Derivation of the Laplace's law correction coefficient for arterial stress evaluation

Understanding of mechanical behavior of human arteries is in the centre of attention of many researchers. It is crucial in medical treatment improvement especially in the intracranial surgery. Consequently, a number of ex vivo experiments was described, and mathematical models of different degree of complexity was formulated in literature. Despite all these efforts, frequently a very simple Laplace formula is used to calculate values of circumferential stresses in arterial wall. Nevertheless, in some cases this formula is over exploit, as the main assumptions lying at its base are not fulfilled (like the thin cylinder assumption and wall homogeneousness). On the other hand, even in cases where using Laplace law is justified we are faced with a problem with arterial compliance and nonlinear material behavior that are not involved in the formula. To solve this problem we introduced deformations of thin cylinder as well as exponential stress-strain material characteristic and modified Laplace law. As a result we obtained still simple, but novel analytical formula. The proposed model was used for calculation of adventitia's rupture stress from ex vivo experiments. Obtained results were compared with the original Laplace equation and the numerical simulations.