A System for Reproducible 3D Ultrasound Measurements of Skeletal Muscles

In 3D freehand ultrasound imaging, operator dependent variations in applied forces and movements can lead to errors in the reconstructed images. In this paper, we introduce an automated 3D ultrasound system, which enables acquisitions with controlled movement trajectories by using motors, which electrically move the probe. Due to integrated encoders there is no need of position sensors. An included force control mechanism ensures a constant contact force to the skin. We conducted 8 trials with the automated 3D ultrasound system on 2 different phantoms with 3 force settings and 10 trials on a human tibialis anterior muscle with 2 force settings. For comparison, we also conducted 8 freehand 3D ultrasound scans from 2 operators (4 force settings) on one phantom and 10 with one operator on the tibialis anterior muscle. Both freehand and automated trials showed small errors in volume and length computations of the reconstructions, however the freehand trials showed larger standard deviations. We also computed the thickness of the phantom and the tibialis anterior muscle. We found significant differences in force settings for the operators and higher coefficients of variation for the freehand trials. Overall, the automated 3D ultrasound system shows a high accuracy in reconstruction. Due to the smaller coefficients of variation, the automated 3D ultrasound system enables more reproducible ultrasound examinations than the freehand scanning. Therefore, the automated 3D ultrasound system is a reliable tool for 3D investigations of skeletal muscle.


I. INTRODUCTION
T HREE-DIMENSIONAL information on skeletal muscle such as volume and length are important measures of a muscle and can be used to compute muscle architecture and relate to the muscle's mechanical behavior.Muscle volume and length have been found to be reduced in disorders such as cerebral palsy [1], [2], [3], compared to typical subjects.Moreover, accurate definitions of these properties can serve as input geometries for subject-specific computational models of skeletal muscles.
One common and accurate method for obtaining muscle length and volume in vivo is Magnetic Resonance Imaging (MRI).However, MRI is an expensive technique which requires long acquisition times, making it prohibitive to collect data in some cases, and limiting experimental conditions where a participant would be asked to maintain muscle contraction during imaging.Furthermore, due to the size and requirements of an MRI system, it is stationary and not suitable for studies where imaging might take place in a variety of different settings.Additionally, in an MRI system, there are limitations due to the narrow space of the imaging bore, and difficulties or prohibitions with patients with metal implants.
Ultrasound is an imaging modality which enables faster acquisition times than MRI, is less expensive, and is portable.In 2D, ultrasound is often used to determine architectural parameters of skeletal muscles such as pennation angle, fascicle length and muscle thickness [4], [5], [6], [7].Over the last two decades freehand 3D ultrasound (f3DUS) has been developed and used for musculoskeletal examinations [8], [9], [10], [11], [12] for both healthy and pathological cases.In f3DUS, the probe is equipped with some form of position sensor.The operator then scans along the longitudinal axis of the muscle taking several cross-sectional images.Knowing the position and orientation of the probe for each ultrasound image and applying a series of coordinate transformations, a 3D volume can be reconstructed.Many f3DUS applications use a motion capture system with optical reflective markers for accurate determination of the position and orientation of the probe.This usually requires a costly laboratory system that is generally not highly mobile due to its size and configuration.A further limitation to these systems is the requirement that the reflective markers have to be visible at all times to the infra red cameras.
When manually moving the ultrasound probe, the operator's contact force varies, for instance due to the natural curvature of the lower limb.This leads to deformation of muscle tissue [13].Gilbertson and Anthony [14] developed a hand held force controlled ultrasound probe for 2D imaging which enables a constant contact force between the ultrasound probe and skin.Other studies combined force sensors and ultrasound probe [15], [16], [17] to measure or control contact forces, and previous robot-assisted approaches have been developed [18], [19].
Other systems, which are primarily designed for 2D ultrasound imaging, have an integrated passive mechanism to maintain a contact force realized by a spring [20], [21], [22].Passive systems enable a constant contact force in the vertical downward direction; in cases where the contact angle of the transducer may change -such as while traversing the skin over a skeletal muscle -passive systems would not maintain a constant normal contact force [21].
For 3D examinations of skeletal muscles, scanning can be done in a water tank as no contact force is needed; this approach can be used to prevent inconsistent deformations.One previous study designed a tomographic ultrasound scanner [23] that has been used for 3D imaging of stumps of lower limb amputees [24], [25].The stump is submerged in a water bath, and the electrically actuated ultrasound probe moves on a circle with another degree of freedom in the vertical direction.However, when recording in a water bath, electronic measurements such as electromyography (EMG) readings using electrodes, are prohibitive.Other studies proposed approaches such as a large gel pad [26] or a gel pad attachable to the probe [27].Furthermore, manual movement of the probe is accompanied not only by variability of the applied force, but also by variability of the movement trajectory rendering it a low-reproducibility method.Approaches for automatically moving the ultrasound probe with 1 [28] or 3 [29], [30] degrees of freedom (DOF) exist.In one study the ultrasound probe was mounted on a rig comprised of three linear axes, which facilitate the translational DOFs [30].In the proposed system, the position of the ultrasound probe was recorded by an electromagnetic measurement system.A more sophisticated version of such system for controlled and automated 3D ultrasound examinations was proposed in 2018 [29] using a digital 3D translating device comprising 3 linear axis, thus enabling three translational DOFs, and a depth camera for obtaining the contours of the tissue surface.The system enabled automated 3D ultrasound measurements, with the ultrasound probe attached in a vertical direction.Such linear position systems enable controlled movement trajectories.They prohibit, however, scanning from oblique angles making measurements difficult, particularly on the curved surfaces of limbs.Another proposed small system [31] contains a motorized assembly attached to the ultrasound probe which enables tilting motion in a tilt range of -30 • to 30 • and linear motions in a 3 cm range, which would for most muscles not enable acquisition of the whole volume.Other approaches used a robot arm for controlled movement of the ultrasound probe in a variety of applications such as spine imaging [32], acoustic radiation force elastography [19], [33], abdominal examinations [34], or general imaging applications [35].While robotic arms are capable of scanning tissue surfaces from oblique angles due to their DOFs, they are mostly not easily portable, rather expensive and implementation can be rather complex.
This paper proposes a novel 3D ultrasound system which enables controlled and automated 3D ultrasound scans by combining: 1) portability due to a small size, 2) consistent tissue deformations by using an included force control, 3) controlled movement trajectories by the use of motors which electrically move the probe and 4) no need of a position sensor on the ultrasound probe due to integrated encoders knowing the position of the probe.The controlled movement trajectories and contact forces enable reproducible results.This paper is a proof-of-concept study.Therefore, for validation purpose, we will demonstrate our method on phantom data.Furthermore, we will use the proposed system to obtain 3D ultrasound images of the human tibialis anterior muscle (TA) for demonstrating the possibility of the in vivo method exemplarily on skeletal muscles.

A. System Overview
The automated 3D ultrasound scanning system (a3DUS) consists of the following components: the custom-designed device, an ultrasound system (Aixplorer MACH30, SuperSonic Imagine) with a linear probe (L18-5), an industrial PC (CX2040, Beckhoff) embedded in a control cabinet to control the movement of the probe and a video capture device (USB3HDCAP, StarTech.comLtd).The custom-designed device is shown in Fig. 1.It contains two custom-designed semicircular axes (30 cm radius) which are connected by a horizontal axis.In total, a scanning length of 40 cm is possible with this prototype.Therefore, for scans of the lower leg, the custom-designed device is capable of scanning a wide range of body sizes within the percentile range according to [36].Moreover, the size of the customdesigned device enables 3D acquisition of different muscles of the body, e.g., muscles of the back or abdominal muscles.For such a setup, the subject can lie under the semicircles.A limiting factor here would be the depth of the ultrasound probe that can be imaged, or the resolution at the corresponding depth.Scanning other limb muscles, e.g., arm muscles is also enabled.Here, the subject needs to place the arm under the device.Furthermore, the components of the custom-designed device are very easily interchangeable and configurable, therefore an extension of the measurement area can also be made possible.Thus, for scans of larger body parts, it is also possible to exchange the horizontal axis with a longer one.An expendable vertical axis is mounted on a moveable carriage on the horizontal axis.We designed a 3D-printed ultrasound probe hold to rigidly attach it to the vertical axis.
The horizontal axis is moved manually on semicircles as this prototype is designed for scanning muscles, and this design allowed for 3D muscle data to be recorded within a single sweep.An extension to move this with a motor is possible, however manual adjustment of the horizontal axis' position is easy and fast.Through the semicircular structure, scanning is possible from oblique angles, in both vertical and azimuthal directions.The semicircular axes are equipped with gears to ensure that the carriage will move simultaneously on both semicircles axes, and to prevent any bending due to different movements.For moving the probe along the longitudinal axis of the muscle, the horizontal axis is realized as a spindle axis which is driven by a servomotor.The vertical movement of the ultrasound probe is actuated by a direct linear motor with an integrated drive.The position of the probe within the device coordinate system is recorded by encoders in all axes: The horizontal and the vertical axes include linear encoders measuring the position of the carriage in mm.The angular position of the horizontal axis in degree on the semicircles is recorded by a rotary encoder.The encoders of the horizontal and vertical axis scan the position every 2 ms, while the rotary encoder operates in 10 ms cycles.
Force Control: The direct linear motor of the vertical axis of the device has an inbuilt mechanism for force control applications.This force control mechanism works via a cascade controller in the drive inverter, which sequentially controls position, speed and motor current with a combination of proportionalintegral-derivative (PID) controllers.The motor current can be directly converted into applied force via the electromechanical properties of the motor.Through this mechanism, we ensure that the ultrasound probe makes contact with the skin with a consistent contact force.Therefore, muscle deformation due to probe pressure will be consistent.Different force settings in a range of 1 to 200 can be set by the user through an interface on the industrial PC.The corresponding force values in N have been determined experimentally and can be obtained from the fitted curve in Fig. 2. Different azimuthal angles can lead to different applied forces.Within one scan along the scanning length, the angle of the horizontal axis does not change, so the applied force does not vary within one sweep.Therefore, within one sweep, the tissue deformation over the scanning length will be consistent.For multiple sweep examinations, it is possible to adjust the force setting according to the current angle at the semi circles, as this can be computed using geometric relations.

B. Device Control
The a3DUS is controlled via an industrial PC with a custom written program in TWINCAT (version 3.1.4024.32)including four main movement modes illustrated in Fig. 3.For all modes, position information of the encoders are saved during the recording and can be exported in csv-format afterwards.Movement velocity of the axes can be set manually for all modes.For movement modes 2-4, the user can set a desired force setting as in Fig. 2.These movement modes are possible with contact force on the scanned medium or within a liquid medium (e.g.water).
1) Vertical Movement: The user specifies an end point on the horizontal axis.The device moves the probe to the end point.The probe is then moved upwards and downwards, until the user stops the acquisition.This mode is used for the temporal calibration of the a3DUS, therefore it is mainly used in a liquid medium, mainly a water bath.
2) Move to Target: The a3DUS moves to a user defined point on the horizontal axis.Then, the vertical axis moves down and presses on a surface until the user stops the acquisition.
3) Scanning Movement: The device moves from a defined start point to a defined end point on the horizontal axis.

4) Pendulum Movement:
The pendulum mode works the same way as Scanning Movement, but does not stop after reaching the endpoint.Instead, it moves back and forth between the start and endpoint until the user stops the measurement via a stop button.
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C. Synchronization
To synchronize the recording of the ultrasound images and the positional encoder data, a trigger signal is activated each time the device starts or stops a movement (Fig. 4).A custom written Python script receives the signal and starts or stops a recording in OBS studio (version 27.2.4).For the f3DUS trials, it is necessary to synchronize the recording of the ultrasound images with the motion capture system.To achieve this, we used a custom-written LABview script (version 2021.0).It is also possible to synchronize the encoder data with the motion capture data.For this, the device sends a trigger signal (5 V) to the motion capture acquisition board's trigger input and starts or stops a recording in VICON.

D. System Calibration
1) Spatial Calibration: Spatial calibration is the process of determining the transformation between the ultrasound image pixel coordinates in the image plane and the coordinate system of the device.We used a Z-wire phantom [37] to spatially calibrate the a3DUS.This phantom consists of 5 nylon wires (diameter 0.3 mm) on top of each other in a Z-shape.The intersection of the image plane and each wire is visible as a point on the ultrasound image.Due to the known geometry of the phantom, the pixel positions in the ultrasound image can be mapped to the device coordinate system.
2) Temporal Calibration: For determining the temporal offset between the ultrasound images and the encoder data, the device moves the probe up and down in a water tank in Vertical movement mode, where the vertical movement of the bottom of the water tank is visible in the ultrasound images as a line moving up and down.The line position in the image can be computed  automatically using a random sample consensus (RANSAC) algorithm.We then defined the time-offset by a cross correlation of the positional encoder data and line position in the image.

E. 3D Reconstruction
For the reconstruction of the ultrasound images to a 3D volume, the following sequence of transformations between coordinate systems needs to be applied (Fig. 5): Rec describes a defined reconstruction volume, Dev is the device coordinate system, I the ultrasound image plane.Therefore, I x x x and R x x x are the positions of each image pixel in image and reconstruction space.Rec T T T Dev is the transformation from the device coordinate system to the reconstruction volume space, Dev T T T P r is the transformation from probe to device coordinates, P r T T T I is the transformation from the image scan plane to the probe coordinate system, this transformation is obtained from the calibration protocol.Dev T T T P r can be obtained from the encoder data.This transformation consists of a translation T T T t and a rotation R R R. For the rotation around the horizontal z-axis, a rotation matrix is applied.The translation vector is composed of the z position which can be directly determined by the horizontal axis encoder.The y positions can be determined from the information of the vertical and rotary encoders.The device coordinate system's origin is located in the center of the semicircle at ϕ = 0 • .Further, with ϕ being the angle from the rotary encoder in degrees, r the semicircle radius (300 mm), v the current location of the vertical axis in mm and h is the current location on the horizontal axis in mm.Translation and rotation can be combined in a 4 × 4 roto-translation matrix: For defining the reconstruction volume, we applied a principal component analysis (PCA) on the coordinates of the corners of the ultrasound image frames to rotate the image stack.After rotation, x-and y-axis in Rec determine the image plane.We then shifted the image stack to the smallest possible volume in this orientation.We chose the voxel spacing in the reconstruction volume as the pixel spacing in x-and y-direction and in z-direction (scanning direction), voxel spacing is the product of the actual length of the image stack and the inverse of number of images.
We assigned image pixel values to the reconstruction volume by applying a nearest-neighbour algorithm.This step is called bin-filling.In case of incomplete filling during the bin-filling step, we used another nearest-neighbour algorithm to fill empty voxels in a hole-filling step.We exported the reconstructed and filled volume as VTK files.All of these steps were implemented with custom code written in Matlab (R2020a).

F. Experimental Trials
We used two custom designed phantoms, cast in a customdesigned 3D printed mold.Both phantoms consist of a mixture of distilled water, evaporated milk, n-propanol in a 2% agarose concentration, and silicon dioxide powder for soft-tissue-like scatter [38], [39].The muscle-like phantom (Fig. 7(a)) has an idealized shape of a muscle cut along it's longitudinal axis, a cylinder with narrow ends and a muscle belly with a larger crosssection.The cylindrical phantom (Fig. 7(d)) is a cylinder with a length of 170 mm and a diameter of 20 mm.The volume of the cylindrical phantom can be computed from geometric relations.For the muscle-like phantom, we used water displacement to determine the volume.Both phantoms are placed in a cuboid mold.The mold surrounding the phantom is filled with a material consisting of a 4% agarose mixture, similar to the phantom material, however without included scattering powder, so that the phantom can be clearly delineated in the ultrasound image.Due to the cuboid shape of the phantoms mold, the surface of the phantoms over which the ultrasound transducer moves is straight.
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We placed the phantom cuboid blocks on a table for conducting measurements.For avoiding sliding of the phantom, we used screw clamps to attach wooden boards on the table which touched the phantom sidewalls.Therefore, the phantom blocks were hold on place by the wooden boards.
The experimental protocol was designed as follows: At first, we scanned the muscle-like phantom 8 times using the a3DUS with force setting 25, which corresponds to 4.5 N. Further, we used the a3DUS to scan the cylindrical phantom in 3 different force settings: low, moderate and high (force settings 1, 100 and 200, corresponding to 4.1 N, 5.5 N and 6.5 N).Each scan of the contact forces was repeated 8 times.We will refer to these trials in the following as automated.The duration for each scan for the automated trials was 17 seconds for TA trials and 15 seconds for phantom trials.
We also conducted f3DUS trials where two different operators manually scanned the cylindrical phantom with four different contact force modes: (1) the operators were not told to scan with any specific contact force, just so that scanning feels comfortable for the operator.We will refer to this in the following as individual force.The operators were then told to apply (2) low contact force, (3) moderate contact force, and (4) high contact force.Each scan of the contact forces was repeated 8 times.The duration time for freehand trials ranged from 9-20 seconds for phantom trials and 11-19 seconds for TA trials.
Since the operators should freely adjust the contact forces to the defaults "low", "moderate" and "high", they differ accordingly between the operators and also between a3DUS and f3DUS.This was deliberately chosen since in the real clinical setup the contact forces of the sonographers are also not subject to precise specifications.
We also collected data from a human TA of a healthy 22 year old female subject (height 166 cm, weight 57 kg).The experimental procedures involving human subjects described in this paper were approved by the University of Stuttgarts Committee on Responsibility in Research (number: Az. 21-011, date: 12 July 2021).We used the a3DUS to scan the TA of the same subject with two different force settings (1 and 200).For the analysis of the TA, one operator also conducted f3DUS scans.In both the manual and the automated TA scanning protocol, the measurement was repeated 10 times.For both manual and automated scans, we applied large amounts of ultrasound transmission gel.

G. Volume Analysis
We used The Medical Imaging Interaction Toolkit (MITK, v2021-02) for segmentation of our volumes.For the phantom data, we first applied a Watershed transformation for segmenting the phantom's cross section.We then manually corrected for inaccurate automatically segmented slices.For muscle data, we segmented several slices and used the inbuilt algorithm of the program for interpolation between those slices to generate 3D volumes of the segmented slices.We exported the segmentations as nifti images.We computed the muscle and phantom volume and length from the segmentation images.We defined volume as the sum of the segmented voxels multiplied by their resolution in each dimension.Length was defined as the euclidean distance from the centroids of the first and last segmented slice (most proximal and most distal for TA).We computed the thickness from the segmented images as the maximum vertical distance in the cross-section (Fig. 6), after applying a PCA to get the segmentation in the right orientation, similar to the study of Raiteri et al. [8].

H. Statistical Analysis
For statistical analysis, we used a Kruskal-Wallis test for examining significant differences.Significance was defined as a p-value < 0.05.As a measure of statistical dispersion, we computed the mean coefficient of variation (CoV) for movement trajectories and thickness computations.

Fig. 7(b) and 7(d) show an exemplary reconstruction of the cylindrical and the muscle-like phantom from a3DUS trials
where the shapes of the reconstructed volumes visually align with the original phantoms.Fig. 7(e) and 7(f) show a reconstructed volume of the TA measurement with the three main planes and the segmented muscle.Fig. 7(g) illustrates a slice of the reconstruction volume in sagittal direction revealing the central aponeurosis and fascicle orientations within this plane.Table I lists volume and length measurements and mean error for the muscle-like phantom measured with the a3DUS.The average error was 0.94 mm (0.23%) for length and 0.08 ml (0.67%) for volume, indicating a high accuracy of the reconstructions.Volume and length analysis for the cylindrical phantom for automated scans and f3DUS trials with different operators is shown in Table II.For length measurements, both f3DUS scans show a higher mean error than the a3DUS scans, whereas for volume measurements, operator 2 has a slightly smaller mean error than the a3DUS scans.For the TA, volume results were 64.91 ± 1.21 ml for automated and 66.13 ± 3.16 ml for f3DUS trials, length measurements were 193.19 ± 0.62 mm for automated and 191.62 ± 1.24 mm for f3DUS trials.
For the cylindrical phantom, both f3DUS and a3DUS scans tend to underestimate the phantom volume, whereas for phantom length, the f3DUS scans slightly overestimate the trials while the automated trials slightly underestimate phantom length.Overall, errors for the muscle-like phantom are smaller for volume and length than for the cylindrical phantom.
In order to make sure that the validity of the proposed method is independent on movement variability, we ensured to minimize the inter-trial variability by enforcing a rather reproducible trajectory of the limb.Fig. 8 shows the image stack in the reconstructed volume for an automated and two different f3DUS TA muscle trials.We transformed the marker coordinates of the freehand scans into the probe coordinate system and compared the trajectories (Fig. 9).From visual inspection, we observed that the f3DUS trajectories show sliding movements in the left/right and up/down movement whereas the a3DUS trajectory shows straight lined up image stack.We found a mean CoV of 36% in x-direction (left-right), 71% in y-direction (up-down) and 12.63% in z-direction (forward-backward) for the f3DUS scans.This indicates a variation in movements when repeatedly conducting f3DUS scans compared to automated scans.We also observed a dispersion in movement trajectories in f3DUS scans for the phantom trials.
We computed the muscle and phantom thickness to determine the deformation over the muscle and phantom length for automated and f3DUS trials.We computed the deformation of the phantom as the difference of the original thickness of the known geometry and the computed mean thickness from 20 to 80% of the phantom length (top part of Fig. 11).In general, higher deformation values can be assumed with a higher contact force.Deformation values differ between a3DUS and f3DUS and Fig. 9. Marker and encoder trajectories in probe space.X-direction is left-right, Y-direction is up-down and Z-direction is forward-backward.
between the two operators, although force settings were similar, indicating operator-dependent contact forces.For a3DUS scans, the deformation increases relatively constant from low to high force setting.The mid and bottom part of Fig. 11 show the volume and length errors for the different force settings for a3DUS and f3DUS.For a3DUS scans, volume and length errors are overall small.According to Fig 11, larger volume errors are found at higher deformations, i.e. stronger contact forces, whereas this does not apply to length errors.The length errors are in general smaller for a3DUS scans than for f3DUS scans.The top part of Fig. 10 reveals a variation in thickness values for both operators and the automated scans for phantom trials.Thickness for moderate, high and individual force level are significantly different (p < 0.05) between operator 1 and operator 2 indicating an operator-dependency in the applied forces.Interestingly, for operator 1 all force levels besides the low and the individual differ significantly while for operator 2, all force levels besides the moderate and the individual force level differ significantly.The shaded areas in the bottom part of Fig. 10 show the standard Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Fig. 10.Mean thickness values over phantom length for automated scans and 2 operators.The shaded areas in the bottom part of the figure illustrate the standard deviations.Note that the absolute forces may differ for Low, Medium, and High settings between Operators and a3DUS, which explains between-user differences in thickness.deviation of the thickness over the phantom length for two force levels.For the automated trials, the dispersion is smaller than for the f3DUS trials indicating a lower variation between trials.For quantitative analysis, we computed the mean CoV for all trials (Table III) and found higher CoVs for the f3DUS trials than for the automated trials.We also computed the thickness of the TA over the muscle length (Fig. 6(b)) for automated and f3DUS scans as shown in Fig. 12. CoVs for muscle thickness were also lower for the automated scans, as listed in Table IV.We did not find significant differences in mean thickness over muscle length between automated and f3DUS scans.Also, muscle thickness did not differ significantly for automated scans with high and low pressure settings.

IV. DISCUSSION
In this paper, we introduced an automated 3D ultrasound system for enabling controlled 3D ultrasound measurements.Since the a3DUS can be used with any ultrasound machine, the current large ultrasound machine (Aixplorer MACH 30) used in this study can easily be exchanged with a portable one.Therefore, due to the currently relatively small size of the proposed a3DUS, it is a portable system and can be moved freely between rooms or institutions with different available ultrasound machines.In comparison with other 3D medical imaging modalities such as MRI, this enables more flexible 3D examinations.Furthermore, with the a3DUS, there is no need for a laboratory environment with an optical motion capture system.Therefore, the operator does not need to ensure no markers are hidden during measurements, which is particularly advantageous for complex experimental configurations.Therefore, the a3DUS can be used for clinical research for obtaining volumetric information of skeletal muscles.With the possibility to add another motor and conduct automated multiple sweep studies, the a3DUS is also capable of acquiring volumes of larger muscles.Thus, the a3DUS presents a less complex and portable alternative to other imaging techniques, such as MRI, which are currently used for these examinations.
We found a high accuracy in reconstructing the 3D volume of both the cylindrical and the muscle-like phantom for volume and length measurements.Furthermore, standard deviations for these parameters were smaller for the automated trials than for f3DUS trials indicating a more reproducible reconstruction of the scanned volumes when using the a3DUS.Effects on tissue deformation due to transducer pressure have been found in previous studies [13], [14].The higher CoVs for thickness for f3DUS scans demonstrate that the operators' applied force values also varies between scans.Furthermore, the operators applied different amounts of forces when they were told to scan the phantoms without considering the amount of applied force.Thus, there seems to be an operator dependency in applied force during f3DUS ultrasound acquisitions leading to errors of quantitative morphological measurements of skeletal muscle.Studies have developed hand-held or robot-assisted force control mechanisms to attach to an ultrasound probe [14], [19], [32], [35] to overcome this issue.However, previous studies [40], [41] cited effects of probe orientation on measurements of muscle thickness and pennation angle.The trajectories for f3DUS TA scans in our study show large dispersions also indicating probe tilt and rotation.These changes in trajectories and exerted force may be influenced by an appropriate level of training and experience on the part of the operator.Therefore, these variables should also be investigated in future studies.Still, our proposed a3DUS ensures consistent trajectories for repeated measurements and a stable probe orientation during the scan, regardless of the training or experience level.Furthermore, the implemented pendulum movement mode allows scanning along an axis repeatedly back and forth.When simultaneously enabling a controlled movement of the foot, the a3DUS can in future studies be used for advanced automated and controlled 3D dynamic investigations of skeletal muscle [42].This can provide completely new insights into the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.muscle during movement.Moreover, since the a3DUS can conduct measurements with ultrasound and is not designed for use in a water bath, data from other investigation methods such as EMG can be collected simultaneously ultrasound transparent electrodes [43] which can reveal new of the relation between muscle deformation and electrical activation.
The custom-designed device is an electrically driven ultrasound probe holder, which is constructed for the purpose of 3D ultrasound imaging.This can be beneficial, since the safety of the examined subject is ensured through the intrinsic construction.Therefore, if different subjects or body parts are be examined, then only minor settings have to be adjusted, such as the start and end positions of the scan trajectory.Such adjustment can be less simple for robot arms, which are configured for 3D ultrasound imaging.In comparison to other compact non-commercial 3D ultrasound systems that do not use a robot arm [28], [29], [30], the a3DUS enables scanning from oblique angles, which is relevant for scanning the curved surfaces of the human body.Other automated 2D ultrasound systems, however, ensure both patient safety and enable scanning from oblique angles by making use of passive mechanisms for ensuring a contact force on the skin [20], [21], [22].These systems are well-designed for 2D ultrasound examinations in the field of focused assessment with ultrasound for trauma [20], fetal ultrasound [21], and lung ultrasound [22].Here, the passive force mechanism is realized by a spring, which ensures contact between the skin and the probe.However, the spring applies a specific force only in a vertical downwards direction, and the force may vary for other probe angles [21].This suggests that the passive spring mechanism may deform tissues inconsistently along the scanning path, whereas consistent tissue deformation would be preferable for 3D ultrasound examinations.We thus consider an active force control mechanism, as realized in the a3DUS, to be more suitable for 3D ultrasound examinations of skeletal muscle.
In addition, [20], [21], [22] are designed for 2D ultrasound examinations and therefore do not include a position sensing mechanism.This means that the acquisition of the ultrasound probe position may rely on optical motion capture markers, which can lead to occlusion problems.
Furthermore, [20] and [21] would require an extended scan range to capture the TA or multiple other lower extremity muscles.
Therefore, the a3DUS enables force-controlled 3D ultrasound imaging from oblique angles, in a safe setup with low complexity.
Previous studies observed applied forces for ultrasound examinations is in a range of 5-20 N [44], [45].Lee et al. [46] found significant differences on TA thickness for inward probe pressures in the range of 1-4 N. Ishida and Watanabe [47] found significant changes in thickness of the transversus abdominis muscle for small forces under 2 N.These studies are in contrast to our findings on mean TA thickness which did not change significantly between low and high force level.One explanation is the force range we covered by our experiments, i.e. 4.1 N and 6.5 N.They did not reach a low enough force value to observe thickness changes, as were observed by Ishida and Watanabe.For further development, this range can be extended for larger and smaller force values.The current lower limit of 4.1 N exists because of the gravitational force due to the weight of the components attached to the vertical axis.By changing the materials of these components from metal to more lightweight materials such as plastics, this weight can be reduced and thus also decrease the lower force limit.With this, we can in future examine the effects of lower forces on the TA.
One limitation of our study is that we used the segmentation images from the semi-manual segmentation of the reconstruction volumes.Therefore, volume and length are dependent on the quality of the image segmentation.Even though standard deviations for computed volumes and lengths were low for both f3DUS and a3DUS scans, small changes in segmentation can result in errors in volume and length measurements.Also, segmentation inconsistencies can lead to changes in thickness distribution over length, which can also explain the spikes in the phantom thickness curve for the automated scans (Fig. 10).To be consistent with segmentation, all trials in our study were segmented by the same operator.However, a fully automatic segmentation algorithm could lead to an improvement in segmentation consistency and thus also volume and length computation accuracy.

V. CONCLUSION
In conclusion, the a3DUS allows accurate and reproducible measurements.The small size makes the a3DUS portable and therefore enables fast and flexible acquisition of 3D volumes of skeletal muscles.In future studies, the a3DUS can be used for static and dynamic investigations of healthy and pathological muscles, also combined with data collection with other techniques such as EMG.In future studies, we will use the a3DUS to obtain 3D images of other muscles as well, e.g., muscles of the torso.To further increase reproducibility, accurate positioning of the subject can be important.Therefore, it is useful for future studies to ensure that the subjects are clearly positioned relative to the device.This can be achieved by means of a design which is attached to the device and includes a fixture for the leg, or respectively the examined body part.
In addition, future studies should investigate the effects of the operator's level of experience.

Fig. 1 .
Fig. 1.Custom-designed device with its components.The red solid line illustrates the vertical direction, the red dashed line illustrates the azimuthal direction.

Fig. 4 .
Fig.4.Synchronization: Once a movement of the system is commenced using the industrial PC (IPC), it simultaneously sends a trigger to the laptop running OBS studio, which starts a video recording until it receives a stop signal.If desired, it also triggers a recording in the motion capture (MoCap) system.

Fig. 5 .
Fig. 5. Coordinate systems and transformations of the 3D ultrasound system, I: Image Pixel Coordinate System, Pr: Probe Coordinate System, Dev: Device Coordinate System, Rec: Reconstruction Volume.

Fig. 11 .
Fig. 11.Mean deformation, volume and length error for a3DUS and f3DUS scans and different force values for the cylindrical phantom trials.Errorbars indicate standard deviations.

TABLE IV COEFFICIENT
OF VARIATION FOR THICKNESS VALUES OF THE TA [%]