Validation of a Power Law Model in Upper Extremity Vessels: Potential Application in Ultrasound Bleed Detection

Vascular ultrasound can provide quick and reliable diagnosis of arterial bleeding but it requires trained and experienced personnel. Development of automated sonographic bleed detection methods would potentially be valuable for trauma management in the field. We propose a detection method that (1) measures blood flow in a trauma victim, (2) determines the victim's expected normal limb arterial flow using a power law biofluid model where flow is proportional to the vessel diameter taken to a power of k and (3) quantifies the difference between measured and expected flow with a novel metric, flow split deviation (FSD). FSD was devised to give a quantitative value for the likelihood of arterial bleeding and validated in human upper extremities. We used ultrasound to demonstrate that the power law with k = 2.75 appropriately described the normal brachial artery bifurcation geometry and adequately determined the expected normal flows. Our metric was then applied to three-dimensional (3-D) computational models of forearm bleeding and on dialysis patients undergoing surgical construction of wrist arteriovenous fistulas. Computational models showed that larger sized arterial defects produced larger flow deviations. FSD values were statistically higher (paired t-test) for arms with fistulas than those without, with average FSDs of 0.41 ± 0.12 and 0.047 ± 0.021 (mean ± SD), respectively. The average of the differences was 0.36 ± 0.12 (mean ± SD).