This is the 11th Summer School on Biomechanics in the series we have organized since 2001. Its aim is to provide a state-of-the-art overview of physics-informed modeling, simulation and experiments on the cardiovascular system, the stomach and brain tissues.
The lectures will cover the key ingredients of continuum mechanics, focusing on nonlinear elasticity. Details of the mechanical and structural modeling of fiber-reinforced soft materials, and characterization of their properties will be explained along with an analysis of the influence of residual stresses and the cross-linking of collagen fibers. In addition, aortic dissection and related in silico models with fluid-structure interactions will be analysed. Machine learning and physics-based computational modeling for solving real-world mathematical problems will be discussed, including simulating cardiac function in both normal and diseased states. Benchmark tests based on the finite element method will be discussed with examples taken from collaborations with cardiologists.
There will also be a discussion of viscoelastic tissues and their modeling, in particular application of fractional viscoelasticity to models of the heart and arteries. A study is presented on the different effects between muscular and elastic arteries during aging. With a focus on biomechanics, machine learning and data-driven modeling are discussed. Attention is devoted to constitutive artificial neural networks. Homogenized constrained mixture theory with restricted mixing is provided. The biomechanics of stomach and brain tissues will also be analyzed. Experimental techniques for the determination of the mechanical properties of tissues, cells, cellular components, and proteins will be described. The area of parameter identification is covered by using full-field optical measurements with the virtual fields method in elasticity.
Future directions for research in physics-informed biomechanics and mechanobiology will be identified during the lectures. This offers significant challenges for the advancement of knowledge of mechanical, biological, electrical effects and fluid-structure interactions.
Audience
The Summer School is addressed to PhD students and postdoctoral researchers in biomedical engineering, biophysics, mechanical and civil engineering, applied mathematics and mechanics, materials science and physiology and more senior scientists and engineers (including some from relevant industries) whose interests are in the area of biomechanics and mechanobiology of soft biological tissues.
Preliminary Suggested Readings
S Avril. Hyperelasticity of soft tissues and related inverse problems, in: S Avril, S Evans, eds., Material Parameter Identification and Inverse Problems in Soft Tissue Biomechanics, CISM Courses and Lectures No. 573, International Centre for Mechanical Sciences, Springer, 2017, pp. 37-66 [link]
S Budday, TC Ovaert, GA Holzapfel, P Steinmann and E Kuhl. Fifty shades of brain. A review on the mechanical testing and modeling of brain tissue. Arch Comput Methods Eng, 27:1187–1230, 2020. [link]
R CJ Cyron, RC Aydin and JD Humphrey. A homogenized constrained mixture (and mechanical analog) model for growth and remodeling of soft tissue. Biomech Model Mechanobiol, 15:1389-1403, 2016. [link]
M Fedele, R Piersanti, F Regazzoni, M Salvador, PC Africa, M Bucelli, A Zingaro, L Dede and A Quarteroni. A comprehensive and biophysically detailed computational model of the whole human heart electromechanics. Comput Methods Appl Mech Engrg, 410:115983, 2023. [link]
GA Holzapfel, JA Niestrawska, RW Ogden, AJ Reinisch and AJ Schriefl. Modelling non-symmetric collagen fibre dispersion in arterial walls . J R Soc Interface, 12:20150188, 2015. [link]
GA Holzapfel, RW Ogden. An arterial constitutive model accounting for collagen content and cross-linking. J Mech Phys Solids, 136:103682, 2020. [link]
GA Holzapfel, RW Ogden. On fiber dispersion models: exclusion of compressed fibers and spurious model comparisons. J Elasticity, 129:49–68, 2017. [link]
GA Holzapfel, RW Ogden. On planar biaxial tests for anisotropic nonlinearly elastic solids. A continuum mechanical framework. Math. Mech. Solids, 14:474-489, 2009. [pdf]
B Lane, S Sherifova, VA Santamaría, J Molimard, GA Holzapfel and S Avril. Novel experimental methods to characterize the mechanical properties of the aorta, in: "Biomechanics of the Aorta", Academic Press, 2024, pp. 91-108 [link]
K Linka, M Hillgärtner, KP Abdolazizi, RC Aydin, M Itskov and CJ Cyron. Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. J Comput Phys, 429, 110010, 2021. [link]
R Miller, E Kerfoot, C Mauger, TF Ismail, AA Young, DA Nordsletten. An implementation of patient-specific biventricular mechanics simulations with a deep learning and computational pipeline. Front Physiol, 1398, 2021. [link]
SJ Mousavi, S Farzaneh, S Avril. Patient-specific predictions of aneurysm growth and remodeling in the ascending thoracic aorta using the homogenized constrained mixture model. Biomech Model Mechanobiol, 18:1895-1913, 2019. [link]
D Nordsletten, A Capilnasiu, W Zhang, A Wittgenstein, M Hadjicharalambous, G Sommer, R Sinkus, GA Holzapfel. A viscoelastic model for human myocardium. Acta Biomater, 135:441-457, 2021. [link]
RW Ogden. Nonlinear continuum mechanics and modelling the elasticity of soft biological tissues with a focus on artery walls, in GA Holzapfel, RW Ogden, eds., Biomechanics: Trends in Modeling and Simulation, Springer, 2016, pp. 83- 156. [pdf]
A Quarteroni, L Dede, A Manzoni and C Vergara. Mathematical Modelling of the Human Cardiovascular System. Data, Numerical Approximation, Clinical Applications. Cambridge University Press, 2019. [link]
M Rolf-Pissarczyk, R Schussnig, T-P Fries, D Fleischmann, JA Elefteriades, JD Humphrey and GA Holzapfel. Mechanisms of aortic dissection: from pathological changes to experimental and in silico models. Prog Mater Sci, in press. [pdf]
A Wineman. Nonlinear viscoelastic solids—a review. Math Mech Solids, 14:300-366, 2009. [pdf]
A W Zhang, M Jadidi, SA Razian, GA Holzapfel, A Kamenskiy and DA Nordsletten. A viscoelastic constitutive framework for aging muscular and elastic arteries. Acta Biomater, in press. [pdf]