Mathematical explanation of the buckling of the vessels after twisting of the microanastomosis

Abstract

To obtain free flap success, microvascular anastomosis must be perfectly constructed. External compression, twisting (torsion) of the anastomosis site, tension on the anastomosis site, and kinking of the pedicle must be avoided. Few experimental studies report the patency rates of rat vessels after twisting (torsion) of the microanastomosis: these results recently opened a discussion for the maximal angle of torsion, which can be impressed to a vessel in order to have the best patency rates. To describe specifically the changing of shape of the vessels after the twisting of the microanastomosis, we extrapolate, to our experimental model (constituted by the femoral vessels of Wistar rats), the mathematical formula that engineers use to calculate the torsion of a beam when a torsion force is applied. The mathematical model used is the shell theory. Then, with a computer program using MATLAB, we could obtain the representation of these shapes at any degree of torsion. If a small load is applied to the vessels, it maintains its straight geometry. However, as soon as the load exceeds a critical value, which is a function of the vessel geometry and its mechanical characteristics, it snaps suddenly to a different equilibrium configuration. This phenomenon is called "buckling." When buckling occurs, wave-like deformations appear on the wall of the vessels. We calculate, in our experimental rat model, the critical twisting angle that induces buckling: maintaining a constant length of dissection of 25 mm, a minimum twisting angle of 360 degrees + 161 degrees, or 105 degrees, is required, respectively, for the femoral artery or vein, to have the buckling phenomenon and the appearance of two waves and decreased section area. In surgical practice, with the parameters of our experimental Wistar rats model (vessel diameter, length of dissection), it is fundamental to be below 105 degrees of torsion angle for the vein microanastomosis, in order to decrease its risk of failure.