On Impulse Response Functions Computed from Dynamic Contrast-enhanced Image Data by Algebraic Deconvolution and Compartmental Modeling

Concentration-time courses measured by dynamic contrast-enhanced (DCE) imaging can be described by a convolution of the arterial input with an impulse response function, Q(T)(t), characterizing tissue microcirculation. Data analysis is based on two different approaches: computation of Q(T)(t) by algebraic deconvolution (AD) and subsequent evaluation according to the indicator dilution theory (IDT) or parameterization of Q(T)(t) by analytical expressions derived by compartmental modeling. Pitfalls of both strategies will be addressed in this study. Tissue data acquired by DCE-CT in patients with head-and-neck cancer and simulated by a reference model (MMID4) were analyzed by a two-compartment model (TCM), a permeability-limited two-compartment model (PL-TCM) and AD. Additionally, MMID4 was used to compute the 'true' response function that corresponds to the simulated tumor data. TCM and AD yielded accurate fits, whereas PL-TCM performed worse. Nevertheless, the corresponding response functions diverge markedly. The response curves obtained by TCM decrease exponentially in the early perfusion phase and overestimate the tissue perfusion, Q(T)(0). AD also resulted in response curves starting with a negative slope and not - as the 'true' response function in accordance with the IDT - with a horizontal plateau. They are thus not valid responses in the sense of the IDT that can be used unconditionally for parameter estimation. Response functions differing considerably in shape can result in virtually identical tissue curves. This non-uniqueness makes a strong argument not to use algebraic but rather analytical deconvolution to reduce the class of solutions to representatives that are in accordance with a-priori knowledge. To avoid misinterpretations and systematic errors, users must be aware of the pitfalls inherent to the different concepts.