The study of blood-tissue exchange by the multiple indicator dilution technique often needs frequent sampling in the blood of the indicator dilution curves (IDC). Usually, this requires the use of a catheter supported by a pump. This causes a distortion in the IDC, which must be removed for proper interpretation of the data. A deconvolution-based methodology to remove IDC distortion is presented. First, the catheter impulse response is modelled by means of data obtained from a suitable experiment. Then the reconstruction of the blood IDC is tackled by a new nonparametric deconvolution algorithm, which provides (quasi) time-continuous signals and exploits statistically based criteria for the choice of the regularisation parameter. The methodology is applied to the removal of catheter distortion in studies of glucose blood-tissue exchange in the human forearm and myocardium.