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We propose a semi-analytical solution for the advection-diffusion equation in cylindrical domains, with an aim towards extracting blood flow rates from contrast variations in a coronary computed tomography angiography image. The solution proposed in this work, in contrast with existing methods, which only consider advection, incorporates both radial velocity variation and diffusion. By means of a Galerkin approach using Bessel functions, a solution for a three-dimensional concentration field at a single time point is obtained after a Laplace transformation. This semi-analytical solution forms the basis for a novel advection-diffusion flow estimation (ADFE) method. The ADFE is derived, validated through numerical spectral-element method computations, and shown to exhibit improved accuracy against the state-of-the-art method for image-based blood flow extraction.

Patient-specific models of blood flow are being used clinically to diagnose and plan treatment for coronary artery disease. A remaining challenge is bridging scales from flow in arteries to the micro-circulation supplying the myocardium. Previously proposed models are descriptive rather than predictive and have not been applied to human data. The goal here is to develop a multiscale patient-specific model enabling blood flow simulation from large coronary arteries to myocardial tissue. Patient vasculatures are segmented from coronary computed tomography angiography data and extended from the image-based model down to the arteriole level using a space-filling forest of synthetic trees. Blood flow is modeled by coupling a 1D model of the coronary arteries to a single-compartment Darcy myocardium model. Simulated results on five patients with non-obstructive coronary artery disease compare overall well to [$$^{15}$$ 15 O]$$\text {H}_{{2}}$$ H 2 O PET exam data for both resting and hyperemic conditions. Results on a patient with severe obstructive disease link coronary artery narrowing with impaired myocardial blood flow, demonstrating the model’s ability to predict myocardial regions with perfusion deficit. This is the first report of a computational model for simulating blood flow from the epicardial coronary arteries to the left ventricle myocardium applied to and validated on human data.

Author(s): Chen, Zhennong; Contijoch, Francisco; Schluchter, Andrew; Grady, Leo; Schaap, Michiel; Stayman, Web; Pack, Jed; McVeigh, Elliot | Abstract: PurposeCoronary x-ray computed tomography angiography (CCTA) continues to develop as a noninvasive method for the assessment of coronary vessel geometry and the identification of physiologically significant lesions. The uncertainty of quantitative lesion diameter measurement due to limited spatial resolution and vessel motion reduces the accuracy of CCTA diagnoses. In this paper, we introduce a new technique called computed tomography (CT)-number-Calibrated Diameter to improve the accuracy of the vessel and stenosis diameter measurements with CCTA.MethodsA calibration phantom containing cylindrical holes (diameters spanning from 0.8nmm through 4.0nmm) capturing the range of diameters found in human coronary vessels was three-dimensional printed. We also printed a human stenosis phantom with 17 tubular channels having the geometry of lesions derived from patient data. We acquired CT scans of the two phantoms with seven different imaging protocols. Calibration curves relating vessel intraluminal maximum voxel value (maximum CT number of a voxel, described in Hounsfield Units, HU) to true diameter, and full-width-at-half maximum (FWHM) to true diameter were constructed for each CCTA protocol. In addition, we acquired scans with a small constant motion (15nmm/s) and used a motion correction reconstruction (Snapshot Freeze) algorithm to correct motion artifacts. We applied our technique to measure the lesion diameter in the 17 lesions in the stenosis phantom and compared the performance of CT-number-Calibrated Diameter to the ground truth diameter and a FWHM estimate.ResultsIn all cases, vessel intraluminal maximum voxel value vs diameter was found to have a simple functional form based on the two-dimensional point spread function yielding a constant maximum voxel value region above a cutoff diameter, and a decreasing maximum voxel value vs decreasing diameter below a cutoff diameter. After normalization, focal spot size and reconstruction kernel were the principal determinants of cutoff diameter and the rate of maximum voxel value reduction vs decreasing diameter. The small constant motion had a significant effect on the CT number calibration; however, the motion-correction algorithm returned the maximum voxel value vs diameter curve to that of stationary vessels. The CT number Calibration technique showed better performance than FWHM estimation of diameter, yielding a high accuracy in the tested range (0.8nmm through 2.5nmm). We found a strong linear correlation between the smallest diameter in each of 17 lesions measured by CT-number-Calibrated Diameter (DC ) and ground truth diameter (Dgt ), (DC n=n0.951n×nDgt n+n0.023nmm, rn=n0.998 with a slope very close to 1.0 and intercept very close to 0nmm.ConclusionsComputed tomography-number-Calibrated Diameter is an effective method to enhance the accuracy of the estimate of small vessel diameters and degree of coronary stenosis in CCTA.