ARMA modeling for estimation of permeability from perfusion MRI

We develop noninvasive MRI techniques that quantify the permeability of the Blood-Brain Barrier (BBB). Using such gadolinium compounds as Gd-DTPA and gadomer-17, changes in R1 (R1=1/T1) can be measured and used as estimates of tissue concentration versus time, thus permitting estimates of BBB permeability parameters. Estimating BBB permeability parameters requires deconvolution in a linear system, a task that has been accomplished heretofore by nonlinear least-squares procedures, although these techniques tend to instability in the presence of noise. We introduce a method using Z-transform and Autoregressive Moving Average (ARMA) modeling to perform this deconvolution. This method has the advantage that it linearizes the optimization procedure by which parametric estimates are formed, and it stabilizes the deconvolution. in the presence of noise.