Numerical simulations of the nonsymmetric growth and remodeling of arteries under axial twisting

Abstract

Blood vessels are often subjected to axial twisting during body movement or surgery. Sustained twisting may lead to blood vessel growth and remodeling, however, it remains unclear how the extracellular matrix in the blood vessels remodel under sustained axial twisting. This study aimed to develop a computational model to simulate stress-induced growth and remodeling (G&R) of thin-walled blood vessels under axial twisting. Cylindrical vessels were subjected to a step increase in axial torque while the axial stretch and lumen pressure remained constant. The vessel walls were modeled based on the constrained mixture theory given as microstructure-based discrete fiber families with isotropic matrix structure models. Simulation results demonstrated that in response to a constant twist angle loading, arterial wall thickness, mass, and twisting torque gradually increase towards a new steady state. However, the stress and mass decrease in one diagonal fiber family while increasing in the other diagonal fiber family before reaching plateaus. A novel finding was that the two helical collagen fiber families showed different growth rates and patterns during remodeling, driven by the different fiber stresses generated by the twisting, and led to non-symmetric material properties. This study sheds new light on arterial wall remodeling under axial twisting.

Keywords: Adaptation; Artery; Asymmetric; Fiber model; Mathematical model; Nonsymmetric; Remodeling; Torsion; Twisting.

Figure 1.

Schematic of artery deformation under axial twist and collagen fiber alignment.

Figure 2.

Deformation and stress in an artery under torsion. (a) change of torque as a function of twist angle, (b) change of radius with twist angle, (c) change of wall stress with twist angle. β=−α are the diagonal fiber directions while σθ and σζ are the stresses in the circumferential and axial directions, respectively. The lumen pressure was kept constant at 13.3 kPa and the axial stretch ratio was kept at 1.2.

Figure 3.

Adaptation of muscle and collagen fibers under torsion using 4-fiber model. (a) and (b): change in mass of muscle (Mm) and 4 collagen fiber families (M1, M2, M3, & M4) with growth time. (c) and (d): Changes of fiber stresses with time. The lumen pressure was kept constant at 13.3 kPa and the axial stretch ratio was kept at 1.2.

Figure 4.

Arterial wall remodeling under torsion using 4-fiber model. The changes of (a) torque, (b) axial tension, (c) total mass, and (d) wall thickness over time. The time is growth time without specific unit. The lumen pressure was kept constant at 13.3 kPa and the axial stretch ratio was kept at 1.2.

Figure 5.

Adaptation of muscle and collagen fibers under torsion using 2-fiber model. (a) Change mass of the two diagonal collagen fiber families (Mass3 and Mass4) with growth time. (b) Changes of fiber stresses with time. The lumen pressure was kept constant at 13.3 kPa and the axial stretch ratio was kept at 1.2.

Figure 6.

Arterial wall remodeling under torsion using 2-fiber model. The changes of (a) torque, (b) total mass, (c) wall thickness and (d) radius over time. The lumen pressure was kept constant at 13.3 kPa and the axial stretch ratio was kept at 1.2.