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Accurate determination of the input function is essential for absolute quantification of physiological parameters in positron emission tomography and single-photon emission computed tomography imaging, but it requires an invasive and tedious procedure of blood sampling that is impractical in clinical studies. We previously proposed a technique that estimates simultaneously kinetic parameters and the input function from the tissue impulse response functions and requires two blood samples. A nonlinear least squares method estimated all the parameters in the impulse response functions and the input function but failed occasionally due to high noise levels in the data, causing an ill-conditioned cost function. This paper investigates the feasibility of applying a Monte Carlo method called simulated annealing to estimate kinetic parameters in the impulse response functions and the input function. Time-activity curves of teboroxime, which is very sensitive to changes in the input function, were simulated based on published data obtained from a canine model. The equations describing the tracer kinetics in different regions were minimized simultaneously by simulated annealing and nonlinear least squares. We found that the physiological parameters obtained with simulated annealing are accurate, and the estimated input function more closely resembled the simulated curve. We conclude that simulated annealing reduces bias in the estimation of physiological parameters and determination of the input function.