Novel Approaches to the Measurement of Arterial Blood ... - IEEE Xplore

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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 24, NO. 4, APRIL 2005

Novel Approaches to the Measurement of Arterial Blood Flow From Dynamic Digital X-ray Images Kawal S. Rhode*, Tryphon Lambrou, David J. Hawkes, and Alexander M. Seifalian

Abstract—We have developed two new algorithms for the measurement of blood flow from dynamic X-ray angiographic images. Both algorithms aim to improve on existing techniques. First, a model-based (MB) algorithm is used to constrain the concentration-distance curve matching approach. Second, a weighted optical flow algorithm (OP) is used to improve on point-based optical flow methods by averaging velocity estimates along a vessel with weighting based on the magnitude of the spatial derivative. The OP algorithm was validated using a computer simulation of pulsatile blood flow. Both the OP and the MB algorithms were validated using a physiological blood flow circuit. Dynamic biplane digital X-ray images were acquired following injection of iodine contrast medium into a variety of simulated arterial vessels. The image data were analyzed using our integrated angiographic analysis software SARA to give blood flow waveforms using the MB and OP algorithms. These waveforms were compared to flow measured using an electromagnetic flow meter (EMF). In total 4935 instantaneous measurements of flow were made and compared to the EMF recordings. It was found that the new algorithms showed low measurement bias and narrow limits of agreement and also outperformed the concentration-distance curve matching algorithm (ORG) and a modification of this algorithm (PA) in all studies. Index Terms—Blood flow measurement, X-ray angiography, X-ray measurements.

I. INTRODUCTION

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ANY vascular procedures, such as coronary angioplasty and the treatment of cerebral aneurysms, are performed under X-ray guidance. It is of interest to ascertain the haemodynamic effect of such procedures both intraoperatively and post-operatively. Detecting changes in the haemodynamic function may influence treatment or demonstrate the effectiveness of treatment. Interpretation of angiographic images is still largely subjective and the quantitative information that can be derived from these images is not commonly used. Several algorithms have been proposed to estimate blood flow in arteries from dynamic digital X-ray images following

Manuscript received May 8, 2004; revised November 17, 2004. Asterisk indicates corresponding author. *K. S. Rhode is with the Division of Imaging Sciences, Guy’s, King’s and St. Thomas’ School of Medicine, King’s College London, 5th Floor Thomas Guy House, Guy’s Hospital, London SE1 9RT, U.K. (e-mail: [email protected]). T. Lambrou is with the Department of Medical Physics and Bioengineering, University College London, London WC1E 6JA, U.K. (e-mail: tlambrou@ medphys.ucl.ac.uk). D. J. Hawkes is with the Centre for Medical Image Computing, University College London, London WC1E 6BT, U.K. (e-mail: [email protected]). A. M. Seifalian is with the Biomaterial and Tissue Engineering Centre, University College London, London NW3 2PF, U.K. (e-mail: [email protected]). Digital Object Identifier 10.1109/TMI.2004.843202

an intra-arterial injection of iodine contrast material. These algorithms can be divided into six categories. 1) Indicator dilution techniques [1]–[5]. 2) Techniques based on the measurement of the variation of iodine concentration as a function of time (concentrationtime curves) at two sites along the target vessel [6]–[9]. 3) Techniques based on the measurement of the variation iodine concentration as a function of distance along the target vessel and of time (concentration-distance-time curves) [10]–[21]. 4) First pass analysis (FPA) techniques [22]–[25]. 5) Techniques based on optical flow [26]–[29]. 6) Techniques based on the inverse advection problem [30], [31]. A thorough review of these techniques can be found in [32]. In general, the techniques based on indicator dilution theory and on concentration-time curve analysis at two sites, fail in the physiological condition of pulsatile flow. FPA techniques are limited due to the need to accurately calibrate for the iodine signal. Methods based on the solution of the inverse advection problem have the distinct advantage of being able to deal with stenosed vessels but are computationally expensive. Techniques based on the analysis of concentration-distance-time curves and on optical flow have reported a degree of success. These techniques perform well in conditions of pulsatile flow and are also able to detect instances of reverse flow. Of the concentration-distance-time curve techniques, one of the most successful algorithms is the concentration-distance curve matching algorithm. In this approach, the optimal shift is found in the distance axis between consecutive concentration-distance curves. The blood flow velocity is then calculated by dividing this shift by the time interval between the curves. Several variations have been reported on this algorithm and all have shown promising results [15]–[21]. Of the optical flow techniques, those proposed by Imbert et al. [28] and Huang et al. [29] have shown promising results. We aimed to improve on these approaches by considering their limitations. Both of the leading approaches are severely noise limited. For the concentration-distance curve matching algorithms, noise in the image data can lead to the incorrect identification of matches between consecutive concentration-distance curves. For the optical flow algorithms, noise in the image data leads to errors in calculation of spatial and temporal derivatives of iodine contrast material concentration. Since the blood flow velocity is dependent on the ratio of the temporal to the spatial derivative, large errors are encountered when there are very small values of the spatial derivative [33]. For the concentration-distance curve matching approach, we hypothesized that a priori knowledge of the shape of the blood flow waveform might be used to constrain the curve matching

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RHODE et al.: NOVEL APPROACHES TO THE MEASUREMENT OF ARTERIAL BLOOD FLOW FROM DYNAMIC DIGITAL X-RAY IMAGES

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process. For the optical flow approach, we hypothesized that performing a weighted average of velocity estimates along an arterial segment according to the magnitude of the spatial derivative might improve flow estimation. In this paper we report two novel algorithms for the determination of blood flow from dynamic digital X-ray images. The first algorithm is based on the concentration-distance curve matching approach, and the second is based on an optical flow approach. We have validated these algorithms using first a computer simulation of pulsatile blood flow, and second using a physiological pulsatile blood flow circuit. II. METHODS Both of our algorithms operate on a parametric representation of the motion of iodine contrast material through a target blood vessel. In this representation, the concentration of iodine is expressed as a function of distance along the blood vessel and of time. This can be represented as a parametric image, an example of which is shown in Fig. 1. These images can either be formed from X-ray angiographic data or synthesized from a computer simulation. For angiographic images, the concentration of iodine contrast material present at a particular distance along a vessel segment is found by integrating the pixel intensities across the vessel lumen perpendicular to the centerline [18], [19]. The iodine concentration is proportional to this integral once corrected for vessel angulation and magnification. This assumption is valid if the images have been log subtracted and if the vessel cross-sectional area remains constant. The formation of parametric images from computer simulation is described in Section II-C1.

Fig. 1. Example of a parametric image. The grey level is proportional to the concentration of iodine, the y -axis represents the distance along the vessel, and the x-axis represents the time.

variation of the mean waveform shape with variance equal to the corresponding eigenvalue. Any of the input waveforms can now be expressed as the sum of the mean waveform shape and a linear combination of the eigenvectors (4) where is the weighting factor for eigenvector for waveform . For each input waveform there is a set of eigenvector weighting factors . These weighting factors are known as the principal components (PCs) of the waveform . The principal components can be calculated by (5)

A. Blood Flow Waveform Shape Model Constrained Algorithm For the first of our blood flow measurement algorithms, initially a blood flow waveform shape model needs to be constructed for the target blood vessel. This shape model is constructed by collecting many sample waveforms from the vessel under investigation and subjecting these to principal component analysis (PCA). 1) Construction of the Blood Flow Shape Model Using Principal Component Analysis: Let the sample waveforms , where total number of input wavebe consists of sample points forms. Each input waveform . The input waveforms are averaged to produce a mean waveform shape (1) The input waveforms are then transformed by subtracting the mean waveform shape (2) for The

. covariance matrix

is the th principal component of waveform . where It is possible to approximate each of the input waveforms by using only the first few modes of variation. The input waveform can be approximated by the reconstructed waveform using the first modes of variation by (6) There are several methods that can be used to decide how many principal components to retain. A detailed description of these methods is presented in [34]. In our case, the analysis of residuals was used to decide the number of modes of variation that could be used to represent the waveform shape information. If the input waveform is approximated by using only the first modes of variation as given in (6), then (7) where is the vector of residuals. The sum of squares of the residuals is given by

is calculated (8)

(3) Eigen analysis of this real symmetric covariance matrix yields normalized eigenvectors with corresponding eigenvalues , . Each eigenvector accounts for one mode of

The root mean square of the residuals is given by (9)

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The root mean square of the residuals is a measure of the error when using only out of the possible PCs when reconstructing the input waveforms. The error can be expressed as a percentage of the mean flow rate (10)

The average percentage error can be calculated for all input waveforms (11) The number of retained PCs should be enough to model the waveform signal without modeling the noise component of this signal. 2) Use of the Waveform Shape Model for X-ray Blood Flow Measurement: Having formed the waveform shape model it was possible to use this to constrain the measurement of blood flow from dynamic angiographic images. The concentrationdistance curve matching algorithm was modified to include the information from the shape model. We will initially describe the concentration-distance curve matching algorithm and then show how the waveform shape model was incorporated into this algorithm. a) Concentration-distance curve matching algorithm: The concentration of contrast medium along an arterial vessel segment can be expressed as a function of distance along the . The distance is measured in vessel and of time, millimeters and . The segment length is then mm. The time is measured in sampling frames and . This gives rise to a series of concentration-distance curves where is the last frame in the series. Fourth order polynomials are fitted to these curves to reduce the effects of noise. The order of the polynomial fit was chosen because the concentration-distance curves had at most three stationary points. is shifted by mm with respect to If curve , the cost function is calculated as curve

For the purpose of this paper, if the original concentration-distance curve data are used then the algorithm is termed the original algorithm (ORG algorithm). If the polynomial fit concentration-distance curve data are used then the algorithm is termed the polynomial approximation algorithm (PA algorithm). b) Waveform shape model constrained concentration-distance curve matching algorithm: The concentration-distance curve matching algorithm was modified to include the waveform shape information derived from PCA. For the purpose of this paper, this modified algorithm was called the model-based algorithm (MB algorithm). where volumetric Let the volumetric flow waveform be flow is measured in milliliters/minute. Using the waveform shape model, is estimated by (16) that The model fitting task entails selecting the values of minimize the mean value of the cost function . Stage 1: The concentration-distance curve function will contain one or more cardiac cycles depending on the cardiac rate and the number of frames acquired. For the cycle for which the shape model is to be fitted, is the starting frame and is the end frame of the cycle. The cycle length is then given by (17) Initially, consists of sample points. is now rescaled to sample points to give where . Stage 2: The velocity , measured in centimeters/minute, is calculated by (18) where is the vessel cross-sectional area in centimeters squared. Stage 3: The velocity waveform is converted into units of mm shift/frame by (19)

(12) if

if

and,

. The velocity

where is the unit conversion factor. Stage 4: The cost function is calculated by

(13)

(20)

in millimeters/second for shift is given by

The values of the weighting factors are found which minimize the cost function . This is done by the downhill simplex method [35].

(14) is the frame rate in frames/s. where The concentration-curve matching algorithm selects the value of for which is minimum. This value, , is the value for which there is the best match in the least squares sense between consecutive concentration-distance curves. The estimated contrast medium velocity is then given by (15)

B. Weighted Optical Flow Algorithm For the parametric image consider two consecutive concentration-distance curves, and , separated in time by one sampling interval . If the shape of the curves are not different then, (21)


where is the contrast medium bolus velocity. Using the first order Taylor series approximation

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TABLE I PARAMETERS FOR COMPUTER FLOW SIMULATION

(22) Substituting (22) into (21) and rearranging (23) In the limit

, (24)

Equation (24) is the one-dimensional form of the optical flow constraint equation. Applying this equation to the parametric , for pixel in the image, the initial velocity estimate, image is (25) is the acquisition frame rate, and and are the temporal and spatial derivatives respectively for pixel . The estimation of these derivatives is a key step in the determination of the blood flow velocity along the vessel. With typical temporal and spatial sampling intervals, the magnitude of the temporal changes in contrast medium concentration is much greater than that of the spatial changes for the majority of points in the parametric image. Therefore, the estimation of the spatial derivative is more sensitive to noise in the image data than the estimation of the temporal derivative. Several approaches were investigated for derivative estimation. The method that proved to be least noise-sensitive was that of modeling the concentration-distance curves by polynomials. Fourth order polynomials were fitted to the concentration-distance profiles by the method of least squares. The spatial derivative was then estimated by differentiating these polynomials. The temporal derivative was estimated from the polynomial-fitted profiles by method of finite differences. In order to overcome errors that occur when the value of the spatial derivative is low, each initial velocity estimate is weighted according to the magnitude of the spatial derivative. , is The weighted velocity, where

(26) and is the maximum value where of spatial derivative in the parametric image. The weighted velocities are then averaged along the length of the vessel to yield an average velocity value, , for each frame in the image sequence. The average instantaneous velocity is given by

(27)

C. Validation of Weighted Optical Flow Algorithm by Computer Simulation of Blood Flow in Straight Tubes The weighted optical flow algorithm was initially validated with a computer simulation of blood flow in straight tubes. 1) Generation of Synthetic Parametric Images: For the generation of synthetic parametric images, a computer model was designed to simulate blood flow in a straight tube of circular cross-section. The model allowed for injection of contrast medium into the vessel and calculated the total mass of contrast medium present in the vessel as a function of distance from the injection site and of time from the start of the injection. The output from the model was a parametric image. Table I shows the parameters used for the flow model and the definition of the symbols used in this section. The assumptions made in the computer flow model were as follows. a) The blood flow profile across the vessel lumen is parabolic. b) The vessel is of constant circular cross section, does not have any branches, and is rigid. c) There is zero diffusion of contrast material. d) The contrast material mixes uniformly with the blood at the injection site. e) The flow of contrast material is additive to the blood flow in the vessel. The simulated vessel was divided into cylindrical laminae each of constant width . The velocity profile across the vessel lumen was parabolic laminar. In the case of parabolic laminar flow, the maximum velocity of the blood flow was given by (28) The fraction of the blood flow in lamina was

where

(29) where

is the vessel segment length in mm.

where

.

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The fraction of the added flow due to contrast medium injection in lamina was (30) Therefore the total flow in lamina

was (31)

Now, the velocity as a function of time in lamina by

is given

(32) Also, the injected mass of iodine as a function of time in lamina is given by (33) Therefore, for each lamina, both the velocity and mass of injected iodine are known as a function of time. The velocity-time curves and the mass-time curves for each lamina are then used to calculate the total mass of iodine as a function of time and and , respectively, to form a space in discrete steps of parametric image. Zero mean Gaussian noise with standard deviation equal to a specified percentage of the maximum grey value could then be added to the images. This would simulate the additive effects of all sources of noise in the formation of the parametric image from an actual radiographic sequence. The main limitations of the computer flow model are as follows. a) The radial velocity profile is not constant during the cardiac cycle and varies between the extremes of plug and laminar flow. b) Arterial vessels usually show a gradual tapering of cross-sectional area with distance. They are also elastic and will undergo cross-sectional area changes due to the pulsatile pressure variations within their lumens. Regions of stenosis will have marked changes in vessel cross-sectional area and will exhibit modified elastic properties. Vessels undergo branching and it is uncommon to find unbranched vessel lengths exceeding 100 mm in the human arterial tree. c) Contrast medium undergoes diffusion as it propagates along a vessel. However, the effects of diffusion are minimal over the time periods for which angiographic images are acquired following arterial injection. d) Contrast medium does not mix uniformly with blood. Since the diameter of injection catheters is small compared to the vessel under investigation, the contrast medium is usually introduced into a small cross-sectional region of the blood vessel. This may produce streaming of the contrast medium along laminae. Also contrast medium is denser than blood and undergoes a degree of settling. e) The introduction of contrast medium into a blood vessel will not cause a purely additive effect on the total flow with the vessel. Due to the upstream vascular resistance, the effects of the injection are damped. Also, there may be some back flow of contrast medium. Despite the limitations mentioned, the computer flow model was thought to provide a useful initial tool for the assessment of

the performance of the weighted optical flow algorithm. It was possible to study the effect on velocity estimation of varying many parameters and from these results proceed to physical flow model studies. 2) Method of Simulation Study: Two simulation studies were performed, simulation study 1 and simulation study 2. The first simulation study was carried to assess the effect of the following parameters on the velocity measurement made by the weighted optical flow algorithm. a) The distance from the contrast medium injection site. b) The length of the vessel segment over which velocities were averaged. c) The noise in the image data. Table I shows the parameters that were used for simulation study 1. The input waveform was derived from an electromagnetic flow meter (EMF) recording during a physical flow model study. The mean flow rate for this waveform was 121.3 ml/min and the instantaneous flow values ranged from 0.0 ml/min to 432.9 ml/min. This corresponds to a mean velocity of 71.5 mm/s and instantaneous velocities from 0.0 to 255.2 mm/s. This waveform was repeated at 1-s intervals for 5 s and added to the contrast medium injection waveform to form the total flow waveform. The parametric image generated by the computer flow model was used to generate three other images with increasing levels of zero mean Gaussian noise of standard deviation 2%, 5%, and 10% of the maximum grey value. The velocity waveforms for the total four images were calculated using the weighted optical flow algorithm. The vessel segment length over which velocities were averaged and the distance of measurements from the contrast medium injection site were varied by placing a moving window over the parametric images. Vessel segment lengths of 25, 50, 75, 100, 125, and 150 mm were used. Also, for each length, the distance from the injection site at which measurements were started was varied from 0 to 300 mm in steps of 5 mm. If is the length of the vessel segment used for flow calculation and is the distance from the injection site for which measurements were made, then the location of the average point used for measurements is (34) For the second simulation study, the ability of the algorithm to measure blood flow velocity for a range of different mean velocities was assessed. The input parameters used for simulation study 2 were identical to those for simulation study 1 (Table I). However, the input waveforms were derived from the PCA shape model of many EMF recordings as described in Section II-D1. Thirty-one input waveforms were generated using this PCA-based waveform model by adding a variable amount of the first mode of variation to the mean waveform to standard deviations of the first eigenvector shape. where added to the mean shape to generate the waveforms. The mean flow rate ranged from 119.3 to 294.0 ml/min and the instantaneous flow values ranged from to 890.8 ml/min. This corresponds to mean velocity from 70.3 to 173.3 mm/sec and instantaneous velocity from to 525.1 mm/s. The parametric images generated from the computer flow model were corrupted by 2% added noise. Velocities were estimated for a segment length of 100 mm and at a starting distance of


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Fig. 2. Components of the physiological blood flow circuit used for phantom validation of blood flow extraction algorithms.

75 mm from the injection site, which corresponds to an average measurement distance of 125 mm. 3) Statistical Analysis: The computed flow velocities were compared to the known simulated flow velocities by calculation of the correlation coefficient between the two values, and also by calculation of the error between the two values (measured-true). The correlation coefficient gives a measure of the linear relationship between the measured and the true velocity values. The mean error gives a measure of the measurement bias, and the standard deviation of the error gives a measure of the variability of velocity estimation. Calculation of the 95% confidence interval (CI) of the error was also carried out to give the 95% limits of agreement between the measured and the true velocities [36]. D. Validation With Physiological Blood Flow Circuit 1) The Physiological Blood Flow Circuit: a) General overview: Fig. 2 shows a schematic of the blood flow circuit. A pulsatile pump (pulsatile blood pump 1405, Harvard Apparatus) provided the pulsatile pressure variations in the circuit. Date-expired whole blood was used as the circulating fluid. An electromagnetic flow sensor (electromagnetic blood flow sensor, Skalar) was placed in-line with the circuit. The sensor was connected to the EMF (electromagnetic blood flow and velocity meter, Skalar). This device provided the gold-standard measurement of volumetric flow rate. Calibration of the EMF was carried out using fluid collection under conditions of constant flow (55.9 ml/min to 828.2 ml/min).

b) Collection of sample waveforms to form PCA shape model: In order to construct a blood flow waveform shape model, a representative sample of waveforms must be collected from the arteries under investigation. For the purposes of the phantom studies this entailed collecting sample waveforms from the physiological blood flow circuit. Recordings were collected from the EMF for varying conditions of flow. The parameters altered were: 1) the stroke volume of the pump; 2) the pumping frequency; 3) the mean pressure; 4) the output impedance; 5) the vessel size; and 6) the rate of contrast medium injection. For each flow condition approximately 10 s of the flow signal was captured and the individual cycles were isolated. In order to overcome the effects of different cycle lengths, each cycle was normalized over time to 100 sample points by resampling using linear interpolation. In total, 434 cycles were isolated under the varying conditions in the flow circuit and these were used as the input waveforms for PCA. The mean flow rates ranged from 43 ml/min to 375 ml/min. The instantaneous flow rates ranged from (reverse flow) to 1056 ml/min. This range of flow rates covered the values for which X-ray determination of flow was to be carried out in the flow circuit. Once PCA was performed [37], [38], the number PCs to retain was determined. The noise level of measurements made by the EMF was determined by using the data collected during calibration of this device under conditions of steady flow. The average percentage noise was determined

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to be 4.9%. The average percentage error [see (11)] when nine PCs were retained was 5.39% and 4.68% when ten PCs were retained. Therefore, it was decided that ten PCs would be sufficient to represent the waveform shape information without modeling the noise component. c) Details of different types of simulated vessel: The blood flow extraction algorithms were tested using progressively more challenging vascular phantoms. • Silicone tubing: For the first series of experiments, silicone tubing was used to simulate an arterial vessel. The tubing had a circular cross section and internal diameters of 3, 4, and 6 mm were used. This tubing was more rigid than a real artery and underwent no noticeable diameter changes during the pumping cycle. This meant that the cross-sectional area would be known accurately and errors in flow measurement incurred due to diameter change during the pumping cycle would be minimal. The tubing was mounted either flat or at a fixed angle to the X-ray table. For the second series of experiments, a section of 6-mmdiameter tubing was fixed to a specially designed vessel manipulator [37]. The vessel was placed with one end fixed to the base of the manipulator and the other end fixed to a moveable caddy. The caddy was moved along a linear drive axis by a computer-controlled motor. Although the vessel motion was purely linear, out-of-plane motion was achieved by X-raying the moving vessel at oblique angles. • Prosthetic vascular grafts: For the third series of experiments, polytetrafluoroethene (PTFE) and compliant polyurethane (CPU) grafts were used as simulated arteries. The grafts were thin-walled and more compliant than the silicone tubes. Therefore, they underwent more diameter change during the pumping cycle. Therefore, the error incurred due to changes in the vessel diameter during the pumping cycle would be included in this series of experiments and the vessel cross-sectional area was calculated using a densitometric approach [39]. The PTFE and CPU grafts were placed flat on the X-ray table for the flow experiments. • Cerebral vascular phantom: For the final series of phantom experiments, an anthropomorphic cerebral vascular model was used [38]. This was made from a wax cast of the cerebral vessels of a pathological human brain containing two cerebral aneurysms. The model had one input vessel, the internal carotid artery, and three output vessels, modeling one half of the circle of Willis. The model was mounted in a clear Perspex box with three-way valves on the outside connecting to each of the entry and exit vessels. The box was filled with gelatin to simulate surrounding tissue and give realistic X-ray attenuation and scatter. Flow estimation was carried out for the internal carotid artery segment. 2) X-ray Imaging Protocol: All images were acquired using a GE Advantx DX X-ray system (GE Medical Systems) and transferred to a personal computer using a frame capture card (Matrox Imaging). Biplane X-ray images were acquired at 25 frames/s with injection of contrast material for typically five different mean flow rates for each type of simulated vessel. After each study, a calibration cube [18] was positioned as close as possible to the simulated vessel and orientated to give a clear view of all calibration markers in the X-ray images. X-ray im-


ages of the cube were acquired under the same views as used for the simulated vessel. 3) X-ray Image Analysis: All image data were analyzed using our integrated angiographic analysis software (SARA—System for Angiographic Reconstruction and Analysis) [18]. This is a single Microsoft Windows application that incorporates all the tools required to compute volumetric blood flow from biplane dynamic X-ray angiographic images. The software has the ability to capture images from the X-ray system, to perform image subtraction, to perform three-dimensional vascular reconstruction from biplane images, to compute parametric images of the motion of iodine contrast material allowing for vessel angulation and magnification, to perform velocity extraction, and to perform vessel cross-sectional area calculation, resulting in the output of a volumetric flow waveform. The extracted volumetric waveforms were compared to the EMF waveforms using the statistical methods outlined in Section II-C3. 4) Investigation of Adding Image Noise and Reducing Vessel Length: A parametric image was selected from the in vitro results to study the effects of image noise and vessel length on X-ray flow measurements. This was taken from the analysis of the moving vessel phantom image data for a mean flow rate of 468 ml/min. To study the effects of image noise, different amounts of zero mean Gaussian distributed random noise were added to this parametric image. The amounts chosen were of standard deviations of 1%, 2%, 5%, 10%, 20%, and 30% of the maximum grey value in this parametric image. The flow waveforms were calculated using each of the four flow extraction algorithms for each of the parametric images with increasing added noise. Fifty instantaneous flow values were obtained covering two complete flow cycles. To study the effect of changing the vessel length, different sized windows were placed over the parametric image. The windows spanned the parametric image in the time axis and varied in their extent in the distance axis. The vessel lengths chosen were from 25 mm to 125 mm in steps of 5 mm. The flow waveforms were calculated using the four flow extraction algorithms for each of the different vessel lengths. III. RESULTS A. Results of Velocity Extraction Using the Weighted Optical Flow Algorithm From Simulation Data 1) Simulation Study 1: Five pulsatile cycles were simulated. The first two cycles were not used to estimate velocity since the contrast medium had not opacified the simulated vessel completely. The results from the next three cycles were very similar and we have presented those from the third cycle. Since each cycle was divided into 25 time intervals, the statistical analysis was carried out on 25 velocity estimates. Fig. 3 shows the variation in mean measurement error, standard deviation of measurement error, and correlation coefficient with distance from the contrast medium injection site for vessel lengths of 150–25 mm. Fig. 4 shows the variation of mean measurement error, standard deviation of measurement error, and correlation coefficient with distance from the injection site for increasing amounts of added noise from 0 to 10%. 2) Simulation Study 2: Table II summarizes the results for simulation study 2.


(a)

(a)

(b)

(b)

(c)

(c)

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Fig. 3. Simulation study 1. Variation of mean measurement error (a), standard deviation of measurement error (b), and correlation coefficient (c) with distance from injection site for vessel lengths of 25–150 mm.

Fig. 4. Simulation study 1. Variation of mean measurement error (a), standard deviation of measurement error (b), and correlation coefficient (c) with distance from injection site for 0%–10% added noise. Vessel length is 100 mm.

B. Results From Physiological Blood Flow Circuit

tion algorithms. Table III shows the vessel and flow parameters for these studies. Fig. 10 is an example of variation of the mean flow rate with the first PC found by the MB algorithm. 2) Investigation of Adding Noise and Reducing Vessel Length: Fig. 11 shows the effects on the mean measurement error, standard deviation of the measurement error, and the correlation coefficient of adding 0%–30% noise to a parametric image. Fig. 12 shows the effects on the mean measurement

Fig. 5 shows an example of biplane subtracted angiographic images used for analysis by the SARA software. This image pair was taken from the cerebral vascular phantom study and the extracted vessel center line can be seen. 1) Phantom Studies: Figs. 6–9 show the mean measurement error, 95% CI of the measurement error, and the correlation coefficient for all four phantom studies using the four flow extrac-

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Fig. 5. Biplane subtracted X-ray images of the cerebral vascular phantom. The internal carotid artery center line and edges have been extracted using the SARA software. TABLE II SUMMARY OF RESULTS FOR SIMULATION STUDY 2

Fig. 6. Stationary silicone tubes: Mean measurement error, 95% limits of agreement, and correlation coefficient for the different flow extraction algorithms.

error, standard deviation of the measurement error, and the correlation coefficient of varying the vessel length from 125 to 25 mm. IV. DISCUSSION A. Validation of Weighted Optical Flow Algorithm Using Computer Simulation The simulation studies illustrate some interesting properties of the weighted optical flow algorithm. In simulation study 1

the blood flow input waveform was constant and the effects of changing the vessel segment length, the distance from the contrast medium injection site, and the amount of noise in the image data were examined. It was found that as the vessel segment length was decreased from 150 mm to 25 mm in steps of 25 mm, the magnitude of the flow measurement bias increased, the variability of measurements increased, and the correlation with the true flow decreased [Fig. 3(a)–(c)]. Since the weighted optical flow algorithm is carrying out a weighted average along the length of the vessel segment, for smaller vessel segments


Fig. 7. Moving silicone tubes: Mean measurement error, 95% limits of agreement, and correlation coefficient for the different flow extraction algorithms.

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Fig. 10. Prosthetic vascular grafts: Variation of mean flow rate with the value of the first principal component score found by the MB algorithm.

TABLE III VESSEL AND FLOW PARAMETERS FOR PHANTOM STUDIES

Fig. 8. Prosthetic vascular grafts: Mean measurement error, 95% limits of agreement, and correlation coefficient for the different flow extraction algorithms.

Fig. 9. Cerebral vascular phantom: Mean measurement error, 95% limits of agreement, and correlation coefficient for the different flow extraction algorithms.

there will be less points along the vessel for which this can be done. The performance of the algorithm was most affected when the vessel segment length was 50 mm or below. For reliable measurements, the length of the vessel over which measurements are to be made depends on the maximum instantaneous

velocity. The segment length should be chosen so that the contrast medium bolus does not move entirely out of the segment between successive sampling intervals. The measured flow was also shown to be dependent on the distance that measurements were made from the contrast medium injection site. It was found that measurement bias increased as the distance from the injection site was increased [Fig. 3(a)]. For all segment lengths, the algorithm produced an underestimation of the true flow for the minimum distance from the injection site to an overestimation of flow for the maximum distance from the injection site. This distance-based dependency was also reported by Huang et al. [29] for their point-based optical flow estimation algorithm. This can be explained by the effect of convective dispersion of the contrast medium bolus. The parts of the bolus traveling closer to the center of the blood vessel are transported at a greater velocity in the case of parabolic laminar flow. Therefore, as the bolus evolves with time, the leading edge of the bolus will have a velocity that is greater than the trailing edge. The velocity of the leading edge will be more than the average flow velocity of

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(a) (a)

(b) (b)

(c) Fig. 11. Physiological blood flow circuit. Variation of mean measurement error (a), standard deviation of measurement error (b), and correlation coefficient (c) with 0%–30% added noise for the four flow extraction algorithms.

the fluid whereas the trailing edge will have a velocity that is lower. With increasing added image noise, the algorithm produced flow measurements with increasing tendency to underestimate the true flow, with increasing variability, and with reduced cor-

(c) Fig. 12. Physiological blood flow circuit. Variation of mean measurement error (a), standard deviation of measurement error (b), and correlation coefficient (c) with 25–125 mm vessel length for the four flow extraction algorithms.

relation with the true flow [Fig. 4(a)–(c)]. The added noise will increase the errors in the estimation of the spatial and temporal


derivatives required to calculate the flow velocity. This explains the increased variability and the reduced correlation in measurements. It can be shown that for differential optical flow techniques that there is underestimation of true optical flow in the presence of image noise [40]. This was confirmed by the simulation study results. For the second simulation study, the algorithm was used to measure flow for a range of input waveforms (Table II). The vessel segment length was kept constant at 100 mm and measurements were started at 75 mm from the contrast medium injection site. For instantaneous flow rates there was highly significant correlation with true flow. The measurement bias showed a small overestimation and the 95% limits of agreement were narrow when compared to the range of flows that were measured. B. Validation of Algorithms Using Physiological Blood Flow Circuit For the phantom experiments, the flow measurement algorithms were tested with progressively more challenging vascular phantoms. Initially stationary silicone tubing was used. The silicone tubing was placed in air so that the effects of X-ray scatter were minimal. Also, the tubing was rigid so that there was no noticeable change in vessel diameter with the pulsatile pressure changes in the flow circuit and the vessel cross-sectional area was computed from the known vessel diameters. A total of 2025 instantaneous flow measurements were made using the four flow measurement algorithms. The MB algorithm produced the best correlation with the EMF recordings , followed by the OP algorithm , the PA algorithm , and finally the ORG algorithm . The MB algorithm also showed the least variation in measurement . This was followed algorithm, the PA algorithm by the OP , and the ORG algorithm (Table III and Fig. 6). For the moving silicone tubing experiments, the motion of the vessel phantom would contribute to increased difficulty in flow measurement. The ability to exactly phase match the biplane image sequences for subtraction and analysis, to correctly extract the vessel centerline when the vessel was not entirely filled with contrast medium, and the presence of motion blur in the images would increase the measurement errors. 520 instantaneous flow measurements were computed using the four algorithms. The MB algorithm showed the best , followed by the correlation with EMF recordings OP , PA , and ORG algorithms successively. The variation in measurement was least for the MB algorithm , followed by the OP , PA , and ORG algorithms. The measurement variation was more than that with the stationary silicone tubing as expected due to the vessel motion (Table III and Fig. 7). Prosthetic vascular grafts are compliant like real arterial vessels. These underwent visible diameter changes due to the pulsatile pressure variation in the flow circuit. In the experiments where these grafts were used as the vascular phantom, the vessel cross-sectional area was computed using the densitometric approach. The changing vessel diameter with the pumping cycle

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would introduce errors in the computation of flow since the algorithms assume that vessel cross-sectional area is fixed. A total of 1533 instantaneous flow measurements were made using the four algorithms. The MB algorithm showed the best correla, followed by the OP tion with EMF recordings , PA , and ORG algorithms. Also, the MB algorithm showed the least variation , followed by the OP in measurement , PA , and ORG algorithms (Table III and Fig. 8). Finally, the cerebral vascular phantom was the most challenging for flow measurement. The vascular structures in this were made from thin-walled silicone so that they underwent diameter changes with the pulsatile pressure variations. Also, the vessels were embedded in gelatin to produce realistic X-ray attenuation and scatter. The image quality of the X-ray sequences obtained from this series of experiments was noticeably worse than the other experiments involving tubing placed in air alone. In total 857 instantaneous flow measurements were made using the four algorithms. The MB algorithm showed the best corre, followed by the lation with the EMF recordings , PA , and ORG alOP gorithms. The MB algorithm also showed the least variation in , followed by OP measurement , PA , and ORG algorithms (Table III and Fig. 9). In these experiments there was the most striking difference between the ORG algorithm and the novel MB and OP algorithms. The vessel lengths over which measurements were made were less for this phantom than the previously discussed phantoms. The vessel lengths were 92.2–96.0 mm as compared to 114.2–125.7 mm for the prosthetic vascular grafts, 132.8–136.0 mm for the moving silicone tubing, and 131.7–167.1 mm for the stationary silicone tubing. This reduced vessel length would also be a factor contributing to the larger variation in measurement seen with this phantom. For the MB algorithm, the variation of first principal component score with mean EMF flow recording was investigated. A linear relationship was found for all experiments and the correfor stationary sililation coefficient was cone tubing, for moving silicone tubing, for prosthetic vascular grafts (Fig. 10), and for the cerebral vascular phantom. This would suggest that the first principal component score alone could be a good estimator for the mean flow rate. The measurement bias, as indicated by the mean error of flow measurements, did not show a consistent trend between the four algorithms. However, in going from the best image quality for the stationary silicone tubing to the worst image quality for the cerebral vascular phantom, the algorithms went from a positive measurement bias (overestimation of true flow) to a negative measurement bias (underestimation of true flow). This was most marked for the OP algorithm that showed a measurement bias of for stationary silicone tubing to for the cerebral vascular phantom. As mentioned earlier, differential based optical flow techniques tend to produce an increasing underestimation of velocity as image noise is increased. The effect on flow measurement of added image noise and of changing the vessel length was investigated. A parametric

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image generated from a particularly low noise image sequence was chosen and corrupted by increasing amounts of zero mean Gaussian distributed noise. Fig. 11(a)–(c) shows that increasing image noise has least effect on variation of measurement error and correlation coefficient for the OP and MB algorithms, whereas the ORG and PA algorithms show marked changes in these values. The general trend in the measurement bias was going from over estimation to under estimation as image noise was increased. This was especially marked for the OP algorithm. Fig. 12(a)–(c) shows the effect of reducing vessel length from 125 to 25 mm. It can be seen that the OP and MB algorithms maintain relatively high correlation as vessel length is decreased and also low variation of measurement error. The general trend in measurement bias was going from over estimation to under estimation as vessel length was decreased. However, the MB algorithm did not follow this trend. This was found to be due to over estimation of peak flows as vessel length was decreased.

The effect of different contrast medium injection profiles was not examined. Constant rate injection is usual during angiography so this was used for the computer simulation studies and for the phantom studies. The weighted optical flow algorithm can be easily extended to clinical application. However, the use of the MB algorithm requires a suitable sample of flow waveforms from the target artery. Collection of such data is readily possible using Doppler ultrasound systems, whether intra-arterial or transcutaneous. The sample waveforms would have to include both normal and pathological data. Extensive work on the modeling of arterial waveforms derived from Doppler ultrasound using PCA has demonstrated that this technique can be used successfully to characterize arterial flow and to differentiate between healthy and diseased states using only the first few PCs.

C. Extension to Clinical Flow Measurement

In summary, we have developed and validated two algorithms for the measurement of arterial blood flow using dynamic digital X-ray images. The first algorithm is based on the concentration-distance curve matching approach and improves on this by constraining flow estimates using a principal component analysis shape model of flow waveforms. The second algorithm is based on a differential optical flow technique and improves on point-based optical flow estimation by performing a weighted average of velocity estimates along a vessel based on the magnitude of the spatial derivative of iodine contrast material concentration. The properties of the weighted optical flow algorithm were examined using both a computer simulation of pulsatile flow and a physiological blood flow circuit. The MB algorithm was validated using the blood flow circuit alone. It was found that the MB algorithm out performed the three other algorithms for all phantom studies with the weighted optical flow algorithm following in second place. Both the MB and the OP algorithms showed better immunity to added image noise and to reducing the length of vessel over which measurements were made than the ORG and PA algorithms when considering the correlation with true flows and the variation of measurement error. However, the OP algorithm showed marked changes in measurement bias as image noise and vessel length were changed. The extension to clinical flow measurement is possible with both new algorithms, however, the clinical requirement of short vessel length may prove to be the limiting factor.

Blood flow measurement would be useful to ascertain the haemodynamic effect of arterial interventional procedures such as the treatment of cerebral aneurysms and arteriovenous malformations, and the treatment of coronary artery disease. Let us consider the criteria that an X-ray angiographic flow extraction algorithm should meet in order to be applied clinically: 1) it should make use of the angiographic images that are routinely acquired during procedures so as to impose a minimal radiation dose penalty; 2) it should operate on short vessel segments in the order of a few centimeters. 3) it should show measurement linearity so that changes in blood flow can be assessed relative to a base-line value; 4) it should show low measurement variability; 5) its performance should be independent of contrast medium injection profile. We will now discuss to what extent the new algorithms presented in this paper meet the following criteria. The use of multiple X-ray views and low dose fluoroscopy at 25 frames/s is routine during procedures. The algorithms can use this image data since they are designed for better noise immunity. Calibration can be performed off-line so it does not add to patient radiation dose; Both algorithms show decreased performance 2) when vessel segment length is reduced. Moreover, they operate on vessels with constant cross-sectional area whereas arteries show gradual taper and may have stenosis. The algorithms are able to deal with vessel overlap by excluding regions of overlap in the parametric images. However, this effectively shortens the vessel length and reduces performance. These factors are likely to be limiting for clinical application; 3) and 4) Both algorithms show good measurement linearity and low measurement variability that are better maintained with increasing image noise or reducing vessel length than previous approaches; 1)

5)

V. CONCLUSION

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