Extended Kalman Filtering for the Modeling and Estimation of ICG Pharmacokinetics in Cancerous Tumors Using NIR Measurements

Abstract

Near infrared (NIR) diffuse optical imaging and spectroscopy methods provide quantitative functional information that cannot be obtained by the conventional radiological methods (Yodh & Chance, 1995; Intes & Chance, 2005; Boas et al., 2001a). NIR techniques can provide in vivo measurements of the oxygenation and vascularization states, uptake and release of optical contrast agents, and chromophore concentrations with high sensitivity. In particular, NIR diffuse optical techniques in conjunction with optical contrast agents have the potential to characterize angiogenesis, and to differentiate between malignant and benign tumors (Hawrys & Sevick-Muraca, 2000; Furukawa et al., 1995; Chen et al., 2003; Becker et al., 1997). Among many commercially available optical contrast agents, only indocyanine green (ICG) is approved for human use by the Food and Drug Administration (El Deosky et al., 1999; Hansen et al, 1993; Shinohara et al., 1996). ICG is a blood pooling agent that has different delivery behaviour between normal and cancer vasculature. In normal tissue, ICG acts as a blood flow indicator in tight capillaries of normal vessel. However in tumor, ICG may act as a diffusible (extravascular) flow in leaky capillary of vessels (Alacam et al., 2006; Cuccia et al., 2003; Ntziachristos et al., 2000; Vaupel et al., 1991). Therefore, pharmacokinetics of ICG has the potential to provide new tools for tumor detection, diagnosis, and staging. A number of research groups reported compartmental modeling of ICG time-kinetic measurements using NIR methods for tumor diagnosis in animal and human subjects (Gurfinkel et al., 2000; Cuccia et al., 2003; Intes et al., 2003; Milstein et al., 2005). A compartmental model is a mathematical description of the concentrations of contrast agents in which each compartment represents a kinetically distinct tissue type (Tornoe, 2002; Anderson, 1983; Cobelli et al., 2000). It consists of a set of coupled ordinary differential equations (ODE) and a measurement model. Coefficients of the ODE's are the physiological parameters of interest that represent rates of exchange between different compartments. These parameters are non-linearly related to the total concentration of ICG measured by NIR methods. Furthermore, concentration of ICG in each compartment cannot be directly measured non-invasively by NIR techniques, making the pharmacokinetic parameter estimation a highly non-linear problem. Current methods of ICG compartmental modeling involve curve fitting methods and various techniques for solving differential equations. Gurfinkel et al. presented a twoO pe n A cc es s D at ab as e w w w .in te ch w eb .o rg