Kinetic parameters of the compartment models give important information about the physiology. These kinetic parameters are estimated from the time activity curves (TACs) that are obtained from dynamic positron emission tomography (PET). As the signal to noise (SNR) ratio of dynamic PET is low, the estimated kinetic parameters have low precision. The parametric images are formed by the kinetic parameters that are estimated for each pixel. Typically, the parametric images have large spatial variance due to low SNR and high variance of the estimated kinetic parameters. Many methods have been developed to reduce this variance. These methods concentrate on TAC denoising and population based constraints. Spatial regularization on the kinetic parameter domain is not used commonly, and its effects on the parametric images have not been investigated. The aim of this paper is to investigate the effect of a quadratic spatial regularization that is applied directly on the parametric images in terms of bias and variance. For this objective, bias and variance are investigated using two simulated datasets at different noise and spatial regularization levels. The results on simulated phantom indicate that the effects of spatial regularization on bias and variance depend on the size of the region and the amount of difference in parameter values in the neighbouring regions. Hence, spatial regularization should be used carefully, if the region of interest is small in size and has a large difference in kinetic parameter value with its surrounding regions. In addition, the effects of noise level on the bias and variance of estimated kinetic parameters decrease with the increasing level of spatial regularization. 
Effects of spatial regularization on kinetic parameter estimation for dynamic PET