Retrospective four‐dimensional magnetic resonance imaging of liver: Method development

Abstract Purpose of our research was to develop a four‐dimensional (4D) magnetic resonance imaging (MRI) method of liver. Requirements of the method were to create a clinical procedure with acceptable imaging time and sufficient temporal and spatial accuracy. The method should produce useful planning image sets for stereotactic body radiation therapy delivery both during breath‐hold and in free breathing. The purpose of the method was to improve the localization of liver metastasis. The method was validated with phantom tests. Imaging parameters were optimized to create a 4D dataset compressed to one respiratory cycle of the whole liver with clinically reasonable level of image contrast and artifacts. Five healthy volunteers were imaged with T2‐weighted SSFSE research sequence. The respiratory surrogate signal was observed by the linear navigator interleaved with the anatomical liver images. The navigator was set on head‐feet — direction on the superior surface of the liver to detect the edge of diaphragm. The navigator signal and 2D liver image data were retrospectively processed with a self‐developed MATLAB algorithm. A deformable phantom for 4D imaging tests was constructed by combining deformable tissue‐equivalent material and a commercial programmable motor unit of the 4D phantom with a clinically relevant range of deformation patterns. 4D Computed Tomography images were used as reference to validate the MRI protocol. The best compromise of reasonable accuracy and imaging time was found with 2D T2‐weighted SSFSE imaging sequence using parameters: TR = 500–550 ms, images/slices = 20, slice thickness = 3 mm. Then, image processing with number of respiratory phases = 8 constructed accurate 4D images of liver. We have developed the 4D‐MRI method visualizing liver motions three‐dimensionally in one representative respiratory cycle. From phantom tests it was found that the spatial agreement to 4D‐CT is within 2 mm that is considered sufficient for clinical applications.

Motion of the liver is mainly caused by three separate factors: respiration, random peristaltic motion, and pulsatile cardiac motion. 2 While respiratory motion can affect a relatively large portion of the liver, cardiac-induced motion of the liver is mainly found in the area underneath the heart. 3 Respiratory-induced motion is continuous and repeated, which enables averaging the motion of the whole liver. Liver tissue is deformable; as these separate motion forces affect from different directions, the resultant motion pattern in different parts of liver will also be complex.
The SBRT treatments can be delivered either with reduced respiratory motion or with free breathing. The reduced respiratory treatment can be delivered either with breath-hold or with abdominal compression. 4 Sometimes, treatment with breath-hold or with abdominal compression is impossible for multiple reasons. A patient may be incapable of repeating the breath-hold instructions, which would lead to treatment being delivered in free breathing during all or parts of the patient's breathing phases. Subsequently accurate estimation of target motion is required to define comprehensive margin coverage to the clinical target volume.
Computed tomography (CT) images, with or without contrast agent, are current standard with supplementary co-registered MR and/or PET images in radiotherapy planning (RTP) to contour the target volumes. Dose planning and calculations are mostly made based on the CT images. During RT, the patient is set up to the correct treatment position by using the CT images as a reference image to cone beam CT images (CBCT) of image guidance. However, a single CT image series does not model the motion of tissues and has inferior soft-tissue contrast than magnetic resonance images. In CBCT, the liver lesions are poorly visible.
Magnetic resonance imaging (MRI) has become the general modality for delineation purposes of liver tumors. 5,6 . Image quality affects the quality of delineation and thus needs consideration. 7 MR images have much better soft-tissue contrast, but it has more challenges with the imaging of moving objects. The moving objects are usually imaged using breath-hold and/or triggered imaging (expiration). The MRI is time-consuming and therefore image quality suffers from motion artifacts especially when imaging the abdomen area.
The purpose of this work was to overcome these limitations of MRI in moving objects and produce similar 4D dataset as from CT but with improved soft-tissue contrast.
1.B | Imaging method of predicting motion of liver MRI with cine, 9 interleaved, 10 and sequential acquisitions. 11 The main respiratory-induced displacement in liver is in cranio-caudal (CC) direction and it can be up to several centimeters. 2,10,12 The liver additionally shows rigid 1-12 mm anterior-posterior (AP) and 1-3 mm left-right (LR) transformations. In addition to the rigid transformations, there occur also nonrigid deformations in liver tissues (up to 20 mm). 13 Uh et al. (2017) 14 has also researched relations between organ motion and specific patient characteristics.
2D MRI acquisition can be made in either coronal, transversal, or sagittal plane and the other two planes are reconstructed. There are publications of 4D-MRI methods in all three 2D acquisition planes. 2 Transversal acquisition plane is the most natural orientation for delineation purposes, since it is most commonly used in RTP. 2  | 305 sorting 3D MRI volumes than the respiratory bellows. There are multiple different methods for sorting slices: sorting k-space or images, amplitude binning, or phase binning. Amplitude binning sorts respiratory data in N number of bins based on the amplitude of signal and phase binning sorts each respiratory cycle in N number of bins. Generally, the number of bins is 4-10 but 4D-CT generates 10 bins that it is used in most of the published studies. Phase and amplitude binning can be used as combination. Respiratory data are sorted at first in phases and predefined amplitude range is chosen to the final 4D image. 11 There are also approaches of collecting data or modeling only part of the breathing phase such as mid-ventilation 9 and midposition 19 methods. Usually sorting is made in one breathing cycle, which simplifies the breathing. In addition, sorting can be made over tens of minutes to time resolved 3D to study irregularities in organ motion during free breathing 10 All retrospective methods, however, have the disadvantage that the sequence is agnostic of the respiratory waveform during the acquisition. 2 The aim of this research was to develop a retrospective 4D-MRI protocol for clinical use in the liver SBRT. The research is focused to optimize accurate MRI method and data processing methods. The developed method is tested and evaluated with self-manufactured 4D phantom. The T2-w MRI was performed for the upper abdomen area to study liver motion as a function of time. The T2-w SSFSE has clinically accurate soft-tissue contrast in liver area. 11 Navigator echoes were used to collect 1D image data to get the position of liver-lung interface. The navigator was mounted and centered according to the 2D localizer images on the dome of the liver to observe the motion range of the diaphragm. Each 1D navigator image corresponds to one T2-w SSFSE image slice.
At first, we tested the clinical cine MRI by the FIESTA (bSSFE) sequence to acquire liver motion. With the 1.5 T MRI scanner, the cine imaging has unreasonable long imaging time for our purposes (imaging time would be at least 40 min with 3 mm slice thickness). Therefore, we used the investigational 4D SSFSE sequence with acquiring time of 10-15 min. The image quality was partly better in the SSFSE sequence compared to the FIESTA sequence; there occurred less artifacts, like banding.
Imaging parameters were optimized according to clinical purposes and requirements of the developed method. The optimal imaging method should be clinically usable; reasonable long imaging time and the quality of the images at the reasonable level. MR images are being used in order to determine liver motion three-dimensionally during the whole respiratory cycle with sufficient accuracy. In order to get a high-quality 4D liver model, each anatomical position needs to be covered over the full respiratory cycle.
MR images must have acceptable resolution (3 mm, mentioned in the reference [15]) and low number of artifacts in the acquisition direction. Artifacts were minimized with fixation in RT treatment position to minimize extra motion. RT treatment position typically requires a flat tabletop, MR compatible fixation and lasers.

2.C | Optimization of parameters
The 4D-MRI sequence 20  F I G 1 . A diagram of the workflow of the developed method. Volunteers were imaged with T2-w 2D SSFSE MRI sequence interleaved with linear navigator echoes. Navigator echoes were used to collect 1D image data to get the position of liver-lung interface. The 2D MR images and navigator data were retrospectively processed with self-developed MATLAB algorithm. Navigator data were used as respiratory surrogate signal and the data were sorted into breathing phases. The 2D image slices of liver were sorted into N number of bins according to breathing phases. Respiratory-induced liver motion was observed from resulted 4D-MR images. The 4D images are used to track the motion of small liver lesions and to build deformable liver model for SBRT use Imaging directions were optimized to get two orthogonal views, which enables true 3D tracking of the liver.

2.D | Phantom test
The 4D-MRI method was tested and validated with a self-developed deformable 4D phantom. A deformable phantom for 4D imaging tests was constructed by combining self-made deformable tissueequivalent material and a commercial programmable motor unit from the 4D phantom (CIRS, Model 008A). A phantom was prepared by a 3D-printed rigid, hollow, and rectangular shell that was filled with silicone gel, an air-filled balloon and plastic pellets forming a contrast in the MR image. The shell was left open on one side leaving one surface of the flexible material free for deformation. The purpose was to mimic liver-lung interphase with the phantom. The pellets were used as small targets (diameter = 6 mm) to be tracked threedimensionally during the simulation of respiratory motion. A motor and piston part of the 4D phantom was employed to produce a controlled movement pattern in the phantom. The piston was directed in the "SI" direction at the center of the flexible surface of the phantom. The maximal movement was observed at the flexible surface of the phantom and the movement was damped as going deeper in the phantom.
The 4D phantom was imaged with the 4D protocol in MRI using T2-w SSFSE sequence interleaved with 1D navigator (1.5 T GE F I G 2 . A diagram of the proposed workflow of the methodology. At first, the liver is imaged with the 4D-MRI sequence. Secondly, the MR images are sorted with self-developed algorithm in MATLAB to reconstruct the dynamic 4D-MR image. The 4D-MR image is utilized in radiotherapy planning to get more accurate CTV to ITV margins. In addition, the 4D-MR image is utilized to create deformable liver model that will be introduced in our future studies. Prefer treatment volumes and deformable liver model will be utilized in image-guided radiotherapy (IGRT) Optima 450w GEM) and in CT (Siemens Somatom Confidence RT).
Imaging was made with different input transformation signals; the shape of cos 6 (x) with 10 and 15 mm displacements with frequency of 7.08 cycles/min. 4D-CT images were used as a reference image to validate the 4D-MRI protocol. The MRI and CT images were sorted into 10 bins to get comparable 4D images. Resulted 4D images were compared and center location of the phantom surface was measured with tools in 3D Slicer software. 22 3 | RESULTS

3.A | Sequence optimization
The imaging parameter TR and the combination of slice thickness, images/slices, and imaging time were optimized. TR was tested with range from 400 to 1500 ms. With lower TR (TR = 400 ms), there occurred remarkable noise in the navigator data. The noise caused inaccuracy to the surrogate respiratory signal. With higher TR, a sampling problem was observed as the frequency of data acquiring was decreased. When TR was increased, the imaging time was increasing excessively. TR 500-550 ms was found feasible for our purpose. The 4D sorting algorithm was tested with variable number of bins (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), and as a measure of data quality, the number of empty slices were calculated. The results are shown in Fig. 3. With the number of bins ≤10, the data loss is below 18 %. The number of bins = 8 was chosen to reconstruct the 4D-MR image of healthy volunteers, since it has low amount of stitching artifact (Fig 4, visually observed) and low number of missing data. Interestingly, the different curves have similar shapes, independent from the volunteer imaged.
The imaging sequence results in adequate soft-tissue contrast in abdomen area and different tissues (fat, muscle, liver, and lung) can easily be visualized (see Fig. 4) with similar quality to the breath-hold technique. The 4D-MR images of all five volunteers were visually evaluated, and it was observed that the 4D-MR images have corresponding image quality as in Fig. 4.

3.B | Phantom tests
Phantom result showed that output deformations measured from the surface of the phantom are compatible with the input movement. Displacements of the surface of the phantom were measured from the 4D-MRI and 4D-CT images (Fig. 5). Displacements measured from the images were compared with the shape of the actual "input" movement of the 4D phantom piston, and it was observed that both image modalities visualize 4D motion with a similar accuracy. In case of the maximum displacement of the input movement was 15 mm, the resulted maximum deformations deviated less than 2 mm in 4D-MRI and 1 mm in 4D-CT from the input. All displacements of the 4D-MRI and the 4D-CT were compared to each other.
Phantom results showed that the developed method is able to detect the motion with accuracy of 1.2 mm mean, 1.1 mm standard deviation, compared to 4D-CT when the frequency of the movement was less than 7.08 cycles/min.

| DISCUSSION
The 4D-MRI method of liver was developed 20 and optimized. In addition, self-developed MATLAB algorithm was produced for data processing. The resulted 4D-MR image models the liver motion three-dimensionally in one respiratory cycle with an acceptable imaging time and sufficient temporal and spatial accuracy. The method fulfills clinical prerequisites and method was successfully tested and validated with a self-developed phantom.
Navigator data consist of 1D images collected from the liverlung interphase. The navigator is centered manually on the dome of the liver by using the 2D localizer images, which are taken during free breathing of volunteer. Navigator image data have a certain amount of noise caused by physiological motion, thus the processing of navigator data requires filtering before the respiratory surrogate signal is reconstructed. 23 According to Wang et al. (1996), 23 the least square algorithm removes noise and profile deformations from navigator data. We were able to optimize imaging sequence to reduce noise and therefore to determine the respiratory signal by thresholding the navigator signal. The developed 4D method suffers from missing data problem caused by data sampling. In our method, missed slices were replaced with slice from previous bin, which may reduce the quality of the resulted image. The replace method was used to mimic the real situation without additional interpolation that may cause image blurring artifact. Other studies have used image averaging to interpolate missing slices. 19 Van de Lindt et al. (2018) 24 missing data were interpolated using iterative interpolation algorithm, which uses both time and space to predict the missing values based on discrete cosine transforms. Missing data problem does not occur with cine imaging that is used in some papers. 9 Cine imaging reduces the risk of missing slices since the same location is imaged until whole respiratory cycle is acquired and only then moving to next location. However, the imaging time is longer in cine-mode than in interleaved or in sequential acquisition. [9][10][11] The interleaved acquisition order ensures longer relaxation time before next excitation, which reduces cross talk and improves image contrast. 2 The quality of the resulted 4D image varies for each imaged volunteer. The quality of the 4D-MR image is mainly reduced by the F I G 3 . Proportion of missing data as a function of the number of bins for five volunteers (VOL = volunteer). The amount of missing data increases monotonically as the number of bins is increased stitching artifact caused by the irregularity of volunteer's breathing.
Our results show that stitching artifact is more visible in inspiration phase (Fig 4). Van  The 4D image can model the motion of the liver and therefore, it enables tracking motion of the liver. The image models the liver motion accurately especially in expiration phase where the stitching artifact caused by irregular breathing is minimal. Our method models the liver three-dimensionally in eight respiratory phases with more accurate resolution and larger FOV than most of the published studies. 2 The resulted images had also illustrative contrast, thus small details such as veins can be observed. F I G 4 . T2-w SSFSE sagittal (above) and coronal (below) plane MR images from abdomen area (coronal image acquisition) in eight respiratory phases. Images from expiration phases (phase 4,5) has fewer stitching artifacts (marked with arrows at inspiration, phase 1) caused by irregular breathing of volunteer (VOL1). Maximum displacement of the liver dome between the inspiration and expiration phases was 10.6 mm

| CONCLUSIONS
A novel method of 4D-MRI of liver was developed in order to produce dynamic MRI sequence for planning of SBRT treatments of liver metastasis. The developed method has promising features to meet clinical requirements, and achieve acceptable resolution and lowest degree of artifacts to resulted images. The 4D-MRI method robustly demonstrates the 3D motion of the liver in one respiratory cycle. The method was successfully tested with five volunteers, and with a 4D phantom test it reached similar accuracy than the reference 4D-CT method.

AUTHOR' S CONTRIBUTION
Henna Kavaluus is the corresponding author, and involved in data collection, data analysis, and manuscript writing. Tiina Seppälä involved in data collection, data analysis, and reviewing the manuscript. Lauri Koivula involved in data collection and reviewing the manuscript. Eero Salli involved in designing the study, data analysis, and reviewing the manuscript. Juhani Collan involved in reviewing the manuscript. Kauko Saarilahti and Mikko Tenhunen involved in designing the study and reviewing the manuscript.
F I G 5 . 4D phantom displacement as a function of phases. Measured deformations of the 4D-MRI and 4D-CT from the surface of the phantom. The input signal was cos 6 (x) with 15 mm displacement and 7.08 cycles/min frequency. The maximum observed displacement as measured from MRI was 13 and 14 mm with CT. The deformable nature of the phantom causes that the resulted surface displacements are shallower in MRI and CT than the input displacement