[en] This paper investigates the complex time-dependent behavior of cortex tissue, under adiabatic condition, using a two-phase flow poroelastic model. Motivated by experiments and Biot's consolidation theory, we tackle time-dependent uniaxial loading, confined and unconfined, with various geometries and loading rates from 1 micrometer/sec to 100 micrometer/sec. The cortex tissue is modeled as the porous solid saturated by two immiscible fluids, with dynamic viscosities separated by four orders, resulting in two different characteristic times. These are respectively associated to interstitial fluid and glial cells. The partial differential equations system is discretised in space by the finite element method and in time by Euler-implicit scheme. The solution is computed using a monolithic scheme within the open-source computational framework FEniCS. The parameters calibration is based on Sobol sensitivity analysis, which divides them into two groups: the tissue specific group, whose parameters represent general properties, and sample specific group, whose parameters have greater variations. Our results show that the experimental curves can be reproduced without the need to resort to viscous solid effects, by adding an additional fluid phase. Through this process, we aim to present multiphase poromechanics as a promising way to a unified brain tissue modeling framework in a variety of settings.
Disciplines :
Materials science & engineering
Author, co-author :
Urcun, Stephane ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
Rohan, PIerre-Yves; Arts et Metiers Institute of Technology > IHBGC
Sciumè, Giuseppe; Unversity of Bordeaux, FR > I2M Bordeaux
Bordas, Stéphane ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
External co-authors :
yes
Language :
English
Title :
Cortex tissue relaxation and slow to medium load rates dependency can be captured by a two-phase flow poroelastic model
Publication date :
30 November 2021
Journal title :
Journal of the Mechanical Behavior of Biomedical Materials
Azevedo, Frederico A.C., Carvalho, Ludmila R.B., Grinberg, Lea T., Farfel, José Marcelo, Ferretti, Renata E.L., Leite, Renata E.P., Filho, Wilson Jacob, Lent, Roberto, Herculano-Houzel, Suzana, Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain. J. Comp. Neurol. 513:5 (2009), 532–541.
Barnes, Matthew J., Przybyla, Laralynne, Weaver, Valerie M., Ewald, Andrew, Tissue mechanics regulate brain development, homeostasis and disease. J. Cell Sci. 130:1 (2017), 71–82.
Basilio, Andrew V., Xu, Peng, Takahashi, Yukou, Yanaoka, Toshiyuki, Sugaya, Hisaki, Ateshian, Gerard A., Morrison III, Barclay, Simulating cerebral edema and delayed fatality after traumatic brain injury using triphasic swelling biomechanics. Traffic Inj. Prev. 20:8 (2019), 820–825, 10.1080/15389588.2019.1663347.
Bender, Benjamin, Klose, Uwe, Cerebrospinal fluid and interstitial fluid volume measurements in the human brain at 3T with EPI. Magn. Reson. Med. 61:4 (2009), 834–841.
Biot, Maurice A., General theory of three-dimensional consolidation. J. Appl. Phys. 12:2 (1941), 155–164.
Budday, Silvia, Nay, Richard, de Rooij, Rijk, Steinmann, Paul, Wyrobek, Thomas, Ovaert, Timothy C., Kuhl, Ellen, Mechanical properties of gray and white matter brain tissue by indentation. J. Mech. Behav. Biomed. Mater. 46 (2015), 318–330.
Budday, Silvia, Ovaert, Timothy C., Holzapfel, Gerhard A., Steinmann, Paul, Kuhl, Ellen, Fifty shades of brain: A review on the mechanical testing and modeling of brain tissue. Arch. Comput. Methods Eng. 14 (2019), 931–965.
Budday, Silvia, Raybaud, Charles, Kuhl, Ellen, A mechanical model predicts morphological abnormalities in the developing human brain. Sci. Rep., 4(1), 2014, 5644.
Budday, Silvia, Raybaud, Charles, Kuhl, Ellen, A mechanical model predicts morphological abnormalities in the developing human brain. Sci. Rep. 4 (2014), 266–273.
Budday, S., Sommer, G., Holzapfel, G.A., Steinmann, P., Kuhl, E., Viscoelastic parameter identification of human brain tissue. J. Mech. Behav. Biomed. Mater. 74 (2017), 463–476.
Budday, S., Sommer, G., Paulsen, F., Holzapfel, G.A., Steinmann, P., Kuhl, E., Region- and loading-specific finite viscoelasticity of human brain tissue. PAMM, 18(1), 2018, e201800169.
Bui, Huu Phuoc, Tomar, Satyendra, Courtecuisse, Hadrien, Audette, Michel, Cotin, Stéphane, Bordas, Stéphane P.A., Controlling the error on target motion through real-time mesh adaptation: Applications to deep brain stimulation. Int. J. Numer. Methods Biomed. Eng., 34(5), 2018, e2958 e2958 cnm.2958.
Bui, Huu Phuoc, Tomar, Satyendra, Courtecuisse, Hadrien, Cotin, Stéphane., Bordas, Stéphane P.A., Real-time error control for surgical simulation. IEEE Trans. Biomed. Eng. 65:3 (2018), 596–607.
Castellano Smith, Andrew D., Crum, William R., Hill, Derek L.G., Thacker, Neil A., Bromiley, Paul A., Biomechanical simulation of atrophy in MR images. Milan, Sonka, Fitzpatrick, J. Michael, (eds.) Medical Imaging 2003: Image Processing, vol. 5032, 2003, International Society for Optics and Photonics, SPIE, 481–490.
Chatelin, S., Constantinesco, André, Willinger, Rémy, Fifty years of brain tissue mechanical testing: From in vitro to in vivo investigations. Biorheology 47:5–6 (2010), 255–276.
Cheng, Shaokoon, Bilston, Lynne E., Unconfined compression of white matter. J. Biomech. 40:1 (2007), 117–124.
Comellas, Ester, Budday, Silvia, Pelteret, Jean-Paul, Holzapfel, Gerhard A., Steinmann, Paul, Modeling the porous and viscous responses of human brain tissue behavior. Comput. Methods Appl. Mech. Engrg., 369, 2020, 113128.
Dutta-Roy, Tonmoy, Wittek, Adam, Miller, Karol, Biomechanical modelling of normal pressure hydrocephalus. J. Biomech. 41:10 (2008), 2263–2271.
Ehlers, Wolfgang, Wagner, Arndt, Multi-component modelling of human brain tissue: A contribution to the constitutive and computational description of deformation, flow and diffusion processes with application to the invasive drug-delivery problem. Comput. Methods Biomech. Biomed. Eng. 18:8 (2015), 861–879 PMID: 24261340.
Ehlers, Wolfgang, Wagner, Arndt, Multi-component modelling of human brain tissue: A contribution to the constitutive and computational description of deformation, flow and diffusion processes with application to the invasive drug-delivery problem. Comput. Methods Biomech. Biomed. Eng. 18:8 (2015), 861–879 PMID: 24261340.
Fletcher, Tim L., Kolias, Angelos G., Hutchinson, Peter J.A., Sutcliffe, Michael P.F., Development of a finite element model of decompressive craniectomy. PLoS One 9:7 (2014), 1–9.
Forero Rueda, M.A., Cui, L., Gilchrist, M.D., Finite element modelling of equestrian helmet impacts exposes the need to address rotational kinematics in future helmet designs. Comput. Methods Biomech. Biomed. Eng. 14:12 (2011), 1021–1031, 10.1080/10255842.2010.504922.
Forte, Antonio E., Gentleman, Stephen M., Dini, Daniele, On the characterization of the heterogeneous mechanical response of human brain tissue. Biomech. Model. Mechanobiol. 16 (2017), 907–920.
Franceschini, G., Bigoni, D., Regitnig, P., Holzapfel, G.A., Brain tissue deforms similarly to filled elastomers and follows consolidation theory. J. Mech. Phys. Solids 54:12 (2006), 2592–2620.
van Genuchten, M.Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Am. J. 44:5 (1980), 892–898.
Gerard, Pierre, Léonard, Angélique, Masekanya, Jean-Pierre, Charlier, Robert, Collin, Frédéric, Study of the soil–atmosphere moisture exchanges through convective drying tests in non-isothermal conditions. Int. J. Numer. Anal. Methods Geomech. 34:12 (2010), 1297–1320.
Gray, William G., Miller, Cass T., Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems. 2014, Springer.
Hakim, S, Venegas, JG, Burton, JD, The physics of the cranial cavity, hydrocephalus and normal pressure hydrocephalus: mechanical interpretation and mathematical model. Surgical Neurol. 0090-3019, 5(3), 1976, 187210.
Haslach, Henry W., Leahy, Lauren N., Riley, Peter, Gullapalli, Rao, Xu, Su, Hsieh, Adam H., Solid–extracellular fluid interaction and damage in the mechanical response of rat brain tissue under confined compression. J. Mech. Behav. Biomed. Mater. 29 (2014), 138–150.
Hosseini-Farid, Mohammad, Ramzanpour, Mohammadreza, McLean, Jayse, Ziejewski, Mariusz, Karami, Ghodrat, A poro-hyper-viscoelastic rate-dependent constitutive modeling for the analysis of brain tissues. J. Mech. Behav. Biomed. Mater., 102, 2020, 103475.
Jamal, Asad, Mongelli, Maria Teresa, Vidotto, Marco, Madekurozwa, Michael, Bernardini, Andrea, Overby, Darryl R., De Momi, Elena, y Baena, Ferdinando Rodriguez, Sherwood, Joseph M., Dini, Daniele, Infusion mechanisms in brain white matter and their dependence on microstructure: An experimental study of hydraulic permeability. IEEE Trans. Biomed. Eng. 68:4 (2021), 1229–1237.
Kaster, T., Sack, I., Samani, A., Measurement of the hyperelastic properties of ex vivo brain tissue slices. J. Biomech. 44:6 (2011), 1158–1163.
Lang, Georgina E., Stewart, Peter S., Vella, Dominic, Waters, Sarah L., Goriely, Alain, Is the donnan effect sufficient to explain swelling in brain tissue slices?. J. R. Soc. Interface, 11(96), 2014, 20140123.
Lefever, Joel A., García, José Jaime, Smith, Joshua H., A patient-specific, finite element model for noncommunicating hydrocephalus capable of large deformation. J. Biomech. 46:8 (2013), 1447–1453.
Lei, Yiming, Han, Hongbin, Yuan, Fan, Javeed, Aqeel, Zhao, Yong, The brain interstitial system: Anatomy, modeling, in vivo measurement, and applications. Prog. Neurobiol. 157 (2017), 230–246 New Perspectives on Healthy Aging.
Li, Xiaogai, von Holst, Hans, Kleiven, Svein, Influences of brain tissue poroelastic constants on intracranial pressure (ICP) during constant-rate infusion. Comput. Methods Biomech. Biomed. Eng. 16:12 (2013), 1330–1343 PMID: 22452461.
MacManus, David B., Pierrat, Baptiste, Murphy, Jeremiah G., Gilchrist, Michael D., A viscoelastic analysis of the p56 mouse brain under large-deformation dynamic indentation. Acta Biomater. 48 (2017), 309–318.
Mascheroni, Pietro, Stigliano, Cinzia, Carfagna, Melania, Boso, Daniela P., Preziosi, Luigi, Decuzzi, Paolo, Schrefler, Bernhard A., Predicting the growth of glioblastoma multiforme spheroids using a multiphase porous media model. Biomech. Model. Mechanobiol. 15:1 (2016), 1215–1228.
Meroi, E.A., Schrefler, B.A., Large Strain Static and Dynamic Hydro-Mechanical Analysis of Porous Media. 1995, Springer Vienna, Vienna, 397–447.
Morin, Fanny, Chabanas, Matthieu, Courtecuisse, Hadrien, Payan, Yohan, Biomechanical Modeling of Brain Soft Tissues for Medical Applications. 2017, Academic Press.
Nagashima, Tatsuya, Tamaki, Norihiko, Matsumoto, Satoshi, Horwitz, Barry, Seguchi, Yasuyuki, Biomechanics of hydrocephalus: A new theoretical model. Neurosurgery 21:6 (1987), 898–904.
Nicolle, S., Lounis, M., Willinger, R., Shear properties of brain tissue over a frequency range relevant for automotive impact situations: New experimental results. Stapp Car Crash J. 11 (2004), 239–258.
Ning, Xinguo, Zhu, Qiliang, Lanir, Yoram, Margulies, Susan S., A transversely isotropic viscoelastic constitutive equation for brainstem undergoing finite deformation. J. Biomech. Eng. 128:6 (2006), 925–933.
Ogden, Raymond William, Hill, Rodney, Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 326:1567 (1972), 565–584.
Owler, Brian K., Pena, Alonso, Momjian, Shahan, Czosnyka, Zofia, Czosnyka, Marek, Harris, Neil G., Smielewski, Piotr, Fryer, Tim, Donvan, Tim, Carpenter, Adrian, Pickard, John D., Changes in cerebral blood flow during cerebrospinal fluid pressure manipulation in patients with normal pressure hydrocephalus: A methodological study. J. Cereb. Blood Flow Metab. 24:5 (2004), 579–587 PMID: 15129190.
Prange, Michael T., Margulies, Susan S., Regional, directional, and age-dependent properties of the brain undergoing large deformation. J. Biomech. Eng. 124:2 (2002), 244–252.
Rashid, Badar, Destrade, Michel, Gilchrist, Michael D., Mechanical characterization of brain tissue in compression at dynamic strain rates. J. Mech. Behav. Biomed. Mater. 10 (2012), 23–38.
Santagiuliana, Raffaella, Milosevic, Miljan, Milicevic, Bogdan, Sciumè, Giuseppe, Simic, Vladimir, Ziemys, Arturas, Kojic, Milos, Schrefler, Bernhard A., Coupling tumor growth and bio distribution models. Biomed. Microdevices, 21, 2019.
Schiavone, P., Chassat, F., Boudou, T., Promayon, E., Valdivia, F., Payan, Y., In vivo measurement of human brain elasticity using a light aspiration device. Med. Image Anal. 13:4 (2009), 673–678.
Sciumè, Giuseppe, Mechanistic modeling of vascular tumor growth: An extension of Biot's theory to hierarchical bi-compartment porous medium systems. Acta Mech. 232 (2021), 1445–1478.
Sciumè, G., Boso, D.P., Gray, W.G., Cobelli, C., Schrefler, B.A., A two-phase model of plantar tissue: A step toward prediction of diabetic foot ulceration. Int. J. Numer. Methods Biomed. Eng. 30:11 (2014), 1153–1169.
Sciumè, Giuseppe, Ferrari, Mauro, Schrefler, Bernhard A., Saturation–pressure relationships for two- and three-phase flow analogies for soft matter. Mech. Res. Commun. 62 (2014), 132–137.
Sciumè, G., Santagiuliana, R., Ferrari, M., Decuzzi, P., Schrefler, B.A., A tumor growth model with deformable ECM. Phys. Biol., 11(6), 2014.
Seo, Hyeon, Kim, Donghyeon, Jun, Sung Chan, Effect of anatomically realistic full-head model on activation of cortical neurons in subdural cortical stimulation-A computational study. Sci. Rep., 6, 2016, 27353.
Sobey, Ian, Eisentraeger, Almut, Wirth, B., Czosnyka, Marek, Simulation of cerebral infusion tests using a poroelastic model. Int. J. Numer. Anal. Model. Ser. B 3:01 (2012), 52–64.
Sowinski, Damian R., McGarry, Matthew D.J., Van Houten, Elijah E.W., Gordon-Wylie, Scott, Weaver, John B., Paulsen, Keith D., Poroelasticity as a model of soft tissue structure: Hydraulic permeability reconstruction for magnetic resonance elastography in silico. Front. Phys., 8, 2021, 637.
Varrette, S., Bouvry, P., Cartiaux, H., Georgatos, F., Management of an academic HPC cluster: The UL experience. Proc. of the 2014 Intl. Conf. on High Performance Computing & Simulation, HPCS 2014, Bologna, Italy, 2014, IEEE, 959–967.
Verruijt, A., Theory and Problems of Poroelasticity. 2013.
Wittek, Adam, Hawkins, Trent, Miller, Karol, On the unimportance of constitutive models in computing brain deformation for image-guided surgery. Biomech. Model. Mechanobiol. 8 (2009), 77–84.
Yeoh, O., Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66 (1993), 754–771.
Zeraatpisheh, Milad, Bordas, Stephane P.A., Beex, Lars A.A., Bayesian model uncertainty quantification for hyperelastic soft tissue models. Data-Cent. Eng., 2, 2021, e9.