Computational Tools for the Reliability Assessment and the Engineering Design of Procedures and Devices in Bariatric Surgery

Abstract

Obesity is one of the main health concerns worldwide. Bariatric Surgery (BS) is the gold standard treatment for severe obesity. Nevertheless, unsatisfactory weight loss and complications can occur. The efficacy of BS is mainly defined on experiential bases; therefore, a more rational approach is required. The here reported activities aim to show the strength of experimental and computational biomechanics in evaluating stomach functionality depending on bariatric procedure. The experimental activities consisted in insufflation tests on samples of swine stomach to assess the pressure-volume behaviour both in pre- and post-surgical configurations. The investigation pertained to two main bariatric procedures: adjustable gastric banding (AGB) and laparoscopic sleeve gastrectomy (LSG). Subsequently, a computational model of the stomach was exploited to validate and to integrate results from experimental activities, as well as to broad the investigation to a wider scenario of surgical procedures and techniques. Furthermore, the computational approach allowed analysing stress and strain fields within stomach tissues because of food ingestion. Such fields elicit mechanical stimulation of gastric receptors, contributing to release satiety signals. Pressure-volume curves assessed stomach capacity and stiffness according to the surgical procedure. Both AGB and LSG proved to reduce stomach capacity and to increase stiffness, with markedly greater effect for LSG. At an internal pressure of 5 kPa, outcomes showed that in pre-surgical configuration the inflated volume was about 1000 mL, after AGB the inflated volume was slightly lower, while after LSG it fell significantly, reaching 100 mL. Computational modelling techniques showed the influence of bariatric intervention on mechanical stimulation of gastric receptors due to food ingestion. AGB markedly enhanced the mechanical stimulation within the fundus region, while LSG significantly reduced stress and strain intensities. Further computational investigations revealed the potentialities of hybrid endoscopic procedures to induce both reduction of stomach capacity and enhancement of gastric receptors mechanical stimulation. In conclusion, biomechanics proved to be useful for the investigation of BS effects. Future exploitations of the biomechanical methods may largely improve BS reliability, efficacy and penetration rate.

Appendices

Appendix 1

An anisotropic visco-hyperelastic formulation was exploited to characterize the mechanical behavior of stomach tissues, as fully reported by Fontanella et al.16 The model was based on the following relationship between the first Piola-Kirchhoff stress tensor P, the right Cauchy-Green strain tensor (c) and viscous variables qⁱ:

$$ \mathcal{P}\left( {\mathcal{C},{\mathbf{q}}^{i} } \right) = 2\mathcal{F}\frac{{\partial W^{0} \left( \mathcal{C} \right)}}{{\partial \mathcal{C}}} - \sum\limits_{i = 1}^{n} {{\mathbf{q}}^{i} } $$

(1)

where $W^{0}$ is an hyperelastic potential that specifies the instantaneous response of the tissue, while F is the deformation gradient. The evolution of viscous variables qⁱ was specified by standard differential equations:

$$ {\dot{\mathbf{q}}}^{i} + \frac{1}{{\tau^{i} }}{\mathbf{q}}^{i} = \frac{{\gamma^{i} }}{{\tau^{i} }}{\mathbf{P}}^{0} $$

(2)

relaxation time $\tau^{i}$ evaluates the time the ith viscous process requires to develop. Relative stiffness parameter $\gamma^{i}$ specifies the contribution of the ith viscous process to the stress drop the material undergoes because of relaxation phenomena.

The fiber-reinforced configuration of both connective stratum and muscularis externa suggested to define the strain energy function by means of contributions from an isotropic ground matrix, as $W_{m}^{0}$, and from fibers, as $W_{f}^{0}$:

$$ W^{0} \left( {\mathbf{C}} \right) = W_{m}^{0} \left( {\mathbf{C}} \right) + W_{f}^{0} \left( {{\mathbf{C}},{\mathbf{a}}_{0} ,{\mathbf{b}}_{0} } \right) $$

(3)

$$ W_{m}^{0} \left( {\mathbf{C}} \right) = - p\left( {I_{3}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} - 1} \right) + \left[ {{{C_{1} } \mathord{\left/ {\vphantom {{C_{1} } {\alpha_{1} }}} \right. \kern-0pt} {\alpha_{1} }}} \right]\left\{ {\exp \left[ {\alpha_{1} \left( {I_{1} - 3} \right)} \right] - 1} \right\} $$

(4)

$$ W_{f}^{0} \left( {{\mathbf{C}},{\mathbf{a}}_{0} ,{\mathbf{b}}_{0} } \right) = \frac{{C_{4} }}{{\alpha_{4}^{2} }}\left\{ {\exp \left[ {\alpha_{4} \left( {I_{4} - 1} \right)} \right] - \alpha_{4} \left( {I_{4} - 1} \right) - 1} \right\} + \frac{{C_{6} }}{{\alpha_{6}^{2} }}\left\{ {\exp \left[ {\alpha_{6} \left( {I_{6} - 1} \right)} \right] - \alpha_{6} \left( {I_{6} - 1} \right) - 1} \right\} $$

(5)

where $I_{1}$ and $I_{3}$ are the first and the third invariants of the right Cauchy-Green strain tensor, ${\mathbf{a}}_{0}$ and ${\mathbf{b}}_{0}$ define the orientation of collagen (within the connective stratum) or muscular (within the muscularis externa) fibers, while $I_{4}$ and $I_{6}$ are structural invariants that specify the square of tissue stretch along directions ${\mathbf{a}}_{0}$ and ${\mathbf{b}}_{0}$, respectively. The term p is a Lagrange multiplier that ensures the incompressibility constraint. Constitutive parameter $C_{1}$ specifies the tissue initial shear stiffness, while parameter $\alpha_{1}$ regulates the non-linearity of the shear response. Parameters $C_{4}$ and $C_{6}$ are constants that define the fibers initial stiffness, while $\alpha_{4}$ and $\alpha_{6}$ depend on fibers stiffening with stretch.

Appendix 2

Figure 9 shows rough experimental points that were obtained from the experimentations on the ten swine stomachs (six AGB and four LSG). Each curve was composed of the data at the relaxation points (the pressure values at the end of the rest period of 600 s). Although samples were taken from similar animals, morphometry and stiffness were necessarily slightly different, leading to a high rate of scatter, which is typical in biological tissues and structures mechanics.

Figure 9

Experimental rough data for pre-surgical and AGB configurations (a), and for LSG products (b).