Accuracy and Performance of Functional Parameter Estimation Using a Novel Numerical Optimization Approach for GPU-Based Kinetic Compartmental Modeling

Abstract

Quantitative kinetic parameters derived from dynamic contrast-enhanced (DCE) data are dependent on signal measurement quality and choice of pharmacokinetic model. However, the fundamental optimization analysis method is equally important and its impact on pharmacokinetic parameters has been mostly overlooked. We examine the effects of those choices on accuracy and performance of parameter estimation using both computer processing unit and graphical processing unit (GPU) numerical optimization implementations and evaluate the improvements offered by a novel optimization approach. A test framework was developed where experimentally derived population-average arterial input function and randomly sampled parameter sets { K trans , K ep , V b , τ} were used to generate known tissue curves. Five numerical optimization algorithms were evaluated: sequential quadratic programming, downhill simplex (Nelder–Mead), pattern search, simulated annealing, and differential evolution. This was combined with various objective function implementation details: delay approximation, discretization and varying sampling rates. Then, impact of noise and CPU/GPU implementation was tested for speed and accuracy. Finally, the optimal method was compared to conventional implementation as applied to clinical DCE computed tomography. Nelder–Mead, differential evolution and sequential quadratic programming produced good results on clean and noisy input data outperforming simulated annealing and pattern search in terms of speed and accuracy in the respective order of 10 −8 %, 10 −7 %, and ×10 −6 %). A novel approach for DCE numerical optimization (infinite impulse response with fractional delay approximation) was implemented on GPU for speed increase of at least 2 orders of magnitude. Applied to clinical data, the magnitude of overall parameter error was <10%.