Fourier domain closed-form formulas for estimation of kinetic parameters in multi-compartment models

Dynamic emission computed tomographic imaging with compartment modeling can quantify in vivo physiologic processes, eliciting more information regarding underlying molecular disease processes than can be obtained from static imaging. However, estimation of kinetic rate parameters for multi-compartment models can be computationally demanding and problematic in the presence of high statistical noise. A number of techniques for kinetic parameter estimation have been studied and are in use today, generally offering a tradeoff between computation time, robustness of fit, and flexibility with differing sets of assumptions. This paper offers a new perspective to the compartment model fitting problem where Fourier linear system theory is applied to derive closed-form formulas for estimating kinetic parameters for one- and two-tissue compartment models. The proposed Fourier domain estimation method is computationally efficient, provides a unique solution, and offers very different noise response as compared to traditional non-linear chi-squared minimization techniques. The unique feature of the proposed Fourier domain method is that the DC (Direct Current) component in the data is treated as the most important information. Only low frequency components are used for kinetic parameter estimation, and high frequency components that tend to be corrupted by statistical noise are discarded. Computer simulations show that the proposed method is robust without specifying the initial condition.