Validation of a Compact Microwave Imaging System for Bone Fracture Detection

This work presents a systematic evaluation of the effectiveness of an air-operated microwave imaging (MWI) system for the detection of arbitrarily oriented thin fractures in superficial bones, like the tibia. This includes the proposal of a new compact, portable setup where a single Vivaldi antenna performs a semi-cylindrical scan of the limb. The antenna is operated in monostatic radar mode, near the skin but without contact, thus ensuring hygiene and patient comfort during the exam. The image is reconstructed using a wave-migration algorithm in the frequency domain combined with an adaptative algorithm based on singular value decomposition which removes the skin artifact taking into account the non-uniform bone profile and tissue cover. The study investigates the system resolution, the robustness of the method to the uncertainty of the permittivity and thickness of the involved tested tissues, as well as the robustness to involuntary patient movement. The experimental validation was performed for the first time on an integral ex-vivo animal leg, with all tissues present, including skin and fur. It confirmed both the effectiveness of the method, and the feasibility of the setup.

MWI clinical system was installed in hospitals in Germany for breast scanning [9].
There are research teams evaluating the feasibility of medical diagnostics using MWI specifically for bone lesions and fractures. In [10], the authors reconstructed bone profiles immersed in a coupling medium. This approach is unattractive for practical applications and complicates the setup. In [11] and [12] the authors use an adapted free space setup, based on a previous clinical prototype Mammowave [13], to detect longitudinal bone fractures and lesions using a 3D tube model. The experimental setup is fixed and bulky, otherwise used for MW breast scan, and not so practical to use with a leg in a clinical scenario. The diameter of the used cortical bone phantom is 11 cm, the marrow diameter is 7 cm, and the longitudinal lesion has 7 mm radius. These unrealistic dimensions may affect the generalization of the results for a real case. In all the previous works, a regular and uniform phantom was used.
In [14] and [15] a portable setup is presented for detecting knee tears, although not being applied for detecting bone fractures. In the proposed setup, the examination is performed with the phantom in a standing posture, without using immobilization. This may be problematic because the proposed MWI reconstruction is based on limb symmetry, which may require precise antenna positioning. It also requires limbs symmetry.
Recently, we proposed in [16] and [17] a MWI-based method for detection of very thin fractures in superficial bones, like the tibia. It was developed for contactless operation, without the need for any coupling medium. The antenna scan was performed along a parallel line to the bone axis, aiming at the detection of thin transversal fractures. The experimental validation was done with 3D-printed cylindrical phantoms, and with ex vivo animal bones stripped of tissues.
In the present paper we expand that study to detect arbitrarily oriented thin fractures, namely double transversal and oblique ones. This requires extending the scan from one line to a cylindrical surface and adapting the previous algorithms to deal with the non-uniform distance of the antenna to the bone and the skin artifact. We also evolve the low-cost setup presented in [17] to introduce scanning over a cylindrical surface semi-encircling the leg. The setup is conceived such that the patient may be sitting or in supine posture, and it is the setup, not the patient that needs to be positioned. The longitudinal scan for fixed angular planes is automatic, but at the current stage of development, the angular planes are set manually. In the future all movements of the antenna support can be made automatic.
The most important outcome of this study is that a successful test was made with a fractured integral ex-vivo animal limb, without removing any tissue layer, or even the fur. The result showed a clear positive identification of the fracture, demonstrating the effectiveness of the proposed concept and of the dedicated algorithms developed for the inverse scattering problem and image reconstruction. The simplicity of the proposed compact portable system makes it attractive for future use in first-response screening in ambulances, retirement houses, school infirmaries, football fields, veterinary clinics, farms, or low-income settings.

II. SYSTEM DESCRIPTION
The proposed microwave radar-based fracture detection system comprises an antenna capable of spatial scanning around the limb under test, a vector network analyzer to acquire the s 11 (P a , f l ) scattering parameter at the antenna port as function of the position P a (x q , θ h ) and frequency f l . A PC is used to control the measurement setup, run the procedures to calibrate the acquired signals, run the dedicated image inversion algorithms, and present the image reconstruction results (see Fig. 1). The details are described next.

A. MICROWAVE DETECTION SYSTEM
Unlike several MWI systems that report the use of immersion liquid to minimize wave reflections at the skin [10], this setup is contactless, requiring no coupling liquids for maximum hygiene and simplest operation in the field. This air operated VOLUME 11, 2023 approach is challenging, but it has been shown to be feasible and preferable [4], [16].
Our MWI setup works in monostatic radar configuration. The antenna scans the limb along a cylindrical grid around the bone thus favoring the detection and location of different types of fractures, such as oblique, transversal, and double transversal. The cylindrical grid radius is r ant = d bone +r bone , respectively the distance of the antenna tip to the bone surface and the bone radius. The θ h angle is defined between the zxplane and the measurement radial plane, with positive values along positive y-axis direction, as shown in Fig. 1(a).
A single Vivaldi antenna acquires the antenna input reflection coefficient s 11 (P a , f l ) at each position P a of the cylindrical grid shown in Fig. 1(a), for all f l frequencies with l = 1 . . . N f , within a given broad range. In Cartesian coordinates, this corresponds to P a x q , θ h = (x q , y = r ant sin (θ h ) , z = r ant cos (θ h )), where r ant = r bone + d bone . The total set of measurements is represented as s 11 , represent the scanning grid points.
For each θ h -angle, the single antenna translates longitudinally acquiring the signal at each x q position, with the help of a linear guided system, using a precision lead screw connected to a NEMA 17 motor, as shown in Fig. 1(b). Distance d bone form the tip of the antenna to the bone surface is much smaller than the wavelength, in the order of 10 mm, to benefit from the better resolution associated with the antenna reactive field.
The system is controlled via an Arduino Uno that is connected to the laptop and to the linear guided system using an USB interface. The antenna is connected to an Agilent E5071C Vector Network Analyzer (VNA) using RF cables to collect the backscattered signals (s 11 ). The application for signal processing and image algorithm is coded in MATLAB and runs on a laptop.

B. ANTENNA
Medical imaging requires high resolution, which requires the smallest possible wavelengths. However, microwaves lose penetration depth with increasing frequency. Given that this work is intended for superficial bones, a reasonable compromise between penetration depth, and image resolution is obtained for the 8.3-11.1 GHz frequency interval.
We use a Vivaldi antenna operating in this frequency band. with dimensions 28.0 mm × 29.1 mm × 1.5 mm, as shown in Fig. 2. This antenna was designed to be compact, present a wideband impedance match, and stable near-field distribution with frequency, as required for medical imaging [16]. We highlight that this antenna is compact, mainly for systems operating in air [4], [14]. Fig. 3 shows the result of the full-wave simulation of the antenna s 11 in free space. The spatial distribution of the amplitude and phase of the E-field is presented in Fig. 4. for the antenna reactive region. The E-field magnitude is reasonably well confined in the forward region of the antenna, with negligible back radiation as desired. The phase plot shows   the formation of an almost spherical wave, right from the reactive-field region, allowing the identification of a phasecenter-like point. These amplitude and phase characteristics are maintained over the frequency band (not shown), making this a very appropriate antenna for the imaging setup.

C. IMAGING ALGORITMH
Studies involving real bones, in contactless microwave measurements, present some challenges related to the strong reflection at the air-skin boundary, aggravated by the unknown variation of the bone diameter, skin thickness and texture, along x. These features originate unwanted contributions to the acquired backscattered s 11 (x, θ, f ) signals, which can mask the much weaker response from the fracture.
To remove these unwanted signals, some pre-processing is necessary on s 11 (x, θ, f ). In this work, we first apply a regional average filter (RAF) to the signal. Considering the non-uniform shape of the target, we divide the x set into B non-overlapping sub-regions where the backscattered signals are more likely to be considered locally similar. Each sub-region has the same number of positions, e.g., The RAF is applied to each backscattered signal in the regional subset by subtracting from it the regional average signal calculated over the xdimension, The filtered signal of the full set is then obtained by concatenating each regional subset as s cal The unwanted signals that persist after (1), may still create artifacts in the reconstructed image. In this step, it is common to use an artifact removal algorithm to separate the wanted from the unwanted contributions [3], [18], [19] and [20].
In our work, we used an algorithm based on Singular Value Decomposition (SVD) [21], [22], and [23] for the skin artifact removal. It allows separating the stronger response of the non-uniform bone surface and skin, from the weak bone fracture response. The SVD is described by in which U is the unitary matrix of left singular values, V H is the Hermitian of the unitary matrix of right singular values, and represents a square diagonal matrix composed of the singular values σ k of s cal 11 (P a , f l ) ordered in decreasing amplitude sequence. The maximum value of k is the rank of the matrix s cal 11 (P a , f l ). The filtered signal is obtained by removing the strongest (k < g) singular values from the signal, which are responsible for the artifacts Parameter g is determined after proper analysis of a set of representative examples of the tested scenarios.
Direct use of this process for all data, for instance as in [23], works better for uniform shapes. It may not be so effective for non-uniform shapes, where its effect may still overshadow the response of the fracture. In order to mitigate the effect of non-uniformities, an adaptive SVD approach was used by the authors in [4] for breast cancer detection, and in [16] for bone fractures detection. In the present work we also implement an adaptative SVD process: the scanned area s cal 11 (P a , f l ), is divided into Q subregions, each one with Na/Q elements, in which the backscattered signal can be considered locally similar. The number of these Q subregions is not necessarily equal to the number of B subregions of the previous step.
Equations (2) and (3) are then applied to each subregion of s cal 11 (P a , f l ). All the subregion vectors are non-overlapping and contain the same number of antenna positions. In each subregion, the same number of singular values are removed. Eq (4) is the SVD filtered response, g is applied according to each scenario.
The subsequent step is to concatenate the subregion results into a vector s s 11 (P a , f l ). This signal is free from spurious scattering and denotes the complete set of values for all N f frequencies.
The reconstructed image is based on wave migration [24], obtained from with the straight path distance between the measurement point and test point on the limb pixel in which d 0 and d 1 are travelled lengths in air and tissues, respectively. At each test pixel where a target (fracture) exists, the sums in (5) add up coherently, increasing its value with P a i and N f . Otherwise, the signals add-up incoherently, and the sum tends to zero. In I mn the frequencies are summed, considering the contributions of all antenna positions P a (x, θ) and frequencies to the (m, n) pixel.
In practical situations, it is not possible to know exactly the permittivity values of each patient's tissues. Therefore, an average tissue permittivity, ε r av is estimated following [14], where we consider an estimated thickness of each tissue.
where ε r j represents the dielectric constant of each tissue, t j its thickness, t total the total thickness of the tissues in the phantom section, N T the total number of tissues, and jthe index of the tissue. The thickness of each animal tissue was obtained experimentally. The measurements were taken in a transversal section of the fracture, and are shown in Table 1. The values of the dielectric properties were obtained in [25]. When available, it is possible to use online image databases to better estimate the human tissue thickness, as mentioned in [14], [26], and [27]. We discuss ahead the sensitivity of the imaging process to the expected uncertainty in these values. We use a performance indicator to quantify the quality of the image reconstruction algorithm: signal-to-clutter ratio (SCR) [2]. SCR is defined as the ratio between the maximum intensity corresponding to response in the fracture region, S, and the maximum intensity of the background clutter, C, within the scanned region.

III. SIMULATIONS RESULTS
This section focuses on four main aspects, A) minimum detectable fracture thickness; B) tolerance to permittivity uncertainty; C) resolving power of the imaging system (resolution); D) detection of oblique fractures. We also test the robustness of the imaging process to limb position errors due to involuntary patient movement. Full-wave simulations are preformed using CST Microwave Studio [28]. We consider a simplified numerical model of the tibia [16], represented by a uniform 40 mm diameter, 150 mm long cylindrical phantom (see Fig. 5), with the dielectric properties of cortical bone ε r = 8.4 (except where mentioned otherwise). The fracture is represented by different thickness discs, with dielectric properties of blood. The dielectric properties of all tissues are found in [26]. Previous studies [17] and the results in later sections of this paper show that simulation results for this model compare well with our measured results in biological bones.
As mentioned in a previous work [16], even if more elaborate phantoms can be analyzed, these simpler ones already describe the main features of the response, enabling to conclude about the detection feasibility.
The antenna is oriented such that the E-field is parallel to the bone axis. For each θ h plane, out of seven planes in the [−24 • < θ h < 24 • ] interval (see Fig. 1(a)), the antenna performs a linear scan along x, stopping at N x = 41 positions in the −40 < x q < 40 mm interval, where the s 11 at the antenna port is calculated for N f = 201 frequencies.
The nominal distance between the antenna tip and the bone boundary is d bone = 10 mm.
Analysis of simulations for different scenarios showed that that a reasonable number of subregions for the regional average is B = 3. The same is used for the adaptive SVD, that is, Q = 3. This allows to cope with the increase of bone diameter towards the bone ends, compared to the mid region. In general, the number of removed singular values is g = 2 in the region of the bone ends, and g = 1 in the mid region.

A. DETECTABLE FRACTURE THICKNESS
We investigate the capability of the system to detect and locate thin fractures. In optical systems, the image resolution is diffraction limited to λ m /2, where λ m is the wavelength in the medium with ε r permittivity. In our case, this would correspond to about 10 mm, at mid-band. In this study, we test transversal fractures with 0.5-mm, 1-mm, 2-mm, and 4-mm thicknesses, which are narrower than the resolution limit, but relevant cases in the context of the practical application. The corresponding image calculated using Eq. (5), is shown in Fig. 6. It is a map of the reflected intensity, where the dotted black line indicates the position and thickness of the fracture in the numerical model, and the white lines indicate the bone boundary. The result shows that all tested fracture thicknesses produce an identifiable response, although with smaller amplitudes as the thickness decreases. Its effective detectability in a more complex scenario will depend on the relative strength of this response compared to possible artifacts in that scenario. As expected, according to the theorical resolution limit, the width of the detection spot in the image remains in the order of 10 mm for all these cases, preventing the determination of the actual fracture thickness. As a conclusion, subwavelength fracture thicknesses produce a response that may allow the identification of its location, but not its thickness.

B. TOLERANCE TO PERMITTIVITY UNCERTAINTY
We instigate the impact of permittivity value uncertainty on image reconstruction. This verification is relevant because, in a real exam, it is not possible to determine the exact values of the parameters that appear in eq. (6).
We consider, as an example, a scenario where the permittivity value used in the inversion algorithm matches the nominal permittivity value of the phantom (cortical bone) ε r = 8.4. This result in presented in Fig. 6 (b). We compare it with the cases where the permittivity used in the image reconstruction deviates from this nominal value by ±10% and by ±40%. Results in Fig. 7 and Table 2 show that the fracture is detected in any case at its true position, although with slight variation of the maximum intensity, but with SCR almost unchanged within the ±10% interval, and reduced by only 1.9 dB for ±40% deviation with respect to nominal. This degradation is negligible and the identification remains clear, confirming the required robustness of the image inversion algorithm with respect to permittivity uncertainty.

C. RESOLVING POWER OF THE IMAGING SYSTEM
Still related to system resolution, it is relevant to determine the capability of the imaging system to distinguish between two close fractures. This gives a measure of the resolving power of the imaging system, and it is relevant e.g. in clinical situations involving multiples lesions.
Different authors analyze resolution in microwave imaging of the breast and of the lungs [8], [29], [30], [31], [32], and [33]. In these studies, the targets are PEC or dielectric cylinders, with radius ranging from 5 mm to a few cm, separated by distances of the order of 50 mm. These authors report the appearance of coupling effects that may limit the separability of the targets in the image. They resolve two contiguous targets down to a distance of 40 mm between them.  In our work, the targets are 1-mm thick transversal bone fractures, with much smaller separation, of 10 mm and 15 mm, as shown in Fig. 8. The results are presented in Fig. 9 (a) for 10-mm separation and in Fig. 9 (b) for 15 mm separation. The computed metric value is SCR = 4.5 dB. Indeed, for the 10-mm case, the proximity of the two fractures creates an overlap of their responses in the reconstructed image that prevents a neat separation of their images. However, for the 15-mm distance case, the fractures' image already separate well.
For the 15-mm separation, we also evaluate how patients' involuntary movement during an examination may impact this result, since movement is a critical factor in medical image quality. For that, we change the distance d bone in some of the seven θ scan planes scanned in the same exam. We consider two cases: in case 1), we make d bone = [10,5,10,5,10,5,10] mm in the consecutive θ scan planes, and the result is shown in Fig. 10 (a) with SCR = 3.8 dB. For case 2), we make d bone = [10,15,10,15,10,15,10] mm, and the result is shown in Fig. 10 (b) with SCR = 4 dB. Comparison with the nominal case of Fig. 9 (b), where d bone = 10 mm for all θ scan planes, allows to conclude that the fractures are still resolvable despite the simulated target movement during the exam.

D. DETECTION OF OBLIQUE FRACTURES
In this section, we present results obtained for oblique fractures, aligned at 45 • angle with respect to the x-axis, as shown in the Fig. 11.
The results in Fig. 12 (a)-(b), still show the fracture detection, with an inclined response, although not exactly with the same tilt as the fracture. The metric value is SCR = 6.37 dB, which indicates good detection.
In this case we also evaluate the influence of patient's involuntary movement during the examination, considering the same d bone variation approach used in the previous example. The results for case 1) are shown in Fig. 13 (a)-(b) with SCR = 6.1 dB, and case 2) are shown in Fig. 13 (c)-(d) with SCR = 6 dB, respectively. There is a slight increase of the artifacts and decrease of the amplitude, but the fracture is still detectable. This demonstrates the robustness of the detection to different conditions that are expected in a realistic scenario.

IV. EXPERIMENTAL RESULTS
To validate the effectiveness of our system for detection of arbitrary fractures in superficial bones, four distinct ex-vivo phantoms were used. In all cases the fresh animal tissues were obtained from the local consumer market, kept refrigerated and hydrated until the measurement. In Section IV-A and B we introduce fractures in bovine bones, in Section IV-C we use an ovine leg and in Section IV-D a goat leg is used with all tissues present, including the skin and fur.
The s 11 x q , θ h , f l was acquired in this experiment for N x = 41 points in the [−40 < x q < 40] mm interval for successive N θ = 7 angular positions with angular positions with [−24 • < θ h < 24 • ] at every 8 • , N f = 201 frequency points. The tip of the antenna was positioned at d bone = 15 mm away from the boundary bone, at its mid length along x. The fractured tibia was aligned and measured. The antenna was fed with 10 dBm signal level. The values of B, Q and g used in the inversion algorithm are indicated in the each of the following sections.

A. DOUBLE TRANSVERSAL FRACTURES
In the first test we used an ex-vivo stripped bovine tibia bone, with 40-mm minimum diameter and 150-mm length. We tested experimentally the capability of the system to detect and locate two closely spaced bone fractures. Two cuts were opened on the surface of the bovine bone about 15 mm apart from each other, about 1-mm thick and 20-mm deep, as shown is Fig. 14. The fractured tibia was carefully aligned in the setup before measurement.
The corresponding results in Fig. 15 were calculated considering B = 3, Q = 3 and g = 1 for the central region of the bone and g = 1 for the edge regions, and a permittivity ε r = 8.4 [25]. The image clearly shows two well separated fractures, in the correct position. In these measured results, the cross-coupling effect between the fractures seems to be  lower than predicted by simulations, confirmed by SCR = 5.8 dB. In the general rule can be established with this respect, but this experimental result is enough to confirm that these thin fractures can be detected in biological bones, reinforcing the robustness of the proposed image inversion methods.

B. OBLIQUE FRACTURES
For this first test we also used an ex-vivo stripped bovine tibia bone, with 40-mm minimum diameter and 150-mm length. An oblique cut, with 50 • inclination relative to the x-axis was opened in the mid region of the animal bone, about 1-mm thick and 15-mm deep, as shown is Fig. 16. It is possible to observe in the zx-plane ( Fig. 17 (b)), that the system could detect the fracture depth along z, although with some image artifacts. In fact, the image depth of field along the y-axis is not narrow enough to prevent the projection of the fracture length from appearing also in the y = 0 plane, as can be confirmed in Fig 17 (a). The metric value for this image is SCR = 5.65 dB, which indicates good detection.

C. TRANSVERSAL FRACTURE IN OVINE LEG WITHOUT SKIN
We significantly evolved our study by using fresh animal limbs, with integral flesh, obtained from a local supplier.   We used an ovine leg, with all the tissues present, except the skin, as shown in Fig. 18 (a).
The bone was carefully sectioned, preserving tendon, nerves, and muscle in the scanning area. The fractured leg was then positioned and aligned in the setup, with the incised bone at the bottom. The antenna scanned the region above the intact tissues of the leg, as shown in Fig. 18 (a). The leg cross-section was of course not axis symmetrical; the tibia was located for negative y and z, closer to the muscle-air interface. VOLUME 11, 2023 Considering that this shape was cluttered with muscles, we measured the scattered fields just in 3 planes, , within the [−30 < x q < 30] interval, and with d bone = 16 mm measured at its mid length along x. The total scanning time was 6 minutes and the computational time to process all measurements was 1.5 minutes. The results are shown in Fig. 19 (a) and (b), which include muscle, tendon and bone regions, the latter delimited with the white lines. The soft tissues are present in the region delimited between the brown line and white line. The fracture is indicated by the black dotted line. The parameters values t j and ε r j used in Eq. (6) are shown in column named ''Ovine'' in Table 1, which compute to ε r av = 20.19. The other parameters are B = 3, Q = 3 and g = 2 for the central region of the bone and g = 3 for the edge regions. It is possible to identify the presence of the fracture in both planes represented in Fig. 19 (a), by its strong response. The quantitative metric gives SCR = 6.6 dB in this case, indicating good detection.

D. TRANSVERSAL FRACTURE IN GOAT LEG WITH ALL TISSUES
In this test we used an ex-vivo leg from a goat with all the tissues, including skin and fur. This is very close to a clinical scenario for testing our concept. The antenna positioning was the same as described for the ovine leg fracture. The tibia was carefully sectioned, preserving tendon, nerves, and skin in the scanning area, as shown in Fig. 20 (a). The fractured leg was positioned and aligned in the setup, with the skin incision at the opposite side of the scanning area, Fig. 19 (b).
The reconstructed image of the fractured leg is shown in Fig. 21 in two planes. The bone region is delimited by the  Table 1 which compute to ε r av = 20.07. B = 3, Q = 3 and g = 2 for the central region of the bone and g = 3 for the edge regions. The fracture is clearly detected in the correct location, with SCR = 7.8 dB. We also instigated the impact that the uncertainty in the estimation of the average permittivity has on the image reconstruction, given the uncertainty of the different tissue thicknesses and dielectric constants involved in the calculation. For that, we repeated the image reconstruction for this leg example, with different average permittivity values ranging in the −20% to +20% interval with respect to nominal. The SCR remains almost unchanged within the ±10% interval, while it reduces by 1.4 dB for ±20% deviation with respect to nominal, i.e., ε r av = 16 and ε r av = 24. We present in Fig. 22 the result for the latter, corresponding to SCR = 6.4 dB. The degradation of the SCR comes from a slight increase in the artifact level away from the fracture location. However, it is still a clear detection, in the correct location, with an SCR above a minimum of 3 dB.
This experimental result reinforces that the method is robust enough to cope with the uncertainties that are expected in practical real-life applications, with actual biologic limbs. It is stressed that the image quality obtained for this airoperated system, without using any contact liquid, is made possible by the developed very robust image inversion algorithm, which evolved from [8]. Table 3 shows the comparison between our proposed MWI system to detect bone fractures with existing ones.

V. CONCLUSION
This study demonstrates the feasibility of detection of thin arbitrarily oriented fractures in superficial bones like the tibia, using a portable, compact, low complexity, and contactless MWI system. This required the generalization for 3D geometry of our previous inverse scattering formulation, which involved only 2D measurement data taken in a single linear scan.
Furthermore, the work evolved from tests on ideal cylindrical shape phantoms, or on stripped bones, now to complete ovine and caprine legs, with all the involved natural tissues, including skin and fur. The used cylindrical grid scan reinforced the detection and location of the bone fractures, providing information on its depth and shape.
Our image reconstruction algorithm detected all the tested fractures, with high SCR quality metric values even with the fully preserved tissues, without the need for considering previous knowledge of the phantom shape, or severe leg positioning restrictions. We accessed the system resolution showing that it approaches the theoretical limit. We also demonstrated good robustness of the method to permittivity and tissue thickness estimation uncertainty, and to slight involuntary movement of the patient during the exam, which certainly occur in practical clinical cases.
The obtained results prove the interest and feasibility of our method for positive fracture detection in superficial bones in very close to pre-clinical use cases, and the feasibility of using a quite simple portable and inexpensive examination setup. This contributes to making this imaging modality accessible for first response screening in ambulances, retirement houses, school infirmary, in low-income settings, and veterinary clinics.