An Isotropic Hyperelastic Model of Esophagus Tissue Layers along with three-dimensional Simulation of Esophageal Peristaltic Behavior

Document Type : Original Article


1 Research Engineer; Young Researchers and Elite Club Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Assistant Professor at Shiraz University



Understanding mechanical characterization of the esophagus tissue layers is a step forward to the development of esophageal behavior, peristaltic simulation, and advanced clinical practices. Esophagus tissue layers behave nonlinear with a large amount of malformation. In this paper, different models based on the hyperelastic theory are discussed and compared to investigate the accuracy of the simulations in esophagus tissue mechanics. The simulated tissues were assumed as nonlinear, incompressible, and homogenous isotropic material. We have used the least square method for the best curve-fitting materials corresponding to the Mooney-Rivlin, Ogden, and Neo Hookean models. The results show a perfect agreement with Ogden hyperelastic model compared to the experimental studies. Moreover, based on our results, we have developed the three-dimensional finite element (FE) models by simulation of esophageal dynamic movements. Hence, FE analyses are taken into account for both simplicity and simulation of esophageal peristaltic behavior. By the numerical solutions, an interactive coding between MATLAB and ABAQUS software have been developed to achieve our goal. Current investigation is an effort to simulate esophagus, which would be used as a predictable tool for the medical and physio-mechanical study as well as educational purposes.

Graphical Abstract

An Isotropic Hyperelastic Model of Esophagus Tissue Layers along with three-dimensional Simulation of Esophageal Peristaltic Behavior


[1] Malagelada J, Bazzoli F, Boeckxstaens G, De Looze D, Fried M, Kahrilas P. World Gastroenterology Organisation Global Guidelines. Dysphagia [Internet]. Milwaukee, WI: World Gastroenterology Organisation; 2014 [accessed 2015 Dec 8]. 2014.
[2]   Cook IJ. Diagnostic evaluation of dysphagia. Nature Clinical Practice Gastroenterology & Hepatology. 2008;5:393-403.
[3]   Hunter P, Nielsen P. A strategy for integrative computational physiology. Physiology. 2005;20:316-25.
[4] Li M, Brasseur JG, Dodds WJ. Analyses of normal and abnormal esophageal transport using computer simulations. American Journal of Physiology-Gastrointestinal and Liver Physiology. 1994;266:G525-G43.
[5] Gregersen H, Kassab G. Biomechanics of the gastrointestinal tract. Neurogastroenterology & Motility. 1996;8:277-97.
[6]   Du P, Yassi R, Gregersen H, Windsor JA, Hunter PJ. The virtual esophagus: investigating esophageal functions in silico. Annals of the New York Academy of Sciences. 2016;1380:19-26.
[7] Gregersen H, Liao D, Brasseur JG. The Esophagiome: concept, status, and future perspectives. Annals of the New York Academy of Sciences. 2016;1380:6-18.
[8]   Gregersen H. Biomechanics of the gastrointestinal tract: new perspectives in motility research and diagnostics: Springer Science & Business Media; 2003.
[9] Saladin KS. Anatomy & physiology: WCB/McGraw-Hill; 1998.
[10] Paterson WG. Esophageal peristalsis. GI Motility online. doi:10.1038/gimo13. 2006.
[11] Nguyen H, Silny J, Albers D, Roeb E, Gartung C, Rau G, et al. Dynamics of esophageal bolus transport in healthy subjects studied using multiple intraluminal impedancometry. American Journal of Physiology-Gastrointestinal and Liver Physiology. 1997;273:G958-G64.
[12] Ghosh S, Janiak P, Fox M, Schwizer W, Hebbard G, Brasseur J. Physiology of the oesophageal transition zone in the presence of chronic bolus retention: studies using concurrent high resolution manometry and digital fluoroscopy. Neurogastroenterology & Motility. 2008;20:750-9.
[13] Dai Q, Liu J-B, Brasseur JG, Thangada VK, Thomas B, Parkman H, et al. Volume (3-dimensional) space-time reconstruction of esophageal peristaltic contraction by using simultaneous US and manometry. Gastrointestinal endoscopy. 2003;58:913-9.
[14] Ren J, Massey BT, Dodds WJ, Kern MK, Brasseur JG, Shaker R, et al. Determinants of intrabolus pressure during esophageal peristaltic bolus transport. American Journal of Physiology-Gastrointestinal and Liver Physiology. 1993;264:G407-G13.
[15] Ghosh SK, Janiak P, Schwizer W, Hebbard GS, Brasseur JG. Physiology of the esophageal pressure transition zone: separate contraction waves above and below. American Journal of Physiology-Gastrointestinal and Liver Physiology. 2006;290:G568-G76.
[16] Ghosh SK, Kahrilas PJ, Lodhia N, Pandolfino JE. Utilizing intraluminal pressure differences to predict esophageal bolus flow dynamics. American Journal of Physiology-Gastrointestinal and Liver Physiology. 2007;293:G1023-G8.
[17] Ogden RW. Nonlinear elasticity, anisotropy, material stability and residual stresses in soft tissue.  Biomechanics of soft tissue in cardiovascular systems: Springer; 2003. p. 65-108.
[18] Stavropoulou EA, Dafalias YF, Sokolis DP. Biomechanical and histological characteristics of passive esophagus: experimental investigation and comparative constitutive modeling. Journal of biomechanics. 2009;42:2654-63.
[19] Yang W, Fung T, Chian K, Chong C. Directional, regional, and layer variations of mechanical properties of esophageal tissue and its interpretation using a structure-based constitutive model. Journal of biomechanical engineering. 2006;128:409-18.
[20] Yang W, Fung T, Chian K, Chong C. 3D mechanical properties of the layered esophagus: experiment and constitutive model. Journal of biomechanical engineering. 2006;128:899-908.
[21] Natali AN, Carniel EL, Gregersen H. Biomechanical behaviour of oesophageal tissues: material and structural configuration, experimental data and constitutive analysis. Medical engineering & physics. 2009;31:1056-62.
[22] Sommer G, Schriefl A, Zeindlinger G, Katzensteiner A, Ainödhofer H, Saxena A, et al. Multiaxial mechanical response and constitutive modeling of esophageal tissues: impact on esophageal tissue engineering. Acta biomaterialia. 2013;9:9379-91.
[23] Egorov VI, Schastlivtsev IV, Prut EV, Baranov AO, Turusov RA. Mechanical properties of the human gastrointestinal tract. Journal of biomechanics. 2002;35:1417-25.
[24] Sanchez-Molina D, Velazquez-Ameijide J, Arregui-Dalmases C, Rodríguez D, Quintana V, Shafieian M, et al. A microcontinuum model for mechanical properties of esophageal tissue: experimental methodology and constitutive analysis. Annals of biomedical engineering. 2014;42:62-72.
[25] Liao D, Lelic D, Gao F, Drewes AM, Gregersen H. Biomechanical functional and sensory modelling of the gastrointestinal tract. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2008;366:3281-99.
[26] Liao D, Zhao J, Fan Y, Gregersen H. Two-layered quasi-3D finite element model of the oesophagus. Medical engineering & physics. 2004;26:535-43.
[27] Yang W, Fung TC, Chian KS, Chong CK. Finite element simulation of food transport through the esophageal body. World journal of gastroenterology. 2007;13:1352-9.
[28] Yassi R, Cheng L, Rajagopal V, Nash M, Windsor J, Pullan A. Modeling of the mechanical function of the human gastroesophageal junction using an anatomically realistic three-dimensional model. Journal of biomechanics. 2009;42:1604-9.
[29] Yassi R, Cheng L, Al-Ali S, Smith N, Pullan A, Windsor J. An anatomically based mathematical model of the gastroesophageal junction.  Engineering in Medicine and Biology Society, 2004 IEMBS'04 26th Annual International Conference of the IEEE: IEEE; 2004. p. 635-8.
[30] Gastelum A, Mata L, Brito-de-la-Fuente E, Delmas P, Vicente W, Salinas-Vázquez M, et al. Building a three-dimensional model of the upper gastrointestinal tract for computer simulations of swallowing. Medical & biological engineering & computing. 2016;54:525-34.
[31] Sarma P, Pidaparti R, Moulik P, Meiss R. Nonā€linear material models for tracheal smooth muscle tissue. Bio-medical materials and engineering. 2003;13:235-45.
[32] Trabelsi O, del Palomar AP, Tobar AM, López-Villalobos J, Ginel A, Doblaré M. FE simulation of human trachea swallowing movement before and after the implantation of an endoprothesis. Applied Mathematical Modelling. 2011;35:4902-12.
[33] Ogden RW. Non-linear elastic deformations: Courier Corporation; 1997.
[34] Macosko C. Rheology: Principles, measurements, and applications. 1994. VCH, New York.
[35] Campion R, Gent AN. Engineering with rubber: Hanser; 2001.
[36] Rivlin R. Large elastic deformations of isotropic materials. IV. Further developments of the general theory. Philosophical Transactions of the Royal Society of London Series A, Mathematical and Physical Sciences. 1948;241:379-97.
[37] Mooney M. A theory of large elastic deformation. Journal of applied physics. 1940;11:582-92.
[38] Kelley CT. Iterative methods for optimization: Siam; 1999.
[39] Kenney J, Keeping E. Moving averages. Kenney JF Mathematics of statics Princeton NJ: Van Nostrand. 1962:59-60.
[40] Xia F, Mao J, Ding J, Yang H. Observation of normal appearance and wall thickness of esophagus on CT images. European journal of radiology. 2009;72:406-11.
[41] Kuo B, Urma D. Esophagus-anatomy and development. GI Motility online. 2006.
[42] Urbanchek MG, Picken EB, Kalliainen LK, Kuzon WM. Specific force deficit in skeletal muscles of old rats is partially explained by the existence of denervated muscle fibers. The Journals of Gerontology Series A: Biological Sciences and Medical Sciences. 2001;56:B191-B7.
[43] Babuška I, Guo B. The h, p and h-p version of the finite element method; basis theory and applications. Advances in Engineering Software. 1992;15:159-74.
[44] Mott P, Roland C. Limits to Poisson’s ratio in isotropic materials. Physical review B. 2009;80:132104.
[45] South JT. Mechanical properties and durability of natural rubber compounds and composites. 2001.
[46] Paterson W, Goyal R, Habib F. Esophageal motility disorders. GI Motility Online. doi:10.1038/gimo20. 2006.
[47] Pioletti DP, Rakotomanana LR. Non-linear viscoelastic laws for soft biological tissues. European Journal of Mechanics a-Solids. 2000;19:749-59.
[48] Ahani E, Montazer M, Toliyat T, Mahmoudi Rad M. A novel biocompatible antibacterial product: Nanoliposomes loaded with poly(hexamethylene biguanide chloride). Journal of Bioactive and Compatible Polymers. 2017;32(3):242-262.