Suture Line Response of End-to-Side Anastomosis: A Stress Concentration Methodology

Abstract

End-to-side vascular anastomosis has a considerable complexity regarding the suturing of the juncture line between the artery and the graft. The present study proposes a stress–concentration methodology for the prediction of the stress distribution at the juncture line, aiming to provide generic expressions describing the response of an end-to-side anastomosis. The proposed methodology is based on general results obtained from the analysis of pipe connections, a topic that has been investigated in recent years in the field of offshore structural engineering. A key aspect for implementing the stress–concentration–factor approach is the recognition that the axial load due to pressure and flow dynamics exerted along the graft axis controls the “hot spots” on the juncture line, which in turn affects the mechanical response of the sutures. Several parameters, identified to influence the suture line response, are introduced in closed-form expressions for the suture line response calculations. The obtained results compare favorably with finite element results published in the literature. The proposed model predicts analytically the suture line response of end-to-side anastomosis, while capturing the influence of and interdependence among the problem parameters. Lower values of the graft radius, the distance between sequential stitches, and the intersecting angle between the artery and the graft are some of the key parameters that reduce the suture line response. The findings of this study are broad in scope and potentially applicable to improving the end-to-side anastomosis technique through improved functionality of the sutures and optimal selection of materials and anastomosis angle.

Appendix A

By utilizing Bernoulli’s momentum and continuity equation (Q ₁ = Q ₂ + Q ₃), the far-field forces along the z and x directions may be simplified as follows12:

$$ R_{z} = \cos \theta \left[ {\frac{{\rho Q_{1}^{2} }}{{2A_{1} }}\left( {\frac{{k_{1}^{2} }}{{k_{2} }} + k_{2} } \right) + k_{2} A_{1} p_{1} } \right] + \frac{{\rho Q_{1}^{2} }}{{2A_{1} }}k_{1} \left( {k_{1} - 2} \right) $$

(20)

$$ R_{x} = \sin \theta \left[ {\frac{{\rho Q_{1}^{2} }}{{2A_{1} }}\left( {\frac{{k_{1}^{2} }}{{k_{2} }} + k_{2} } \right) + k_{2} A_{1} p_{1} } \right] $$

(21)

in which k ₁ = Q ₂/Q ₁, k ₂ = A ₂/A ₁ and ρ denotes the density of the blood. The tensile far-field force in the direction of the graft is

$$ R_{\theta } = \frac{{\rho Q_{1}^{2} }}{{2A_{1} }}\left( {\frac{{k_{1}^{2} }}{{k_{2} }} + k_{2} } \right) + k_{2} A_{1} p_{1} + \frac{{\rho Q_{1}^{2} }}{{2A_{1} }}k_{1} \left( {k_{1} - 2} \right)\cos \theta $$

(22)

On normalizing the tensile far-field force in the direction of the graft by ρQ ²₁ /2A ₁, Eq. (22) takes the form

$$ \frac{{R_{\theta } }}{{\frac{{\rho Q_{1}^{2} }}{{2A_{1} }}}} = \frac{{k_{1}^{2} }}{{k_{2} }} + k_{2} + k_{2} \frac{{2A_{1}^{2} p_{1} }}{{\rho Q_{1}^{2} }} + k_{1} \left( {k_{1} - 2} \right)\cos \theta $$

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The dimensionless ratio k ₁ typically varies between 0 and 1, and the dimensionless ratio k ₂ varies between 0.2 and 1. For large- and medium-size arteries under pressure, the expression 2A ²₁ p ₁/ρQ ²₁ typically varies between 340 and 3400. Therefore, R _θ can be approximated by

$$ R_{\theta } \approx A_{2} p_{1} $$

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In the case of veins, in which the blood pressure is low, R _θ may be approximated by

$$ R_{\theta } \approx \frac{{\rho Q_{1}^{2} }}{{2A_{1} }}\left[ {\frac{{k_{1}^{2} }}{{k_{2} }} + k_{2} + k_{1} \left( {k_{1} - 2} \right)\cos \theta } \right] $$

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