Neuroangiographic assessment of aneurysm stability and impending rupture based on a non-linear biomathematical model

The probability or risk of aneurysm rupture is assessed using conventional angiography by applying the aneurysm radius and systolic blood pressure obtained at examination to a non-linear biomathematical model of an aneurysm. A non-linear biomathematical model was developed based on Laplace's law to represent the viscoelastic relation between the wall tension and the radius. A differential expression of this relation was used to derive the critical radius: Rc = [2Et/P]2At/P where E is the elastic modulus of the aneurysm, t is the wall thickness, P is the pressure, and A is the elastic modulus of collagen. Using average values of E, A, and t, the risk of aneurysm rupture is defined as the area of integration under the curve defined by the minimum value of pressure (50 mmHg) and the patient pressure recorded at examination. This area was normalized by the area of integration defined by the pressure limits: 50 to 300 mmHg. This method of risk assessment was applied to four previously published case studies of patients with documented aneurysm rupture in which both the aneurysm size at rupture and the patient systolic blood pressure were reported. Two additional parameters were calculated to further evaluate aneurysm stability: (1) a ratio given as (Rexp/Rth) where Rexp is the radius of aneurysm rupture measured from angiography and Rth is the critical radius based on the model; and (2) chi 2 analysis defined by chi 2 = (O - E)2/E where O and E are the observed (Rexp) and expected (Rth) variables, respectively. The average systolic blood pressure and radius of aneurysm rupture was 147.2 mmHg and 3.95 mm, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)