Practical application of deconvolution techniques to dynamic studies

The stability of the impulse retention function (IRF) as derived by deconvolution of activity-time (A/T) curves obtained from a dynamic study, is dependent both on the nature of the input function and on the degree of statistical noise present on the raw data. For the type of input function obtained in first pass circulation studies the derived IRF is potentially unstable. Methods have been investigated which seek to achieve a satisfactory solution by the incorporation of a prior knowledge of the system expressed in mathematical form as a set of constraints. The best recovery of a theoretical IRF is achieved by the incorporation of a combination of smoothness, monotonicity and non-negativity constraints using a regularization method applied in the frequency domain by means of the fast Fourier transform. In a cerebral blood flow study using a non-diffusible tracer, the method has been evaluated relative to errors from statistical noise and preprocessing of the raw data. The resultant expected error on the mean transit time (MTT) proved slightly lower than the variation found in patient reproducibility studies. For an input function expressible as a sum of exponential terms, the IRF derived using unconstrained least-squares methods proved relatively stable. In the renogram study, the matrix algorithm method yielded good estimates of the MTT. To facilitate interpretation of the transit time spectrum (TTS), a model is proposed in which TTS is calculated corresponding to two zones whose principal contributions arise from the cortical and medullary regions of the kidney respectively. After appropriate noise reduction, combination of the TTS leads to enhanced resolution of modes originating in the separate zones. A possible advantage of this method over methods which seek to resolve a bimodal distribution from a single TTS is indicated