Errors in power-law estimations of inflow rates for intracranial aneurysm CFD.

Patient-specific inflow rates are rarely available for computational fluid dynamics (CFD) studies of intracranial aneurysms. Instead, inflow rates are often estimated from parent artery diameters via power laws, i.e. Q ∝ Dn, reflecting adaptation of conduit arteries to demanded flow. The present study aimed to validate the accuracy of these power laws. Internal carotid artery (ICA) flow rates were measured from 25 ICA aneurysm patients via 2D phase contrast MRI. ICA diameters, derived from 3D segmentation of rotational angiograms, were used to estimate inflow rates via power laws from the aneurysm CFD literature assuming the same inlet wall shear stress (WSS) (n = 3), velocity (n = 2) or flow rate (n = 0) for all cases. To illustrate the potential impact of errors in flow rate estimates, pulsatile CFD was carried out for four cases having large errors for at least one power law. Flow rates estimated by n = 3 and n = 0 power laws had significant (p < 0.01) mean biases of -22% to +32%, respectively, but with individual errors ranging from -78% to +120%. The n = 2 power law had no significant bias, but had non-negligible individual errors of -58% to +71%. CFD showed similarly large errors for time-averaged sac WSS; however, these were reduced after normalizing by parent artery WSS. High frequency WSS fluctuations, evident in 2/4 aneurysms, were also sensitive to inflow rate errors. Care should therefore be exercised in the interpretation of aneurysm CFD studies that rely on power law estimates of inflow rates, especially if absolute (vs. normalized) WSS, or WSS instabilities, are of interest.

Better Than Nothing: A Rational Approach for Minimizing the Impact of Outflow Strategy on Cerebrovascular Simulations.

BACKGROUND AND PURPOSE: Computational fluid dynamics simulations of neurovascular diseases are impacted by various modeling assumptions and uncertainties, including outlet boundary conditions. Many studies of intracranial aneurysms, for example, assume zero pressure at all outlets, often the default ("do-nothing") strategy, with no physiological basis. Others divide outflow according to the outlet diameters cubed, nominally based on the more physiological Murray's law but still susceptible to subjective choices about the segmented model extent. Here we demonstrate the limitations and impact of these outflow strategies, against a novel "splitting" method introduced here. MATERIALS AND METHODS: With our method, the segmented lumen is split into its constituent bifurcations, where flow divisions are estimated locally using a power law. Together these provide the global outflow rate boundary conditions. The impact of outflow strategy on flow rates was tested for 70 cases of MCA aneurysm with 0D simulations. The impact on hemodynamic indices used for rupture status assessment was tested for 10 cases with 3D simulations. RESULTS: Differences in flow rates among the various strategies were up to 70%, with a non-negligible impact on average and oscillatory wall shear stresses in some cases. Murray-law and splitting methods gave flow rates closest to physiological values reported in the literature; however, only the splitting method was insensitive to arbitrary truncation of the model extent. CONCLUSIONS: Cerebrovascular simulations can depend strongly on the outflow strategy. The default zero-pressure method should be avoided in favor of Murray-law or splitting methods, the latter being released as an open-source tool to encourage the standardization of outflow strategies.

Vessel calibre and flow splitting relationships at the internal carotid artery terminal bifurcation.

OBJECTIVE: Vessel lumen calibres and flow rates are thought to be related by mathematical power laws, reflecting the optimization of cardiac versus metabolic work. While these laws have been confirmed indirectly via measurement of branch calibres, there is little data confirming power law relationships of flow distribution to branch calibres at individual bifurcations. APPROACH: Flow rates and diameters of parent and daughter vessels of the internal carotid artery terminal bifurcation were determined, via robust and automated methods, from 4D phase-contrast magnetic resonance imaging and 3D rotational angiography of 31 patients. MAIN RESULTS: Junction exponents were 2.06 ± 0.44 for relating parent to daughter branch diameters (geometrical exponent), and 2.45 ± 0.75 for relating daughter branch diameters to their flow division (flow split exponent). These exponents were not significantly different, but showed large inter- and intra-individual variations, and with confidence intervals excluding the theoretical optimum of 3. Power law fits of flow split versus diameter ratio and pooled flow rates versus diameters showed exponents of 2.17 and 1.96, respectively. A significant negative correlation was found between age and the geometrical exponent (r = -0.55, p = 0.003) but not the flow split exponent. We also found a dependence of our results on how lumen diameter is measured, possibly explaining some of the variability in the literature. SIGNIFICANCE: Our study confirms that, on average, division of flow to the middle and anterior cerebral arteries is related to these vessels' relative calibres via a power law, but it is closer to a square law than a cube law as commonly assumed.

Improved reduced-order modelling of cerebrovascular flow distribution by accounting for arterial bifurcation pressure drops.

Reduced-order modelling offers the possibility to study global flow features in cardiovascular networks. In order to validate these models, previous studies have been conducted in which they compared 3D computational fluid dynamics simulations with reduced-order simulations. Discrepancies have been reported between the two methods. The loss of energy at the bifurcations is usually neglected and has been pointed out as a possible explanation for these discrepancies. We present distributed lumped models of cerebrovasculatures created automatically from 70 cerebrovascular networks segmented from 3D angiograms. The outflow rate repartitions predicted with and without modelling the energy loss at the bifurcations are compared against 3D simulations. When neglecting the energy loss at the bifurcations, the flow rates though the anterior cerebral arteries are overestimated by 4.7±6.8% (error relative to the inlet flow rate, mean ± standard deviation), impacting the remaining volume of flow going to the other vessels. When the energy loss is modelled, this error is dropping to 0.1±3.2%. Overall, over the total of 337 outlet vessels, when the energy losses at the bifurcations are not modelled the 95% of agreement is in the range of ±13.5% and is down to ±6.5% when the energy losses are considered. With minimal input and computational resources, the presented method can estimate the outflow rates reliably. This study constitutes the largest validation of a reduced-order flow model against 3D simulations. The impact of the energy loss at the bifurcations is here demonstrated for cerebrovasculatures but can be applied to other physiological networks.

Image-Based Simulations Show Important Flow Fluctuations in a Normal Left Ventricle: What Could be the Implications?

Intra-cardiac flow has been explored for decades but there is still no consensus on whether or not healthy left ventricles (LV) may harbour turbulent-like flow despite its potential physiological and clinical relevance. The purpose of this study is to elucidate if a healthy LV could harbour flow instabilities, using image-based computational fluid dynamics (CFD). 35 cardiac cycles were simulated in a patient-specific left heart model obtained from cardiovascular magnetic resonance (CMR). The model includes the valves, atrium, ventricle, papillary muscles and ascending aorta. We computed phase-averaged flow patterns, fluctuating kinetic energy (FKE) and associated frequency components. The LV harbours disturbed flow during diastole with cycle-to-cycle variations. However, phase-averaged velocity fields much resemble those of CMR measurements and usually reported CFD results. The peak FKE value occurs during the E wave deceleration and reaches 25% of the maximum phase-averaged flow kinetic energy. Highest FKE values are predominantly located in the basal region and their frequency content reach more than 200 Hz. This study suggests that high-frequency flow fluctuations in normal LV may be common, implying deficiencies in the hypothesis usually made when computing cardiac flows and highlighting biases when deriving quantities from velocity fields measured with CMR.