Continuous-Time Flow-Limited Modeling by Convolution Area Property and Differentiation Product Rule in 4-Phase Liver Dynamic Contrast-Enhanced CT

Parametric-fitting approaches for tracer kinetic modeling depend on the capability of a computational method to describe underlying physiologic processes that cause temporal intensity changes in dynamic contrast-enhanced (DCE) images. Rapid scan techniques allow perfusion CT imaging with high temporal resolution. In clinical practice, however, the perfusion CT protocol is especially a trade-off between the number of data points and the total radiation dose. Considering availability and radiation exposure, use of DCE-CT imaging derived from 4 temporal phases, which include precontrast, arterial, portal, and delayed phases, is highly desirable for the liver. However, low-temporalresolution images like 4-phase liver DCE-CT present several barriers to modeling of tracer kinetics because of the lack of temporal enhancement data, which limits obtaining reliable physiologic information. The major reason for the limited application of a tracer kinetic model in temporally sparse dynamic data is that general computational algorithms such as deconvolution techniques require discretizing of arterial (or portal-vein) and tissue curves for estimation of kinetic parameters, leading to an unstable computational solution. The numerical instability due to the discretization of the enhancement curves can be more pronounced in the low-temporal-resolution data like those gleaned from 4-phase DCE-CT. For this reason, we propose a novel dual-input continuoustime tracer kinetic modeling method based on a new mathematical approach that uses the convolution area property and the differentiation product rule, without any discretization of the enhancement curves. This model was applied to case studies of hepatocellular carcinoma in 4-phase DCE-CT to illustrate the potential effectiveness of continuous-time tracer kinetic modeling. The proposed analytic scheme was shown to be feasible for estimation of kinetic parameters even in 4-phase liver DCE-CT, potentially being a practical guide for tracer kinetic model-based curve-fitting in temporally sparse data.