|Year : 2015 | Volume
| Issue : 1 | Page : 16-20
Extracting Breathing Signal Using Fourier Transform from Cine Magnetic Resonance Imaging
Jing Cai1, Yilin Liu2, Fangfang Yin1
1 Department of Radiation Oncology, Duke University Medical Center; Medical Physics Graduate Program, Duke University, Durham, NC, USA
2 Medical Physics Graduate Program, Duke University, Durham, NC, USA
|Date of Submission||14-Jan-2015|
|Date of Acceptance||05-Feb-2015|
|Date of Web Publication||16-Feb-2015|
Department of Radiation Oncology, Duke University Medical Center, Box 3295, Durham, NC 27710
Source of Support: This work was partly supported by a National Institute of Health grant (1R21CA165384) and funding from the Golfers Against Cancer foundation,, Conflict of Interest: None
Aim: The objective of this study is to investigate the feasibility of extracting breathing signal from the cine magnetic resonance images (MRI) using Fourier transform (FT) and its application in four-dimensional-MRI.
Methods: A total of 10 subjects were imaged continuously during free breathing using a true fast imaging with steady-state precession MR sequence. Breathing signal of each subject was determined by two means: (1) by tracking the displacement of a region of interest (ROI) (ROI-displacement); and (2) by tracking the phase change of pixel (0, 1) in the FT of cine MRI (FT-phase). Respiratory phases were calculated from the breathing signal and compared between the two methods. To test the application of FT-phase method in four-dimensional-MRI, an in-house built MR-compatible motion phantom was imaged using multi-slice cine MRI. Four-dimensional-MRI were retrospectively reconstructed using the breathing signal determined using the FT-phase method.
Results: The mean difference in the respiratory phase between the two methods is −3.13 ± 4.85%, and the mean correlation coefficient is 0.97 ± 0.02. In the phantom study, four-dimensional-MRI clearly revealed sinusoidal motions of the object with minimal artifacts.
Conclusion: Our preliminary results demonstrated that breathing signal can be extracted using FT-phase method with highly accurate respiratory phase information, and can be used for four-dimensional-MRI reconstruction.
Keywords: Four-dimensional-MRI, Fourier transform, motion management, respiratory motion
|How to cite this article:|
Cai J, Liu Y, Yin F. Extracting Breathing Signal Using Fourier Transform from Cine Magnetic Resonance Imaging. Cancer Transl Med 2015;1:16-20
|How to cite this URL:|
Cai J, Liu Y, Yin F. Extracting Breathing Signal Using Fourier Transform from Cine Magnetic Resonance Imaging. Cancer Transl Med [serial online] 2015 [cited 2017 Sep 24];1:16-20. Available from: http://www.cancertm.com/text.asp?2015/1/1/16/151476
| Introduction|| |
Organ respiratory motion is a source of potential failure in treating mobile tumors by radiation therapy (RT). Since tumors and organs in the thorax and abdomen move during breathing, precise delivery of radiation dose to the target is highly challenging. Inadequate coverage of tumor in motion can result in insufficient therapeutic dose to the tumor while excessive coverage delivers unnecessary radiation to surrounding healthy tissues. In conventional RT, large safety treatment margins up to 2 cm are often applied to account for tumor motion. However, this greatly limits the dose to the tumor for keeping normal tissue complication under an acceptable limit, achieving a low 3-year overall survival rate (between 10% and 30%). ,, Tumor motion management is especially crucial in modern RT such as stereotactic-body RT, which requires highly conformal radiation distribution around the target and sharp radiation fall-off outside of the target. ,,
Motion management is involved in each step of RT, including imaging, treatment planning, and treatment verification. Existing methodologies to manage respiratory motion in RT include motion compensation using large safety margins, breathe-hold (voluntarily or forced), respiratory gating, and real-time tumor tracking. Real-time magnetic resonance images (MRI) cine images of the tumor demonstrate tumor and organs' motion. However, it shows the real-time motion on one image slice only, not including the three-dimensional shape and motion of the tumor and organs. Three-dimensional motion is important for RT treatment planning, especially for determining individual tumor safety margins. Detailed descriptions of the above methods and instructions on their clinical practices can be found in the literature. ,, A vital factor in any of the motion management methodologies is the patients' breathing signal. For instance, it is widely used to assess patient-specific breathing motion to determine individual tumor safety margins by triggering or gating breath-hold and free breathing MRI acquisition. ,,, A variety of methods have been used to acquire patients' breathing signal, which can generally be categorized into three types: external surrogates, internal markers, and image-based features. Examples of external surrogates are reflective markers as those used in real-time position management (RPM) system (Varian Medical Systems, Inc., Palo Alto, CA) and the strain-gauged Anzai belt (Anzai Medical Systems, Tokyo, Japan). Advantages of the external surrogates are the robustness in their clinical implementation; disadvantages are the increased equipment cost and an unclear correlation with internal tumor motion. Internal markers often refer to gold markers implanted surgically, which is an invasive procedure, and medical risks including pneumothorax which may be associated with seed implantation. ,
Recently, a number of studies have demonstrated the feasibility of extracting breathing signal from image features, ,,, such as lung air content, lung air density, body area, deformable image registration, and normalized cross correlation. A universal advantage of the image-based surrogates is the elimination of breathing monitoring device and invasive procedure. Using image-based surrogates for four-dimensional imaging may significantly simplify the simulation process, reduce cost, and improve the efficiency of scanner usage.
This study investigated a new technique for extracting breathing signal based on Fourier transform (FT) theory and its application in four-dimensional-MRI. Compared with four-dimensional-computed tomography (CT), the current clinical standard of four-dimensional respiratory imaging, four-dimensional-MRI provides improved soft-tissue contrast and avoids radiation hazards. ,,, It allows for more accurate determination of target volumes for mobile tumor in the abdomen, such as liver cancer and pancreatic cancer, holding great promises in improving the outcome of radiotherapy of these cancers. In current four-dimensional-MRI developments, the search for a reliable respiratory surrogate remains a challenging task. It is, therefore, the aim of this study to investigate a novel FT-based method for breathing signal extraction and its application in four-dimensional-MRI. The rationale for the FT-based method is from the translation property of FT, which dictates that geometric shift in the space-domain corresponds to a phase shift in Fourier space.  In this study, we presented preliminary results of using the FT-phase method in extracting breathing signal from cine MRI, and the feasibility of using the FT-phase method for four-dimensional-MRI.
| Methods|| |
Extracting breathing signal using Fourier transform-phase method
[Figure 1]a illustrates the workflow to extract breathing signal using the FT-phase method. Firstly, two-dimensional FT was performed on each frame of the images:
|Figure 1: Workflows of extracting breathing signal from cine magnetic resonance images using (a) the Fourier transform-phase method and (b) the region of interest-displacement method|
Click here to view
Any displacement in the images, such as respiratory motion, will change the values in its FT. Supposing the movement on a two-dimensional plan can be represented by "a0" in x direction (corresponding to anterior-posterior direction in sagittal MR cine and medial-lateral direction in coronal MR cine) and "b" in y direction (superior-inferior [SI] direction), the relationship between displacements in Cartesian domain and phase shifts in frequency domain can be derived as below:
Secondly, a low frequency pixel (u = 0, v = 1) in the frequency domain was selected and its corresponding phase angle was recorded as a respiratory surrogate. Pixel (0, 1) is chosen because it correlates to motion in the SI direction, which is the main motion direction of respiration. The relationship can be further derived for pixel (0, 1) as:
During breathing, a will change with time, that is, a = a (t). Breathing signal s (t) can be expressed as:
That is, a (t) can be derived from phase angle signal acquired in the frequency domain at each image frame as a function of time. It should be noted that the signal a (t) needs to be "unwrapped" to remove discontinuities in the phase between consecutive data points by adding multiples of ± 2π. Finally, a low-pass filter was applied to measured breathing signal a (t) to remove the high frequency component from cardiac motion and breathing signal. All image processing and data analysis was performed with an in-house developed Matlab program (The Mathworks, Inc., Natick, MA, USA). The FT-method can be applied to extract respiratory motion from MRI of multiple moving organs. Because lung is the most related organ to respiratory motion, we tested the FT-method on lung MRI as a preliminary study. The extracted signal can be used to reconstruct four-dimensional-MRI for other organs demonstrating how these organs' motion is affected by respiratory motion.
Comparison between region of interest-displacement and Fourier transform-phase methods
A total of 10 subjects (4 males and 6 females, mean age 67.2 years) were included in this study. The study was conducted under institutional review board approved protocols. All subjects were instructed to breath normally during scanning. MR scans were performed on a 1.5-Tesla whole-body clinical MRI scanner (Avanto, Siemens Medical Solutions, Erlangen, Germany), using a four-element phased-array body coil and a spinal coil. A true fast imaging with steady-state precession sequence was used to acquire cine MRI of the lungs during breathing. All images were acquired in a single coronal (n = 5) or sagittal (n = 5) plane. A mid-plane for the healthy subjects or the plane across the tumor center for the patients, was selected for a continuous 300 s MRI scan. The imaging parameters (repetition time (TR)/echo time (TE), 3.1/0.93 ms; field of view (FOV), 300 mm × 206 mm; flip angle (FA), 52°; slice thickness, 7 mm; matrix, 128 × 128; phase sharing, 120) were chosen to generate a fast acquisition (5-10 frames/s) while maintaining adequate spatial resolution.
For each subject, the breathing signal was determined using two methods: (1) By tracking the displacement of a region of interest (ROI) such as tumor or pulmonary vessel, as illustrated in [Figure 1]b.  Firstly, a rectangular template encompassing the ROI was manually selected in the first frame of the cine MRI. Automatic ROI displacement tracking was achieved by searching for the maximal cross-correlative region to the template in the following frames. Breathing signal was calculated as the change of the coordinates of the ROI centroid. ROI tracking method is widely used in four-dimensional imaging publications as a standard respiratory motion tracking method.  It is considered as the reference in this study; and (2) by tracking the change of phase angle at a selected low frequency pixel (0, 1) in the Fourier space of the images. The two methods were labeled as ROI-displacement and FT-phase throughout the study, respectively. The breathing signal was then processed to detect the respiratory peaks, followed by calculation of respiratory phases at each image frame. Since the ROI-displacement method is a direct measurement of internal respiratory motion, it was used as the reference to evaluate the FT-phase method. The validation and applications of the ROI-displacement method have been detailed in our previous applications. , Agreement between the two methods were evaluated using Pearson correlation coefficients (R), mean difference in the respiratory phase (D), and mean difference in absolute respiratory phase (DA ).
Feasibility of four-dimensional-magnetic resonance images using breathing signal extracted using the Fourier transform-phase method
We tested the feasibility of four-dimensional-MRI using breathing signal determined from the FT-phase method on an in-house built MR-compatible motion phantom. , The sketch of the phantom apparatus and the experimental setup is shown in [Figure 2]. The phantom consists of a two-stage (a horizontal stage and a vertical stage) motion platform (BrainLAB, Inc., Feldkirchen, Germany), a cylindrical imaging object placed on the horizontal motion stage, and a 1.0 cm thick bolus piece on a plastic flat board that is propped against the vertical motion stage. During the experiment, the two motion stages were to set to move synchronously in a sinusoid motion pattern (period: 5 s). As a result, the imaging object moved along with the horizontal stage in the SI direction to simulate tumor motion; the bolus piece slided up and down against the vertical stage to simulate body surface movement. The RPM box with two reflective markers was placed on the vertical stage to obtain motion signal. MRI of the phantom was acquired on a 1.5T GE MR scanner using a fast imaging employed steady-state acquisition with the following parameters (TR/TE, 3.7 ms/1.21 ms; matrix, 256 × 166; FOV, 350 mm × 300 mm; FA, 52°; slice thickness, 5 mm). Multiple slice images of the phantom were acquired in the sagittal planes with each slice imaged for 6 s.
|Figure 2: (a) Sketch of design of the in-house built motion phantom. Items within the dashed line were placed in MR scanner during the experiment. (b) The actual motion phantom consists of a cylindrical imaging object made from gel, a MR-compatible motion stage, and a 5 mm bolus pieces on a plastic board. MR: Magnetic resonance|
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Breathing signal was determined using the FT-phase method as described above. Respiratory phases were calculated for each data point (i.e. each image frame) of the breathing signal in a 3-step process:  (1) Detecting all respiratory peaks of the breathing signal; (2) Assigning respiratory phase of 50% to the peaks; (3) Calculating the respiratory phases at other data points via linear interpolation. The range of respiratory phase value is from 0% to 100%. Finally, four-dimensional-MRI were retrospectively sorted according to the respiratory phase. The sorting algorithm has been extensively described in the literature, ,, and will only be briefed here. In short, the breathing cycle is divided into 10 respiratory phases (0%, 10%, 20%,… 90%). MRI with the same respiratory phase but at different slice, positions were binned together to create a three-dimensional volumetric MRI corresponding to that respiratory phase. This sorting and binning process was repeated for all 10 respiratory phases. In case a phase was missing, the nearest adjacent phase (and the corresponding MRI) was used instead for four-dimensional-MRI reconstruction. Motion trajectories of the imaging objective determined from four-dimensional-MRI were compared against the input sinusoid trajectory.
| Results|| |
[Figure 3] shows the comparisons of breathing signal and respiratory phases between the ROI-displacement and FT-phase methods in an example case. It can be seen that the amplitudes of the breathing signal was different between the two methods, which is expected since the two methods measure two different quantities: the ROI-displacement method measures the actual movements of the tracked ROI, while the FT-phase method measures the phase angle change of a low frequency pixel (0,1) in the k-space of the images. Despite that, the respiratory phases of the breathing signal were largely consistent between the two methods (R = 0.97, D = −0.10%, DA = 2.36%), even with apparent breathing variations of the subject. [Table 1] summarizes the measurements for all subjects. Overall, breathing signal determined using the FT-phase method matched well with those determined using the ROI-displacement method. On average, the mean (±SD) R, D, and DA were 0.97 (±0.02), −3.13% (±4.85%), and 6.14% (±2.61%), respectively.
|Figure 3: (a) A representative sagittal magnetic resonance image of a healthy volunteer. The red circle indicates the tracked ROI (a pulmonary vessel). (b) Comparison of breathing signal and (c) respiratory phases determined from the ROI-displacement method and the Fourier transform-phase method. ROI: Region of interest|
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In the phantom study, motion signals determined using the FT-phase method revealed the same periodic motion pattern as the input signal as shown in [Figure 4]. The top row showed the breathing signal extracted using FT-phase method; the middle row reveals the peaks (labeled with blue circles) and valleys (labeled with red circles) detected; the bottom row showed the phase calculated from breathing signal. Sinusoidal motions of the object were clearly seen in all three planes of the reconstructed four-dimensional-MRI [Figure 5], with only minimal image artifacts, such as discontinuity between consecutive slices, stripes and inhomogeneous signal intensity in the coronal and sagittal image. The artifacts are mainly caused by MRI acquisition and retrospective sorting. These related to retrospective sorting are caused by errors in respiratory phase calculation and by breathing irregularities. However, the overall image quality was barely influenced by the image artifacts. Motion trajectories of the object measured from the four-dimensional-MRI matched to the input sinusoid curve, with a mean difference in motion amplitude of − 0.5 ± 0.6 mm.
|Figure 4: Determination of the motion signals for the phantom study. From top to bottom: raw FT signal, normalized FT signal, and respiratory phases. The top row showed the breathing signal extracted using FT-phase method; the middle row reveals the peaks (labeled with blue circles) and valleys (labeled with red circles) detected; the bottom row showed the phase calculated from breathing signal. FT: Fourier transform|
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|Figure 5: Reconstructed 10-phase (0-90%) four-dimensional-magnetic resonance images of the cylindrical imaging object of the phantom in the (a) axial, (b) coronal, and (c) sagittal planes|
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| Discussion|| |
In this study, we have demonstrated the feasibility of extracting breathing signal from cine MRI using a novel FT-phase method. We have also tested the use of this method for four-dimensional-MRI reconstruction on a motion phantom. It was found that the breathing signal derived using the FT-phase method was highly comparable to those derived using the ROI-displacement method, indicating that the FT-phase method is potentially a simple yet accurate image-based respiratory surrogate. Since ROI-tracked signals represent the true internal lung motion, our findings also imply that the FT-phase method may be superior to external respiratory surrogates in the correlation with internal tumor motion. It should be noted, however, that the FT-phase method provides only accurate information about respiratory phase, but not respiratory amplitude. The amplitude of the FT-phase derived breathing signal reflects only the relative change of phase angle of a low frequency pixel (0,1) in the Fourier domain; it does not represent a direct measurement of respiratory motion of any organ or structure. In applications that rely on signals of actual organ motion, such as breath-hold and amplitude-gated image and treatment, the role of FT-phase method has yet to be determined.
The FT-phase method extracts breathing signal from the entire image, that is, the motion of every pixel of the image contributes to the overall signal. Image processing is thus critical in order to suppress noise and enhance only the respiratory signal. Furthermore, the FT-phase method is ideally used on images that present dominated respiratory motion, such as sagittal or coronal cine MRI. Other images, which are potentially suitable for the FT-phase method, include cone-beam CT projections, kV fluoroscopy, surface imaging, cine mega-voltage, etc., Considering the significant difference between these imaging modalities, thorough validation on the robustness of the FT-phase method needs to be carried out separately for each modality.
The feasibility of four-dimensional-MRI reconstruction using the FT-phase as a respiratory surrogate has been demonstrated with the motion phantom. Patient data would allow for stronger validation of the technique, which is currently under investigation at our institution. In addition, accuracy and robustness of the FT-phase method require further assessment in a larger number of subjects.
In conclusion, our preliminary results demonstrated that breathing signal can be extracted from image FT-phase with highly accurate respiratory phase information, and can be used as respiratory surrogate for retrospective reconstruction of four-dimensional-MRI.
| Acknowledgments|| |
This work was partly supported by a National Institute of Health grant (1R21CA165384) and funding from the Golfers Against Cancer foundation.
| References|| |
Armstrong JG, Minsky BD. Radiation therapy for medically inoperable stage I and II non-small cell lung cancer. Cancer Treat Rev
1989; 16(4): 247 -0 55.
Baumann P, Nyman J, Hoyer M, Wennberg B, Gagliardi G, Lax I, Drugge N, Ekberg L, Friesland S, Johansson KA, Lund JA, Morhed E, Nilsson K, Levin N, Paludan M, Sederholm C, Traberg A, Wittgren L, Lewensohn R. Outcome in a prospective phase II trial of medically inoperable stage I non-small-cell lung cancer patients treated with stereotactic body radiotherapy. J Clin Oncol
2009; 27(20): 3290-6.
Bracewell R. The Fourier Transform and its Applications. In: Terman FE, editors. Electrical and Electronic Engineering Series. 1 st
ed. New York: McGraw-Hill; 1965. p. 372.
Cai J, Chang Z, O'Daniel J, Yoo S, Ge H, Kelsey C, Yin FF. Investigation of Sliced Body Volume (SBV) as Respiratory Surrogate. J Am Clin Med Phys
2013; 14(1): 71-80.
Cai J, Chang Z, Wang Z, Segars WP, Yin FF. Four-dimensional magnetic resonance imaging (4D-MRI) using image-based respiratory surrogate: a feasibility study. Med Phys
2011; 38(12): 6384-94.
Cai J, Read PW, Larner JM, Benedict SH, Sheng K. Reproducibility of interfraction lung motion probability distribution function using dynamic MRI: statistical analysis. Int J Radiat Oncol Biol Phys
2008; 72(4): 1228-35.
Cai J, Read PW, Altes TA, Molly J, Brookeman JR, Sheng K. Evaluation of the reproducibility of lung motion probability distribution function (PDF) using dynamic MRI. Phys Med Biol
2007; 52(2): 365-73.
Carnes G, Gaede S, Yu E, Van Dyk J, Battista J, Lee TY. A fully automated non-external marker 4DCT sorting algorithm using a serial cine scanning protocol. Phys Med Biol
2009; 54(7): 2049-66.
Cervino L, Chao A, Sandhu A, Jiang SB. The diaphragm as an anatomic surrogate for lung tumor motion. Phys Med Biol
2009; 54(11): 3529-41.
Kong FM, Zhao L, Hayman JA. The role of radiation therapy in thoracic tumors. Hematol Oncol Clin North Am
2006; 20(2): 363-400.
Eck K, Bredno J, Stehle T. Absolute alignment of breathing states using image similarity derivatives. Proceedings of Society of Photo-Optical Instrumentation Engineers 5744; 2005 February 12; San Diego, USA. Bellingham: Society of Photo-Optical Instrumentation Engineers; 2005.
Fakiris AJ, McGarry RC, Yiannoutsos CT, Papiez L, Williams M, Henderson MA, Timmerman R. Stereotactic body radiation therapy for early-stage non-small-cell lung carcinoma: four-year results of a prospective phase II study. Int J Radiat Oncol Biol Phys
2009; 75(3): 677-82.
Gaede S, Carnes G, Yu E, Van Dyk J, Battista J, Lee TY. The use of CT density changes at internal tissue interfaces to correlate internal organ motion with an external surrogate. Phys Med Biol
2009; 54(2): 259-73.
Hu Y, Caruthers SD, Low DA, Parikh PJ, Mutic S. Respiratory amplitude guised 4-dimensional magnetic resonance imaging. Int J Radiat Oncol Biol Phys
2013; 86(1): 198-204.
Imura M, Yamazaki K, Shirato H, Onimaru R, Fujino M, Shimizu S, Harada T, Ogura S, Dosaka-Akita H, Miyasaka K, Nishimura M. Insertion and fixation of fiducial markers for setup and tracking of lung tumors in radiotherapy. Int J Radiat Oncol Biol Phys
2005; 63(5): 1442-7.
Kaskowitz L, Graham MV, Emami B, Halverson KJ, Rush C. Radiation therapy alone for stage I non-small cell lung cancer. Int J Radiat Oncol Biol Phys
1993; 27(3): 517-23.
Keall P. 4-dimensional computed tomography imaging and treatment planning. Semin Radiat Oncol
2004; 14(1): 81-90.
wKeall PJ, Mageras GS, Balter JM, Emery RS, Forster KM, Jiang SB, Kapatoes JM, Low DA, Murphy MJ, Murray BR, Ramsey CR, Van Herk MB, Vedam SS, Wong JW, Yorke E. The management of respiratory motion in radiation oncology, report of the AAPM task group 76. Med Phys. Med Phys
2006; 33(10): 3874-900.
Li R, Lewis JH, Cerviño LI, Jiang SB. 4D CT sorting Based on patient internal anatomy. Phys Med Biol
2009; 54(15): 4821-33.
Low DA, Nystrom M, Kalinin E, Parikh P, Dempsey JF, Bradley JD, Mutic S, Wahab SH, Islam T, Christensen G, Politte DG, Whiting BR. A method for the reconstruction of four-dimensional synchronized CT scans acquired during free breathing. Med Phys
2003; 30(6): 1254-63.
Nicholas K, Liu HH, Starkschall G, Jacobson M, Forster K, Liao Z, Komaki R, Stevens CW. Evaluation of internal lung motion for respiratory-gated radiotherapy using MRI: part I-correlating internal lung motion with skin fiducial motion. Int J Radiat Oncol Biol Phys
2004; 60(5): 1459-72.
Kupelian PA, Forbes A, Willoughby TR, Wallace K, Mañon RR, Meeks SL, Herrera L, Johnston A, Herran JJ. Implantation and stability of metallic fiducials within pulmonary lesions. Int J Radiat Oncol Biol Phys
2007; 69(3): 777-85.
Schreibmann E, Chen GT, Xing L. Image interpolation in 4D CT using a B Spline deformable registration model. Int J Radiat Oncol Biol Phys
2006; 64(5): 1537-50.
Takeda A, Sanuki N, Kunieda E , Ohashi T, Oku Y, Takeda T, Shigematsu N, Kubo A. Stereotactic body radiotherapy for primary lung cancer at a dose of 50 Gy total in five fractions to the periphery of the planning target volume calculated using a superposition algorithm. Int J Radiat Oncol Biol Phys
2009; 73(2): 442-8.
Tryggestad E, Flammang A, Han-Oh, Hales R, Herman J, McNutt T, Roland T, Shea SM, Wong J. Respiration-based sorting of dynamic MRI to derive representative 4D-MRI for radiotherapy planning. Med Phys
2013; 40(5): 051909.
Webb S. Motion effects in (intensity modulated) radiation therapy: a review. Phys Med Biol
2006; 51(13): R403-25.
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]