Computational simulations of the helical buckling behavior of blood vessels

Abstract

Tortuous vessels are often observed in vivo and could hinder or even disrupt blood flow to distal organs. Besides genetic and biological factors, the in vivo mechanical loading seems to play a role in the formation of tortuous vessels, but the mechanism for formation of helical vessel shape remains unclear. Accordingly, the aim of this study was to investigate the biomechanical loads that trigger the occurrence of helical buckling in blood vessels using finite element analysis. Porcine carotid arteries were modeled as thick-walled cylindrical tubes using generalized Fung and Holzapfel-Gasser-Ogden constitutive models. Physiological loadings, including axial tension, lumen pressure, and axial torque, were applied. Simulations of various geometric dimensions, different constitutive models and at various levels of axial stretch ratios, lumen pressures, and twist angles were performed to identify the mechanical factors that determine the helical stability. Our results demonstrated that axial torsion can cause wringing (twist buckling) that leads to kinking or helical coiling and even looping and winding. The specific buckling patterns depend on the combination of lumen pressure, axial torque, axial tension, and the dimensions of the vessels. This study elucidates the mechanism of how blood vessels buckle under various mechanical loads and how complex mechanical loads yield helical buckling.

Keywords: artery; finite element analysis; kinking; mechanical instability; tortuosity; wringing.

Fig. 1

Comparison of torque versus rotation angle curves generated by the Fung model, HGO model and experimental data for five porcine carotid arteries under an axial stretch ratio of 1.3 and a lumen pressure of 20 mmHg. The curves are truncated at the critical buckling torque, the point with a sharp drop in the value of axial torque.

Fig. 2

Buckling behavior of arteries and definition of the various buckling patterns (curving, wringing, kinking, helical coiling, looping, and winding). Each artery was first axially stretched, pressurized and then axially twisted. (A) artery 1 (HGO model): (a) curving (bent buckling), (b) post-bent buckling (in-plane) at higher lumen pressure (75 mmHg), (c) helical buckling (out-of-plane) at a critical rotation angle (36 degrees), (d) looping and (e) winding occurred under increasing rotation angle (shown at smaller scale). (B) Artery 5 (HGO model): (a) wringing (at a rotation angle of 18 degrees), (b-c) helical buckling (at a critical rotation angle of 42 degrees and higher), (d) looping and (e) winding under increasing rotation angle (shown at smaller scale). (C) Artery 2 (Fung model): (a) wringing (twist buckling), (b-c) kinking under increasing rotation angle.

Fig. 3

The impact of vessel length (L/3, 2L/3, L) and axial tension: (a) 1.1, (b) 1.3, (c) 1.5, (d) 1.7 on helical buckling behavior of an artery at a constant lumen pressure (20 mmHg) and critical axial torque (Artery 2, Fung model).

Fig. 4

Comparison of (a) critical twist angle (normalized to stretched vessel length) and (b) critical torque plotted as functions of axial stretch (Artery 2, Fung model) at three different vessel lengths under a lumen pressure of 20 mmHg. Diamond symbols are the experimental measurements of artery 2 (mean ± SD of repeated measurements) [13].

Fig. 5

The effect of wall thickness to lumen radius ratio on helical buckling behavior at a constant lumen pressure of 20 mmHg (Artery 2, Fung model). SR = axial stretch ratio.

Fig. 6

The effect of shear constant (b₇) in the Fung model on the critical buckling loads in five porcine carotid arteries (see Table 1): (a) twist buckling torque at a stretch ratio of 1.1 and a lumen pressure of 20 mmHg (artery 4 was not included since its FEA failed to converge at the specified loading conditions with the material parameters given in Table 2), (b) bent buckling pressure at a stretch ratio of 1.1. The parameter b₇ was increased while keeping other material constants unchanged.

Fig. 7

Summary of wringing, kinking, helical coiling, looping, and winding patterns as results of various lumen pressures, axial torques, and axial tensions based on simulation results of the 5 arteries. All 5 arteries demonstrated similar artery buckling patterns (see text for details) but the magnitude of the critical buckling loads were different due to their different material properties and dimensions (SRtr = transition stretch ratio).

Fig. 8

Variations of axial torque and the vessel configurations with rotation angle in an artery (artery 1, HGO model) at a lumen pressure of 75 mmHg and an axial stretch ratio of 1.3. The artery buckled initially under lumen pressure (40 mmHg). (a-f) deformations with increasing twist angle at a constant lumen pressure. The maximum principal stress is color-coded.

Fig. 9

Photographs of porcine carotid arteries demonstrating (a) wringing, (b) kinking (at high stretch ratios ≥1.5), (c-d) helical coiling and looping (at low stretch ratios ≤1.3) pattern under combined mechanical loads. All arteries were under a lumen pressure less than the critical (bent) buckling pressure.

Fig. 10

Comparison of torque versus rotation angle curves from experimental measurements [13] and computational simulations. (a) Artery 5 (HGO model): (1) wringing and (2) kinking, under an axial stretch ratio of 1.5 and a lumen pressure of 40 mmHg. (b) Artery 5 (HGO model): (1) helical buckling, (2) looping, and (3) winding, under an axial stretch ratio of 1.3 and a lumen pressure of 40 mmHg.