Myocardial blood flow (MBF) is a marker for myocardial perfusion. It can be measured via T1-weighted contrast-enhanced first-pass myocardial perfusion MRI. Therefor, the arterial input function (AIF) should be measured inside a supplying vessel as close as possible to the tissue of interest (TOI). However, for technical reasons the AIF is usually measured inside the blood pool of the left ventricle (LV) in myocardial perfusion MRI. Unfortunately, dispersion (deformation) of the contrast agent (CA) bolus might occur between the LV and the myocardium. In case of the negligence of this dispersion a systematic error of the measured MBF might arise. If an additional measurement for pharmacologically induced stress has been accomplished, the calculated myocardial perfusion reserve (MPR) might be inaccurate as well.

Mathematically, the dispersed AIF can be represented as the convolution of the undispersed AIF of the LV and a so called vascular transport function (VTF)¹: $$$AIF_{TOI}=VTF\otimes AIF_{LV}$$$. The variance σ² of this VTF can be considered as a quantitative measure for the CA bolus dispersion¹. Graafen et al. and Schmidt et al. observed an underestimation of the MBF and an overestimation of MPR inside idealized coronary artery geometries due to negligence of CA bolus dispersion by means of computational fluid dynamics (CFD) simulations in previous studies^2-7. The aim of this study was to investigate the influence of vessel tortuosity on CA bolus dispersion. This vessel tortuosity was found to be positively correlated with several parameters, e.g. age⁸, female gender⁹ or hypertension⁹, and negatively correlated with other parameters, e.g. coronary artery disease⁹.

Several idealized cylindrical geometries of the left anterior descending (LAD) with different extent of vessel tortuosity and a straight vessel geometry of identical dimensions have been generated (Fig. 1). All geometries exhibit a radius of 1.85 mm¹⁰ and a length of 110 mm including a straight flow extension of 10 mm at the outlet. CFD simulations have been performed for rest and stress using the Fluent software package (Fluent 15, Ansys, Darmstadt, Germany) at the High Performance Cluster ,Elwetritsch’ (RHRK, TU Kaiserslautern, Germany). A pulsatile velocity pattern measured at rest and stress, respectively, was set as inlet boundary condition¹¹. A resistance model was implemented at the outlet, where the pressure $$$p(t)$$$ at the outlet was calculated for each time step according to the equation $$$p(t)=R\cdot q(t)$$$ ^12,13, where $$$R$$$ represents the resistance of the entire downstream vascular system and $$$q(t)$$$ the outflow at the outlet. The resistance $$$R$$$ was calculated according to the structured tree model by Olufsen et al.^12,13,14. The blood was considered as a non-Newtonian Fluid and the diffusion coefficient of the commonly used CA Gd-DOTA was used. Furthermore, the variation of the corresponding diffusion coefficient of the CA according to the local shear rate due to the influence of the erythrocytes in blood has been implemented.In general, a negative correlation between the extent of tortuosity and the CA bolus dispersion was observed (Fig. 2). A decrease or a reduced increase of dispersion was found in the area at and closely behind the turning points of the tortuous vessel geometries (Fig. 2). Furthermore, CA bolus dispersion is larger at rest compared to stress (Fig. 2).

The smaller CA bolus dispersion with increasing extent of tortuosity might be explained by the deformation of the velocity profile in the regions of high curvature close to the turning points of the vessel geometries (Fig. 3). The increase in CA bolus dispersion closely behind the turning points for the geometry with the largest extent of tortuosity (Fig. 2) may be explained by the formation of a small recirculation zone at the inner wall at this region, which can be seen at the small negative axial velocities in Fig. 3. Thus, the CA bolus is stretched. The larger CA bolus dispersion at rest compared to stress can be explained by the lower velocity of blood at rest. This negative correlation of velocity and CA bolus dispersion has been observed before in several studies^2-7.

The error in MBF and MPR due to negligence of CA bolus dispersion at quantitative analysis with the MMID4 model is calculated for the simulation data of this study at the moment. An underestimation of the MBF, which has been found in several previous studies^2-7, can cause a false positive classification of a patient. Furthermore, CFD simulations in realistic geometries of the right coronary artery (RCA) are currently performed for more realistic results.