A modified logistic model to describe gadolinium kinetics in breast tumors

A five-parameter modified logistic equation is presented that describes the signal enhancement in magnetic resonance dynamic contrast enhanced imaging (MRI-DCE). In this heuristic model, P1 approximates the baseline signal, P2 is related to the magnitude of the peak signal enhancement, P3 is the approximate time of the maximum rate of increase of signal, P4 is related to the maximum rate of signal enhancement, and P5 is the terminal slope of the signal enhancement curve. Six breast tumors were studied that exhibited diverse patterns of signal enhancement, and in each case, estimated model parameters were well identified. Three of the model parameters, P2, P4 and P5 describe attributes of the signal enhancement curve that have previously been shown to have diagnostic value with respect to breast cancer. Procedures for using the primary model parameters to derive a number of secondary parameters that may also have diagnostic value are discussed. Sensitivity analysis shows that the signal enhancement curve is highly sensitive to P3 in the region of the signal intensity curve associated with rapid uptake of the contrast reagent. Consequently, frequent signal sampling in this time domain is indicated to enable identification of P3 and sensitive fitting of the signal intensity curve. The advantages of this heuristic model compared to commonly used compartmental modeling approaches are discussed.