Thin-Film Flexible Wireless Pressure Sensor for Continuous Pressure Monitoring in Medical Applications

Physiological pressure measurement is one of the most common applications of sensors in healthcare. Particularly, continuous pressure monitoring provides key information for early diagnosis, patient-specific treatment, and preventive healthcare. This paper presents a thin-film flexible wireless pressure sensor for continuous pressure measurement in a wide range of medical applications but mainly focused on interface pressure monitoring during compression therapy to treat venous insufficiency. The sensor is based on a pressure-dependent capacitor (C) and printed inductive coil (L) that form an inductor-capacitor (LC) resonant circuit. A matched reader coil provides an excellent coupling at the fundamental resonance frequency of the sensor. Considering varying requirements of venous ulceration, two versions of the sensor, with different sizes, were finalized after design parameter optimization and fabricated using a cost-effective and simple etching method. A test setup consisting of a glass pressure chamber and a vacuum pump was developed to test and characterize the response of the sensors. Both sensors were tested for a narrow range (0–100 mmHg) and a wide range (0–300 mmHg) to cover most of the physiological pressure measurement applications. Both sensors showed good linearity with high sensitivity in the lower pressure range <100 mmHg, providing a wireless monitoring platform for compression therapy in venous ulceration.


Introduction
Physiological pressure, including intraocular, intracranial, and cardiovascular pressure, is a key parameter for the assessment of human health and provides opportunities for early diagnosis, personalized therapy, and preventive healthcare [1]. Pressure monitoring has been used in diagnosing lower limb problems, muscle rehabilitation, and wound monitoring [1][2][3][4]. A common medical application of non-invasive pressure sensing is the monitoring of compression therapy to treat venous leg ulcers. Venous insufficiency occurs when blood is unable to return to the heart and accumulates in the lower limbs. Chronic venous insufficiency (CVI) may cause swelling, pain, edema, and ulcerations [5,6]. The most effective treatment for CVI is compression therapy, in which a compression bandage is used to apply gradual pressure between the ankle and knee to improve the circulation of blood in the lower rehabilitation monitoring; although, in this instance it has been designed mainly for interface pressure monitoring during compression therapy.
Considering varying ulcer sizes and lower limb curvatures, as well as different positions, two versions of the sensor with different sizes were fabricated, after optimization of their design parameters for best quality factor and resonance frequencies. Nevertheless, both sensors are LC resonant tank circuits and work on a capacitive sensing mechanism. The optimization of such parameters is reported as analytical results. In the experimental work, the performance of these sensors was evaluated over a pressure range of 0-100 mmHg. In addition, both sensors were also tested for a wider pressure range of 0-300 mmHg, as to suit a varying range of medical applications.
The rest of the paper is organized as follows: Section 2 describes the methodology, including the design, fabrication, and validation of the sensor; Section 3 presents the results obtained (analytical and experimental); Sections 4 and 5 provide the final discussion and conclusions, respectively.

Materials and Methods
The proposed sensor is based on an LC resonance circuit, where the resonance frequency of the LC circuit is proportional to the applied pressure. The schematic diagram of the wireless sensing system is presented in Figure 1a. By placing multiple sensors under compression bandage as shown in Figure 1b, an array of wireless sensors can be formed to help in delivering a more controlled personalized compression therapy for the fast recovery of venous ulcers. A wearable readout band can keep records of pressure profiles during the daily routine.
Sensors 2020, 20, x FOR PEER REVIEW 4 of 22 resonant tank circuits and work on a capacitive sensing mechanism. The optimization of such parameters is reported as analytical results. In the experimental work, the performance of these sensors was evaluated over a pressure range of 0-100 mmHg. In addition, both sensors were also tested for a wider pressure range of 0-300 mmHg, as to suit a varying range of medical applications. The rest of the paper is organized as follows: Section 2 describes the methodology, including the design, fabrication, and validation of the sensor; Section 3 presents the results obtained (analytical and experimental); Section 4 and Section 5 provide the final discussion and conclusions, respectively.

Materials and Methods
The proposed sensor is based on an LC resonance circuit, where the resonance frequency of the LC circuit is proportional to the applied pressure. The schematic diagram of the wireless sensing system is presented in Figure 1a. By placing multiple sensors under compression bandage as shown in Figure 1b, an array of wireless sensors can be formed to help in delivering a more controlled personalized compression therapy for the fast recovery of venous ulcers. A wearable readout band can keep records of pressure profiles during the daily routine.

Sensor Design
The LC sensor is designed as a disc capacitor made of two parallel circular plates, and the inductor is a planar circular spiral coil located around one of the capacitor electrodes suited for a flexible design for a bandage-skin interface. A geometrical representation of the sensor and reader are shown in Figure 2a,b respectively. The resonance frequency ( ) of the proposed LC sensor depends on the inductance ( ) and capacitance ( ) of the sensor, as given in Equation (1)

Sensor Design
The LC sensor is designed as a disc capacitor made of two parallel circular plates, and the inductor is a planar circular spiral coil located around one of the capacitor electrodes suited for a flexible design for a bandage-skin interface. A geometrical representation of the sensor and reader are shown in Figure 2a,b respectively. The resonance frequency ( f o ) of the proposed LC sensor depends on the inductance (L s ) and capacitance (C s ) of the sensor, as given in Equation (1): The capacitance of the sensor can be calculated as in Equation (2): where o is the permittivity of free space, r is the relative permittivity of dielectric material in the capacitor, and r is the radius of the disk capacitor. The inductance of the planar spiral inductor is calculated using its current sheet expression [46], which depends on the inner diameter d in , outer diameter d out and number of turns N, as given in Equation (3): where µ o is the permeability of free space, N is the number of turns, d avg = (d out +d in ) , and C 1 , C 2 , C 3 and C 4 are the coefficients for the current sheet expression, which are 1, 2.46, 0, and 0.2 for a circular design [46]. The capacitance of the sensor can be calculated as in Equation (2): where is the permittivity of free space, is the relative permittivity of dielectric material in the capacitor, and is the radius of the disk capacitor. The inductance of the planar spiral inductor is calculated using its current sheet expression [46], which depends on the inner diameter , outer diameter and number of turns , as given in Equation (3): where is the permeability of free space, is the number of turns, , and , , and are the coefficients for the current sheet expression, which are 1, 2.46, 0, and 0.2 for a circular design [46].

Parasitic Components
The inductive part of the sensor, consisting of circular spirals, can be modeled accurately using lumped elements. Its elements are an inductor ( ) , a parasitic resistance ( ), and parasitic capacitance ( ), where and are in series in parallel to as shown in Figure 3a.

Parasitic Components
The inductive part of the sensor, consisting of circular spirals, can be modeled accurately using lumped elements. Its elements are an inductor (L s ), a parasitic resistance (R tot ), and parasitic capacitance (C p ), where L s and R tot are in series in parallel to C p as shown in Figure 3a. The capacitance of the sensor can be calculated as in Equation (2): where is the permittivity of free space, is the relative permittivity of dielectric material in the capacitor, and is the radius of the disk capacitor. The inductance of the planar spiral inductor is calculated using its current sheet expression [46], which depends on the inner diameter , outer diameter and number of turns , as given in Equation (3): where is the permeability of free space, is the number of turns, , and , , and are the coefficients for the current sheet expression, which are 1, 2.46, 0, and 0.2 for a circular design [46].

Parasitic Components
The inductive part of the sensor, consisting of circular spirals, can be modeled accurately using lumped elements. Its elements are an inductor ( ) , a parasitic resistance ( ), and parasitic capacitance ( ), where and are in series in parallel to as shown in Figure 3a. One of the major parasitic effects that play a major role in the quality factor of the inductor is the series resistance, which is modeled as in this paper. A large will result in a poor quality The parasitic capacitance is due to the air gap between coil turns C pc and the substrate material (C ps ).
One of the major parasitic effects that play a major role in the quality factor of the inductor is the series resistance, which is modeled as R tot in this paper. A large R tot will result in a poor quality factor of the inductor in the sensor, as well as in the reader coil. This R tot can be represented by Equation (4), which includes direct current resistance (R dc ) and alternating current resistance (R ac ).
R dc can be calculated according to Equation (5), where ρ is the resistivity of the conductor, l is the length of the spiral conductor, w is the trace width and t is the trace thickness.
For a spiral inductor with N number of turns, outer and inner diameters d out and d in , the length of the conductive traces can be calculated using Equation (6).
The component R ac in Equation (4) is affected by the values of R skin and R prox , which correspond to the skin effect and proximity effect, respectively: The skin effect occurs at higher frequencies when current does not flow through the complete cross-sectional area of the conductor, and it starts flowing only through its surface as shown in Figure 3b, which increases the effective resistance. In Figure 3b, the red color represents the skin depth (δ) for current flow and the blue color shows the area without electric current. This effect is represented by the skin depth δ. The mathematical expression to compute R skin is given in Equation (8) [47]. Here µ o is the permeability constant and µ r is the relative permeability of the conductor and f is the operational frequency.
The proximity effect is another major contributor to R ac that becomes significant above a frequency specific to the design, known as crowding frequency, f crit . In the signal frequencies above f crit , magnetic forces surrounding the conductor become significant and result in a nonuniform current flow through the conductor. This redistribution of the current causes an increase in effective resistance and can be calculated through Equation (9) [48].
The parasitic capacitance between the nearby turns can be computed from Equation (10) [49,50], where α and β are 0.9 and 0.1, respectively, and represent the parasitic contribution due to the air gap between the coil turns, and the gap between the metallic tracks and the substrate, as shown in Figure 3c. rc and rs are the relative permittivity of air and substrate material respectively.
The value of the self-resonance frequency f SRF of an inductor is critical, as above this frequency the parasitic capacitance of the inductor becomes dominant. The f SRF can be calculated using Equation (11) [50].

Device Fabrication
After the optimization of design parameters that is discussed in Section 3.1, a wet etching process was used to fabricate the two different sensors and their reader antennas. Figure 4 shows the stages in the fabrication process. In step I, as shown in Figure 4a, the mask of the sensor was directly printed on a 50 µm thick copper-coated polyimide film (Flexible isolating circuit 50 µm-coppered 35 µm-1 side, CIF, Buc, France) with a LaserJet printer (HP M553, HP Technology, Dublin, Ireland). In step II, the printed copper sheets were immersed in an etchant solution (CIF, Boosted ferric chloride solution). After manual stirring for 15 min at room temperature, all the unwanted copper was removed as shown in Figure 4b, and the patterned sheet was washed with hot water. Acetone was used to remove the ink particles from the copper surface after the etching process. In the next step, a polydimethylsiloxane (PDMS) layer (Ultra-thin film, 30 • shore A hardness, Silex Ltd., Bordon, UK) of 200 µm thickness was cut into a circular shape equal to the diameter of the capacitor electrodes and was placed on the bottom electrode as shown in Figure 4c. PDMS is widely used as a dielectric layer in capacitive pressure sensors due to its low Young's modulus and compressibility. An adhesive layer composed of polypropylene and synthetic rubber of 90 µm thickness (Tesa64621, Tesa, Norderstedt, Germany) was placed around the PDMS layer as shown in Figure 4d. In the final step, the top layer of the sensor was folded onto the PDMS layer for the final assembly of the sensor.

Device Fabrication
After the optimization of design parameters that is discussed in Section 3.1, a wet etching process was used to fabricate the two different sensors and their reader antennas. Figure 4 shows the stages in the fabrication process. In step I, as shown in Figure 4a, the mask of the sensor was directly printed on a 50 μm thick copper-coated polyimide film (Flexible isolating circuit 50 μm-coppered 35 μm-1 side, CIF, Buc, France) with a LaserJet printer (HP M553, HP Technology, Dublin, Ireland). In step II, the printed copper sheets were immersed in an etchant solution (CIF, Boosted ferric chloride solution). After manual stirring for 15 min at room temperature, all the unwanted copper was removed as shown in Figure 4b, and the patterned sheet was washed with hot water. Acetone was used to remove the ink particles from the copper surface after the etching process. In the next step, a polydimethylsiloxane (PDMS) layer (Ultra-thin film, 30° shore A hardness, Silex Ltd., Bordon, UK) of 200 μm thickness was cut into a circular shape equal to the diameter of the capacitor electrodes and was placed on the bottom electrode as shown in Figure 4c. PDMS is widely used as a dielectric layer in capacitive pressure sensors due to its low Young's modulus and compressibility. An adhesive layer composed of polypropylene and synthetic rubber of 90 μm thickness (Tesa64621, Tesa, Norderstedt, Germany) was placed around the PDMS layer as shown in Figure 4d. In the final step, the top layer of the sensor was folded onto the PDMS layer for the final assembly of the sensor. Figure 4e,f shows the top and bottom views of the fabricated sensor. The reader antenna was also fabricated by the same etching procedure, and flexible multithread wires were soldered to connect with a Sub-Miniature version A (SMA) connector.

Device Validation
To test the fabricated system (sensor with reader coils), a bench-test model was developed using a vector network analyzer (VNA E5063, Keysight Technologies Inc., Santa Rosa, CA, USA), a high-pressure glass bottle (Pressure+ 1000, Duran, Mainz, Germany) , and a digital pressure gauge (Traceable 3462, Fisher Scientific Ltd., Loughborough, UK), as shown in Figure 5. The sensor was placed inside the pressure chamber and its response recorded using the reader antenna, which was placed outside the wall of the chamber. The pressure was varied using a vacuum pump (FB70155 Pump, Fisher Scientific Ltd., Loughborough, UK) to produce positive pressure inside the chamber, which was measured as well

Device Validation
To test the fabricated system (sensor with reader coils), a bench-test model was developed using a vector network analyzer (VNA E5063, Keysight Technologies Inc., Santa Rosa, CA, USA), Sensors 2020, 20, 6653 8 of 22 a high-pressure glass bottle (Pressure+ 1000, Duran, Mainz, Germany), and a digital pressure gauge (Traceable 3462, Fisher Scientific Ltd., Loughborough, UK), as shown in Figure 5. The sensor was placed inside the pressure chamber and its response recorded using the reader antenna, which was placed outside the wall of the chamber. The pressure was varied using a vacuum pump (FB70155 Pump, Fisher Scientific Ltd., Loughborough, UK) to produce positive pressure inside the chamber, which was measured as well by the digital pressure gauge. The input impedance of the VNA was 50 Ω. A frequency sweep was generated from the VNA to observe the variation in resonance frequency against the varying pressure, and the S parameters of the sensor were recorded simultaneously.
Sensors 2020, 20, x FOR PEER REVIEW 8 of 22 by the digital pressure gauge. The input impedance of the VNA was 50 Ω. A frequency sweep was generated from the VNA to observe the variation in resonance frequency against the varying pressure, and the S parameters of the sensor were recorded simultaneously. Figure 5. Bench test setup for sensor validation where reader coil is connected to vector network analyzer and sensor is kept inside the pressure chamber and pressure is varied using pressure pump.

Results
The results presented in this paper comprise of the outcomes of two types of investigation: analytical investigations (Section 3.1) and experimental investigations (Section 3.2). The analytical investigations are performed for optimization of design parameters ( , , , ) to achieve the best quality factor ( ) , and lower resonance frequencies ( ). The experimental investigations are performed to test and characterize the performance of the two fabricated prototype sensors on suitable testbeds.

Analytical Results: Numerical Estimation of Sensor Parameters
Sensor optimization was done in two steps. In the first step, the outer diameter ( ) and the number of turns ( ) of the inductor were optimized while keeping the trace width ( ) and trace separation ( ) constant. In the second step, after selecting the optimal values of and , both and were adjusted to achieve the best quality factor ( ) with a low resonance frequency ( ).

Optimization of Outer Diameter ( ) and Number of Turns ( )
Before the fabrication stage of the sensor, MATLAB numerical modeling was performed to achieve the best quality factor ( ) within low resonance frequency ( ) range to achieve a better signal to noise ratio (SNR). The two different designs of the sensor, sensor 1 (S1) and sensor 2 (S2), were characterized according to their individual parameters. S1 was modeled for different values, between 36 and 45 mm, and a varying from 1 to 10, while keeping = = 500 μm. As can be seen from the data point shown in Figure 6, the best was 106.4, with a correspondent resonance frequency of 17.147 MHz, when and were 45 mm and 10 respectively. However, to keep the sensor size small, we selected = 40 mm and = 10 for the fabrication as there was no significant loss in (97. 46), and was also low (19.188 MHz).

Figure 5.
Bench test setup for sensor validation where reader coil is connected to vector network analyzer and sensor is kept inside the pressure chamber and pressure is varied using pressure pump.

Results
The results presented in this paper comprise of the outcomes of two types of investigation: analytical investigations (Section 3.1) and experimental investigations (Section 3.2). The analytical investigations are performed for optimization of design parameters (d out , N, w, s) to achieve the best quality factor (QF), and lower resonance frequencies ( f o ). The experimental investigations are performed to test and characterize the performance of the two fabricated prototype sensors on suitable testbeds.

Analytical Results: Numerical Estimation of Sensor Parameters
Sensor optimization was done in two steps. In the first step, the outer diameter (d out ) and the number of turns (N) of the inductor were optimized while keeping the trace width (w) and trace separation (s) constant. In the second step, after selecting the optimal values of d out and N, both s and w were adjusted to achieve the best quality factor (QF) with a low resonance frequency ( f o ).

Optimization of Outer Diameter (d out ) and Number of Turns (N)
Before the fabrication stage of the sensor, MATLAB numerical modeling was performed to achieve the best quality factor (QF) within low resonance frequency ( f o ) range to achieve a better signal to noise ratio (SNR). The two different designs of the sensor, sensor 1 (S 1 ) and sensor 2 (S 2 ), were characterized according to their individual parameters. S 1 was modeled for different d out values, between 36 and 45 mm, and a varying N from 1 to 10, while keeping s = w = 500 µm. As can be seen from the data point shown in Figure 6, the best QF was 106.4, with a correspondent resonance frequency of 17.147 MHz, when d out and N were 45 mm and 10 respectively. However, to keep the sensor size small, we selected d out = 40 mm and N = 10 for the fabrication as there was no significant loss in QF (97. 46), and f o was also low (19.188 MHz).
Sensors 2020, 20, x FOR PEER REVIEW 9 of 22 Figure 6. Analysis of S1 quality factor and resonance frequency for different number of turns and outer diameters, when trace separation and width were kept constant at 500 μm.
A similar model was computed for S2 as shown in Figure 7. In this case, the objective was to design a relatively small sensor; therefore, was varied between 10 and 14 mm and between 1 and 5 turns, while and were kept constant at 500 and 200 μm respectively. For S2, the highest was ~32, with a of 222.4 MHz for = 14 mm and = 5; however, we selected = 12 mm and = 5 to achieve an optimal set of (23.93) and (259.44 MHz) against the size of the sensor.

Optimization of Trace width ( ) and Trace separation ( )
Trace width and trace separation also affect the and resonance frequency; therefore, complete numerical modeling was performed for the selection of the trace geometry. and were analyzed for different values of and , while the number of turns and were fixed this time. Both trace width ( ) and trace gap ( ) were varied within the maximum allowable range to fit within the limits of given sensor size and number of turns. For S1, values of and were modeled between 200 and 600 μm and and were 40 mm and 10, respectively. As shown in Figure 8, the highest (103.5) was observed for = 325 μm and = 400 μm, with a resonance frequency A similar model was computed for S 2 as shown in Figure 7. In this case, the objective was to design a relatively small sensor; therefore, d out was varied between 10 and 14 mm and N between 1 and 5 turns, while s and w were kept constant at 500 and 200 µm respectively. For S 2 , the highest QF  A similar model was computed for S2 as shown in Figure 7. In this case, the objective was to design a relatively small sensor; therefore, was varied between 10 and 14 mm and between 1 and 5 turns, while and were kept constant at 500 and 200 μm respectively. For S2, the highest was ~32, with a of 222.4 MHz for = 14 mm and = 5; however, we selected = 12 mm and = 5 to achieve an optimal set of (23.93) and (259.44 MHz) against the size of the sensor.

Optimization of Trace width ( ) and Trace separation ( )
Trace width and trace separation also affect the and resonance frequency; therefore, complete numerical modeling was performed for the selection of the trace geometry. and were analyzed for different values of and , while the number of turns and were fixed this time. Both trace width ( ) and trace gap ( ) were varied within the maximum allowable range to fit within the limits of given sensor size and number of turns. For S1, values of and were modeled between 200 and 600 μm and and were 40 mm and 10, respectively. As shown in Figure 8, the highest (103.5) was observed for = 325 μm and = 400 μm, with a resonance frequency

Optimization of Trace Width (w) and Trace Separation (s)
Trace width and trace separation also affect the QF and resonance frequency; therefore, complete numerical modeling was performed for the selection of the trace geometry. QF and f o were analyzed for different values of s and w, while the number of turns and d out were fixed this time. Both trace width (w) and trace gap (s) were varied within the maximum allowable range to fit within the limits of given sensor size and number of turns. For S 1 , values of s and w were modeled between 200 and 600 µm and d out and N were 40 mm and 10, respectively. As shown in Figure 8, the highest QF (103.5) was observed for s = 325 µm and w = 400 µm, with a resonance frequency of 16.82 MHz. For an equally distributed pattern with a trace width (w) and trace gap (s) of 500 µm, a very small loss in QF (~5%) was observed, therefore, w = s = 500 µm were chosen for the design of S 1 . of 16.82 MHz. For an equally distributed pattern with a trace width ( ) and trace gap ( ) of 500 μm, a very small loss in (~5%) was observed, therefore, = = 500 μm were chosen for the design of S1. Figure 8. Analysis of S1 quality factor and resonance frequency for different trace separation and trace width, when the number of turns and outer diameter were 10 and 40 mm, respectively.
S2 was modeled by varying between 200 and 300 μm and from 200 and 500 μm, while keeping = 12 mm and = 5 fixed, as shown in Figure 9. Maximum was 23.93 with a resonance frequency of 259.44 MHz for a combination of = 500 μm and = 200 μm. As both the and the resonance frequency of S2 were very sensitive to trace width and separation, the combination of and that produced the best were chosen for S2.

Experimental Prototype and Results
After selecting the optimized design parameters ( , , , and ) , two sensors, of outer diameters 40 and 12 mm (shown in Figure 10), were fabricated and tested using the test-bench described in Section 2.3. The key design parameters, results, and operating frequencies for both sensors and respective reader coils are listed in Table 1.   For an equally distributed pattern with a trace width ( ) and trace gap ( ) of 500 μm, a very small loss in (~5%) was observed, therefore, = = 500 μm were chosen for the design of S1. Figure 8. Analysis of S1 quality factor and resonance frequency for different trace separation and trace width, when the number of turns and outer diameter were 10 and 40 mm, respectively.
S2 was modeled by varying between 200 and 300 μm and from 200 and 500 μm, while keeping = 12 mm and = 5 fixed, as shown in Figure 9. Maximum was 23.93 with a resonance frequency of 259.44 MHz for a combination of = 500 μm and = 200 μm. As both the and the resonance frequency of S2 were very sensitive to trace width and separation, the combination of and that produced the best were chosen for S2.

Experimental Prototype and Results
After selecting the optimized design parameters ( , , , and ) , two sensors, of outer diameters 40 and 12 mm (shown in Figure 10), were fabricated and tested using the test-bench described in Section 2.3. The key design parameters, results, and operating frequencies for both sensors and respective reader coils are listed in Table 1.

Experimental Prototype and Results
After selecting the optimized design parameters (d out , N, s, and w), two sensors, of outer diameters 40 and 12 mm (shown in Figure 10), were fabricated and tested using the test-bench described in Section 2.3. The key design parameters, results, and operating frequencies for both sensors and respective reader coils are listed in Table 1.   As discussed in Section 1, since bandage pressure varies between 10 and 60 mmHg during compression therapy, both fabricated sensors were tested for a pressure range of 0 to 100 mmHg. The reader coil connected with the network analyzer was magnetically coupled with the sensor, and the response of the sensor over varying pressure was measured. The measurements from VNA were triggered at an interval of 5 mmHg for a narrow range of 0-100 mmHg. These measurements are the reflection coefficients (S11 parameter) and are shown in Figures 11 and 12 for the sensors S 1 and S 2 , respectively. As discussed in Section 1, since bandage pressure varies between 10 and 60 mmHg during compression therapy, both fabricated sensors were tested for a pressure range of 0 to 100 mmHg. The reader coil connected with the network analyzer was magnetically coupled with the sensor, and the response of the sensor over varying pressure was measured. The measurements from VNA were triggered at an interval of 5 mmHg for a narrow range of 0-100 mmHg. These measurements are the reflection coefficients (S11 parameter) and are shown in Figures 11 and 12 for the sensors S1 and S2, respectively. Figure 11. Reflection coefficients (S11 parameter) of S1 for a pressure range of 0 to 100 mmHg. Figure 11. Reflection coefficients (S11 parameter) of S 1 for a pressure range of 0 to 100 mmHg. In addition to the compression therapy monitoring, the proposed sensors could be used for other medical applications, including physiological pressure measurement. Therefore, both sensors were also tested over a wider range of 0 to 300 mmHg that covers almost the entire physiological pressure range. The measurements from VNA were triggered at an interval of 25 mmHg for a wide range of 0-300 mmHg. Figures 13 and 14 show the measured reflection coefficients (S11 parameter) of S1 and S2 over this broad pressure range. Figure 13. Reflection coefficients (S11 parameter) of S1 for a pressure range between 0 to 300 mmHg. In addition to the compression therapy monitoring, the proposed sensors could be used for other medical applications, including physiological pressure measurement. Therefore, both sensors were also tested over a wider range of 0 to 300 mmHg that covers almost the entire physiological pressure range. The measurements from VNA were triggered at an interval of 25 mmHg for a wide range of 0-300 mmHg. Figures 13 and 14 show the measured reflection coefficients (S11 parameter) of S 1 and S 2 over this broad pressure range. In addition to the compression therapy monitoring, the proposed sensors could be used for other medical applications, including physiological pressure measurement. Therefore, both sensors were also tested over a wider range of 0 to 300 mmHg that covers almost the entire physiological pressure range. The measurements from VNA were triggered at an interval of 25 mmHg for a wide range of 0-300 mmHg. Figures 13 and 14 show the measured reflection coefficients (S11 parameter) of S1 and S2 over this broad pressure range. Figure 13. Reflection coefficients (S11 parameter) of S1 for a pressure range between 0 to 300 mmHg. Figure 13. Reflection coefficients (S11 parameter) of S 1 for a pressure range between 0 to 300 mmHg. Sensors 2020, 20, x FOR PEER REVIEW 14 of 22 Figure 14. Reflection coefficients (S11 parameter) of S2 for a pressure range between 0 to 300 mmHg.
As the response of both the sensors was linear within the targeted pressure range of 0 to 100 mmHg, a first-order polynomial was fitted over the measured response of the sensors. The coefficients of the linear fitted model are given in Table 2. The measure sensor response (dotted) and fitted curve (solid) for both sensors are shown in Figure 15. In the sensor response over a wide range of pressure up to 300 mmHg, a nonlinearity, associated with compression saturation of the dielectric layer, was observed at higher pressures as shown in Figure 16. Therefore, a second-order polynomial function was fitted to the measured response to obtain a model relating the resonance frequency to the pressure. The values of R-square (goodness of fit) and the model coefficients are listed in Table 3. Reflection coefficients (S11 parameter) of S 2 for a pressure range between 0 to 300 mmHg.
As the response of both the sensors was linear within the targeted pressure range of 0 to 100 mmHg, a first-order polynomial was fitted over the measured response of the sensors. The coefficients of the linear fitted model are given in Table 2. The measure sensor response (dotted) and fitted curve (solid) for both sensors are shown in Figure 15. Table 2. Coefficients of the polynomial equation ( f (P) = m × P + β; where P is pressure) curve fitting between measured resonance frequencies and applied pressure. Reflection coefficients (S11 parameter) of S2 for a pressure range between 0 to 300 mmHg.
As the response of both the sensors was linear within the targeted pressure range of 0 to 100 mmHg, a first-order polynomial was fitted over the measured response of the sensors. The coefficients of the linear fitted model are given in Table 2. The measure sensor response (dotted) and fitted curve (solid) for both sensors are shown in Figure 15. In the sensor response over a wide range of pressure up to 300 mmHg, a nonlinearity, associated with compression saturation of the dielectric layer, was observed at higher pressures as shown in Figure 16. Therefore, a second-order polynomial function was fitted to the measured response to obtain a model relating the resonance frequency to the pressure. The values of R-square (goodness of fit) and the model coefficients are listed in Table 3. In the sensor response over a wide range of pressure up to 300 mmHg, a nonlinearity, associated with compression saturation of the dielectric layer, was observed at higher pressures as shown in Figure 16. Therefore, a second-order polynomial function was fitted to the measured response to obtain a model relating the resonance frequency to the pressure. The values of R-square (goodness of fit) and the model coefficients are listed in Table 3.  To assess the repeatability of pressure measurement with both sensors, the response of the sensors for six different pressure points between 0 and 100 mmHg was measured repeatedly for 10 cycles. Figures 17 and 18 show the repeatability of S1 and S2, respectively. The mean values of the frequency response against applied pressure ( ) and standard deviation ( ) of 10 repeated measurements at 6 pressure points (100, 80, 60, 40, 20, 0) mmHg are given in Table 4.   Table 3. Coefficients of 2nd order polynomial ( f (P) = a × P 2 + b × P + β; where P is pressure) curve fitting between measured resonance frequencies and applied pressure. To assess the repeatability of pressure measurement with both sensors, the response of the sensors for six different pressure points between 0 and 100 mmHg was measured repeatedly for 10 cycles. Figures 17 and 18 show the repeatability of S 1 and S 2 , respectively. The mean values of the frequency response against applied pressure ( f u ) and standard deviation (σ) of 10 repeated measurements at 6 pressure points (100, 80, 60, 40, 20, 0) mmHg are given in Table 4.  To assess the repeatability of pressure measurement with both sensors, the response of the sensors for six different pressure points between 0 and 100 mmHg was measured repeatedly for 10 cycles. Figures 17 and 18 show the repeatability of S1 and S2, respectively. The mean values of the frequency response against applied pressure ( ) and standard deviation ( ) of 10 repeated measurements at 6 pressure points (100, 80, 60, 40, 20, 0) mmHg are given in Table 4. Figure 17. Repeatability of measurements with S1 over 10 cycles.

Discussion
An LC pressure sensing system is developed to measure the pressure in compression therapy due to wireless communication between sensor and reader coil. Optimization of the sensors is essential to achieve the best quality factor and resonance frequency while keeping the sensor size limited. Optimized values of outer diameter ( ) and the number of turns ( ), trace width ( ), and trace separation ( ) are listed in Table 1. The parasitic components of the sensor which are parasitic capacitance and parasitic resistance at resonance frequency were analyzed through numerical modeling and their values are reported in Table 1. The reported sensors were fabricated using a wet etching process, which is cost-effective and very simple but comes at the cost of less control on trace widths. In these circumstances, the thinnest trace width achieved was 200 μm. Both sensors were characterized using a bench test setup that was developed during this research work. Both sensors showed good linearity and repeatability for a pressure <100 mmHg. As shown in Figure 15, the response of both designed sensors was linear over a pressure range of 0-100 mmHg, with a sensitivity of 8 kHz/mmHg for S1 and 65 kHz/mmHg for S2. The sensor response was observed as nonlinear at the higher pressure range of 0 to 300 mmHg, as shown in Figure 16. This is due to the nonlinear effect of the compression saturation of the dielectric layer of the capacitor in the sensor. Up to 100 mmHg, the sensitivity of S1 was 8.11 kHz/mmHg, which was reduced at higher pressure due to the dielectric layer saturation. Similar behavior was noticed for S2, where sensitivity was 65.48 kHz/mmHg up to 100 mmHg, and was reduced when the sensor was loaded with higher values of pressure.
Both sensors offered good repeatability as shown in Figures 17 and 18, for a pressure range <80 mmHg; however, variability in measurements started growing in the sensor response for higher applied pressures (>80 mmHg), due to the already mentioned hysteresis of the dielectric layer. As it

Discussion
An LC pressure sensing system is developed to measure the pressure in compression therapy due to wireless communication between sensor and reader coil. Optimization of the sensors is essential to achieve the best quality factor and resonance frequency while keeping the sensor size limited. Optimized values of outer diameter (d out ) and the number of turns (N), trace width (w), and trace separation (s) are listed in Table 1. The parasitic components of the sensor which are parasitic capacitance and parasitic resistance at resonance frequency were analyzed through numerical modeling and their values are reported in Table 1. The reported sensors were fabricated using a wet etching process, which is cost-effective and very simple but comes at the cost of less control on trace widths. In these circumstances, the thinnest trace width achieved was 200 µm. Both sensors were characterized using a bench test setup that was developed during this research work. Both sensors showed good linearity and repeatability for a pressure <100 mmHg.
As shown in Figure 15, the response of both designed sensors was linear over a pressure range of 0-100 mmHg, with a sensitivity of 8 kHz/mmHg for S 1 and 65 kHz/mmHg for S 2 . The sensor response was observed as nonlinear at the higher pressure range of 0 to 300 mmHg, as shown in Figure 16. This is due to the nonlinear effect of the compression saturation of the dielectric layer of the capacitor in the sensor. Up to 100 mmHg, the sensitivity of S 1 was 8.11 kHz/mmHg, which was reduced at higher pressure due to the dielectric layer saturation. Similar behavior was noticed for S 2 , where sensitivity was 65.48 kHz/mmHg up to 100 mmHg, and was reduced when the sensor was loaded with higher values of pressure.
Both sensors offered good repeatability as shown in Figures 17 and 18, for a pressure range <80 mmHg; however, variability in measurements started growing in the sensor response for higher applied pressures (>80 mmHg), due to the already mentioned hysteresis of the dielectric layer. As it can be noticed from Table 4 that the average repeatability for both the sensors over the pressure range of 0-100 mmHg is slightly larger than the sensitivity per mmHg, the measurement uncertainty is estimated as less than ±1 mmHg.
From Table 1, it can be noticed that QF of S 1 was better than S 2 , which is due to the exponential increase of the ac resistance at higher frequencies for S 2 caused by the skin effect. In addition, by comparing the amplitude of S parameters of both sensors in Figures 13 and 14, it is quite clear that S 1 has a better signal to noise ratio (SNR) compared to S 2 .
There was noticed a difference between the calculated and measured resonance frequencies of both sensors (S 1 and S 2 ) was due to numerous possible reasons. The first possible reason might be the value of the PDMS dielectric constant ( r_PDMS ), which reported between 2.3 and 2.8 in literature [52]; however, for this research r_PDMS was selected 2.65 as stated in Table 1. The second reason for this difference might be due to the roughness of conductive traces caused by an over-etching effect during the fabrication process. This difference was greater for S 1 due to the uneven distribution of the dielectric layer and air gaps between the capacitor plates, which were relatively bigger as compared to S 2 . In the future, a more controlled fabrication process can be used to improve the etching process and dielectric layer deposition to overcome the mismatch between analytical and real values of sensor parameters.
A comparison of the developed sensors with previously reported systems is given in Table 5. It includes sensors developed explicitly for wound compression therapy, and as an extension, implantable sensors that measure bodily pressures in different locations. Although not designed specifically for the application targeted in this work, these implantable sensors are based on the same sensing concept of LC systems and operate in similar pressure ranges (as shown in Table 5). From the observation of the values listed in the table, it is noticeable that the sensitivity of the S 2 sensor, 65.48 kHz/mmHg, is comparable with the prototypes reported in the literature. This is, in the author's view, a noteworthy achievement, considering the fact that the sensor proposed here is based on a very simple and non-expensive fabrication method. By contrast, most states of the art sensors are based on microfabrication techniques, which are very expensive and laborious.

Conclusions
This work presented the design of a wireless capacitive pressure sensor of low-cost fabrication for medical applications. In particular, the sensor is designed to be used for monitoring of compression therapy in venous leg ulcers. The sensor design was optimized to achieve an optimal quality factor and resonance frequency by numerical modeling of the design parameters. The proposed thin-film flexible wireless pressure sensor was fabricated using a simple and cost-effective fabrication method. Two versions of the sensors, with 40 and 12 mm outer diameters respectively, were developed and characterized between 0-100 and 0-300 mmHg to cover the pressure range of compression therapy and the nominal range of all other physiological applications. A bench test setup was also developed for sensor validation using a glass pressure bottle, pressure pump, and a network analyzer. Both sensors showed good sensitivity, linearity, and repeatability for the lower pressure regime (0-100 mmHg). A MATLAB curve-fitting tool was used to model the relationship between the shift in resonance frequency and the change in pressure.
The focus of this research work was on the early prototype development of the sensor, which is characterized by the benchtop model. However, in the future, improved and miniaturized prototypes will be fabricated by a more controlled fabrication process, and an extensive study will be performed on human subjects to validate the effectiveness. The miniaturization and replacement of the dielectric material used in the proposed sensors with other elastomeric polymers, can improve the linearity, sensitivity, and repeatability of the sensor and will make it more suitable for numerous medical applications.