^{1}, Wei Lu

^{1}, Daniel A. Low

^{1}, Joseph O. Deasy

^{1}, Andrew J. Hope

^{1}and Issam El Naqa

^{1,a)}

### Abstract

Four-dimensional computed tomography (4D-CT) imaging technology has been developed for radiation therapy to provide tumor and organ images at the different breathing phases. In this work, a procedure is proposed for estimating and modeling the respiratory motion field from acquired 4D-CT imaging data and predicting tissue motion at the different breathing phases. The 4D-CT image data consist of series of multislice CT volume segments acquired in ciné mode. A modified optical flow deformable image registration algorithm is used to compute the image motion from the CT segments to a common full volume 3D-CT reference. This reference volume is reconstructed using the acquired 4D-CT data at the end-of-exhalation phase. The segments are optimally aligned to the reference volume according to a proposed *a priori* alignment procedure. The registration is applied using a multigrid approach and a feature-preserving image downsampling maxfilter to achieve better computational speed and higher registration accuracy. The registration accuracy is about for the lung region according to our verification using manually selected landmarks and artificially deformed CT volumes. The estimated motion fields are fitted to two 5D (spatial rate) motion models: forward model and inverse model. The forward model predicts tissue movements and the inverse model predicts CT density changes as a function of tidal volume and airflow rate. A leave-one-out procedure is used to validate these motion models. The estimated modeling prediction errors are about for the forward model and for the inverse model.

This research is partially supported by a grant from the American Cancer Society No. IRG-58-010-50, by NIH No. R01 CA 96679, and NIH No. R01 CA116712. Part of this work was presented at the Laughlin Science Council Research Symposium, AAPM, 2008.

I. INTRODUCTION

II. MATERIALS AND METHODS

II.A. 4D-CT data acquisition

II.B. Reconstructing the reference 3D-CT volume

II.C. Motion estimation

II.C.1. Challenges and solutions for lungCTimage registration

II.C.2. The deformable image registration algorithm

II.C.3. Preprocessing

II.C.4. A priori alignment (APA)

II.C.5. Reference volume cropping

II.C.6. The multigrid approach and the multiple pass approach

II.C.7. Maxfilter for feature preserving downsampling

II.C.8. Other considerations

II.D. Registration accuracy validation

II.D.1. Validation using artificially deformed CT volume

II.D.2. Validation of the maxfilter for image downsampling

II.D.3. Validation using patient 4D-CT data

II.D.4. Validation using full volume 4D-CT images

II.E. Inverse motion modeling

II.E.1. The 5D inverse motion field prediction model

II.E.2. Evaluation of the 5D inverse motion prediction model

II.E.3. Evaluation of the discontinuity at the segment boundaries

II.F. Forward motion modeling

II.G. Implementation

III. RESULTS

IV. DISCUSSION

IV.A. Deformable registration accuracy

IV.B. Slice misalignments in the reference volumes

IV.C. Quality of the respiration data

IV.D. Motion computation efficiency

IV.E. Applications of the inverse motion model

IV.F. Relation and differences between the two 5D motion models

IV.G. Different 4D-CT acquisition protocols

V. CONCLUSION

### Key Topics

- Computed tomography
- 96.0
- Medical imaging
- 70.0
- Lungs
- 58.0
- Flow visualization
- 22.0
- Image registration
- 21.0

## Figures

Plot of measured bellow values vs. time for two couch positions. The small black dots show when CT scans are taken and the corresponding bellow values. There are 25 scans at each couch position. The durations of a couch position are indicated by the big dashed lines.

Plot of measured bellow values vs. time for two couch positions. The small black dots show when CT scans are taken and the corresponding bellow values. There are 25 scans at each couch position. The durations of a couch position are indicated by the big dashed lines.

Comparison of image downsampling uses the maxfilter and the Laplacian pyramid filter: (a) the original image, (b), (c), and (d) are images sequentially downsampled by 2, 4, and 8 using the Laplacian filter; (e), (f), and (g) are images sequentially downsampled by 2, 4, and 8 using the maxfilter.

Comparison of image downsampling uses the maxfilter and the Laplacian pyramid filter: (a) the original image, (b), (c), and (d) are images sequentially downsampled by 2, 4, and 8 using the Laplacian filter; (e), (f), and (g) are images sequentially downsampled by 2, 4, and 8 using the maxfilter.

The artificially deformed CT images: (a) the original image; (b) the image deformed with synthesized motion field, the dashed lines mark the 16-slice partitions, (c) the difference image with the motion vectors, (d) the difference image in the axial view.

The artificially deformed CT images: (a) the original image; (b) the image deformed with synthesized motion field, the dashed lines mark the 16-slice partitions, (c) the difference image with the motion vectors, (d) the difference image in the axial view.

Comparison of final registration results for using the maxfilter and the Laplacian pyramid filter for image downsampling in the multigrid approach. Dashed lines mark the areas where the most incorrect registration happens in this example: (a) the ground truth target slice, (b) the result by using the maxfilter, (c) the result by using the Laplacian pyramid filter.

Comparison of final registration results for using the maxfilter and the Laplacian pyramid filter for image downsampling in the multigrid approach. Dashed lines mark the areas where the most incorrect registration happens in this example: (a) the ground truth target slice, (b) the result by using the maxfilter, (c) the result by using the Laplacian pyramid filter.

Example of the *a priori* alignment (APA) procedure: (a) the reference volume section, (b) a CT segment, (c) the difference image that the CT segment is aligned with the reference volume according to the couch table position, (d) the reference volume section shifted by APA, (e) the difference image for the CT segment aligned to the reference volume by APA, (f) the final registration difference image, (g) the target slice in transverse view, (h) the registration result achieved without using APA, (i) the registration result achieved using APA. Regions with most apparent improved results by APA are circled by dashed lines.

Example of the *a priori* alignment (APA) procedure: (a) the reference volume section, (b) a CT segment, (c) the difference image that the CT segment is aligned with the reference volume according to the couch table position, (d) the reference volume section shifted by APA, (e) the difference image for the CT segment aligned to the reference volume by APA, (f) the final registration difference image, (g) the target slice in transverse view, (h) the registration result achieved without using APA, (i) the registration result achieved using APA. Regions with most apparent improved results by APA are circled by dashed lines.

Example of the inverse motion field fitting for a point selected in the left-inferior lung of a patient. All motion values are in voxels: (a) the tidal volume vs time for the selected point, where the numbered circles mark the time of the CT scan, (b) the SI motion fitting where the circles are the original motion values and the squares are the fitted values, (c) the LR motion fitting, (d) the AP motion fitting, (e) the AP motion vs the LR motion, (f) the SI motion vs the LR motion, (g) the SI motion vs the AP motion, (h) the motion fitting presented in 3D.

Example of the inverse motion field fitting for a point selected in the left-inferior lung of a patient. All motion values are in voxels: (a) the tidal volume vs time for the selected point, where the numbered circles mark the time of the CT scan, (b) the SI motion fitting where the circles are the original motion values and the squares are the fitted values, (c) the LR motion fitting, (d) the AP motion fitting, (e) the AP motion vs the LR motion, (f) the SI motion vs the LR motion, (g) the SI motion vs the AP motion, (h) the motion fitting presented in 3D.

Examples of the forward motion field fitting for the same point as used for Fig. 6. All motion values are in voxels: (a) SI motion fitting, (b) LR motion fitting, (c) AP motion fitting, (d) the motion fitting presented in 3D.

Examples of the forward motion field fitting for the same point as used for Fig. 6. All motion values are in voxels: (a) SI motion fitting, (b) LR motion fitting, (c) AP motion fitting, (d) the motion fitting presented in 3D.

Examples of the reference volume being deformed to generate 3D-CT volumes for different breathing phases. Columns 1, 2, and 3 are for the exhaling phases of tidal volumes equal to 30, 60, and 90% of the 90th percentile tidal volume. Row (a) is the 3D-CT volume reconstructed by using the amplitude sorting method. Row (b) is the 3D-CT volume generated by deforming the reference volume by the motion fields that are predicted by the inverse 5D motion model. Row (c) is the difference between row (b) and the reference volume. Row (d) is the difference between row (a) and row (b).

Examples of the reference volume being deformed to generate 3D-CT volumes for different breathing phases. Columns 1, 2, and 3 are for the exhaling phases of tidal volumes equal to 30, 60, and 90% of the 90th percentile tidal volume. Row (a) is the 3D-CT volume reconstructed by using the amplitude sorting method. Row (b) is the 3D-CT volume generated by deforming the reference volume by the motion fields that are predicted by the inverse 5D motion model. Row (c) is the difference between row (b) and the reference volume. Row (d) is the difference between row (a) and row (b).

Slice views of the estimated fitting parameters of the forward 5D motion model for patient 2. Column (1) is the coronal view of the parameter [Eq. (9)] vector field, units are in mm/L. Column (2) is the coronal view of the parameter , units are in mm/L/s. Column (3) is the view of parameter , units are in mm. Row (a) is the parameter vector field projection in the AP direction. Row (b) is the LR projection. Row (c) is the SI projection. Row (d) is the magnitude of the vector fields.

Slice views of the estimated fitting parameters of the forward 5D motion model for patient 2. Column (1) is the coronal view of the parameter [Eq. (9)] vector field, units are in mm/L. Column (2) is the coronal view of the parameter , units are in mm/L/s. Column (3) is the view of parameter , units are in mm. Row (a) is the parameter vector field projection in the AP direction. Row (b) is the LR projection. Row (c) is the SI projection. Row (d) is the magnitude of the vector fields.

## Tables

Preliminary comparison of four deformable image registration algorithms using the landmarks. In addition, we show results of Horn–Schunck optical flow algorithm without CT number truncation for comparison with the CT number truncation case.

Preliminary comparison of four deformable image registration algorithms using the landmarks. In addition, we show results of Horn–Schunck optical flow algorithm without CT number truncation for comparison with the CT number truncation case.

Registration error comparison between using the maxfilter and the Laplacian pyramid filter for image downsampling. Reported values are the mean and the standard deviation of the absolute magnitude of registration errors.

Registration error comparison between using the maxfilter and the Laplacian pyramid filter for image downsampling. Reported values are the mean and the standard deviation of the absolute magnitude of registration errors.

Registration error tested with the artificially deformed CT (Sect. ???) with and without using *a priori* alignment (APA) procedure. The reported registration error values are the mean and the standard deviation of the absolute magnitudes.

Registration error tested with the artificially deformed CT (Sect. ???) with and without using *a priori* alignment (APA) procedure. The reported registration error values are the mean and the standard deviation of the absolute magnitudes.

Validation of registration errors using landmarks. For patients 1 to 3, the landmarks were manually selected in the CT segments and the reference volume. The CT segments used in the validation were randomly selected from the middle to inferior lung and with higher corresponding tidal volumes so that image motions were the largest with respect to the reference volume.

Validation of registration errors using landmarks. For patients 1 to 3, the landmarks were manually selected in the CT segments and the reference volume. The CT segments used in the validation were randomly selected from the middle to inferior lung and with higher corresponding tidal volumes so that image motions were the largest with respect to the reference volume.

Number of landmark pairs (LPs) used to compute target modeling errors (TME), modeling error (ME), modeling prediction error (MPE), and boundary discontinuity (BD). Values enclosed in braces are the maximum error values.

Number of landmark pairs (LPs) used to compute target modeling errors (TME), modeling error (ME), modeling prediction error (MPE), and boundary discontinuity (BD). Values enclosed in braces are the maximum error values.

Average computation time of important tasks.

Average computation time of important tasks.

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