Fractional calculus tracer kinetic compartment model for quantification of microvascular perfusion

Abstract

Objective. We evaluate a tracer kinetic model for quantification of physiological perfusion and microvascular residue time kurtosis (RTK) in skeletal muscle vasculature with first pass bolus experiments in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). Approach. A decreasing stretched Mittag-Leffler function (f1C model) was obtained as the impulse response solution of a rate equation of real-valued (‘fractional’) derivation order. The method was validated in skeletal muscle in the lower limb of seven female pigs examined by DCE-MRI. Dynamic imaging during blood pool contrast agent elimination was performed using a 3D gradient echo sequence with k-space sharing. Blood flow was augmented by continuous infusion of the vasodilator adenosine into the femoral artery increasing blood flow up to four times. Blood flow measured by a Doppler flow probe placed at the femoral artery served as ground truth. Main results. Goodness of fit and correlation with the Doppler measurements, r = 0.80 (P < 0.001), of the 4-parameter f1C model was comparable with the results obtained with a previously tested 6-parameter two-compartment (2C) model. The derivation order α of the f1C model can be interpreted as a measure of microvascular RTK. With increasing blood flow, α dropped significantly, leading to an increase in RTK. Significance. The f1C model is a practical approach based on hemodynamic principles to quantify physiological microvascular perfusion but it is impaired due to its compartmental nature.