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Parameter estimation and change-point detection from dynamic contrast enhanced MRI data using stochastic differential equations. (English) Zbl 1226.92046

Summary: Dynamic Contrast Enhanced imaging (DCE-imaging) following a contrast agent bolus allows the extraction of information on tissue micro-vascularization. The dynamic signals obtained from DCE-imaging are modeled by pharmacokinetic compartmental models which integrate the Arterial Input Function. These models use ordinary differential equations (ODEs) to describe the exchanges between the arterial and capillary plasma and the extravascular – extracellular space. Their least squares fitting takes into account measurement noises but fails to deal with unpredictable fluctuations due to external/internal sources of variations (patients’ anxiety, time-varying parameters, measurement errors in the input function, etc.). Adding Brownian components to the ODEs leads to stochastic differential equations (SDEs). In DCE-imaging, SDEs are discretely observed with an additional measurement noise. We propose to estimate the parameters of these noisy SDEs by maximum likelihood, using the Kalman filter. In DCE-imaging, the contrast agent injected in vein arrives in plasma with an unknown time delay. The delay parameter induces a change-point in the drift of the SDE and ODE models, which is also estimated. Estimations based on the SDE and ODE pharmacokinetic models are compared to real DCE-MRI data. They show that the use of SDE provides robustness in the estimation results. A simulation study confirms these results.

MSC:

92C55 Biomedical imaging and signal processing
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
62M20 Inference from stochastic processes and prediction
65C20 Probabilistic models, generic numerical methods in probability and statistics
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