Quantitative coronary arteriography: improving catheter calibration by an efficient correction for differential magnification

Abstract

Differential magnification of the vessel and of the scaling catheter in the X-ray field causes signGCant errors in calibration of imaged vessel size. To correct for differential magnification properly, laborous and costly calculations are required. We derived the equations of accurate correction for differential magnification. Starting from these equations we reduced the correction effort to the acquisition of a second complementary angiogram and two digitizing operations.The validation of this approximate procedure in computer simulations and in vitro phantom studies showed a correction for differential magnification up to 85 %. IntroductionIn quantitative coronary arteriography (QCA) the lumen size of a coronary segment is commonly calculated from its imaged size using the coronary catheter as a scaling device. Due to different spatial location along the illuminating x-ray beam (out-of-plane) a differential magnification (DM) of lesion and catheter occurs, thus yielding to falsified measurement of vessel dimensions [ Fig. 11. To correct for DM, the out-of-plane can be calculated from its projection in a complementary view. Using the angiographic projection parameters of the view chosen for catheter calibration the resulting DM is computable and can be considered in the calibration factor.The accurate correction for DM requires tedious calculations, biplane angiography (simultaneously or sequentially taken) and measurement devices for gantry settings. To make correction for DM practicable the accurate correction has to be simplified in order to achieve a compromise between effort and remaining calibration error. Since the precise formulas for DM-correction have not been published yet, it is difficult to perform such an optimization in a comprehensible manner. In both basic publications describing out-of-plane ,2] approximate corrections for DM were proposed. These proposals are hard to verify without any knowledge of accurate correction formulas for DM. Fig. 1: Scheme of out-of-plane error in catheter calibration. The vessel is "out-of-plane'' closer to the xray tube than the scaling catheter. Consequently the catheter is smaller imaged than the vessel according to differential magnification DM = (out-of-plane)/fii. Since the absolute vessel size is calculated from the equation vabs =(CnOm/(C + AC))*V, the vessel size is overestimated. See grey shadowed parts of the figure illustrating the correct calibration. vabs = (Cnom/C)*V instead of This paper deals with the description of accurate correction equations for DM. Using these we derived several procedures of approximate correction and evaluated their performance in phantom measurements. I C a t h e t e V fii Methods TheoryWe derived formulas for the accurate correction for DM assuming perpendicular angiograms and estimated the required effort. Subsequently the measurement, acquisition and analysis effort was reduced stepwise by the following simplifications: 0276-6547195 $4.00 0 1995 IEEE 553 Computers iu Cardioiogy 1995