An Asymptotically Correct Mean Recovery Coefficient Equation for Both Small and Large Objects of Arbitrary Shape

Mean recovery coefficients (RC) in nuclear medicine are an important tool for partial volume correction in quantitative imaging, phantom studies and dosimetry. For sphere and cubes theoretical equations are known. The asymptotically correct equations for small objects and large objects of arbitrary shapes are combined. A three-dimensional Gaussian point spread function is assumed. An extra function is added to describe the transition between large and small objects. Numerical simulations for the mean RC-curves were performed for spheres, cubes, cylinders, and ellipsoids. It was shown that the new combined equation fits the theoretical and simulated RCcurves for the different shapes very well. The extra added function can be approximated by a power function, where the power is limited to values between one and three. The new equation has correct asymptotic behavior for objects of arbitrary shape. Only one (fixed power) or two fit parameters are needed. For objects with comparable size in all three dimensions the same power function and thus the same RC-equation can be used.