Computational Models for the Mechanical Investigation of Stomach Tissues and Structure

Abstract

Bariatric surgery is performed on obese people aiming at reducing the capacity of the stomach and/or the absorbing capability of the gastrointestinal tract. A more reliable and effective approach to bariatric surgery may integrate different expertise, in the areas of surgery, physiology and biomechanics, availing of a strong cooperation between clinicians and engineers. This work aimed at developing a computational model of the stomach, as a computational tool for the physio-mechanical investigation of stomach functionality and the planning of bariatric procedures. In this sense, coupled experimental and numerical activities were developed. Experimental investigations on pig and piglet stomachs aimed at providing information about stomach geometrical configuration and structural behavior. The computational model was defined starting from the analysis of data from histo-morphometric investigations and mechanical tests. A fiber-reinforced visco-hyperelastic constitutive model was developed to interpret the mechanical response of stomach tissues; constitutive parameters were identified considering mechanical tests at both tissue and structure levels. Computational analyses were performed to investigate the pressure–volume behavior of the stomach. The developed model satisfactorily interpreted results from experimental activities, suggesting its reliability. Furthermore, the model was exploited to investigate stress and strain fields within gastric tissues, as the stimuli for mechanoreceptors that interact with the central nervous system leading to the feeling of satiety. In this respect, the developed computational model may be employed to evaluate the influence of bariatric intervention on the stimulation of mechanoreceptors, and the following meal induced satiety.

This is a preview of subscription content, log in to check access.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

References

  1. 1.

    Anderson, A. E., C. L. Peters, B. D. Tuttle, and J. A. Weiss. Subject-specific finite element model of the pelvis: development, validation and sensitivity studies. J. Biomech. Eng. 127:364–373, 2005.

    Article  PubMed  Google Scholar 

  2. 2.

    Aydin, R. C., S. Brandstaeter, F. A. Braeu, M. Steigenberger, R. P. Marcus, K. Nikolaou, M. Notohamiprodjo, and C. J. Cyron. Experimental characterization of the biaxial mechanical properties of porcine gastric tissue. J. Mech. Behav. Biomed. Mater. 74:499–506, 2017.

    Article  CAS  PubMed  Google Scholar 

  3. 3.

    Bellini, C., P. Glass, M. Sitti, and E. S. Di Martino. Biaxial mechanical modeling of the small intestine. J. Mech. Behav. Biomed. 4:1727–1740, 2011.

    Article  Google Scholar 

  4. 4.

    Berenson, G. S. Health Consequences of Obesity. Pediatr. Blood Cancer 58:117–121, 2012.

    Article  PubMed  Google Scholar 

  5. 5.

    Burton, P. R., W. A. Brown, C. Laurie, M. Richards, G. Hebbard, and P. E. O’Brien. Effects of gastric band adjustments on intraluminal pressure. Obes. Surg. 19:1508–1514, 2009.

    Article  PubMed  Google Scholar 

  6. 6.

    Carmagnola, S., P. Cantù, and R. Penagini. Mechanoreceptors of the Proximal Stomach and Perception of Gastric Distension. Am. J. Gastroenterol. 100:1704–1710, 2005.

    Article  PubMed  Google Scholar 

  7. 7.

    Carniel, E. L., C. G. Fontanella, L. Polese, S. Merigliano, and A. N. Natali. Computational tools for the analysis of mechanical functionality of gastrointestinal structures. Technol. Health Care 21:271–283, 2013.

    PubMed  Google Scholar 

  8. 8.

    Carniel, E. L., C. G. Fontanella, C. Stefanini, and A. N. Natali. A procedure for the computational investigation of stress-relaxation phenomena. Mech. Time-Depend. Mater. 17:25–38, 2013.

    Article  CAS  Google Scholar 

  9. 9.

    Carniel, E. L., A. Frigo, C. G. Fontanella, G. M. De Benedictis, A. Rubini, L. Barp, G. Pluchino, B. Sabbadini, and L. Polese. A biomechanical approach to the analysis of methods and procedures of bariatric surgery. J. Biomech. 56:32–41, 2017.

    Article  PubMed  Google Scholar 

  10. 10.

    Carniel, E. L., V. Gramigna, C. G. Fontanella, C. Stefanini, and A. N. Natali. Constitutive formulations for the mechanical investigation of colonic tissues. J. Biomed. Mater. Res. A 102:1243–1254, 2014.

    Article  CAS  PubMed  Google Scholar 

  11. 11.

    Carniel, E. L., M. Mencattelli, G. Bonsignori, C. G. Fontanella, A. Frigo, A. Rubini, C. Stefanini, and A. N. Natali. Analysis of the structural behaviour of colonic segments by inflation tests: experimental activity and physio-mechanical model. Proc. Inst. Mech. Eng. H 229:794–803, 2015.

    Article  PubMed  Google Scholar 

  12. 12.

    Carniel, E. L., A. Rubini, A. Frigo, and A. N. Natali. Analysis of the biomechanical behaviour of gastrointestinal regions adopting an experimental and computational approach. Comput. Methods Programs Biomed. 113:338–345, 2014.

    Article  CAS  PubMed  Google Scholar 

  13. 13.

    Chang, S. H., C. R. Stoll, J. Song, J. E. Varela, C. J. Eagon, and G. A. Colditz. The effectiveness and risks of bariatric surgery: an updated systematic review and meta-analysis, 2003–2012. JAMA Surg. 149:275–287, 2014.

    Article  PubMed  PubMed Central  Google Scholar 

  14. 14.

    Ciarletta, P., P. Dario, F. Tendick, and S. Micera. Hyperelastic model of anisotropic fiber reinforcements within intestinal walls for applications in medical robotics. Int. J. Robot. Res. 28:1279–1288, 2009.

    Article  Google Scholar 

  15. 15.

    Colville, T. P., and J. M. Bassert. Clinical Anatomy and Physiology for Veterinary Technicians (3rd ed.). St. Louis: Elsevier, 2015.

    Google Scholar 

  16. 16.

    Dario, P., P. Ciarletta, A. Menciassi, and B. Kim. Modelling and experimental validation of the locomotion of endoscopic robots in the colon. Int. J. Robot. Res. 23:549–556, 2004.

    Article  Google Scholar 

  17. 17.

    Donahue, T. L., M. L. Hull, M. M. Rashid, and C. R. Jacobs. A finite element model of the human knee joint for the study of tibio-femoral contact. J. Biomech. Eng. 124:273–280, 2002.

    Article  PubMed  Google Scholar 

  18. 18.

    Egorov, V. I., I. V. Schastlivtsev, E. V. Prut, A. O. Baranov, and R. A. Turusov. Mechanical properties of the human gastrointestinal tract. J. Biomech. 35:1417–1425, 2002.

    Article  PubMed  Google Scholar 

  19. 19.

    Fallah, A., M. T. Ahmadian, K. Firozbakhsh, and M. M. Aghdam. Micromechanical modeling of rate-dependent behavior of connective tissues. J. Theor. Biol. 416:119–128, 2017.

    Article  CAS  PubMed  Google Scholar 

  20. 20.

    Ferrua, M. J., and R. P. Singh. Modeling the fluid dynamics in a human stomach to gain insight of food digestion. J. Food Sci. 75:R151–R162, 2010.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. 21.

    Fung, Y. C. Biomechanics. New York: Springer, 1993.

    Google Scholar 

  22. 22.

    Furness, J. B., B. P. Callaghan, L. R. Rivera, and H. J. Cho. The enteric nervous system and gastrointestinal innervation: integrated local and central control. In: Microbial Endocrinology: The Microbiota-Gut-Brain Axis in Health and Disease. Advances in Experimental Medicine and Biology, Vol. 817, edited by M. Lyte, and J. F. Cryan. New York: Springer, 2014.

    Google Scholar 

  23. 23.

    Gao, F., D. Liao, J. Zhao, A. M. Drewes, and H. Gregersen. Numerical analysis of pouch filling and emptying after laparoscopic gastric banding surgery. Obes. Surg. 18:243–250, 2008.

    Article  PubMed  Google Scholar 

  24. 24.

    Gloy, V. L., M. Briel, D. L. Bhatt, S. R. Kashyap, P. R. Schauer, G. Mingrone, H. C. Bucher, and A. J. Nordmann. Bariatric surgery versus non-surgical treatment for obesity: a systematic review and meta-analysis of randomised controlled trials. BMJ 347:f5934, 2013.

    Article  PubMed  PubMed Central  Google Scholar 

  25. 25.

    Gravetter, F. J., and L. B. Wallnau. Statistic for the Behavioral Sciences (8th ed.). Belmont, CA: Wadsworth/Cenage Learning, 2009.

    Google Scholar 

  26. 26.

    Gregersen, H., J. L. Emery, and A. D. McCulloch. History-dependent mechanical behavior of guinea-pig small intestine. Ann. Biomed. Eng. 26:850–858, 1998.

    Article  CAS  PubMed  Google Scholar 

  27. 27.

    Holzapfel, G. A. Nonlinear Solid Mechanics: A Continuum Approach for Engineering. Chichester: Wiley, 2000.

    Google Scholar 

  28. 28.

    Janssen, P., S. Verschueren, H. G. Ly, R. Vos, L. Van Oudenhove, and J. Tack. Intragastric pressure during food intake: a physiological and minimally invasive method to assess gastric accommodation. Neurogastroenterol. Motil. 23:316–322, 2011.

    Article  CAS  PubMed  Google Scholar 

  29. 29.

    Jia, Z. G., W. Li, and Z. R. Zhou. Mechanical characterization of stomach tissue under uniaxial tensile action. J. Biomech. 48:651–658, 2015.

    Article  CAS  PubMed  Google Scholar 

  30. 30.

    Kampe, J., A. Stefanidis, S. H. Lockie, W. A. Brown, J. B. Dixon, A. Odoi, S. J. Spencer, J. Raven, and B. J. Oldfield. Neural and humoral changes associated with the adjustable gastric band: insights from a rodent model. Int. J. Obes. (London) 36:1403–1411, 2012.

    Article  CAS  Google Scholar 

  31. 31.

    Kelly, K. A. Gastric emptying of liquids and solids: roles of proximal and distal stomach. Am. J. Physiol. 239:G71–G76, 1980.

    CAS  PubMed  Google Scholar 

  32. 32.

    Kitahara, C. M., A. J. Flint, A. Berrington-de-Gonzalez, L. Bernstein, M. Brotzman, R. J. MacInnis, S. C. Moore, K. Robien, P. S. Rosenberg, P. N. Singh, E. Weiderpass, H. O. Adami, H. Anton-Culver, R. Ballard-Barbash, J. E. Buring, D. M. Freedman, G. E. Fraser, L. E. Beane-Freeman, S. M. Gapstur, J. M. Gaziano, G. G. Giles, N. Håkansson, J. A. Hoppin, F. B. Hu, K. Koenig, M. S. Linet, Y. Park, A. V. Patel, M. P. Purdue, C. Schairer, H. D. Sesso, K. Visvanathan, E. White, A. Wolk, A. Zeleniuch-Jacquotte, and P. Hartge. Association between class III obesity (BMI of 40–59 kg/m2) and mortality: a pooled analysis of 20 prospective studies. PLoS Med. 11:1001673, 2014.

    Article  Google Scholar 

  33. 33.

    Lehnert, T., D. Sonntag, A. Konnopka, S. Riedel-Heller, and H. H. König. Economic costs of overweight and obesity. Best Pract. Res. Clin. Endocrinol. Metab. 27:105–115, 2013.

    Article  PubMed  Google Scholar 

  34. 34.

    Marieb, E. N., and K. Hoehn. Human Anatomy and Physiology (7th ed.). San Francisco: Pearson International Edition, 2007.

    Google Scholar 

  35. 35.

    Miftahof, R. N. Biomechanics of the Human Stomach. Cham: Springer, 2017.

    Google Scholar 

  36. 36.

    Mingrone, G., S. Panunzi, A. De Gaetano, C. Guidone, A. Iaconelli, G. Nanni, M. Castagneto, S. Bornstein, and F. Rubino. Bariatric-metabolic surgery versus conventional medical treatment in obese patients with type 2 diabetes: 5 year follow-up of an open-label, single-centre, randomised controlled trial. Lancet 386:964–973, 2015.

    Article  Google Scholar 

  37. 37.

    Natali, A. N., E. L. Carniel, C. G. Fontanella, A. Frigo, S. Todros, A. Rubini, G. M. De Benedictis, M. A. Cerruto, and W. Artibani. Mechanics of the urethral duct: tissue constitutive formulation and structural modeling for the investigation of lumen occlusion. Biomech. Model. Mechanobiol. 16:439–447, 2017.

    Article  PubMed  Google Scholar 

  38. 38.

    Natali, A. N., E. L. Carniel, A. Frigo, C. G. Fontanella, A. Rubini, Y. Avital, and G. M. De Benedictis. Experimental investigation of the structural behavior of equine urethra. Comput. Methods Programs Biomed. 141:35–41, 2017.

    Article  PubMed  Google Scholar 

  39. 39.

    Natali, A. N., E. L. Carniel, A. Frigo, P. G. Pavan, S. Todros, P. Pachera, C. G. Fontanella, A. Rubini, L. Cavicchioli, Y. Avital, and G. M. De Benedictis. Experimental investigation of the biomechanics of urethral tissues and structures. Exp. Physiol. 101:641–656, 2016.

    Article  PubMed  Google Scholar 

  40. 40.

    Natali, A. N., C. G. Fontanella, and E. L. Carniel. Constitutive formulation and numerical analysis of the heel pad region. Comput. Methods Biomech. Biomed. Eng. 15:401–409, 2012.

    Article  CAS  Google Scholar 

  41. 41.

    Palanca, M., G. Tozzi, and L. Cristofolini. The use of digital image correlation in the biomechanical area: a review. Int. Biomech. 3:1–21, 2016.

    Article  Google Scholar 

  42. 42.

    Phillips, R. J., and T. L. Powley. Tension and stretch receptors in gastrointestinal smooth muscle: re-evaluating vagal mechanoreceptor electrophysiology. Brain Res. Brain Res. Rev. 34:1–26, 2000.

    Article  CAS  PubMed  Google Scholar 

  43. 43.

    Pories, W. J. Bariatric surgery: risks and rewards. J. Clin. Endocrinol. Metab. 93:S89–S96, 2008.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. 44.

    Powley, T. L., C. N. Hudson, J. L. McAdams, E. A. Baronowsky, F. N. Martin, J. K. Mason, and R. J. Phillips. Organization of vagal afferents in pylorus: mechanoreceptors arrayed for high sensitivity and fine spatial resolution? Auton. Neurosci. 183:36–48, 2014.

    Article  PubMed  Google Scholar 

  45. 45.

    Rolls, B. J., V. H. Castellanos, J. C. Halford, A. Kilara, D. Panyam, C. L. Pelkman, G. P. Smith, and M. L. Thorwart. Volume of food consumed affects satiety in men. Am. J. Clin. Nutr. 67:1170–1177, 1998.

    Article  CAS  PubMed  Google Scholar 

  46. 46.

    Schauer, P. R., S. R. Kashyap, K. Wolski, S. A. Brethauer, J. P. Kirwan, C. E. Pothier, S. Thomas, B. Abood, S. E. Nissen, and D. L. Bhatt. Bariatric surgery versus intensive medical therapy in obese patients with diabetes. N. Engl. J. Med. 366:1567–1576, 2012.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. 47.

    Screen, H. R., S. Toorani, and J. C. Shelton. Microstructural stress relaxation mechanics in functionally different tendons. Med. Eng. Phys. 35:96–102, 2013.

    Article  CAS  PubMed  Google Scholar 

  48. 48.

    Simo, J. C., and T. J. R. Hughes. Computational Inelasticity. New York: Springer, 1998.

    Google Scholar 

  49. 49.

    Sunyer, F. X. P. Health implications of obesity. Am. J. Clin. Nutr. 53:1595S–1603S, 1991.

    Article  Google Scholar 

  50. 50.

    Wang, F. B., and T. L. Powley. Topographic inventories of vagal afferents in gastrointestinal muscle. J. Comp. Neurol. 421:302–324, 2000.

    Article  CAS  PubMed  Google Scholar 

  51. 51.

    Wang, G. J., D. Tomasi, W. Backus, R. Wang, F. Telang, A. Geliebter, J. Korner, A. Bauman, J. S. Fowler, K. Panayotis, P. K. Thanos, and N. D. Volkow. Gastric distention activates satiety circuitry in the human brain. NeuroImage 39:1824–1831, 2008.

    Article  PubMed  Google Scholar 

  52. 52.

    Weiss, J. A., B. N. Makerc, and S. Govindjeed. Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput. Methods. Appl. Mech. Eng. 135:107–128, 1996.

    Article  Google Scholar 

  53. 53.

    Woods, S. C. Gastrointestinal satiety signals I. An overview of gastrointestinal signals that influence food intake. Am. J. Physiol. Gastrointest. Liver Physiol. 286:7–13, 2004.

    Article  Google Scholar 

  54. 54.

    Yang, W., T. C. Fung, K. S. Chian, and C. K. Chong. Viscoelasticity of esophageal tissue and application of a QLV model. J. Biomech. Eng. 128:909–916, 2006.

    Article  CAS  PubMed  Google Scholar 

  55. 55.

    Zagorodnyuk, V. P., B. N. Chen, and S. J. H. Brookes. Intraganglionic laminar endings are mechanotransduction sites of vagal tension receptors in the guinea-pig stomach. J. Physiol. 534:255–268, 2001.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  56. 56.

    Zhao, J., D. Liao, P. Chen, P. Kunwald, and H. Gregersen. Stomach stress and strain depend on location, direction and the layered structure. J. Biomech. 41:3441–3447, 2008.

    Article  PubMed  Google Scholar 

  57. 57.

    Zienkiewicz, O. C., and R. L. Taylor. The Finite Element Method (5th ed.). Oxford: Butterworth Heinemann, 2000.

    Google Scholar 

Download references

Acknowledgments

The authors warrant that the article is the authors’ original work, hasn’t received prior publication and isn’t under consideration for publication elsewhere. No specifying funding was received to support the reported research activities.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Chiara Giulia Fontanella.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Associate Editor Jane Grande-Allen oversaw the review of this article.

Appendix A

Appendix A

Constitutive parameters were identified by the inverse analysis of experimental activities. Aiming at investigating the complex distribution of stomach tissues, experimentations performed by Zhao et al.56 were analysed. Tensile tests were developed on tissue specimens harvested from pig stomachs, considering the influence of location, as fundus, corpus and antrum, wall layer, as connective layer and muscular layers, and direction, as circumferential and longitudinal ones. Specimens loading occurred at low strain rate, leading to almost equilibrium response. Mathematical procedures led to the following model formulation that allowed interpreting results from tensile tests:

$${\mathbf{P}}^{\infty } \left( {\mathbf{C}} \right) = \gamma^{\infty } {\mathbf{P}}^{0} \left( {\mathbf{C}} \right) = 2\gamma^{\infty } {\mathbf{F}}\frac{{\partial W^{0} \left( {\mathbf{C}} \right)}}{{\partial {\mathbf{C}}}} = 2\gamma^{\infty } {\mathbf{F}}\frac{{\partial W_{m}^{0} \left( {\mathbf{C}} \right)}}{{\partial {\mathbf{C}}}} + 2\gamma^{\infty } {\mathbf{F}}\frac{{\partial W_{fL}^{0} \left( {I_{4} } \right)}}{{\partial {\mathbf{C}}}} + 2\gamma^{\infty } {\mathbf{F}}\frac{{\partial W_{fC}^{0} \left( {I_{6} } \right)}}{{\partial {\mathbf{C}}}} = {\mathbf{P}}_{m}^{\infty } \left( {\mathbf{C}} \right) + {\mathbf{P}}_{fL}^{\infty } \left( {I_{4} } \right) + {\mathbf{P}}_{fC}^{\infty } \left( {I_{6} } \right)$$
(A.1)
$${\mathbf{P}}_{m}^{\infty } \left( {\mathbf{C}} \right) = - \gamma^{\infty } pF^{ - T} + C_{1}^{\infty } \exp \left[ {\alpha_{1} \left( {I_{1} - 3} \right)} \right]\left( {2{\mathbf{F}} - {2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-0pt} 3}I_{1} {\mathbf{F}}^{ - T} } \right)$$
(A.2)
$${\mathbf{P}}_{fL}^{\infty } = 2\left( {{{C_{4}^{\infty } } \mathord{\left/ {\vphantom {{C_{4}^{\infty } } {\alpha_{4} }}} \right. \kern-0pt} {\alpha_{4} }}} \right)\left\{ {\exp \left[ {\alpha_{4} \left( {I_{4} - 1} \right)} \right] - 1} \right\}{\mathbf{F}}\left( {{\mathbf{a}}_{0} \otimes {\mathbf{a}}_{0} } \right)$$
(A.3)
$${\mathbf{P}}_{fC}^{\infty } = 2\left( {{{C_{6}^{\infty } } \mathord{\left/ {\vphantom {{C_{6}^{\infty } } {\alpha_{6} }}} \right. \kern-0pt} {\alpha_{6} }}} \right)\left\{ {\exp \left[ {\alpha_{6} \left( {I_{6} - 1} \right)} \right] - 1} \right\}{\mathbf{F}}\left( {{\mathbf{b}}_{0} \otimes {\mathbf{b}}_{0} } \right)$$
(A.4)

where \(\gamma^{\infty } = 1 - \sum\limits_{i = 1}^{n} {\gamma^{i} }\) is a parameter that specifies the equilibrium relative stiffness of the tissue, while parameters \(C_{r}^{\infty } = \gamma^{\infty } C_{r}\) (r = 1,4,6) specify equilibrium initial stiffness terms. The specific formulation of the deformation gradient F was derived by considering the orientation of the specific tensile test along longitudinal or circumferential direction, the boundary conditions, as null values of normal stress components along lateral directions, and the incompressibility constraint.10

The comparison between model results and experimental data was performed by a cost function, which specified a measure of relative error, rather than an absolute one to provide a better approximation for both low and high result values:

$$\Upomega \left( {\varvec{\upomega}} \right) = \frac{1}{u}\sqrt {\sum\limits_{j = 1}^{u} {\left[ {2 - \frac{{P_{j}^{\exp } \left( {\lambda_{j}^{\exp } } \right)}}{{P_{j}^{\bmod } \left( {{\varvec{\upomega}},\lambda_{j}^{\exp } } \right)}} - \frac{{P_{j}^{\bmod } \left( {{\varvec{\upomega}},\lambda_{j}^{\exp } } \right)}}{{P_{j}^{\exp } \left( {\lambda_{j}^{\exp } } \right)}}} \right]}^{2} }$$
(A.5)

where ω is the set of constitutive parameters, u the number of experimental data, \(\lambda_{j}^{\exp }\) the jth experimentally imposed input data (in terms of strain), \(P_{j}^{\exp }\) the jth experimentally measured output data (in terms of stress), \(P_{j}^{\bmod }\) the model output data evaluated by assuming constitutive parameters ω and input condition \(\lambda_{j}^{\exp }\). With regard to each stomach region and each wall layer, the cost function was evaluated considering results from tensile tests developed along both longitudinal and circumferential directions. Optimization techniques were adopted to minimize the cost function,7 leading to the constitutive parameters \(C_{r}^{\infty } ,\alpha_{r} \;(r = 1, 4, 6)\) for connective layer and muscular layers from fundus, corpus and antrum. Data from tensile tests along circumferential and longitudinal directions only were at disposal. Aiming at the almost univocal identification of constitutive parameters,7 all the gastric tissues were assumed to have the same mechanical contribution from the isotropic ground matrix. It follows that the same values of C1 and α1 parameters were assumed for connective layer and muscular layers from fundus, corpus and antrum.

Viscous parameters τi and γi were identified by analyzing relaxation data from structural tests developed on piglet stomachs. The following model formulation was assumed to interpret exponential decay of the normalized pressure Pnorm with time8,39:

$$P^{norm} \left( t \right) = \gamma^{\infty } + \sum\limits_{i = 1}^{n} {\gamma^{i} \exp \left[ { - \frac{t}{{\tau^{i} }}} \right]}$$
(A.6)

Again, parameters identification was performed by minimizing the discrepancy between experimental and model results. Two viscous branches were assumed to contemporarily minimize the number of parameters and correctly interpret the trend of experimental data.12 The same viscous parameters were assumed for all the stomach tissues. Subsequently, the instantaneous initial stiffness terms \(C_{r} = C_{r}^{\infty } /\gamma^{\infty } (r = 1,4,6)\) were calculated.

The developed computational model of the stomach was exploited to evaluate and enhance its capability in interpreting the stomach mechanical behavior. Inflation tests were analyzed to compare computational results and data from experimental tests. Directly assuming the identified constitutive parameters led to imprecise results. In detail, the pressure–volume curves from computational and experimental analyses showed similar stiffness values (as the curve slope in the quasi-linear region), but at different inflation conditions. The situation is typical in the field of soft tissue mechanics, because of unsuitable post-processing of data from mechanical tests at tissue level. In detail, the tensile response of soft biological tissues shows an initial toe region and a subsequent quasi-linear tract. Experimental results are usually post-processed by low-pass filtering procedures, aiming to remove force data that are below the load cell sensitivity. The operation fundamentally concerns data from the toe region, leading to move the zero stress condition of the specimen to an actually strained specimen length. It follows a reduction of the strain amplitude of the toe region and the subsequent shift of the high stiffness quasi-linear region to improper low strain conditions.

Aiming to actually interpret the mechanical response of the stomach, constitutive parameters have been updated. Different sets of parameters were evaluated by defining a grid around the basic set, according to a variational process by using multipliers mC and mα of groups of parameters, as initial stiffness Cr and non linearity αr parameters (r = 1,4,6), respectively. Each set of parameters was evaluated assuming the same multipliers for tissues from the different stomach regions and the different layers. With regard to each set, tensile loading conditions were simulated aiming to evaluate tissues tensile stiffness values in the quasi-linear region. Among all the sets of parameters, a sub-domain of multipliers mC and mα was identified, which provided stiffness values in the quasi-linear regions matching the experimental quasi-linear tracts. On the other side, the sets of the sub-domain provided different strain amplitudes of the toe regions. Computational analyses of stomach inflation were performed considering sets of parameters from the sub-domain. The final set of parameters (Table 1) was identified by comparing computational results with experimental data from inflation tests (Fig. 4c).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fontanella, C.G., Salmaso, C., Toniolo, I. et al. Computational Models for the Mechanical Investigation of Stomach Tissues and Structure. Ann Biomed Eng 47, 1237–1249 (2019). https://doi.org/10.1007/s10439-019-02229-w

Download citation

Keywords

  • Stomach mechanics
  • Experimental methods
  • Anisotropic constitutive formulation
  • Constitutive parameters
  • Computational biomechanics