Kalman filtering for reliable estimation of BBB permeability

Abstract

The blood-brain barrier (BBB) plays an important role in the pathophysiology of a number of central nervous system disorders. In the past, a number of laboratory techniques have been proposed to quantify permeability coefficient ki, an important index of barrier function. Recently, magnetic resonance imaging (MRI) has been used to estimate ki based on graphical plot technique. The MR technique was found to be in good agreement with the gold standard, quantitative autoradiography (QAR). However, a reduced image signal-to-noise ratio, among other factors such as partial volume effects, did not allow reliable estimation of permeability coefficients. This proof-of-principle study proposes the use of Kalman filter as a filtering technique for a reliable estimation of permeability coefficients. The results are compared to those obtained using the Wiener filter technique. MRI experiments were performed in Wistar rats (N=2) using a 4.7-T Bruker Biospec MR system (Bruker Biospin, Billerica, MA). After acquiring localizer images, T2-weighted diffusion-weighted imaging images were acquired. Finally, a rapid T1 mapping protocol was implemented to acquire one pre-gadolinium diethylenetriamine pentaacetic acid baseline data set followed by postinjection data sets at 3-min intervals for 45 min. Data were postprocessed with and without the application of Kalman and Wiener filters to obtain an estimate of ki. Comparing T1 maps, Patlak plots and permeability maps with and without the Kalman filtering presented several interesting observations. Kalman-filtered Patlak plots, compared to nonfiltered plots, showed that discrete data points on the plot were closer to the line fit. The number of time points used for the construction of the graphical plot had no effect on permeability coefficient estimates when the Kalman filter was used. A box-and-whiskers plot showed longer Y-error bars for nonfiltered and Wiener data compared to Kalman-filtered data. These observations suggest that it may be possible to obtain reliable permeability coefficient estimates in a short study time by applying the Kalman filter to the data. Future work involves investigating the application of this filter on a large-sample-size animal study and evaluating the role of partial volume effects on BBB permeability estimation.