A NONLINEAR QUASI-STATIC MODEL OF INTRACRANIAL ANEURYSMS

Biomathematical models of intracranial aneurysms can provide qualitati ve and quantitative information on stages of aneurysm development thro ugh elucidation of biophysical interactions and phenomena. However, mo st current aneurysm models, based on Laplace's law, are renditions of static, linearly elastic spheres. The primary goal of this study is to : 1. develop a nonlinear constitutive quasi-static model and 2. derive an expression for the critical size/pressure of an aneurysm, with sub sequent applications to clinical data. A constitutive model of an aneu rysm, based on experimental data of tissue specimens available in the literature, was incorporated into a time-dependent set of equations de scribing the dynamic behavior of a saccular aneurysm in response to pu lsatile blood flow. The set of differential equations was solved numer ically, yielding mathematical expressions for aneurysm radius and pres sure. This model was applied to clinical data obtained from 24 patient s presenting with ruptured aneurysms. Aneurysm development and eventua l rupture exhibited an inverse relationship between aneurysm size and blood pressure. In general, the model revealed that rupture becomes hi ghly probable for an aneurysm diameter greater than 2.0mm and a system ic blood pressure greater than 125mmHg. However, an interesting observ ation was that the critical pressure demonstrated a minimal sensitivit y to the critical radius, substantiating similar clinical and experime ntal observations that blood pressure was not correlated, to any degre e, with aneurysm rupture. Undulations in the aneurysm wall, presented by irregular multilobulated morphologies, could play an important role in aneurysm rupture. However, due to the large variation in results, more extensive studies will be necessary for further evaluation and va lidation of this model.