Purpose: This paper investigates the validity of the analytical framework for variance ("analytical variance") in kinetic parameter and macroparameter estimations. Analytical variance is compared against the variance obtained from Monte Carlo simulations ("MC variance") for two different compartment models at different noise levels.
Methods: Kinetic parameters for one-tissue (1T) and two-tissue (2T) compartment models are used to generate time-activity curves (TAC). Gaussian noise is added to the noiseless TAC to generate noise realizations for each noise level. The kinetic parameters are then estimated by minimizing the weighted squared error between the noisy TAC and the model output. Standard deviation is computed statistically from the estimated parameters and computed analytically using the framework at each noise level. The ratio of standard deviation to true parameter value obtained from Monte Carlo simulations and analytical computations is compared.
Results: Difference between the analytical and MC variance increases with the level of noise and complexity of the compartment model. The standard deviation of the analytical variance also increases with the noise-level and model complexity. The difference between the analytical and MC variance is less than 3% for 1T compartment model and less than 10% for 2T compartment model at all noise levels. In addition, the standard deviation in the analytical variance is less than 15% for 1T and 2T compartment models at all noise levels.
Conclusions: These results indicate that the proposed framework for the variance in the kinetic parameter estimations can be used for 1T and 2T compartment models even in the existence of high noise.