A numerical feasibility study on monitoring bone health using microwave tomography: towards a wearable design


 Background: Osteoporosis is the major cause of bone weakness and fragility in more than 10 million people in the United States. This disease causes bone fractures in the hip or spine, which result in increasing the risk of disabilities or even death. The current gold standard in osteoporosis diagnostics, X-ray, although reliable, it uses ionizing radiations that makes it unfeasible for early and continuous monitoring applications. Recently, microwave tomography (MWT) has been emerging as a biomedical imaging modality that utilizes non-ionizing electromagnetic signals to screen bones' electrical properties. These properties are highly correlated to bones' density, which makes MWT to be an effective and safe alternative for frequent testing in osteoporosis diagnostics. Results: Both of the conventional and wearable simulated systems were successful in localizing the tibia and fibula bones in the enhanced MWT images. Furthermore, structure extraction of the leg’s model from the blind MWT images had a minimal error compared to the original one (L2-norm: 15.60%). Under five sequentially-incremental bone volume fraction (BVF) scenarios simulating bones' treatment procedure, bones were detected successfully and their density were found to be inversely proportional to the real-part of the relative permittivity values. Conclusions: This study paves the way towards implementing a safe and user-friendly MWT system that can be wearable to monitor bone degradation or treatment for osteoporosis cases. Methods: An anatomically-realistic finite-element (FE) model representing the human leg was initially generated and filled with corresponding tissues' (skin, fat, muscles, and bones) dielectric properties. Then, numerically, the forward and inverse MWT problems were solved within the framework of the finite-element method contrast source inversion algorithm (FEM-CSI). Furthermore, image reconstruction enhancements were investigated by utilizing prior information about different tissues as an inhomogeneous background as well as by adjusting the imaging domain and antennas locations based on the prior structural information. In addition, the utilization of a medically-approved matching medium that can be used in wearable applications, namely an ultrasound gel, was suggested. Additionally, an approach based on k-means clustering was developed to extract the prior structural information from blind reconstructions. Lastly. the enhanced images were used to monitor variations in BVF.

1 Introduction Figure 1: The structure of the proposed numerical microwave tomography (MWT) approach for bone degradation analysis: (a) numerically modeling a cross-sectional MRI-derived image to generate an anatomically-realistic finiteelement (FE) model with filled-in values for the real and imaginary parts of the relative complex permittivity of each tissue layer (which includes the matching medium, skin, fat, muscles, and bones); (b) calculating the synthetic data (scattered electric field values) at the antennas; (c) an initial image of the object-of-interest (OI) reconstructed blindly; (d) several image enhancements techniques were used to better enhance bones reconstruction. The enhanced image illustrates a reconstruction of a MWT where antennas and imaging domain are fitting the boundaries of the leg with an ultrasound gel being used as the matching medium. Two approaches were followed; including the use of the initial FE model and the use of a k-means clustering approach to acquire the prior structural information about the OI; (e) bone degradation monitoring following an expert-eye approach to detect variations in bone volume fraction (BVF) as variations in the corresponding dielectric properties.
The current state-of-art in using MWT for bone imaging focuses on extracting the electrical properties of the 80 calcaneus, which is also called the heel bone [6,[21][22][23]. In this paper, microwave imaging is performed across the 81 lower midsection of the leg to estimate the electrical properties of the tibia and/or fibula bones; the tibia is the 82 bigger bone located in the shaft of the lower leg, while the fibula is the smaller bone. This section of the leg is 83 chosen because here the bones consist mostly of cortical bones, unlike the proximal and distal parts of both bones 84 that are comprised of mostly trabecular (spongy) tissues [24]. In studying the effect of bone degeneration and 85 treatment processes, it is important to target the cortical bones as they are more denser and contains less fluids in 86 comparison to the trabecular bones. In addition, the midsection of the lower leg was selected due to its accessibility, 87 with the ability to position the antenna array of a MWT system around it easily. Further, the objectives of a MWT 88 system would be to locate the bone(s) within the leg, and estimate its (their) electrical properties. By monitoring 89 changes in the bone's properties, the efficacy of bone density degradation treatments can be assessed. 90 In this paper, a numerical feasibility study (Fig. 1) is conducted towards the design of a wearable microwave 91 tomography system to monitor changes in bone density within a human leg as a result of treatment. The term 92 "wearable" here highlights the fact that the microwave system transducers are in close proximity to the human leg 93 being imaged. The study was carried out using an anatomically-realistic MRI-derived numerical model of human 94 leg cross-section. Using the model, synthetic data are generated using an in-house two-dimensional (2D) finite-95 element method (FEM) solver [25,26] with the transverse magnetic (TM) approximation; due to the nature of the 96 leg cylindrical structure, this approximation is valid. The synthetic data were then inverted using the finite-element with respect to their old positions and the outermost contour of the leg. In addition, to be able to use AquaSonic 126 100 as a matching medium, its electrical properties had to be known (details in Section 6. of the measurements between 0.5 GHz to 1.5 GHz are shown in Figure 9(b). Furthermore, the value of the gel's 129 relative complex permittivity at 0.8 GHz is r = 71.4 − j10.3.

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Herein, we utilized the blindly reconstructed image to obtain information about the structure of different tissues.

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The complete procedure is briefly described in Section 6.2 using the k-mean clustering algorithm. This algorithm 141 clustered or grouped different tissue layers according to their relative permittivity and conductivity values. Thus, 142 such clusters were used to determine tissue boundaries prior to using them within the inversion algorithm with the 143 same enhancement steps mentioned in the previous section.

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The results of the clustering algorithm are represented in layer, but with the additional extraction of some pixels within the OI. This is considered acceptable as the main 152 objective of the whole procedure is to estimate the boundaries of the layers regardless of the values within them.

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The procedure for estimating the leg's contour through k-mean algorithm and using it as prior information is  The extracted prior information is incorporated as inhomogeneous background are shown in Figure 4(c),(d).

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Finally, the results of the inversion algorithm using the extracted prior information are shown in Figure 4

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As discussed in the introduction, bones' density is measured via the BVF parameter. Furthermore, changes in

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These values were based on the study conducted in [19]. Further, bones with 0.5 BVF was selected as an example 175 of healthy bones case. Moreover, bones with 0.1 BVF was a scenario with severe bone density loss.

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The synthetic data set were initially inverted blindly with no prior information. The blind reconstruction results

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were used to extract prior information about the leg as discussed in Section 2.2. This prior information was used to   We developed an approach for a numerical MWT system that is capable of monitoring bone density variations  Since the gold standards in evaluating bone density involves X-ray, which an an ionizing and harmful radiations, 227 it is desired to have an imaging modality that is simple, yet effective, and does not cause any harm to tissues. The The initial step of the study was to create the anatomically-realistic model of human leg cross-section using MRI 261 image. This model will be used to generate synthetic numerical data using an FEM forward solver. In this paper, 262 the cross-sectional MRI image representing the middle-part of a human lower leg was selected from [37] as shown 263 in Fig. 7. Next, the MRI image was imported into MATLAB, and the points corresponding to the boundaries of 264 each tissue layer are extracted; these include skin, fat, muscle, tibia, and fibula boundary points.   built for the MWT system should be reasonably size (the smaller the frequency, the larger the antenna).

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As for number of TX and RX, twenty-four antennas were chosen as they will be enough to capture the scattering After collecting the synthetic data for developed model, this data was used as input for the inversion algorithm.

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The inversion algorithm considered in this work is the multiplicatively-regularized contrast source inversion (CSI) 304 method implemented within the framework of the finite-element method (FEM) [25,27]. The details of the FEM-305 CSI algorithm as well as multiplicative regularization are outlined in [26].

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To prevent inverse crime, the forward and inversion meshes were chosen to be different. In addition, 3% uniform 307 noise was added to the scattered field synthetic data as done in [25,42]; this is a common practice in numerical Here r,high and r,low are, respectively, the highest and lowest values of expected bulk permittivity within the 327 imaging domain. In the example herein, the highest value corresponds to the muscle's relative permittivity while 328 the lowest value is the fat's relative permittivity.

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Unlike the work done by [34,46], no information about the different tissues layers within the human leg was   The location of the antennas were adjusted to surround the contour of a breast using a secondary ultrasound system.

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The results showed that by having the antennas located in a close distance from the OI, the tumor localization 347 improves, in comparison to having the antennas' on a circular surface.

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In this study, the location of antennas was changed from being on a circle of 15 cm radius to antenna locations  water. This matching medium was used as a starting point as it was very effective for breast microwave imaging

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[33] as it reduced the reflections at the matching medium/skin interface. However, a disadvantage of this mixture 359 solution is that it is liquid and will not be suitable for wearable MWT applications.

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An alternative matching medium that is considered in this work is the ultrasound gel, which is commonly used 361 for medical imaging purposes. The ultrasound gel is aqueous, bacterio-static, non-sensitizing, and non-irritating.

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Further, since it is of a gel-form it can be easily applied and cleaned in a wearable MWT system. The world 363 standard for ultrasound gels is the AquaSonic 100 [47]. To the best of the authors' knowledge, there has been no 364 previous research on the use of AquaSonic 100 ultrasound gels in microwave tomographic applications; thus it is 365 considered investigated as a matching medium in this section.

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To be able to use AquaSonic 100 as a matching medium, its electrical properties need to be known. This was 367 Figure 10: Relative complex permittivity value of AquaSonic 100 gel.
not found in literature so it was measured experimentally using Keysight's N1501A Coaxial Dielectric Probe [32]; 368 the results of the measurements between 0.5 GHz to 1.5 GHz are shown in Fig. 10. Furthermore, the value of the 369 gel's relative complex permittivity at 0.8 GHz is r = 71.4 − j10.3.

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With the new matching medium, noisy synthetic data were generated again. Next, the inversion algorithm was MWT; thus it will adopted for the remainder of the work in this study.  The utilized k-means clustering algorithm applies on a uniform square grid; however in FEM-CSI the estimated 384 electrical properties are calculated on the nodes of the triangular mesh. Thus, the first step in pre-processing 385 was to interpolate the inversion algorithm output onto a uniform square grid. After obtaining a square grid for 386 the relative complex permittivity of the blind reconstructions, pixels with values close to the matching medium 387 electrical properties were extracted and assigned a value of one for later further processing. The purpose of this 388 step is to ensure that the k-means algorithm is applied only on pixels corresponding to the reconstructed OI.

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Since the estimated values of the reconstructed images are non-uniform, and may be an over-or under-estimate 390 of the actual matching medium relative complex permittivity, the extracted pixels are selected such that the real 391 part of the relative permittivity is within the following limit: Here r,match and r,reconstr. are the real parts of the relative complex permittivity for the matching medium and as a function of mineralization at microwave frequencies,"