**2. Capacitive Sensors**

The custom designed sensors developed in collaboration with StretchSense Ltd. for this research are capacitive tactile sensors operating on the principle of a deformable parallel plate capacitor model (shown schematically in Figure 2). The dielectric layer is made of a silicone-based DEAP. The model consists of two compliant electrode layers of length l and width w separated by a dielectric material of thickness d forming a compliant capacitor [29].

**Figure 2.** Parallel plate capacitor model of the pressure sensor.

The capacitance *C*, for a parallel plate capacitor is described by:

$$\mathbf{C} = \varepsilon\_r \varepsilon\_0 \frac{lw}{d} \tag{1}$$

where ε*r* and ε0 are the relative permittivity of the dielectric layer and the vacuum permittivity respectively. Compression of the capacitive sensor along the *z*-axis, (see Figure 2), causes a decrease in the dielectric layer thickness and the distance between the two electrodes, *d*. Assuming unconstrained

edges and an incompressible material for the dielectric layer, this results in an increase in the area, (*lw*), [26]. Both changes result in an increase of the capacitance, which can then be correlated to an applied pressure.

A picture of the capacitive sensor used in this study is shown in Figure 3. This is the third generation of the sensor developed by the authors, which has better sensitivity, increased sampling frequency, wider moving average filter, improved manufacturing procedure and improved noise rejection. The system consists of a battery-powered circuit capable of measuring the capacitance of five sensing elements. There is a trade-o ff with respect to sensor head size, as the change in capacitance with pressure is directly proportional to the sensor area, while the spatial resolution reduces with increasing size. In order to maintain a small footprint, the outer surface of the sensor is electrically insulated and folded onto itself like an accordion to increase the capacitor area. This folding of the sensor effectively creates a multi-layer sensor, where each layer experiences the same pressure, resulting in a higher initial capacitance and improved pressure sensitivity. As evident in Figure 3, the sensor head is perforated with a series of holes. These holes decrease the overall sti ffness of the sensor, allowing greater deformation during compression. Figure 4 shows a simplified schematic of the pressure sensor with major dimensions labeled. Table 1 provides the dimensions and elastic modulus of the StretchSense pressure sensor, as well as specifications of the battery used. The elastic modulus was averaged between two sample tensile tests at a strain rate of 12 mm/minute and is applicable for strains below 10%. In comparison to pneumatic sensors, the sensor design used is only ~25% of the PicoPress bladder surface area. This provides a significant advantage in terms of the design's spatial resolution.

**Figure 3.** StretchSense pressure sensor, wireless measurement circuit, and battery.


**Table 1.** StretchSense pressure sensor and measurement equipment details.

**Figure 4.** StretchSense pressure sensor schematic.

The capacitance of the sensor is sampled at 660 Hz by a measurement circuit made by StretchSense. The circuit then applies a moving average of 20 data points to generate a final output at 285 Hz. A merit of using capacitive sensing is the stability of sampling rates that are largely independent from experimental setup conditions. Conversely, pneumatic sensor sampling rates are more susceptible to setup conditions as discussed in Section 1. This high sampling rate is particularly useful for the physiological applications where more dynamic pressure applications, such as pulsations tuned at a person's heart rate, are used to increase the cardiac performance [4,5]. The control circuitry used is designed to minimize noise while maximizing the output data rate.

#### *Comparison to Alternative Capacitive Sensors*

The unique DEAP construction presents multiple advantages compared to many parallel plate and floating electrode constructions. Since the electrodes are made of a compliant material with similar stiffness to the silicone dielectric layer, interlayer stresses during bending and stretching are minimized. This construction avoids using thin traces that are common for many parallel plate structures, which may break under repeated bending loads, as also noted by M-Y Cheng et al. [30]. Additionally, a major advantage of the DEAP parallel plate construction used is its simplicity and resistance to fail under many cycles of loading. The fabrication of the floating electrode and parallel plate sensors is often more complex, requiring multi-step micromachining processes to create air gaps and metal layers [25,31]. Conversely, the sensor presented avoids such process steps during fabrication. This greatly improves manufacturing scalability and reduces design complexity.

When compared to the DEAP parallel electrode construction used, Q. Guo et al. [25] presented a floating electrode design using a robust construction and good linearity over a wider pressure sensing range (up to 350 kPa, or 2625 mmHg). However, the target application of medical compression garments where pulsations are used requires much lower pressure ranges, (0–100 mmHg). Within the scope of these smaller signals, sensor noise and error reduction becomes increasingly critical for the target design. M-Y Cheng et al. [30] showed that while theoretical sensitivities of parallel plate and floating electrode constructions are the same, parallel plate constructions are predicted to have a better signal-to-noise ratio (SNR). Thus, for the application's low-pressure operating range, the parallel plate construction used is more advantageous to maximize SNR.

## **3. Experimental Methods**

In this section, the test procedures assessing sensor performance in representative configurations are outlined. One of the challenges in assessing in-situ pressure sensor performance is the difficulty in applying a realistic and measurable (known) boundary (loading) condition. Research that includes the measurement of pressures applied to the leg often neglects the measurement errors introduced when moving from laboratory testing facilities to in-situ measurements. For example, sensor calibration is typically performed on a flat, solid surface; the effect of curvature and compliance of the leg are not examined [16]. Therefore, one of the objectives of this section is to study the errors that are introduced when taking in-situ pressure measurements on a leg. For this purpose, a series of representative tests were formulated to examine the behaviour of these capacitance-based sensors in different modes. Figure 5 depicts four test setups used to validate the sensor. The tests in all configurations were repeated several times to gather relevant statistics.

**Figure 5.** Test configurations for pressure sensor validation. (**a**) Mass Test, (**b**) Bladder Test, (**c**) Piston Test, (**d**) Curvature Test.

The mass test (Figure 5a) is performed on a flat surface where the sensor sits with masses stacked on top of it. The mass applied increases in 50 g increments from 0 g up to 550 g. The applied pressure to the sensor is determined by measuring the total weight placed on the sensor over the area of the sensor. The sensor is subjected to static loads at increments of approximately 7 mmHg that are held for 30 s at a time, up to a maximum pressure of 80 mmHg. The average and standard deviation of the capacitance for a 10 s period is collected for each increment. The 10 s period is taken after the load has been applied and the measurement reading has settled. The loading profile (shown in Figure 6) has four incremental loading and unloading cycles and nine direct loading and unloading cycles. The incremental cycles are used to measure the hysteresis inherent in the sensor. Meanwhile, the direct loading cycles closely match the use-case for these sensors when applied under, for example, intermittent pneumatic compression devices. The results from the first incremental loading and unloading cycle (white section in Figure 5) are discarded as a "bedding-in" cycle, as recommended by StretchSense, to allow the sensor to acclimate to a stable position. The second incremental loading and unloading cycle (light grey section) is then used to calibrate the sensor. A fit is applied to the calibration data and this curve fit is then used to convert the capacitance measurements of the remaining validation data (dark grey section) to pressure estimates. This test is meant to examine repeatability, linearity and hysteresis of the sensor in static conditions.

**Figure 6.** Testing protocol for applied load on sensor in the static tests.

Figure 5b depicts the bladder test, whereby the sensor is placed between two inflatable (18 cm × 38 cm) bladders. The bladders are inflated by a hand pump up to a pressure of 110 mmHg following the same timing procedure as used in the mass test, while the air pressure is measured using a manometer. The assumption is that the internal pressure of the bladder is transmitted to the pressure on the sensor. The main purpose of this test is to mimic a condition where the sensor rests on a soft surface and is used as additional verification for the previous test. It should be noted that the sensor is extremely lightweight, weighing only 1.28 g, as stated in Section 2. As such, the weight of the sensor per area is negligible compared to the pressures of interest.

In the piston test (Figure 5c), the sensor is placed on top of a dynamic load cell (PCB Piezotronics 208C01, Depew, NY, USA) and an impulse is applied to the unit by a pneumatic cylinder. The pneumatic cylinder is controlled with a pressure regulator and flow restrictor valve to enable dynamic pressure application at 1–2 Hz. In this test, the peak values from the load cell and the sensor measurements in each cycle of the pneumatic cylinder were compared. Similar to the mass test, the pressure being applied to the sensor is simply the force measured by the load cell over the area of the sensor. With this test, the dynamic response and repeatability over 400 loading cycles was tested at peak pressures ranging from 0 to 120 mmHg.

The fourth test (Figure 5d) is used to determine the change in behaviour due to the curvature of the sensor. The curvature is expected to change the response of the sensor since it deforms when it conforms to a curved surface and, therefore, the capacitance changes. In the curvature test, the sensor is placed inside pipes of 19.9 mm and 39.9 mm radii, and a balloon is inserted and inflated to apply pressure in the range of 0 to 110 mmHg. The static pressure of the balloon is compared to the sensor reading, similar to the bladder test. It is noted that the curvature in this test remains constant and one of the surfaces is rigid, which is not the actual use case. However, this configuration was selected to isolate the effect of sensor curvature.

Finally, two additional testing configurations not shown in Figure 5 are employed. First, the effect of temperature and humidity on the no-load capacitance of the sensor was examined. This is done by repeating the mass test at 26 ◦C and then comparing it to the data from the 29 ◦C mass test. In addition, the variance in capacitance of the sensor is observed for a range of 17 to 42 ◦C and 45 to 69 %RH. Second, a curvature test compares the response of the capacitive sensor to that of the PicoPress pneumatic sensor. This test involved a 3D printed cylinder with a radius of 60 mm to serve as a rigid dummy leg (see Figure 7). The two sensors are placed on the cylinder with the StretchSense sensor against the cylinder and the PicoPress directly on top of it. Since the PicoPress sensor is considerably larger in size than the StretchSense sensor, the entirety of the StretchSense sensor contacts the PicoPress bladder. A sphygmomanometer is then wrapped around the cylinder and sensors to apply a known pressure. The pressure in the sphygmomanometer is manually controlled with the hand pump. The test involves a series of 10 inflations and deflations of the sphygmomanometer at three different pressures. The applied pressures are 40 mmHg, 60 mmHg, and 80 mmHg, respectively. During deflation, a minimum pressure of 5 mmHg is kept in the sphygmomanometer to prevent the cuff from moving and/or slipping. In this test, the sensor responses were both compared to the sphygmomanometer pressure and each sensor error were calculated.

**Figure 7.** PicoPress and StretchSense pneumatic comparison test.

#### **4. Results and Discussion**

The tests described in the previous section were performed on the capacitive pressure sensor presented in Section 2. The results for each test are presented in this section.

#### *4.1. Mass Test*

The results of the mass test are shown in Figure 8, where the mean capacitance measurement is plotted along with error bars for each increment. The error bars indicate +/− twice the standard deviation of the measurement at each point, which gives a 95 % confidence that values lie between the bars. The graph is plotted with the capacitance on the x-axis since the interpretation of the sensor would require the reading of the capacitance to determine the pressure applied. The slope of a linear fit through all the data points (loading and unloading) indicates that the sensor sensitivity is 0.0847 pF/mmHg. The average error bar width is +/− 0.12 pF, which corresponds to an average pressure error of +/− 1.4 mmHg when converted using the sensitivity defined above.

**Figure 8.** Sensor capacitance at various applied pressures–mass test results.

There is a discrepancy between measurements when the masses are being loaded versus unloaded, indicating that there is hysteresis in the system. The hysteresis error is defined as half of the span of the capacitance at a given pressure from loading versus unloading. The data points with increasing load are shown with triangles pointed upwards, while the decreasing loads are shown with triangles pointed downwards. The average hysteresis error across the applied pressures was computed to be +/− 3.0 mmHg. The overall error of the sensor in this test setup is just outside +/− 5.0 mmHg as also shown in Figure 9 which displays the predicted pressures versus the actual pressures using the aforementioned sensitivity calibration. As shown in this figure, the percentage error is significantly smaller for the upper range of pressure.

#### *4.2. Bladder Test*

The bladder test described in Section 3 was repeated three times and the results are shown in Figure 10. To ensure repeatability, the setup was disassembled and reassembled after every test. The pressure was applied using a sphygmomanometer of +/− 3 mmHg accuracy. The test results show an offset of 2 pF in one of the tests for all pressure ranges shown, however, it is noteworthy that the sensor sensitivity for the three tests remains the same. The causes for the offset are explored in the coming section that examines the effect of temperature and humidity on the sensor performance. The sensor sensitivity from the bladder test calibration was found to be 0.100 pF/mmHg, which is approximately 18% higher than the results from the mass test. This is likely due to the softer material

in contact with the sensor during these tests that allows for larger expansion along the plane of the sensor, thus increasing its deformation. On a hard, rigid surface, the sensor sticks to the surface and the friction restricts deformation. In the case of the mass test, the rigid surface in contact with the sensor ultimately results in a smaller sensitivity for similar pressure values. The average measurement noise is approximately +/− 0.18 pF (+/− 1.8 mmHg).

**Figure 9.** Predicted pressure compared to actual applied pressure in mass test.

**Figure 10.** Sensor capacitance at various applied pressures–bladder test results.

#### *4.3. Piston Test*

The piston test setup is designed to examine the repeatability of the sensor readings over the course of over 400 loading and unloading cycles. Figure 11 presents the peak values of the load cell pressure readings versus the capacitance of the pressure sensor. The degree of vertical scatter in these data points for a given capacitance represents the repeatability of the sensor measurements, which is considerably smaller at larger pressure values. The hysteresis is not captured during this test since only the maximum load at each cycle is recorded. This results in a smaller overall error of +/− 5.0 mmHg when measuring the vertical scatter in the plot. The best curve fit for Figure 11 corresponds to a sensitivity value of 0.067 pF/mmHg which is on the same order of magnitude as the mass test sensitivity.

**Figure 11.** Capacitance change with dynamic pressure application–piston test results.

The temporal signals during one piston stroke are presented for the load cell and capacitive sensor in Figure 12. A sharp peak is noted at the start of the signal, which is attributed to the initial impact of the piston against the sensors. This impact is disregarded in the analysis. In order to allow for a comparison between the load cell and the StretchSense measurements, the capacitance was converted to pressure using a linear curve fit as the calibration. As shown in this figure, the magnitudes of the calibrated StretchSense signal and the load cell are in good agreement. The negligible 10–20 ms latency in the capacitive sensor measurements is expected, given the data smoothing done by the measurement circuit board.

**Figure 12.** Dynamic response of load cell versus StretchSense sensor during one piston load.

The samples did not show signs of structural damage, including on the electrical connections, after applying more than 400 loading and unloading cycles. This is believed to be due to the perforated geometry and soft sensor material, which allows for compliance in the structure. This allows the sensor to perform better under fatigue loads, in comparison to a solid geometry. Electrical connections are also insulated and reinforced with Kapton tape to improve durability.
