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. Additionally, a recently developed hierarchical hp-refinement scheme is used to locally refine the FCM meshes to resolve singularities and local solution features at the interfaces. Thereby, higher convergence rates are achievable for nonsmooth problems. A series of numerical experiments with 2- and 3-dimensional benchmark problems is presented, showing that the proposed hp-refinement scheme in conjunction with the weak enforcement of the interface conditions leads to a significant improvement of the convergence rates, even in the presence of singularities. Finally, the proposed technique is applied to simulate a vertebra-implant model. The application showcases the method's potential as an accurate simulation tool for biomechanical problems involving complex geometry, and it demonstrates its flexibility in dealing with different types of geometric description.

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 = 3.19 MPa) and ∼100 times tougher (WExt = ∼2000 kJ m-3) than its hydrogel counterpart.

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. However, these fiber-reinforced constructs underperformed under dynamic and prolonged loading conditions, suggesting that more targeted design approaches and material selection are required to fully exploit the potential of fibers as reinforcing agents for cartilage tissue engineering. In the present study, we emulated the proteoglycan matrix of articular cartilage by using highly negatively charged star-shaped poly(ethylene glycol)/heparin hydrogel (sPEG/Hep) as the soft matrix. These soft hydrogels combined with mPCL melt electrospun fibrous networks exhibited mechanical anisotropy, nonlinearity, viscoelasticity and morphology analogous to those of their native counterpart, and provided a suitable microenvironment for in vitro human chondrocyte culture and neocartilage formation. In addition, a numerical model using the p-version of the finite element method (p-FEM) was developed in order to gain further insights into the deformation mechanisms of the constructs in silico, as well as to predict compressive moduli. To our knowledge, this is the first study presenting cartilage tissue-engineered constructs that capture the overall transient, equilibrium and dynamic biomechanical properties of human articular cartilage.