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Trabecular bone fracture is a traumatic and localized event studied worldwide in order to predict it. During the years, researchers focused over the mechanical characterization of the trabecular tissue to understand its mechanics. Several studies pointed out the very local nature of the trabecular failure, finally identifying the fracture zone with the aim to study it separately. The complexity of the three-dimensional trabecular framework and the local nature of the fracture event do not allow the direct evaluation of a single trabecula's behavior within its natural environment. For this reason, micro-Finite Element Modeling has been seen as the best way to investigate this biomechanical issue. Mechanical strain analysis is adopted in the literature for the identification of micro fracture using criteria based on principal strains. However, it was never verified if the fracture zone is actually the zone where principal strains are concentrated. Here, we show how the maximum strain of the tissue might not be directly correlated to the fracture. In the present work, a previously validated technique was used to identify the fracture zone of 10 trabecular specimen mechanically tested in compression and scanned in micro-CT before and after the mechanical test. Before-compression datasets were used to develop 10 micro-FE models were the same boundary conditions of the mechanical test were reproduced. Our results show how the known linear behavior of the trabecular framework might not be directly related to the development of the fracture suggesting other non-linear phenomenon, like buckling or microdamage, as actual cause of the traumatic event. This result might have several implications both in micro-modeling and in clinical applications for the study of fracture related pathology, like osteoporosis. ; The micro-CT datasets were produced by Laboratorio di Tecnologia Medica, Istituto Ortopedico Rizzoli, Bologna, Italy, with the financial support of the EU project LHDL (IST-2004-026932). This work was partially supported by the Spanish Government (project number RYC—2015-18888) and by Chair QUAES-UPF Computational Technologies for Healthcare.

Computational modeling has become a powerful tool in biomedical engineering thanks to its potential to simulate coupled systems. However, real parameters are usually not accurately known, and variability is inherent in living organisms. To cope with this, probabilistic tools, statistical analysis and stochastic approaches have been used. This article aims to review the analysis of uncertainty and variability in the context of finite element modeling in biomedical engineering. Characterization techniques and propagation methods are presented, as well as examples of their applications in biomedical finite element simulations. Uncertainty propagation methods, both non-intrusive and intrusive, are described. Finally, pros and cons of the different approaches and their use in the scientific community are presented. This leads us to identify future directions for research and methodological development of uncertainty modeling in biomedical engineering. ; This work is partly supported by the Spanish Ministry of Economy and Competitiveness under the Maria de Maeztu Units of Excellence Programme (MDM-2015-0502) and by the European Union Seventh Frame Programme (FP7/2007-2013), Grant agreement 304857, HEAR-EU project.

Cardiac modeling has recently emerged as a promising tool to study pathophysiology mechanisms and to predict treatment outcomes for personalized clinical decision support. Nevertheless, achieving convergence under large deformation and defining a robust meshing for realistic heart geometries remain challenging, especially when maintaining the computational cost reasonable. Smoothed particle hydrodynamics (SPH) appears to be a promising alternative to the finite element method (FEM) since it removes the burden of mesh generation. A point cloud is used where each point (particle) contains all the physical properties that are updated throughout the simulation. SPH was evaluated for solid mechanics applications in the last decade but its capacity to address the challenge of simulating the mechanics of the heart has never been evaluated. In this paper, a total Lagrangian formulation of a corrected SPH was used to solve three solid mechanics problems designed to test important features that a cardiac mechanics solver should have. SPH results, in terms of ventricle displacements and strains, were compared to results obtained with 11 different FEM-based solvers, by using synthetic cardiac data from a benchmark study. In particular, passive dilation and active contraction were simulated in an ellipsoidal left ventricle with the exponential anisotropic constitutive law of Guccione following the direction of fibers. The proposed meshless method is able to reproduce the results of three benchmark problems for cardiac mechanics. Hyperelastic material with fiber orientation and high Poisson ratio allows wall thickening/thinning when large deformation is present. ; The work is supported by the European Union Horizon 2020 research and innovation programme under grant agreement No 642676 (CardioFunXion).

Intervertebral disc (IVD) degeneration is a major risk factor of low back pain. It is defined by a progressive loss of the IVD structure and functionality, leading to severe impairments with restricted treatment options due to the highly demanding mechanical exposure of the IVD. Degenerative changes in the IVD usually increase with age but at an accelerated rate in some individuals. To understand the initiation and progression of this disease, it is crucial to identify key top-down and bottom-up regulations' processes, across the cell, tissue, and organ levels, in health and disease. Owing to unremitting investigation of experimental research, the comprehension of detailed cell signaling pathways and their effect on matrix turnover significantly rose. Likewise, in silico research substantially contributed to a holistic understanding of spatiotemporal effects and complex, multifactorial interactions within the IVD. Together with important achievements in the research of biomaterials, manifold promising approaches for regenerative treatment options were presented over the last years. This review provides an integrative analysis of the current knowledge about (1) the multiscale function and regulation of the IVD in health and disease, (2) the possible regenerative strategies, and (3) the in silico models that shall eventually support the development of advanced therapies ; M.N. acknowledges financial support from the German Research Foundation (DFG) via the scholarship "Forschungsstipendium" (PN: 387071423). L.G.A. acknowledges funding through the Operational Program Competitiveness, Entrepreneurship and Innovation, under the call RESEARCH–CREATE–INNOVATE co-financed by the European Union and Greek national funds (Project Code: T1EDK-02829). K.W. acknowledges funding from the Swiss National Science Foundation (SNF PP00P2_163678/1). L.B., C.R.W., M.A.G.B., and J.N. acknowledge financial support from the Spanish Ministry of Science and Innovation (HOLOA-DPI2016-80283-C2-1-R, RYC-2015-18888). L.B., C.L.M., C.R.W., L.G.A., M.A.G.B., and J.N. further acknowledge financial support from the European Commission (Disc4All-H2020-MSCA-ITN-ETN-2020 GA: 955735).