# Modular Dynamic Torso Phantom Featuring Respiratory and Cardiac Motion for Magnetic Resonance Imaging

Jean-Lynce Gnanago, Ernesto Gomez Tamm, Andreas Hodul, Quang Nguyen, Markus Ortner, Zacharias Chalampalakis, Onisim Soanca, Michael Woletz, Lena Nohava, Karyna Isaieva, et al.

► To cite this version:

Jean-Lynce Gnanago, Ernesto Gomez Tamm, Andreas Hodul, Quang Nguyen, Markus Ortner, et al. Modular Dynamic Torso Phantom Featuring Respiratory and Cardiac Motion for Magnetic Resonance Imaging. IEEE Transactions on Instrumentation and Measurement, 2025, 74, pp.1-9. 10.1109/TIM.2025.3529573.1. hal-04928383

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Accepted version

This research was funded in whole or in part by the Austrian Science Fund (FWF), grant DOIs:
10.55776/P37189 & 10.55776/P35305. For open access purposes, the author has applied a CC BY public
copyright license to the author accepted manuscript version arising from this submission.

Citation of final, published version:

J.-L. Gnanago *et al.*, "Modular Dynamic Torso Phantom Featuring Respiratory and Cardiac Motion for Magnetic Resonance Imaging," in *IEEE Transactions on Instrumentation and Measurement*, doi: 10.1109/TIM.2025.3529573.
# Modular Dynamic Torso Phantom Featuring
Respiratory and Cardiac Motion for Magnetic
Resonance Imaging

Jean-Lynce Gnanago, Ernesto Gomez Tamm, Andreas Hodul, Quang Nguyen, Markus Ortner, Zacharias Chalampalakis, Onisim Soanca, Michael Woletz, Lena Nohava, Karyna Isaieva, Elmar Laistler, Ivo Rausch, and Roberta Frass-Kriegl

**Abstract**—The design, fabrication, assembly and testing of a modular dynamic torso phantom for magnetic resonance imaging (MRI) is presented. The phantom is composed of fully MRI-compatible materials and consists of a saline-filled acrylic shell, with dimensions comparable to a human torso, and three distinct interior motion modules. Two linear piezo stages are used to mimic respiratory motion of the chest-wall (≤ 10 mm; cycle time ≥ 2 s) and the abdominal organs (≤ 45 mm; cycle time ≥ 2 s). A pneumatic system is used to move a heart mock-up to represent cardiac motion (≤ 19 mm, rate ≤ 3 Hz). The motion capabilities and MRI compatibility of the phantom are tested in 3 T MRI experiments. The closed-loop control of the phantom's breathing modules allows for accurate positioning and timing with absolute differences between input and output values ≤ 0.61 mm and ≤ 0.06 s. The purpose of this phantom is to serve as a scientific instrument for the future development and evaluation of motion tracking and artifact compensation techniques.

**Index Terms**— Biomedical engineering, Biomedical instruments, Magnetic resonance imaging, MRI phantom, Medical imaging

## I. INTRODUCTION

MAGNETIC resonance imaging (MRI) is a major medical imaging modality that can provide a multitude of high-quality anatomical and functional tomographic information without using ionizing radiation. Besides imaging of the head and the extremities, MRI is also used for examinations of the torso, especially the heart, liver, breast, spine, etc.

For torso MRI in particular, inevitable respiratory and cardiac subject motion represent a major challenge. While heartbeat motion is almost exclusively affecting cardiac MRI,

respiratory motion generally affects all torso MRI applications. Organ motion with the respiratory cycle is rather complex, i.e. three-dimensional and non-rigid. However, the principal motion axes can be identified: the chest and/or abdominal wall move mainly in anteroposterior direction (with an amplitude of approximately 3 – 8 mm for quiet/normal respiration) [1], [2], while the heart as well as the abdominal organs move predominantly in craniocaudal direction (with an amplitude of approximately 7 – 30 mm for quiet/normal respiration) [3], [4]. Depending on the employed image acquisition technique, motion can cause a variety of artifacts, including blurring, ghosting, signal dropouts and unwanted signal enhancement [5].

To address these challenges, motion tracking and compensation algorithms are subject of past and ongoing research [6], [7]. Motion compensation techniques include for example gating-methods [8], motion-resolved reconstruction [9], [10], or image-based registration techniques [11]. One common requirement for all motion compensation techniques is the efficient measurement or estimation of a motion signal. Traditionally, this is achieved by using external motion sensors [12], [13], [14], e.g. breathing belts or accelerometers, or by applying navigator techniques which either determine the motion signal from the k-space data [15], [16] or object tracking in the reconstructed images [17]. Alternatively, the Pilot Tone [18], [19] and Beat Pilot Tone [20] methods have been proposed which record the motion modulation of an external reference signal within the MR receiver bandwidth.

In all cases, the development of novel motion tracking or compensation techniques requires suitable test objects, so-called phantoms, that provide user-adjustable motion models with sufficient spatial and temporal accuracy and repeatability for testing and validation. Therefore, the goal of the presented work is the development of a dynamic modular torso motion phantom for MRI, i.e. a scientific instrument that can serve as ground truth for the investigation and characterization of novel motion compensation and tracking methods.

Motion phantoms naturally rely on mechanical actuators to perform the envisioned movements. In this regard, the MRI environment poses distinct limitations: The high static magnetic field (typically 1.5 or 3 T) precludes ferro- or strongly paramagnetic materials. Strong magnetic gradient fields (tens of mT/m) switched at kHz rate can cause eddy currents in conductive materials leading to unwanted heating or vibrations. Finally, high power radiofrequency (RF) pulses

This work was supported by the Austrian Science Fund FWF: P37189-N OPTIMAL and P35305-B AquaLactEMISM, as well as the Focus Grant "T4MR" from CMPBME, MedUni Vienna.

Ernesto Gomez Tamm and Jean-Lynce Gnanago are co-first authors.

Corresponding author: Roberta Frass-Kriegl.

Karyna Isaieva is with IADI, Université de Lorraine, INSERM U1254, Nancy, France. All other authors are with the Center for Medical Physics and Biomedical Engineering, Medical University of Vienna, 1090 Vienna, Austria (e-mail: e.gomez.tamm@gmail.com, jean-lynce.gnanago@muv.ac.at, andreas.hodul@muv.ac.at, quang.nguyen@muv.ac.at, markus.ortner@muv.ac.at, zacharias.chalampalakis@muv.ac.at, onisim.soanca@muv.ac.at, michael.woletz@muv.ac.at, lena.nohava@muv.ac.at, karyna.isaieva@univ-lorraine.fr, elmar.laistler@muv.ac.at, ivo.rausch@muv.ac.at, roberta.frass@muv.ac.at)

Data are available online at https://zenodo.org/records/10997616
(kW range) can lead to the malfunctioning of electronic
devices as well as heating phenomena.

Another constraint in the choice of suitable phantom
materials is MR visibility. Phantom parts that mimic the
patient anatomy should be visible on MR images, and
therefore must have a sufficiently high density of hydrogen
nuclei and sufficiently long relaxation times T₁ and T₂ so as to
produce a measurable MR signal. This is typically the case for
soft materials, e.g. aqueous solutions or gels, in contrast to
hard materials which appear mostly invisible in MRI.

The literature on motion phantoms is as diverse as the
challenges resulting from these constraints in combination
with application-specific requirements. However, only few
works describe torso phantoms featuring both, respiratory and
cardiac motion [21], [22]. Others focus either on respiration
only [23], [24], [25], [26], [27], or on a single organ such as
the heart [28], [29], [30], [31], [32], [33] or the liver [34].
Respiration is most often realized using pneumatics or simple
inflation systems, for which absolute position control is hard
to achieve, resulting in limitations for characterizing the

accuracy of novel motion tracking methods. Further, none of
these phantoms features an independently controlled,
moveable chest wall. Many heart models are based on pump
systems featuring expansion and flow [21], [22], [28], [33],
[35]. Purely mechanical heart models have been proposed
using pneumatics [32] and stepper motors [29], [30].
However, they were not embedded in full dynamic torso
phantoms and/or have limited degrees of freedom, i.e.
respiration and heartbeat cannot be independently controlled.

This work targets a dynamic torso phantom featuring
motion with three independent degrees of freedom (DOFs):
(1) respiratory motion of the chest wall, (2) respiratory motion
of the heart and abdominal organs, and (3) cardiac motion.
The primary target application is the characterization of novel
motion tracking methods. Therefore, mechanical motion
models, i.e. simple moving objects, are prioritized over
functional and physiological features like blood flow, for
instance.

It should be declared that this paper, in section II, reuses
some content from a thesis [36] with permission.

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** a) Sketch of the phantom set-up in the MRI Environment. b) Isometric CAD drawing of the dynamic torso phantom body with its modules. c) Photograph of the phantom at the edge of the 3 T MRI bore. d, e) Sideview and topview of the phantom CAD model. Dimensions are given in mm.</figcaption></figure>
## II. MATERIALS AND METHODS

### A. Phantom design

#### 1) Concept and overview:

The developed dynamic torso phantom (previously presented in a preliminary version [37]) is composed of an in-bore unit (i.e. phantom body and actuators) to be positioned in a whole-body MR scanner with a field strength up to 3 T and a control unit to be positioned outside the MR scanner room (e.g., in the console room), as shown in Fig. 1a. The phantom position in the scanner corresponds to *feet-first supine*. The phantom body is composed of an acrylic shell that holds three distinct motion modules, i.e. chest wall, abdominal organ and heart modules (color-coded in Fig. 1b). Respiratory motion is achieved with two independent piezo-electric linear stages placed on the ground plate at a distance of 40 cm from the main body, and cardiac motion with a pneumatic system. Both actuating systems are operated and supplied with power or pressurized air via the control unit.

#### 2) Acrylic shell and mechanical framework:

The phantom was developed employing a modular approach, facilitating the exchange of one part or subsystem in case of damage or due to different requirements set by future applications. The ground plate holding the phantom body and the actuators is equipped with an adjustable fixation system that prevents the phantom body from shifting to either side, and the piezo stages are mounted on a separate actuator plate. The motion modules of the phantom body are constructed on a separate plate that is placed inside the acrylic shell with a fixed connection to the actuator plate (see Fig. 1c-e).

The acrylic shell (fabricated by Acrylstudio GmbH, Austria) itself is the form-determining structure encompassing all motion modules and mimicking the tissues surrounding the thoracic and abdominal cavities. To this end, the shell is double-walled and its chamber is filled with a saline solution consisting of approximately 5 l distilled water, 5 g/l of NaCl to adjust its conductivity, as well as 1 ml/l of contrast agent (ProHance 20 ml, Bracco Imaging, Italy). The geometry is inspired by an MR scan of an average adult torso. The shape has a cutout to facilitate mounting a moveable chest wall.

Most parts used for phantom construction (e.g., plates, bolts, etc.) were fabricated from polyvinyl carbonate (PVC) material with standard CNC milling machines and lathes. Parts for which it is explicitly stated in the description below, were additively manufactured using either an FDM printer (Pro2 Plus, Raise3D, USA; material: RS Pro PLA), or an SLA printer for structures that need to be watertight (Form 3B+, Formlabs, USA; material: Clear Resin V4).

#### 3) Respiratory motion:

The phantom is capable of simulating two different components of the respiratory cycle, i.e. anteroposterior motion of the chest wall (DOF 1), and motion of the heart and abdominal organs in craniocaudal direction (DOF 2). For both DOFs, non-magnetic, ultrasonic linear piezo stages were used (Xeryon, Leuven, Belgium; models XLS-3-80-1250-SC-NM

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Detailed isometric CAD drawings of the motion modules. a) Gear box for chest motion. 1 Push head. 2 Gear system. b) Abdominal organ module. 3 Position at which the heart module is attached to the wagon. 4 Sectional view of the bulk shell and the liver phantom. c) Heart module with sliding box. 5 Double-action pneumatic piston, with details shown in the explosion drawing below.</figcaption></figure>

& XLS-3-120-1250-SC-NM; manufactured and calibrated in September 2023) with a nominal driving force of 3 N, maximum travel range of 69 mm and 109 mm, a speed of up to 200 mm/s and an encoder resolution of 1.25 µm.

The chest wall is represented by a low-cost flexible gel mat (260 mm x 210 mm x 10 mm) made of elastic polyurethane fiber (DBM Factory SRLS, Italy), which can be replaced by a commercially available silicone breast mock-up (Vollence Dolls World, USA) to mimic female anatomy. For DOF 1, the horizontal movement of the piezo stage is translated into a vertical movement via a gear box (see Fig. 2a) containing a compound gear with a ratio of 1:5, providing a five-fold increase of the driving force at the cost of a longer required travel range (gears purchased from igus GmbH, Germany). This gear box also holds a push head that contacts and lifts the gel mat through an opening in a solid fixation sheet that prevents sagging of the gel mat. The maximum configurable displacement is a 10 mm vertical lift of the gel mat.

For abdominal organ motion (DOF 2), a monorail track and a wagon holding an FDM-printed bulk shell were constructed (see Fig. 2b). In the bulk shell, different organ phantoms can be placed, e.g., the SLA-printed liver mock-up [38] shown in Fig. 2b, filled with the same saline solution as the outer shell. The heart module (described in the next section) is attached to the abdominal organ wagon to emulate heart movement with the respiratory cycle in addition to the heart's primary movement with the cardiac cycle. The attachment position is shown in Figs. 1b and 2b (marker 3). A second compound gear with a ratio of 1:2 is placed between the piezo stage for DOF 2 and the wagon to increase the driving force. The maximum configurable displacement is a 45 mm horizontal shift of the abdominal organ wagon.

Rigid fiber-reinforced plastic rods with 4 mm diameter, gear racks and 3D-printed holders are used to connect the piezo stages and the motion modules (see Fig. 1c-e).

The stages are operated via a laptop and the piezo controller provided by the manufacturer. To suppress electromagnetic
interference (EMI), a low pass filter (243A13860X, Amphenol CONEC) is placed on each cable (standard DSUB 15 HD cable provided by piezo stage manufacturer) from the controller to the in-bore piezo stages (see Fig. 1a).

In principle, DOFs 1 and 2 can be controlled independently from each other. However, when mimicking respiratory motion, the stages are configured to move synchronously with a $\pi$ phase shift, resulting in a lift of the chest wall simultaneous to a caudal shift of the abdominal organ wagon.

### 4) Cardiac motion:

The heart module (DOF 3) is comprised of a sliding box holding a heart phantom (i.e., SLA-printed heart segmented from an MRI scan filled with gel), and a full-plastic pneumatic movement system connected underneath, Fig. 2c.

The heart phantom contains approximately 300 g of gel made of 48.34 % (weight percent) deionized water, 48.34 % ethylene glycol, 0.58 % NaCl, 1.94 % Agarose, 0.39 % KH₂PO₄, 0.34 % K₂HPO₄, 0.05 % Sodium azide, and 0.02 % Magnevist contrast agent. Gel is preferred over an aqueous solution to avoid fluid turbulences, which could occur for high-frequency cardiac motion. The phosphorous components were added to enable ³¹P MR spectroscopy experiments on the heart model in the future.

For the full-plastic pneumatic system, a double-action cylinder was developed to avoid the need for a metal spring for the piston to retract. With shock absorptions on both sides of the cylinder, the path for the piston is limited to approximately 19 mm.

This piston is supplied with pressurized air from the control unit outside the scanner room via a 5/2-way double solenoid electromagnetic valve (VUVG-LK14-B52-T-G18-1H2L-S, Festo GmbH, Germany) and two pneumatic lines with 3 mm diameter. The valve is operated by a MATLAB-controlled data acquisition card (NI-USB-6001, National Instruments, USA). Pressurized air is provided by an air compressor (Adler, Austria) with maximum pressure of 11 bar, which is reduced to 1.8 bar via a pressure regulator (MS4-LR-1/8-D5-AS, Festo GmbH, Germany) to operate the polymer piston safely.

The described heart module facilitates simplified cardiac motion in form of a high frequency (up to several Hz) linear displacement in the craniocaudal direction. With this heart model, only the frequency of the motion can be adjusted, while the displacement is fixed by construction. Thanks to the flexible pneumatic lines, the pneumatic system can be easily combined with the piezo actuator to enable heart motion due to both, heartbeat and respiration.

## B. Testing and Evaluation

### 1) Basic MR compatibility:

Before validating the motion capabilities of the developed phantom, the basic MR compatibility of the static phantom was investigated. The phantom was positioned in a 3 T MRI scanner (Prisma Fit, Siemens Healthineers, Erlangen, Germany). For simplicity, the built-in whole-body RF coil was used for excitation and reception of the MR signal in all measurements. A basic localizer sequence with two slices in

each orientation (2D FLASH: TR = 7.5 ms, TE = 3.69 ms, slice thickness 7 mm, FOV 350 x 350 mm, acq. matrix 256 x 233, 2 averages, TA = 6 x 3.48 s) was acquired. A careful visual inspection of the resulting images was performed (1) to verify MR visibility of the respective phantom parts, i.e. outer shell, gel mat, heart and liver models, and (2) to identify potential imaging artifacts, e.g. related to susceptibility.

A so-called RF noise sequence acquiring spectroscopic data across the maximum bandwidth of the MR scanner's receiver electronics without RF excitation or imaging gradients (BW = 1 MHz, TR = 16.39 ms, vector size 8192, 80 measurements) was used to investigate potential EMI caused by the phantom. The sequence was run with the non-moving torso phantom, the moving torso phantom, as well as with a static reference phantom of comparable size [39].

<table><caption>TABLE I
MOTION PATTERNS FOR PHANTOM EVALUATION</caption><thead><tr><th>Label</th><th>Heart Rate</th><th>Respiratory Cycle</th><th>Chest Amplitude</th><th>Abdomen Amplitude</th></tr></thead><tbody><tr><td>Shallow</td><td>1.5 Hz</td><td>2 s</td><td>5 mm</td><td>10 mm</td></tr><tr><td>Normal</td><td>1 Hz</td><td>5 s</td><td>7 mm</td><td>20 mm</td></tr><tr><td>Heavy</td><td>1 Hz</td><td>8 s</td><td>10 mm</td><td>35 mm</td></tr><tr><td>Extreme</td><td>2 Hz</td><td>2.5 s</td><td>10 mm</td><td>45 mm</td></tr></tbody></table>

### 2) Motion Patterns:

The developed motion phantom exhibits a high number of degrees of freedom: different heart rates can be combined with different chest and abdomen motion patterns of variable frequency and amplitude. In the scope of this paper, a limited but representative variety of respiratory and cardiac motion patterns has been defined as test scenarios, see Table I.

The motion patterns labelled as *shallow*, *normal* and *heavy*

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Example time courses for respiratory motion. a) Heavy linear motion pattern for DOF1 (chest, red) and DOF2 (abdomen, blue) extracted from the piezo stage log files. b) *Shark-fin* motion pattern performed by the abdomen piezo stage, recorded with the motion tracking camera. The equations for forward (blue) and backward motion (red) are displayed, both constants A and B can be tuned to modify the shape of the curve. Both measurements (a, b) were performed during MR imaging and while simultaneously running the heart module.</figcaption></figure>
represent quasi-realistic cases according to literature values [1], [2], [3], [4]. The *extreme* scenario has the purpose to demonstrate the minimum cycle duration for the maximum respiration amplitudes, in combination with fast heart motion. In the aforementioned patterns, the piezo stages perform a linear, i.e. back-and-forth movement at constant speed (see also Figure 3a), generated using the scan function in the manufacturer's control software. The maximum used driving speed of the piezo stages was approximately 70 mm/s.

### 3) Motion Tracking:

Two independent means of position tracking were employed to validate whether the motion performed by the phantom corresponds to the desired pattern: First, the built-in controller function of the piezo stages logging the actual stage position over time was used (available for linear motion patterns only). Timestamps in milliseconds are stored over a 2¹⁶-bit memory and position data is stored in encoder units, with a conversion factor of 1:1.25 µm.

Second, an MR-adapted Polaris Vega infrared camera (P9-00687, NDI, Waterloo, Canada; calibrated by the manufacturer in November 2017; nominal measurement resolution of displacement ≤ 0.25 mm) mounted on a movable stand was used. This system was set up to monitor the relative position between two markers consisting of three retroreflective spheres at a frame rate of 20 Hz; one marker was placed on the static outer shell of the phantom, the second on a moveable part, e.g., the heart model or a piezo stage.

After validating the agreement between the piezo stage logs and the camera data, the log files were used whenever possible (i.e., linear motion for DOFs 1 and 2) and the camera for all other cases (i.e., non-linear respiration and all heart motion).

### 4) Motion experiments:

The defined motion patterns (i.e., shallow, normal, heavy, extreme) were used to establish an in-depth characterization of the phantom's motion performance in terms of accuracy, precision, repeatability, and resilience to the MR environment.

The first tests were performed with the phantom outside the MR scanner. To determine the control accuracy of the phantom, the average amplitude and frequency values were extracted from the recorded motion time series for all DOFs and compared to the input values. Precision was evaluated in terms of standard deviation.

To characterize the repeatability of the respiratory patterns, all scenarios have been tested twice (outside the MR scanner) on different days, including the complete setup of all involved hardware components by the same operators.

To demonstrate that the motion performance of the phantom is not impaired by the MR environment, time courses of all four motion scenarios were recorded with the phantom inside the MR scanner while running one T₁-weighted (axial; TR = 3.7 ms, TE = 1.13 ms, FOV = 280 mm x 368 mm, 256 slices, voxel size 1.5 mm x 1.5 mm x 1 mm) and two T₂-weighted (axial and coronal; TR = 1980 ms, TE = 65 ms, FOV = 280 mm x 368 mm, 12 slices, voxel size 0.9 mm x 0.9 mm x 3 mm) sequences. T₁- and T₂-weighted sequences approached the limits of gradient induced peripheral nerve stimulation and RF induced specific absorption rate, respectively, so as to represent harsh electromagnetic test conditions. The total scan

time for all three sequences was approximately 5 min.

In addition to the motion scenarios in Table I, the performance of the heart module (DOF 3) was characterized in more detail by monitoring the amplitude of displacement of the heart model over a range of heart rates (0.1 – 3.0 Hz).

Further, to demonstrate that the piezo stages can also be configured to perform arbitrary user-defined movements, a *shark-fin* pattern was prepared and played out via the piezo-controller using a custom Python script based on a look-up table approach with positions dictated by pre-calculated exponential functions (see Figure 3b).

Finally, data were acquired to showcase one potential future application for the developed phantom, i.e. investigating motion correction in supine breast MRI. To this end, the female breast mock-up and a dedicated RF receiver array for supine breast MRI [40] were placed on the chest motion module which was configured to perform respiratory motion with an amplitude of 7 mm and a cycle time of 5 s. Axial T₂-weighted images (TR = 1480 ms, TE = 156 ms, FOV = 330 mm x 192 mm, 9 slices, voxel size 0.6 mm x 0.6 mm x 3 mm) were acquired of the moving and non-moving phantom. The GRICS algorithm [10] was used for motion resolved image reconstruction based on motion time courses recorded with the camera system so as to perform motion correction on the acquired data.

## III. RESULTS

MR images of the non-moving phantom are free from imaging artifacts, apart from image distortions at the edges of the large FOV (450 mm in z-direction) due to typical gradient nonlinearities [41], see Figure 4. Further, all models (i.e., outer shell, liver, heart and chest models) are MR visible with adequate signal intensity. The noise spectra shown in Figure

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** a) Basic MR images (2D FLASH) of the non-moving dynamic torso phantom showing transversal, coronal and sagittal slices centered at the heart (top) and the liver (bottom), respectively. b) Noise spectra with maximum RF bandwidth comparing the moving motion phantom with and without lowpass EMI filters to a static reference phantom of comparable size.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Example motion artifacts observed in axial and coronal T₂-weighted scans of the dynamic torso phantom for different motion patterns (shallow, normal, heavy, extreme). a) Running respiratory and heartbeat motion together. (cf. Fig. 8a for displacement values for the heart model.) b) Separating respiratory and heartbeat motion.</figcaption></figure>

4b demonstrate the necessity as well as the efficacy of the lowpass EMI filters placed at the connection cables of the piezo stages. Without the EMI filters, signal intensity spikes like those shown in the noise spectrum (Fig. 4b) can lead to image artifacts if they fall within the imaging bandwidth.

Figure 5a illustrates the motion artifacts occurring in the acquired T₂-weighted MR images for each motion pattern. Qualitatively, the severity of the artifacts is increasing with the intensity of the motion, as expected. Figure 5b presents a comparison between the motion artifacts caused by fast heartbeat motion and slower respiratory motion.

Motion artifact compensation is demonstrated by the application showcase of motion correction for supine breast MRI using the GRICS algorithm for motion-resolved image reconstruction [10] with the results shown in Figure 6.

The analysis of the respiratory modules' performance is summarized in Figure 7. Good agreement between input (c.f. Table I) and measured values for amplitudes and cycle times was observed. For the chest module, the differences between the mean amplitude and cycle time values to the input values were within intervals of [-0.61 mm; +0.10 mm] and [-0.05 s; +0.06 s], respectively. The largest absolute difference was found when targeting the maximum amplitude of 10 mm, for which the limit of the piezo stage's driving force is reached. For the abdomen module, smaller differences within intervals of [0 mm; +0.10 mm] and [-0.05 s; +0.06 s] were observed. The performance was very stable over time within each measurement series with standard deviation values ≤ 0.84 % for amplitudes and ≤ 3.6 % for cycle times, respectively.

Further, the respiratory performance was not impaired by the MR environment (relative standard deviation between measurement series inside and outside the scanner ≤ 3.25 %), and excellent repeatability (relative standard deviation between the two measurement series outside the scanner ≤ 3.16 %) was observed for amplitudes and cycle times for all motion patterns; Corresponding mean values are compared in Figures 7c and 7f.

Figure 8 highlights the performance of the heart module (DOF 3). Also, for this module, high frequency stability and repeatability were observed as well as resilience to the MR environment, as expected for the full plastic pneumatic system. However, the amplitude of the heartbeat motion decreased with heart rate above 1.5 Hz, as shown in Figure 8a. Since the heart module is attached to the abdominal organ wagon, the heart model is subject to heartbeat as well as respiratory motion. Figures 8b and 8c show corresponding exemplary displacement time courses with heartbeat motion alone and the superposition of heartbeat and respiratory motion, respectively.

## IV. DISCUSSION & CONCLUSION

In this work, a modular dynamic torso phantom was presented, that can be used to mimic respiratory motion of the chest wall, respiratory motion of the heart and abdominal organs, and cardiac motion. The mechanical design and construction are described in detail, and the complete CAD model of the phantom is available as open-source material alongside with additional information and control scripts [42].

The phantom was characterized and evaluated in a comprehensive set of experiments, validating the mechanical design and the selection of materials and actuators. Overall, the presented results demonstrate excellent control accuracy (i.e., sub-millimeter spatial and tenth-of-a-second temporal accuracy), stability and repeatability of the phantom's motion performance over a large range of physiologically realistic dynamic conditions. This confirms its viability as a scientific instrument to develop motion tracking and correction hardware and software solutions in the demanding MR environment.

Performance limitations of the current design are encountered when driving the phantom at high motion frequencies and maximum amplitudes at the edge of quasi-realistic use cases. This is related to the restrained driving

<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Application showcase of motion correction for supine breast MRI. Axial T₂-weighted images of the phantom with the female chest model, with (left) and without (right) respiratory chest motion (7 mm amplitude, 5 s cycle time). Images after applying the GRICS algorithm for motion correction are shown in the middle.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 7** Summary of the respiratory modules' performance (DOFs 1 & 2). a,b) Cycle time and motion amplitude for the chest module over time. Shown data were recorded with the phantom inside the MR scanner while running imaging sequences. c) Comparison of the amplitudes and cycle times (mean values) for the three measurement series inside and outside the MR scanner. Error bars for standard deviation values are not shown as they would be smaller than the plot symbols. Note that the green color indicates an overlap of blue and yellow symbols. d-f) Corresponding data for the abdominal organ module.</figcaption></figure>

force of the piezo stages and the design and construction of the pneumatic system. Specifically, limitations in motion amplitude could be encountered for the chest module when it is loaded with a heavier breast mock-up and an additional MR

receiver coil. Potential improvements include upgrading the compound gears but also the design of more lightweight modules as well as increasing the airtightness or shortening the movement range of the pneumatic system.

The usability and handling of the motion phantom benefit from the central control interface via a standard laptop and the robust setup of all in-bore components on a single ground plate. Installation and dismantling of the phantom must be carried out by two persons due to the overall mass (~ 30 kg) and size (~ 130 cm x 50 cm x 30 cm) and requires 15-20 min. In future work, potential streamlining the design or simple mechanisms for disassembling and assembling the phantom while maintaining robustness to improve user experience and usability will be investigated.

The presented torso motion phantom features a modular design. Firstly, all three motion DOFs can be configured and operated independently from each other. Secondly, the mechanical framework of the phantom is designed to accommodate various organ models, i.e. the simple chest, heart and liver models used in this work as well as more advanced models with different anatomical features potentially investigated in the future. For example, the female version of the chest wall could be designed including tissue equivalent breast models [43] to better investigate motion artifacts in supine breast MRI [40]. To overcome the limitation of an over-simplified cardiac phantom featuring only linear cranio-caudal motion, the static heart model could be replaced by phantoms supporting deformation and/or flow [22], [32], [33], [35], [44], [45], or stiffness changes for MR elastography experiments [46], [47]. In addition to an elastic heart phantom, these advanced heart models might require liquid-filled hoses and a pump system that have to be mounted and routed next to the phantom hardware presented in this work. Also, the abdominal bulk shell can be populated with other organ models, e.g. kidneys or prostate, potentially making use of 3D printable MR visible polymers [48]. Filling the complete abdominal bulk shell with respective organ

<figure><img src="image_9.png" /><figcaption>**Fig. 8.** Performance of the heart module. a) Motion amplitude as function of the heart rate. The physiologically realistic range of heart rates during MR examinations is marked in orange. b, c) Exemplary time courses for heartbeat motion only and combined heartbeat and respiratory motion.</figcaption></figure>
phantoms would result in more realistic MR images with fewer sharp edges in signal intensity, but this would result in a greatly increased mass to be moved by the piezo stage and might require a compound gear with a higher gear ratio.

## ACKNOWLEDGMENT

We thank Albrecht Ingo Schmid, Lorenz Kiss, Stefan Wampl, Wolfgang Birkfellner, Bastian Rapp, Vivian Janicaud, and Monika Todorova (all with the Medical University of Vienna) for their contributions.

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