Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial experimental validation of such software is performed using a wind tunnel with the final validation coming in full-scale testing, e.g. flight tests.
A landmark study by Lin et al. addressed the problem of fluid characteristics in ventricular catheters using a two-dimensional simulation program of computational fluid dynamics (CFD).
Most commercially available ventricular catheters have an abnormally increase flow distribution pattern. New catheter designs with variable hole diameters along the catheter tip will allow the fluid to enter the catheter more uniformly along its length, thereby reducing the probability of its becoming occluded 1).
Liu et al., studied 27 paraclinoid aneurysms (seven recanalized and 20 stable) treated with coils and Enterprise stents. Computational fluid dynamic simulations were performed on patient-specific aneurysm geometries using virtual stenting and porous media technology.
After stent placement in 27 cases, aneurysm flow velocity decreased significantly, the reduction gradually increasing from the neck plane (11.9%), to the residual neck (12.3%), to the aneurysm dome (16.3%). Subsequent coil embolization was performed after stent placement and the hemodynamic factors decreased further and significantly at all aneurysm regions except the neck plane. In a comparison of recanalized and stable cases, univariate analysis showed no significant differences in any parameter before treatment. After stent-assisted coiling, only the reduction in area-averaged velocity at the neck plane differed significantly between recanalized (8.1%) and stable cases (20.5%) (p=0.016).
Aneurysm flow velocity can be significantly decreased by stent placement and coil embolization. However, hemodynamics at the aneurysm neck plane is less sensitive to coils. Significant reduction in flow velocity at the neck plane may be an important factor in preventing recanalization of paraclinoid aneurysms after subtotal stent-assisted coil embolization (SACE) 2).
Fifty unruptured middle cerebral artery aneurysms were analyzed. Spatial and temporal maximum pressure (Pmax) areas were determined with a fluid-flow formula under pulsatile blood flow conditions. Intraoperatively, TWRs of aneurysm domes were identified as reddish areas relative to the healthy normal middle cerebral arteries; 5 neurosurgeons evaluated and divided these regions according to Pmax area and TWR correspondence. Pressure difference (PD) was defined as the degree of pressure elevation on the aneurysmal wall at Pmax and was calculated by subtracting the average pressure from the Pmax and dividing by the dynamic pressure at the aneurysm inlet side for normalization.
In 41 of the 50 cases (82.0%), the Pmax areas and TWRs corresponded. PD values were significantly higher in the correspondence group than in the noncorrespondence group (P = .008). A receiver-operating characteristic curve demonstrated that PD accurately predicted TWRs at Pmax areas (area under the curve, 0.764; 95% confidence interval, 0.574-0.955; cutoff value, 0.607; sensitivity, 66.7%; specificity, 82.9%).
A high PD may be a key parameter for predicting TWRs in unruptured cerebral aneurysms 3).
Park et al., created paired virtual models of computational fluid dynamics (CFD) in five aneurysms which were initially regarded as having achieved complete occlusion and then recurred during follow-up. Paired virtual models consisted of the CFD model of 3D rotational angiography obtained in the recurred aneurysm and the control model of the initial, parent artery after artificial removal of the coiled and recanalized aneurysm. Using the CFD analysis of the virtual model, they analyzed the hemodynamic characteristics on the neck of each aneurysm before and after its recurrence.
High wall shear stress (WSS) was identified at the cross-sectionally identified aneurysm neck at which recurrence developed in all cases. A small vortex formation with relatively low velocity in front of the neck was also identified in four cases. The aneurysm recurrence locations corresponded to the location of high WSS and/or small vortex formation.
Recanalized aneurysms revealed increased WSS and small vortex formation at the cross-sectional neck of the aneurysm. This observation may partially explain the hemodynamic causes of future recanalization after coil embolization 4)
Computational Fluid Dynamics of a Fatal Ruptured Anterior Communicating Artery Aneurysm 5).
Sejkorová et al., analyzed a case of a ruptured middle cerebral artery aneurysm for which they acquired imaging data at three time points, including at rupture. A patient with an observed MCA aneurysm was admitted to the emergency department with clinical symptoms of a subarachnoid hemorrhage. During three-dimensional (3D) digital subtraction angiography (DSA), the aneurysm ruptured again. Imaging data from two visits before rupture and this 3D DSA images at the moment of rupture were acquired, and computational fluid dynamics (CFD) simulations were performed. Results were used to describe the time-dependent changes of the hemodynamic variables associated with rupture. Time-dependent hemodynamic changes at the rupture location were characterized by decreased wall shear stress WSS and flow velocity magnitude. The impingement jet in the dome changed its position in time and the impingement area at follow-up moved near the rupture location. The results suggest that the increased WSS on the dome and increased low wall shear stress area (LSA) and decreased WSS on the daughter bleb with slower flow and slow vortex may be associated with rupture. CFD performed during the follow-up period may be part of diagnostic tools used to determine the risk of aneurysm rupture 6).
A 75-year-old male patient underwent magnetic resonance angiography, which revealed a large internal carotid artery aneurysm with inflow jet inside the aneurysm. The aneurysm was stable for 18 months, but a new daughter sac developed at the tip of the aneurysm during the next 6 months. The daughter sac seemed to be related to the inflow jet on MR angiography. Aneurysm geometries before and after daughter sac formation were reconstructed using the longitudinal data of MR angiography. Computational fluid dynamic simulations were conducted under the patient-specific pulsatile inlet conditions measured by MR velocimetry.
The hemodynamic simulation revealed that the inflow jet impinged on two sites of the aneurysm: the right side of the aneurysmal dome and tip of the aneurysm. The flow impingement caused elevation of pressure at both sites. However, the daughter sac formed at the latter site surrounded by basal cistern, but did not form at the former site that was in contact with the right temporal lobe.
Blood inflow jet caused local elevation of pressure, and the formation of the daughter sac occurred at the site with high pressure but without the surrounding structure that may cancel the perpendicular wall tension 7).