Analysis of Intra-Aneurysmal Flow for Cerebral Aneurysms with Cerebral Angiography

Discussion

We propose a new technique for analysis of intra-aneurysmal flow, and this new technique has been tested on a small number of patients with aneurysm. The intra-aneurysmal flow ratio is found to be proportional to the value predicted by CFD calculation. This new technique offers several advantages over other traditional techniques. First, the new technique shows a beat-to-beat variation of intra-aneurysmal flow that is often ignored in previous analyses.^10,11 This beat-to-beat variation is especially important for flow-diverter evaluation (Fig 5). Second, the new technique is less affected by the overlap of an aneurysm with its parent vessels. Measuring cross-section area and diameter of a vessel is easier than a similar measurement at an aneurysm. Third, a comparison between signals proximal and distal to the aneurysm provides a unique way of examining the flow activity in the aneurysm. The difference between these 2 signals is independent of the imaging processing because they are acquired at the same run. The c_a-curves before and after the treatment, however, are subject to different x-ray voltages and electric currents and magnification factors, and a direct comparison of these curves obtained at different angiographic runs may not reveal the same information that we desire. Last, this new technique can serve as a real-time evaluation of aneurysm condition. It can be implemented in a clinical setting and provides an easy and effective way to evaluate flow diversion efficiency.

DSA has been used for flow quantification before, and it has been used by others for velocity measurement,^16⇓–18 and aneurysmal flow evaluation.^9⇓–11 These studies demonstrate that the change of signal does have a potential to assist us in understanding the hemodynamics in arteries and aneurysms. The new technique differs from all previous approaches in the location and shape of ROIs, the mathematic model that compares the concentration curves, controlled injection protocol, and the use of 3D DSA. In our experience, it is essential to normalize the signal intensity with the 3D DSA. Normalizing the signal by the area of a region of interest may be convenient, but it does not account for the 3-dimensionality of a complex arterial or aneurysmal geometry. When the vessel is not parallel to the projection plane where the 2D DSA is acquired, comparison between signals at various regions may be a challenge. For example, both a sphere and a cylinder with the same concentration of contrast medium appear on an angiogram as a circle, and normalizing the signal by the area of the circle does not produce a variable that is proportional to the contrast concentration for the sphere. Because 3D DSA provides visualization of anatomy and morphology and is already part of our existing clinical protocol, these 3D images offer us an additional opportunity for better quantifying the signal on 2D DSA. The detailed mathematic derivation of imaging processing is provided in the On-line Appendix.

Another critical aspect of our technique is the use of a rectangular region of interest rather than a circular region of interest, as is commonly used. If we select a circular region of interest, then the contrast needs to be well mixed with blood; otherwise, the region-of-interest signal will not be representative of the contrast concentration within the bulk flow. To capture both the motion of blood and contrast, the shape of the region of interest of our choice is rectangular and the region of interest includes the entire cross-section of the parent vessel (Fig 1). As long as the contrast moves forward along the vessel, it will appear within the region of interest. At any time interval dt, the contrast moving through the region of interest is Q_c dt, and the blood through the region of interest Q_b dt, where Q_c and Q_b are the flow rate of the contrast and blood, respectively. Then the concentration of the contrast is Q_c/(Q_b+ Q_c), and this variable will affect the x-ray signal at the region of interest because the amount of contrast in the region of interest is VQ_c/(Q_b+ Q_c), where V is the volume of the region of interest. This variable is the focus of our measurement. Q_c is a constant during the injection (2 mL/s), but blood flow (Q_b) is pulsatile, so one cannot expect a constant and steady contrast concentration in the blood at any given time. Because the region of interest covers the entire vessel section, our technique avoids the contrast streaming and other situations where the contrast and blood may not be perfectly mixed. An analogy of our region of interest is a tollbooth on a highway that collects tolls on all the passing contrast and blood. There is no need to require uniform mixing of the contrast and blood, and all we need is the total amounts of contrast and blood passing through the vessel during a short period of time. Whether the contrast is uniformly distributed across the vessel is not required for our technique.

A slow injection rate is required to produce signal pulsatility during the injection. First, the injection does not disturb the blood flow significantly and affect the measurement. Second, 2 mL/s is equivalent to half of the mean flow rate at the ICA, so the mean contrast concentration is approximately 33%. At this concentration, the signal can still be treated as linear to the concentration (e^−x ∼ x for small x). Signal variation is much smaller once the concentration reaches 80% because the signal is an exponential function of the attenuation. Dynamic range of digital images limits the range of concentration that we can utilize. In our preliminary in vitro experiments, a faster injection produces mostly saturated or nonpulsatile signals. For example, a 4 mL/s injection reduces the signal pulsatility by 70% and doubles the Reynolds number, which may potentially induce flow instability. For aneurysms in the posterior cerebral circulation, the injection rate may need to be reduced accordingly.

At 125kV, the Hounsfield units for Omnipaque 300 (300 mgI/mL) is 7300,¹⁹ and the linear attenuation coefficient for water is 16 m⁻¹,²⁰ so the linear attenuation coefficient for Omnipaque 300 is 133 m⁻¹. We can then estimate the blood flow rate using the last few pulses before the end of contrast injection in Fig 4 based on this information; the flow rate for blood is 6.9 mL/s for 30 m⁻¹, 3.3 mL/s for 50 m⁻¹, and 1.9 mL/s for 70 m⁻¹. Although the ICA flow rates obtained from attenuation estimate seem to be reasonable and are in the physiologic range, these numbers cannot be verified independently by our technique.

The slope between our prediction and CFD calculation is 0.79, different from the unity that we anticipated. Several reasons might have contributed to this difference. The attenuation difference between contrast medium and blood is 35%, and this may produce different flow patterns for contrast medium and for blood, allowing contrast medium residing within the aneurysm for a longer period than blood. In addition, Omnipaque is also more viscous than blood. In CFD simulations, the motion of contrast medium is not explicitly modeled, so this difference may not be well appreciated. We assume in our calculation that the contrast and blood are moving independently from each other, so the CFD simulations are conducted based on an arterial flow rate without an injection. The true flow rate after an injection may be very different from the sum of the arterial flow rate and contrast injection rate, and there is currently no proven technique available for an in vivo measurement of this kind. Because the true flow rate with an injection is not available, we opt to use the arterial waveform without an injection. This might introduce a difference in the intra-aneurysmal flow rate. What really interests us is the hemodynamics of an aneurysm at normal condition, not at the time of injection when the patient is under angiographic examination; the purpose of our technique is to establish a correlation between high-frame-rate DSA and the intra-aneurysmal flow at normal condition, so the use of the linear relationship between our technique and CFD calculation provides an easy way to estimate intra-aneurysmal flow. We recognize that the injection of contrast agent may affect the flow field in the artery, but this flow change is difficult to evaluate. The systemic difference of 20% underestimation by high-frame-rate DSA can be partly attributed to the effect of injection, but this difference can be easily compensated for each case by the linear coefficient.

Our new technique provides real-time dynamic information on intra-aneurysmal hemodynamics, but it cannot offer wall shear stress distribution on the aneurysm wall. It is also unclear if our technique can be applied to bifurcation aneurysms. The bifurcation itself may affect the signal distribution and this effect is difficult to evaluate based on our experience so far. However, our technique does not have the limitations of most CFD simulations, for which various assumptions need to be made, such as rigid wall, laminar flow, and Newtonian fluid. In vivo x-ray signal behavior captures the true event that occurs inside the aneurysm. Moreover, our analysis is not limited to those aneurysms that have no overlap with other arteries, as the aneurysm signal is not used directly. For cases in which an aneurysm overlaps with arteries, the aneurysmal signal includes a significant contribution from the artery, and an additional adjustment for this arterial signal contribution may be required.