Constrained adaptive temporal B-splines (CAT B-splines) for use in medical imaging dynamic curve modelling

Accurate modeling of temporal changes plays important role in several applications in dynamic imaging such as list mode data acquisition, kinetic modeling, deconvolution of dynamic studies, or factor analysis. We present an algorithm that uses B-splines and allows modeling of any time curve. During the optimization the CAT B-spline adaptively reconfigures to model the temporal curve. Both, positions and values of intensity for the control points, are optimized. Physiological constraints put on the CAT B-spline model were used. Optimization was performed by minimization of the least squares objective function using the simulated annealing method with an adaptive temperature control. Computer simulations were performed to test the algorithm. Gaussian curves with different widths were simulated and CAT B-splines were fitted to those curves. Noiseless and noisy data were simulated. As an example of a CAT B-spline application we performed computer simulation of the deconvolution of the input function and transfer function. The results from CAT B-spline deconvolution were compared to standard algebraic SVD method. We found good performance of our algorithm in modeling of Gaussian dynamic curves. The deconvolution based on CAT B-splines performed well compared to the SVD yielding similar values of bias. However, the results from CAT B-spline method were less prone to a selection of regularization parameter which was a number of control points for CAT B-splines. CAT B-splines may be very useful in dynamic imaging.