Question 3.4: Modeling a saccular aneurysm as a thin-walled sphere, assume...

Given P=120 mmHg\cong 16,000N/m^{2},  where 1 mmHg\cong 133.32N/m^{2},a=2.5    mm=2.5\times 10^{-3}  m,   and    h=15   \mu m=15\times 10^{-6}  m,  we have,  by Eq. (3.58),

                                    \sigma _{\theta \theta }=\frac{Pa^{2}}{2ah+h^{2}}\rightarrow \sigma _{\theta \theta }=\frac{Pa}{2h}=\sigma _{\phi \phi }.                                (3.58)

which, albeit less than the critical stress, is of the same order of magnitude. The factor of safety in prediction is thus only \sim4. Given the 50 % mortality rate associated with rupture and the sparseness of data on the mechanical behavior of saccular aneurysms, this may not be a sufficient factor of safety—one may well prefer a factor of at least 10. Note, therefore, that if the same size lesion were 60 μm in thickness rather than 15 μm, the stress decreases proportionately to 0.33 MPa, which is an order of magnitude less than the stated failure stress. In this case, because of the morbidity associated with such delicate neurosurgery (Humphrey 2002), one may feel that such a lesion could simply be monitored over time rather than surgically treated right away. In this simple example, therefore, we see the potential utility of biomechanical analyses in surgical planning, the importance of high-resolution medical imaging (to resolve between 15- and 60-μm-thick lesions),  and  perhaps,  most   importantly,  the  need  for  better  data  and  theories  for  studying saccular aneurysms (Humphrey 2002).