The Measurement of Blood Flow from Dynamic Digital X-Ray Images Using a Weighted Optical Flow Algorithm: Validation in a Moving-Vessel Flow Phantom Kawal Rhode a , Gareth Ennew a , Tryphon Lambrou a , David Hawkes a , and Alexander Seifalian b a Division of Radiological Sciences and Medical Engineering, Guy's, King's and St. Thomas' Hospitals Medical School, Guy's Hospital, London, U.K., SE1 9RT b University Department of Surgery, Royal Free and University College Medical School, The Royal Free Hospital, Pond Street, London, U.K., NW3 2QG Abstract. We have developed an algorithm based on optical flow for the extraction of flow waveforms from dynamic digital x-ray images. The aim of this study was to extend the validation of this technique to blood flow measurement in moving vessels. A pulsatile blood flow circuit was constructed to simulate the human arterial circulation using a length of silicone tubing as a model artery. A computer-programmable manipulator was used to move the model artery. Instantaneous recording of flow from an electromagnetic flow meter (EMF) provided the “gold standard” measurement. Dynamic biplane x-ray images with injection of iodine contrast medium were acquired for different flow rates. The image data were formed into parametric images in which grey level represents contrast medium concentration as a function of time and distance along the vessel. The blood flow velocities were calculated as the ratio of temporal and spatial derivatives in the parametric image and then averaged along the vessel length using a weighting scheme based on the magnitude of the spatial derivative. The correlation coefficient between x-ray and EMF measurements was 0.922 (p<0.001) for instantaneous flows and 0.891 (p<0.001) for average flows. The mean difference (X-ray - EMF) was –15.8 ml/min for instantaneous flows and 0.3 ml/min for average flows. 1 Introduction Many vascular procedures, such as coronary angioplasty and the treatment of cerebral aneurysms, are performed under x-ray guidance. It is of interest to ascertain the haemodynamic effect of such procedures both intra- operatively and post-operatively. Detecting changes in the haemodynamic function may influence treatment or demonstrate the effectiveness of treatment. Interpretation of angiographic images is still largely subjective and the quantitative information that can be derived from these images is not commonly used. We have developed techniques to measure blood flow from a dynamic series of angiograms following injection of iodine contrast material (1,2) . Such images are commonly acquired during x-ray guided surgery and diagnostic angiography. A group of techniques based on optical flow have demonstrated promising results for angiographic blood flow measurement (3-5) . One of the inherent problems with these techniques is the error that arises when the spatial derivative of the signal becomes small. We have developed an algorithm based on optical flow and overcome the latter problem using a weighted average based on the magnitude of the spatial derivative. We have previously validated this technique in a stationary vessel phantom and now extend this validation to a moving vessel phantom. 2 Method Figure 1 shows a schematic of the physiological blood flow circuit used to simulate pulsatile blood flow in the human circulation. A 15 cm section of silicone tubing was used to simulate a blood vessel. Date-expired whole blood was obtained and used as the circulated fluid. Pulsatile flow was generated using a pulsatile syringe pump (Pulsatile Blood Pump 1405, Harvard Apparatus). This allowed adjustment of mean flow rate by two means: (1) by altering the pumping frequency; (2) by altering the stroke volume. A 6mm calibre electromagnetic flow meter (Electromagnetic Blood Flow Sensor / Electromagnetic Blood Flow and Velocity Meter, Skalar) was placed downstream from the simulated blood vessel. This provided outputs of instantaneous and mean flow rate. These were recorded using an analogue recording system (MacLab 8s, AD Instruments) that was interfaced to a Macintosh notebook. The EMF provided the gold standard measurement of flow rate and our x-ray technique was validated by correlating x-ray measurements with those made independently by the EMF. The pressure in the circuit was monitored using a pressure transducer connected to the MacLab. Physiological pressures were maintained by varying the height of the fluid reservoir. A 4-F catheter was inserted just upstream from the blood vessel to allow injection of iodine-based contrast medium using a 10 ml syringe. Figure 2 shows the programmable vessel manipulator that simulated vessel motion such as that seen in the coronary arteries during the cardiac cycle. This consisted of a geared d.c. electric motor driving a caddy on a linear axis. The motor speed