Flexible Capacitive Sensing and Ultrasound Calibration for Skeletal Muscle Deformations

Abstract

Skeletal muscles are critical to human-limb motion dynamics and energetics, where their mechanical states are seldom explored in vitro due to practical limitations of sensing technologies. This article aims to capture mechanical deformations of muscle contraction using wearable flexible sensors, which is justified with model calibration and experimental validation. The capacitive sensor is designed with the composite of conductive fabric electrodes and the porous dielectric layer to increase the pressure sensitivity and prevent lateral expansions. In this way, the compressive displacement of muscle deformation is captured in the muscle-sensor coupling model in terms of sensor deformation and parameters of pretension, material, and shape properties. The sensing model is calibrated in a linear form using ultrasound medical imaging. The sensor is capable of measuring muscle strain of 70% with an error of <3.6% and temperature disturbance of <5.6%. After 10K cycles of compression, the drift is only 3.3%. Immediate application of the proposed method is illustrated by gait pattern identification, where the K-nearest neighbor prediction accuracy of squats, level walking, stair ascent/descent, and ramp ascent is over 97% with a standard deviation below 2.6% compared to that of 94.61 ± 4.24% for ramp descent, and the response time is 14.37 ± 0.52 ms. The wearable sensing method is valid for muscle deformation monitoring and gait pattern identification, and it provides an alternative approach to capture mechanical motions of muscles, which is anticipated to contribute to understand locomotion biomechanics in terms of muscle forces and metabolic landscapes.

Introduction

Skeletal muscles are the unique power source for voluntary joint motions and the main unit for energy consumption in human locomotion.¹ As wearable robots like prosthesis and exoskeletons have been developed to assist human motions and reduce metabolic cost,² mechanical quantification of muscle contractions should have been a major approach in locomotion monitoring. However, there is very little work on monitoring muscle deformations due to technical challenges and practical limitations; thus, muscle deformations during locomotion are undervalued and underexploited in research. This article proposes a wearable sensing method to monitor muscle deformations, and its immediate application is illustrated with gait pattern identification, which is anticipated to contribute to understand locomotion biomechanics in terms of muscle forces and metabolic landscapes.³

Typical sensing methods to monitor muscle physiological states and mechanical motions include electromyography (EMG), electrical impedance tomography (EIT), and ultrasound (US) imaging. An EMG detects electric potential in muscle cells generated by neurological activation before actual muscle contraction, so it has advantages in response time to recognize motion intents⁴ and estimate joint torques.⁵ However, time-varying factors such as electrode drift, skin sweat, and muscle fatigue seriously affect the signal quality of EMG.⁶ Moreover, direct contact between metal electrodes and skins or muscles would cause tissue inflammation with long-term use. Recently, the above issues are relieved by the microneedle array design with stable interface impedance to achieve high signal-to-noise ratio.⁷ As an alternative to EMG approaches, the wearable capacitive sensing system was first proposed to monitor leg-shape changes due to muscle contractions in both able-bodied subjects and transtibial amputees,⁸ and its robustness was further justified.⁹

As an imaging technique, EIT captures interior impedance distribution at the cross section surrounded by electrodes on the body surface. The wearable wrist band incorporating with EIT was able to recognize 11 hand gestures for hand prosthesis control,¹⁰ demonstrating that the amplitude of EIT signal is adjustable and the frequency is tunable from 25 kHz up to 500 kHz compared to that of EMG up to about 500 Hz. Then, the portable EIT system was developed to recognize static hand gestures and detect contact using seven electrodes for human–computer interaction.¹¹

US sensing used less sensors and achieved higher prediction accuracy than surface EMG in continuous classification of five ambulation modes.¹² With the portable A-mode transducer, the wearable US system has been developed to measure muscular morphological deformations.¹³ Sonomyography has been applied to decode volitional motor intent of forearm musculature by optimizing the number and placement of US transducers.¹⁴ The B-mode ultrasonography has been used to measure soleus (SOL) muscle dynamics for individualized exosuit assistance during versatile walking; however, the image processing takes about 10 s to update the assistance profile.¹⁵ Besides, the coupled US and EIT system was developed for the first time to extract muscle properties for clinical applications.¹⁶ For the purpose of muscle deformation sensing, the above measured electric potentials, bioimpedances, or image pixels need complicated postprocessing and further calibration, which requires for advanced algorithms and high-end processors, as well as bulky equipment, that are among the challenges in developing wearable flexible devices conformal to musculoskeletal deformations.

Wearable technologies have been developed for motion sensing,¹⁷ health monitoring,¹⁸ terrain detection,¹⁹ and human–machine interaction^20–22 with emerging sensing methods. For example, fusion of a microflow sensor and inertial measurement unit (IMU) effectively restrains signal drifts in posture sensing.^23,24 Recently, flexible sensors featured with soft conductive materials like carbon nanotubes,²⁵ graphene,²⁶ liquid metals,²⁷ and conductive fabrics²⁸ are critical to wearable robotics. Given the highly nonlinear nature of muscle deformations, it is a challenge to develop a wearable sensor to adapt to musculoskeletal motions with good linearity and repeatability, as well as robustness for sensing performance in unstructured environments.

Two main streams of sensor development include the resistive and capacitive sensing. The resistive sensor can achieve an extremely high gauge factor (GF) of 10⁶ with graphene woven fabrics.²⁹ But it is also well known that resistive sensing in general is subjected to nonlinearity with temperature drift. In contrast, capacitive strain sensing, whose theoretical GF is limited by one, has the advantages of excellent linearity, fast response, and improved hysteresis, and its sensitivity can be improved with microstructures.²⁵ In this way, capacitive sensors to capture compressive strains or pressures³⁰ become a competent candidate for muscle motion sensing. Immediate applications of muscle shape monitoring with capacitive sensing have been illustrated by locomotion transition recognition,³¹ gait phase estimation,³² and hip exoskeleton control.³³ Due to the lack of a benchmark of muscle deformation measurements, it is also desired to develop a proper calibration method to justify the results of capacitive sensing, especially when capacitor reading is vulnerable to environmental electromagnetic interference.

To address the above challenges, this article proposes a wearable flexible sensor to capture mechanical deformations of muscle contraction, in which sensing model can be physically interpretated and experimentally calibrated. Considering the silicone-textile design with advantages of high linearity, low hysteresis, and good sensitivity,^28,34 this article extends it to compression sensing where the porous dielectric silicone layer increases the pressure sensitivity and the fabric electrodes constrain lateral expansions. Different from the previous work^8,9 where the human body acts as a component in the capacitive sensing system, the proposed flexible sensor is a stand-alone system so that its sensing model can be rigorously formulated and experimentally validated. US is used to calibrate wearable sensors for muscle motion tracking for the first time.

The rest of the article is organized as follows: The capacitive sensing model is formulated to illustrate the design concept and fabrication process. Then the sensing model is calibrated using US medical imaging, and sensor performance is characterized. Finally, an immediate application to gait pattern identification is illustrated together with result discussion on implementation issues.

Capacitive Sensing of Muscle Deformation

With the concept of capturing muscle deformations with capacitive sensing, this section formulates the theoretical model for the muscle-sensor coupling and illustrates the implementation process.

Muscle-sensor coupling model

The schematics in Figure 1 illustrate the relationship between the sensor and limb-muscle deformations, where the capacitive sensor is constrained with an inextensible bandage and compressed by the bulging muscle on a human limb. As a muscle contracts in the longitudinal direction and bulges in the cross section, the extended nylon cover applies tensions T on the bandage and effectively exerts normal compression N on the sensor-muscle coupling (Fig. 1a). The rigid bone serves as a baseline reference to analyze deformations of the sensor and muscle, in which thicknesses are denoted as d and r, respectively. The initial unloaded, passive, and activated states of the sensor-muscle coupling are represented by the subscripts 0, 1, and 2, respectively. The passive compression is composed of u₁ for the muscle and v₁ for the sensor due to the bandage pretension. When the muscle actively expands by u₂, the muscle and bandage further squeeze the sensor by v₂. In this way, the kinematics of deformation is given by

FIG. 1.

Working principle of the capacitive sensor for muscle deformations. (a) Coupling of sensor and muscle. (b) Capacitive sensing with a porous dielectric layer.

where u = [u_i, v_i]^T, x = [r_i, d_i]^T, i = 1, 2. As shown in Figure 1b, the capacitive sensor consists of a porous dielectric elastomer between two conductive fabric sheets, where the capacitance only changes with the thickness of dielectric layer, because the fabric electrodes do not change in size.

To facilitate the design analysis, several conditions are assumed in the model formulation as follows:

(A1) Small dimensions: The sensor dimensions are relatively small compared to the limb radius, so the corresponding central angle satisfies sin2θ ≈ 2θ.

(A2) Inextensible electrodes: The fabric dimensions (L and W) stay unchanged over different states: $L = (r_{j} + d_{j}) 2 θ_{j}$ (2)

(A3) Small friction: The friction between the sensor and skin is much smaller than the tension T, so that $N_{i} = - 2 T_{i} sin θ_{i}$ (3)

(A4) Negligible thicknesses: Thicknesses of the bandage, nylon, and skin, as well as their respective changes, are neglected compared to the muscle thickness.

(A5) Constant parameters: The sandwich structure has constant equivalent elastic modulus E and cross-section area A, so its deformation is characterized by $v_{i} = N_{i} d_{0} ∕ E A$ (4)

(A6) Constitutive relation: The bandage length is negligible compared with the length of nylon, so the nylon tension can be estimated by $T_{i} = K [2 π (d_{i} + r_{i}) - L_{0}]$ (5)

where L₀ is the initial free length and K is the stiffness of the nylon sheet. In the above, i = 0, 1 and j = 0, 1, and 2.

Eliminating θ_i, N_i, T₂, and L₀ in Eqs. (2–5) produces $θ_{i} = - \frac{E A v_{i}}{2 T_{i} d_{0}}, L_{0} = 2 π (d_{1} + r_{1}) - \frac{T_{1}}{K}$ (6)

and one can obtain the active muscle deformation u₂-u₁ in terms of sensor deformations v₁ and v₂: $u_{2} - u_{1} = \frac{d_{0} L (T_{1} - 2 π K v_{1}) - E A v_{1} v_{2}}{v_{1} (2 π K d_{0} L + E A v_{2})} (v_{2} - v_{1})$ (7)

The following rules are used for dimensionless analysis, $\bar{T} = \frac{T}{E A}, \bar{K} = \frac{K L}{E A}, ū = \frac{u}{d_{0}}, \bar{v} = \frac{v}{d_{0}}, η = \frac{L}{d_{0}}$

and Eq. (7) is reduced to $ū_{2} - ū_{1} = q ({\bar{v}}_{2} - {\bar{v}}_{1})$ (8a)

where $q = \frac{η {\bar{T}}_{1}}{{\bar{v}}_{1} (2 π \bar{K} + {\bar{v}}_{2})} - 1$ (8b)

If the sensor capacitance is given by C_i = ɛA/d_i, where ɛ is the dielectric coefficient, then ${\bar{v}}_{i}$ is interpreted as the relative change in measured capacitance: ${\bar{v}}_{i} = \frac{C_{0}}{C_{i}} - 1$ (9)

So Eq. (8a) reveals that the measured muscle deformation can be linear with the relative capacitance change, and the proportional factor q depends on the factors of pretension ( ${\bar{T}}_{1}$ ), material, and shape properties ( $\bar{K}$ and ƞ).

Development of sensing module

The fabrication and assembly process of the sensing module is illustrated in Figure 2, where shape deposition manufacturing was employed with molds 3D printed using photosensitive resin. Steps of development are illustrated by Supplementary Movie S1 and organized as follows:

FIG. 2.

Fabrication process of the sensing module. (a) Filling the mold with sugar. (b) Casting Ecoflex 00–30 with the mold. (c) Assembling the upper electrode. (d) Dissolving the sugar using ultrasonic process. (e) Assembling the lower electrode. (f) Assembling the circuit and protection shell. (g) Explosive view of the sensor structure.

Step 1: Figure 2a shows that the bottom mold fully accommodates sugar particles in which diameter was carefully controlled between 1.4 and 1.7 mm with a set of sieves.

Step 2: In Figure 2b, the Ecoflex solution, mixed by the 0300-A and B components at the equal volume ratio, was poured into the container assembled by the upper and bottom molds with alignment pins. To ensure that the viscous fluid took up the gaps among the sugar particles, a vent slot on the bottom mold helped to evacuate the inner air. After curing at 80℃ for 40 min, the Ecoflex-sugar composite was released from the molds.

Step 3: Two layers of conductive fabric (Mileqi Adhesive D010) and insulating tape cover the Ecoflex-sugar composite on one side (Fig. 2c). To stably connect electric wires to the fabric electrode, a copper slice was soldered to the fabric where the soldering was set at 300℃ within 1 s to prevent burning the fabric. Then the fabric was covered with an insulating layer, which can be insulating tape or Ecoflex. The Ecoflex should be cured for 25 min at 80℃.

Step 4: The Ecoflex-sugar composite was immersed in water for ultrasonic processing powered at 250 W, and the sugar was dissolved and removed in two stages to produce the porous structure: (1) the first stage lasted for 40 min to shatter and dissolve most of the sugar; (2) the second stage used another cup of fresh water to avoid sugar saturation, and residual sugar was removed after 20-min of ultrasonic processing. Supplementary Figure S1 illustrates complete removal of the sugar, which was validated by the component mass measured at different fabrication steps. Supplementary Figure S2 shows the pore distribution in the dielectric layer, and the porosity is estimated as 45.5% based on mass measurement (Supplementary Fig. S1) and image processing (Supplementary Fig. S2).

Step 5: The porous structure was fixed on the outer surface of the protection shell with the super glue (Deli 7146 502), and another fabric electrode was connected to the data collection circuit within the shell as illustrated in Figure 2e. There were two controller area network (CAN) ports for serial data transmission among the sensor network, another two ports for connection to the central controller, power supply, or ground (Fig. 2f). The electronic system was grounded with the human body to effectively reduce sensing noises.

Step 6: The capacitive sensor was finally assembled, and each port was sealed with hot glue after connection (Fig. 2g).

Figure 3 shows the prototype of the capacitive sensor, where the initial and deformed states of the porous Ecoflex matrix are compared in Figure 3a–c. The deformation is much larger compared with the nonporous elastomer under the same weight (Supplementary Fig. S3). Dimensions of the capacitor were L = W = 15 mm and d₀ = 3 mm. The overall size of sensor assembly is comparable to a common coin (Fig. 3d). The measured capacitance is collected by the analog-digital converter (AD7746) with a resolution up to 21 bits and sensing range of ±4 pF which can be extended to 0–21 pF by incorporating a serial capacitor in the circuit.

FIG. 3.

Prototype of the compliant capacitive sensor: (a) initial state. (b) Compression under 100 g. (c) Compression under 200 g. (d) Sensor assembly and inside circuit board.

Sensor Performance and Calibration

Experiments were carried out to characterize the sensor performance and calibrate the sensing model, which are organized in three groups: (1) stability and robustness of capacitive sensing were investigated in terms of quasi-statics, temperature, noise, and fatigue. (2) The capacitance model (Eq. 9) was calibrated to address issues of system parameter estimation. (3) The muscle-deformation sensing model (Eq. 8a) was calibrated using US imaging.

Sensor performance characterization

In an unstructured environment, performance of the wearable sensor could be affected by human body interference and environmental disturbances like loading steps, temperature variation, underwater turbulence, and so on. Since muscle motions mainly exert compressions on the sensor as shown in Figure 1, sensor performance quantified in terms of repeatability, robustness, and fatigue is investigated by compression tests. The loading platform (ZQ-990) compressed the capacitive sensor, and the thermostat (101–00BS) regulated the temperature under different conditions to characterize performance of the sensor. Specifications of the loading platform and thermostat are listed in Table 1. The initial referenced capacitance C₀ was measured as 1.5 pF for tests in Figure 4a, b, e on land and 0.5 pF for tests in Figure 4c, d underwater. Experimental results and observations are organized in the following:

FIG. 4.

Performance characterization of the capacitive sensor: (a) quasi-static response of sensor under different compression steps. (b) Temperature response of sensor. (c) Effect of signal noise reduction after human and sensor are grounded. (d) Flow disturbance response of sensor. (e) Repeated response of sensor in 10K cycles.

Table 1.

Specification of Experimental Equipment

Loading platform (ZQ-990)
Range of loading	0–50 N
Resolution of force	0.001 N
Accuracy of force	<±1%
Loading distance	350 mm (without jig)/248 mm (with jig)
Loading velocity	1–500 mm/min
Size (width × depth × height)	300 × 420 × 650 mm
Weight	28 kg

Quasi-static loading

Starting from the unloaded state with the initial capacitance C₀, the sensor was compressed by a deformation of 2 mm with an increment of 0.3, 0.4, and 0.5 mm to emulate different speeds of muscle motions, where each step was held for 5 s to obtain the average of measured capacitance C. Then the sensor was unloaded in the same way to its initial state. Customized Delrin fixture was used to prevent potential inference of the metal loading head with the capacitance electrodes. Figure 4a shows that the capacitance-strain relation is nonlinear but consistent among different step sizes for both loading and unloading. Little hysteresis can be observed probably due to the porous structure design, which improves pressure sensitivity as illustrated in Supplementary Figure S4. This constitutive relation will be calibrated in the next section.

Thermal effect

The whole sensor assembly (Fig. 3c), including the compliant electrode and data-processing board, was put inside the thermostat for testing from 25℃ to 80℃. In Figure 4b, the capacitance decreases with the increasing temperature, which can be explained by the larger thermal expansion of the dielectric layer thickness compared with the fabric electrode area, as well as the decreasing dielectric coefficient. It can be seen that percentage change of the measured capacitance is within 2% for the range of 25–70℃, and it is still lower than 6% when the temperature is over 70℃. It is noted that this variation is negligible compared to the effect of muscle loads as indicated in Figure 4a. Minor deviation from the decreasing trend may be due to inhomogeneous heating and temperature fluctuation at the starting stage. Thermal effect for the underwater case is illustrated in Supplementary Figure S5.

Signal-to-noise ratio

In Figure 4c, the measured C increases from C₀ to 2.4 pF under the static compression of 2 mm underwater; when one of the capacitive electrodes is grounded with the human body, which is equivalent to connect the sensor to the human capacitor in parallel, C increases to 2.5 pF. It is observed that the noise amplitude is reduced by 50% from 1.8 to 0.09 pF, and the signal-to-noise ratio (SNR) increases by more than twice from 13.3 for the ungrounded case to 27.8 for the grounded case. Since the sensor was compressed to the extreme of 66.7%, the SNRs can be estimated at the similar level for other experimental results.

Flow disturbance

The sensor was also compressed by 1 mm when it was grounded underwater and subjected to flow disturbance (Fig. 4d). The measured signal did not reflect the low frequency of flow motion, and the resulting noise amplitude of 0.09 pF is the same as that for the grounded case in Figure 4c, implying that the sensor is robust to flow disturbance.

Fatigue effect

To investigate the robustness to cyclic loading, multiple sensors were compressed and released with a period of 1.55 s by a deformation of 2 mm for over 10,000 times at 28℃. Figure 4e shows one result of the many sensors, where a drift of 0.05 pF can be observed during the first 200 cycles and was gradually stabilized afterward, justifying that the sensor is robust and stable to fatigue.

Capacitance model calibration

The dielectric layer of the capacitive sensor consists of the porous layer, protection shell, as well as super glue, so its thickness is underestimated by the nominal value of d₀ = 3 mm. To calibrate the model (Eq. 9), the correction coefficient η_d is introduced to account for the effective thickness of the dielectric layer: $v = η_{d} d_{0} (\frac{C_{0}}{C} - 1)$ (10)

The loading platform (ZQ-990) was used to calibrate the sensor. The sensing capacitance C and displacement v of compression deformation were recorded simultaneously. Embedded with the photo of the testing platform, Figure 5 shows the experimental data (circles), and η_d is calibrated as 1.5 through linear regression shown by the solid line. The optimal case of Eq. (9) or η_d = 1 for Eq. (10) is presented by the dashed line for comparison, illustrating that η_d is the slope of each line. In this way, the deviation of experimental data from the regression line can be interpreted as nonlinearity of the dielectric coefficient due to air evacuation from the cellular structure leading to effective thickness change of the dielectric layer.

FIG. 5.

Calibration of the deformation-capacitance relation.

Calibration of muscle-deformation sensing

US imaging, as one of the few technologies to capture soft tissue motions, was used to calibrate the nodal capacitive sensing for muscle deformations. The experiment was approved by the Local Ethics Committee of Huazhong University of Science and Technology (Wuhan, Hubei, China). The professional medical practitioner performed the US examination on a volunteer, where the ultrasonic probe was manually placed close to the capacitive sensor on the venter of each targeted muscle (Fig. 6a). The nylon reduces interference between the capacitance electrode and human body and protects the capacitive sensor from US couplant.

FIG. 6.

Experiment of US imaging. (a) Test setup. (b) Cross-sectional schematics of lower-limb anatomical structures. (c) US images of lower-limb muscles. US, ultrasound.

Major skeletal muscles for lower-limb motions, including the rectus femoris (RF) for the thigh and tibialis anterior (TA) and medial gastrocnemius (MG) for the shank, were monitored during joint rotations. Figure 6b schematically shows the anatomical structures from the cross-sectional view at the venter of each targeted muscle. The RF was examined in knee joint rotation, and the TA and MG were monitored during the ankle bending, which motions repeatedly for 10 times in one test and the subject rested for couple of minutes among tests to prevent muscle fatigue.

Figure 6c illustrates the US images of each muscle, where the upper curved boundary denotes the skin attached by the probe and the boundaries are highlighted between the muscles and the reference bones. To be consistent with the formulation in Section II, the deformation displacement u_us is measured as the change of normal distance d_us between the bone boundary and skin in the images. For the TA case, d_us is measured from the skin to the fascia between the tibia and fibula bones. As shown in Figure 6c, the deformation captured by capacitive sensing at the RF affected the adjacent muscles like the vastus medialis, vastus lateralis, and vastus intermedius. Similar cases can be observed for the TA surrounded by the extensor digitalis longus and extensor hallucis longus and for the MG next to the SOL, as well as inner muscles. Since the deformation displacements were measured at the targeted muscle on the skin, they represent the collective deformations contributed by the interested muscle and adjacent soft tissues with reference to the rigid bones. Specifications of the US device (GE LOGIQ E9) are listed in Table 2.

Table 2.

Specification of Ultrasound Device

(GE LOGIQ E9)
Frequency	50/60 Hz
Power	1.2 KVA
Resolution	1280 × 1024
Horizontal/vertical viewing angle	±170°
Weight	132 kg

Since the handheld rigid transducer could move on the limb due to hand tremors, this unstable manual manipulation affected the US imaging with deviations and vibrations. To correct hand trembling effects on experimental validation, the time-varying function f(t) is added in the sensing model (Eq. 8a) $Ū = η_{q} \bar{V} + f (t)$ (11)

where $Ū = \frac{Δ u - {(Δ u)}_{min}}{{(Δ u)}_{max} - {(Δ u)}_{min}}$ and $\bar{V} = \frac{Δ v - {(Δ v)}_{min}}{{(Δ v)}_{max} - {(Δ v)}_{min}}$

normalize the magnitudes to unity; $Δ u = ū_{2} - ū_{1}$ , $Δ v = {\bar{v}}_{2} - {\bar{v}}_{1}$ . If f(t) assumes a linear form of t, differentiation of Eq. (11) gives $d Ū ∕ d t = η_{q} d \bar{V} ∕ d t + b$ (12)

where η_q and b are introduced as the correction factors to be calibrated. Comparing Eqs. (12 and 8a), q can be numerically calculated as $q = η_{q} \frac{{(Δ u)}_{max} - {(Δ u)}_{min}}{{(Δ v)}_{max} - {(Δ v)}_{min}}$ (13)

Figure 7a compares the normalized change $\bar{V}$ of sensor deformation displacement against that of muscle deformation $Ū$ measured at the RF, TA, and MG, and the Supplementary Movie S2 compare the transient results of capacitive sensing and US imaging in real time. Although the US results have obvious shifts with hand tremors for TA and MG and the capacitive measurements return to zero when the muscles relax to the initial states, they match in the time of varying thus their rates of changing can be matched. As shown in Figure 7b that linear regression for the normalized speed of deformation is obtained, η_q is close to one justifying Eq. (8a) with Eq. (13), and the small b indicates the minor effect of hand tremors on capacitive sensing validation. Detailed calculation results for each muscle are listed in Table 3.

FIG. 7.

Calibration of muscle-deformation sensing. (a) Displacements of deformations. (b) Deformation rates.

Table 3.

Ultrasound Calibration for Capacitive Sensing

Coefficients	RF	TA	MG
η_q	0.91	1.3	0.94
b	−0.0066	−0.024	−0.054
q	96.044	93.302	54.22

MG, medial gastrocnemius; RF, rectus femoris; TA, tibialis anterior.

Gait Pattern Identification

As muscle motions are closely related to lower-limb joint movements, a method to capture mechanical deformations of muscles should be robust to different subjects, terrains, and algorithms, which is experimentally validated by an immediate application of gait pattern identification.

Measurements of gaits

Nine healthy volunteers (172.48 ± 5.58 cm height, 63.73 ± 5.11 kg weight) were recruited without a medical history of injuries that could affect lower limb movements. During the motion tests, they wore tight nylon pants with bandages sewed on the surface to secure six sensors on the venters of RF, TA, and MG of both legs that have major contributions to lower-limb motions. Figure 8a shows setup of the sensing system, where the sensors were connected in series with the CAN communication protocol. One capacitive electrode was grounded to reduce sensing noises using a metal ring that was connected to the human body on the waist.

FIG. 8.

Experiments for gait pattern identification. (a) Wearable sensing system. (b) Terrain for gait motions. (c) Multiple cycles of gait movements. (d) Features of muscle deformation rates.

As shown in Figure 8b, the motion tests consisted of seven gaits, including static standing (SS), squats (SQ), ramp descent (RD), ramp ascent (RA), stair descent (SD), stair ascent (SA), and level-ground walking (LW), where the stairs have 26 steps, the ramp slope is 6°, and the distances for LW and RA/RD are 40 and 30 m, respectively. Each subject was asked to perform three trial tests on all gaits. There are 21 features extracted for analysis and they are categorized into four sets, including the velocities, accelerations, standard deviations, and correlation coefficients: $f_{1 i} = d i f f (Ū_{i}), f_{2 i} = d i f f (f_{1 i})$ (14a,b) $f_{3 i} = s t d (f_{1 i}), f_{4 j} = c o r r c o e f (f_{1 j}, f_{1 (j + 3)})$ (14c,d)

where i = 1, 2, and 3 refer to RF, TA, and MG on the left leg, and i = 4, 5, and 6 denote those on the right leg, respectively, and j = 1, 2, and 3 represent the muscle correlation between both legs. Figure 8c shows the deformation rates $f_{1 i}'$ s of RF, TA, and MG on the left leg for one trial of all movement gaits in sequency. In Figure 8d, $f_{1 i}'$ s for the left leg are compared among different movement gaits of multiple cycles, where features of SS are not plotted because they are smaller than threshold values in the prediction model. In Figure 8c, d, the gait frequencies are proportional to the motion speeds. Figure 8c shows that SQ produces the maximum deformation rates of RF and MG, and LW/RD gives rise to the minimum besides SS. In Figure 8d, all the three muscles for SQ are in phase, and RF leads about 25% period ahead of TA and MG for RD; in contrast, RF and MG are out of phase while the phase of TA varies for other gaits. In this way, the motion difference in terms of signal amplitudes and phases provides a basis for pattern identification.

Identification of gait patterns

The features given by Eq. (14) were used for gait pattern identification implemented with the weighted K-nearest neighbor (KNN), linear discriminant analysis (LDA), and support vector machine (SVM) algorithms in the Matlab classification tool kit. In the three trial tests, the first two, in which each subject performed the sequential gaits with SS for 5–10 s to separate different locomotion, provided data to train the prediction model for 1 min; while the last trial, where the sequential gaits were continuous without SS, was used for model validation. The confusion matrix is defined to quantify the performance of pattern identification, and the matrix elements are defined as $c_{i j} = n_{i j} ∕ \sum_{j = 1}^{m} n_{i j} \times 100 %$ (15)

where n_ij represents the number of cases that the true ith gait is predicted as the jth class, m is the number of classes, and i, j = 1, 2, …, m. Figure 9 illustrates robustness of the sensing system with the confusion matrices using the three identification algorithms for all tested subjects. The ground truth is sampled once about every 0.55 s in which interval consisted of 50-time instances, and the predictions are made at every data point where the highest vote is taken as the predicted class for each interval. The upper part of Table 4 lists the diagonal elements of the KNN confusion matrix for each subject, in which average and standard deviation are summarized and compared against those of LDA and SVM in the lower part.

FIG. 9.

Confusion matrices for different algorithms of LDA, SVM, and KNN. KNN, K-nearest neighbor; LDA, linear discriminant analysis; SVM, support vector machine.

Table 4.

Gait Prediction Accuracy and Efficiency

Subject	SS (%)	SQ (%)	LW (%)	SA (%)	SD (%)	RA (%)	RD (%)	Time (ms)
1	100	97.29	93.27	97.48	98.81	93.59	96.83	15.2
2	100	99.43	100	100	100	99.87	89.47	13.5
3	100	100	96.48	100	97.31	96.42	87.90	14.7
4	100	92.27	96.09	95.62	99.24	93.66	98.20	14.5
5	99.87	96.98	99.59	96.37	98.84	99.66	96.44	14.8
6	100	99.61	94.50	99.65	93.73	95.82	89.88	14.2
7	99.75	98.08	100	98.70	100	98.06	98.58	13.8
8	79.22	100	99.36	96.62	99.47	98.25	96.19	14.3
9	100	99.93	96.72	100	100	98.85	97.97	14.3
KNN	97.65 ± 6.91	98.18 ± 2.51	99.33 ± 2.52	98.27 ± 1.77	98.60 ± 2.02	97.13 ± 2.39	94.61 ± 4.24	14.37 ± 0.52
LDA	97.65 ± 6.91	96.02 ± 3.59	94.91 ± 4.77	95.96 ± 3.49	93.41 ± 6.36	85.04 ± 25.31	85.05 ± 14.04	8.61 ± 0.25
SVM	97.65 ± 6.91	97.09 ± 3.23	97.11 ± 3.59	96.83 ± 2.99	96.81 ± 3.62	97.97 ± 1.67	96.53 ± 3.28	17.74 ± 0.74

KNN, K-nearest neighbor; LDA, linear discriminant analysis; LW, level-ground walking; RA, ramp ascent; RD, ramp descent; SA, stair ascent; SD, stair descent; SQ, squats; SS, static standing; SVM, support vector machine.

Result discussion

This section further analyzes the robustness of the flexible sensor for different subjects, terrains, and algorithms and discusses the above presented results to clarify technical issues in model validation and data processing when implementing the proposed sensor. Detailed discussion is organized as follows:

‒ The large deformations of muscles require the wearable sensor to be capable of nonlinear compression or extension, which leads to the use of compliant materials, porous structure design, and the nonlinear model (Eq. 10) of v and C. The calibrated Eq. (12) with ultrasonic medical imaging provides a linear relation of the same physical quantities of deformation rates in a nonlinear behavior. In this way, the sensor deformations, which are obtained by the nonlinear sensing model in terms of the measured C, truly capture muscle motions as validated in the US experiment. All the features in Eq. (14) are derived from differentiation of the sensor measurements, which usually introduces noises that may affect the prediction accuracy. So it is anticipated that features based on the original measurements can further improve the performance of gait pattern identification.

‒ The upper half of Table 4 shows details of the gait recognition for each subject using KNN, and the same statistical analyses were performed with LDA and SVM without showing subject-wise results for a concise and clear comparison. Considering all subjects' data together, prediction accuracies of all gait patterns are high with small standard deviations, indicating that the proposed method is robust when it is implemented on various tested subjects within three different algorithm frameworks. The three algorithms have individual features in processing data. LDA shows the shortest response time, SVM has a high prediction accuracy, and KNN embodies a good balance between efficiency and accuracy. Overall, the response time <20 ms for all three algorithms on the same computer (Intel core i7-5500U CPU 2.40 Ghz) has justified the proposed method for real-time applications. The success of gait pattern identification can be physically interpretated as the achievement to capture amplitude and phase differences of muscle deformations. Figure 8c, d suggests that SQ and ascending motions with larger signal amplitudes exert more muscle work than level and descending motions. RF, TA, and MG are in phase for SQ and out of phase for other motions. Occurrence of heel strikes can be identified by the phase of TA compared against that of RF, as TA absorbs impacts from the ground. In an ascending gait cycle, a heel strikes the ground earlier than that in LW; in comparison, descending motions have delayed heel strikes in a gait cycle. These features contribute to the lead and lag of TA phase for ascending and descending gaits, respectively.

‒ This research regards SS as the referenced state when the wearable sensors are donned on the body and the measurement amplitudes are small (Fig. 8c). So the SS state is first recognized when f₁₂ for the left TA (or f₁₅ for the right TA) is smaller than a prescribed threshold value that is determined from the training data dependent on each subject. Other motion patterns are then identified by a recognition model with a training accuracy over 99%. In this way, the threshold value determines the accuracy of SS prediction. For example, the SS accuracy is only 79.22% for subject 8 in Table 4, probably because posture swing during SS causes TA deformations exceeding the threshold. This indicates that TA can be critical to balance maintenance and fall precaution.

‒ Personal preference in locomotion behaviors can affect gait pattern identification. In Figure 9, LDA mistakes RA (9.61%) and RD (11.91%) for LW, and Table 4 shows that KNN has relatively low prediction accuracies of RD for subjects 2 and 3 (89.47% and 87.90%, respectively), probably because of small steps in ramp walking. These special cases suggest that individualization of a generally applicable method¹⁵ for a specific user would be future development of wearable robotic technologies. Toward this goal, this article provides a mechanical sensing method to monitor muscle deformations with a physical interpretable model that can be potentially generalized to muscle force and metabolic cost estimation among a large population and in the meantime quantitatively calibrated for individualized applications under specific working conditions.

Conclusion

This article has proposed a mechanical sensing method to monitor muscle deformations during locomotion and provided a wearable technology to identify gait motion patterns.

The sensing model has been formulated to relate deformations of the sensor and targeted muscle, where the proportional coefficient accounting for the bandage pretension, material, and shape properties can be calibrated with US measurements in experiment. Because of hand trembling in manual manipulation of the probe, the sensing model was calibrated with the deformation rates where linear relations were obtained for the RF, TA, and MG muscles. Fabrication process of the sensing module illustrates details of shape deposition manufacturing the cellular dielectric layer and assembly of the fabric electrodes and mechatronic components. Sensor characterization shows precise and robust performance under quasi-static loading, heating, cyclic loading, and underwater conditions. Immediate application of the proposed method is illustrated with gait pattern identification, justifying its robustness to different subjects and recognition algorithms.

It is anticipated that the proposed method can be potentially generalized to muscle force and metabolic cost estimation among a large population and in the meantime quantitatively calibrated for individualized applications under specific working conditions.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This research was supported by the National Natural Science Foundation of China (grants 51875221, 51922015, 91948302, U22A20249, 52027806).

Supplementary Material

Supporting Information

References

Winter

. Biomechanics and Motor Control of Human Movement. Hoboken, NY: John Wiley & Sons, Inc., 2009.

Zhang

, Fiers

, Witte

, et al. Human-in-the-loop optimization of exoskeleton assistance during walking. Science, 2017; 356:1280–1283.

Schumann

, Chen

, Wang

, et al. Maximal isometric strength indices are associated with the oxygen cost of walking and running in recreationally active men and women. Res Sports Med, 2022; 30:540–553.

Zhang

, Yang

, Qian

, et al. Real-time surface EMG pattern recognition for hand gestures based on an artificial neural network. Sensors (Basel), 2019; 19:3170.

Selinger

, Donelan

. Myoelectric control for adaptable biomechanical energy harvesting. IEEE Trans Neural Syst Rehabil, 2016; 24:364–373.

, Wang

. Noninvasive human-prosthesis interfaces for locomotion intent recognition: a review. Cyborg Bionic Syst, 2021; 9863761:1–14.

Wang

, Jiang

, Ren

, et al. Towards improving the quality of electrophysiological signal recordings by using microneedle electrode arrays. IEEE Trans Bio-med Eng, 2021; 68:3327–3335.

Chen

, Zheng

, Fan

, et al. Locomotion mode classification using a wearable capacitive sensing system. IEEE Trans Neural Syst Rehabil, 2013; 21:744–755.

Zheng

, Wang

, Wei

, et al. A noncontact capacitive sensing system for recognizing locomotion modes of transtibial amputees. IEEE Trans Bio-med Eng, 2014; 61:2911–2920.

10.

, Jiang

, Liu

, et al. A human-machine interface using electrical impedance tomography for hand prosthesis control. IEEE Trans Biomed Circ Syst, 2018; 12:1322–1333.

11.

, Hao

, Wu

, et al. An optimal electrical impedance tomography drive pattern for human-computer interaction applications. IEEE Trans Biomed Circ Syst, 2020; 14:402–411.

12.

Rabe

, Jahanandish

, Boehm

, et al. Ultrasound sensing can improve continuous classification of discrete ambulation modes compared to surface electromyography. IEEE Trans Bio-med Eng, 2021; 68:1379–1388.

13.

Yang

, Chen

, Hettiarachchi

, et al. A wearable ultrasound system for sensing muscular morphological deformations. IEEE Trans Syst Man Cybern-Syst, 2021; 51:3370–3379.

14.

Akhlaghi

, Dhawan

, Khan

, et al. Sparsity analysis of a sonomyographic muscle-computer interface. IEEE Trans Bio-med Eng, 2020; 67:688–696.

15.

Nuckols

, Lee

, Swaminathan

, et al. Individualization of exosuit assistance based on measured muscle dynamics during versatile walking. Sci Rob, 2021; 6:eabj1362.

16.

Murphy

, Skinner

, Martucci

, et al. Toward electrical impedance tomography coupled ultrasound imaging for assessing muscle health. IEEE Trans Med Imaging, 2019; 38:1409–1419.

17.

Lim

G-H

, Lee

N-E

, Lim

. Highly sensitive, tunable, and durable gold nanosheet strain sensors for human motion detection. J Mater Chem C, 2016; 4:5642–5647.

18.

Song

, Xie

, Bai

, et al. Miniaturized electromechanical devices for the characterization of the biomechanics of deep tissue. Nat Biomed Eng, 2021; 5:759–771.

19.

Al-dabbagh

AHA

, Ronsse

. A review of terrain detection systems for applications in locomotion assistance. Rob Auton Syst, 2020; 133:103628.

20.

Ahmed

, Zhang

, Hassan

, et al. A washable, stretchable, and self-powered human-machine interfacing Triboelectric nanogenerator for wireless communications and soft robotics pressure sensor arrays. Extreme Mech Lett, 2017; 13:25–35.

21.

, Wang

, Liu

, et al. A capacitive and piezoresistive hybrid sensor for long-distance proximity and wide-range force detection in human-robot collaboration. Adv Intell Syst, 2022; 4:2100213.

22.

Wang

, Xu

, Chen

, et al. Wearable human-machine interface based on the self-healing strain sensors array for control interface of unmanned aerial vehicle. Sens Actuators A, 2021; 321:112583.

23.

Liu

, Zhang

, Zhu

. A wearable human motion tracking device using micro flow sensor incorporating a micro accelerometer. IEEE Trans Bio-med Eng, 2020; 67:940–948.

24.

Liu

, Zhang

, Li

, et al. A wearable flow-MIMU device for monitoring human dynamic motion. IEEE Trans Neural Syst Rehabil, 2020; 28:637–645.

25.

Qiu

, Guo

, Chu

, et al. Rapid-response, low detection limit, and high-sensitivity capacitive flexible tactile sensor based on three-dimensional porous dielectric layer for wearable electronic skin. ACS Appl Mater Interfaces, 2019; 11:40716–40725.

26.

Kim

, Mondal

, Min

, et al. Highly sensitive and flexible strain-pressure sensors with cracked paddy-shaped MoS2/graphene foam/Ecoflex hybrid nanostructures. ACS Appl Mater Interfaces, 2018; 10:36377–36384.

27.

Zheng

, Yu

, Mao

, et al. A wearable capacitive sensor based on ring/disk-shaped electrode and porous dielectric for noncontact healthcare monitoring. Glob Chall, 2020; 4:1900079.

28.

Atalay

, Atalay

, Gafford

, et al. A highly sensitive capacitive-based soft pressure sensor based on a conductive fabric and a microporous dielectric layer. Adv Mater Technol, 2018; 3:1700237.

29.

, Zhang

, Yu

, et al. Stretchable and highly sensitive graphene-on-polymer strain sensors. Sci Rep, 2012; 2:870.

30.

Qin

, Yin

L-J

, Hao

Y-N

, et al. Flexible and stretchable capacitive sensors with different microstructures. Adv Mater, 2021; 33:2008267.

31.

Zheng

, Wang

. Noncontact capacitive sensing-based locomotion transition recognition for amputees with robotic transtibial prostheses. IEEE Trans Neural Syst Rehabil, 2017; 25:161–170.

32.

Zheng

, Manca

, Yan

, et al. Gait phase estimation based on noncontact capacitive sensing and adaptive oscillators. IEEE Trans Bio-med Eng, 2017; 64:2419–2430.

33.

Crea

, Manca

, Parri

, et al. Controlling a robotic hip exoskeleton with noncontact capacitive sensors. IEEE/ASME Trans Mechatron, 2019; 24:2227–2235.

34.

Atalay

, Sanchez

, Atalay

, et al. Batch fabrication of customizable silicone-textile composite capacitive strain sensors for human motion tracking. Adv Mater Technol, 2017; 2:1700136.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

1.40 MB

9.40 MB

82.21 MB

0.00 MB