Quantification of operative benefit for unruptured cerebral aneurysms: a theoretical approach

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Abstract
The indications for surgery on unruptured asymptomatic cerebral aneurysms are still unclear. In this report, the authors use mathematical methods to attempt to quantify the benefit of surgery for unruptured aneurysms. Theoretical survival curves for either operative or conservative treatment were obtained by solving differential equations on the survival rate of a patient harboring an unruptured aneurysm. Patients' life expectancies were calculated as areas under these curves, and operative benefit was quantified as a gain in average life expectancy. To analyze morbidity, two concepts were introduced: premorbid survival rate and average premorbid survival period, and the operative gain of average premorbid survival period was calculated under certain assumptions. Larger operative benefit was observed in younger patients, with increasingly less benefit in the elderly. The operative gain of average life expectancy was 3.9 years for a 40-year-old patient, 2.4 years for 50, 1.3 years for 60, and 0.6 years for a 70-year-old. Quantified operative benefit is presented in a table for various patient ages, yearly rupture rates, and expected operative morbidity and mortality. This mathematical method would be useful to both surgeons and patients in making their decisions on surgery.