title: Parameter estimation and change-point detection from Dynamic Contrast Enhanced MRI data using stochastic differential equations.
abstract: 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 estimated also. 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.
authors: Université Paris Descartes, HEGP Radiology, France; LRI at PARC, INSERM U970, France.
authors: Charles-André
authors: CA
authors: Cuenod
authors: Benjamin
authors: B
authors: Favetto
authors: Valentine
authors: V
authors: Genon-Catalot
authors: Yves
authors: Y
authors: Rozenholc
authors: Adeline
authors: A
authors: Samson
mesh_terms: D003287:Contrast Media / Q000493:pharmacokinetics; D005260:Female; D006571:Heterocyclic Compounds / Q000493:pharmacokinetics; D006801:Humans; D016018:Least-Squares Analysis; D018810:Magnetic Resonance Angiography / Q000379:methods / Q000706:statistics & numerical data; D008279:Magnetic Resonance Imaging / Q000379:methods / Q000706:statistics & numerical data*; D055641:Mathematical Concepts; D008833:Microcirculation; D008954:Models, Biological; D009942:Organometallic Compounds / Q000493:pharmacokinetics; D013269:Stochastic Processes
chemical_list: D003287:Contrast Media; D006571:Heterocyclic Compounds; D009942:Organometallic Compounds; C050823:gadolinium 1,4,7,10-tetraazacyclododecane-N,N',N'',N'''-tetraacetate