur specimens with a large spread due to uncertainties. The first goal of this study is to pool and analyze the relevant available experimental data and develop a stochasticE-ρ relationship.

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.

Lattice Boltzmann simulations of binary fluid flow through porous media.

The lattice Boltzmann equation is often advocated as a simulation tool that is particularly effective for complex fluids such as multiphase and multicomponent flows through porous media. We construct a three-dimensional 19 velocity lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio based on the model proposed by Gunstensen. The model is tested for the following binary fluid flow problems: a stationary planar interface among two fluids; channel flow of immiscible binary fluids; the Laplace problem; and a rising bubble.