Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Bioengineering

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Summary

We analyzed joint kinematics from four-dimensional computed tomography data. The sequential 3D-3D registration method semiautomatically provides the kinematics of the moving bone with respect to the subject bone from four-dimensional computed tomography data.

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Oki, S., Kaneda, K., Yamada, Y., Yamada, M., Morishige, Y., Harato, K., Matsumura, N., Nagura, T., Jinzaki, M. Four-Dimensional CT Analysis Using Sequential 3D-3D Registration. J. Vis. Exp. (153), e59857, doi:10.3791/59857 (2019).

Abstract

Four-dimensional computed tomography (4DCT) provides a series of volume data and visualizes joint motions. However, numerical analysis of 4DCT data remains difficult because segmentation in all volumetric frames is time-consuming. We aimed to analyze joint kinematics using a sequential 3D-3D registration technique to provide the kinematics of the moving bone with respect to the fixed bone semiautomatically using 4DCT DICOM data and existing software. Surface data of the source bones are reconstructed from 3DCT. The trimmed surface data are respectively matched with surface data from the first frame in 4DCT. These trimmed surfaces are sequentially matched until the last frame. These processes provide positional information for target bones in all frames of the 4DCT. Once the coordinate systems of the target bones are decided, translation and rotation angles between any two bones can be calculated. This 4DCT analysis offers advantages in kinematic analyses of complex structures such as carpal or tarsal bones. However, fast or large-scale motions cannot be traced because of motion artifacts.

Introduction

Joint kinematics have been described using a number of methodologies, such as motion capture sensors, 2D-3D registration, and cadaveric studies. Each method has specific advantages and disadvantages. For example, motion capture sensors can measure fast, large-scale motions using infrared cameras with or without sensors on the subject1,2. However, these methods measure skin motion to infer joint kinematics, and therefore contain skin motion errors3.

Cadaveric studies have been used to evaluate ranges of motion, instability, and contact areas4,5,6. This approach can measure small changes in small joints using CT or optical sensors attached directly to bone using pins or screws. Cadaveric models can mainly evaluate passive motions, although multiple actuators have been used to apply external forces to tendons to simulate dynamic motion7. Active joint motion can be measured by 2D-3D registration techniques, matching 3DCT images to 2D fluoroscopy images. Although the accuracy of the registration process remains controversial, the reported accuracy is generally high enough for large joint kinematics8,9. However, this method cannot be applied to small bones or multiple bones in narrow spaces.

In contrast, 4DCT is a dynamic CT method that obtains a series of volumetric data. Active joint motions can be analyzed using this approach10. This technology provides precise 3D positional data of all substances inside the CT gantry. The 3D joint motions are clearly visualized in a viewer. However, describing joint kinematics from such a series of volume data is still difficult, because all the bones are moving and no landmarks can be traced during the active motions in vivo.

We developed a method for 4DCT analysis that provides the in vivo joint kinematics of the whole bones around the joint during active motions. The aim of this article is to present our method, the sequential 3D-3D registration technique for 4DCT analysis, and show representative results obtained using this method.

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Protocol

All methods described here have been approved by the Institutional Review Board of Keio University School of Medicine.

NOTE: Joint kinematics are measured by reconstructing the motion of a moving bone around a fixed bone. For knee joint kinematics, the femur is defined as the fixed bone and the tibia is defined as the moving bone.

1. CT imaging protocol

  1. Set up the CT machine. Acquire CT examinations with a 320-detector-row CT system to allow for multiple phases of 3D volume data with 160 mm craniocaudal coverage. For example, in the analysis of knee kinematics, the image acquisition consists of 51 volume scans with a rotation time of 0.275 s, and all images are reconstructed using half reconstruction, so that the temporal resolution is approximately 0.16 s.
  2. Use the following scanning parameters: peak tube voltage = 100 kVp; tube current = 40 mA; scan coverage = 160 mm; matrix size= 512 x 512 pixels; and reconstruction section thickness and section interval = 0.5 mm.
  3. Place the target joint of the subject inside the CT gantry in the starting position of the 4DCT exam (Figure 1).
  4. Before the CT exam, rehearse movements of the joint from the start position to the end position within the required examination time. Ask the subject to move the joint during the 10.275 s scan time and obtain a series of volume data. Store the sequential volume data in DICOM format.
  5. Perform static 3DCT of all the target bones and store the data in DICOM format.

2. Surface reconstruction

  1. Perform semiautomatic segmentation of 3DCT data (Figure 2A).
    1. Load CT DICOM data by selecting all DICOM files of the static 3DCT data.
    2. Open the label field by clicking Edit New Label Field and check which threshold CT attenuation value is appropriate to extract cortical bone from the source bone. Select materials with CT attenuation values above the threshold. For example, the bone cortex threshold for a young subject is set as 250. Check the label for bone cortex selection and manually modify the demarcation using an editing tool for consistency with the shape of the bone.
    3. Generate the surface data (triangle meshes) from the labeled bone cortex position data (point cloud in the software). Store the surface data by exporting data in Standard Triangulated Language (STL) format.
    4. Click Generate Surface|Apply on the label of the cortical bone. Click File|Export Data As|STL Binary Little Endian to save the surface data in STL format.
  2. Perform automatic segmentation of 4DCT volume data (Figure 2B).
    NOTE: Each frame of the DICOM data includes the distribution of the CT attenuation values in the CT gantry.
    1. Set the threshold of the bone cortex as in static CT, and extract geometric data showing CT attenuation values above the threshold from all 51 frames of the 4DCT data using the DICOM reading module in the programming software. Adjust the threshold according to the bone density of the source bone. For example, for the osteoporotic bone, set the threshold lower.
    2. Translate all positional data that have already been obtained in the previous step into a format that can be interpreted by image processing software (e.g., Avizo). In the image processing software, reconstruct all surface data of the point cloud with higher CT attenuation values than the threshold for all 4DCT frames using a batch processing script. The image processing software contains the function to read the script and export the surface data from the DICOM series data automatically. The batch script is shown in the Supplemental Coding File.

3. Image registration

NOTE: In this step, reconstruct the motions of the moving bone with respect to the fixed bone from the raw 4DCT DICOM data.

  1. Perform surface registration from static 3DCT to the first frame of the 4DCT.
    1. Trim the bones in a static 3DCT into partial segment data that are included in all frames of 4DCT for use with the iterative closest point (ICP) algorithm11 in the 3D mesh editing software using the Selecting Face function (Figure 3A) by referring 4DCT movie data. The surface data from 4DCT are only partial segments that are included in each volume imagebecause surface registration requires that one surface data point is included in another surface.
    2. Pick three landmarks in the fixed and moving bones that can be easily identified from the trimmed 3DCT surface and the surface data of the first frame of 4DCT in the 3D mesh editing software using the PickPoints function (Figure 3B).
    3. Match the partial fixed and moving bones roughly on the first frame of the 4DCT surface data (Figure 3C) according to the picked landmarks in 3.1.2. Next, perform surface registration using the ICP algorithm11 using the open source software (e.g., VTK).
      NOTE: This process provides homogeneous transformation matrices of the fixed and moving bones from the static 3DCT to the first frame of 4DCT (Figure 3D). These matrices are 4 x 4 matrices consisting of rotation and translation, as shown in Figure 4. The transformation matrix causing the reverse action can also be calculated.
  2. Perform sequential surface registration (Figure 5).
    1. Match the partial surfaces of the fixed and moving bone in the first 4DCT frame onto the surface data of the second frame. Next, match the partial surfaces of the ith frame onto the (i + 1)th frame of 4DCT sequentially. Repeat this process until the last frame of the 4DCT by programming with use of the ICP module in the open source software.
  3. Calculate transformation matrices from the static 3DCT to all frames in 4DCT according to the results of 3.1 and 3.2.
  4. Reconstruct moving bone motion with respect to the fixed bone (Figure 6).
    1. Reconstruct the kinematics of the moving bone with respect to the fixed bone from the matrices that represent the transformation from the static 3DCT to each 4DCT frame. Define the coordinate systems of the fixed and moving bones when the rotation parameters are measured (e.g., flexion angle or rotation angle calculated by the Euler/Cardan angle)12,13,14.

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Representative Results

We describe the motion of the tibia during knee extension. The knee joint was positioned in the CT gantry. A triangle pillow was used to support the femur at the starting position. The knee was extended to a straight position over the course of 10 s. Radiation exposure was measured. In addition to 4DCT, static 3DCT of the whole femur, tibia, and patella was performed. Surface data of the whole femur and tibia were reconstructed. The threshold for HU numbers of the bone cortex was set as 250 HU and the surface data of all 51 frames were reconstructed.

The femur and tibia were trimmed into partial surface data that were included in all 4DCT framesby visually checking 4DCT movie data, which is created in the preset 4DCT software. In the static 3DCT surfaces and the first frame of the 4DCT, the landmarks of each segment were plotted. On the femur, the medial and lateral epicondyles and intercondylar notch were identified. On the tibia, the medial and lateral ends of the joint surface and tibial tuberosity were also identified as corresponding landmarks. Partial surface data of the femur and tibia were roughly matched with the first frame of the 4DCT data according to these three landmarks. These surfaces were then completely matched using the ICP algorithm.

Partial segments of the femur and tibia of the first frame were matched with the whole surface in the second frame. Partial fragments in the ith frame were thus matched with the whole surface data of the (i + 1)th frame sequentially. In the ICP algorithm, the convergence criteria for mean distance between iterations was set as 0.01 mm.

The femur was defined as the fixed bone and the tibia as the moving bone. The 4 x 4 matrix that describes translation and rotation from the global coordinate system in the original CT DICOM data to the local coordinate system of the fixed bone is calculated. The coordinate system of the femur and tibia were defined in accordance with a previous report15. We calculated the motion of the tibia from the Euler/Cardan angles in 'zxy' order, meaning flexion, varus, and internal rotation, in that order14.

Our method depends on the accuracy of image registration from the partial segments onto the whole surface data. We validated the accuracy of partial surface registration by decreasing the length of the femur and tibia incrementally by 1% along the long axis from 20%-1%. Surface registration of partial segments to the whole bones was performed for the entire set of lengths of the femur and tibia, and errors for rotation and translation from the parameters calculated from the whole bones were evaluated.

Results showed that the varus angle of the tibia gradually decreased as the tibia was extended (Figure 7). Tibial external rotation increased at the end of the extension. This external rotation corresponds with the "screw home movement" of the knee in previous reports16,17.

The effective dose estimate for this CT protocol was 0.075 mSv, as determined by the dose length product measurement (187.5 mGy∙cm) and appropriate normalized coefficients (0.0004) as reported in the literature18.

In validation, graphs of the error for translation and rotation show that the error was tolerable for femur lengths longer than 9% of the whole length and tibia lengths longer than 7% of the whole length (Figure 8). At 10% of the length of the femur and 8% of the length of the tibia, errors were 0.02° for varus/valgus rotation, 0.02° for internal/external rotation, 0.01° for extension/flexion rotation, 0.10 mm for anterior/posterior translation, 0.14 mm for proximal/distal translation, and 0.11 mm lateral/medial translation. These translation errors are considered negligible because CT slice thickness is 0.5 mm and exceeds the error size. Internal and external rotation errors tended to fluctuate. This was thought to be caused by local minimum fit for iterative rotation along the long axis due to the symmetrical shape of the tibial joint surface.

As additional data, patellar kinematics were also calculated using the same method. We demonstrated the lateral tilt of the patella by tracking the norm of the patellar surface corresponding to the knee flexion angle as calculated from analysis of the tibia (Supplemental Figure 1).

Figure 1
Figure 1: Acquisition of 4DCT. The 4DCT examination for knee extension. The subject is instructed to lie down and position the knee in the CT gantry. At the starting position, the knee is set in the flexed position and extended within 10 s after the examination starts. In this figure, the subject extends the knee from 60° of flexion to maximum extension in 10 s. Please click here to view a larger version of this figure.

Figure 2
Figure 2: Reconstruction of surface data. (A) Surface data of the whole femur (fixed bone) and whole tibia (moving bone) are reconstructed. (B) Using DICOM data from 4DCT, the positional data of the bone cortex showing CT attenuation values above the threshold are extracted in each frame. These positional data are input into the software and the surface data of all frames are reconstructed. The femur also moves (green arrow) with respect to the tibia (blue arrow). Please click here to view a larger version of this figure.

Figure 3
Figure 3: Surface registration. (A) Surface data of the fixed and moving bones from 3DCT are trimmed into partial segments that are included in all 4DCT frames because the surface data from 4DCT are only partial segments, which are included in the CT gantry. (B) Three landmarks are picked in the partial segments of the static 3DCT and the first frame of the 4DCT. (C) The partial segments are matched with the first frame according to the landmarks. (D) The iterative closest point (ICP) algorithm is applied to match surface data. Please click here to view a larger version of this figure.

Figure 4
Figure 4: Transformation matrix is calculated from surface registration. (A) Translation and rotation of surface data can be described in a 4 x 4 matrix (homogeneous transformation matrix). Mref represents the matrix of the fixed bone and Mobj represents the matrix of the moving bone. The lower right value represents the starting position and the upper left value represents the target position. For example, 1Mrefs translates the fixed bone in the static 3DCT position to the fixed bone in the first frame of 4DCT. (B) The rotation matrix is a 4 x 4 matrix. R3 is a 3 x 3 matrix that defines rotation and d is a 1 x 3 matrix that defines translation. tR3 is a transverse matrix of R3. (C) The upper right "inv" means the reverse action matrix. Please click here to view a larger version of this figure.

Figure 5
Figure 5: Steps of sequential surface registration of all frames. The difference between ith and (i + 1)th frames is very small. Partial segments of the ith frame can be matched with whole surface data of the (i + 1)th frame only by the ICP algorithm. Surface registration is repeated sequentially until the last frame. The transformation matrix from the static 3DCT to each frame (iMs) is calculated. Please click here to view a larger version of this figure.

Figure 6
Figure 6: Rotation angles are calculated using the defined coordinate systems of the fixed and moving bones. (A) The coordinate system of the fixed bone is defined15. The rotation matrices from static 3DCT to the local coordinate system of the fixed bone (LMrefS) are calculated. (B) The coordinate system of the moving bone is defined and drawn over the fixed bone in its local coordinate system15. Rotation matrices from the local moving bone to the local coordinate system of the fixed bone are calculated (Mi). From these matrices, angles of the moving bone with respect to the fixed bone are calculated using the Euler/Cardan angle. Please click here to view a larger version of this figure.

Figure 7
Figure 7: Representative results show kinematics of the tibia during knee extension. (A) Extension of the tibia. From the starting frame, the tibia is extended almost constantly and extension speed increases around the end frame. (B) Tibial internal rotation. The transverse axis is the tibial extension angle. The tibia rotates internally to 10° of flexion and rotates externally until the end frame. (C) The valgus angles increase constantly during all frames of knee extension. Please click here to view a larger version of this figure.

Figure 8
Figure 8: Validation of surface registration of the partial segment onto the whole bone. The lengths of the femur and tibia are decreased incrementally by 1% along the long axis from 20%-1%. Surface registration of partial segments to whole bones are performed for all sets of lengths of the femur and tibia, and errors for rotation and translation from the parameters calculated from the whole bones are evaluated. Perturbation analysis is shown in Supplemental Figure 2. Please click here to view a larger version of this figure.

Supplemental Figure 1
Supplemental Figure 1: Patellar kinematics during knee extension. Patellar kinematics are also calculated using the same method. (A) A surface was fit on the surface data of the patella. The norm of the surface pointing anteriorly is calculated. The lateral tilt is defined as the lateral tilting angle of the norm in the coordinate system of the femur. (B) The patellar lateral tilt during knee extension is plotted corresponding to knee extension as calculated from tibial kinematics. Please click here to view a larger version of this figure.

Supplemental Figure 2
Supplemental Figure 2: Perturbation analysis. Please click here to view a larger version of this figure.

Supplemental Coding File. Please click here to download this file.

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Discussion

Our method allows visualization and quantification of the motions of whole bones and provides numerical positional data of the moving bone with respect to the fixed bone from 4DCT data. Many tools have been suggested for measuring joint kinematics. Motion skin markers can analyze total body motions over a long time. However, this method contains skin motion errors3. Joint kinematics should be estimated from the motion of adjacent bones. The 2D-3D registration method uses fluoroscopy and infers 3D kinematics from sequential 2D images. Translational errors are still present, although the analysis software has evolved to account for this. Many cadaveric studies have measured joint kinematics by taking CT images in different cadaver positions19. However, these represent passive motions from sequential static 3D images, and thus differ qualitatively from active motions.

There are several critical steps in this protocol. The surface data from 3DCT should be created precisely because this quality affects the accuracy of the initial surface registration to the first frame of 4DCT. Around the joint area, the threshold for the bone cortex may be different from the bone shaft. Threshold adjustment will be needed when the border of the bone cortex is unclear. Once the surface registration of all frames is finished, reconstructed motion should be checked. If surface registration for one frame fails, automated surface registration can be restarted from the next frame by picking the landmarks in the next frame and repeating the protocol.

The 4DCT method provides sequential volume data with accuracy almost as high as static 3DCT because CT DICOM data contain absolute coordinate values of all tissues in the CT gantry. Several studies have used 4DCT for investigations of joint kinematics20,21. However, in most, the observers picked landmarks from several frames and calculated the parameters (e.g., angles, translation). These data analysis processes contain human error that leads to measurement error. Our method of surface registration provides high accuracy image matching. Once plotted, the landmarks for the parameters can be traced according to the shape of the surface in each frame. Theoretically, manual surface segmentation for all 4DCT frames provides the most accurate data, but this process is far too time intensive. Recently, 4DCT has been used for motion analysis for wrist joints because the carpal bones are small and overlapped structures22. There have been several reports about automated bone tracing23,24. Goto et al. analyzed finger motions using normalized correlation coefficients that detect the similarity between two images25. We used surface registration because the position of the bone cortex surface is the most important landmark to describe joint kinematics.

We used an iterative closest point algorithm to trace the motion of the surface data in all frames. An iterative closest point algorithm matches two groups of point clouds or surface data to minimize surface-to-surface distance11 but has several drawbacks. This algorithm is generally used to match two close surfaces. Therefore, when the two surfaces are located distant to each other, registration would occur in the 'local minimum' position, not the true matched position26. We overcome this drawback by taking three landmarks in each bone at first. The two surfaces are roughly matched according to these three landmarks. From these two positions, the ICP serves as the closest position. The frame rate of 4DCT is very short (0.2 s), so the surface position in the current frame is close to the surface position in the next frame. In cases of slow joint motion, the rough match step will not be needed for further frame-to-frame sequential surface registration. In addition, the relationship between the entirety of the two bones is reproduced by matching the entire static 3DCT surface data onto the partial 4DCT frame surface data. Generally, the coordinate system of the bone is defined from its entirety12,27. Reconstruction of the whole bone motion thus contributes to the description of joint angles. This accuracy largely depends on surface registration of the partial surface onto the whole surface data. In the representative data, we demonstrated that the availability of over 10% of the segments provides sufficient accuracy for the knee joint.

CT data provide all positional data included within the CT gantry area. The quality of the data depends solely on the quality of the CT machine. This method can thus be applied to small bones or multiple bones such as the carpal bones, which are difficult to trace by 2D-3D registration.

Several limitations must be mentioned. First, ICP depends on the shape of the partial segment. ICP is more accurate when the surface has geometric features such as bone spurs or cortical edges. On the other hand, when the surface shape is symmetrical, such as the radial head or sesamoid, ICP will provide a wrong rotation of the original surface. In addition, ICP also depends on the quality of the surface data. In case of osteoporotic bones, surface reconstruction largely depends on manual segmentation. That may lead to interobserver errors. Recently, computerized tissue segmentation on CT slices has been developed. However, human manual segmentation is still considered more reliable when identifying specific tissues28,29. Although the quality of the CT image cannot be changed, other limitations can be overcome by manual surface segmentation and registration. Second, when the joint motion is too fast, this method cannot trace the bone motions, because the CT images become blurry30. Frame-to-frame surface registration then fails because the two surfaces are too distant. Tolerable velocity depends on the target joint, because the joint morphology affects the success rate of surface registration. Studies of velocity tolerance for each joint will be needed in the future. In addition, joint motion should be performed inside the CT gantry. Therefore, for analysis of loading kinematics, optic sensors or 2D-2D registration are best.

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Disclosures

The authors have no competing financial interests.

Acknowledgments

This study was approved by the Institutional Review Board of our institution (approval number: 20150128).

Materials

Name Company Catalog Number Comments
4DCT scanner Canon medical systems (Tochigi, Japan) N/A 4DCT scan, Static 3DCT scan
AVIZO(9.3.0)* Thermo Fisher Scientific (OR, USA) Image processing software.
Surface reconstruction from CT DICOM data and point cloud data.
* Ryan, T. M. & Walker, A. Trabecular bone structure in the humeral and femoral heads of anthropoid primates. Anat Rec (Hoboken). 293 (4), 719-729, doi:10.1002/ar.21139, (2010).
Meshlab** ISTI (Pisa, Italy) N/A Surface trimming and landmark picking
** MeshLab: an Open-Source Mesh Processing Tool. Sixth Eurographics Italian Chapter Conference, page 129-136, 2008.
P. Cignoni, M. Callieri, M. Corsini, M. Dellepiane, F. Ganovelli, G. Ranzuglia
VTK(6.3.0)*** Kitware (New York, USA) N/A Iterative Closest Points algorithm. Used in python language programming.
*** https://vtk.org
Python(3.6.1) Python Software Foundation N/A DICOM file processing to extract the point cloud from the bone cortex ('dicom.py' module).
Calculation of the rotation matrices. (Numpy module)
Sequential image regestration using ICP algorithm

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References

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