Absolute diameter measurements of coronary arteries based on the first zero crossing of the Fourier spectrum.

Current edge detection methods used to determine coronary artery dimensions from digital (DSA) images suffer a strong dependence on the system's modulation transfer function (MTF). The videodensitometric algorithms are less sensitive to MTF blurring, yet still result in an overestimation of the vessel size of 10% to 25% for blurring aperture sizes of 50% to 80% of the vessel diameter. We propose a new algorithm to measure the absolute diameter of a vessel which has a lower sensitivity to the system MTF for blurring aperture sizes up to 80% of the vessel diameter. A consequence of the similarity theorem of Fourier transform pairs is that the "width" of the Fourier transform, as characterized by the first zero crossing in frequency space, is inversely proportional to the width of the vessel profile. For an ideal (unblurred) vessel image, the width of the vessel profile is equal to the diameter of the vessel. For a blurred image this is not true. In frequency space, however, the transform of the blurred profile is simply the product of the transformed ideal profile and the system MTF. Thus, if the blurring aperture of the system is below some critical value, the first zero of the unblurred profile will still dominate the transform of the blurred profile. For vessels of circular cross section and a rectangular blurring aperture, this critical aperture size is approximately 80% of the vessel diameter. A more detailed explanation of the theory and calculations involved in this measurement, along with measurements of computer simulated and phantom vessels is presented.