1 Limits of Accuracy in Assessing Vessel Permeabilities Using Permeability-Surface(PS)-Limited Two-Compartment Models Guido Correia Carreira 1 , Matthias Taupitz 1 , Dirk Beyersdorff 1 , Lutz Lüdemann 2 1 Department of Radiology, CharitØ - Universittsmedizin Berlin, CharitØ Campus Mitte, Berlin, Germany 2 Department of Radiotherapy, CharitØ - Universittsmedizin Berlin, CharitØ Campus Virchow-Klinikum, Berlin, Germany Abstract Compartment models such as the Tofts model are widely used to quantify physiological parameters such as capillary permeability, P, or extravascular extracellular fractional volume, ve. Compartment models may show a variation of P and ve due to diffusion even when there is no such change in these parameters, but in different ones, i.e. tissue tortuosity. The numerical simulation of CM-diffusion was performed in two spatial dimensions. It was found that neither the capillary permeability P nor ve were predicted correctly by the Tofts model. Determination of capillary permeability by the Tofts model tends to underestimate the actual vessel permeability. Extravascular extracellular fractional volume ve depends strongly on vessel distance, a property with is completely unconsidered in the Tofts model. Therefore changing ve may indicate wrongly to extravascular extracellular fractional volume when in fact the vessel distance is varying and vice versa. Keywords Diffusion, Tofts model, DCE-MRI, perfusion, permeability INTRODUCTION Compartment models are widely used to quantify physiological parameters such as capillary permeability, P, or extravascular extracellular fractional volume, ve [1] . Usually the extravasation of low-molecular-weight contrast media (CM) in dynamic contrast enhanced magnetic resonance imaging (DCE- MRI) lead to intensity time curves. To these the respective compartment models are fitted. Even though this is a standard procedure, little systematic work has been done on the limitations of compartment models. The aim of this work is to show that compartment models may show a variation of P and ve even when there is no such change in these parameters, but in different ones, i.e. tissue tortuosity, , [2] and vessel distance. To this end, numerical diffusion simulations for several tissue models, describing the CM distribution process at the microscopic scale, are compared with a standard PS-limited (low permeability) two- compartment Tofts model [1] . MATERIAL AND METHODS The numerical simulation of CM-diffusion was performed in two spatial dimensions with a finite difference forward in time centered in space (FTCS) scheme in a regular grid with  spatial discretization of 1 m and a field of     view of 50 m x 50 m up to 300 m x 300 m. Using the FTCS scheme the CM-concentration, C, was calculated for each spatial grid point by solving the diffusion equation in tissue [2] numerically. Tortuosity  accounts for the impact of granular structure of tissue on the diffusion [2]. Tortuosity is defined as  = (D/Deff) 0.5 , wc2009.doc  C  t = D  2  2 C Q 