Spatiotemporal frequency domain analysis for blood velocity measurement during embolization procedures

Abstract

Background:

Currently, determining procedural endpoints and treatment efficacy of vascular interventions is largely qualitative and relies on subjective visual assessment of digital subtraction angiography (DSA) images leading to large interobserver variabilities and poor reproducibility. Quantitative metrics such as the residual blood velocity in embolized vessel branches could help establish objective and reproducible endpoints. Recently, velocity quantification techniques based on a contrast enhanced x-ray sequence such as qDSA and 4D DSA have been proposed. These techniques must be robust, and, to avoid radiation dose concerns, they should be compatible with low dose per frame image acquisition.

Purpose:

To develop and evaluate a technique for robust blood velocity quantification from low dose contrast enhanced x-ray image sequences that leverages the oscillating signal created by pulsatile blood flow.

Methods:

The proposed spatiotemporal frequency domain (STF) approach quantifies velocities from time attenuation maps (TAMs) representing the oscillating signal over time for all points along a vessel centerline. Due to the time it takes a contrast bolus to travel along the vessel centerline, the resulting TAM resembles a sheared sine wave. The shear angle is related to the velocity and can be determined in the spatiotemporal frequency domain after applying the 2D Fourier transform to the TAM. The approach was evaluated in a straight tube phantom using three different radiation dose levels and compared to ultrasound transit-time-based measurements. The STF velocity results were also compared to previously published approaches for the measurement of blood velocity from contrast enhanced x-ray sequences including shifted least squared (SLS) and phase shift (PHS). Additionally, an in vivo porcine study (n=8) was performed where increasing amounts of embolic particles were injected into a hepatic or splenic artery with intermittent velocity measurements after each injection to monitor the resulting reduction in velocity.

Results:

At the lowest evaluated dose level (average air kerma rate 1.3mGy/s at the interventional reference point) the Pearson correlation between ultrasound and STF velocity measurements was 99%. This was significantly higher (p< 0.0001) than corresponding correlation results between ultrasound and the previously published SLS and PHS approaches (91% and 93%, respectively). In the in vivo study, a reduction in velocity was observed in 85.7% of cases after injection of 1ml, 96.4% after 3ml, and 100.0% after 4ml of embolic particles.

Conclusions:

The results show good agreement of the spatiotemporal frequency domain approach with ultrasound even in low dose per frame image sequences. Additionally, the in vivo study demonstrates the ability to monitor the physiological changes due to embolization. This could provide quantitative metrics during vascular procedures to establish objective and reproducible endpoints.

I. Introduction

Digital subtraction angiography (DSA) plays a critical role in vascular procedures such as angioplasty, stent placement, and transarterial embolization (TAE) as it is used universally for vascular image guidance. Currently, vascular interventions are largely qualitative, relying on subjective visual assessment of DSA images to diagnose pathology, determine procedural endpoints, and evaluate treatment efficacy. Assessment of DSA images depends on observer experience and perceptual bias, both of which are a significant source of interpretive error¹. This leads to high interobserver variability and a decrease in reproducibility^2,3,4,5. For example, liver embolization is a minimally invasive treatment option for patients with intermediate or advanced HCC and select patients with liver metastases which has shown to be safe and effective^6,7,8. Embolization reduces the amount of blood flow to the tumor by injecting embolic material (e.g. microspheres) into tumor feeding arteries. The amount of blood flow reduction achieved during embolization procedures is crucial to achieve favorable outcomes. Under-embolization may fail to achieve tumor necrosis while over-embolization may result in increased loss of healthy tissue and may lead to complications. Currently, no quantitative metrics exist to determine procedure endpoints and radiologists primarily rely on subjective visual assessments of digital subtraction angiography (DSA) images. Quantitative metrics such as the residual blood velocity in embolized vessel branches could help establish objective and reproducible endpoints and evaluate treatment efficacy during vascular procedures.

Quantitative DSA (qDSA)^9,10 and 4D DSA^{11,12,13,14,15,16} have previously been proposed as non-invasive methods to determine blood velocity and flow intraprocedurally. Both methods rely on contrast-enhanced image sequences, where information on blood velocity can be inferred by tracking the movement of contrast agent in the vessels of interest. Generally, the dynamic information is extracted in the form of time-attenuation curves (TACs) describing the change in signal at one location over time. In the case of qDSA, 2D DSA sequences are used where TACs are calculated for a series of points along a vessel of interest. The 4D DSA approach uses a rotational acquisition, where each projection image is acquired from a different orientation enabling the 3D reconstruction of the vessel anatomy. The dynamic information is then extracted by back-projecting each 2D image into the 3D space of the sparse vessel anatomy.

Blood velocity can be determined by comparing the TACs at different points along a vessel centerline. The shifted least-squares approach¹⁶ estimates the time shift between each pair of TACs from a given centerline using an iterative approach which minimizes the mean squared error. A linear fit to the observed time shifts versus distance shifts along the centerline is used to compute velocity for the vessel segment. A similar approach using the cross-correlation to align TACs was proposed by Bursch et al.¹⁷ Shaughnessy et al.¹⁸ proposed the use of frequency space phase shifts in periodic bolus curves instead of time shifts. Disadvantages of these approaches include the individual processing of point pairs, which usually results in larger errors for pairs with smaller distances between points. Additionally, these approaches can be sensitive to contrast dispersion, where the shape of a TAC changes along the vessel centerline. Finally, the iterative fitting and alignment may cause inaccuracies due to local minima. Another group of approaches uses Indicator-dilution theory to determine flow and velocity in a volume of interest^19,20,21. However, these approaches generally require knowledge about the exact amount of injected contrast, are not well suited for cases with pulsatile flow, and require conversion of image intensity to contrast material concentration, which can lead to inaccuracies²². A more comprehensive review of quantitative blood flow and velocity analysis approaches is given in Shpilfoygel et al.²². All of the above-mentioned approaches require high frame rate (up to 30 frames per second) x-ray acquisitions leading to concerns about radiation dose^9,23,24. Using even higher frame rates (up to 1000 frames per second) enables the use of optical flow tracking techniques as well as particle image velocimetry to determine complex flow patterns e.g. within aneurysms and could offer advantages in the evaluation of vessel segment blood velocity as well.^25,26,27 High frame rate qDSA should be paired with methods to manage dose, and to this end, image analysis techniques which perform well at low dose per frame are desirable.

The purpose of this work was to develop and evaluate a velocity quantification approach for contrast enhanced x-ray sequences with periodic contrast signal (pulsatile flow), which is robust against imaging noise. The proposed spatiotemporal frequency domain approach provides a single step algorithm (non-iterative) that uses information from all TACs along a vessel centerline simultaneously.

II. Materials and Methods

The proposed technique analyses 2D x-ray image sequences acquired during injection of contrast agent to quantify the blood velocity along vessel centerlines. The mixing of pulsatile blood flow in arteries with an injected contrast agent generates periodic changes in contrast which can be tracked as the blood flow carries the contrast agent downstream. A preprocessing step extracts the dynamic contrast signal from the x-ray sequences to generate time attenuation curves for each point in a vessel. Velocity quantification is then performed based on an analysis of the spatiotemporal frequencies.

II.A. Data Preparation

To extract the oscillating contrast signal and remove static background in the x-ray image sequence, a non-contrast x-ray image frame may be logarithmically subtracted from each contrast enhanced image (DSA). This process removes any static signal but may cause artifacts in cases with motion or overlap between different vessels. In the latter case, the dynamic signal from two different vessels may interfere and affect velocity quantification. Within this work, two additional strategies will be investigated and compared to static mask subtraction. In the first approach, each pair of temporally adjacent x-ray images in the sequence were subtracted resulting in peaks near the leading and trailing edge of each contrast pulse. The very short time difference between the two image frames helps minimize motion artifacts. Additionally, the risk of observing overlapping signal from two different vessels is reduced since accumulating contrast in the vessels is subtracted and signal is only observed around the edges of each contrast pulse. The second approach uses the native x-ray images without subtraction for velocity quantification and relies on the frequency analysis (see section II.B.) to distinguish between dynamic and static signal. Fig. 1 shows examples of each subtraction approach.

Figure 1:

A) Original contrast-enhanced x-ray image frame without subtraction. B) Subtracted contrast enhanced x-ray image using static mask (DSA). C) Sequence of x-ray image frames with adjacent frame subtraction, where the leading bolus edge is annotated with a white arrow.

Independent of the type of subtraction, time-attenuation maps (TAMs) are computed for the vessels of interest. To this end, the vessel centerline was extracted by manually placing start and end points. The vessel was then segmented using a threshold-based approach within a region of interest containing both points. Subsequently, a distance map D was computed, where each pixel represents the Euclidean distance to the closest non-vessel pixel. Using Dykstra’s algorithm, the centerline was extracted by determining the path P = [p₁,p₂,…,p_n] from start to end point which minimizes

$$\mathit{\text{cost}}(P)=-\sum _{i=1}^{n}D{\left(p_i\right)}^2.$$ (1)

To calculate the TAM for velocity quantification, the centerline was sampled at equidistant points. For each point, the intensity value in each x-ray image frame was interpolated resulting in a 2D map, where the x- and y-axes represent time and distance from the start point respectively and the pixel value is the corresponding contrast signal. Fig. 2 shows examples of a vessel centerline and corresponding TAM.

Figure 2:

A) Annotated centerline with user selected start and end point on subtracted x-ray frame. B) Time attenuation map showing periodic contrast changes along the time axis at approximately 1 Hz with increasing shift with distance to the injection site (shear).

A preprocessing step was employed to remove low frequency signal from the time attenuation curves, e.g. due to the accumulation of contrast in the vessel. To this end, a fourth degree polynomial was fit to each row of the TAM and subsequently subtracted. A least absolute residual approach was used to reduce the influence of outliers (e.g. due to the high frequency pulsatile signal).

Since in vivo, vessel motion due to the pulsatile flow changes may occur during the acquisition of the contrast enhanced images sequences, a motion compensation approach proposed by Whitehead et al.¹⁰ was implemented to update the vessel centerline shape and position on a frame by frame basis. The approach uses a small ROI around the centerline and performs a local rigid registration followed by a deformable registration using the diffeomorphic demons approach²⁸. The resulting deformation vector fields (DVFs) were then smoothed over time by fitting a 3D smoothing spline to each pixel. A dynamic centerline is then calculated by applying the DVF for each frame to the static centerline extracted from a single image frame.

II.B. Velocity Quantification

The variations in contrast agent concentration (“contrast pulses”) which are tracked to estimate blood velocity are visible in the TAM as periodic intensity oscillations along the temporal axis. Let f(x,y) be the 2-dimensional function representing the TAM with x being the time from the start of the contrast injection in seconds and y the distance from the start point in cm. The corresponding 2D (spatiotemporal) Fourier space is represented by function F(ξ,ψ) with

$$F(\xi ,\psi )={\iint }_{-\infty }^{\infty }f(x,y)e^{-i2\pi (\xi x+\psi y)}\mathit{\text{dxdy}}.$$ (2)

Based on the Fourier theorem, any periodic function that satisfies the Dirichlet conditions can be represented by a linear combination of harmonic sinusoidal functions. In the frequency space, this can be represented by a series of Dirac delta functions at the fundamental and harmonic frequencies. If the periodic pattern is strictly parallel to the spatial axis, the peaks are located at ψ = 0 and ξ = λω, where λ is an integer and ω is the fundamental frequency of the periodic signal. For any velocity v, where 0 < v < ∞, the time of arrival Δt_i of a contrast pulse at the i^th point along a defined vessel segment is dependent on the distance Δd_i from the start point. The intensity variations present at the first point appear temporally shifted for more distal points creating a shear in the periodic pattern. The slope m of this sheared pattern is directly related to the total distance d and the total time t for the transit of the contrast pulse along the segment and thus the average velocity v,

$$v=\frac{d}{t}=m.$$ (3)

The shear operation along the temporal direction can be written as

$$x^{\prime }=x+\frac{y}{m}\text{and}y\text{'}=y.$$ (4)

In the frequency domain this transformation is manifested as an inverse shear along the spatial frequency direction, which can be shown using the substitution method. If F^′(ξ,ψ) is the 2D Fourier transform of the sheared function f(x + y/m,y)

$$\begin{array}{c}{F}^{\prime }(\xi ,\psi )={\iint }_{-\infty }^{\infty }f(x+y/m,y)e^{-i2\pi (\xi x+\psi y)}dxdy\\ ={\iint }_{-\infty }^{\infty }f\left(x^{\prime },y^{\prime }\right)e^{-i2\pi \left(\xi \left(x^{\prime }-y^{\prime }/m\right)+\psi y^{\prime }\right)}\left|J\right|d{x}^{\prime }d{y}^{\prime }\\ ={\iint }_{-\infty }^{\infty }f\left(x^{\prime },y^{\prime }\right)e^{-i2\pi \left(\xi x^{\prime }+(\psi -\xi /m)y^{\prime }\right)}d{x}^{\prime }d{y}^{\prime }\\ =F(\xi ,\psi -\xi /m)\end{array}$$ (5)

where |J| = 1 is the determinant of the Jacobian matrix of the shear operation. Thus, the slope and therefore the velocity v can be determined based on the location of the fundamental frequency peak (ξ_ω,ψ_ω) = (ω,−ω/m) in the 2D Fourier space using

$$v=m=-\frac{{\xi }_{\omega }}{{\psi }_{\omega }}.$$ (6)

To identify the fundamental frequency peak location, the 2D power spectrum PS(f) = ∥F(ξ,ψ)∥² was calculated for the TAM using the 2-dimensional fast Fourier transform (FFT). Prior to applying the FFT, the global mean of the TAM was subtracted to remove the constant offset and zero padding was used to decrease the spacing between frequencies. The location corresponding to the maximum value in the power spectrum was then used as the fundamental frequency peak. Fig. 3 shows a 2D Fourier transform of a TAM with fundamental frequency peak.

Figure 3:

2D Fourier transform (absolute values) of the time attenuation curve with fundamental frequency peak at (u_ω,v_ω).

II.C. Study Design

A phantom study was performed to evaluate the accuracy of the proposed velocity quantification approach. The phantom setup consisted of a straight PVC tube (6.35 mm diameter) representing the vessel of interest, which was connected to a pulsatile flow pump (BDC Laboratories, Wheat Ride, CO). A Y-adapter for contrast injection was placed between the tube and pump, where a 5 Fr flush tipped injection catheter was inserted into the straight tube. Contrast injection (Omnipaque 300 mgI/mL) was performed using a Nemoto Press Duo power injector (Nemoto Kyorindo, Bunkyo-ku, Tokyo) with a flow rate of 2.0 ml/s for 7.0 s. The end of the straight tube and the input to the pulsatile pump were connected to a reservoir containing blood mimicking fluid (60–40 water-glycerol mix by volume). Reference flow measurements were performed with an external volumetric flow ultrasound probe (lc, Ithaca, NY) placed around the straight tube approximately 40 cm after the injection site. Flow measurements were subsequently converted to average velocities using the known tube diameter. The flow probe determines velocity based on the ultrasound transit time between two piezoelectrical crystals in both up and downstream directions. Immediately prior to each experiment, the ultrasound flow probe was calibrated by measuring flow at 5 different baseline velocities ranging from 25 to 45 cm/s. The references flow was calculated using a bucket test and a linear fit between reference and ultrasound measurements was calculated.

During the experiment, a biplane angiography system (Artis zee, Siemens Healthineers, Forchheim, Germany) was used to acquire x-ray image sequences. The pump settings were adjusted to provide velocities between 20 and 40 cm/s (without contrast injection) in intervals of 5 cm/s as measured with the reference ultrasound probe in the straight tube. During contrast injection a slight increase in velocity was observed in each case. For each baseline velocity, 6 image sequences with separate contrast injections were acquired to determine the variance within repeat measurements at the same condition. To this end, errors were calculated for each individual measurement and the standard deviation for each group calculated. This provides a measure of the repeatability of qDSA measurements and is important to determine whether qDSA can be used to determine relative changes in velocity during procedures. The tube was positioned along the rotation axis of the C-arm approximately at isocenter resulting in a magnification factor of 1.6 at the detector. Since the length of the analyzed vessel segment impacts the accuracy of velocity measurements, the qDSA analysis was performed on a 1 to 3 cm long segments of the tube representative of typical vessels of interest in the liver (around 2 to 4 cm).

Image sequences were acquired at 3 dose levels (11.3 mGy/s, 3.6 mGy/s, 1.3 mGy/s air kerma at the interventional reference point) for each velocity with a frame rate of 25 frames per second (fps), isotropic pixel size of 0.308 mm, and source detector distance of 120 cm. The air kerma rates and exact frame rates for all protocols were measured using a RadCal AccuGold meter with an AGMS-D+ sensor (102.4 μs sample period). The RadCal meter was attached to the detector of the C-arm without the phantom in the beam and the x-ray tube techniques employed with the phantom scans were reproduced. The measurements were subsequently scaled to the interventional reference point using the inverse square law (60 cm from focal spot). The highest air kerma rate corresponds to a 25 fps acquisition with the same kerma per frame as a clinical DSA with automatic exposure control programmed to 3.6 μGy/frame at the detector. Clinical DSA is normally performed at a low frame rate (< 5 fps). The lowest air kerma rate evaluated corresponds to a 25 fps acquisition with the same kerma per second as a clinical 3 fps DSA acquisition. The maximum frame rate available for the qDSA scan (25 fps) was chosen since high temporal resolution is important to capture the dynamic changes in contrast.

An animal study was performed in 8 female swine (~50 kg) to evaluate the feasibility of this approach to provide progressive in vivo velocity measurements during an embolization procedure. Approval for this study was obtained from the local Institutional Animal Care and Use Committee (IACUC) of the University of Wisconsin School of Medicine and Public Health. In each animal, an embolization study was performed with intermittent acquisition of x-ray image sequences for blood velocity measurements. While no gold standard velocity measurements were available, a reduction in blood velocity was expected with increasing amount of embolic particles injected. Embolization was performed in the left hepatic (n=2), left medial hepatic (n=4), right medial hepatic (n=1), or splenic artery (n=1) by injection of embolic microspheres (Embospheres 100–300 μm, Merit Medical, South Jordan, UT) in increments of 1 ml (n=5) or 2 ml (n=2) aliquots. At baseline and after each injection, x-ray sequences were acquired while injecting contrast agent (Omnipaque 350 mgI/mL, 16 ml at 4 ml/s) through a 4 Fr Cobra C2 Glidecath (Terumo Corporation, Shibuya City, Tokyo, Japan) into the common hepatic or splenic artery, respectively. A total of 6–10 ml of microspheres was injected for each case. The velocity in the embolized branch was calculated for each stage of embolization. To account for vessel motion during image acquisition, the motion-compensation approach described in Whitehead et al.¹⁰ was used to extract the time attenuation maps for velocity estimation.

II.D. Computational Fluid Dynamics (CFD) Simulation

The purpose of the CFD analysis in this study was to investigate 1) how the dimensional reduction associated with 2D qDSA impacts velocity measurement and 2) the difference between contrast agent velocity and bulk fluid velocity. The reason for the dimensionality reduction is that 1) qDSA only analyzes signal along the centerline of a vessel, and 2) each pixel along the centerline represents an average signal along the line projected from the x-ray source to the detector pixel. Thus, only points within a plane intersecting the centerline of the vessel are considered for qDSA velocity calculation. The ultrasound-based probe, however, was calibrated (see Section II.C.) based on the total volumetric flow and therefore represents the average bulk fluid velocity in the tube. To obtain a better understanding of this relationship, a simple CFD simulation was performed where the experimental setup described in Section II.C. was replicated in a digital phantom. The tube was represented by a cylindrical mesh with 57,600 cells. A 2-phase blood and contrast flow model was used for the simulation. The constant contrast injection (2.0 ml/s) was simulated through the central 0.83 mm diameter circle of the inlet, while pulsatile blood flow was simulated at the surrounding region of the inlet. The pulsatile flow was represented by a sinusoidal curve with a frequency of 1 Hz. Amplitude and offset of the sine wave were determined from the ultrasound measurements (see Section II.C.) and the simulation was performed for each baseline velocity in the experimental setup. The simulation used a Newtonian model with kinematic viscosity ν = 3.3 × 10⁻⁶m²/s and density ρ = 1060kg/m³ for blood.^29,30 For the contrast agent, a concentration of 300 mgI/ml was assumed with ν = 7.36 × 10⁻⁶m²/s and a measured density ρ = 1340kg/m³.³¹ In the initial state, the tube was assumed to be completely filled with blood (no contrast). The 8 s injection was then simulated in time steps of 0.25 ms. The simulation was performed using the open-source software InterFoam (OpenFoam, version 2212). The solution for each step was obtained using the PIMPLE algorithm (a combination of pressure implicit split operator (PISO) and semi-implicit method for pressure-linked equations (SIMPLE)). The velocity and the concentration of contrast agent in cell was written out every 133^rd time step to achieve a simulated frame rate of 30 fps. The average (temporal and spatial) velocity along the tube within a 3 cm long segment was then calculated using 1) the bulk fluid velocity values within the whole volume and 2) the contrast agent velocity within a vertical plane through the centerline. A linear regression analysis was then performed to determine the expected relationship between US and qDSA-based velocities based on the differences in the underlying approach.

II.E. Evaluation and Statistical Analysis

All velocities for the phantom study were calculated using the proposed spatiotemporal frequency domain (STF) approach as well as two previously published techniques, the shifted least squares method¹⁶ (SLS) and the phase shift method¹⁸ (PHS). The precision of a single velocity measurement was evaluated by computing the standard deviation of the repeat measurements for each baseline velocity. This can be written as

$$s_r=\sqrt{\sum _{i=1}^5\sum _{j=1}^6{\left(r_{ij}\right)}^2}\text{, with }{r}_{ij}=v_{ij}-\frac{{\sum }_{k=1}^6{v}_{ik}}{6}\text{, }$$ (7)

where v_ij is the j^th repeat qDSA velocity measurement at baseline velocity i. To evaluate the relationship between precision and vessel segment length, velocity estimation was performed for 1 to 3 cm long sections of the straight tube phantom in 0.5 cm increments. A Bartlett’s test for equal variances was applied to the residuals r_ij of each segment length to determine whether a significant change in uncertainty was observed between the repeat measurements. Additionally, the results were compared to reference measurements from the ultrasound probe by performing a linear regression analysis. To determine whether a linear relationship between reference US and qDSA measurements exists, the Pearson correlation was determined according to

$$\text{corr}=\frac{{\sum }_{\forall i}\left(v_{\text{xray},i}-{\overline{v}}_{\text{xray}}\right)\left(v_{\text{ref},i}-{\overline{v}}_{\text{ref}}\right)}{\sqrt{{\sum }_{\forall i}{\left(v_{\text{xray},i}-{\overline{v}}_{\text{xray}}\right)}^2{\sum }_{\forall i}{\left(v_{\text{ref},i}-{\overline{v}}_{\text{ref}}\right)}^2}}$$ (8)

where v_xray,i and v_ref,i are the qDSA and US velocity measurements for a single measurment, respectively, and ${\overline{v}}_{\text{xray }}$ and ${\overline{v}}_{\text{ref}}$ are the arithmetic means over all cases. Additionally, a linear regression analysis was performed by estimating slope a and intercept b for

$$v_{\text{xray }}=a{v}_{\text{ref }}+b\text{, }$$ (9)

using singular value decomposition (SVD). R-squared was reported to assess goodness of fit for all regression models. Additionally, Fisher’s z-transform was used to test for statistically significant differences between correlation coefficients for the three approaches.

Due to the lack of a robust reference standard for in vivo blood velocity measurements, the animal data was evaluated by comparing different embolization stages to show a consistent reduction of blood velocity in the embolized arteries. To this end, pairs of velocity measurements within an embolization procedure were analyzed to compute the percentage of injections with a measured reduction in velocity. The percentage reduction was computed for 1, 2, 3, and 4 ml injections of embolic particles to explore the dependence of velocity reduction on injection volume.. The x-ray image data for all cases were preprocessed using each of the two aforementioned subtraction approaches (DSA, adjacent frame subtraction (AFS)) and also native imaging without subtraction). The AFS and native approach were compared to the conventional DSA type subtraction using the signed difference of the resulting velocities. A Kruskal-Wallis one way analysis of variance (ANOVA) was used to test for statistically significant differences between the three preprocessing approaches.

III. Results

Unless otherwise noted results were computed using conventional DSA type background subtraction. The 5-point calibration of the ultrasound probe was successfully performed with R² = 0.998 for the linear fit and a residual error of ±0.36 cm/s. The analysis of the phantom data with different segment length showed a significant increase in the variance of repeat measurements for segment lengths ≤ 1.5 cm (p< 0.00001; σ₁ = 4.3 cm/s and σ_1.5 = 2.7 cm/s). No significant change compared to 3 cm long segments was observed for vessel length ≥ 2 cm (p₂ = 0.08, p_2.5 = 0.72, σ₂ = 1.48 cm/s, σ_2.5 = 1.17 cm/s, and σ₃ = 1.12 cm/s), where σ_l is the standard deviation of the residual errors r_ij for vessel segment length l and p_l is the corresponding p-value. A comparison between the residual errors for all three approaches is shown in Fig. 4.

Figure 4:

Straight tube phantom study results: standard deviation of the residual errors of the qDSA measurements using shifted least squares (SLS), phase shift (PHS), and the proposed spatiotemporal frequency (STF) approach depending on segment length.

A significant correlation between qDSA and reference velocities (p< 0.0001) was found for all methods across all three dose levels. For the lowest dose level, the highest correlation (ρ = 0.99) was found for the STF approach. In comparison the correlation was 0.91 and 0.93 for the SLS and PHS methods. Only small differences between the slope (a ∈ [1.00;1.02]) and intercept (b ∈ [4.6;5.5]) values of the three dose levels were observed for the STF approach. The corresponding ranges for slope and intercept were larger for the SLS approach (a ∈ [0.92;1.65], b ∈ [−7.0;12.5]) and PHS approach (a ∈ [0.92;1.00], b ∈ [−0.3;2.5]) with the largest discrepancy for SLS.

For the lowest air kerma rate, the best fit (highest R² values) was observed for the proposed STF approach (0.97) followed by PHS (0.87) and SLS (0.83). A detailed summary of all correlation and linear regression results is given in Table 1. For the two higher dose levels, no statistical differences between the correlations of SLS, PHS, and STF with the ultrasound data were observed. For the lowest dose level, the correlation between STF and ultrasound measurements was significantly higher (p< 0.0001) than the correlation of the SLS and PHS approaches with ultrasound. Additionally, Fig. 5 shows individual velocity measurements and linear regression results for all three approaches (STF, SLS, and PHS) and dose rates compared to the reference velocities measured using the ultrasound probe.

Table 1.

Correlation and linear regression results

	11.3 mGy/s			3.6 mGy/s			1.3 mGy/s
	SLS	PHS	STF	SLS	PHS	STF	SLS	PHS	STF
$\rho$	0.98	0.99	0.99	0.98	0.99	0.99	0.91	0.93	0.99*
$p$	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
$a$	1.59	0.93	1.00	1.65	1.00	1.01	0.92	0.92	1.02
$b$	−5.67	2.21	5.45	−7.05	−0.29	5.53	12.47	2.51	4.60
$R^2$	0.96	0.98	0.97	0.96	0.98	0.98	0.83	0.87	0.97

Pearson correlation $\rho$ and corresponding p-value are shown for least squared fit (SLS), phase shift (PHS), and the proposed spatiotemporal frequency (STF) approach and all three pre-patient air kerma rates (scaled to the interventional reference point). Additionally, linear regression parameters $a$ and $b$ and corresponding goodness of fit ($R^2$) are listed.

Figure 5:

Phantom study results for the proposed spatiotemporal frequency domain (STF), shifted least squares (SLS), and phase shift (PHS) approach shown in rows 1 through 3, respectively. Velocities from qDSA are compared to the reference ultrasound measurements. Each column represents a different dose rate in descending order. Estimated velocities are shown as blue markers and the linear regression results as a red line.

The results of the CFD simulation also show a strong linear relationship (correlation ρ = 0.999, p< 0.00001) between the cross-sectional average fluid velocity corresponding to the ultrasound measurements and the average velocity of contrast agent along the central plane corresponding to the qDSA measurements. The individual results are shown in Fig. 6. The linear regression analysis yielded a slope a = 1.08 and bias b = 5.82 showing a slightly higher average velocity for contrast along the central plane (as used for qDSA based measurements) compared to the average velocity in the whole tube.

Figure 6:

Computational fluid dynamics (CFD) simulation results showing a comparison between the cross-sectional average fluid velocity (comparable to ultrasound-based measurements) and the average velocity of contrast agent along the projection of the centerline (comparable to qDSA measurements).

Fig. 7 shows the absolute velocities in relation to the amount of injected embolic particles for each case of the in vivo embolization study. In most cases, there was a continuous reduction with increasing amount of embolic particles injected. The median percent reduction in velocity per milliliter embolic particles was 3.8% with an interquartile range of 10.1%. Fig. 8 shows a box plot of the average percent reduction in velocity relative to the previous state after adding between 1 and 10 ml of particles. In 85.7% of cases a velocity reduction was observed after injection of an additional 1 ml of particles. For 2, 3 and 4 ml, this percentage increases to 85.0%, 96.4%, and 100.0%, respectively.

Figure 7:

Individual in vivo results for all 8 cases showing absolute velocities (calculated using the spatiotemporal frequency domain approach) in the embolized vessel branches relative to the total amount of injected embolic material.

Figure 8:

Boxplot showing median, lower, and upper quartiles of the percent reduction in velocity after addition of 1 to 10 ml of embolic material. Circles represent outliers and the whiskers represent minimum and maximum. Boxes where notches do not overlap have different medians at a 5% significance level.

In the in vivo study, the signed mean differences and standard deviations between STF velocity measurements calculated using no background subtraction (STF-N) and adjacent frame subtraction (STF-A) compared to conventional DSA type background subtraction (STF) were 0.3±1.1 cm/s and −0.1±1.7 cm/s, respectively. No significant differences were observed between the three groups (Kruskal-Wallis, p = 0.844, respectively). The average range of vessel motion during a sequence was 0.8 mm (maximum = 1.4 mm).

IV. Discussion

A robust velocity quantification approach for contrast enhanced x-ray image sequences was presented. It leverages the shear property of the 2D Fourier transform to determine the slope of a time-attenuation map by locating the fundamental frequency peak in the spatiotemporal domain. The non-iterative design of the approach allows fast computation on most systems without a requirement for advanced hardware and avoids the risk of local minima during optimization, which can reduce the accuracy of iterative approaches such as the shifted least squares and phase shift approaches. Additionally, the algorithm uses information from all centerline points simultaneously, thus avoiding the calculation of time shifts between pairs of points, which can be error prone for points in close vicinity. The method was evaluated in a straight tube phantom study, where x-ray based velocity measurements were compared to external ultrasound probe measurements as reference standard. Additionally, an in vivo embolization study was performed to evaluate the possibility of monitoring the reduction of blood velocity during embolization procedures to determine quantitative endpoints.

The phantom study showed good agreement between the proposed approach and the reference ultrasound measurement. While for higher dose levels all compared approaches achieved similar high correlation, significant differences were observed for the lowest dose level (right column of Fig. 5), where the STF technique still achieved a 99% correlation with ultrasound, while SLS and PHS correlations were significantly smaller with 91% and 93%, respectively. Due to the high required frame rate, robust velocity estimation from low dose per frame image sequences is critical to reduce radiation exposure and enable the clinical translation of qDSA. Additionally, the standard deviation of the residual errors shows a smaller variation between repeat measurements for the STF approach than for PHS and SLS for all investigated segment lengths. In our study, a significant increase in errors was only observed for vessel segment lengths ≤ 1.5 cm. This aligns well with the assumption that transit time of the contrast through the vessel segment has to be larger than the time difference between two consecutive image frames (33 ms) in order to detect the time shift. For example, assuming a velocity of 50 cm/s, the transit time of contrast through the segment is 0.9 · 33 ms for a 1.5 cm segment and 1.2 · 33 ms for a 2 cm segment. Thus, a combination of STF with higher frame rate imaging techniques (e.g., as proposed by Vanderbilt et al.²⁷) could further reduce the required segment length.

Within the measured range of velocities in the phantom study, a strong linear relationship was observed between STF and ultrasound velocity. The slope and bias (approximately 5 cm/s) observed between STF and ultrasound measurements is similar to the results observed in the CFD simulation. This indicates there are differences between the average contrast velocity in the central plane compared to the overall average velocity. Future work could investigate approaches to compensate for this offset based on theoretical predictions. However, as shown by Periyasamy et al.,⁹ information about the relative change in velocity during an intervention may be just as useful as the exact absolute velocity for many clinical applications.

In the in vivo study, the shapes of the velocity curves relative to the amount of injected particles vary widely across different animals and vessel branches. In four out of eight cases, a sharp reduction in velocity was observed after the injection of the 1 ml of Embospheres. In the other cases, a more gradual reduction was observed, while one case even showed an increase in velocity. These variations are expected since there are a number of factors contributing to the change in velocity such as heart rate, vessel anatomy, vessel dilation, and tissue condition and similar behavior was observed in previous embolization studies⁹. Overall, after most injections, a reduction in velocity was observed which suggests that physiological changes during embolization procedures may be monitored using qDSA in combination with STF. The maximum detected vessel motion was on the order of the vessel diameter, which emphasizes the need for motion compensation during in vivo measurements.

The small deviation between the different preprocessing techniques shows that the Fourier based analysis could be applied to adjacent frame subtraction images or to native images without subtraction. This could enable qDSA or 4D DSA in cases where no mask images are available (e.g. to reduce radiation dose) or in cases with motion between mask and contrast enhanced images without sacrificing accuracy.

One of the limitations of this study is the use of a relatively simple straight tube phantom. Future work is necessary to investigate the accuracy and robustness of the approach in more complex phantoms. In practice, the approach could be applied to non-straight vessel segments as long as the distance between individual points is known. A centerline can be defined in a curved segment,¹⁰ and a correction to the distance along a centerline accounting for magnification and foreshortening could be achieved using an endovascular device with known dimensions (e.g., a guidewire with markers).²³ Alternatively, this information could be obtained from a previously acquired 3D DSA. It should also be noted that the approach calculates average velocities and cannot be used to determine complex flow patterns as observed within aneurysms. Future work is also needed to investigate the suitability of the algorithm for other clinical applications including stenoses or applications in the heart where motion is more prominent. While the contrast injection protocols used for this study are comparable to routine injections in clinical practice, contrast based velocity quantification might be less suitable for cases with a contraindication to iodine. Finally, the lack of established, robust and non-invasive methods and the difficulty in performing intraprocedural flow or velocity quantification via other means makes it difficult to determine in vivo gold standard measurements for comparisons. However, this speaks to the importance of bringing qDSA into clinical practice. The accuracy and robustness of qDSA velocity measurements using STF is demonstrated by the phantom study, in which there was strong agreement with established external ultrasound measurements across all three dose levels.

V. Conclusion

The proposed spatiotemporal velocity quantification approach improves the robustness of qDSA-based intraprocedural blood velocity measurements in short vessel segments (2 cm or larger). The higher accuracy at low radiation dose levels could aid in the clinical translation of qDSA. The approach is device agnostic and does not require specialized hardware and thus could be easily integrated with existing systems. A reliable quantitative blood flow metric may enable the establishment of objective and reproducible endpoints for embolization and other vascular interventions.