Evaluation of Residual Stresses in Human Face as a Function of Growth

Authors: M. A. Askari, M. A. Nazari, P. Perrier, Y. Payan

Abstract:

Growth and remodeling of biological structures have gained lots of attention over the past decades. Determining the response of living tissues to mechanical loads is necessary for a wide range of developing fields such as prosthetics design or computerassisted surgical interventions. It is a well-known fact that biological structures are never stress-free, even when externally unloaded. The exact origin of these residual stresses is not clear, but theoretically, growth is one of the main sources. Extracting body organ’s shapes from medical imaging does not produce any information regarding the existing residual stresses in that organ. The simplest cause of such stresses is gravity since an organ grows under its influence from birth. Ignoring such residual stresses might cause erroneous results in numerical simulations. Accounting for residual stresses due to tissue growth can improve the accuracy of mechanical analysis results. This paper presents an original computational framework based on gradual growth to determine the residual stresses due to growth. To illustrate the method, we apply it to a finite element model of a healthy human face reconstructed from medical images. The distribution of residual stress in facial tissues is computed, which can overcome the effect of gravity and maintain tissues firmness. Our assumption is that tissue wrinkles caused by aging could be a consequence of decreasing residual stress and thus not counteracting gravity. Taking into account these stresses seems therefore extremely important in maxillofacial surgery. It would indeed help surgeons to estimate tissues changes after surgery.

Keywords: Finite element method, growth, residual stress, soft tissue.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1338706

References:

[1] E. K. Rodriguez, A. Hoger, A. D. McCulloch, ‘Stress-dependent finite growth in soft elastic tissue’ J. Biomech. (1994)
[2] Yuan-Cheng Fung, Biomechanics, Shock, 1998, IX.
[3] C J Chuong and Y C Fung, ‘Residual Stress in Arteries’, in Frontiers in Biomechanics SE - 9, ed. by G W Schmid-Schönbein, S.L-Y. Woo, and B W Zweifach (Springer New York, 1986), pp. 117–129.
[4] Y C Fung, ‘Biomechanical Aspects of Growth and Tissue Engineering’, in Biomechanics SE - 13 (Springer New York, 1990), pp. 499–546.
[5] D. Ambrosi, G. A. Ateshian, E. M. Arruda, S. C. Cowin, J. Dumais, A. Goriely, G. A. Holzapfel, J. D. Humphrey, R. Kemkemer, E. Kuhl, J. E. Olberding, L. A. Taber, K. Garikipati, ‘Perspectives on Biological Growth and Remodeling’, Journal of the Mechanics and Physics of Solids, 59 (2011).
[6] Gerhard a. Holzapfel, Thomas C. Gasser and Ray W. Ogden, ‘A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models’, Journal of Elasticity, 61 (2000), 1–48.
[7] Larry a. Taber, ‘Biomechanics of Growth, Remodeling, and Morphogenesis’, Applied Mechanics Reviews, 1995, 487.
[8] Marcelo Epstein and Gérard A. Maugin, ‘Thermomechanics of Volumetric Growth in Uniform Bodies’, International Journal of Plasticity, 16 (2000), 951–978.
[9] V. A. Lubarda and A. Hoger, On the Mechanics of Solids with a Growing Mass, International Journal of Solids and Structures, 2002, XXXI.
[10] A. Guillou and R W Ogden, ‘Growth in Soft Biological Tissue and Residual Stress Development’, Growth (Lakeland).
[11] Manuel K. Rausch and Ellen Kuhl, ‘On the Effect of Prestrain and Residual Stress in Thin Biological Membranes’, Journal of the Mechanics and Physics of Solids, 61 (2013), 1955–1969.
[12] F Morin, H. Courtecuisse, M. Chabanas, Y. Payan ‘Rest Shape Computation for Highly Deformable Model of Brain’, Computer Methods in Biomechanics and Biomedical Engineering, 18 (2015), 2006–2007.
[13] M Genet, K. Rausch, L. C. Lee, S. Choy, X. Zhao, G. S. Kassab, S. Kozerke, J. M. Guccione, E. Kuhl, ‘Heterogeneous Growth-Induced Prestrain in the Heart’, Journal of Biomechanics, 48 (2015), 2080–2089.
[14] Mohammad Ali Nazari, P. Perrier, M. Chabanas, Y. Payan ‘Simulation of Dynamic Orofacial Movements Using a Constitutive Law Varying with Muscle Activation’, Computer Methods in Biomechanics and Biomedical Engineering, 13 (2010), 469–482L.
[15] C Lee, M. Genet, G. Acevedo-Bolton, K. Ordovas, J. M. Guccione, E. Kuhl, ‘A Computational Model That Predicts Reverse Growth in Response to Mechanical Unloading’, Biomechanics and Modeling in Mechanobiology, 14 (2015), 217–229.
[16] H F Choi, J. D’hooge, F. E. Rademakers, P. Claus, ‘Influence of Left-Ventricular Shape on Passive Filling Properties and End-Diastolic Fiber Stress and Strain.’, Journal of biomechanics, 43 (2010), 1745–53.
[17] Alexander M. Zöllner, Adrian Buganza Tepole and Ellen Kuhl, ‘On the Biomechanics and Mechanobiology of Growing Skin’, Journal of Theoretical Biology, 297 (2012), 166–175.
[18] Alexander M. Zöllner, A. B. Tepole, A. K. Gosain, E. Kuhl ‘Growing Skin: Tissue Expansion in Pediatric Forehead Reconstruction’, Biomechanics and Modeling in Mechanobiology, 11 (2012), 855–867.