Image-based view-angle independent cardiorespiratory motion gating and coronary sinus catheter tracking for x-ray-guided cardiac electrophysiology procedures

Determination of the cardiorespiratory phase of the heart has numerous applications during cardiac imaging. In this article we propose a novel view-angle independent near-real time cardiorespiratory motion gating and coronary sinus (CS) catheter tracking technique for x-ray fluoroscopy images that are used to guide cardiac electrophysiology procedures. The method is based on learning CS catheter motion using principal component analysis and then applying the derived motion model to unseen images taken at arbitrary projections, using the epipolar constraint. This method is also able to track the CS catheter throughout the x-ray images in any arbitrary subsequent view. We also demonstrate the clinical application of our model on rotational angiography sequences. We validated our technique in normal and very low dose phantom and clinical datasets. For the normal dose clinical images we established average systole, end-expiration and end-inspiration gating success rates of 100%, 85.7%, and 92.3%, respectively. For very low dose applications, the technique was able to track the CS catheter with median errors not exceeding 1 mm for all tracked electrodes. Average gating success rates of 80.3%, 71.4%, and 69.2% were established for the application of the technique on clinical datasets, even with a dose reduction of more than 10 times. In rotational sequences at normal dose, CS tracking median errors were within 1.2 mm for all electrodes, and the gating success rate was 100%, for view angles from RAO 90° to LAO 90°. This view-angle independent technique can extract clinically useful cardiorespiratory motion information using x-ray doses significantly lower than those currently used in clinical practice.


Introduction
Electrophysiology (EP) procedures are minimally invasive catheterization procedures that are used to treat cardiac arrhythmias. These procedures are typically performed using 2D x-ray fluoroscopy to guide the insertion and movement of catheters. While x-ray fluoroscopy provides high temporal and spatial resolution, the guidance of such procedures is compromised by the inability of x-ray to effectively visualise soft tissues. In order to enhance image guidance for such cardiac interventions, intra-procedure x-ray fluoroscopy images can be registered and overlaid with pre-procedural 3D anatomical models derived from other imaging modalities, such as magnetic resonance imaging (MRI) (De Buck et al 2005, Rhode et al 2005, Gutiérrez et al 2007 and computed tomography (CT) (Sra et al 2006). X-ray fluoroscopy images can also be registered and overlaid with 3D rotational x-ray angiography (3DRXA), which is particularly suited to the clinical workflow (Li et al 2009). However, the anatomical models will be static and will not update with the intra-procedural situation. Cardiorespiratory motion causes mis-registration of these models and this must be corrected by motion compensation techniques, which require the cardiorespiratory phase to be determined in real time.
Motion gating is useful to obtain synchronised x-ray views at two oblique angles. These can provide image registration of the pre-procedure image (Truong et al 2009) both for procedure guidance and for the off-line fusion of cardiac image data for applications in biophysical modelling research. Synchronised x-ray views are also important when performing catheter-based ablation treatment or electrical measurement. The treatment or measurement sites relative to an anatomical model are often determined using sequential biplane x-ray, both for procedure guidance and for retrospective biophysical modelling (Rhode and Sermesant 2011). Motion compensation via gating is crucial for achieving the required accuracy.
One technique for cardiac gating is by synchronizing the fluoroscopic images with the electrocardiogram. However, this requires extra hardware, is normally an optional extra when purchasing an x-ray system and, when present, there may be latency between the acquisition of the ECG and x-ray data that needs to be calibrated for accurate gating. Respiratory gating can be achieved using the breath-hold technique, commonly used during MRI (Paling andBrookeman 1986, Mageras andYorke 2004), although this is not practical in the catheter laboratory where patients can be heavily sedated. Furthermore, respiratory motion can be handled by the use of external fiducial markers placed on the patient's body (Khamene et al 2004).
Alternatively, detecting the cardiorespiratory phase using the fluoroscopy images is more suited to the routine clinical workflow, as this does not require any fiducial markers, or special hardware. Image-based methods can be divided into those that measure respiratory phase only, cardiac phase only and both. Methods of measuring the respiratory phase only include diaphragm (Condurache et al 2005, Timinger et al 2005, Ma et al 2009, heart border (Ma et al 2012) and EP catheter (Brost et al 2009, Ma et al 2010 tracking. Other methods for measuring the respiratory phase have studied the motion of the coronary tree using 2D biplane angiograms (Shechter et al 2004, Schneider et al 2010, or the motion of left atrial structures such as the pulmonary veins and mitral valve annulus (Ector et al 2008). In King et al (2009a) and King et al (2009b) an affine motion model for the heart was computed from a series of MRI volumes, and the affine parameters were fitted to polynomial functions of the diaphragm position. The model was applied by tracking the diaphragm position in the x-ray fluoroscopy imaging and updating the roadmap accordingly. Methods of measuring the cardiac phase only include weighted centroid tracking (Lehmann et al 2006). Measuring both types of motion simultaneously is an advantage. Successful methods include the use of phase-correlation between successive x-ray images (Sundar et al 2009) and model-based approaches such as the hierarchical manifold learning based (Panayiotou et al 2014) and the Masked-PCA based (Panayiotou et al 2014b) techniques. Nevertheless, because these are model-based approaches a separate model should be formed every time the angulation of the scanner is changed between frames. Moreover, they are retrospective approaches and consequently, real-time application is not possible. Additionally, a technique that relies on tracking of a circumferential mapping catheter when it is in firm contact with a pulmonary vein during ablation for atrial fibrillation (Brost et al 2012) has been proposed, but this is not generally applicable to other interventional procedures.
We have previously proposed a technique for automated image-based near-real time cardiorespiratory motion gating in normal and very low dose x-ray fluoroscopy images (Panayiotou et al 2013). The technique can determine cardiorespiratory phase and gate previously unseen frames based on a statistical model formed from normal dose images. This model is acquired from a calibration sequence using principal component analysis (PCA) of the motion of the coronary sinus (CS) catheter, a particular catheter that is nearly always present in EP procedures. One major limitation of this and other model-based approaches is the requirement to build a separate model for each x-ray view.
In addition to the above applications of motion compensation and synchronisation of sequential bi-plane images, cardio-respiratory phase determination is also important in rotational sequences for gating of rotational coronary angiography and of C-arm CT. In this application, the view-angle of the x-ray is changing continuously, such that none of the above mentioned image-based methods could be used. To the authors knowledge the only viewangle independent work in the literature is proposed by Lehmann et al (2006). The technique is capable of measuring coronary motion from the 2D projection images acquired during rotational angiography, with the aim of developing an image-based cardiac gating strategy specifically for 3D coronary angiography. The image-based technique is based on the weighted centroid of the opacified coronary arteries. The 1D vector component of the centroid that is parallel to the axis of rotation is chosen as the image-based metric of motion. In coronary angiography the patient's superior-inferior (SI) axis is roughly aligned with the detector's axis of rotation, therefore the image-based metric of motion is the SI component of the weighted centroid (SIC), and this is used to track vessel motion. However, the 1D vector component of the centroid that is parallel to the axis of rotation is independent of the angular position of the detector. Therefore, this technique has the advantage of being view angle independent. Nevertheless, the technique's robustness as a function of angle is not fully tested as the authors analysed data from only two views. Clinically, where small field-of-view x-ray image intensifier detectors are used in coronary angiography, the background structures may move in and out of the field of view and it is important that the effect of this on the SIC measurement be minimized. An additional drawback of this technique is that it can only gate the cardiac motion of the heart. The utility of the technique in 3D coronary angiography has been demonstrated in an animal study. The success of the animal experiment is encouraging, but further analysis of 3D clinical angiograms is necessary.
In this paper, we significantly extend our previous approach (Panayiotou et al 2013) to make it x-ray system view-angle independent and therefore much more clinically useful. Our proposed approach again forms a PCA-based model of the CS catheter in a first or training view. It then uses this to determine both the cardiac and the respiratory phases in near-real time in any arbitrary second or current view. Along with cardiorespiratory motion determination, this technique is able to track the 2D CS catheter electrode positions, again in any arbitrary subsequent view. Thus it is possible to obtain synchronised electrode positions in the two views. The main scientific contributions of this paper are: • Determination of both the cardiac and the respiratory phases in near-real time in any arbitrary view without retraining; • 2D tracking of the CS catheter in any arbitrary view, including those in which other electrode detection methods fail.
We carry out comprehensive validation of our gating and CS tracking technique on clinical and phantom x-ray sequences. In particular, we show how this novel approach can be used for motion gating of 3DRXA for which current methods are limited to breath-holding for respiration and either no gating for cardiac motion or arresting the heart using adenosine or rapid pacing (Kriatselis et al 2011).

Methods
In this section we first describe the formation of our statistical model of catheter motion in the training view (section 2.1), explicitly described in our previous work (Panayiotou et al 2013), and then its application on the current view (section 2.2), which is the novel contribution of this work. Figure 1 gives an overview of our proposed workflow.

Statistical model formation in the training view
The formation of our statistical model comprises two main steps. Firstly, the technique described in Ma et al (2010) is used to track the electrodes of the CS catheter throughout the x-ray sequence. Secondly, PCA is applied to the coordinates of the tracked electrodes. The reasons for choosing the CS catheter instead of other catheters are that it is routinely used during EP procedures, it remains in place throughout the procedure, its position is usually not altered and it is rarely overlapped by other catheters in the x-ray projections. This is due to the positioning of the main part of the CS along the border of the mitral valve annulus. Additionally, since the main part of the CS is a curved structure, it has similar foreshortening in all routinely used x-ray projections, which makes it an ideal choice for derivation of motion. The steps are described below.
2.1.1. CS catheter detection. The CS catheter used here is composed of 10 electrodes, distributed in pairs along the catheter. The CS tracking technique (Ma et al 2010) uses a fast multi-scale blob detection method (Lindeberg 1993) to detect all electrode-like objects in an x-ray image and a cost function to discriminate the CS catheter from other catheters. After application of the tracking algorithm for all frames in the training view, θ 1 , the x and y positions of each of the 10 electrodes are concatenated into a single column vector for each time point. Hence, the data generated by the tracking process consists of: where z i, e, x and z i, e, y represent the x and y coordinates of the eth electrode in the ith frame. e = 1 corresponds to the distal electrode, and N is the number of frames.

Application of statistical model on the current view
The task is to gate previously unseen frames in near-real time in any arbitrary second or current view based on a statistical model formed in a first or training view. The gating is prospective in the sense that we do not need to collect the whole sequence before processing, although it will be performed with a time lag of 1 sample interval because of the need to identify peaks/ troughs in the extracted signals. Consequently, the gating is almost prospective, but because of the phase lag it will be called 'near real-time gating'.
2.2.1. Epipolar line reconstruction. Epipolar reconstruction allows loss of depth information to be recovered from a 2D projection image if another 2D image is taken of the same target from a different view, assuming we know the complete camera parameters of the x-ray fluoroscopy projective modality (Ganapathy 1984, Strat 1987, Rougée et al 1993, Hartley and Zisserman 2004. The camera parameters include ( ) are the coordinates in the image where the beam is normal to the projection plane, f is the distance between the source and the projection plane, ∆ u and ∆ v are the pixel spacing in the (u, v)-axes, respectively on the projection plane, x y z and (θ φ ψ , , ) are the parameters defining the position and orientation of the camera in 3D space. The camera parameters are obtained from the DICOM header of the x-ray images. Using epipolar geometry, each of the 2D electrode positions obtained when forming our statistical model in θ 1 is backward projected to form a 3D line, l b , which is then forward projected to generate a 2D epipolar line, l e , in the current view, θ 2 , that contains the corresponding electrode position. Hence, we generate 10 epipolar lines in θ 2 for each frame in the current view.

Blob detection and 2D CS catheter position estimation.
We now determine the 2D position of the CS catheter in the new image in θ 2 and simultaneously determine its state of cardiorespiratory motion. Although the real-time catheter tracking algorithm (Ma et al 2010) is used in the training sequence, it fails in rotational datasets at view-angles that distort the solid circular shape of the CS catheter electrodes. Additionally, the multi-scale blob detection algorithm misdetects blobs at very low doses. Consequently, we cannot solely use this method for 2D catheter tracking in rotational sequences at low doses. Instead, we determine the cardiorespiratory state in the PCA model of θ 1 that produces epipolar lines that most closely match the catheter electrodes in the new image in θ 2 . First, the fast multi-scale blob detector (Lindeberg 1993) is used to detect all possible electrode-like objects in the new image. The positions of all detected blobs are concatenated into a blob list, BL.
Using the PCA model, an instance of the CS catheter, ŝ, can be generated in θ 1 according tô where w m are the weights for each eigenvector. If the first two eigenvectors are used then we can represent the instance by ŝ w w 1 2 . The weights ŵ 1 and ŵ 2 that represent the cardiorespiratory phase of the image for θ 2 are then estimated according tô[ is a function that computes the sum of the minimum Euclidean distances between the epipolar lines generated by ŝ w w 1 2 and their nearest corresponding blobs from BL. Its purpose is to position the epipolar lines so that they pass through the electrodes in the new view. ( ) A s w w 1 2 is a function that computes the sum of angles between line segments joining successive blobs, in order for the optimisation to favour a smoothly curving line of blobs representing the electrodes. Motivated by the σ 2 rule, which states that for a normal distribution, about 95% of the values lie within 2 standard deviations of the mean, our search space for the weights varies from − d 2 m to + d 2 m , where d m is the mth eigenvalue, and ⩽ ⩽ m 1 2 . We minimized the function using a coarse-scale exhaustive search followed by an iterative optimisation using Matlab's lsqnonlin function with the trust-region-reflective algorithm (MATLAB Release 2013a, The MathWorks, Inc., Natick, Massachusetts, USA). For the application of our model on rotational sequences, where the CS catheter position deviation was larger, our search space for the weights varies from − d 3 m to + d 3 m , to solve the optimisation. Additionally, for the phantom rotational datasets, the exact view angles for each frame were not available in the DICOM headers. Instead, initial estimates for the angles were computed by assuming a constant rotation speed. These were refined by including a search over the angles (±°5 from the initial estimate in steps of 1°) in the exhaustive search for the PCA weights.
The resulting weights indicate the cardiorespiratory phases and the blobs from BL nearest to the epipolar lines give the catheter location in the new image.
2.3. Cardiac and respiratory gating of the current view 2.3.1. Cardiac gating. ŵ 1 is used to detect systolic frames, Ω sys , of the image sequence. These are represented by the peaks of the variation of ŵ 1 with frame number, i.
2.3.2. Respiratory gating. The peaks of the variation of ŵ 2 over time represent end-inspiration (EI ) respiratory frames, Ω EI , while the troughs represent end-expiration (EX ) respiratory frames, Ω EX .

Correction of incorrectly annotated electrodes
In addition to generating gating information, the 2D electrode positions in the new view are determined as part of the gating process. These are useful in EP procedures, for example to register a 3D roadmap to the 2D x-ray images. However, it is possible that an electrode is associated with an incorrect blob in the new image, particularly in very-low-dose x-ray where there may be incorrect blobs close to the epipolar line, and these incorrect electrodes must then be corrected. The correction is an additional step in which the 3D position of the CS catheter is reconstructed from the 2D gated electrode positions in the two views. Each set of CS electrode positions from the two projection planes is back-projected to reconstruct the CS catheter in 3D (Hawkes et al 1987, Penney 2001. The CS catheter's maximum inter-electrode distance is 5 mm and we consider incorrectly annotated electrodes as those that are located more than 9 mm away from their neighbouring electrodes. Clusters of more than 2 electrodes located less than 9 mm away from their neighbours are considered to be correctly annotated. A smooth spline, s r , ⩽ ⩽ r R 1 , comprising a total of R points, is computed to fit the correctly annotated electrodes.
In cases where the proximal or the distal electrodes are incorrectly annotated, the two nearest spline points are used to extrapolate a 3D straight line, l r , passing through them. Taking all vectors as column vectors, the 3D point, c, that minimizes the sum of squared errors to l r and the back projection line l b from the corresponding electrode in θ 1 , is found using the 3D line-to-line distance equation: I is the identity matrix, d is the unit direction vector of l r , d 2 is the unit direction vector of l b , r is the nearest point on the spline, r 2 is a point on l b and ′represents the transpose. We then correct our electrode to r cor , the point on line l b that is closest to c, and therefore l r , using (8) (2015) 8087 In cases where an incorrect electrode is found somewhere in the middle of the CS catheter, it is corrected to the point on line l b that is closest to the nearest point on the spline segment, s r , using (9) We then forward project our 10 final 3D electrode points to θ 2 . Figures 2(a) and (b) illustrate the correction of annotated electrodes at the end and middle of the CS catheter, respectively.

Application to gating and catheter tracking
3.1.1. Accuracy in multiplane sequence pairs at normal and low dose. The accuracy of our gating and catheter tracking were validated at both normal and low dose, on sequential biplane sequence pairs, from clinical and phantom data. The model was formed in one view at normal dose, and used to gate and track the catheter in a second view at either normal or low dose. A comparison to our existing single-view method (Panayiotou et al 2013) was performed to show the effect of the extra step of changing view angle. Comparison to all possible single view methods was not done, as this has already been done in our previous work (Panayiotou et al 2013) and was not our objective in this paper.  phantom data. The model was formed on a training view at a constant angle at normal dose, then applied to a rotational sequence with continuously changing angle between RAO90° and LAO90°.
3.1.4. View angle dependence. Finally, it is important to investigate the dependence of the phase determination accuracy on the view angle of the image sequence. Consequently, experiments were performed on phantom datasets with different view angles used for the formation of the statistical model in the training view. These were then applied to a rotational phantom dataset in the current view. This allowed comparison of different training angles and also investigation of how the accuracy varies with the current angle.  (Ma et al 2010). The manual electrode detection gold standard was validated by two independent observers on 330 frames of phantom data (3300 electrode detections) and 122 frames of clinical data (1220 electrodes). The average Euclidean distance between the results of the two observers over all electrodes and frames of these randomly chosen phantom and rotational clinical sequences were 0.47 mm and 0.35 mm, respectively.
For the gating gold standard in clinical data, manual gating of the cardiac cycle at systole was performed by an experienced observer, by visually detecting the end of contraction of the left ventricle from the fluoroscopic left heart border shadow. Manual gating of the cardiac cycle at end-systole was further validated by three additional observers who were trained to identify the end-systolic frames throughout the x-ray sequences. All four chose identical systolic frames, indicating perfect precision of the gold standard.Manual gating of the cardiac cycle at end-diastole was also performed by three experienced observers, by visually detecting the end of relaxation of the left ventricle from the fluoroscopic left heart border shadow. No variation between the multiple observers was found. For the respiratory gating, a gold standard was obtained for the clinical data using either diaphragm or heart border tracking as described in Ma et al (2012). The respiratory signal obtained was cardiac gated using the manually identified systolic frames.
For the phantom sequences, two different clearly-visible regions of interest moving independently with cardiac and respiratory motion were automatically tracked using the diaphragm/heart border tracking method (Ma et al 2012). The gating accuracy of the automatic diaphragm/heart border tracking technique was found to be identical to manual gating based on landmarks attached to the phantom.

Gating accuracy measure.
For both cardiac and respiratory gating, the absolute frame difference was computed between our technique and the gold standard techniques. Specifically, systolic, end-inspiration, end-expiration, and for one experiment end-diastolic, frames were recorded from our automatic and gold standard methods and their corresponding absolute frame differences were computed. Even though we do detect the whole cycle, for evaluation, we use only these peaks and troughs, where the gold standard is well-defined. Motion gating accuracy objectives were set based on potential clinical applications that the proposed method could tackle. For motion gating of 3D rotational x-ray angiography sequences and 3D catheter reconstruction, cardiac motion is the limiting factor. These applications will use the diastolic cardiac phase, where the heart is more relaxed, and it is expected that its shape will be more repeatable over several cycles. Additionally, when registering a 3D model, the model is almost always from a diastolic image. Since the heart will be relatively stationary in the diastolic phase for a period of about 0.3 s, the motion gating accuracy objective is set to 0.1 s. Faultless gating results are signified when the absolute frame difference is within this motion gating accuracy objective.
3.2.3. 2D catheter tracking accuracy measure. 2D catheter tracking accuracy was evaluated simply as the distance between the measured electrode positions and gold standard positions. For cardiac catheterization procedures such as RF ablation, CS catheter tracking accuracy within 2 mm is an acceptable tolerance (Esteghamatian et al 2008).

Clinical protocol
All imaging was carried out using a monoplane 25 cm flat panel cardiac x-ray system (Philips Allura Xper FD10, Philips Healthcare, Best, The Netherlands) in one of the catheterization laboratories at St. Thomas' Hospital, London.

Intra-procedural image acquisition.
Clinical images were acquired from 11 patients undergoing radiofrequency ablation procedures. Phantom images were acquired using a bespoke beating and breathing left ventricular phantom (Manzke et al 2010) with an inserted CS catheter, designed to emulate the clinical workflow of a typical catheterisation, as illustrated in figure 3(a). For this phantom, polyvinyl alcohol (PVA, Lenticats, GeniaLab, Braunschweig, Germany) (Mano et al 1986, Chu andRutt 1997) was used as a tissue-mimicking material, to mimic the heart during cardiac interventions. A cylindrical PVA phantom with an inner radius of 6.6 cm, an outer radius of 8.2 cm and a length of about 9 cm, providing an initial wall thickness of about 1.6 cm, was generated using one freeze / thaw cycle at 35 C/ 20 C −°+°. The PVA phantom, illustrated in figure 3(b), was placed in an MRcompatible air-pressured actuator (Timinger et al 2004) which compresses and rotates the PVA according to a preset heart rate. Along with the cardiac motion, the phantom actuator can translate the phantom up and down to simulate breathing motion. For the experiments demonstrated in this chapter, the cardiac rate varied between 70 and 100 cycles per minute (cpm), while the respiratory rate varied between 8 and 12 cpm. X-ray imaging was performed at between 3 and 30 frames per second with an image size of either 512 2 or 1024 2 pixels in resolution, with a pixel size, − R x ray , of 0.25 mm pixel −1 . Included in this ratio is the typical magnification factor of the x-ray system.

Application of noise.
The effect of low x-ray doses was investigated by adding Poisson noise to both the clinical and phantom test images. The magnitude of the noise varies across the image, as it depends on the local image intensity. The image noise is therefore specified in terms of the median value of the Poisson mean (Panayiotou et al 2013). We used SNR values of 50, 10, 8, 6 and 5, where the SNR value of 5 represents a dose reduction of more than 10 times. These values were chosen by initially applying our CS catheter tracking algorithm on low noise levels that are almost indistinguishable from the noise-free image, and then gradually increasing the noise level until the algorithm started to fail.

Validation data.
The multiplane normal and low-dose experiments used 3 sequential biplane clinical sequences (244 frames, 6 runs in total, running from a minimum of 8.0 to a maximum of 19.3 s, covering at least 2 respiratory cycles) and 2 sequential multiplane (one biplane and one triplane) phantom sequences (1741 frames, 5 runs in total, running from a minimum of 9.8 to a maximum of 22.7 s). The PCA model was formed for each sequence individually and the method run on each possible combination of sequence pairs, giving a total of 6 clinical and 8 phantom experiments.
For the rotation experiments, 3 clinical rotational x-ray angiography sequences (341 frames) and 2 phantom rotational x-ray sequences (540 frames) were used. Each sequence covered the range RAO 90° to LAO 90°. For the patient sequences the statistical model was formed on a monoplane x-ray sequence acquired for each patient in the AP view. For the application of our technique on the phantom rotational sequences, the model was formed on monoplane x-ray sequences in AP and RAO30° views in turn.
Finally, the angular dependency experiments used the same phantom rotational sequence. The training views used were PA, LAO 30° and RAO 30°. Figure 4 illustrates the results of the CS catheter tracking technique on the 1st image of an uncorrupted example x-ray sequence and the simulated low-dose images, with SNR values of 50, 10, 8, 6 and 5, respectively.

Validation of CS catheter tracking.
Figures 5(a) and 6(a) illustrate the CS catheter tracking median errors per electrode for phantom and patient x-ray images, respectively, at normal dose and for the 5 SNR values. Errors were calculated for each electrode and are shown in different grey scale colours, starting from the proximal (black colour) and moving to the distal (white colour) electrode. For the technique to be acceptable in clinical practice, failure cases were considered to be the ones where median errors per electrode were above 2 mm (Esteghamatian et al 2008). Figures 5(b) and 6(b) show the range of the values in terms of the first quartile (25th percentile) median and third quartile (75th percentile) over all electrodes, for each noise level, for phantom and patient datasets, respectively. Success rates were also calculated and are shown as percentages (%) in figures 7(a) and (b), for the patient and phantom datasets.

Validation of cardiorespiratory motion gating.
For cardiac gating validation, a plot of the first weight for the first 30 frames of an example clinical x-ray sequence is    Figure 9 illustrates the frame difference errors in frequency distribution bar charts, i.e. the number of peaks or troughs with 0, 1 or 2 frames separation from the gold standard for the patient biplane sequences, for all gating tasks and noise levels. For both systolic and diastolic gating, the absolute frame difference was computed between the view-angle independent method and the gold standard methods on the normal dose images. The results showed no difference between end-systolic and end-diastolic gating so they are excluded from the figure. This indicates that the method is just as accurate on diastolic frames, and consequently the systolic accuracy results are relevant for applications that require diastolic gating. For a more comprehensive comparison, percentage (%) success rates for endsystolic, end-expiration (EX) and end-inspiration (EI ) gating were also calculated and are shown in figure 10 for both the used phantom and clinical images. Using the model on unmodified clinical images for near-real time cardiorespiratory motion gating, end-systole, Figure 6. Catheter tracking errors. The meaning of the graphs is the same as in figure 5, but for clinical data. EX and EI gating success rates of 100.0%, 85.7% and 92.3%, respectively, were established, based on the accuracy objective of 0.1 s. Additionally, gating success rates of 80.3%, 71.4% and 69.2% were established, even at the low SNR value of 5. Using the model on unmodified and modified phantom sequences, for near-real time cardiorespiratory motion gating, success rates of 100.0% were established for all gating tasks. To comparatively validate the technique to the Tracked-PCA method (Panayiotou et al 2013), where the statistical model was formed from normal dose images during a calibration phase and applied to low dose images acquired from the same view-angle, % success rates from both techniques for the same sequences are illustrated on the figure. No false positives or negatives (i.e. extra/fewer detected peaks/troughs) over the processed sequences were found. Outcomes show that the  Figures 11 and 12 illustrate the results of the CS catheter tracking technique on normal dose x-ray images at different view angles from a patient and a phantom example x-ray sequence, respectively. The results show that, this novel view-angle independent technique can successfully track the CS catheter in x-ray sequences where the angulation of the scanner is changed between frames. The multi-scale blob detection (Lindeberg 1993) and real-time tracking technique (Ma et al 2010) do not reliably detect the CS catheter electrodes in all views, even at normal dose, because of the different appearance of the electrodes at some angles. Figure 13 illustrates (a) the CS catheter tracking technique median errors per frame per electrode and (b) the % success rates for the patient and phantom x-ray rotational sequences.

Validation of cardiorespiratory motion gating.
For both cardiac and respiratory gating, the absolute frame difference was computed for the phantom procedures. For patient procedures the absolute frame difference was computed only for cardiac gating as patients were in breath-hold. The results can be seen in the frequency distribution bar charts in figure 14 for both patient and phantom rotational sequences. No false positives or negatives (i.e. extra/ fewer detected peaks/troughs) over all processed sequences were found. The results demonstrate that our proposed technique is robust and accurate in tracking the CS catheter and is doing a faultless job in extracting cardiorespiratory motion from any viewangle, over the range of °180 , in normal dose scenarios for rotational acquisitions.

Quantitative validation of view angle dependence.
For both cardiac and respiratory gating, the gating success rate and the median errors per frame over all CS catheter electrodes were computed for the phantom experiments where the model was formed on different training views, PA, LAO 30° and RAO 30°, and tested on the same rotational sequence, ranging from RAO 90° to LAO 90°. This examines whether the difference in the viewing angles between the training and the current image sequences has an effect on the algorithm's success. The results for gating success rates were 100% in all cases. Therefore, the median errors of CS catheter tracking at each angle were compared and are shown in figure 15. CS catheter tracking is related to motion gating in the sense that a correctly annotated CS catheter would correspond to the best motion gating results we could obtain using our algorithm. CS tracking errors therefore indicate a potential for gating errors. The results show that there is no obvious dependence on the current or training angle. A paired two-sided Wilcoxon signed-rank test was conducted under the null hypothesis that there was no difference in building the model on different training views. The test was done on the median errors over all CS catheter electrodes with respect to viewing angles and was conducted for each of the viewing angle pairs. For all three pairs the p-values were more than 0.05, indicating that there is no statistically significant difference when building the model on different viewing-angles.

Discussion
In this manuscript, we have presented a novel technique for near-real time determination of cardiorespiratory gating using a PCA-based model of CS catheter motion that can be applied to a secondary x-ray view. The technique is an extension of our previously proposed technique for automated image-based near-real time cardiorespiratory motion gating in normal and very low dose x-ray fluoroscopy images (Panayiotou et al 2013). It is developed to eliminate the requirement of our previous technique and all other model-based approaches to build a separate model for each x-ray view. Consequently, the current approach is x-ray system view-angle independent and therefore much more clinically useful. To build our model in the training view the real-time tracking technique, proposed by Ma et al (2010), is used. This technique is robust and also performs very well in higher dose images. However, as illustrated in our previous work (Panayiotou et al 2013), success rates calculated for our previously proposed catheter tracking technique are higher than those calculated for the real-time tracking technique in low dose x-ray sequences. In the clinical scenario, the real-time tracking technique will be used to form the PCA model from high dose x-ray images, where this technique is robust. Subsequently, the x-ray dose will be significantly reduced and our proposed view-angle independent technique will be employed for catheter detection in the current view, enabling the subsequent procedure to be carried out at very low x-ray dose.
One limitation of our technique is that if the CS catheter is advanced or pulled back before the second or subsequent views are acquired our statistical model would need to be rebuilt based on the new position of the CS catheter. However, one of the reasons that the CS catheter was chosen for our algorithm was because its position is commonly unchanged throughout the procedures.
In addition to gating, our technique is able to locate synchronised CS catheter electrode positions in the two views. However, even with accurate gating, correct annotation of catheter electrodes is not guaranteed. In very low dose applications there are cases where an electrode is incorrectly annotated, as a noise blob might be closer to the epipolar line than the actual catheter blob. As outlined in section 2.4 our algorithm is able to correct for this incorrect electrode annotation by first reconstructing the catheter in 3D from the two gated views. However, this electrode correction would fail if more than two incorrect neighbouring electrodes happen to be closer than 9 mm away from each other, as these would be seen as correct. We have not quantified the robustness experimentally, although a failure has never occurred in x-ray images with SNR values down to 5. Although correcting for these cases does not alter the gating accuracy, correct CS electrode annotation is clinically useful in EP procedures for relating signals measured at the electrodes to locations on the anatomy. Additionally, for rotational acquisitions, the electrodes can be removed by replacing with adjacent background prior to 3D reconstruction in an attempt to reduce motion artifacts. Our algorithm was able to detect the coronary sinus catheter with median errors of correctly-tracked electrodes not exceeding 1.2 mm, well below the acceptable value in clinical practice which is 2 mm (Esteghamatian et al 2008).
Moreover, regarding the algorithm's performance on the different experiments, depending on the step size, the execution time was between 0.41 and 1.73 seconds per frame. Hence, near-real time implementation is not currently achieved. However, code optimisation was not the focus of this work and would need to be considered for real-time application. Additionally, a decrease in execution time will favour real-time motion compensation in the secondary view in sequences where x-ray imaging is performed at three frames per second or faster.
We have demonstrated the technique's use for gating of rotational sequences. Another potential clinical application of our technique is respiratory motion compensation of unseen images taken at any arbitrary projection, by driving the motion of the 3D MRI roadmaps fused onto live x-ray fluoroscopy. Existing motion compensation techniques (Giraud et al 2000, Jiang and Doppke 2001, Shechter et al 2005, King et al 2009a, Zhu et al 2010, Ma et al 2011 require a respiratory surrogate signal, such as diaphragm tracking, catheter motion or spirometry. This is used as an input to a motion model of the MRI roadmap, which can be a simple 1D translational correction, or a more complex motion model. The respiratory phase found using our technique could be used as the surrogate signal, with the benefit of requiring no additional equipment, working at low dose and at any view angle after an initial training step.

Conclusion
We have presented a novel and potentially clinically useful near-real time gating and catheter tracking technique for the determination of cardiorespiratory gating of x-ray fluoroscopic images in electrophysiology procedures. The technique is based on learning CS catheter motion using PCA and then applying the derived motion model to unseen images taken at arbitrary projections. Unlike most previously developed motion gating techniques, the main novelty of our technique is that it is x-ray system view-angle independent. Therefore, it is applicable and robust to cases where the angulation of the scanner is changed between frames. The method is fully automatic, requires no prior knowledge and can operate at around one second per image. Additionally, it is workflow-friendly, does not require any additional fiducial markers or contrast agent, and has the potential to greatly reduce radiation dose in image-guided cardiac catheter procedures. As a consequence radiation to patients and staff will decrease significantly. Future work will focus on implementing a new more accurate blob detection algorithm in an attempt to increase the % success rates of our technique. Additionally, we are planning to investigate the effect of a more explicit catheter detection, by including temporal constraints, i.e. the electrode will not move drastically between consecutive frames on the 2nd view. Finally, we intend to apply the method to the motion compensation task, using the respiratory gating trace to drive a suitable motion model.