A technique for respiratory motion correction in image ...

A technique for respiratory motion correction in image guided cardiac catheterisation procedures A. P. Kinga , R. Boubertakha , K. L. Nga , Y. L. Maa , P. Chinchapatnamb , G. Gaob , T. Schaefftera , D. J. Hawkesb , R. Razavia and K. S. Rhodea a Interdisciplinary b Centre

Medical Imaging Group, King’s College London, U.K.; for Medical Image Computing, University College London, U.K. ABSTRACT

This paper presents a technique for compensating for respiratory motion and deformation in an augmented reality system for cardiac catheterisation procedures. The technique uses a subject-specific affine model of cardiac motion which is quickly constructed from a pre-procedure magnetic resonance imaging (MRI) scan. Respiratory phase information is acquired during the procedure by tracking the motion of the diaphragm in real-time X-ray images. This information is used as input to the model which uses it to predict the position of structures of interest during respiration. 3-D validation is performed on 4 volunteers and 4 patients using a leave-one-out test on manually identified anatomical landmarks in the MRI scan, and 2-D validation is performed by using the model to predict the respiratory motion of structures of the heart which contain catheters that are visible in X-ray images. The technique is shown to reduce 3-D registration errors due to respiratory motion from up to 15mm down to less than 5mm, which is within clinical requirements for many procedures. 2-D validation showed that accuracy improved from 14mm to 2mm. In addition, we use the model to analyse the effects of different types of breathing on the motion and deformation of the heart, specifically increasing the breathing rate and depth of breathing. Our findings suggest that the accuracy of the model is reduced if the subject breathes in a different way during model construction and application. However, models formed during deep breathing may be accurate enough to be applied to other types of breathing. Keywords: Respiratory motion, cardiac procedures, modelling, multimodality display

1. INTRODUCTION Cardiovascular catheterisation procedures are commonly carried out for diagnostic and interventional purposes. To aid in navigation, such procedures are typically performed under X-ray fluoroscopic guidance. Because of the poor soft-tissue contrast of X-ray images the development of an XMR (X-ray/magnetic resonance) image guidance system that allows the integration of X-ray and a roadmap derived from magnetic resonance imaging (MRI) images was recently reported.1, 2 The accuracy of this system is currently limited by the problem of respiratory motion. In this paper we propose a technique to correct for cardiac respiratory motion to address this problem. Our technique involves forming a model of cardiac respiratory motion from MRI data. A number of researchers have attempted to construct such models before, mostly for the purpose of correcting for motion in MRI image acquisition. The traditional approach has been to approximate cardiac motion by a superio-inferior translation that has a linear relationship with the superio-inferior movement of the diaphragm.3 However, more recent work suggests that this might not be sufficient for some applications. McLeish et al4 described a statistical shape model of cardiac respiratory motion. They reported that the heart often deforms as well as moves, and that there can be significant inter-subject variation in the amount and nature of both motion and deformation. This suggests that a subject-specific model may be required for greater accuracy. This work used MRI images acquired at breath-hold. However, more recently it has been reported that heart motion and deformation are not the same for breath-hold and free-breathing due to the presence of hysteresis in expiration.5 Manke et al6 formed affine and translational models of cardiac respiratory motion by coregistering free-breathing cardiac MRI Further author information: (Send correspondence to Andrew King.) Andrew King: E-mail: [email protected] Medical Imaging 2008: Visualization, Image-guided Procedures, and Modeling, edited by Michael I. Miga, Kevin Robert Cleary, Proc. of SPIE Vol. 6918, 691816, (2008) 1605-7422/08/$18 · doi: 10.1117/12.769377 Proc. of SPIE Vol. 6918 691816-1 2008 SPIE Digital Library -- Subscriber Archive Copy

images. It was concluded that for most subjects an affine model is sufficient. However, it has also been noted that some subjects’ hearts undergo local deformations during respiration, which cannot be captured by a purely affine global model.4, 6 Ablitt et al7 proposed a model of cardiac motion using nonrigid registration of MRI images. To the authors’ knowledge, the only previous example of using a respiratory motion model in X-ray guided catheterisations was described by Shechter et al,8 in which a model of cardiac and respiratory motion of the coronary arteries was constructed from biplane contrast-enhanced X-ray image sequences. So far the aim of most of the previous work has been to improve image quality in coronary MR angiography scans. In this paper we investigate the possibility of using MRI-derived models to correct registration errors due to respiratory motion during an image-guided catheterisation procedure. Although our principal clinical application is electrophysiology (EP) procedures, the technique we describe has potential application to a range of cardiovascular catheterisation procedures. For such procedures there is often a significant delay between MRI image acquisition and the procedure so the patient’s breathing pattern may differ between MRI scanning and the procedure. Furthermore, it is possible that the discomfort induced by the catheter may also lead to a change in breathing pattern. Therefore, as well as assessing the accuracy of our model, we investigate the effects that changes in breathing may have on this accuracy. This paper is structured as follows. In Section 2.1 we describe the construction of the motion model, including details of the MRI data acquisition. In Section 2.2 we describe the application of the model during a catheterisation procedure. The validation procedure is outlined in Section 2.3, the results of which are presented in Section 3. Finally, discussion, conclusions and ideas for further work are given in Section 4.

2. METHOD The technique consists of two main phases. First, a subject-specific affine model of cardiac respiratory motion is constructed based on a pre-procedure MRI scan. Next, during the procedure the motion of the diaphragm is tracked in real-time X-ray images and the resulting respiratory phase information used as input to the model, which predicts the respiratory motion of an MRI-derived roadmap. These two phases are described in the following sections.

2.1 Constructing the motion model 2.1.1 MRI image acquisition A number of MRI images are required to construct the respiratory model. First, a high resolution free-breathing scan (3D balanced TFE, respiratory gated at end-expiration, cardiac triggered and gated at late diastole, typically, 120 sagittal slices, TR=4.4ms, TE=2.2ms, flip angle=90o, acquired voxel size 2.19 × 2.19 × 2.74mm3 , reconstructed to 1.37 × 1.37 × 1.37mm3 , 256 × 256 matrix, scan time approximately 5 minutes) is acquired. This image is used solely to segment the roadmap and is normally acquired as part of the standard clinical protocol. Next, a dynamic scan is acquired obtaining a number of low resolution, near real-time free-breathing scans that cover a range of respiratory positions (3-D TFEPI, typically, 20 slices, TR=11.75ms, TE=5.84ms, flip angle=20o, acquired voxel size 3.81 × 4.27 × 8.0mm3 , reconstructed to 2.22 × 2.22 × 4.0mm3 , 144 × 144 matrix). We typically acquired 100 images for the experiments described in this paper. These images are used to form the model. Whilst acquiring them a pencil-beam navigator is applied on the diaphragm immediately before and after acquisition. The average of these lead and trail navigators is used in forming the model. 2.1.2 Model formation The parameters of the affine model are determined solely from the low resolution MRI images. First, the image with the highest navigator value (end-expiration) is selected as a reference image. Next, all other MRI images are registered to the reference image using an intensity-based affine registration algorithm9 (the Image Registration Toolkit). A manually selected bounding box around the heart is used as a region of interest for this registration. For each image, this results in twelve registration parameters together with an average navigator value. In addition, the breathing direction (i.e. inspiration or expiration) can be determined for each image by comparing its navigator value with those of its predecessor/successor. If the navigator value is less than its predecessor and greater than its successor the image is classified as an inspiration image. If it is greater than its

Proc. of SPIE Vol. 6918 691816-2

predecessor and less than its successor it is an expiration image. Otherwise, the breathing direction changes at the image so it is classified as an end-cycle image. We form two datasets for each affine parameter: an inspiration dataset and an expiration dataset. Data from end-cycle images are included in both inspiration and expiration datasets. The datasets consist of a set of pairs of values: a navigator value and a value for an affine parameter. Finally, second-order polynomial curves are fitted to the data for each parameter using a least-squares fitting technique. Curves are fitted separately for inspiration and expiration to enable analysis of the effects of hysteresis on the parameters, and the least-squares fit is further constrained so that the inspiration and expiration curves must meet at the extreme minimum and maximum navigator values. Since respiration is cyclic, clearly the inspiration and expiration phases must meet at some point, so we believe that constraining the model in this way is reasonable. This technique is similar to that described by Manke et al6 (who used the model for MRI image acquisition) except that we use higher order polynomials to capture the non-linear relationships present in some parameters, and we model the inspiration and expiration phases separately in order to better capture the hysteretic effects present in cardiac respiratory motion.

2.2 Applying the motion model Respiratory phase information during the procedure is acquired by tracking the motion of the diaphragm in real-time X-ray images. These X-ray images are cardiac gated by synchronising X-ray image acquisition with the digital output of the electrocardiogram (ECG) signal from the patient. A time window after the initial R-wave is defined to be the same window used for MRI data acquisition (late diastole). Images not acquired within this time window are rejected. To track diaphragm motion, a rectangular region of interest is manually defined in a single X-ray image (see Figure 1). This image is used as a reference. The respiratory phase of subsequent X-ray images is determined by the 1-D translation (along the long axis of the rectangle) that minimises the mean sum of squared differences between the current X-ray image and the reference X-ray image within the region of interest. These values are scaled so that they have the same range as the MRI scanner navigator values by recording the end-expiration and end-inspiration values for a single cycle and comparing them with the global minimum and maximum of the navigator values. For sedated free-breathing patients these end-expiration and end-inspiration values are recorded whilst the patient takes a deep breath. For general anaesthetic patients the breathing is controlled by a ventilator (and is therefore regular) so this is not necessary.

Figure 1. A manually delimited region of interest for tracking diaphragm motion in live fluoroscopic X-ray images.

2.3 Validation We tested model formation on four volunteers and four patients. All volunteers gave informed consent. Patient B was an adult who underwent a catheter ablation procedure to treat atrial flutter and was sedated and free breathing throughout the procedure. Patients A, C and D were paediatric cases who underwent pulmonary vascular resistance studies whilst under general anaesthetic. Their breathing was controlled by a ventilator.

Proc. of SPIE Vol. 6918 691816-3

For each patient a single respiratory model was formed. For each volunteer five separate models were formed: three using data acquired during normal breathing, one using data acquired with an increased breathing rate and one using data acquired during deep breathing. The three normal breathing models were formed from different normal breathing datasets, and were used to assess the reproducibility of constructing the models. To do this, 100 different respiratory positions were defined to be evenly spaced between end-expiration and end-inspiration (50 in the inhale direction and 50 in the exhale direction). For each respiratory position, each of the three models was used to predict the position and shape of a heart surface segmented from the high resolution MRI image. This resulted in three surfaces for each respiratory position. From these three surfaces a mean surface was computed by averaging the coordinates of each surface point. The root mean square (RMS) error was computed for each surface point on each of the three surfaces away from the corresponding mean surface point. This process was repeated over the whole respiratory cycle to compute an overall RMS repeatability error. To assess the accuracy of the models, we used a leave-one-out test. For each dataset of low resolution images, ten sample images were selected that covered a range of respiratory positions. For each selected sample image, a model was constructed using every other image in the dataset, excluding the selected image. Next, anatomical landmarks were manually located in both the selected image and the reference image. Three anatomical landmarks were used that could be accurately and reproducibly located: the superior interventricular septum, and the superior and inferior boundaries of the left atrium. In tests, these landmarks could be repeatedly localised within the image with a standard deviation of 1.23mm. Using the navigator value and breathing direction for the selected image, the respiratory model was used to transform the anatomical landmarks from the reference image coordinate system to the selected image coordinate system. These transformed landmarks were compared with the manually localised landmarks in the selected image. For volunteers we also investigated whether a model constructed during one breathing state would make accurate enough motion predictions for data acquired during other breathing states. We used the same images and landmarks from the leave-one-out tests for this accuracy assessment. We tested the application of both the normal breathing and the deep breathing models in this way. For the patient datasets 2-D validation was performed by using the motion model to predict the respiratory motion of structures of the heart which contained catheters that are visible in X-ray images. For patient B X-ray images showing a coronary sinus catheter were used, and for patients C and D X-ray images showing a catheter inside the pulmonary artery were used. No X-ray data was available for patient A.

3. RESULTS 3.1 Constructing the motion model In the reproducibility test, all four volunteers had reproducibility errors of approximately 1mm (the figures were 1.17mm, 0.89mm, 0.68mm and 1.02mm). Figure 2 shows three sample plots of the affine registration parameters against navigator values for a normal breathing model for volunteer B. The complete model would require twelve such plots, but we show these three because they tend to be the dominant parameters in most models. The inspiration and expiration curves are shown, together with their coefficients of determination , R2 , a measure of the proportion of the variability in the datasets that is accounted for by the model. (A value of 1 for R2 indicates that the model perfectly accounts for the data.) In these plots a navigator value of zero represents end-expiration. Table 1 shows the RMS and maximum errors for the leave-one-out tests for the five different datasets for each of the four volunteers (three normal breathing models, one increased breathing rate model and one deep breathing model) and the four patient datasets. The model for patient B was formed at deep breathing, whereas patients A, C and D were ventilated. 19 out of the 20 volunteer models and all patient models have an RMS error below 5mm, which is within clinically acceptable bounds for most EP procedures. Patients A, C and D were paediatric cases so their errors were particularly low because of their smaller size. The errors without applying the model were typically 10-15mm for most subjects. Table 2 shows the results for applying a normal breathing model during other breathing states. For each volunteer one normal model was selected that had the highest range of navigator values. The errors for applying

Proc. of SPIE Vol. 6918 691816-4

8-i flanslatlon vs. D(sphrsgm Position, Noneal Breathing M4. Aids Rotation vs. Dtaphr.gm Position, Noneal Breathing

S-I Scaling vs. Diaphragm Position, Normal Breathing 1 03L

Expiration cycla data

expiration cycle data end-cycle data

1 03

—I

0

-2

0

•

Expiration cycle data End-cycle data Expiration carve Inspiration cycle data Inspiration carve

-1E

-10

th -E -E

0

Diaphragm Poaition

20

0995 -15

-10

-5

095

-20

Diaphragm Position

(a)

(b)

-15

-10

-5

0

Diaphragm Position

(c)

Figure 2. Plots of affine registration parameters against diaphragm position for volunteer B: (a) superio-inferior translation (R2 = 0.9629 for expiration, R2 = 0.957 for inspiration); (b) medio-lateral axis rotation; (R2 = 0.7712 for expiration, R2 = 0.8006 for inspiration); (c) superio-inferior scaling (R2 = 0.8592 for expiration, R2 = 0.8212 for inspiration). Note the clear hysteresis (i.e. different inspiration/expiration curves) for (a) and (b).

this model to the other normal breathing datasets are similar to those given in Table 1. However, higher errors are present when applying it to the increased and deep breathing datasets. Table 3 shows the figures for using the deep breathing model. Although the errors are slightly higher than those shown in Table 1, still 14 of the 16 datasets have RMS errors of less than 5mm. This suggests that, for non-standard breathing patterns, a model acquired during deep breathing can more accurately predict respiratory movement than one acquired during normal breathing. For this reason the model for the sedated patient (patient B) was formed during deep breathing.

3.2 Applying the motion model Figure 3 shows some sample X-ray images for patient B overlaid with a model of the coronary sinus which was segmented from a high resolution MRI scan. The model was registered to the same coordinate system as the X-ray images using the technique described by Rhode et al.1, 2 The technique described in Section 2.2 was used to track respiratory phase and based on this information the model predicted the position of the coronary sinus model. The cardiac-gated videos from which these images were taken can be seen in Videos 1 and 2. Observers estimated the registration errors by manual inspection on X-ray images similar to those shown in Figure 3. This was performed for patients B, C and D. For patient A no X-ray data was available. For patient B the estimated errors before and after motion correction were 14mm and 2mm respectively at the end-inspiration position. For patient B they were 8mm and 4mm. For patient D they were 9mm and 2mm.

4. DISCUSSION AND CONCLUSIONS We have presented a technique for updating MRI-derived roadmaps to correct for respiratory motion during image-guided cardiac catheterisation procedures. Constructing the motion model requires minimal manual intervention. Only a bounding box for the image registration needs to be manually specified - the rest of the model construction process is automatic and takes about 13 minutes per model on a Pentium 4 2.16GHz PC. The high resolution scan and segmentation are routinely performed for guidance purposes, so the only extra scanning requirement is the free-breathing low resolution scans, which take less than 2 minutes to acquire. The identification of the region of interest for tracking the diaphragm in the X-ray images is also performed manually. Although the technique can, in principle, be applied to any cardiac catheterisation, our main clinical application is EP procedures. The mean accuracy requirement for these procedures is around 5mm. Section 3.1 has shown that, for models constructed for specific breathing types, our technique can correct for respiratory motion of the heart to within this accuracy. Although we have demonstrated that respiratory motion can be corrected for using this technique, we have not considered the issue of cardiac cycle motion. Currently our model is only valid at late diastole. We will address this problem in future work.

Proc. of SPIE Vol. 6918 691816-5

Table 1. Accuracy of respiratory model construction assessed using a leave-one-out test. Statistics were gathered using manually localised anatomical landmarks from a representative sample of ten images for each dataset. Patients A, C and D were imaged whilst ventilated under general anaesthetic. All other subjects were conscious during scanning.

Subject Volunteer A Volunteer B Volunteer C Volunteer D Patient A Patient B Patient C Patient D

Normal 1 RMS Max. 4.83 9.43 4.81 6.47 3.0 5.37 3.62 6.98 1.41 3.33 1.95 4.0 1.22 2.49

Errors Normal 2 RMS Max. 4.44 8.67 4.17 7.29 3.09 5.26 4.31 9.82 -

for each dataset Normal 3 RMS Max. 4.17 7.04 4.67 6.65 3.49 5.27 3.02 6.59 -

(mm) Increased RMS Max. 4.92 6.72 4.7 6.83 4.55 6.94 3.72 6.4 -

Deep RMS Max. 4.45 6.73 4.28 6.79 4.0 7.48 5.62 11.76 4.18 6.68 -

Table 2. Accuracy assessment for using a normal breathing model to predict motion in the other four datasets. The normal breathing model with the largest range of navigator values was chosen for each volunteer - therefore, results are marked N/A for this model

Subject Volunteer Volunteer Volunteer Volunteer

A B C D

Normal 1 RMS Max. 4.61 8.36 4.25 7.26 N/A N/A 3.86 7.71

Errors Normal 2 RMS Max. N/A N/A 4.23 8.24 3.06 4.95 N/A N/A

for each dataset (mm) Normal 3 Increased RMS Max. RMS Max. 4.0 6.76 5.3 8.47 N/A N/A 5.83 10.51 3.25 5.49 4.15 6.39 3.08 6.46 3.26 7.14

Deep RMS Max. 4.99 8.01 6.57 12.45 3.54 7.36 12.92 32.57

Table 3. Accuracy assessment for using the deep breathing model to predict motion in the other four datasets.

Subject Volunteer Volunteer Volunteer Volunteer

A B C D

Normal 1 RMS Max. 4.47 7.43 6.31 8.76 4.11 7.2 3.58 5.71

Errors for each Normal 2 RMS Max. 4.34 7.81 4.81 9.03 3.63 6.91 3.52 7.56

dataset (mm) Normal 3 RMS Max. 4.4 8.45 5.61 8.64 3.93 6.97 2.84 5.38

Increased RMS Max. 4.74 7.93 4.97 8.12 4.76 6.97 3.02 6.59

In our experience of forming cardiac respiratory motion models we found that the dominant motion parameter is the superio-inferior translation, although smaller superio-inferior scalings, anterio-posterior translations, and medio-lateral axis rotations are also often observed. The nature and relative significance of these parameters is strongly subject-specific. This confirms the findings of previous researchers.6, 10 One of our aims in this work was to assess the effects of different types of breathing on the accuracy of the models. Our results suggest that a model acquired during normal breathing would not have sufficient accuracy when applied during increased and deep breathing states. However, the deep breathing model is more promising. Although not as accurate as a model acquired during the same type of breathing as the test situation, it was within clinical accuracy requirements in 14 out of 16 cases. One reason for this is the greater range of the deep breathing model, but the fact that normal breathing models perform quite poorly during increased breathing (which often have a smaller range) suggests that it is not the only factor. Based on our experience of constructing motion models formed during different breathing patterns, we believe that to achieve greater accuracy a better understanding of the effects of different types of breathing and of respiration in general will be required. This paper proposes a potential methodology for such a study, and in future work we plan to address this issue. To the authors’ knowledge, this work is the only time that an MRI-derived respiratory motion model has been

Proc. of SPIE Vol. 6918 691816-6

(a)

(b)

(c)

(d)

Figure 3. Validation on fluoroscopic X-ray images showing a catheter inside the coronary sinus for patient B overlaid with a surface of the coronary sinus derived from pre-procedure MRI. The end of the catheter is indicated with an arrow in (a). The domes of the diaphragm can be clearly seen. The images were taken at end-expiration without (a) and with (b) motion correction, and end-inspiration without (c) and with (d) motion correction. The improvement in registration after applying the motion model is clear, particularly at end-inspiration. Note that the catheter was positioned inside a tributary of the coronary sinus, which is why it seems to be misregistered towards the left end of the model. The two surface positions (with and without motion correction) are similar at end-expiration, which is to be expected since the high resolution MRI scan from which the surface was segmented was respiratory gated at end-expiration. The videos from which these images were taken can be seen in Videos 1 and 2.

demonstrated and validated on real X-ray images acquired during a clinical procedure. This therefore represents a significant step forward in respiratory motion modelling for image-guided procedures.

Acknowledgements This work was funded by EPSRC grant EP/D061471/1, DTI Technology Programme Grant 17352 and Philips Medical Systems. The Image Registration Toolkit was used under licence from Ixico Ltd. We are grateful to the members of the Interdisciplinary Medical Imaging Group for useful discussions and feedback on this work.

Proc. of SPIE Vol. 6918 691816-7

Video 1: Validation on fluoroscopic X-ray images showing a catheter inside the coronary sinus for patient B, cardiac gated, without motion correction. This is the full video from which the images shown in Figure 3(a) and (c) were taken. http://dx.doi.org/10.1117/12.769377.1

Video 2. Validation on fluoroscopic X-ray images showing a catheter inside the coronary sinus for patient B, cardiac gated, with motion correction. This is the full video from which the images shown in Figure 3(b) and (d) were taken. http://dx.doi.org/10.1117/12.769377.2

Proc. of SPIE Vol. 6918 691816-8

REFERENCES 1. K. S. Rhode, D. L. G. Hill, P. J. Edwards, J. Hipwell, D. Rueckert, G. Sanchez-Ortiz, S. Hegde, V. Rahunathan, and R. Razavi, “Registration and tracking to integrate X-ray and MR images in an XMR facility,” IEEE Transactions on Medical Imaging 22, pp. 1369–1378, Nov 2003. 2. K. S. Rhode, M. Sermesant, D. Brogan, S. Hegde, J. Hipwell, P. Lambiase, E. Rosenthal, C. Bucknall, S. A. Qureshi, J. S. Gill, R. Rezavi, and D. L. G. Hill, “A system for real-time XMR guided cardiovascular intervention,” IEEE Transactions on Medical Imaging 24, pp. 1428–1440, November 2005. 3. Y. Wang, S. J. Riederer, and R. L. Ehman, “Respiratory motion of the heart: Kinematics and the implications for the spatial resolution in coronary imaging,” Magnetic Resonance in Medicine 33, pp. 713–719, November 1995. 4. K. McLeish, D. L. G. Hill, D. Atkinson, J. M. Blackall, and R. Razavi, “A study of the motion and deformation of the heart due to respiration,” IEEE Transactions on Medical Imaging 21, pp. 1142–1150, September 2002. 5. K. Nehrke, P. Bornert, D. Manke, and J. C. Bock, “Free-breathing cardiac MR imaging: Study of implications of respiratory motion - initial results,” Radiology 220, pp. 810–815, 2001. 6. D. Manke, P. Rosch, K. Nehrke, P. Bornert, and O. Dossel, “Model evaluation and calibration for prospective respiratory motion correction in coronary MR angiography based on 3-D image registration,” IEEE Transactions on Medical Imaging 21, pp. 1132–1141, September 2002. 7. N. A. Ablitt, J. Gao, J. Keegan, L. Stegger, D. N. Firmin, and G. Z. Yang, “Predictive cardiac motion modelling and correction with partial least squares regression,” IEEE Transactions on Medical Imaging 23, pp. 1315–1324, October 2004. 8. G. Shechter, B. Shechter, J. R. Resar, and R. Beyar, “Prospective motion correction of X-ray images for coronary interventions,” IEEE Transactions on Medical Imaging 24, pp. 441–450, April 2005. 9. C. Studholme, D. L. G. Hill, and D. J. Hawkes, “An overlap invariant entropy measure of 3-D medical image alignment,” Pattern Recognition 32(1), pp. 71–86, 1999. 10. G. Shechter, C. Ozturk, J. R. Resar, and E. R. McVeigh, “Respiratory motion of the heart from free breathing coronary angiograms,” IEEE Transactions on Medical Imaging 23, pp. 1046–1056, August 2004.

Proc. of SPIE Vol. 6918 691816-9