Applying microwave imaging in biomechanics: a feasibility study using tissue-mimicking phantoms

Applying microwave imaging in biomechanics: a feasibility study using tissue-mimicking phantoms | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Applying microwave imaging in biomechanics: a feasibility study using tissue-mimicking phantoms Vignesh Radhakrishnan, Peter Serano, Martin Robinson, Alex Marchant, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4793365/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Incorporating actual bone movement in kinematic pipelines has shown to reduce the influence of soft tissue artefacts (STA), a critical source of error, in clinical biomechanical analysis. Ultrasound imaging, a non-ionising and cost-effective imaging modality, has been extensively integrated in biomechanics to locate the underlying bone. However, limitations of needing a probe to be held at the location to be imaged and the need for coupling liquid, impedes their widespread applicability. In this study we explore the feasibility of applying another non-ionising and cost-effective imaging modality, microwave imaging, in biomechanics. By collecting data, from both simulated and experimental tissue-mimicking phantoms, under conditions aimed to emulate a wearable system, our results indicate that the underlying bone can be detected from the skin surface using microwave imaging. We believe our findings support the fidelity of microwave imaging as an alternative imaging modality to ultrasound imaging and underscore the need for further research in integrating microwave imaging in biomechanics. Health sciences/Medical research Physical sciences/Engineering Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1 Introduction Gait analysis, the study of human walking, is a clinical tool widely applied to aid in the diagnosis, rehabilitation and surgical planning of neurological and musculoskeletal pathologies, with additional applications in sports medicine 1 , 2 . Skin-mounted marker-based systems are the current gold standard for clinical gait analysis wherein passive (or active) markers are placed at specific landmarks on the human body; the trajectories of these markers are then analysed to qualitatively and quantitatively describe the gait pattern of an individual. Whilst widely applied skin-mounted marker-based systems (e.g. Vicon, Qualisys) boast sub-millimetre accuracies in marker tracking, the clinical usability of data generated by skin-mounted markers is significantly affected by soft tissue artefacts (STA) 3 , 4 . STA are discrepancies in marker movements (when compared with true bone movement) and are caused by the sliding, stretching and gravitational effects of the interposing soft tissues between the skin-mounted markers and the underlying bones, and can result in erroneous clinical outcomes 5 . STA are subject- and task-specific, which makes them difficult to compensate for and have a similar frequency content to actual bone movement, making traditional filtering methods ineffective. The above reasons are why they are considered the most critical source of error in clinical gait analysis 4 , 6 . A plethora of solutions — including pose-estimators, markersets and STA models — have been proposed to mitigate the deleterious effects of STA on clinical gait analysis 7 – 10 . However, no single solution has been found to be effective for all gait patterns and participants. Amongst the proposed solutions, pipelines which incorporate actual bone movement (henceforth referred to as artefact-free bone movement) — acquired using intracortical pins, percutaneous trackers or imaging modalities such as fluoroscopy, magnetic resonance imaging (MRI), or computed tomography — have been found to reduce the effects of STA significantly5,8,10–12. Artefact-free bone movement, acquired using imaging modalities, has been leveraged to investigate bone movements which are too small to be captured by skin-mounted markers, or whose movements are masked by kinematic errors associated with skin-mounted markers, such as STA 13 – 15 . Two notable studies proposed incorporating artefact-free bone movement, acquired using ultrasound imaging, to compensate for STA 12 , 16 – 18 . One study advanced an intelligent skin-mounted ultrasound sensor to determine the actual location of the bone in the lab coordinate system by leveraging two distance vectors: the location of the skin-mounted sensor acquired using conventional skin-mounted marker-based systems; and the distance of the bone from the skin-surface calculated using ultrasound images 16 , 17 . The advanced sensor was tested on a femur immersed in a collagen bath, with rotation errors of 0.1 ◦ reported in the study. The second study proposed combining ultrasound imaging (acquired through a probe) with a skin-mounted marker-based system to track an anatomical landmark under subcutaneous tissues during motion 12 , 18 . The system was able to reconstruct the shape of the femur (by tracking the true location of the greater-trochanter) with fewer errors than conventional skin-mounted marker-based systems. Ultrasound imaging is a safe (non-ionising) and cost-effective imaging modality, with studies reporting the following advantages over MRI: flexible field of view, finer details, real-time dynamic imaging, flexibility to image different locations and the ability to image patients with surgical hardware 19 . However, the following drawbacks need to be overcome or mitigated to incorporate ultrasound imaging in biomechanical applications: the need for a probe to be held at the location to be imaged, the need for coupling liquid to improve resolution and the need for a radiologist’s input when images are unclear. Microwave imaging, also a safe (non-ionising), low power (negligible heating effects) and cost-effective imaging modality 20 , is an operator-independent imaging modality with the potential to be applied for imaging any part of the human body, thereby overcoming the above drawbacks of ultrasound imaging. Microwave imaging leverages the difference in electrical properties (permittivity and conductivity) between various tissues and between healthy and diseased tissues to detect and image the object of interest, and has been extensively applied in breast and brain tumour imaging 21 – 23 . Whilst incorporating microwave imaging in biomechanics is yet to be explored, studies have leveraged microwave imaging to determine the electrical properties of the bone in the human forearm 24 , human leg 25 and in the heel 26 . A typical microwave imaging system is static and incorporates an imaging domain, a radio-frequency switch, a vector network analyser and antennas (Fig. 1 ). The antennas are placed rigidly around the imaging domain, and both the antennas and imaging domain are immersed in a coupling liquid 27 . The antennas are optimised for working when immersed in a coupling liquid and a large number of antennas or scanning positions (when antennas are rotated around the imaging domain) are required to reconstruct the object of interest. Additionally, the systems are of considerable size: an enclosure of radius 22.4 cm and height 44.4 cm was used to image human forearms 24 ; a tank of height 8.2 cm and radius 2.7 cm was used to validate a bone phantom 32 . Therefore application of a generic microwave imaging as described above, would not be feasible for biomechanical applications, especially during motion. In this study we aim to investigate the feasibility of applying microwave imaging in biomechanics - through a wearable and portable system - specifically to determine the location of the bone from the skin surface. To emulate the potential requirements for a wearable and portable system, data will be collected without coupling liquid and using a limited number of antenna/scanning positions. The viability of detecting the location of the bone using microwave imaging will be tested on both simulated and experimental tissue-mimicking phantoms, and data will be collected using antennas designed to be in direct contact with the skin and to operate in the absence of coupling liquid. Through our study, we aim to evaluate whether microwave imaging can be used as an alternative imaging modality to ultrasound imaging in biomechanics. 2 Methods 2.1 Antenna development The antennas developed for this study were based on the dual-patch antiphase antennas proposed to work in the absence of any coupling medium whilst making direct contact with the skin 29 . The antennas incorporated a balun (180 ◦ phase and power splitter) with probe feeds placed on the opposite and far-side of the patches, to increase the penetration of the electric field into the human body. However, the balun leveraged in the initial 29 study (ZFSCJ-2-232-S+, Mini-circuits 30 ) did not allow for the development of a wearable device, with the baluns and matching circuit connected via cables (Fig. 2 a). Therefore, the following changes were made to the antenna proposed in the initial study 29 to tailor it for our investigation: The incorporation of a surface mount (SMT) balun (SYPJ-2-222+, Mini-circuits 31 ) to allow for the development of a wearable antenna The use of varying patch and substrate sizes to develop three antennas operating at different frequency ranges The antenna structure (printed circuit board [PCB], land design and traces on the antenna) were re-developed to incorporate an SMT balun. Probe fields were placed on the near-side (and opposite) of the patches to reduce power losses (Fig. 2 b). To investigate the effect of varying frequency ranges on reconstructed images, three dual-patch antiphase antennas operating at differing frequency ranges were developed. Three different resonant frequency ranges were chosen: 1.5 GHz. These frequency ranges were chosen to optimise both penetration into the human body and resolution of the reconstructed image 24 , 26 ,32 . Using our SMT antenna as the base, a parametric study was performed in Ansys High Frequency Simulation Software (HFSS) Electronics Desktop 2023R2 33 , where the substrate height and patch sizes were altered to maximise antenna efficiency (S11 and S21 parameters) at the requested centre frequency. A high-fidelity model of the antennas (including the traces, matching circuits, SMA connector and balun) were developed in Ansys HFSS 33 , with two antennas placed on either side of a cuboid (block) attributed with the dielectric properties of muscle (Fig. 3 ). The conditions for determining the most efficient antenna design were: Increased coupling with the muscle block, identified through lower S11 (reflection) levels. The condition was set as ’S11 (in dB) < -10dB’. Increased coupling with the antenna on the other side of the muscle block, therefore increasing penetration into the human body. This was identified through higher S21 (transmission) levels. The condition was set as ’S21 (in dB) >= -30dB’. The second condition had a greater weight than the first condition. The electrical properties of muscle were chosen for the block as they are the largest tissue by volume at the thigh, and muscle has an absorbing and highly resistive nature to the flow of electrical field. The block was of a sufficiently large size to prevent S21 parameters from being affected by surface currents (length: 18 cm, breadth: 18 cm, height: 6 cm). The three developed antennas are henceforth referred to as three antenna types. Table 1 Dimensions of leg phantom created to validate microwave imaging algorithms and the antennas Tissue mimicking material Dimensions Height (cm) Radius (cm) Bone 20 2.25 Muscle 20 Inner radius = 2.25 Outer radius = 6.25 Additionally, two antennas from each of the three developed antenna types were fabricated using commercially available materials for experimental validation. 2.2 Experimental phantom development A two-layer phantom of muscle and bone was developed to experimentally validate the feasibility of microwave imaging to detect the location of the bone from the muscle surface. The two-layer phantom was designed to represent the thigh of a human with an average BMI score where muscle makes up the largest proportion of tissue. Cylindrical moulds were 3d printed in acrylonitrile butadiene styrene (ABS) to cast both the muscle and bone portions of the phantom. The bone and muscle were designed to have a radius of 2.25 cm and 6.25 cm respectively, with both having a height of 20cm. The bone was fabricated using polyurethane impregnated with carbon black powder to provide the requisite permittivity and conductivity 34 . Isopropanol was added to the mixture to reduce the viscosity during the casting stage, aiding in the removal of large voids. The ratios are provided in Table 1 . The bone phantoms were removed from the ABS moulds and positioned in the moulds for the muscle. The muscle mixture was made from a mixture of ethanediol, deionised water, and salt held together with gelatine 35 . The mixture required heating to 60 ◦ C to ensure complete incorporation of the gelatine. The ratios of the materials used for the muscle layer are provided in Table 1 . Three phantoms were created using the above steps with two phantoms containing a bone layer and one phantom containing just muscle-mimicking layer. A layer of skin-mimicking material was not added to the phantom due to the following reasons: Whilst the gelatinous nature of the muscle provided sufficient support for the placement of antennas, it did not provide support for a solid layer of skin to be added, as the weight of a skin layer is substantially higher than that of the antennas. Alternative recipes for skin-mimicking phantoms required a higher temperature, which would have resulted in the melting of the gelatinous layer. The dielectric properties of the phantom materials were validated using the principle of resonant cavity perturbation (RCP) 36 . Specifically, a hollow metal cylinder, with holes in the top and bottom plates, resonates at approximately 1 GHz, with a Q-factor of 3000, when empty. When a sample of dielectric material is inserted into the sensor (Fig. 4 ), the resonant frequency and Q-factor reduce. This variation in resonant frequency and Q-factor is measured by a network analyser connected to the cavity, which determines the complex permittivity of the sample. 2.3 Data collection: Simulation Three simulated phantoms — of the same dimensions and materials as the experimental phantoms — were modelled in Ansys HFSS Electronics Desktop 2023R2 33 . Two of the phantoms were modelled with bones, with the bone in one phantom (simulation phantom 1) placed almost at a diametrically opposite location to the bone in the other phantom (simulation phantom 2). The bones were modelled as cuboids - to differentiate from experimental phantoms - with a width of 2.5 cm and height of 20 cm. The third phantom (simulation phantom 3) only consisted of the muscle layer and was used to obtain the reference or empty scan data. During simulation, 8 antennas (of a single antenna type) were placed equidistant on a circle around the phantom, with the dual-patches of the antennas in direct contact with the muscle layer (Fig. 5 ). Three simulations were performed for each of the three antenna types using: simulation phantom 1, simulation phantom 2 and simulation phantom 3 (empty phantom). All simulations were performed with a maximum delta value of 0.005, to ensure that both S21 and S11 parameters were accurate up to 60dB, and were performed in the frequency range of 0.5–2.3 GHz. S-parameters (both reflection and transmission) were recorded in each simulation. Additionally, electric field values inside simulation phantom 3 were recorded for each antenna type. A grid of 5 mm spacing was used to record the electric field values. The electric field was used in-lieu of the Green’s functions for the imaging algorithms discussed below. Computation of Green’s functions for inhomogenous background medium are computationally expensive and whilst the phantom used in this study has only muscle-mimicking material, the phantom is supposed to represent the human thigh, which is inhomogenous. To compare experimental and simulated models of the antennas, one antenna from each of the three antenna types was also simulated radiating into air and into material mimicking a human body. 2.4 Data collection: Experimental An antenna holder with eight slots was 3D printed to be placed around the experimental phantom to collect data. Two antennas of each type were fabricated. The data from the antennas were collected using a vector network analyser (VNA, 8714ES Hewlett Packard) with the VNA calibrated prior to data collection. S-parameters (S11 and S21) were collected in the frequency range of 0.5–2.3 GHz. Two antennas of each type were slotted into the antenna holder placed around the phantom and reflection (S11) and transmission (S21) parameters were recorded (Fig. 6 ). One of the antennas was moved around the phantom (using the remaining slots) and 35 measurements were recorded for each type of antenna and for each phantom. Overall, each type of antenna had three sets of data (experimental phantom 1, experimental phantom 2 and experimental phantom 3) with 35 measurements per set of data. In addition, reflection parameters (S11) were recorded for each antenna type with the antenna radiating into air and when placed against the skin (radiating into the human body). This was done to compare simulated and fabricated models of the antenna. 2.5 Imaging algorithms and metrics Two qualitative imaging algorithms, the multiple signal classification algorithm (MUSIC) 37,38 and the Kirchhoff migration algorithm 39,40 were investigated. MUSIC is built on the principle of time-reversal and has been extensively applied in microwave imaging 21 ,41 . In this study, the multi-frequency variant of MUSIC was leveraged to reconstruct images at each frequency and non-coherently sum them to produce the final image. This was done to reduce artefacts in the reconstructed image and build on additional information obtained at multiple frequencies 42 . In addition, electric field values inside the phantom — computed in the empty phantom simulations (simulation phantom 3) — were used in-lieu of the Green’s function. Similarly, a multi-frequency variant of Kirchhoff migration was investigated in this study. Kirchhoff migration has also been widely applied in microwave imaging 39,40 and has been reported to be a fast, stable and effective imaging technique for detecting small scatterers 43 . The multi-frequency variation of Kirchhoff migration reportedly produces better results than its single-frequency variations 44 . For both experimental and simulated S-parameters, data from a phantom containing a bone were subtracted from data recorded using the empty phantom, which were then fed to the imaging algorithm to reconstruct images and determine the location of the bone from the muscle surface. For reconstructing images based on simulated data, the electric fields recorded using the empty simulated phantom (simulation phantom 3) for each antenna type were used (in lieu of the Green’s function). For image reconstruction based on experimental data, two analyses were pursued: for experimental phantom 1 reconstruction, the difference in data collected from experimental phantom 1 and the simulation phantom 3 was leveraged; for experimental phantom 2 reconstruction, the difference in data collected from the experimental phantom 2 and experimental phantom 3 was used. This was to validate whether simulated empty scans can be used in-lieu of experimental empty scans. For both simulated and experimental phantom image reconstructions, only transmission data (S21) were leveraged. This was informed by both, studies leveraging transmission parameters collected from antennas diametrically opposite to the transmitting antenna 45,46 , and from our initial investigation into microwave imaging 47 . Visual verification of the reconstructed images was initially done to determine if a hotspot (an indication of a scatterer) was present close to the true bone locations. In addition to visual verification, three metrics were used to evaluate the accuracy of the reconstructed image 21 ,48 : Signal-to-cluster ratio (SCR), signal-to-mean ratio (SMR) and localisation error. SCR compares the maximum response within the object of interest to the maximum response in the region outside the object of interest, and SMR compares the maximum response within the object of interest to the average response outside the object of interest. Localisation error is difference between the expected centre of the object of interest to that of the maximum response in the image. A higher SCR and SMR indicate a high-contrast localised region within the image. For all the metrics, the object of interest was the bone (specifically, the femur). 3 Results 3.1 Antennas Three antennas incorporating an SMT balun and operating at different frequencies were developed through the parametric study (Fig. 7 ). Antenna 1 had the same overall size as the antenna model proposed in the original study 29 , but with a centre frequency at 0.653 GHz (the antenna model proposed in the original study resonated at 0.9 GHz). Antenna 2 resonated at 0.85 GHz and had a smaller substrate thickness and smaller patch sizes compared with antenna 1. Antenna 3 resonated at 1.75 GHz and had the same substrate thickness as antenna 1 but with smaller patch sizes. The dimensions of the three antennas are provided in Table 2 . Table 2 Dimensions of the three variations of dual-patch antiphase antennas developed for this study Antenna Length (mm) Breadth (mm) Height (mm) Antenna 1 Board: 50 Patch: 22 Board: 20 Patch: 18 Board: 1.6 Antenna 2 Board: 50 Patch: 14 Board: 20 Patch: 10 Board: 1.2 Antenna 3 Board: 50 Patch: 14 Board: 20 Patch: 10 Board: 1.6 The three antennas were fabricated on commercially available FR-4 substrates of varying thickness (Table 2 ). All antennas were fabricated with outer copper weight of 1oz. S11-parameters of the fabricated antennas closely matched the S11-parameters of the simulated antennas when radiating into air (Fig. 8 a-c) and muscle (Fig. 8 d-f). 3.2 Phantom properties Three tissue-mimicking multi-layered bone phantoms were created (Fig. 9 ), with two phantoms, experimental phantom 1 and experimental phantom 2, had the bone located at two different locations; the third phantom (experimental phantom 3) was made of just muscle-mimicking material, which was then used to obtain the reference or empty scan data. Phantom 1 had the bone located on the line connecting diametrically opposite antennas, antenna 1 and antenna 5, with the position slightly closer to antenna 5 (Fig. 9 a). Therefore, the bone was placed away from the centre position when viewed from antenna 1. Phantom 2 had the bone located in the region spanned by antenna 5 and antenna 7. Therefore, the bone was located towards the left and away from the centre when viewed from antenna 1 (Fig. 9 b). Experimental data were collected using the antenna holder and two antennas of each antenna type (Fig. 6 ). Table 3 Comparison of permittivity values between manufactured muscle and bone mimicking tissues and theoretical values at 1 GHz Tissue name Theoretical value at 1GHz Experimental value at 1GHz Permittivity (F/m) Conductivity (S/m) Permittivity (F/m) Conductivity (S/m) Bone 12.4 0.2 12.5215 0.3414 Muscle 54 0.9 35 0.4 Cylindrical samples of length 40 mm and diameter 12 mm were created from the bone and muscle phantoms. These samples were used to determine the dielectric properties of each tissue-mimicking layer through the principle of resonant cavity perturbation. The permittivity of the bone and muscle samples, in addition to theoretical values obtained from the IT’IS database 49 are provided in Table 3 . 3.3 Image reconstruction Our results indicate that the bone was detected — in both simulated and experimental phantoms — for the three antenna types (antennas resonating at different frequencies) and for all investigated imaging algorithms. The presence of the bone (scatterer) was indicated by visual verification and through the three metrics: SMR, SCR and localisation error. Images could not be reconstructed for experimental phantom 2 using data collected from antenna 3, due to corruption of a subset of data. Further data collection for experimental phantom 2 was impeded by shrinking of the phantom due to evaporation of water from the tissue-mimicking layer. Additionally, the outcome of experimental phantoms could only be verified visually; metrics could not be computed as the true location of the bone in the phantom could not be computed. 3.3.1 Image reconstruction: simulated phantoms Bones were visually detected in both simulated phantoms (simulation phantom 1 and simulation phantom 2) using all three antenna types and both the imaging algorithms (Figs. 10 – 12 a-d). Metrics indicated that images reconstructed using antenna 3 indicated the presence of the bone with higher fidelity and accuracy than antennas 1 and 2. SMR values were maximum for images reconstructed using antenna 3 for both the simulated phantoms and using both the algorithms (MUSIC: 13.3 dB, 11.92 dB; Kirchhoff migration: 16.35 dB, 14.62 dB) (Table 4 ) with images reconstructed using antenna 1 having the smallest SMR values (MUSIC: 7.27 dB, 7.04 dB; Kirchhoff migration: 8.86 dB, 8.57 dB). Within antenna SMR values for simulated phantom 1 were greater than for simulated phantom 2, for both the imaging algorithms and all the antenna types (Table 4 ). For images computed using MUSIC, localisation errors reduced from antenna 1 to antenna 3, with maximum localisation errors less than 2.4 cm. For images computed using Kirchhoff migration, comparable localisation errors were obtained for all antennas, with maximum localisation error less than 2.4 cm (Table 4 ). SCR values were between − 1 and 1 dB for all reconstructed images. Table 4 Comparison of SMR, SCR and localisation errors between the three antenna types, using the two imaging algorithms for the two simulated phantoms. SCR, signal-to-cluster ratio; SMR, signal-to-mean ratio; DAS, delay-and-sum confocal imaging; DMAS, delay-multiply-and-sum confocal imaging; MUSIC, multiple signal classification; Phantom Algorithm SMR (dB) SCR (dB) Localisation error (cm) Simulated phantom 1 MUSIC 7.27 11.12 13.30 -0.69 0.14 0.39 2.11 1.45 0.39 Kirchoff 8.86 14.48 16.35 -0.89 -0.2072 -0.08 2.30 2.30 2.27 Simulated phantom 2 MUSIC 7.04 10.57 11.92 -0.31 0.62 0.27 2.11 1.35 0.53 Kirchoff 8.57 13.0 14.62 -0.78 0.01 0.26 2.31 2.28 2.23 3.3.2 Image reconstruction: experimental phantoms Bones were also visually located in reconstructed images of experimental phantoms. Through visual verification, our results indicated that reconstructed images using antenna 2 showed the location of the bone with higher accuracy than antenna 1 and 3. For antenna 1, images reconstructed using MUSIC indicated the location of the bone with greater clarity than images reconstructed using Kirchhoff migration (Fig. 10 e-h). Specifically, reconstructed images of experimental phantom 1 using MUSIC accurately represented the location of the bone with images reconstructed using Kirchhoff migration indicated a spread and an offset. Reconstructed images of experimental phantom 2 using MUSIC and Kirchhoff migration represented the location to a high accuracy, with images reconstructed using MUSIC affected by scattering at the edge of the domain and images reconstructed using Kirchhoff migration again indicating spread and an offset (Fig. 10 e-h). Reconstructed images using data collected from antenna 2 (Fig. 11 e-h) indicated that the bone could be successfully located in both experimental phantom 1 and experimental phantom 2 when MUSIC was leveraged with Kirchhoff migration representing the location of the bone to high accuracy for experimental phantom 1, and with lesser accuracy in experimental phantom 2. Bones were again visually located in experimental phantom 1 (Fig. 12 e-h) using data collected from antenna 3 and leveraging both MUSIC and Kirchhoff migration, with reconstructed images indicating that MUSIC produced lesser artefacts and spread compared to Kirchhoff migration. 4 Discussion The primary aim of this investigation was to validate — experimentally and in simulation — the efficacy of applying microwave imaging in biomechanics, specifically to determine the location of the bone from the skin surface. The data were collected under specific conditions, with a limited number of antenna positions and no coupling liquid, to mimic a wearable system. Our results indicate that microwave imaging can be applied to determine the location of the bone from the muscle surface, with the bone located successfully in reconstructed images of both simulated and experimental phantoms. Various antenna models have been proposed for microwave imaging applications, with the majority of the designs optimised to work when immersed in a coupling liquid 21 ,50,51 . However, the need to incorporate coupling liquid makes the development of a wearable system infeasible or not cost-effective and cumbersome. Novel antennas — incorporating metamaterials 52–54 , custom-made materials 55 or unique designs 29 ,56 — have been proposed to alleviate the need for coupling liquid. For example, one suggestion which removed the need for a coupling liquid and provided direct contact with the imaged body was an ultra-wide band horn antenna incorporating a substrate of dielectric value equal to that of the average permittivity of the breast tissue 57 . However, the antenna was fabricated using expensive materials, thereby increasing the cost and reducing the cost-effectiveness of microwave imaging applications. The novel on-body antenna design that was chosen as the baseline model in this study, was designed to work in the absence of any coupling liquid and maintain direct contact with the skin 29 . The proposed antenna model incorporated two patches, fed in anti-phase through a balun, with the antennas fabricated using commercially available materials (FR-4) and established fabrication techniques, thereby making them a more cost-effective option. The antenna model was reported to radiate lesser power into the body than a typical cell phone (radiating 0.1 W into the wrist 29 ) and had been applied to distinguish transmission (S21) parameters acquired from healthy and osteopenic bones. However, the components used in the antenna were not conducive with a wearable device. In our study, we built on this baseline antenna model 29 to develop wearable antennas which have the same form factor as the initial design, but with all the components mounted on the antenna. This was accomplished by modifying the existing design to incorporate an SMT balun, thereby requiring a change in the overall design to reduce power loss. Additionally, we also developed three antennas operating at different frequencies to evaluate the effect of frequency on microwave imaging results. The development was done using a parametric study to optimise both coupling into a slab of muscle and penetration into the muscle. The developed antennas exhibited reasonable coupling and penetration, with the three antennas resonating at three different centre frequencies. The three antenna types were furthermore fabricated using commercially available materials, with all antennas being lightweight allowing for the development of a wearable device using 8 antennas. The experimental reflection (S11) parameters of the fabricated antennas showed a good match to the simulated S11 parameters when the antennas radiated in air and when the antennas were placed against a human body. Furthermore, the S11 parameters also indicated that the antennas were optimised to work when in direct contact with the human body. To the best of our knowledge, the phantom developed in our study was the first multi-layered solid bone phantom developed comprising muscle and bone layers. As microwave imaging has predominantly been applied for imaging the breast and the brain, majority of the tissue-mimicking phantoms have been developed to mimic electrical properties of breast and brain tissues 58–60 . We were only able to identify one study which proposed recipes for multi-layer bone phantoms for microwave imaging 34 . These authors described the mixtures and methodology to reproduce liquid and solid tissue-mimicking bone phantoms, with liquid-based phantoms consisting of skin, muscle, cortical bone and trabecular bone layers, and the solid-based phantoms consisting of skin, cortical bone and trabecular bone layers. The solid-based phantoms were made using mixtures of carbon black, graphite, urethane and isopropanol. However, the proposed solid-based phantoms consisted of just bone and skin layers which are not representative of the human body. In our study, we complemented the mixtures for solid-bone based phantom 34 with the muscle-mimicking recipe — incorporating mixtures of ethanediol, deionised water and gelatine — proposed for the development of dielectrically and thermally stable mixtures of fat and muscle 35 . Our developed tissue-mimicking materials showed both a good match to theoretical values, but more pertinently indicated a large enough contrast between bone and muscle layers — which is crucial for microwave imaging. The phantom also indicated good mechanical stability during data collection (was able to support 2 antennas and the antenna holder). Additionally, the dielectric properties of the bone layer closely matched the results obtained in the baseline study 34 (relative permittivity of 13 at 1 GHz). With respect to simulation results, visually, antenna 3 was able to detect the location of the bone with higher accuracy than antennas 1 and 2. Notably, the images reconstructed using antenna 1 had a significant spread and the images reconstructed using antenna 2 only detected the edges of the bone closest to the muscle surface. This is also reflected in the SMR and localisation metrics, as the reconstructed images produced using antenna 3 had the highest SMR values and smallest localisation errors. The smallest SMR and SCR values were obtained for images reconstructed using antenna 1, which can be attributed to the hotspot artefact (a high-intensity region that does not correspond to any known locations of scatterers 61 ) observed close to the centre. The poorer performance of antenna 1 can also likely be attributed to the relationship between lower frequencies and loss in image resolution. Antenna 1 resonates at a frequency considerably lower than that of antenna 3 (0.63 GHz versus 1.65 GHz respectively) and hence would have proportionally poorer image resolution. The reason antenna 2 was only able to detect edges closest to the muscle surface, can likely be attributed to the antenna model. Despite the antenna resonating at a centre frequency (0.8 GHz) which allows for both considerable improvements in resolution and penetration, the S11 parameters of simulated antenna 2 indicate that the antenna is not as optimally designed as simulated antenna 3, with only 40% of the signal being transmitted into the phantom. Antenna 3 produced the best results for simulated phantoms as indicated by higher SMR values and lower localisation errors and can be attributed to a high image resolution obtained by its high resonant frequency and the considerable coupling achieved with the phantom — as indicated by S11 and S12 (Fig. 8 ). The variation in the results between simulation phantom 1 and simulation phantom 2 for each antenna type can be attributed to the difference in the location of the bone in the muscle phantom. The bone phantom was located closer to the surface in simulation phantom 1 compared to simulation phantom 2. Our experimental results indicate that microwave imaging can be applied to locate the bone from the surface of the phantom. Visual verification — which is widely applied in microwave imaging applications 21 ,62,63 — indicates that the bone was successfully located in both the phantoms. In contrast to the simulation results, reconstructed images of experimental phantom 1 using antenna 3 indicated an offset with considerable spread of the high-intensity region (when reconstructed using both MUSIC and Kirchhoff migration). Whereas reconstructed images using both antennas 1 (leveraging MUSIC) and 2 indicated a very high accuracy in determining the location of the underlying bone in both the experimental phantoms. Images of experimental phantom 1 were reconstructed using the difference between data collected using experimental phantom 1 and simulation phantom 3, whilst images of experimental phantom 2 were reconstructed using the difference between data collected using experimental phantom 1 and experimental phantom 3. This may account for the differences in reconstructed images of the two experimental phantoms when using data collected from the same antenna. As our results indicate, whilst the contrast in permittivity between muscle-mimicking layer and bone-mimicking layer were sufficient for the application of microwave imaging, the permittivity values of both the layers (especially the muscle) varies from their respective theoretical values. With simulation phantom 3 attributed with theoretical values of muscle, the differences in the reference scan data (simulation phantom 3 vs experimental phantom 3), may affect the fidelity of the results as the same electric field values were used in the reconstruction of both experimental phantoms. Our results indicate that the performance of antenna 3 was relatively between than antenna 1 and antenna 2 in reconstructing simulation phantoms whilst antenna 2 performed relatively better in reconstructing experimental phantoms. We hypothesise that the variation in antenna performance can be, in part, attributed to the differences between fabricated and simulated antennas, coupled with the differences between simulated and experimental phantoms as discussed above. Our results show that fabricated antenna 2 had better coupling with human-tissue equivalent materials compared to simulated antenna 2. This could have affected the performance of simulated antenna 2. Antenna 3’s performance on experimental phantoms could be attributed to the differences in permittivity between simulated and experimental phantoms, thereby affecting its performance. Notably, our results indicate that images can be successfully reconstructed using experimentally collected data with reference (empty scan) data obtained from simulations. Therefore, empty experimental phantoms do not need to be manufactured for most applications, thereby underscoring the applicability of microwave imaging in biomechanical applications. To reconstruct the images for both the simulated and experimental phantoms, we leveraged two qualitative imaging algorithms: MUSIC and Kirchhoff migration. These two algorithms have primarily been applied to detect small scatterers, with their efficacy varying for extended scatterers 39,64 . Our results obtained using MUSIC — particularly those from the experimental phantoms using antenna 3 — indicated a spread of high-intensity area which represents multiple scattering inside the phantom instead of localising scattering at the boundary of bone and muscle. Similar results were obtained by 64 , who observed that whilst MUSIC can be successfully be applied to determine the location of the scatterer, its ability to determine shape is less effective for extended scatterers. Our results obtained using Kirchhoff migration indicated that the quality of reconstructed images — assessed visually in terms of detecting the location of the bone — improved with higher frequencies, in both simulated and experimental phantoms. Whilst Kirchhoff migration has been noted as a fast, stable and effective imaging technique 43 , it is more sensitive to model assumptions and noise compared with MUSIC. We hypothesise that this may explain our results obtained using Kirchhoff migration, as they exhibit a greater spread and offset when compared with images reconstructed using MUSIC. Despite the spread, the location of the bone was successfully determined from images reconstructed using Kirchhoff migration for all experimental phantoms. Key limitations of this study were the mismatch between theoretical and experimental permittivity values of the muscle-mimicking layer, and the lack of true bone position in experimental phantoms which rendered the computation of imaging metrics for experimental phantoms infeasible. An additional limitation of this study is that the metrics used for the detection of point-like scatterers are non-transferable to extended scatters. For example, despite our reconstructed images indicating the bone has been located at the true edge of the bone, the localisation errors computed from the centre of the bone to the centre of the high-intensity region may generate a large value. Therefore, there is a need for the development of metrics suitable for extended scatterers. In conclusion, we have validated — both experimentally and in simulation — that microwave imaging can be effectively applied in biomechanics, specifically to determine the location of the bone from the skin (muscle) surface. The data collected in this study were taken under specific conditions — fewer number of antenna positions and no coupling liquid — to facilitate the development of a wearable system. We believe our results may be used to further research into the biomechanical application of microwave imaging; in particular, as an alternative to currently used imaging modalities such as ultrasound imaging. Declarations Author Contribution V.R conceived the experiments, conducted the experiments, analysed the results and wrote the manuscript; A.M, T.J.D and M.R assisted in the refinement of methodology, manufactirung of the phantoms and analysed the results; P.S assisted in the methodology of the simulation and analysed the results; S.P and A.P supervised the project. All authors reviewed the manuscript Data Availability Data available upon reasonable request from the corresponding author Additional information The authors declare no competing interests. References Scafetta, N., Marchi, D. & West, B. 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Application of MUSIC algorithm in real-world microwave imaging of unknown anomalies from scattering matrix. Mech. Syst. Signal Process. 153, 107501 (2021). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4793365","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":345483550,"identity":"c6be84ee-057b-4da8-a2c3-627b3f4966a6","order_by":0,"name":"Vignesh Radhakrishnan","email":"data:image/png;base64,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","orcid":"","institution":"University of York","correspondingAuthor":true,"prefix":"","firstName":"Vignesh","middleName":"","lastName":"Radhakrishnan","suffix":""},{"id":345483552,"identity":"bdf8c8c7-4805-4011-a516-e10a06ef23b1","order_by":1,"name":"Peter Serano","email":"","orcid":"","institution":"Worcester Polytechnic Institute","correspondingAuthor":false,"prefix":"","firstName":"Peter","middleName":"","lastName":"Serano","suffix":""},{"id":345483555,"identity":"6097436a-ddb3-45a2-a1b8-a5d9b0d552c9","order_by":2,"name":"Martin Robinson","email":"","orcid":"","institution":"University of York","correspondingAuthor":false,"prefix":"","firstName":"Martin","middleName":"","lastName":"Robinson","suffix":""},{"id":345483556,"identity":"77b09150-d7f7-4e6b-a56a-06778cee7a49","order_by":3,"name":"Alex Marchant","email":"","orcid":"","institution":"University of York","correspondingAuthor":false,"prefix":"","firstName":"Alex","middleName":"","lastName":"Marchant","suffix":""},{"id":345483557,"identity":"1da74b3e-5603-4aa8-8ba1-e80d5cebe01d","order_by":4,"name":"Taito J Dale","email":"","orcid":"","institution":"University of York","correspondingAuthor":false,"prefix":"","firstName":"Taito","middleName":"J","lastName":"Dale","suffix":""},{"id":345483558,"identity":"6cbb55e6-df60-4c96-83d5-f1df461a353f","order_by":5,"name":"Samadhan Patil","email":"","orcid":"","institution":"University of York","correspondingAuthor":false,"prefix":"","firstName":"Samadhan","middleName":"","lastName":"Patil","suffix":""},{"id":345483559,"identity":"5ac1264f-eb0c-431d-be22-de705d1331c4","order_by":6,"name":"Adar Pelah","email":"","orcid":"","institution":"University of York","correspondingAuthor":false,"prefix":"","firstName":"Adar","middleName":"","lastName":"Pelah","suffix":""}],"badges":[],"createdAt":"2024-07-24 07:51:44","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4793365/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4793365/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":64006456,"identity":"336eec0c-e362-4e47-9b5a-bcd12112b76f","added_by":"auto","created_at":"2024-09-04 21:51:22","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":69180,"visible":true,"origin":"","legend":"\u003cp\u003eThe general setup of microwave imaging systems, which consist of an imaging domain, an array of antennas, a vector network analyser and a radio-frequency switch\u003csup\u003e28\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/2f91114a01b5c4c8f60482e4.jpg"},{"id":64006461,"identity":"431048f5-789a-4b94-b6df-130693a434de","added_by":"auto","created_at":"2024-09-04 21:51:22","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":91831,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of antenna proposed by\u003csup\u003e29 \u003c/sup\u003eand our antenna. a) The dual patch antiphase antenna proposed by\u003csup\u003e29 \u003c/sup\u003ewhere the balun is connected by cables. b) Front and back sides of our modified dual patch antiphase antenna with a surface mount balun and SMA connector.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/0c951b2c2925dd8a9e554917.jpg"},{"id":64006457,"identity":"c111a491-7629-4cbc-b929-56c4a8cf9a3a","added_by":"auto","created_at":"2024-09-04 21:51:22","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":105712,"visible":true,"origin":"","legend":"\u003cp\u003eSetup for the parametric study to optimise antennas. The block is attributed with properties of muscle with the conditions of the study to determine the best parameters which optimise coupling and transmission through the block.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/22a8ce7e5b1b93835a6055bc.jpg"},{"id":64007641,"identity":"dbaefde9-bd8b-4fe5-8d62-6147968a547b","added_by":"auto","created_at":"2024-09-04 22:07:23","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":96038,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of the setup for the resonant cavity perturbation method for determining dielectric properties of tissue-mimicking materials\u003csup\u003e36\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/60e6936dd01233a5afb3ab2a.jpg"},{"id":64007485,"identity":"cb3dbab0-7a80-406c-ad02-b422021a3e56","added_by":"auto","created_at":"2024-09-04 21:59:22","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":27362,"visible":true,"origin":"","legend":"\u003cp\u003eSimulation environment of simulated phantom 1, where the square bone is embedded in a cylindrical muscle and 8 antennas are placed around and in contact with the cylinder. Cylinder is of height 20 cm and radius 6.25 cm.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/4001ee0e7f5d8239e7755ce9.jpg"},{"id":64007486,"identity":"d9a867c8-8242-4230-a80c-d144f55a6627","added_by":"auto","created_at":"2024-09-04 21:59:22","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":70360,"visible":true,"origin":"","legend":"\u003cp\u003eData collection from the experimental phantom and the antenna holder. The antenna slot closest to the camera is the location for antenna 1 and the second antenna is rotated around the phantom\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/80f215014c37b444fcecc5c9.jpg"},{"id":64006460,"identity":"d27213ec-a674-4e47-93ee-1dc0d28449bd","added_by":"auto","created_at":"2024-09-04 21:51:22","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":81983,"visible":true,"origin":"","legend":"\u003cp\u003eThree variations of antennas developed based on the dual-patch antiphase antenna proposed by\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/026a3d7db3cd88d3dc742539.jpg"},{"id":64006463,"identity":"ce95afba-e732-4f13-8fee-d49c2f2b66aa","added_by":"auto","created_at":"2024-09-04 21:51:22","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":83420,"visible":true,"origin":"","legend":"\u003cp\u003eComparisons of reflected parameters (S11) between simulated and fabricated antennas when antennas are radiating into air (a-c) and muscle (d-f)\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/bc6e1fd2b5736b96765540af.jpg"},{"id":64007488,"identity":"e33561e4-9de1-4019-9be8-47a0bb6e14f2","added_by":"auto","created_at":"2024-09-04 21:59:23","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":78334,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic vs manufactured phantoms. a) Schematic of phantom 1. b) Schematic of phantom 2. c) Schematic of phantom 3. d) Manufactured phantom 1. e) Manufactured phantom 2. f) Manufactured phantom 3\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/17bbe17a395c2bc917aa6d7c.jpg"},{"id":64007640,"identity":"479f32d4-98ad-458d-84e9-bde092db620d","added_by":"auto","created_at":"2024-09-04 22:07:22","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":118401,"visible":true,"origin":"","legend":"\u003cp\u003eReconstructed images of simulated and experimental phantoms using antenna 1. a) Reconstructed image of simulation phantom 1 computed using MUSIC. b) Reconstructed image of simulation phantom 2 computed using MUSIC. c) Reconstructed image of simulation phantom 1 computed using Kirchhoff migration. d) Reconstructed image of simulation phantom 2 computed using Kirchhoff migration. e) Reconstructed image of experimental phantom 1 computed using MUSIC. f) Reconstructed image of experimental phantom 2 computed using MUSIC. g) Reconstructed image of experimental phantom 1 computed using Kirchhoff migration. h) Reconstructed image of experimental phantom 2 computed using Kirchhoff migration. In all reconstructed images the red dots indicate antenna locations and the black dots indicate the location of the bone.\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/2cd3d61c9b6cd8c8e756743b.jpg"},{"id":64006468,"identity":"6c72f6d6-2931-4061-8c1a-3110cd029921","added_by":"auto","created_at":"2024-09-04 21:51:23","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":118780,"visible":true,"origin":"","legend":"\u003cp\u003eReconstructed images of simulated and experimental phantoms using antenna 2. a) Reconstructed image of simulation phantom 1 computed using MUSIC. b) Reconstructed image of simulation phantom 2 computed using MUSIC. c) Reconstructed image of simulation phantom 1 computed using Kirchhoff migration. d) Reconstructed image of simulation phantom 2 computed using Kirchhoff migration. e) Reconstructed image of experimental phantom 1 computed using MUSIC. f) Reconstructed image of experimental phantom 2 computed using MUSIC. g) Reconstructed image of experimental phantom 1 computed using Kirchhoff migration. h) Reconstructed image of experimental phantom 2 computed using Kirchhoff migration. In all reconstructed images the red dots indicate antenna locations and the black dots indicate the location of the bone.\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/6a59922514cbd364903e754b.jpg"},{"id":64006467,"identity":"c22a1425-0162-4d09-8015-2b100a2ed8a7","added_by":"auto","created_at":"2024-09-04 21:51:23","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":91852,"visible":true,"origin":"","legend":"\u003cp\u003eReconstructed images of simulated and experimental phantoms using antenna 3. a) Reconstructed image of simulation phantom 1 computed using MUSIC. b) Reconstructed image of simulation phantom 2 computed using MUSIC. c) Reconstructed image of simulation phantom 1 computed using Kirchhoff migration. d) Reconstructed image of simulation phantom 2 computed using Kirchhoff migration. e) Reconstructed image of experimental phantom 1 computed using MUSIC. f) Reconstructed image of experimental phantom 2 computed using MUSIC. g) Reconstructed image of experimental phantom 1 computed using Kirchhoff migration. h) Reconstructed image of experimental phantom 2 computed using Kirchhoff migration. In all reconstructed images the red dots indicate antenna locations and the black dots indicate the location of the bone.\u003c/p\u003e","description":"","filename":"12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/7f5ec77f988a2f8bf26fb96c.jpg"},{"id":70597670,"identity":"85e8f4aa-b450-422e-9f3e-867019cbfa35","added_by":"auto","created_at":"2024-12-04 18:38:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1653801,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4793365/v1/c752c1d3-be6b-415f-8b07-e0ed20010d26.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Applying microwave imaging in biomechanics: a feasibility study using tissue-mimicking phantoms","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eGait analysis, the study of human walking, is a clinical tool widely applied to aid in the diagnosis, rehabilitation and surgical planning of neurological and musculoskeletal pathologies, with additional applications in sports medicine\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Skin-mounted marker-based systems are the current gold standard for clinical gait analysis wherein passive (or active) markers are placed at specific landmarks on the human body; the trajectories of these markers are then analysed to qualitatively and quantitatively describe the gait pattern of an individual. Whilst widely applied skin-mounted marker-based systems (e.g. Vicon, Qualisys) boast sub-millimetre accuracies in marker tracking, the clinical usability of data generated by skin-mounted markers is significantly affected by soft tissue artefacts (STA)\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e,\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. STA are discrepancies in marker movements (when compared with true bone movement) and are caused by the sliding, stretching and gravitational effects of the interposing soft tissues between the skin-mounted markers and the underlying bones, and can result in erroneous clinical outcomes\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. STA are subject- and task-specific, which makes them difficult to compensate for and have a similar frequency content to actual bone movement, making traditional filtering methods ineffective. The above reasons are why they are considered the most critical source of error in clinical gait analysis\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eA plethora of solutions \u0026mdash; including pose-estimators, markersets and STA models \u0026mdash; have been proposed to mitigate the deleterious effects of STA on clinical gait analysis\u003csup\u003e\u003cspan additionalcitationids=\"CR8 CR9\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. However, no single solution has been found to be effective for all gait patterns and participants. Amongst the proposed solutions, pipelines which incorporate actual bone movement (henceforth referred to as artefact-free bone movement) \u0026mdash; acquired using intracortical pins, percutaneous trackers or imaging modalities such as fluoroscopy, magnetic resonance imaging (MRI), or computed tomography \u0026mdash; have been found to reduce the effects of STA significantly5,8,10\u0026ndash;12.\u003c/p\u003e \u003cp\u003eArtefact-free bone movement, acquired using imaging modalities, has been leveraged to investigate bone movements which are too small to be captured by skin-mounted markers, or whose movements are masked by kinematic errors associated with skin-mounted markers, such as STA\u003csup\u003e\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Two notable studies proposed incorporating artefact-free bone movement, acquired using ultrasound imaging, to compensate for STA\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. One study advanced an intelligent skin-mounted ultrasound sensor to determine the actual location of the bone in the lab coordinate system by leveraging two distance vectors: the location of the skin-mounted sensor acquired using conventional skin-mounted marker-based systems; and the distance of the bone from the skin-surface calculated using ultrasound images\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. The advanced sensor was tested on a femur immersed in a collagen bath, with rotation errors of 0.1\u003csup\u003e◦\u003c/sup\u003ereported in the study. The second study proposed combining ultrasound imaging (acquired through a probe) with a skin-mounted marker-based system to track an anatomical landmark under subcutaneous tissues during motion\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. The system was able to reconstruct the shape of the femur (by tracking the true location of the greater-trochanter) with fewer errors than conventional skin-mounted marker-based systems.\u003c/p\u003e \u003cp\u003eUltrasound imaging is a safe (non-ionising) and cost-effective imaging modality, with studies reporting the following advantages over MRI: flexible field of view, finer details, real-time dynamic imaging, flexibility to image different locations and the ability to image patients with surgical hardware\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. However, the following drawbacks need to be overcome or mitigated to incorporate ultrasound imaging in biomechanical applications: the need for a probe to be held at the location to be imaged, the need for coupling liquid to improve resolution and the need for a radiologist\u0026rsquo;s input when images are unclear. Microwave imaging, also a safe (non-ionising), low power (negligible heating effects) and cost-effective imaging modality\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, is an operator-independent imaging modality with the potential to be applied for imaging any part of the human body, thereby overcoming the above drawbacks of ultrasound imaging. Microwave imaging leverages the difference in electrical properties (permittivity and conductivity) between various tissues and between healthy and diseased tissues to detect and image the object of interest, and has been extensively applied in breast and brain tumour imaging\u003csup\u003e\u003cspan additionalcitationids=\"CR22\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Whilst incorporating microwave imaging in biomechanics is yet to be explored, studies have leveraged microwave imaging to determine the electrical properties of the bone in the human forearm\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e, human leg\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e and in the heel\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eA typical microwave imaging system is static and incorporates an imaging domain, a radio-frequency switch, a vector network analyser and antennas (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The antennas are placed rigidly around the imaging domain, and both the antennas and imaging domain are immersed in a coupling liquid\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. The antennas are optimised for working when immersed in a coupling liquid and a large number of antennas or scanning positions (when antennas are rotated around the imaging domain) are required to reconstruct the object of interest. Additionally, the systems are of considerable size: an enclosure of radius 22.4 cm and height 44.4 cm was used to image human forearms\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e; a tank of height 8.2 cm and radius 2.7 cm was used to validate a bone phantom\u003csup\u003e32\u003c/sup\u003e. Therefore application of a generic microwave imaging as described above, would not be feasible for biomechanical applications, especially during motion.\u003c/p\u003e \u003cp\u003eIn this study we aim to investigate the feasibility of applying microwave imaging in biomechanics - through a wearable and portable system - specifically to determine the location of the bone from the skin surface. To emulate the potential requirements for a wearable and portable system, data will be collected without coupling liquid and using a limited number of antenna/scanning positions. The viability of detecting the location of the bone using microwave imaging will be tested on both simulated and experimental tissue-mimicking phantoms, and data will be collected using antennas designed to be in direct contact with the skin and to operate in the absence of coupling liquid. Through our study, we aim to evaluate whether microwave imaging can be used as an alternative imaging modality to ultrasound imaging in biomechanics.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2 Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Antenna development\u003c/h2\u003e \u003cp\u003eThe antennas developed for this study were based on the dual-patch antiphase antennas proposed to work in the absence of any coupling medium whilst making direct contact with the skin\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. The antennas incorporated a balun (180\u003csup\u003e◦\u003c/sup\u003e phase and power splitter) with probe feeds placed on the opposite and far-side of the patches, to increase the penetration of the electric field into the human body. However, the balun leveraged in the initial\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e study (ZFSCJ-2-232-S+, Mini-circuits\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e) did not allow for the development of a wearable device, with the baluns and matching circuit connected via cables (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). Therefore, the following changes were made to the antenna proposed in the initial study\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e to tailor it for our investigation:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe incorporation of a surface mount (SMT) balun (SYPJ-2-222+, Mini-circuits\u003csup\u003e31\u003c/sup\u003e) to allow for the development of a wearable antenna\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe use of varying patch and substrate sizes to develop three antennas operating at different frequency ranges\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe antenna structure (printed circuit board [PCB], land design and traces on the antenna) were re-developed to incorporate an SMT balun. Probe fields were placed on the near-side (and opposite) of the patches to reduce power losses (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb).\u003c/p\u003e \u003cp\u003eTo investigate the effect of varying frequency ranges on reconstructed images, three dual-patch antiphase antennas operating at differing frequency ranges were developed. Three different resonant frequency ranges were chosen: \u0026lt;0.750 GHz, 0.750 GHz\u0026ndash;1.2 GHz and \u0026gt;\u0026thinsp;1.5 GHz. These frequency ranges were chosen to optimise both penetration into the human body and resolution of the reconstructed image\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,32\u003c/sup\u003e. Using our SMT antenna as the base, a parametric study was performed in Ansys High Frequency Simulation Software (HFSS) Electronics Desktop 2023R2\u003csup\u003e33\u003c/sup\u003e, where the substrate height and patch sizes were altered to maximise antenna efficiency (S11 and S21 parameters) at the requested centre frequency. A high-fidelity model of the antennas (including the traces, matching circuits, SMA connector and balun) were developed in Ansys HFSS\u003csup\u003e33\u003c/sup\u003e, with two antennas placed on either side of a cuboid (block) attributed with the dielectric properties of muscle (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The conditions for determining the most efficient antenna design were:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eIncreased coupling with the muscle block, identified through lower S11 (reflection) levels. The condition was set as \u0026rsquo;S11 (in dB) \u0026lt; -10dB\u0026rsquo;.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eIncreased coupling with the antenna on the other side of the muscle block, therefore increasing penetration into the human body. This was identified through higher S21 (transmission) levels. The condition was set as \u0026rsquo;S21 (in dB) \u0026gt;= -30dB\u0026rsquo;. The second condition had a greater weight than the first condition.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe electrical properties of muscle were chosen for the block as they are the largest tissue by volume at the thigh, and muscle has an absorbing and highly resistive nature to the flow of electrical field. The block was of a sufficiently large size to prevent S21 parameters from being affected by surface currents (length: 18 cm, breadth: 18 cm, height: 6 cm). The three developed antennas are henceforth referred to as three antenna types.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDimensions of leg phantom created to validate microwave imaging algorithms and the antennas\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTissue mimicking material\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eDimensions\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHeight (cm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRadius (cm)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMuscle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInner radius\u0026thinsp;=\u0026thinsp;2.25 Outer radius\u0026thinsp;=\u0026thinsp;6.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAdditionally, two antennas from each of the three developed antenna types were fabricated using commercially available materials for experimental validation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Experimental phantom development\u003c/h2\u003e \u003cp\u003eA two-layer phantom of muscle and bone was developed to experimentally validate the feasibility of microwave imaging to detect the location of the bone from the muscle surface. The two-layer phantom was designed to represent the thigh of a human with an average BMI score where muscle makes up the largest proportion of tissue.\u003c/p\u003e \u003cp\u003eCylindrical moulds were 3d printed in acrylonitrile butadiene styrene (ABS) to cast both the muscle and bone portions of the phantom. The bone and muscle were designed to have a radius of 2.25 cm and 6.25 cm respectively, with both having a height of 20cm. The bone was fabricated using polyurethane impregnated with carbon black powder to provide the requisite permittivity and conductivity\u003csup\u003e34\u003c/sup\u003e. Isopropanol was added to the mixture to reduce the viscosity during the casting stage, aiding in the removal of large voids. The ratios are provided in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe bone phantoms were removed from the ABS moulds and positioned in the moulds for the muscle. The muscle mixture was made from a mixture of ethanediol, deionised water, and salt held together with gelatine\u003csup\u003e35\u003c/sup\u003e. The mixture required heating to 60\u003csup\u003e◦\u003c/sup\u003eC to ensure complete incorporation of the gelatine. The ratios of the materials used for the muscle layer are provided in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThree phantoms were created using the above steps with two phantoms containing a bone layer and one phantom containing just muscle-mimicking layer.\u003c/p\u003e \u003cp\u003eA layer of skin-mimicking material was not added to the phantom due to the following reasons:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eWhilst the gelatinous nature of the muscle provided sufficient support for the placement of antennas, it did not provide support for a solid layer of skin to be added, as the weight of a skin layer is substantially higher than that of the antennas.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAlternative recipes for skin-mimicking phantoms required a higher temperature, which would have resulted in the melting of the gelatinous layer.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe dielectric properties of the phantom materials were validated using the principle of resonant cavity perturbation (RCP)\u003csup\u003e36\u003c/sup\u003e. Specifically, a hollow metal cylinder, with holes in the top and bottom plates, resonates at approximately 1 GHz, with a Q-factor of 3000, when empty. When a sample of dielectric material is inserted into the sensor (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), the resonant frequency and Q-factor reduce. This variation in resonant frequency and Q-factor is measured by a network analyser connected to the cavity, which determines the complex permittivity of the sample.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Data collection: Simulation\u003c/h2\u003e \u003cp\u003eThree simulated phantoms \u0026mdash; of the same dimensions and materials as the experimental phantoms \u0026mdash; were modelled in\u003c/p\u003e \u003cp\u003eAnsys HFSS Electronics Desktop 2023R2\u003csup\u003e33\u003c/sup\u003e. Two of the phantoms were modelled with bones, with the bone in one phantom\u003c/p\u003e \u003cp\u003e(simulation phantom 1) placed almost at a diametrically opposite location to the bone in the other phantom (simulation phantom 2). The bones were modelled as cuboids - to differentiate from experimental phantoms - with a width of 2.5 cm and height of 20 cm. The third phantom (simulation phantom 3) only consisted of the muscle layer and was used to obtain the reference or empty scan data.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDuring simulation, 8 antennas (of a single antenna type) were placed equidistant on a circle around the phantom, with the dual-patches of the antennas in direct contact with the muscle layer (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Three simulations were performed for each of the three antenna types using: simulation phantom 1, simulation phantom 2 and simulation phantom 3 (empty phantom). All simulations were performed with a maximum delta value of 0.005, to ensure that both S21 and S11 parameters were accurate up to 60dB, and were performed in the frequency range of 0.5\u0026ndash;2.3 GHz.\u003c/p\u003e \u003cp\u003eS-parameters (both reflection and transmission) were recorded in each simulation. Additionally, electric field values inside simulation phantom 3 were recorded for each antenna type. A grid of 5 mm spacing was used to record the electric field values. The electric field was used in-lieu of the Green\u0026rsquo;s functions for the imaging algorithms discussed below. Computation of Green\u0026rsquo;s functions for inhomogenous background medium are computationally expensive and whilst the phantom used in this study has only muscle-mimicking material, the phantom is supposed to represent the human thigh, which is inhomogenous.\u003c/p\u003e \u003cp\u003eTo compare experimental and simulated models of the antennas, one antenna from each of the three antenna types was also simulated radiating into air and into material mimicking a human body.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Data collection: Experimental\u003c/h2\u003e \u003cp\u003eAn antenna holder with eight slots was 3D printed to be placed around the experimental phantom to collect data. Two antennas of each type were fabricated. The data from the antennas were collected using a vector network analyser (VNA, 8714ES Hewlett Packard) with the VNA calibrated prior to data collection. S-parameters (S11 and S21) were collected in the frequency range of 0.5\u0026ndash;2.3 GHz.\u003c/p\u003e \u003cp\u003eTwo antennas of each type were slotted into the antenna holder placed around the phantom and reflection (S11) and transmission (S21) parameters were recorded (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). One of the antennas was moved around the phantom (using the remaining slots) and 35 measurements were recorded for each type of antenna and for each phantom. Overall, each type of antenna had three sets of data (experimental phantom 1, experimental phantom 2 and experimental phantom 3) with 35 measurements per set of data.\u003c/p\u003e \u003cp\u003eIn addition, reflection parameters (S11) were recorded for each antenna type with the antenna radiating into air and when placed against the skin (radiating into the human body). This was done to compare simulated and fabricated models of the antenna.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Imaging algorithms and metrics\u003c/h2\u003e \u003cp\u003eTwo qualitative imaging algorithms, the multiple signal classification algorithm (MUSIC)\u003csup\u003e37,38\u003c/sup\u003e and the Kirchhoff migration algorithm\u003csup\u003e39,40\u003c/sup\u003e were investigated. MUSIC is built on the principle of time-reversal and has been extensively applied in microwave imaging\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,41\u003c/sup\u003e. In this study, the multi-frequency variant of MUSIC was leveraged to reconstruct images at each frequency and non-coherently sum them to produce the final image. This was done to reduce artefacts in the reconstructed image and build on additional information obtained at multiple frequencies\u003csup\u003e42\u003c/sup\u003e. In addition, electric field values inside the phantom \u0026mdash; computed in the empty phantom simulations (simulation phantom 3) \u0026mdash; were used in-lieu of the Green\u0026rsquo;s function. Similarly, a multi-frequency variant of Kirchhoff migration was investigated in this study. Kirchhoff migration has also been widely applied in microwave imaging\u003csup\u003e39,40\u003c/sup\u003e and has been reported to be a fast, stable and effective imaging technique for detecting small scatterers\u003csup\u003e43\u003c/sup\u003e. The multi-frequency variation of Kirchhoff migration reportedly produces better results than its single-frequency variations\u003csup\u003e44\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFor both experimental and simulated S-parameters, data from a phantom containing a bone were subtracted from data recorded using the empty phantom, which were then fed to the imaging algorithm to reconstruct images and determine the location of the bone from the muscle surface. For reconstructing images based on simulated data, the electric fields recorded using the empty simulated phantom (simulation phantom 3) for each antenna type were used (in lieu of the Green\u0026rsquo;s function).\u003c/p\u003e \u003cp\u003eFor image reconstruction based on experimental data, two analyses were pursued: for experimental phantom 1 reconstruction, the difference in data collected from experimental phantom 1 and the simulation phantom 3 was leveraged; for experimental phantom 2 reconstruction, the difference in data collected from the experimental phantom 2 and experimental phantom 3 was used. This was to validate whether simulated empty scans can be used in-lieu of experimental empty scans. For both simulated and experimental phantom image reconstructions, only transmission data (S21) were leveraged. This was informed by both, studies leveraging transmission parameters collected from antennas diametrically opposite to the transmitting antenna\u003csup\u003e45,46\u003c/sup\u003e, and from our initial investigation into microwave imaging\u003csup\u003e47\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eVisual verification of the reconstructed images was initially done to determine if a hotspot (an indication of a scatterer) was present close to the true bone locations. In addition to visual verification, three metrics were used to evaluate the accuracy of the reconstructed image\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,48\u003c/sup\u003e: Signal-to-cluster ratio (SCR), signal-to-mean ratio (SMR) and localisation error. SCR compares the maximum response within the object of interest to the maximum response in the region outside the object of interest, and SMR compares the maximum response within the object of interest to the average response outside the object of interest. Localisation error is difference between the expected centre of the object of interest to that of the maximum response in the image. A higher SCR and SMR indicate a high-contrast localised region within the image. For all the metrics, the object of interest was the bone (specifically, the femur).\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Antennas\u003c/h2\u003e \u003cp\u003eThree antennas incorporating an SMT balun and operating at different frequencies were developed through the parametric study (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). Antenna 1 had the same overall size as the antenna model proposed in the original study\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e, but with a centre frequency at 0.653 GHz (the antenna model proposed in the original study resonated at 0.9 GHz). Antenna 2 resonated at 0.85 GHz and had a smaller substrate thickness and smaller patch sizes compared with antenna 1. Antenna 3 resonated at 1.75 GHz and had the same substrate thickness as antenna 1 but with smaller patch sizes. The dimensions of the three antennas are provided in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDimensions of the three variations of dual-patch antiphase antennas developed for this study\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAntenna\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLength (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBreadth (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHeight (mm)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAntenna 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBoard: 50\u003c/p\u003e \u003cp\u003ePatch: 22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBoard: 20\u003c/p\u003e \u003cp\u003ePatch: 18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBoard: 1.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAntenna 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBoard: 50\u003c/p\u003e \u003cp\u003ePatch: 14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBoard: 20\u003c/p\u003e \u003cp\u003ePatch: 10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBoard: 1.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAntenna 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBoard: 50\u003c/p\u003e \u003cp\u003ePatch: 14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBoard: 20\u003c/p\u003e \u003cp\u003ePatch: 10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBoard: 1.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe three antennas were fabricated on commercially available FR-4 substrates of varying thickness (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). All antennas were fabricated with outer copper weight of 1oz. S11-parameters of the fabricated antennas closely matched the S11-parameters of the simulated antennas when radiating into air (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea-c) and muscle (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ed-f).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Phantom properties\u003c/h2\u003e \u003cp\u003eThree tissue-mimicking multi-layered bone phantoms were created (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e), with two phantoms, experimental phantom 1 and experimental phantom 2, had the bone located at two different locations; the third phantom (experimental phantom 3) was made of just muscle-mimicking material, which was then used to obtain the reference or empty scan data. Phantom 1 had the bone located on the line connecting diametrically opposite antennas, antenna 1 and antenna 5, with the position slightly closer to antenna 5 (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ea). Therefore, the bone was placed away from the centre position when viewed from antenna 1. Phantom 2 had the bone located in the region spanned by antenna 5 and antenna 7. Therefore, the bone was located towards the left and away from the centre when viewed from antenna 1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb). Experimental data were collected using the antenna holder and two antennas of each antenna type (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of permittivity values between manufactured muscle and bone mimicking tissues and theoretical values at 1 GHz\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTissue name\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eTheoretical value at 1GHz\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eExperimental value at 1GHz\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePermittivity (F/m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eConductivity (S/m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePermittivity (F/m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eConductivity (S/m)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e12.5215\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.3414\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMuscle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCylindrical samples of length 40 mm and diameter 12 mm were created from the bone and muscle phantoms. These samples were used to determine the dielectric properties of each tissue-mimicking layer through the principle of resonant cavity perturbation. The permittivity of the bone and muscle samples, in addition to theoretical values obtained from the IT\u0026rsquo;IS database\u003csup\u003e49\u003c/sup\u003e are provided in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Image reconstruction\u003c/h2\u003e \u003cp\u003eOur results indicate that the bone was detected \u0026mdash; in both simulated and experimental phantoms \u0026mdash; for the three antenna types (antennas resonating at different frequencies) and for all investigated imaging algorithms. The presence of the bone (scatterer) was indicated by visual verification and through the three metrics: SMR, SCR and localisation error. Images could not be reconstructed for experimental phantom 2 using data collected from antenna 3, due to corruption of a subset of data. Further data collection for experimental phantom 2 was impeded by shrinking of the phantom due to evaporation of water from the tissue-mimicking layer. Additionally, the outcome of experimental phantoms could only be verified visually; metrics could not be computed as the true location of the bone in the phantom could not be computed.\u003c/p\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Image reconstruction: simulated phantoms\u003c/h2\u003e \u003cp\u003eBones were visually detected in both simulated phantoms (simulation phantom 1 and simulation phantom 2) using all three antenna types and both the imaging algorithms (Figs.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ea-d). Metrics indicated that images reconstructed using antenna 3 indicated the presence of the bone with higher fidelity and accuracy than antennas 1 and 2. SMR values were maximum for images reconstructed using antenna 3 for both the simulated phantoms and using both the algorithms (MUSIC: 13.3 dB, 11.92 dB; Kirchhoff migration: 16.35 dB, 14.62 dB) (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) with images reconstructed using antenna 1 having the smallest SMR values (MUSIC: 7.27 dB, 7.04 dB; Kirchhoff migration: 8.86 dB, 8.57 dB). Within antenna SMR values for simulated phantom 1 were greater than for simulated phantom 2, for both the imaging algorithms and all the antenna types (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). For images computed using MUSIC, localisation errors reduced from antenna 1 to antenna 3, with maximum localisation errors less than 2.4 cm. For images computed using Kirchhoff migration, comparable localisation errors were obtained for all antennas, with maximum localisation error less than 2.4 cm (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). SCR values were between \u0026minus;\u0026thinsp;1 and 1 dB for all reconstructed images.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of SMR, SCR and localisation errors between the three antenna types, using the two imaging algorithms for the two simulated phantoms. SCR, signal-to-cluster ratio; SMR, signal-to-mean ratio; DAS, delay-and-sum confocal imaging; DMAS, delay-multiply-and-sum confocal imaging; MUSIC, multiple signal classification;\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePhantom\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAlgorithm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSMR (dB)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSCR (dB)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLocalisation error (cm)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSimulated phantom 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMUSIC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.27\u003c/p\u003e \u003cp\u003e11.12\u003c/p\u003e \u003cp\u003e13.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.69\u003c/p\u003e \u003cp\u003e0.14\u003c/p\u003e \u003cp\u003e0.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.11 1.45\u003c/p\u003e \u003cp\u003e0.39\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKirchoff\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.86\u003c/p\u003e \u003cp\u003e14.48\u003c/p\u003e \u003cp\u003e16.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.89\u003c/p\u003e \u003cp\u003e-0.2072\u003c/p\u003e \u003cp\u003e-0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.30 2.30\u003c/p\u003e \u003cp\u003e2.27\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSimulated phantom 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMUSIC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.04\u003c/p\u003e \u003cp\u003e10.57\u003c/p\u003e \u003cp\u003e11.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.31\u003c/p\u003e \u003cp\u003e0.62\u003c/p\u003e \u003cp\u003e0.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.11 1.35\u003c/p\u003e \u003cp\u003e0.53\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKirchoff\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.57 13.0\u003c/p\u003e \u003cp\u003e14.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.78\u003c/p\u003e \u003cp\u003e0.01\u003c/p\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.31 2.28\u003c/p\u003e \u003cp\u003e2.23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2 Image reconstruction: experimental phantoms\u003c/h2\u003e \u003cp\u003eBones were also visually located in reconstructed images of experimental phantoms. Through visual verification, our results indicated that reconstructed images using antenna 2 showed the location of the bone with higher accuracy than antenna 1 and 3. For antenna 1, images reconstructed using MUSIC indicated the location of the bone with greater clarity than images reconstructed using Kirchhoff migration (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ee-h). Specifically, reconstructed images of experimental phantom 1 using MUSIC accurately represented the location of the bone with images reconstructed using Kirchhoff migration indicated a spread and an offset. Reconstructed images of experimental phantom 2 using MUSIC and Kirchhoff migration represented the location to a high accuracy, with images reconstructed using MUSIC affected by scattering at the edge of the domain and images reconstructed using Kirchhoff migration again indicating spread and an offset (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ee-h).\u003c/p\u003e \u003cp\u003eReconstructed images using data collected from antenna 2 (Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003ee-h) indicated that the bone could be successfully located in both experimental phantom 1 and experimental phantom 2 when MUSIC was leveraged with Kirchhoff migration representing the location of the bone to high accuracy for experimental phantom 1, and with lesser accuracy in experimental phantom 2.\u003c/p\u003e \u003cp\u003eBones were again visually located in experimental phantom 1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ee-h) using data collected from antenna 3 and leveraging both MUSIC and Kirchhoff migration, with reconstructed images indicating that MUSIC produced lesser artefacts and spread compared to Kirchhoff migration.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4 Discussion","content":"\u003cp\u003eThe primary aim of this investigation was to validate \u0026mdash; experimentally and in simulation \u0026mdash; the efficacy of applying microwave imaging in biomechanics, specifically to determine the location of the bone from the skin surface. The data were collected under specific conditions, with a limited number of antenna positions and no coupling liquid, to mimic a wearable system. Our results indicate that microwave imaging can be applied to determine the location of the bone from the muscle surface, with the bone located successfully in reconstructed images of both simulated and experimental phantoms.\u003c/p\u003e \u003cp\u003eVarious antenna models have been proposed for microwave imaging applications, with the majority of the designs optimised to work when immersed in a coupling liquid\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,50,51\u003c/sup\u003e. However, the need to incorporate coupling liquid makes the development of a wearable system infeasible or not cost-effective and cumbersome. Novel antennas \u0026mdash; incorporating metamaterials\u003csup\u003e52\u0026ndash;54\u003c/sup\u003e, custom-made materials\u003csup\u003e55\u003c/sup\u003e or unique designs\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e,56\u003c/sup\u003e \u0026mdash; have been proposed to alleviate the need for coupling liquid. For example, one suggestion which removed the need for a coupling liquid and provided direct contact with the imaged body was an ultra-wide band horn antenna incorporating a substrate of dielectric value equal to that of the average permittivity of the breast tissue\u003csup\u003e57\u003c/sup\u003e. However, the antenna was fabricated using expensive materials, thereby increasing the cost and reducing the cost-effectiveness of microwave imaging applications.\u003c/p\u003e \u003cp\u003eThe novel on-body antenna design that was chosen as the baseline model in this study, was designed to work in the absence of any coupling liquid and maintain direct contact with the skin\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. The proposed antenna model incorporated two patches, fed in anti-phase through a balun, with the antennas fabricated using commercially available materials (FR-4) and established fabrication techniques, thereby making them a more cost-effective option. The antenna model was reported to radiate lesser power into the body than a typical cell phone (radiating 0.1 W into the wrist\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e) and had been applied to distinguish transmission (S21) parameters acquired from healthy and osteopenic bones. However, the components used in the antenna were not conducive with a wearable device.\u003c/p\u003e \u003cp\u003eIn our study, we built on this baseline antenna model\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e to develop wearable antennas which have the same form factor as the initial design, but with all the components mounted on the antenna. This was accomplished by modifying the existing design to incorporate an SMT balun, thereby requiring a change in the overall design to reduce power loss. Additionally, we also developed three antennas operating at different frequencies to evaluate the effect of frequency on microwave imaging results. The development was done using a parametric study to optimise both coupling into a slab of muscle and penetration into the muscle. The developed antennas exhibited reasonable coupling and penetration, with the three antennas resonating at three different centre frequencies. The three antenna types were furthermore fabricated using commercially available materials, with all antennas being lightweight allowing for the development of a wearable device using 8 antennas. The experimental reflection (S11) parameters of the fabricated antennas showed a good match to the simulated S11 parameters when the antennas radiated in air and when the antennas were placed against a human body. Furthermore, the S11 parameters also indicated that the antennas were optimised to work when in direct contact with the human body.\u003c/p\u003e \u003cp\u003eTo the best of our knowledge, the phantom developed in our study was the first multi-layered solid bone phantom developed comprising muscle and bone layers. As microwave imaging has predominantly been applied for imaging the breast and the brain, majority of the tissue-mimicking phantoms have been developed to mimic electrical properties of breast and brain tissues\u003csup\u003e58\u0026ndash;60\u003c/sup\u003e. We were only able to identify one study which proposed recipes for multi-layer bone phantoms for microwave imaging\u003csup\u003e34\u003c/sup\u003e. These authors described the mixtures and methodology to reproduce liquid and solid tissue-mimicking bone phantoms, with liquid-based phantoms consisting of skin, muscle, cortical bone and trabecular bone layers, and the solid-based phantoms consisting of skin, cortical bone and trabecular bone layers. The solid-based phantoms were made using mixtures of carbon black, graphite, urethane and isopropanol. However, the proposed solid-based phantoms consisted of just bone and skin layers which are not representative of the human body.\u003c/p\u003e \u003cp\u003eIn our study, we complemented the mixtures for solid-bone based phantom\u003csup\u003e34\u003c/sup\u003e with the muscle-mimicking recipe \u0026mdash; incorporating mixtures of ethanediol, deionised water and gelatine \u0026mdash; proposed for the development of dielectrically and thermally stable mixtures of fat and muscle\u003csup\u003e35\u003c/sup\u003e. Our developed tissue-mimicking materials showed both a good match to theoretical values, but more pertinently indicated a large enough contrast between bone and muscle layers \u0026mdash; which is crucial for microwave imaging. The phantom also indicated good mechanical stability during data collection (was able to support 2 antennas and the antenna holder). Additionally, the dielectric properties of the bone layer closely matched the results obtained in the baseline study\u003csup\u003e34\u003c/sup\u003e (relative permittivity of 13 at 1 GHz).\u003c/p\u003e \u003cp\u003eWith respect to simulation results, visually, antenna 3 was able to detect the location of the bone with higher accuracy than antennas 1 and 2. Notably, the images reconstructed using antenna 1 had a significant spread and the images reconstructed using antenna 2 only detected the edges of the bone closest to the muscle surface. This is also reflected in the SMR and localisation metrics, as the reconstructed images produced using antenna 3 had the highest SMR values and smallest localisation errors. The smallest SMR and SCR values were obtained for images reconstructed using antenna 1, which can be attributed to the hotspot artefact (a high-intensity region that does not correspond to any known locations of scatterers\u003csup\u003e61\u003c/sup\u003e) observed close to the centre. The poorer performance of antenna 1 can also likely be attributed to the relationship between lower frequencies and loss in image resolution. Antenna 1 resonates at a frequency considerably lower than that of antenna 3 (0.63 GHz versus 1.65 GHz respectively) and hence would have proportionally poorer image resolution.\u003c/p\u003e \u003cp\u003eThe reason antenna 2 was only able to detect edges closest to the muscle surface, can likely be attributed to the antenna model. Despite the antenna resonating at a centre frequency (0.8 GHz) which allows for both considerable improvements in resolution and penetration, the S11 parameters of simulated antenna 2 indicate that the antenna is not as optimally designed as simulated antenna 3, with only 40% of the signal being transmitted into the phantom. Antenna 3 produced the best results for simulated phantoms as indicated by higher SMR values and lower localisation errors and can be attributed to a high image resolution obtained by its high resonant frequency and the considerable coupling achieved with the phantom \u0026mdash; as indicated by S11 and S12 (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe variation in the results between simulation phantom 1 and simulation phantom 2 for each antenna type can be attributed to the difference in the location of the bone in the muscle phantom. The bone phantom was located closer to the surface in simulation phantom 1 compared to simulation phantom 2.\u003c/p\u003e \u003cp\u003eOur experimental results indicate that microwave imaging can be applied to locate the bone from the surface of the phantom. Visual verification \u0026mdash; which is widely applied in microwave imaging applications\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,62,63\u003c/sup\u003e \u0026mdash; indicates that the bone was successfully located in both the phantoms. In contrast to the simulation results, reconstructed images of experimental phantom 1 using antenna 3 indicated an offset with considerable spread of the high-intensity region (when reconstructed using both MUSIC and Kirchhoff migration). Whereas reconstructed images using both antennas 1 (leveraging MUSIC) and 2 indicated a very high accuracy in determining the location of the underlying bone in both the experimental phantoms.\u003c/p\u003e \u003cp\u003eImages of experimental phantom 1 were reconstructed using the difference between data collected using experimental phantom 1 and simulation phantom 3, whilst images of experimental phantom 2 were reconstructed using the difference between data collected using experimental phantom 1 and experimental phantom 3. This may account for the differences in reconstructed images of the two experimental phantoms when using data collected from the same antenna. As our results indicate, whilst the contrast in permittivity between muscle-mimicking layer and bone-mimicking layer were sufficient for the application of microwave imaging, the permittivity values of both the layers (especially the muscle) varies from their respective theoretical values. With simulation phantom 3 attributed with theoretical values of muscle, the differences in the reference scan data (simulation phantom 3 vs experimental phantom 3), may affect the fidelity of the results as the same electric field values were used in the reconstruction of both experimental phantoms.\u003c/p\u003e \u003cp\u003eOur results indicate that the performance of antenna 3 was relatively between than antenna 1 and antenna 2 in reconstructing simulation phantoms whilst antenna 2 performed relatively better in reconstructing experimental phantoms. We hypothesise that the variation in antenna performance can be, in part, attributed to the differences between fabricated and simulated antennas, coupled with the differences between simulated and experimental phantoms as discussed above. Our results show that fabricated antenna 2 had better coupling with human-tissue equivalent materials compared to simulated antenna 2. This could have affected the performance of simulated antenna 2. Antenna 3\u0026rsquo;s performance on experimental phantoms could be attributed to the differences in permittivity between simulated and experimental phantoms, thereby affecting its performance. Notably, our results indicate that images can be successfully reconstructed using experimentally collected data with reference (empty scan) data obtained from simulations. Therefore, empty experimental phantoms do not need to be manufactured for most applications, thereby underscoring the applicability of microwave imaging in biomechanical applications.\u003c/p\u003e \u003cp\u003eTo reconstruct the images for both the simulated and experimental phantoms, we leveraged two qualitative imaging algorithms: MUSIC and Kirchhoff migration. These two algorithms have primarily been applied to detect small scatterers,\u003c/p\u003e \u003cp\u003ewith their efficacy varying for extended scatterers\u003csup\u003e39,64\u003c/sup\u003e. Our results obtained using MUSIC \u0026mdash; particularly those from the experimental phantoms using antenna 3 \u0026mdash; indicated a spread of high-intensity area which represents multiple scattering inside the phantom instead of localising scattering at the boundary of bone and muscle. Similar results were obtained by\u003csup\u003e64\u003c/sup\u003e, who observed that whilst MUSIC can be successfully be applied to determine the location of the scatterer, its ability to determine shape is less effective for extended scatterers.\u003c/p\u003e \u003cp\u003eOur results obtained using Kirchhoff migration indicated that the quality of reconstructed images \u0026mdash; assessed visually in terms of detecting the location of the bone \u0026mdash; improved with higher frequencies, in both simulated and experimental phantoms. Whilst Kirchhoff migration has been noted as a fast, stable and effective imaging technique\u003csup\u003e43\u003c/sup\u003e, it is more sensitive to model assumptions and noise compared with MUSIC. We hypothesise that this may explain our results obtained using Kirchhoff migration, as they exhibit a greater spread and offset when compared with images reconstructed using MUSIC. Despite the spread, the location of the bone was successfully determined from images reconstructed using Kirchhoff migration for all experimental phantoms.\u003c/p\u003e \u003cp\u003eKey limitations of this study were the mismatch between theoretical and experimental permittivity values of the muscle-mimicking layer, and the lack of true bone position in experimental phantoms which rendered the computation of imaging metrics for experimental phantoms infeasible. An additional limitation of this study is that the metrics used for the detection of point-like scatterers are non-transferable to extended scatters. For example, despite our reconstructed images indicating the bone has been located at the true edge of the bone, the localisation errors computed from the centre of the bone to the centre of the high-intensity region may generate a large value. Therefore, there is a need for the development of metrics suitable for extended scatterers.\u003c/p\u003e \u003cp\u003eIn conclusion, we have validated \u0026mdash; both experimentally and in simulation \u0026mdash; that microwave imaging can be effectively applied in biomechanics, specifically to determine the location of the bone from the skin (muscle) surface. The data collected in this study were taken under specific conditions \u0026mdash; fewer number of antenna positions and no coupling liquid \u0026mdash; to facilitate the development of a wearable system. We believe our results may be used to further research into the biomechanical application of microwave imaging; in particular, as an alternative to currently used imaging modalities such as ultrasound imaging.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eV.R conceived the experiments, conducted the experiments, analysed the results and wrote the manuscript; A.M, T.J.D and M.R assisted in the refinement of methodology, manufactirung of the phantoms and analysed the results; P.S assisted in the methodology of the simulation and analysed the results; S.P and A.P supervised the project. All authors reviewed the manuscript\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData available upon reasonable request from the corresponding author\u003c/p\u003e\u003cp\u003eAdditional information\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eScafetta, N., Marchi, D. \u0026amp; West, B. J. Understanding the complexity of human gait dynamics. \u003cem\u003eChaos \u003c/em\u003e19, 026108 (2009).\u003c/li\u003e\n\u003cli\u003eDicharry, J. Kinematics and kinetics of gait: from lab to clinic. \u003cem\u003eClin. Sports Med. \u003c/em\u003e29, 347\u0026ndash;364 (2010).\u003c/li\u003e\n\u003cli\u003ePeters, A., Galna, B., Sangeux, M., Morris, M. \u0026amp; Baker, R. Quantification of soft tissue artifact in lower limb human motion analysis: a systematic review. \u003cem\u003eGait Posture \u003c/em\u003e31, 1\u0026ndash;8 (2010).\u003c/li\u003e\n\u003cli\u003eCappello, A., Stagni, R., Fantozzi, S. \u0026amp; Leardini, A. Soft tissue artifact compensation in knee kinematics by double anatomical landmark calibration: performance of a novel method during selected motor tasks. \u003cem\u003eIEEE Trans. Biomed. Eng. \u003c/em\u003e52, 992\u0026ndash;998 (2005).\u003c/li\u003e\n\u003cli\u003eSmale, K. B., Potvin, B. M., Shourijeh, M. S. \u0026amp; Benoit, D. L. Knee joint kinematics and kinetics during the hop and cut after soft tissue artifact suppression: Time to reconsider ACL injury mechanisms? \u003cem\u003eJ. Biomech. \u003c/em\u003e62, 132\u0026ndash;139 (2017).\u003c/li\u003e\n\u003cli\u003eLeardini, A., Chiari, L., Della Croce, U. \u0026amp; Cappozzo, A. 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Signal Process. \u003c/em\u003e153, 107501 (2021).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4793365/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4793365/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIncorporating actual bone movement in kinematic pipelines has shown to reduce the influence of soft tissue artefacts (STA), a critical source of error, in clinical biomechanical analysis. Ultrasound imaging, a non-ionising and cost-effective imaging modality, has been extensively integrated in biomechanics to locate the underlying bone. However, limitations of needing a probe to be held at the location to be imaged and the need for coupling liquid, impedes their widespread applicability. In this study we explore the feasibility of applying another non-ionising and cost-effective imaging modality, microwave imaging, in biomechanics. By collecting data, from both simulated and experimental tissue-mimicking phantoms, under conditions aimed to emulate a wearable system, our results indicate that the underlying bone can be detected from the skin surface using microwave imaging. We believe our findings support the fidelity of microwave imaging as an alternative imaging modality to ultrasound imaging and underscore the need for further research in integrating microwave imaging in biomechanics.\u003c/p\u003e","manuscriptTitle":"Applying microwave imaging in biomechanics: a feasibility study using tissue-mimicking phantoms","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-09-04 21:51:17","doi":"10.21203/rs.3.rs-4793365/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a8c1ae78-e25a-4d28-8e89-f09ac5070c51","owner":[],"postedDate":"September 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":36621152,"name":"Health sciences/Medical research"},{"id":36621153,"name":"Physical sciences/Engineering"}],"tags":[],"updatedAt":"2024-12-04T18:38:42+00:00","versionOfRecord":[],"versionCreatedAt":"2024-09-04 21:51:17","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4793365","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4793365","identity":"rs-4793365","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}