Biomathematical models of @entity438 can provide qualitative and quantitative information on stages of @entity439 development through elucidation of biophysical interactions and phenomena. However, most current @entity439 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 @entity439 , with subsequent applications to clinical data. A constitutive model of an @entity439 , based on experimental data of tissue specimens available in the literature, was incorporated into a time-dependent set of equations describing the dynamic behavior of a saccular @entity439 in response to pulsatile blood flow. The set of differential equations was solved numerically, yielding mathematical expressions for @entity439 radius and pressure. This model was applied to clinical data obtained from 24 @entity1 presenting with @entity1756 . @entity439 development and eventual @entity397 exhibited an inverse relationship between @entity439 size and blood pressure. In general, the model revealed that @entity397 becomes highly probable for an @entity439 diameter greater than 2.0 mm and a systemic blood pressure greater than 125 mmHg. However, an interesting observation was that the critical pressure demonstrated a minimal sensitivity to the critical radius, substantiating similar clinical and experimental observations that blood pressure was not correlated, to any degree, with @entity1756 . Undulations in the @entity439 wall, presented by irregular multilobulated morphologies, could play an important role in @entity1756 . However, due to the large variation in results, more extensive studies will be necessary for further evaluation and validation of this model.

A nonlinear quasi-static model of XXXX .

@entity1 :: ('9606', 'Species') :: ['patients'] @entity438 :: ('MESH:D002532', 'Disease') :: ['intracranial aneurysms'] @entity439 :: ('MESH:D000783', 'Disease') :: ['Aneurysm', 'aneurysm'] @entity397 :: ('MESH:D012421', 'Disease') :: ['rupture'] @entity1756 :: ('MESH:D017542', 'Disease') :: ['ruptured aneurysms', 'aneurysm rupture']
@entity438 :: (MESH:D002532,Disease) :: ['intracranial aneurysms']
