Keywords

1 Introduction

Osteoporosis affects approximately 21.2% of women and 6.3% of men over the age of 50 world-wide [1]. In the United States alone, the estimated economic burden of osteoporosis-related fractures in 2005 was $17 billion and is expected to increase to about $25 billion by 2025 [7]. Hip fracture is one of the most serious and debilitating outcomes of osteoporosis [2, 3], with a 14–36% mortality rate during the first year following a fracture [4]. Hip fracture incidence rates increase exponentially with age in both women and men [5]. In 2010, there were estimated to be 158 million persons at high risk for a bone fracture, a staggering statistic expected to double by 2040 [6].

The World Health Organization (WHO) has defined individuals at risk for these fractures based on their areal Bone Mineral Density (aBMD, g/cm2) relative to that of a normal young adult, as measured by Dual-energy X-ray Absorptiometry (DXA) [8]. However, DXA is not without its flaws. These include exposing patients to small ionizing radiation doses of up to 0.86 mrem [9]; measurement errors due to surrounding soft tissues [10, 11]; bone mineral density (BMD) measurements are affected by variations in bone size [12, 13]; and cortical and trabecular bone cannot be differentiated [14]. Additionally, fracture predictions based on aBMD are neither sensitive nor specific [15,16,17,18,19]. While DXA-based aBMD has been previously shown to be an important predictor of hip fracture risk [20], it does not offer a direct assessment of bone’s load bearing capacity [21, 22]. Additionally, the predictive BMD value for fracture decreases in individuals over 70 years [23]. From the age of 60 to 80, the risk of hip fracture increases 13 times, while the decrease in BMD can only account for doubling of the risk [24]. Also, there is a wide overlap in BMD scores of postmenopausal women [25] who do and do not sustain osteoporotic fractures [26], and approximately 50% of fragility fractures occur in patients with DXA-derived BMD T-scores in the normal or low bone mass range [27, 28].

Quantitative ultrasound devices provide a low-cost, non-ionizing alternative to DXA using a specialized ultrasound transceiver to measure bones near the surface of the skin. A commercial example of this, Bindex®, uses the pulse-echo technique to measure the thickness of the frontal cortical shell of the tibia bone [29,30,31,32]. It has been found to correlate strongly with DXA measurements [29], a less than optimal gold standard.

1.1 Why Microwave Imaging

Microwave or radiofrequency imaging of (heel) bone was first introduced by Dr. Keith Paulsen and his research group at Dartmouth College in 2010, as an alternative non-ionizing diagnostic method to assess bone health [2, 33,34,35,36]. Due to the well-known complexity and poor spatial resolution of the standard microwave imaging setup [37, 38] used in these studies, they produced no clinically applicable results. However, the underlying physical idea of this method is simple and powerful. We have previously designed a simpler device to prove the viability of the concept at the wrist [39] and have achieved approximately 83% sensitivity and 94% specificity using a neural network classifier to differentiate between osteoporotic and healthy subjects [40].

1.2 Potential Difficulties

Taking these radiofrequency measurements is not without challenges. The transmission must pass through the bone in the region of interest and arrive at the receiver antenna with sufficient power to be measured, given a range of individuals. This makes measuring bones deeper in the body more difficult compared to more superficial bones. Additionally, the antennas must be placed such that the major component of the received signal is through the bone rather than its surrounding tissues.

1.3 Our Approach

This study consists of a set of simulations to determine field propagation inside the body validated by in vivo experimental measurements under the same conditions. The simulations produced models that included reflection coefficient S11 and transmission coefficient S21 in addition to the fields. These S-parameters can be measured in a physical setup using a network analyzer. The simulations and physical measurements were performed with the same antennas [41]. Additional simulations were performed with different antennas to investigate wideband measurements; these were not verified experimentally. The simulation results were analyzed primarily based on the electric field and Poynting vector.

2 Materials and Methods

This study was divided into two parts: first, a set of in vivo measurements using real antennas and second, a set of simulations using a corresponding human body model. The measurements were taken with Institutional Review Board (IRB) approval (IRB-19-0123) through Worcester Polytechnic Institute. The same human subject was used for all in vivo measurements.

2.1 Experimental Hardware

The antennas featured in this study are dual antiphase patch antennas [41] built using copper on FR4. Two sets of antennas, shown in Fig. 1, were investigated.

Fig. 1
A set of 2 antennas are on the left and on the right are their respective models. On the top is set B and on the bottom is set A with a measurement scale.

Comparison of size between antennas from Set B (top) and from Set A (bottom). The left two are the physical antennas and the right two are the corresponding CAD models. The spacing between patches in both antennas is 0.5 cm. Antennas in Set A had resonators of 2 cm × 1.4 cm and a ground-plane of 5 cm × 1.9 cm. Antennas in Set B had resonators of 2.5 cm × 1.6 cm and a ground-plane of 3 cm × 8 cm. The antennas were fed from the back, the solder joints in the figure are the feeds

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Set A (resonators: 2.0 cm × 1.4 cm, ground-plane: 5.0 cm × 1.9 cm) connected to matching networks that match them to 675 MHz. Matching networks were built with lumped components and applied at the antenna feeds, after the 180° power splitter (Mini-Circuits® ZFSCJ-2-232-S+, 5 MHz to 2.3 GHz).

Set B (resonators: 2.5 cm × 1.6 cm, ground-plane: 3.0 cm × 8.0 cm) were not matched to any particular frequency. The antenna feeds connected directly to the 180° power splitter (Mini-Circuits® ZFRSC-183-S+, DC to 1.8 GHz).

Both antennas had 0.5 cm spacing between the resonators. The antennas were connected to a Keysight FieldFox N9914A network analyzer. The network analyzer transmitted at −15 dBm over a frequency range of 30 kHz to 2 GHz at 401 points. The magnitude in dB and phase in degrees of S11 and S21 were saved to a CSV-file. The measurements were each a single frequency sweep.

2.2 Measurement Sites

To test the viability of various sites for measuring transmission through the femoral neck, we first checked using both sets of antennas to determine if meaningful transmission could occur given the positions of the antennas. The exact positions investigated are shown in Fig. 2.

Fig. 2
An illustration of the coronal plane is on the left and on the right is the sagittal plane. The pelvis and femur along with antennas are highlighted.

(a) Front (coronal plane) view of the right side of the body with antenna positions by number. (b) Right side (sagittal plane) view of the body with antenna positions noted by number. In both, the skin profile, right pelvis, and right femur are shown in addition to the antennas. Antennas were pushed against the body such that gaps, such as the one near position 4, were not present during the measurement. The antenna in position 4 was located over the posterior iliac crest

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The positions investigated were:

  1. 1.

    On the side of the body, positioned over the greater trochanter.

  2. 2.

    On the side of the body, positioned next the iliac crest. The antenna in this position was rotated in the plane of the drawing in Fig. 2 to investigate different polarizations. The orientation shown in the figure (vertically aligned with the body and the antenna in position 1) was considered 0°, and rotation angles were measured toward the front of the body (clockwise on the right side, counterclockwise on the left side).

  3. 3.

    On the front of the body, positioned over the anterior superior iliac spine.

  4. 4.

    On the rear of the body, positioned over the top edge of the gluteus maximus.

  5. 5.

    On the front of the body, positioned horizontally in the same horizontal plane as the greater trochanter.

  6. 6.

    On the rear of the body, positioned horizontally and below the gluteus maximus.

Measurements were taken between two of the positions. The antennas were held to the body by the subject being measured, by pressing on the center of the ground plane of each antenna. This ensured deformation of the body so that the total length of the antenna was contacting skin. The positions that were not in use for a given measurement did not have antennas present. All position combinations measured were measured with both Set A and Set B antennas.

2.3 Simulated Antenna Positioning and Human Body Model

Antenna positions on the simulated body model were the same as those on the in vivo model and are shown in Fig. 3. The base CAD model is the Ansys male human model. It was chosen to match the in vivo subject, who is male.

Fig. 3
A schematic of the coronal plane is on the left and on the right is the sagittal plane. The pelvis and femur along with antennas are highlighted.

(a) Front (coronal plane) view of the right side of the CAD model with antenna positions by number. (b) Right side (sagittal plane) view of the CAD model with antenna positions noted by number. In both, the wireframe body shell, right pelvis, and right femur are shown in addition to the antennas. The body shell was flattened or Boolean-subtracted using the antenna’s shape to eliminate gaps and ensure good coupling at each position. The apparent difference in location of position 4 is due to perspective of the drawing in Fig. 2

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The CAD model includes the full body with bones, muscles, and fat modelled throughout. Some skin layers and fat deposits are represented in aggregate by a volume with the average electric properties of the human body [42, 43]. Cartilage in joints, such as the hip joint, is not modelled by default. We investigated the effects of cartilage by producing a new shell using the area between the femur and pelvis making up the ball joint. This new volume was between 3 to 10 mm thick due mostly to the large-triangle tessellation of the bones’ shells. In addition, two outer skin shells were added with properties derived from the VHP-Female v.5.0 model [44].

2.4 Software Modelling of Matched Antennas

The matching networks were modelled in Ansys using S-Parameter measurements of the physical matching networks. The matching networks’ measurements were taken over the same frequency range (30 kHz to 2 GHz) and with the same resolution (401 points) as the in vivo transmission measurements. However, they were taken at 0 dBm and averaged across 8 sweeps, whereas the in vivo measurements were taken at a lower power (−15 dBm, see above) and with only a single frequency sweep. The input ports were all 50 Ω characteristic impedance, identical to the physical network analyzer. The 180° power splitters were modelled with an ideal splitter model. Figure 4 shows a typical simulation configuration for a single antenna at position 1 compared to a physical measurement at the same site.

Fig. 4
A line graph plots magnitude versus frequency for simulated and measured. Simulated and measured configuration move almost similarly. It has a matching network on the bottom right.

Comparison of reflection coefficient magnitude |S11| for the simulated antenna (red) and the in-vivo antenna (dashed black). This figure additionally shows the configuration of the matching and power splitting circuits in HFSS for the simulated curve. Both the simulated and measured curves were produced from antennas at position 1

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3 Results

This section is divided between the in vivo and simulated results. The in vivo results provide an assessment of the total transmission in a real subject, given a set of antenna positions, and the simulations show where inside the body the transmission occurs.

3.1 In Vivo Measurements

The positions shown in Fig. 2 are positions between which transmission was achieved. Additional sites were measured, including one between sites 4 and 6 through the center of the gluteus maximus, but no meaningful signal was received. Figure 5 shows the transmission coefficient for a selection of antenna position pairs using Set A, while Fig. 6 shows the transmission coefficient for the same position pairs using Set B.

Fig. 5
Two line graphs plot transmission coefficient versus frequency for set A. The upper graph plots for position 1 to 2, 5 to 6, and 3 to 4. Lines fluctuate closely between minus 80 through minus 40 in the above graph. In the below one, lines fluctuate closely between minus 200 to 200.

Comparison of transmission coefficient S21 when using antennas from Set A for three propagation paths: First, position 1 to position 2, a semicircular path through the compartment. Second, position 5 to position 6, a straight path through the upper femur. Third, position 3 to position 4, a straight path through the upper pelvis

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Fig. 6
Two line graphs plot transmission coefficient versus frequency for set B. The upper graph plot curves for position 1 to 2, 5 to 6, and 3 to 4. In the above graph, line trend decreases and remains constant. Closely fluctuating line trend addressed in the below graph.

Comparison of transmission coefficient S21 when using antennas from Set B for three propagation paths: First, position 1 to position 2, a semicircular path through the compartment. Second, position 5 to position 6, a straight path through the upper femur. Third, position 3 to position 4, a straight path through the upper pelvis

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In addition to the measurements shown in the figures, transmission from position 1 to position 2 was measured with varying polarizations achieved by rotating the position 2 antenna in 45° increments. For Set A, the highest average transmission over the bandwidth of the antenna transmission was seen at 45° of rotation while the lowest at 135°. Set B was less consistent but showed similar results: minimum transmission at 270° and maximum at either 45° (on the left side of the body) or 135° (on the right side). Overall, Set B showed less change in S21 over various angles of rotation than Set A, potentially due to noise. Set A showed differences of S21 at the same frequency within the passband of the antenna with different polarizations up to 20 dB, while Set B showed differences up to only 10 dB. Lying down during the measurement process decreased this variation by about half. Table 1 shows the maximum measured magnitude of the transmission coefficient for each orientation tested, for both sets of antennas.

Table 1 Maximum transmission coefficient magnitude |S21| for various relative polarizations using both sets of antennas on the right leg. Measured from position 1 to position 2
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3.2 Simulations

First, the relative agreement between the simulated and measured results is characterized by Fig. 7, in which there are resonances at approximately the same frequencies in the measured and simulated environments, but the simulated environment experiences significantly more attenuation on transmission than the measured environment.

Fig. 7
A line graph plots magnitude versus frequency for measured and simulated position 1 to 2, 3 to 4, and 5 to 6.

Comparison of transmission coefficient S21 when using antennas from Set A for three propagation paths: First (red): position 1 to position 2, a semicircular path through the compartment. Second (blue): position 5 to position 6, a straight path through the upper femur. Third (green): position 3 to position 4, a straight path through the upper pelvis. The dashed lines are the measured in-vivo |S21| (also seen in Fig. 5) and the solid lines are simulated

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Next, the propagation paths of the waves were observed using animated electric field plots in various observation planes and 3-D Poynting vector plots in the bones and the body. At higher frequencies, a surface-propagating wave is present, as seen in Fig. 8. The Poynting vector plots in the femur and pelvis for the three transmission configurations in Figs. 5, 6, and 7 are shown in Fig. 9.

Fig. 8
A set of 3 snapshots of the lower body. The sagittal plane is highlighted to indicate electric field and orientation at different frequency bands of 60,550 and 715 M H Z in a,b and c snapshots respectively.

Electric field magnitude in the sagittal plane at different frequency bands. (a) is 60 MHz, (b) is 550 MHz, and C is 715 MHz. All three are snapshots from animations, taken at a phase of 60°. Note the vertical surface-propagating wave is present in b and c but not in a. The antennas for these measurements are the Set A antennas, located at position 1

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Fig. 9
A 3-part schematic of poynting vector distribution in the femur and pelvis are labeled a, b, and c.

Poynting vector distribution in the femur and pelvis for three antenna position pairs: (a) transmission from position 1 to position 2, (b) transmission from position 3 to position 4, and (c) transmission from position 4 to position 5. Poynting vector magnitude is represented by color, warmer is larger

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In addition to the results shown in the figures, simulations were performed with a dielectric “belt” between the transmitting and receiving antennas to attenuate the surface wave. The effect was not strong enough to reduce the magnitude of the surface wave to a level comparable to that of the wave propagating through the bone.

4 Discussion

4.1 Limitations

This study only considered the strongest component of the received wave. Simulations suggest that this component likely propagates through skin, fat, and muscle when the antennas are on the same side of the body compartment. The same simulations also suggest propagation occurs through the bone and this second component will accrue some phase shift (delay) relative to the one that propagates through the soft tissue.

This study performed in vivo measurements on only one subject, a 26-year-old male, who is not at significant risk of osteoporosis according to standard risk factors.

In vivo spectra were determined from a single frequency sweep; therefore, noise contents in the spectra are more significant than had the measurements been performed using averaging of multiple sweeps.

Matched (Set A) and unmatched (Set B) antennas are not identical and have different resonant frequencies. Set A had a bandwidth of about 230 MHz, centered on about 675 MHz (when matched) and Set B had a bandwidth of about 420 MHz, centered on about 215 MHz.

4.2 Validation of Simulation Using In Vivo Results

While the measured and simulated results are not a perfect match, the resonant frequencies are collocated in the two spectra for the same antenna set and positions. Some of the difference in transmission coefficient magnitude between the measured and simulated spectra is due to differences between the model and the physical subject. These differences include the level of detail of the CAD model, and differences in physical shape between the CAD model and the subject.

4.3 Propagation Paths and Antenna Position

To achieve transmission through the bone, antennas should be placed on the opposite sides of the body compartment. If placed on the same side of the body compartment, the surface wave has the shortest path between the two antennas and thereby dominates the received signal. Direct transmission across a body compartment, contrarily, puts the shortest path between the antennas through the bone at the center of the compartment, and the Poynting vector for such a setup is the largest at the center of the compartment [39]. This is illustrated in Fig. 9, where the distribution in part C shows more even transmission through the femoral neck than part A. Part C’s antennas are transmitting across the compartment while part A’s transmit in a u-shape, starting and ending on the same side of the compartment.

4.4 Frequency Choice for Propagation Through Bone

It is common knowledge that lower frequencies provide better human body penetration but lower spatial resolution in microwave imaging. Our simulations have confirmed this, but we also note that in this application we can consider frequencies that are lower than traditionally considered for microwave imaging of the human body, due to the independence of this approach from spatial features. Therefore, a frequency of operation closer to 60 MHz with a reduced surface wave is preferable in this application to a higher frequency. Any waveguide-like effects from higher-frequency waves propagating through bones are overshadowed by the lack of penetration to reach the bones in the first place, and by the large surface-propagating waves produced by these high frequencies.