NEUROANGIOGRAPHIC ASSESSMENT OF ANEURYSM STABILITY AND IMPENDING RUPTURE BASED ON A NONLINEAR BIOMATHEMATICAL MODEL

The probability or risk of aneurysm rupture is assessed using conventi onal angiography by applying the aneurysm radius and systolic blood pr essure obtained at examination to a non-linear biomathematical model o i an aneurysm. A non-linear biomathematical model was developed based on Laplace's law to represent the viscoelastic relation between the wa ll tension and the radius. A differential expression of this relation was used to derive the critical radius: R(c)=[2Et/P](2At/P) where E is the elastic modulus of the aneurysm, t is the wall thickness, P is th e pressure, and A is the elastic modulus of collagen. Using average va lues pi E, A, and t, the risk of aneurysm rupture is defined as the ar ea oi integration under the curve defined by the minimum value of pres sure (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 an eurysm rupture in which both the aneurysm size at rupture and the pati ent systolic blood pressure were reported. Two additional parameters w ere calculated to further evaluate aneurysm stability: (1) a ratio giv en as (R(exp)/R(th)) where R(exp) is the radius of aneurysm rupture me asured from angiography and R(th) 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 (R(exp)) and expected (R(th)) variables, respec tively. The average systolic blood pressure and radius of aneurysm rup ture was 147.2 mmHg and 3.95 mm, respectively. The corresponding avera ge of the theoretically determined critical radius was 5.15 mm, yieldi ng a ratio of 0.79. Risk of rupture varied from 0.45 to 0.59 with an a verage of 0.49. chi(2) values were representative of the excellent agr eement between the two radii with only one case greater than 7.0. The application of a biomathematical model for the quantitative assessment of aneurysm stability and risk of rupture is easy to implement, can b e applied on a patient-by-patient basis and confirms clinical observat ions that aneurysm rupture is always probable regardless of size and b ecomes more likely for hypertensive individuals. This method of risk a ssessment could serve an instrumental role in the management of unrupt ured intracranial saccular aneurysms and in the selection and assessme nt of therapy.