Magnetic resonance quantification of the myocardial perfusion reserve with a Fermi function model for constrained deconvolution

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Abstract
The myocardial perfusion reserve, defined as the ratio of hyperemic and basal myocardial blood flow, is a useful indicator of the functional significance of a coronary artery lesion. Rapid magnetic resonance (MR) imaging for the noninvasive detection of a bolus-injected contrast agent as a MR tracer is applied to the measurement of regional tissue perfusion during rest and hyperemia, in patients with microvascular dysfunction. A Fermi function model for the distribution of tracer residence times in the myocardium is used to fit the MR signal curves. The myocardial perfusion reserve is calculated from the impulse response amplitudes for rest and hyperemia. The assumptions of the model are tested with Monte Carlo simulations, using a multiple path, axially distributed mathematical model of blood tissue exchange, which allows for systematic variation of blood flow, vascular volume, and capillary permeability. For a contrast-to-noise ratio of 6:1, and over a range of flows from 0.5 to 4.0 ml/min per g of tissue, the ratio of the impulse response amplitudes for hyperemic and basal flows is linearly proportional to the ratio of model blood flows, if the mean transit time of the input function is shorter than approximately 9 s. The uncertainty in the blood flow reserve estimates grows both at low (< 1.0 ml/min/g) and high (> 3-4 ml/min/g) flows. The predictions of the Monte Carlo simulations agree with the results of MR first pass studies in patients without significant coronary artery lesions and microvascular dysfunction, where the perfusion reserve in the territory of the left anterior descending coronary artery (LAD) correlates linearly with the intracoronary Doppler ultrasound flow reserve in the LAD (r = 0.84), in agreement with previous PET studies.