Expanded pharmacokinetic model for population studies in breast MRI

Abstract

We propose a new model for pharmacokinetic analysis based on the one proposed by Tofts. Our model both eliminates the need for estimating the Arterial Input Function (AIF) and normalizes analysis so that comparisons across patients can be performed. Previous methods have attempted to circumvent the AIF estimation by using the pharmacokinetic parameters of multiple reference regions (RR). Viewing anatomical structures as filters, pharmacokinetic analysis tells us that 'similar' structures will be similar filters. By cascading the inverse filter at a RR with the filter at the voxel being analyzed, we obtain a transfer function relating the concentration of a voxel to that of the RR. We show that this transfer function simplifies into a five-parameter nonlinear model with no reference to the AIF. These five parameters are combinations of the three parameters of the original model at the RR and the region of interest. Contrary to existing methods, ours does not require explicit estimation of the pharmacokinetic parameters of the RR. Also, cascading filters in the frequency domain allows us to manipulate more complex models, such as accounting for the vascular tracer component. We believe that our model can improve analysis across MR parameters because the analyzed and reference enhancement series are from the same image. Initial results are promising with the proposed model parameters exhibiting values that are more consistent across lesions in multiple patients. Additionally, our model can be applied to multiple voxels to estimate the original pharmacokinetic parameters as well as the AIF.