Comparison of Arterial Input Function Models for Small-Animal Ultrasound Perfusion Imaging

Background, Motivation and Objective Bolus & burst (B&B) is a method for quantitative ultrasound perfusion analysis combining bolus tracking and burst replenishment. Estimation of perfusion parameters is based on blind deconvolution where the measured concentration curves are modeled as a convolution of an arterial input function (AIF) and a tissue residual function (TRF). Reliable estimation of perfusion parameters requires a realistic model of the AIF and TRF. Two AIF models have been presented for the B&B method so far – based on two lognormal and three gamma variate functions. The aim of this contribution is to suggest other alternative AIF models and test their suitability for the B&B method for small-animal applications by comparison with measured AIFs. Statement of Contribution/Methods Ten different models of the AIF are compared by evaluating their curve-fit quality with respect to the measured AIF data. The models are chosen based on modeling in other imaging modalities. The curve-fitting task is formulated as a least-squares minimization. The proposed AIF models are formulated as a sum of two (2gam) or three (3gam) gamma variate functions or as a sum of two (2logn) or three (3logn) lognormal functions. Alternative models are formulated with some parameters lumped into one – two (2gam_β) or three (3gam_β) gamma variate functions with the same exponent of the time variable, three lognormal functions with the same standard deviation (3logn_σ) or scaling factor (3logn_A). Finally, the last two models are formulated as a sum of a gamma variate (gam+exp) or lognormal (logn+exp) function with a decreasing exponential function. Results/Discussion Preclinical data were recorded on ICR mice using a Vevo 2100 ultrasound system using a bolus of MicroMarker® as a contrast agent. The AIFs were derived from regions within abdominal aorta. Three measured AIFs were then fitted by all models and the fitting quality was evaluated by the mean absolute percentage error (MAPE) and the adjusted R2. The best results were obtained for models with a full set of parameters –3gam, 2gam and 3logn, as they have the most degrees of freedom. The worst results were obtained with lumped-parameter models, indicating a too strict constraint induced by parameter lumping. Fairly good results were obtained for the models gam+exp and logn+exp, suggesting that these models might be a compromise between the fit quality and the low number of parameters.