Development Of A Mathematical Model To Assist In Assessing Risk Associated With Abdominal Aortic Aneuryms (AAA).
Douglas L. Wooster, MD, Elizabeth M. Wooster, M.Ed., PhD Candidate, Yuang Chen, MD candidate.
Univ of Toronto, Toronto, ON, Canada.
Objectives: The objectives of this study were to develop and refine a mathematical model that would assist in the assessment of the risk associated with abdominal aortic aneurysms. Methods: Data was retrospectively collected from patients who presented at a vascular ultrasound clinic for aortic ultrasound. Data was collected irrespective of findings of aortic ultrasound. Patients were excluded from data set collection if there was a prior history of intervention or unusual aortic findings. Demographics collected included: age, sec, hypertension, smoking, diabetes, dyslipidemia, family history, alcoholism, and history of atherosclerosis. Data was used to develop, refine and beta test the mathematical model. Results: Data was collected from 110 patients. Data from the first 50 patients was used to develop the following mathematical model: 0.5Te0/Et0 + Te1/Et1+ 2Te2/Et2 + 8Te3/Et3 + R, where Te = Total expansion in aneurysm diameter experienced by the patient at a given diametre interval; Et = Total time elapsed in months between clinical tests for a given interval of aneurysm diameter Te0;Et0 = expansion and time for aneurysm size 2.5cm - 3cm aneurysm diameter Te1;Et1 = expansion and time for aneurysm size 3cm - 4cm aneurysm diameter Te2;Et2 = expansion and time for aneurysm size 4cm - 5cm aneurysm diameter Te3;Et3 = expansion and time for the aneurysm size 5cm+ aneurysm diameter R = The number of relevant risk factors The data from the remaining 60 patients was used to beta test and refine the formula. The beta test was conducted by comparing the resulting score to clinical results of continued follow up and natural course of the disease. The resulting score from the mathematical model may be used to stratify patients within risk categories and result in recommended follow up and treatment. Scores are as follows: 0 - 1.5 low risk, 1.5 - 4 moderate risk, 4 and higher high risk. Conclusions: Multiple factors relate to expansion rates of AAA. A ‘standard’ or ‘expected’ expansion rate of 3 to 5 mm may oversimplify the natural history of AAA. Expansion rates are used to define surveillance protocols and are considered as triggers for intervention. The postulated mathematical model may help redefine these strategies and serve to inform artificial intelligence algorithms.
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