Enhancing cerebral vasculature analysis with pathlength-corrected 2D angiographic parametric imaging: A feasibility study

Abstract

Background:

2D angiographic parametric imaging (API) quantitatively extracts imaging biomarkers related to contrast flow and is conventionally applied to 2D digitally subtracted angiograms (DSA’s). In the interventional suite, API is typically performed using 1–2 projection views and is limited by vessel overlap, foreshortening, and depth-integration of contrast motion.

Purpose:

This work explores the use of a pathlength-correction metric to overcome the limitations of 2D-API: the primary objective was to study the effect of converting 3D contrast flow to projected contrast flow using a simulated angiographic framework created with computational fluid dynamics (CFD) simulations, thereby removing acquisition variability.

Methods:

The pathlength-correction framework was applied to in-silico angiograms, generating a reference (i.e., ground-truth) volumetric contrast distribution in four patient-specific intracranial aneurysm geometries. Biplane projections of contrast flow were created from the reference volumetric contrast distributions, assuming a cone-beam geometry. A Parker-weighted reconstruction was performed to obtain a binary representation of the vessel structure in 3D. Standard ray tracing techniques were then used to track the intersection of a ray from the focal spot with each voxel of the reconstructed vessel wall to a pixel in the detector plane. The lengths of each ray through the 3D vessel lumen were then projected along each ray-path to create a pathlength-correction map, where the pixel intensity in the detector plane corresponds to the vessel width along each source-detector ray. By dividing the projection sequences with this correction map, 2D pathlength-corrected in-silico angiograms were obtained. We then performed voxel-wise (3D) API on the ground-truth contrast distribution and compared it to pixel-wise (2D) API, both with and without pathlength correction for each biplane view. The percentage difference (PD) between the resultant API biomarkers in each dataset were calculated within the aneurysm region of interest.

Results:

Intensity-based API parameters, such as the area under the curve (AUC) and peak height (PH), exhibited notable changes in magnitude and spatial distribution following pathlength correction: these now accurately represent conservation of mass of injected contrast media within each arterial geometry and accurately reflect regions of stagnation and recirculation in each aneurysm region of interest. Improved agreement was observed between these biomarkers in the pathlength-corrected biplane maps: the maximum PD within the aneurysm ROI is 3.3% with pathlength correction and 47.7% without pathlength correction. As expected, improved agreement with ROI-averaged ground-truth 3D counterparts was observed for all aneurysm geometries, particularly large aneurysms: the maximum PD for both AUC and PH was 5.8%. Temporal parameters (mean transit time, MTT, time-to-peak, TTP, time-to-arrival, TTA) remained unaffected after pathlength correction.

Conclusions:

This study indicates that the values of intensity-based API parameters obtained with conventional 2D-API, without pathlength correction, are highly dependent on the projection orientation, and uncorrected API should be avoided for hemodynamic analysis. The proposed metric can standardize 2D API-derived biomarkers independent of projection orientation, potentially improving the diagnostic value of all acquired 2D-DSA’s. Integration of a pathlength correction map into the imaging process can allow for improved interpretation of biomarkers in 2D space, which may lead to improved diagnostic accuracy during procedures involving the cerebral vasculature.

I. Introduction

Digital subtraction angiography (DSA) is the most-used imaging modality during endovascular interventions, providing accurate structural evaluations of neurovascular diseases such as intracranial aneurysms (IA’s), arteriovenous malformations (AVMs), and vessel stenoses.^1,2 Beyond geometric assessment, DSA's superior temporal and spatial resolution allows for qualitative appraisals of contrast flow changes within the lesion of interest.

Quantitative methods such as two-dimensional angiographic parametric imaging (2D-API) have emerged as a potential tool for real-time therapeutic optimization by providing functional assessment of contrast media transport characteristics. This approach is based on synthesis of time-density curves (TDCs) on a pixel-by-pixel basis in the vessels of interest, producing a color-coded map related to the underlying local hemodynamics.³ By parametrization of the TDCs, imaging biomarkers can be analyzed: temporal parameters such as mean transit time (MTT), time to peak (TTP), and time to arrival (TTA), and intensity-based parameters peak height (PH) and area under the time–density curve (AUC). These metrics have been used to examine flow characteristics in IA’s ^4,5, AVM’s ^6,7, and flow changes due to endovascular intervention.^8–10

The interpretation of 2D-API maps has historically been challenging due to the nuanced relationship between 2D imaging biomarkers, the complexity of blood flow conditions, and variability in treatment outcomes. Further complicating matters is patient heterogeneity, which adds a layer of complexity when utilizing API as a diagnostic tool to assess disease severity or predict treatment outcomes. To surmount these obstacles, recent studies by Bhurwani et al.^11,12 have shown that there is substantial evidence that the flow of contrast during DSA is strongly correlated with the underlying hemodynamics: specifically of interest, that predictions can be made on the likelihood of IA occlusion from pre- and post-treatment 2D-API maps. However, relevant to this work, several technical features were indicated which might improve the accuracy of such an assessment: 1) a standardized injection protocol, as the injection should not perturb the underlying hemodynamics¹³, 2) a higher acquisition frame rate for improved temporal sampling of TDC’s, and 3) better matching of the pre-and post-treatment C-arm view, as vessel overlap and geometric foreshortening degrade the relative 2D-API analysis.¹⁴

A major criticism of 2D quantitative angiography is the inherent limitation of depth-integrated flow information along the source-detector direction. Essentially, in the projection view, 3D information gets compressed into 2D, resulting in an amalgamation of data at each pixel without a clear indication of its original depth. This limitation has been addressed to an extent in the development of the 4D-DSA technique by Davis et al.¹⁵: time-resolved 3D-DSA can provide additional information on the filling characteristics of abnormal vascular geometries, i.e., TTA, by recovering the average contrast intensity in the vessel cross-section over time.¹⁶ However, intensity-based parameters like PH and AUC are not internally recovered within the 3D vessel with the current approach. From a clinical workflow perspective, the constraints of iodinated contrast usage, radiation dose, and the impracticality of multiple 4D-DSAs during a single procedure to monitor ongoing treatment pose additional challenges. Further confounding this problem, the exact relation of the recoverable 3D contrast flow and the present analysis performed with 2D-API is unclear, particularly for IA’s.

This work aims to better understand several of the above limitations in the development of an in-silico framework for 2D-API analysis: widely considered to be a robust method for hemodynamic analysis¹⁷, computational fluid dynamics (CFD) simulations are used to generate in-silico angiograms using CT angiography (CTA)-derived patient-specific geometries. The proposed framework allows for the generation of a ground-truth volumetric contrast distribution in any vessel of interest.^18,19 Using the simulated acquisition geometry and known contrast conditions, a pathlength-correction metric is investigated to further reduce the effects of depth integration, vessel overlap, and foreshortening on conventional 2D-API analysis, improving the interpretability of these angiography-derived biomarkers. We performed voxel-wise (3D) API on the ground-truth contrast distribution and compared it to pixel-wise (2D) API, both with and without pathlength correction.

II. Methods and Materials

A. Patient-Specific IA Models and Mesh Generation

The patient data used for the creation of the virtual models analyzed in this study were collected in accordance with Institutional Review Board (IRB) approval, ensuring ethical research practices. In-silico angiograms were generated using four CTA-generated patient-specific models of the internal carotid artery (ICA), each containing a saccular aneurysm (Figure 1).²⁰ A variety of aneurysm sizes were selected, including two small aneurysms (<10 mm, M2 and M4) and two large aneurysms (10 – 25 mm, M1 and M3), where the largest aneurysm dome was approximately 25 mm (M3).²¹ These models were first segmented semi-automatically (Vitrea 3D station, Vital Images, Inc. Minnetonka MN), focusing on the aneurysm as the region of interest (ROI) and simplifying the geometry by trimming vessel branches. Further refinements were manually performed on the exported stereolithographic (STL) files (Autodesk Meshmixer, Autodesk Inc., San Francisco, CA) to smooth the vessel structure and remove small residual arteries and disconnected structures.

Figure 1:

Top: Each of the four 3D aneurysm geometries are shown, where red arrows indicate the inflow direction and blue arrows are the outflow direction. M3 (red dotted line) is displayed in rows A – C. Bottom: Example simulated angiograms are shown for M3; biplane views of each model were generated, where every 8th projection is shown in rows A and B. In row C, every 18^th projection is shown for the corresponding rotational angiogram (RDSA) over an angular range of 202°.

High-resolution meshes, containing between 600,000 and 1 million elements based on vessel morphology, were generated from the refined STL files using ICEM (Ansys Inc., Canonsburg, PA). These meshes included surface prism layers and ensured a high-quality tetrahedral mesh throughout the vessel lumen. This specific mesh resolution was selected to balance memory resources and accuracy in capturing dominant flow patterns within the aneurysm.

B. Resolving Contrast Flow

To obtain the velocity fields, each mesh was imported into Fluent (Ansys Inc., Canonsburg, PA), where steady-state laminar flow simulations were performed by numerically solving the incompressible Navier-Stokes equations. The blood medium was modeled as a Newtonian fluid with a density of 1060 kg/m³ and viscosity of 0.0035 Pa·s. All vessel walls were modeled as rigid with the no-slip condition applied, and a zero-pressure gradient was prescribed at all model outlets. A parabolic velocity function was defined at each inlet cross-section, with a mean velocity of 25 cm/s. The convergence criteria were set to 1e⁻⁶ for continuity and momentum, and the SIMPLE scheme was implemented with a second order formulation.

Once a converged velocity field was obtained, contrast flow was generated using a transient passive scalar approach.²² A passive scalar numerically representing the mass fraction of contrast medium is “injected” at each inlet, where the transport of the scalar species through the fluid domain is modeled by solving the transient advection-diffusion equation (Equation 1).²³ For the $i^{th}$ species, given the steady-state velocity field:

$$\frac{\delta }{\delta t}\left(\rho Y_i\right)+\nabla \cdot \left(\rho \overrightarrow{v}{Y}_i\right)=-\nabla \cdot \overrightarrow{J_i}+S_i$$ (1)

where $Y_i$ is the species mass fraction, $\rho$ is density, and $t$ is time. The change in species concentration is dependent on advection due to velocity $\overrightarrow{v}$, and $S_i$ represents the source of the scalar species. The species mass fraction is unitless and represents the percentage of the tracer contained in each finite element per unit mass of fluid. The total tracer mass fraction throughout the lumen will sum to unity, meaning all tracer injected at the inlet will flow through the outlets: it is assumed that the transport of the species is advection-dominant, such that the diffusive flux $\overrightarrow{J_i}$ is assumed to be negligible.²² Inherent to this approach, there is a one-way coupling between the contrast scalar and blood flow, meaning the contrast flow does not change the blood flow.

The tracer mass fraction was initialized as zero across the cross-sectional area of the inlet surface, and then set to a value of one for a user-defined duration, i.e., the duration of the injection. This value was set to ensure complete filling of the contrast tracer in the model, anywhere from 0.5 – 0.7 seconds, depending on the vessel morphology. Because the contrast traces the velocity field and does not interact with the blood medium, the injection does not perturb the underlying hemodynamics, representing an idealized scenario for API analysis. Again, the simulations met the convergence criteria of 1e⁻⁶ at each timestep, and the SIMPLE scheme was implemented with a second order formulation. A 1-millisecond timestep was chosen to balance both computational resources and simulation accuracy, and the transient contrast scalar fraction at each location in the finite element mesh was exported at every timestep for further manipulation outside of Ansys software.

C. Discretization of the In-Silico Dataset

The solution of the advection-diffusion equations results in a time-resolved, volumetric contrast agent concentration throughout the in-silico model. Initially, each dataset is represented as a point cloud with non-uniform spacing. We used in-house software (MATLAB vR2021b, Natick, MA) for all point cloud operations. Sequential rotations were manually applied to the point cloud to determine the best viewing angle of the aneurysm. To simulate the pulsing of the x-ray source at conventional frame rates (e.g., 3 – 30 fps), select point clouds and the corresponding contrast distributions were either temporally integrated or discarded according to the user-defined pulse width. In accordance with Bhurwani et al.¹¹, a higher frame rate of 25 fps was chosen to better capture the transient contrast dynamics within each model. In order to create the projection sequence, the point cloud data was then interpolated onto a structured Cartesian grid. The largest grid dimension was set at 512, and the other two dimensions were scaled accordingly for each model. Each gridded volume was then zero-padded to obtain an isotropic 3D matrix of size 512 x 512 x 512. A binary masking operation was performed to ensure that interpolation of the contrast data only occurred within the limits of the vessel lumen, while also ensuring the smooth contours of the original vessel structure were maintained. In the final gridded virtual angiogram, each voxel contains a numeric value directly representative of the contrast concentration during the pulse period, expressed as a value between zero (no contrast) and one (maximum concentration). Only the contrast-enhanced vessel is present in the resultant image, with no other attenuating structures.

D. X-Ray Projections and 3D Vessel Reconstruction

To generate simulated x-ray projections from the gridded in-silico contrast dataset, each volumetric contrast distribution was forward-projected along the source-detector axis using the open-source ASTRA toolbox²⁴ implemented in Python (Python 3.10, Wilmington, DE), assuming a cone beam geometry and monoenergetic source. Our in-silico dataset is already representative of the contrast concentration per voxel: thus, no logarithmic corrections were necessary prior to forward projection and the line integrals were calculated directly. A summary of all parameters related to the virtual projection geometry can be found in Table 1. The resultant projection images were 512 x 512 pixels and free of quantum mottle or motion-related artifacts (Figure 1A). In addition to the viewing angle determined by the user, a secondary biplane acquisition at 90° with respect to the user-defined viewing angle was generated (Figure 1B).

Table 1:

Projection geometry

Frame Rate	25 fps
Source-Object Distance	900 mm
Source-Image Distance	1100 mm
Pixel Size	200 µm
Angular Scan Range	202°
Number of Projections	108
3D Reconstruction Algorithm	Parker-Weighted FDK

A 3D reconstruction of the vessel of interest is necessary to create the pathlength-correction map. One option would be to use the corresponding patient CTA, and another option, which was used here, is to generate a reconstruction in the angiography suite directly with a cone-beam acquisition. Because the in-silico dataset used for API analysis requires a dynamic contrast injection, a separate “fully-enhanced” acquisition was generated using a temporal maximum intensity projection (MIP) through each gridded volume: the fully-opacified MIP provides the limits of contrast motion within the vessel geometry in 3D. From the MIP, rotational cone-beam projections were generated over an angular range of 202°, consistent with rotational DSA protocols at our institution (Figure 1C). The virtual scanner geometry matched that of the dynamic injection acquisition. A standard Parker-weighted²⁵ cone-beam reconstruction was performed, where the reconstructed volume was 512 x 512 x 512 voxels. The cone-beam-derived vessel reconstruction was used to generate the pathlength-correction map, as described below.

E. Pathlength Correction

The creation of the pathlength-correction map is straightforward: the x-ray path lengths are computed via a ray-driven forward projection operation using Siddon’s method.²⁶ A collection of line integrals through the vessel can be approximated as:

$$d= \int \rho \left(r\right)dr$$ (2)

where the digitally-subtracted image $d$ represents the integral of the voxel intensities $\rho$, and $r$ is a 3-dimensional vector. Using a binary reconstruction of the 3D vessel structure (either from CTA or cone-beam CT), the voxel indices corresponding to the vessel lumen are identified, and the corresponding intersection pathlengths $l$ are integrated along each ray path:

$$l=\int dr$$ (3)

The result of this process is a 2D map that visually appears almost identical to the projection image, but the pixel intensity is representative of the vessel thickness, as defined by the limits of contrast motion along each ray path. A pathlength correction map is obtained by:

$${\rho }_0=\frac{d}{l}$$ (4)

where the weighted contrast intensity ${\rho }_0$ along the ray path is recovered. Each frame of the dynamic contrast projection series is divided by this map such that the resulting sequence becomes “pathlength corrected”.

F. Angiographic Parametric Imaging Analysis

API was performed on three sets of data: 1) the ground-truth, gridded 3D contrast distribution, 2) the uncorrected 2D projection sequence, and 3) the pathlength-corrected 2D projection sequence. A TDC is calculated at each pixel or voxel and is parametrized to generate several biomarkers related to the underlying blood flow. The intensity-based parameters include peak height (PH), representative of the maximum contrast intensity, and area under the TDC (AUC), indicative of how much contrast has flown through that pixel or voxel. Temporal parameters include mean transit time (MTT), a measure of the time taken for the contrast to pass through a particular location, time to arrival (TTA), which indicates how much time it takes for the contrast to first arrive at that location (this is equivalent to 10% of the PH value), and time to peak (TTP), which indicates how much time it takes for the contrast to reach the PH value. Each TDC was fitted using a spline curve: because the in-silico sequences do not contain any quantum mottle or other imaging-related artifacts, the curves should only be representative of contrast flow, whether in 3D or projected.

Each biomarker is displayed as a color-coded map. Comparisons made between biplane views with and without pathlength-correction are quantified in terms of absolute percentage difference (PD) of biomarkers within the aneurysm ROI, where the aneurysm ROI is carefully segmented in each biplane views to minimize vessel overlap. Additionally, the PD of biomarkers within the aneurysm sac in the pathlength-corrected dataset is compared to the ground-truth 3D dataset. For this comparison, a volume of interest (3D-ROI) was carefully delineated around the aneurysm ROI. This 3D-ROI was then compared against the two-dimensional regions of interest (2D-ROIs) from each view in the pathlength-corrected maps. The average and standard deviation of each API parameter within the 3D aneurysm ROI served as the reference for comparison with pathlength-corrected 2D API values.

III. Results

A. Pathlength Correction Map

The biplane pathlength correction maps generated by the ray tracing operation are shown in Figure 2, where the color of each pixel is representative of the ray path length contribution. M1 and M3, having the largest aneurysms, show the greatest correction in the aneurysm sac where there is overlap with the outflow vessels (over 100 voxels). M2 and M4, having smaller aneurysms, show the greatest correction in regions of vessel foreshortening.

Figure 2:

Pathlength correction maps for biplane views of each aneurysm model (M1 – M4). Each map is color-coded according to the ray path length for each pixel on the detector plane.

B. Projection Dataset Comparison

Temporal biomarkers (MTT, TTP, TTA) were identical irrespective of pathlength correction, so these maps are not displayed. Figure 3 shows a comparison of biplane AUC and PH maps with and without pathlength correction, where the color scale is mapped to the maximum value for each parameter; note the lower bounds of the pathlength-corrected colormaps, which have been adjusted for improved visualization. The white arrows highlight regions of greater discrepancy between the maps, which correspond to areas of vessel foreshortening. As expected, the greatest differences occur where the vessel path lengths are the longest.

Figure 3:

Comparison of AUC and PH parameters with and without pathlength correction (PC) in M1 – M4 for biplane views (V1, V2). Each colormap is scaled to the maximum value for each parameter, for each view. Note the lower bounds of each colormap for the pathlength-corrected parameters, which have been adjusted for clarity. Aneurysm ROIs are indicated by the yellow dotted line. The white arrows indicate regions of a greater discrepancy, corresponding to vessel overlap and foreshortening.

CFD-derived velocity fields are provided for the biplane views of each model (supplemental material, Figure S-1) to aid in interpretation of API parameters. Notable differences are observed in the perceived accumulation of contrast media in the aneurysm sac for M1 and M3 with and without pathlength correction. For instance, the spatial distribution of PH values in M3 view 1 illustrates that the greatest accumulation of contrast occurs along the outer left edge of the aneurysm dome in the corrected map. In the uncorrected map, the maximal PH values are found in the center of the aneurysm sac, where the interfering flow from the parent artery would cause recirculation rather than stagnation. The PH “hot spot” is a result of vessel overlap; the same focal region of elevated PH values is not replicated in the uncorrected view 2 map.

The corrected AUC maps indicate that the contrast media is advected through the inflow vessel and recirculates in the aneurysm, whereas the uncorrected maps suggest that more contrast is flowing through foreshortened vessels. In M1, similar behavior is observed: the residual recirculating contrast in the aneurysm dome is reflected in the AUC maps, where the maximal AUC value is consistent across the inflow and outflow vessels in both views. Across all models, corrected AUC maps adhere more closely to the principle of mass conservation: there should be little variation in AUC if a complete washout of the contrast media is achieved. PH values should be relatively constant in M2 and M4 as these aneurysms are smaller, and less recirculation occurs. A small amount of diffusion of contrast media is expected as it is injected from the inlet to the outflow vessels, thus, a small decrease in PH moving distally is expected.

Quantitative comparisons within each 2D aneurysm ROI (yellow outline around each aneurysm sac, Figure 3) are given in Table 2, including temporal parameters TTA, MTT, and TTP. Because pathlength correction had no effect on the temporal parameters, single values are reported for each biplane view. Unless otherwise indicated, ROI averages are reported as the mean value ± standard deviation, where the standard deviation is indicative of the heterogeneity of the biomarker within the ROI. The PD between biplane views, with and without pathlength correction, is reported for the intensity-based parameters: in each aneurysm ROI, the maximum PD between views for both AUC and PH is 3.3% with pathlength correction and 47.7% without pathlength correction. The difference in the magnitude of ROI-averaged AUC and PH is as high as a factor of 75 after pathlength correction. For example, in M1, pathlength correction substantially reduces the maximum and average AUC and PH values, implying that pathlength correction is crucial for accurate representation in this model. For M2, pathlength correction doesn't notably affect the AUC values, either average or maximum. The PH values, however, show a slight decrease with pathlength correction. This suggests that pathlength correction may not significantly impact AUC in this model but does affect PH. Overall, these results suggest that the impact of pathlength correction can vary depending on the vessel morphology and the parameters being measured (AUC or PH). While the effect on AUC seems minimal in some models, the PH values tend to show more noticeable changes with pathlength correction. Therefore, pathlength correction appears to be an essential step in obtaining accurate PH values across all models, while its influence on AUC may depend on the vessel morphology and projection view in question. The ROI-averaged temporal parameters are consistent between views, with greater differences in the maximum values (maximally 24.4% between biplane views). Across all models, one of the biplane projections contains a view of the aneurysm sac where there is appreciable vessel overlap and foreshortening. While the magnitude of the contrast value per pixel is changed with pathlength correction, the relative change per-frame is not: the greatest differences are seen with TTA, where any vessel overlap will skew the perceived arrival time of contrast in the projection image.

Table 2:

Quantitative comparison between biplane views of projected datasets, aneurysm ROI. Temporal parameters are given in seconds. Because pathlength correction (PC) had no effect on the temporal parameters, single values are reported for each biplane view. Intensity parameters represent the contrast concentration, either the integral in the case of no PC, or weighted average in the case of PC.

Intensity-based parameters										Temporal parameters
		2D AUC				2D PH					2D MTT		2D TTA		2D TTP
Model #		PC		No PC		PC		No PC			Average	Max	Average	Max	Average	Max
				Average	Max	Average	Max	Average	Max								Average	Max
1
View 1		7.97 ± 0.26	9.00	600.88 ± 56.12	1018.14	6.73 ± 0.46	8.98	486.34 ± 37.55	842.17	View 1	1.18 ± 0.08	2.23	0.27 ± 0.05	1.44	1.20 ± 0.06	2.76
View 2		7.82 ± 0.32	9.01	388.24 ± 38.39	683.67	6.51 ± 0.42	8.98	316.11 ± 42.40	656.02	View 2	1.23 ± 0.06	2.43	0.29 ± 0.06	1.84	1.22 ± 0.07	2.76
P.D.		1.9%	0.1%	43.0%	39.3%	3.3%	0.0%	42.4%	24.9%	P.D.	4.2%	8.6%	7.1%	24.4%	1.7%	0.0%
2
View 1		4.48 ± 0.01	4.49	110.21 ± 22.82	276.04	8.78 ± 0.08	8.88	216.18 ± 44.53	542.63	View 1	0.58 ± 0.02	0.82	0.23 ± 0.02	0.40	0.67 ± 0.02	0.83
View 2		4.48 ± 0.00	4.49	104.18 ± 13.42	169.79	8.81 ± 0.04	8.88	204.93 ± 26.53	334.42	View 2	0.58 ± 0.01	0.71	0.23 ± 0.01	0.34	0.67 ± 0.01	0.76
P.D.		0.0%	0.0%	5.6%	47.7%	0.3%	0.0%	5.3%	47.5%	P.D.	0.0%	14.4%	0.0%	16.2%	0.0%	8.8%
3
View 1		7.74 ± 0.06	8.08	475.92 ± 72.83	905.41	7.40 ± 0.19	8.99	446.64 ± 62.28	827.55	View 1	1.14 ± 0.03	1.57	0.31 ± 0.01	0.72	1.12 ± 0.02	1.60
View 2		7.73 ± 0.10	8.07	540.05 ± 52.77	1075.61	7.36 ± 0.15	8.98	509.25 ± 50.25	1004.78	View 2	1.14 ± 0.05	1.60	0.31 ± 0.04	0.67	1.12 ± 0.04	1.84
P.D.		0.1%	0.1%	12.6%	17.2%	0.5%	0.1%	13.1%	19.4%	P.D.	0.0%	1.9%	0.0%	7.2%	0.0%	14.0%
4
View 1		4.48 ± 0.00	4.49	183.21 ± 15.48	284.63	8.89 ± 0.02	8.93	362.99 ± 30.51	563.02	View 1	0.55 ± 0.01	0.64	0.21 ± 0.00	0.30	0.64 ± 0.01	0.72
View 2		4.48 ± 0.0	4.49	199.61 ± 14.67	337.35	8.89 ± 0.01	8.94	395.46 ± 28.98	667.35	View 2	0.55 ± 0.00	0.63	0.22 ± 0.00	0.28	0.64 ± 0.00	0.72
P.D.		0.0%	0.0%	8.6%	17.0%	0.0%	0.1%	8.6%	17.0%	P.D.	0.0%	1.6%	4.7%	6.9%	0.0%	0.0%

C. Ground-Truth Dataset Comparison

Moving forward, the pathlength-corrected 2D-API maps are compared to the ground-truth 3D-API maps. Several axial slices within the ground-truth aneurysm ROI are plotted in Figure 4 for M1 and M3. Compared to the pathlength-corrected maps in Figure 3, several features are replicated: with regards to spatial distribution, the PH values in M3 are again greatest along the outer periphery of the aneurysm dome, with greater heterogeneity in proximity to the inflow artery. In M1, the AUC values are lowest in the center of the aneurysm. Also shown are the temporal descriptors of contrast flow (MTT, TTA, TTP). In each case, the temporal flow behavior is complex and spatially variant from the center of the aneurysm sac to the outer edges but can be correlated with the intensity-based biomarkers.

Figure 4:

Comparison of all ground-truth, 3D-API biomarkers in M1 (left) and M3 (right). Three axial slice locations are shown for each model (planes 1, 2, and 3). Each color bar is representative of the voxel value for each biomarker: the PH and AUC maps are scaled to match the corresponding 2D maps, the temporal maps are scaled to the maximum value.

Table 3 offers a detailed comparative analysis of all biomarkers between the ground-truth volume and the pathlength-corrected dataset, focusing on the region of interest (ROI) around the aneurysm. The PD between each view and the ground-truth volume is reported: the maximum PD for both AUD and PH does not exceed 5.8%, showcasing a reasonable alignment between the pathlength-corrected 2D projections and the ground-truth 3D volume. Reinforcing the findings from the 2D comparison in Table 2, the PD in magnitude for AUC and PH demonstrated more pronounced variations for the larger aneurysm models, namely M1 and M3. This suggests that the size of the aneurysm may impact the accuracy of pathlength-corrected 2D projections. When comparing temporal parameters within the aneurysm ROI, higher PD values are encountered. However, it's important to note that the magnitudes of these parameters across all cases are quite low (less than 3 seconds). Thus, although the relative PD appears larger, the absolute differences remain relatively small, suggesting that the pathlength-corrected projections still provide a reasonably accurate representation of the ground-truth 3D data. This is the result irrespective of correcting for the vessel thickness, as the temporal metrics should indeed be independent of intensity magnitude. This is crucial in ensuring the reliability of these pathlength-corrected 2D projections for analyzing aneurysm contrast flow behavior.

Table 3:

Quantitative comparison between ground-truth volume and pathlength-corrected (PC) projections, aneurysm ROI. Temporal parameters are given in seconds. Intensity parameters represent the contrast concentration.

Intensity-based parameters						Temporal parameters
Model #		3D AUC		3D PH			MTT		TTA		TTP
		Average	Max	Average	Max		Average	Max	Average	Max	Average	Max
1
3D ROI		7.83 ± 0.17	9.11	6.90 ± 0.19	9.00	3D ROI	1.25 ± 0.04	2.65	0.39 ± 0.04	2.45	1.34 ± 0.06	2.76
P.D. V1		1.8%	1.2%	2.5%	0.2%	P.D. V1	8.1%	15.0%	36.4%	51.9%	11.0%	0.0%
P.D. V2		0.1%	1.1%	5.8%	0.2%	P.D. V2	4.8%	9.1%	29.4%	28.4%	9.3%	0.0%
2
3D ROI		4.48 ± 0.03	4.50	8.82 ± 0.08	8.90	3D ROI	0.57 ± 0.01	0.98	0.23 ± 0.02	0.50	0.67 ± 0.01	1.28
P.D. V1		0.0%	0.2%	0.5%	0.2%	P.D. V1	1.7%	17.8%	0.0%	22.2%	0.0%	42.7%
P.D. V2		0.0%	0.2%	0.1%	0.2%	P.D. V2	1.7%	32.0%	0.0%	38.1%	0.0%	51.0%
3
3D ROI		7.74 ± 0.03	8.10	7.8 ± 0.07	8.99	3D ROI	1.15 ± 0.02	1.74	0.39 ± 0.02	0.95	1.21 ± 0.02	2.20
P.D. V1		0.0%	0.3%	5.3%	0.0%	P.D. V1	1%	10%	23%	28%	8%	32%
P.D. V2		0.1%	0.4%	5.8%	0.1%	P.D. V2	1%	8%	23%	35%	7%	18%
4
3D ROI		4.48 ± 0.00	4.50	8.9 ± 0.01	8.96	3D ROI	0.55 ± 0.00	0.81	0.23 ± 0.00	0.46	0.66 ± 0.00	0.84
P.D. V1		0.0%	0.2%	0.1%	0.3%	P.D. V1	0.0%	23.5%	9.1%	42.1%	3.1%	15.4%
P.D. V2		0.0%	0.2%	0.1%	0.2%	P.D. V2	0.0%	25.0%	4.4%	48.7%	3.1%	15.4%

IV. Discussion

DSA is commonly used to qualitatively diagnose, treat, and evaluate neurovascular diseases, such as IA’s. The importance of hemodynamics in the initiation and development of IA’s is undeniable, and their treatment often involves modulation of the local hemodynamic environment through the use of coils and stents.^27,28 While there is value in extracting this information directly from diagnostic imaging, obtaining quantitative hemodynamic data in the interventional suite remains a complex task.²⁹ Multiple strategies have been used in an attempt to quantify these hemodynamic changes in-vivo, including API, where there is substantial evidence that contrast flow is strongly correlated with the underlying hemodynamics, provided the contrast injection does not overpower the systemic flow.^30–34

DSA offers superior spatial resolution, necessary for the visualization of complex vessel morphology and placement of endovascular devices, and sufficient temporal resolution to visualize the transit of contrast media. Yet, the standard 2D projections of the vasculature can result in vessel overlap and foreshortening of vessels positioned along the source-detector axis, making an assessment of flow fields in complex morphologies difficult. To address this, we explored the use of a pathlength-correction metric to improve the interpretability of conventional projection imaging-derived biomarkers. This metric was assessed on four aneurysm geometries, ranging from small and relatively simple aneurysms to large aneurysms with tortuous vessels. To assess the performance of such a metric, an in-silico CFD framework was developed to provide a ground-truth distribution of contrast in 3D. Mimicking a standard cone beam geometry, corresponding projection sequences were then generated in an effort to quantify the effect of projection imaging on recoverable hemodynamics, in the absence of any other confounding factors such as quantum mottle or other attenuating tissues.

Our preliminary analysis indicated that correcting for the vessel thickness along the source-detector axis brings our 2D imaging biomarkers into better agreement with that of their 3D counterparts, both quantitatively as averaged over the aneurysm ROI, and qualitatively, in terms of spatial distribution of the biomarkers and interpretable flow in 2D. The effect was more profound for the larger aneurysm geometries (M1, M3), as the depth-integrating effect is more prominent. The flow fields in these vessels are inherently more complex, complicating the evaluation of recirculation, stagnation, and jet impingement due to the projection imaging effect. Comparing all API biomarkers between the corrected 2D and ground-truth 3D datasets, the ROI-averaged intensity-based parameters aligned well, with greater variation observed with the larger aneurysms. Because the pathlength-corrected maps are representative of the voxel-averaged intensity, we would expect this to be the case. Importantly, the hemodynamic information post-correction better correlates with that shown in the 3D axial slices, illustrating that recovery of the average intensity per voxel may be sufficient in interpreting flow from 2D images. When comparing temporal parameters between the datasets, there was no difference between the 2D projected datasets before and after pathlength correction, but more variation compared to the ground-truth 3D data. However, the intensity-based parameters' magnitudes were much higher compared to the temporal parameters, so the PD between the temporal parameters was effectively larger. Additionally, a threshold was used for TTA (10% of the PH value), which is used in the clinical environment to ensure contrast motion is forming the basis of these temporal biomarkers, rather than noise or motion artifacts.

Comparing biplane views across all models, a profound difference in the spatial distribution of 2D-API biomarkers was obtained in regions of vessel foreshortening, which otherwise results in artificial inflation of PH and AUC that is inconsistent with our understanding of fluid mass conservation. AUC and PH “hotspots” are present in the uncorrected dataset, often in regions of vessel overlap at the aneurysm neck. This effect can be mitigated through the use of multiple projection views, but the relative 2D-API maps visually do not correlate well between views. This poses a significant limitation of the 2D-API, which makes a quantitative angiography diagnosis view-dependent. By removing vessel thickness dependence, the relative PD between biplane biomarkers was minimal, and a qualitative evaluation of the API maps showed good agreement between views. It should be emphasized that the applied correction is different for each projection view, but the end result shows negligible differences between biplane views when averaged over an ROI, which is expected as the same flow conditions are present. Importantly, this correction could therefore allow comparisons of biomarkers from multiple DSA acquisitions without requiring an identical acquisition angle or field of view, provided additional measures are taken to compensate for injection variability. Moreover, the correction will provide a more robust framework to correlate observed 2D-API patterns with neurovascular disease severity and treatment outcome.

Although the use of CFD to diagnose patient-specific aneurysm hemodynamics can be controversial, in this context, it is a useful tool in generating a reference for 3D contrast flow. Further, CFD is one of the most established methods used for the evaluation of intra-aneurysmal hemodynamics.^35,36 By generating ground-truth contrast distributions, we can continue to not only test the algorithm accuracy to recover hemodynamic-correlated 2D and 3D imaging biomarkers, but we can also explore the effects other elements within the imaging chain will have on flow quantification: image noise, frame rate, and angular coverage, to name a few. Future studies will need to evaluate the potential contribution of these effects when translating a pathlength correction metric to the actual C-arm gantry, where additional parameters such as scattered radiation and kV-dependence would cause further variability as compared to the idealized, monoenergetic simulation framework used in this study. Applied to clinical data, use of this correction factor would represent the weighted average of linear attenuation along each ray path, which would possess an energy dependence due to the nature of the polychromatic x-ray source. This assumption would affect the recovery of intensity-based parameters PH and AUC, thus calibration factors for typical spectra should be investigated for use with a clinical system.

Additionally, further exploration of the effect of the contrast injection parameters on image-derived biomarkers is warranted. It should be noted that additional methodologies have been developed to simulate the physical interaction between both the blood and contrast materials¹⁸: because our focus was to generate a 3D ground-truth contrast flow object, thus enabling a deeper exploration of foreshortening effects and the development of an appropriate correction schema, the passive scalar approach provided the optimal framework to complete this investigation. The use of an automated contrast injection at an appropriate distance from the aneurysmal ROI ideally will not perturb the underlying hemodynamics, although this a general limitation of all quantitative angiographic methods. The API methodology is meant to convey bulk flow parameters, which relies on the assumption that the vessel is homogeneously filled with contrast at depth: detailed filling, inflow jet impingement, and recirculation of contrast streamlines within the aneurysm dome would not be captured. Alternative contrast injection techniques in conjunction with high resolution hemodynamic analysis have been proposed to analyze these finer flow details.^37,38 In both cases, higher acquisition frame rates have been shown to improve hemodynamic analysis along with greater consideration for the contrast injection technique.

It is important to note that many studies have also highlighted the advantages of transitioning towards a volumetric, 4D-DSA approach, which is largely applied to temporal imaging biomarkers at this time.^15,39 When applying current clinically-implemented 4D-DSA techniques to aneurysm models, the rotational acquisition results in the deposition of an average intensity throughout the vessel cross-section per image frame, similar to the 2D pathlength-corrected series, but the contrast motion is not captured fully in all projection views.¹⁹ This is a somewhat straightforward conclusion as we still have a limited resolution of contrast flow along the source-detector direction; however, additional methodologies are currently under investigation with the aim of reconstructing true 3D flow details within complex vascular geometries.⁴⁰ The benefit of the proposed correction metric is its use with all acquired planar DSA’s without an additional rotational acquisition, provided a 3D reconstruction of the vessel of interest is available. Additional quantitative methodologies based on the motion of contrast media have been explored and could potentially benefit from such a correction.^37,38

The 4D-DSA approach does take vessel overlap into account, which was not explored here: we would expect erroneous deposition of contrast signal in overlapping vessels to cause further deviation of temporal parameters from the true 3D contrast flow, as is shown in Table 3. For overlapping parent vessels, the correction metric improves the qualitative interpretation of AUC and PH, although it does not mitigate the effect entirely. However, interventionalists commonly acquire DSA’s using the projection view with the least vessel overlap for pre-/post-treatment, although these exact views may differ, which makes the use of these API maps difficult for true interpretation of flow. We intend for this correction to be applied to such acquisitions, where a focal aneurysmal ROI is evaluated.

Paramount to the use of a pathlength-correction metric in a clinical setting is an accurate 3D reconstruction of the vessel morphology. This could be derived from cone-beam CT or CTA and would require a 3D–to–2D registration procedure. Most studies contain one or both of these acquisitions, and in the potential case of patient motion, the feasibility of such a co-registration procedure must be explored in future studies. All geometric inputs to the current in-silico framework can be derived from the associated DSA DICOM header, making the current pathlength-correction framework translatable for future benchtop studies. Additionally, the ray tracing operation used to generate the correction map is well suited to CPU parallelization, which was implemented in this study. It is expected that offloading these calculations to the GPU would further optimize processing time.

V. Conclusions

A simulated angiographic framework was designed to better understand the limitations of quantitative angiography in the projection domain: biplane results indicate that intensity-based 2D-API parameters without pathlength correction are highly dependent on the C-arm orientation and should be avoided for hemodynamic analysis. Pathlength correction can standardize API-derived biomarkers independent of the C-arm orientation, potentially improving the diagnostic value of all acquired 2D-DSA’s, and thereby offering a promising avenue for improved intraoperative diagnostic accuracy in cerebral vasculature analysis.

Supplementary Material

Supinfo

Supplemental Figure 1: Biplane (V1, V2) velocity streamlines displayed for each 3D model (M1 – M4), where the velocity field is constant over time. The color bar represents velocity magnitude (cm/s). Regions of recirculation can be seen in each aneurysm sac, while variations in vessel morphology produce a range of velocities in the inflow and outflow vasculature.