Factor analysis and deconvolution are commonly used tools in analysis of time activity analysis of biological organs in scintigraphic data. Typically, these are used independently such that the output of the former is taken as an input to the latter. Each method is thus unaware of the restrictions imposed by the other and fails to respect them. In this paper, we propose a probabilistic model that integrates convolution into the factor analysis model. We develop an approximate Bayesian estimation of the model parameters based on Variational Bayes approximation. The new variant of the factor analysis model is suitable for modeling of a range of biological processes where convolution kernels are known to have restricted shapes. Properties of the new model are illustrated on analysis of data from dynamic renal scintigraphy. The proposed model provides more realistic estimates of the convolution kernels.