In this paper we present a widely applicable computational method for the description of the initial concentration-time-course after intravenous injection of a substance. The intravascular concentration-time course, r, is described as r = c0 + g x r, where the asterisk denotes the convolution operation, c0 is the concentration-time course during the first passage of the substance and g is the transport function of the body. If the body transport function is known, then the concentration-time course of a substance can be predicted. The site of interest can be chosen arbitrarily, i.e. the concentration-time course in the arterial circulation supplying any organ can be described. This might be of special interest for the optimal design of intravenous injections of contrast media, where initial concentrations at the region of interest determine the success of the diagnostic procedure.