Numerical methods
The solution of both applied engineering problems and test cases for fundamental research require computational tools and methods in order to solve these problems, translated into sets of equations and algorithms. To run these numerical simulations, we use a wide range of computational methods, ranging from proprietary finite element software, and programs for numeric and symbolic computing, over a variety of open source software to custom scripts and programs based on our own code developments. Constitutive models developed or adapted for our groups' research are integrated in this software with special regard to robust and consistent formulations, e.g. [1-3].
Numerical simulations play a particular role in our research to address the "inverse problem" [4] posed by many of our applications. The solution of this problem is required e.g. when the objective of the experiment is the determination of a suitable constitutive or computational model that is representative of the tested tissue. While the experimental design and measured data deliver the input and output, one searches for the yet unknown model specification able to link the two. Conventional material testing (e.g. tensile, torsion and bending tests) aim at characterizing the mechanical response under simple and homogeneous deformation and stress states. In this way, the inverse problem is straightforward and constitutive model parameters can be determined directly from the experimental data or by use of simple analytical procedures. Our “unconventional” experiments investigate the response of soft biological tissue to large and non-homogeneous deformations related to multi-axial, multi-physical and time-dependent loads. Moreover, our “test pieces” are often non-homogeneous, and display non-linear time-dependent behavior described by complex constitutive equations. Therefore iterative computer simulations of the problem are required and the determined parameter sets need to be analyzed with regard to uniqueness. Our group has comprehensive experience in developing optimization routines and algorithms for the iterative determination of “best fit” model parameters [5-15], and with model validation through predictive simulations [14-19] in various fields of application.
The calibrated models can then be used for predictive simulations of the mechanical response of tissues, such as for simulation of surgery (planning or virtual reality based training, e.g. [20], for design and optimization of implants and devices [21,22], or for improvement of our experimental procedures through "virtual experiments", i.e. computer simulations of the laboratory tests [23-26]. Lately, we use calibrated computational models that resolve the tissue microstructure to unravel the complex microscale mechanisms responsible for the remarkable macroscopic characteristics of soft biological tissues and fiber networks, including their particular tension compression and volumetric behavior and outstanding defect tolerance [27-32].
[1] Helfenstein J. Continuum Mechanical Investigations of the Intervertebral Disc, ETH Diss. Nr. 19545 (2011).
[2] Marc Hollenstein M., Mechanics of the Human Liver: Experiments and Modeling”, ETH Diss. Nr. 19587 (2011).
[3] Helfenstein J., Jabareen M., Mazza E., Govindjee S. (2010) On non-physical response in models for fiber-reinforced hyperelastic materials, Int. J Solids Struct. 47, 2056-2061. DOI: 10.1016/j.ijsolstr.2010.04.00
[4] Weickenmeier J., Mazza E. (2019) Inverse methods. In G. Limbert (Ed.), Studies in mechanobiology, tissue engineering and biomaterials (SMTEB): Vol. 22. Skin biophysics. From experimental characterisation to advanced modelling, pp. 193-213. DOI: 10.1007/978-3-030-13279-8_6
[5] Valtorta D. Dynamic Torsion Test for the Mechanical Characterization of Soft Biological Tissue”, ETH Diss. Nr. 17028 (2007)
[6] Nava A. In vivo characterization of the mechanical response of soft human tissue, ETH Diss. Nr. 17060 (2007)
[7] Michael Wissler, „Modeling Dielectric Elastomer Actuators“, ETH Diss. Nr. 17142
[8] Arne Schmidt, „Modeling dielectric elastomers“, ETH Diss. Nr. 19873.
[9] Nava A., Mazza E., Kleinermann F., Avis N. J., McClure J. (2003) Determination of the Mechanical Properties of Soft Human Tissues through Aspiration Experiments, MICCAI 2003, Lect. Notes Comp. Sci. 2878, 222-229. DOI: 10.1007/978-3-540-39899-8_28
[10] Nava A., Mazza E., Häfner O., Bajka M. (2004) Experimental Observation and Modelling of Preconditioning in Soft Biological Tissues, MICCAI 2004, Lect. Notes Comp. Sci 3078, 1-8. DOI: 10.1007/978-3-540-25968-8_1
[11] Nava A., Mazza E., Kleinermann F., Avis N. J., McClure J., Bajka M. (2004) Evaluation of the Mechanical Properties of Human Liver and Kidney through Aspiration Experiments, Technol. Health Care, 12, 269-280.
[12] Valtorta D., Mazza E. (2005) Dynamic Measurements of Soft Tissue Viscoelastic Properties with a Torsional Resonator Device, Med. Image Anal. 481-490. DOI: 10.1007/978-3-540-30136-3_36
[13] Nava A., Mazza E., Furrer M., Villiger P., Reinhart W. H. (2008) In vivo mechanical characterization of human liver, Med. Image Anal., 12, 203-216. DOI: 10.1016/j.media.2007.10.001
[14] Schmidt A., Bergamini A., Kovacs G., Mazza E. (2011) Multiaxial Mechanical Characterization of Interpenetrating Polymer Network Reinforced Acrylic Elastomer, Exp. Mech. 51, 1421-1433. DOI: 10.1007/s11340-010-9462-z
[15] Sachs D., Wahlsten, A., Kozerke S., Restivo G., Mazza E. (2021) A biphasic multilayer computational model of human skin. Bioemch. Model. Mechanobiol. 20, 969-982. DOI: 10.1007/s10237-021-01424-w
[16] Hollenstein M., Nava A., Valtorta D., Snedeker J. G., Mazza E. (2006) Mechanical Characterization of the Liver Capsule and Parenchyma, ISBMS 2006, Lect. Notes Comp. Sci. 4072, 150-158. DOI: 10.1007/11790273_17
[17] Valtorta D., Mazza E. (2006) Measurement of Rheological Properties of Soft Biological Tissue with a Novel Torsional Resonator Device, Rheol. Acta 45, 677-692. DOI: 10.1007/s00397-005-0026-6
[18] Haller C., Buerzle W., Kivelio A., Perrini M., Brubacker C. E., Gubeli R. J., Mallik A. S., Weber W., Messersmith P. B., Mazza E., Ochsenbein-Koelble N., Zimmermann R., Ehrbar M. (2012) Mussel-mimetic tissue adhesive for fetal membrane repair: An ex vivo evaluation, Acta Biomater. 8, 4365-4370. DOI: 10.1016/j.actbio.2012.07.047
[19] Stracuzzi A., Dittmann J., Böl M., Ehret A.E. (2021). Visco- and poroelastic contributions of the zona pellucida to the mechanical response of oocytes. Biomech. Model. Mechanobiol. 20, 20, 751-765 DOI: 10.1007/s10237-020-01414-4
[20] Weiss S., Bajka M., Nava A., Mazza E., Niederer P., 2004, Finite Element Model for the Simulation of Hydrometra, Technology and Health Care, 12(3), 259-267. DOI: 10.3233/THC-2004-1230
[21] Mazza E., Ehret A.E. (2015) Mechanical biocompatibility of highly deformable biomedical materials. J. Mech. Behav. Biomed. Mater. 48, 100-124 (2015). DOI: 10.1016/j.jmbbm.2015.03.023
[22] M.M. Maurer, M. M., Röhrnbauer, B. Feola, A., Deprest, J., Mazza, E. Mechanical biocompatibility of prosthetic meshes: a comprehensive protocol for mechanical characterization. J Mech Behav Biomed Mater 40, 42-58 (2014). https://doi.org/10.1016/j.jmbbm.2014.08.005
[23] Helfenstein J., Hollenstein J., Mazza E. (2009) Investigation on the optimal specimen design for planar-biaxial materials testing of soft materials. 6th European Conference on Constitutive Models for Rubber 2009, pp.371-376, Boca Raton: CRC Press, September 7-10. DOI: 10.1201/NOE0415563277.ch60
[24] Badir S., Bajka M., Mazza E. (2013) A Novel Procedure for the Mechanical Characterization of the Uterine Cervix during Pregnancy, J. Mech. Behav. Biomed. Mater. 27, 143-153. DOI: 10.1016/j.jmbbm.2012.11.020
[25] Pensalfini M. Meneghello S., Lintas V., Bircher K. Ehret A.E. Mazza E. (2018) The suture retention test, revisited and revised. J. Mech. Behav Biomed. Mater. 77, 711-717. DOI: 10.1016/j.jmbbm.2017.08.021
[26] Bernardi L., Mazza E., Ehret A.E. (2018) The effect of clamping conditions on tearing energy estimation for highly stretchable materials. Eng. Frac. Mech. 188, 300-308. DOI: 10.1016/j.engfracmech.2017.08.035
[27] Bircher K., Zündel M., Pensalfini M., Ehret A.E., Mazza E. (2019) Tear resistance of soft collagenous tissues. Nat. Commun. 10, 792. DOI: 10.1038/s41467-019-08723-y
[28] Ehret, A. E., Bircher, K., Stracuzzi, A., Marina, V., Zündel, M., Mazza, E. (2017) Inverse poroelasticity as a fundamental mechanism in biomechanics and mechanobiology. Nat. Commun. 8, 1002. DOI: 10.1038/s41467-017-00801-3
[29] Kuravi R., Leichsenring K., Böl M., Ehret A.E. (2021) 3D finite element models from serial section histology of skeletal muscle tissue – The role of micro-architecture on mechanical behaviour. J. Mech. Behav. Biomed. Mater. 113, 104109 (2021). DOI: 10.1016/j.jmbbm.2020.104109
[30] Kuravi R., Leichsenring K., Trostorf R., Morales-Orcajo E., Böl M., Ehret A.E. (2021) Predicting muscle tissue response from calibrated component models and histology-based finite element models. J. Mech. Behav. Biomed. Mater. 117, 104375. DOI: 10.1016/j.jmbbm.2021.104375
[31] Domaschke S., Morel A., Fortunato G., Ehret A.E. (2019) Random auxetics from buckling fibre networks. Nat. Commun. 10, 4863. DOI: 10.1038/s41467-019-12757-7
[32] Domaschke S., Zündel M., Mazza E., Ehret A.E. (2019) A 3D computational model of electrospun networks and its application to inform a reduced modelling approach, Int. J. Solids Struct. 158, 76-89. DOI: 10.1016/j.ijsolstr.2018.08.030