Conference Agenda

Bones have the ability to adapt their structure and thus their density to external loads. Cancellous bone, which forms the spongy interior of bones, is a microstructural network of rods. Under- or overloading strengthens or narrows these rods, altering the microstructural pattern. In this adaption process, osteocytes act as mechanosensors, activated by mechanical signals and regulating the mechanical adaptation of bone. That is, they communicate with bone-forming or bone-resorbing cells. Thus, bone remodelling at a particular point is triggered by non-local mechanosensors in its vicinity, i.e. the sensors involved act in a specific sphere of influence and not only locally.

In this work, we present a micromorphic approach that extends the established concept of local bone adaption to account for both the non-locality of bone remodelling and the heterogeneous structure of the material without explicitly resolving it within a two-scale approach. Our approach enables a simple implementation in the open source finite element environment deal.II and avoids the need for laborious neighborhood sampling, as is the case with integral approaches, or for higher continuity requirements, as is the case with higher gradient approaches.

Our approach is phenomenological in nature and refers to nominal bone density to be interpreted as a macroscopic measure of the ratio of bone mass to pore volume in the underlying trabecular microstructure. This way, we account for the heterogeneous microstructure of bone by capturing its effect on nominal bone density, but without actually resolving individual trabeculae. Since bone is a living material, in the continuum approach to bone remodelling we apply the theory of open-system thermodynamics, which assumes that there is a mass source corresponding to the change in nominal density over time. The mass source is equated with a mechanical stimulus, comparing the stored energy to an attractor. The attractor can be interpreted as a biological stimulus that drives remodelling. In the local case, the stored energy is a purely local quantity that depends on the macroscopic deformation. In our novel non-local approach, we now extend this by adding a micromorphic and a scale-bridging component to the stored energy. This allows us to account for non-locality with a characteristic length scale, which acts as a measure for the heterogeneous microstructure and a scale-bridging parameter that penalizes the deviation of the micromorphic from a higher gradient model.

The approach is illustrated in depth and its implications are discussed using benchmark examples. In addition, the modeling approach is discussed using long tubular bones and compared with CT images in health and osteoporosis.

Gastric peristalsis refers to the coordinated contraction and relaxation of the muscles in the stomach wall that mixes and grinds food and propels chyme down the digestive tract. Gastric peristalsis is realized by an intricate electromechanical system. We present a computational multiphysics framework for its simulation on patient-specific stomach geometries. It combines a robust gastric electrophysiology model with an active-strain finite elasticity model for the tissue mechanics [1,2,3]. The patient-specific spatially varying parameter distributions are determined by a novel algorithm mapping a two-dimensional parameter distribution function onto a general tube-like surface. The capability of the proposed computational framework for large-scale in silico analyses of gastric electromechanics is demonstrated on patient-specific human stomach models derived from magnetic resonance images. The proposed framework can reproduce essential phenomena on patient-specific stomach geometries, including the entrainment and propagation of stable ICC slow waves as well as the propagation of physiological ring-shaped peristaltic contraction waves. In summary, the presented framework provides a powerful tool to study gastric electromechanics in health and disease. This can enable optimized patient-specific diagnosis and therapy planning.

References

[1] Brandstaeter, S., et al., Computational model of gastric motility with active-strain electromechanics. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2018.

[2] Djabella, K., M. Landau, and M. Sorine, A two-variable model of cardiac action potential with controlled pacemaker activity and ionic current interpretation, in 2007 46th IEEE Conference on Decision and Control. 2007, Institute of Electrical & Electronics Engineers (IEEE). p. 5186 - 5191.

[3] Ruiz-Baier, R., et al., Mathematical modelling of active contraction in isolated cardiomyocytes. Mathematical Medicine and Biology, 2014. 31: p. 259-283.

Human brain tissue shows complex, nonlinear, and time dependent mechanical behavior, and thus presents a significant challenge to those interested in developing accurate constitutive models. Research in our group is focused on better understanding the factors that influence the mechanical response of the tissue. To this end, we combine the mechanical testing of tissue samples from different brain regions under finite deformation in compression, tension and shear with microstructural analyses, continuum mechanics modeling, and finite element simulations. The application of an inverse parameter identification allows us to determine material parameters with a subsequent statistical analysis revealing their regional dependence. Here, we find that the corpus callosum and corona radiata in particular have to be considered as regions with distinct mechanical properties when modeling the whole brain. Furthermore, we analyze the protein content of the tested specimens by enzyme-linked immunosorbent assays and show their correlation with the identified material parameters. These results may motivate and guide the development of microstructurally informed constitutive models that may enable patient-specific predictions.

Traumatic brain injury (TBI) brought on by a severe head impact in a car accident, a fall, or a sports injury results in internal tissue damage beyond recovery. The human brain mainly has two vital tissues; gray matter and white matter. During accidental impact, forces and torques are imparted in the brain tissues to trigger significant local damage. Although the brain can recover from a TBI, the force necessary to cause permanent brain damage is still not fully understood. One aspect of investigating TBI is to provide a mathematical model and a computational framework to identify the level of injury. Mechanical characterization of the brain tissue is essential to understand brain damage caused by TBI. Since 1960, many studies have been done to understand the brain’s mechanical behavior. It is found that brain tissue’s behavior is an incompressible, viscoelastic material and anisotropic material. The human brain’s finite element (FE) models have been utilized to investigate the risk and mechanisms of traumatic brain injuries. Many human brain FE models have been developed. Many different constitutive models have been used for different parts of the human head. Still, there is scope for improvement in constitutive modeling and its finite element implementation. In this work, we present an anisotropic viscoelastic constitutive model and essential equations for finite element simulations. We implemented the constitutive model by ABAQUS UMAT for doing finite element simulations of the human head FE-model for real-life loading cases. Our uniaxial and cyclic loading simulation using UMAT agree with experimental and MATLAB results.