© 2020 Institute of Physics Publishing. All rights reserved. Objective: To investigate the diameter and flow rate of aortic arch arteries, their post-operative changes, and relationship in patients undergoing thoracic endovascular repair (TEVAR). Approach: Patient-specific diameters and flow rates were collected in common carotid (CCA), subclavian (SA), and vertebral (VA) arteries using duplex ultrasound pre-operatively and up to post-operative 6 months. Main results: For either diameter or flow rate of CCA, SA, and VA, there was no significant difference between the left and right sides for the 12 patients (age 64 } 12 years, mean } SD). The diameters of CCA, SA, and VA did not change over time and the average diameters of all measures were 7.4 } 1.0, 7.3 } 1.0, and 3.9 } 1.9 mm, respectively. The CCA and VA flow rates did not change over time and averaged 494 } 142 and 100 } 56 ml min-1, respectively, while the SA flow rates were 147 } 80, 230 } 104, 136 } 73, and 116 } 55 ml min-1 at pre-operative, post-operative 1 week, 1 months, 6 months, with a decrease from 1 week to 6 months (P = .017). The total flow rate of all branches decreased at 6 months compared to 1 week (P = .020). The CCA, SA, and VA best diameter-flow rate relationships showed power values of 1.6 (R2 = 0.51), 1.8 (R2 = 0.20), and 2.4 (R2 = 0.60), respectively. Excluding the SA, a strong quadratic diameter-flow rate relationship was observed for the CCA and VA combined (Q = 8.5*D2, R2 = 0.87). Significance: There is a strong quadratic relationship between diameters and flow rates for the CCA and VA, but not SA. Our study provides reference diameter and flow rate boundary condition data of aortic arch arteries for computational modeling of patients undergoing TEVAR procedures.