Materials, designs, integration schemes and performance characteristics. Fig. 1a presents a schematic illustration and an image of a representative device, which we refer to as an electromechanical modulus (EMM) sensor. The stack involves (1) a top layer that generates a time-dependent Lorenz force, as the source for vibratory actuation (Fig. 1b), (2) a thin strain sensor in the form of a serpentine metal trace, as the basis for mechanical sensing (Fig. 1c) and (3) a supporting thin elastomeric layer, as a reversible, soft interface to a tissue surface. The total thickness of this example is 2.5 mm and the contacting area is ~2 cm2 (lower inset of Fig. 1a). The fabrication begins with patterning of serpentine-shaped electrical traces as resistive strain sensors, followed by transfer printing onto a soft, flexible substrate (poly(dimethylsiloxane) (PDMS), ~30 μm thick). Thin gold (Au) lines form an open mesh structure (100 nm thick) to define a sensing area of ~0.5 cm2, embedded above and below by layers of polyimide (1 μm thick), as illustrated in Figs 1c and d. A sequence of assembly steps prepares the actuator and wired connections for integration with the underlying sensor to yield a functional system. The actuator includes a nickel-coated neodymium magnet (8 mm diameter, 1.5 mm thick) on a thin polyimide disk (75 μm thick) and a copper coil (Cu, 50 μm wire diameter, 240 turns with an outer diameter of 12 mm, electrical resistance of ~70 Ohm (Yisu Electronics, Inc.)), as displayed in Fig. 1b. Detailed information appears in the Supplementary Figs 1 and 2.
As illustrated in the equivalent circuit diagram in the upper inset of Fig. 1a, the magnet undergoes vibratory motions upon application of alternating current through the copper coil (VA; < 5 V, sine-wave, 50 Hz), with a travelling amplitude of several hundreds of micrometers (Supplementary Movie 1). The ring-shaped shell (PDMS, 2.4 mm thick) around the actuator defines space for out-of-plane motions of the magnet, thereby creating forces on the contacting tissues under test due to inertial effects (Fig. 1a) and directed deformations that extend to millimeter-scale depths of tissue. The result yields strains distributed over the metal traces of the strain sensor, thus leading to periodic variations in the electrical resistance. Analysis of these responses by simultaneous measurements of the voltage across the strain sensor (output voltage, VS) via lock-in techniques (SR830, Stanford Research Systems) allows quantitative determination of the elastic modulus of the tissues. Specifically, a constant current (IS) delivered from a current source to the strain sensor (Fig. 1d and Supplementary Fig. 2) provides an input channel to the lock-in amplifier, to capture the amplitudes of periodic variations in the sensor resistance, as VS at the frequency of the vibration. By comparison to existing methods for sensing tissue biomechanics at superficial depths (micrometer-scale) by use of piezoelectric actuators/sensors20,21, these devices mechanically couple with contacting tissues through millimeter-scale thicknesses and thereby allow characterization of deep tissue biomechanics on length scales defined by the geometry of the sensor, as described subsequently. Information on the measurement mechanism and operational principles appear in Supplementary Fig. 3.
The surface of the strain sensor allows intimate, stable interfaces to tissues of interest (i.e. forearm, Fig. 1e). Conformal contact occurs via lamination in a simple, reversible manner that enables multiple cycles of use (100×), without significant change in measurement accuracy (Fig. 1e and Supplementary Fig. 4). Fig. 1f shows a device conformally mounted on the curved surface of the skin of the fingertip of a volunteer subject. As shown in Supplementary Fig. 5a, the performance remains the same, to within experimental uncertainties, after 103 cycles of bending into cylindrical shapes. The encapsulation layers (polyimide/PDMS, 1 μm/30 μm thick)27 isolate the system from moisture or biofluids. Specifically, the devices offer consistent performance before and after 7 days of immersion in artificial sweat solution at 50 oC (Supplementary Fig. 5b). With the actuator mounted on top, the devices offer stable measurement results on curved surfaces with different radii of curvature (Fig. 1g and Supplementary Fig. 6).
These simple designs and fabrication strategies yield reliable devices at high yields. Statistical data for the resistance of the strain sensor (Rsensor), the device yield and the signal-to-noise ratio (SNR) associated with 100 devices appear in Supplementary Fig. 7. The yield corresponds to the percentage of functional devices, and the SNR is the ratio between VS and the noise level with a sine wave with amplitude, VA, of 5V at a frequency, f, of 50 Hz in the top actuator, during measurements. Failure most typically results from fractures in the strain sensor or from disconnections between the wires of the coil in the actuator. These results suggest high levels of uniformity and consistency in device performance (e.g. Rsensor ~103 Ohm, total yield 96 % and SNR ~ 40 dB). Although this system can apply to a range of biological tissues, the results reported here focus on human skin through studies of healthy volunteers (Fig. 1g) and patients associated with a dermatology clinic, on various body locations, including curved surfaces of the face, forearm, shoulder, etc (Supplementary Fig. 8).
Experimental and computational analysis of the device operation. For a given VA and f, the magnet responds at the same frequency with an amplitude that depends on the properties of the sample and the parameters of the device (see Methods). The motions of the magnet deform contacting tissues and induce associated strains in the metal traces of the sensor (Fig. 2a). Periodic variations of the resistances of these traces produce changes in VS upon application of a constant current IS. The magnitude of the strain, and therefore VS, depends on the elastic modulus of the tissue. Finite element analysis (FEA) quantifies the mechanical coupling between the actuator, the sensor and the tissues. The distribution of equivalent strain across the sensor structure appears in Fig. 2a for the case of measurements (VA of 5V at 50 Hz) on artificial skin substrates (PDMS, 1 cm thick) with elastic moduli of 10 kPa, 100 kPa and 600 kPa. This range is relevant to human skin and other related tissues. The normalized strain in the sensor structure increases by a factor of ~2 as the tissue modulus decreases from 600 kPa to 10 kPa, with a corresponding increase in VS. Details for FEA simulation is in the Supplementary Information.
Results of Fig. 2b and Supplementary Fig. 9 summarize the dependence of the amplitude of the motion of the magnet on VA and f during operation on a sample of artificial skin (PDMS, 3 mm thick, 200 kPa). Here, different weight ratios of crosslinker in PDMS samples yield various desired moduli for these substrates. Independent measurements of elastic modulus exploit a biosoft intender (Hysitron Biosoft Indenter, Bruker) under quasi-static conditions (Supplementary Fig. 10). A high-speed camera allows direct visualization of the motions of the magnet during operation (see details in Methods), as a means for measuring amplitudes as small as a few hundreds of micrometers. The amplitude increases with VA, with values of ~300 μm at a VA of 5 V at 50 Hz (Fig. 2b), and also depends on f, with a resonance at ~200 Hz (Supplementary Fig. 9), consistent with results in recent publications26.
As the alternating current drives the actuators, the lock-in amplifier determines VS (Supplementary Fig. S3) at the same frequency. According to previous reports21, the viscoelastic effects of typical biological samples are negligible at the relatively low operating frequencies explored here (<1000 Hz), such that measurements can be considered as quasi-static24. As such, VS relates to the static modulus of elasticity, as per FEA results. Figs 2c and d present values of VS for artificial skin samples with elastic moduli of 10, 100 and 500 kPa (3 mm thick), as a function of VA and f. The value of VS increases with VA (from 1 to 5 V) and f (from 30 to 110 Hz), consistent with trends in the amplitudes of the motions of the magnet (Fig. 2b and Supplementary Fig. 9). Here, samples with high modulus lead to low strain, and therefore low VS, in agreement with FEA results in Fig. 2a. An important engineering consideration is that the coil can create electromagnetic induction effects on the sensor during measurements, thus generating some cross-talk with VS at high frequency (~10 μV at 1000 Hz with VA of 5 V, see details in Supplementary Fig. 11). This consideration favors low frequency (<100 Hz) operation, where such inductive effects induce voltages that are approximately two orders of magnitude lower than those associated with the sensor signals. Unless otherwise stated, the following studies use a fixed f (e.g. 50 Hz) and VA (5V).
Fig. 2e demonstrates that the value of VS decreases with increasing modulus (10 kPa to 2 MPa) at various f (30, 50 and 70 Hz) for samples of artificial skin with thicknesses of 3 mm, each supported by a glass wafer (Supplementary Fig. 10) to simulate underlying bones. In the regime of low modulus, the actuator vibrates relatively freely, with correspondingly high levels of localized deformation, large strains and thus large VS. For high modulus, the sample limits the deformations, thereby yielding small VS. Samples with moduli less than 500 kPa (red in Fig. 2e) are of particular interest because they are most relevant to many soft biological tissues, also with high sensitivity to output VS (Fig. 2f). The experimentally measured (symbols) and FEA-simulated (lines) VS vary consistently with modulus from 10 kPa to 500 kPa. Here, increasing the thickness also increases VS, mostly due to the decreasing effects of the rigid support (glass wafer) in limiting the deformations. Fig. 2g summarizes FEA and experimental results for the thickness dependence of VS for different tissue moduli. Such thickness effects diminish as the thickness of the target increases to values larger than several millimeters, to define a saturation depth (7~8 mm) for the measurements, as demonstrated in Fig. 2g. As in Supplementary Fig. 12, the results reveal the dependence of VS on tissue modulus for samples with thicknesses (2 cm) that exceed the saturation depth.
An analytical expression can be determined for the output voltage VS = f (E, H, and VA) in the case of small deformations (Equation 1), by fitting the experimental and simulation data (Supplementary Fig. 13) as
where the VS is linearly proportional to the input VA (5 V in the current experiments) in this regime of small deformations, H is the thickness of the target tissue and H0 is the saturation depth. C(E) is a dimensionless coefficient that depends on the elastic modulus (E) of the tissue, as in Supplementary Table 1 obtained from FEA results. For a given device design, the measured VS and H, together with Equation 1 and Supplementary Table 1, provide a simple, yet accurate way to determine the modulus of the target tissue. The dimensionless coefficient C should only depend on the non-dimensional, normalized tissue modulus, such as the ratio of E to the effective modulus of the device.
Measurements on hydrogels, and on porcine and human skin. The EMM sensor can characterize the mechanical properties of a range of biomaterials and skin regions both ex vivo and in vivo (Figure 3). Recent research shows that hydrogels (poly(ethylene-glycol) diacrylate, Sigma-Aldrich) at different levels of hydration (water concentration) have Young’s moduli that span those associated with most soft biological tissues in animal models and human subjects28-30. Fig. 3a presents results from samples with various levels of hydration, at thicknesses of ~4 mm (inset of Fig. 3a). VS increases with hydration from 30 wt% to 80 wt%. The results in Fig. 2g yield corresponding values of elastic modulus, as in Fig. 3b (blue), that range from ~37 kPa to ~1.5 MPa, consistent with values (green in Fig. 3b) obtained using the biosoft indenter (Hysitron Biosoft Indenter, Bruker). Similarly, Fig. 3c shows results obtained with samples of abdominal porcine skin (2 mm thick; inset of Fig. 3c). Here, increasing the hydration level to 40 wt% yields VS of ~34 μV. Comparisons are quantitatively consistent with measurements using the indenter for each hydration level, corresponding to a range from 95 kPa to ~1 MPa (Fig. 3d). Details on preparation steps and measurement results appear in Methods.
Capabilities extend to direct measurements of skin at various locations of the body of volunteer subjects, as illustrated in Fig. 3e. A collection of photographs illustrate applications across main regions (e.g. biceps, abdomen, thigh, forearm, etc). The measurement repeatability at a specific location represents an important metric. Results of multiple cycles of measurement from the forearm appear in Fig. 3f (i.e. 10 times). The average and standard deviation of VS are 47.5 μV and 0.8 μV, respectively. The inset (Fig. 3f) shows that the noise decreases with the square root of averaging time for an individual measurement (i.e. integration time, t; the duration of a measurement operation that yields the value of VS). As an example, increasing the integration time from 1 ms to 10 s decreases the noise from ~1 μV to ~10-2 μV, approximately two orders of magnitude smaller than the signal.
The measurements determine the average elastic modulus of the skin to a characteristic depth of ~8 mm, as previously demonstrated in Fig. 2g. Each location in Fig. 3e includes the skin, superficial fat, underlying muscle tissues, etc, with a total tissue thickness that exceeds this characteristic depth31-33. Measurements of elastic modulus at different locations on the body from ten healthy volunteer subjects with ages between 25-32 years and ten with ages between 60-68 years are in Fig. 3g (determination of modulus values rely on results in Supplementary Fig. 12). The results lie within expected values for human skin and ex vivo biomaterials determined in the small strain regime using techniques based on suction11,12, torsion13 and indentation10. The devices operate well on both hair bearing and hairless areas of the skin (Supplementary Fig. 14). Bending around curved surfaces induces only minor changes in the results (Supplementary Fig. 6). Consistent with expectation and recent reports2, the moduli increase with age, typically due to a loss in hydration34, in accordance with Figs. 3b and d. Detailed information for these clinical tests appears in SI Appendix. The modulus can also depend on the tension in the skin due to non-linear mechanical responses associated with collagen and elastin fibers in the dermis35. The tension typically decreases with increasing age2, thereby reducing the apparent modulus36.
Muscle activity can also affect the moduli measured across depths associated with the devices reported here. An example in Fig. 3h shows a device on the forearm in a relaxed state and in a tensed condition due to lifting a dumbbell. Repetitive cycles of movements during real-time recordings of VS yield moduli values that vary continuously between minimum and maximum values of 205 kPa and 320 kPa, respectively (details of dynamic measurements appear in Methods). These values correspond to average moduli of the skin and underlying muscles to a characteristic depth of ~8 mm. Recent studies based on ultrasound elastography methods37 report muscle moduli that exhibit a similar trend (e.g. the modulus of biceps muscles increases by ~100 kPa due to contraction)38,39. Such capabilities may support various applications in kinesiology and rehabilitation.
Results obtained from patients with skin diseases in clinical settings appear in Figure 4. These measurements reveal localized variations in skin modulus associated with lesions. A tissue-phantom model (Supplementary Fig. 15) for this case combines a low modulus silicone substrate (8 mm thick, 5 cm diameter) as healthy skin (~100 kPa) with a local high modulus silicone insert in the center (1 cm diameter; ~500 kPa) as the lesion. Measurements of modulus in the central region and nearby surrounding parts yield expected results (Supplementary Fig. 16). Evaluations of five patients (ages: 28-37) with psoriasis distributed across various body regions (arm, hand and lower back) appear in Figs 4a, c and e. Details are in Methods. This condition leads to lesions in red patches of thick, scaly skin (over 1 cm diameter), and pathological changes in skin properties, such as thickness, stiffness and hydration40,41. An adhesive medical film (3M Tegaderm) placed over the structure and onto adjacent skin prevents relative motion during evaluations. The measurements yield modulus values for the lesions and for nearby regions of normal skin (Figs 4b, d and f) for each location (Supplementary Fig. 17). As expected, the lesions (black frames, Figure 4) exhibit higher moduli than those of nearby skin, due primarily to differences in skin elasticity and hydration42. These rapid (~1 min), simple measurements have potential clinical significance in rapidly identifying and targeting of skin lesions, with quantitative metrics that have promise as diagnostic biomarkers for a range of skin conditions.
Miniaturized designs for multilayer biological targets. In addition to measuring elastic modulus to relatively large depths (over 8 mm), the lateral dimensions of the devices can be reduced, in a manner guided by computational modeling, to reduce these depths to values approaching those of the dermis (~1 mm). As an example, Fig. 5a summarizes devices that have sensing areas (surface area of the magnet) with diameters (D) from 8 mm to 1.5 mm, all with magnets that have the same thickness (1.5 mm). Fig. 5b shows experimental (symbols) and simulated (lines) FEA results for VS from devices with different D (3 mm and 1.4 mm) on a single, thick layer of artificial skin (PDMS, 2 cm thick) as a function of elastic modulus. Here, reducing D decreases the contacting area between the device and sensor, and therefore lead to decreases in VS for a given f (50 Hz) and VA (5 V). Fig. 5c shows the cross-sectional strain distributions obtained by FEA in a sufficiently thick tissue with elastic modulus of 200 kPa, subjected to pressure on the surface from devices with different D. The distributions exhibit saturation depths (red lines in Fig. 5c) that decrease with D (i.e. ~8.2 mm for D= 8 mm, ~3.3 mm for D= 3 mm and ~1.6 mm for D= 1.5 mm), consistent with experimental results (Fig. 2g and Supplementary Fig. 18). The results suggest the basis for depth profiling of the modulus, of relevance for many types of biological tissues. For skin, the stratum corneum, epidermis and upper dermis (typically 1~2 mm thick) serve as protective barriers against environmental hazards for subcutaneous tissues that consist of superficial fat and connective muscles over bones. These layers exhibit different moduli and thicknesses. Fig. 5d presents a bilayer architecture of silicone materials that approximates the structure of skin/tissue, fabricated with different thicknesses (hA = 1.8 mm; hB >> 1 cm) and different moduli (EA = 200 kPa; EB = 50 kPa). Measurements using devices with different D can determine the equivalent mechanical properties of this bilayer structure. Here, VS is 30 μV and 20 μV for devices with D of 3 mm and 1.5 mm, respectively. These VS depend on both (1) sensing area (D), and (2) the modulus of each layer. Fig. 5e shows the results of FEA simulation of VS for layer moduli in the ranges of EA = 100~300 kPa and EB = 10~100 kPa, with different EMM sensors (D of 3 mm and 1.5 mm). For VS = 30 μV and D = 3 mm, the simulated relationship between EA and EB, marked with the red curve, appears in the left of Fig. 5e. Similarly, for VS = 20 μV and D = 1.5 mm, the relationship between EA and EB marked with the black curve, appears in the right of Fig. 5e. The intersection of these two curves thus determines the calculated modulus for each layer, as 198 kPa and 52 kPa for EA and EB (Fig. 5f), respectively, which are in excellent agreement (within 5 % error) with the moduli of the sample in Fig. 5d.
To showcase this multilayer capability in clinical practice, Fig. 5g summarizes the results of moduli measured on the cheek areas and fingertip joint (near the nail plate) in human subjects (details appear in Supplementary Fig. 19). As an example of the former, literature reports indicate that the combined thickness of the epidermis and dermis is ~1.8 mm in the cheek region43, and that other tissues (i.e. superficial fat and muscle) appear beneath the dermis. Measurements using devices with D of 3 mm and of 1.5 mm yield VS of 28.7 μV and 19.3 μV on cheek, respectively. By utilizing the simulation curves of VS for both cases from Fig. 5e and locating the intersection point as in Supplementary Fig. 19a, the cheek moduli are (1) 248 kPa for the skin layer with thickness of 1.8 mm; and (2) 59 kPa for inner tissues (blue in Fig. 5g). These measured moduli are consistent with values reported for the cheek region44 and associated superficial fat in human subjects45.
In addition to body areas such as the cheek with comparatively large tissue thicknesses, measurements on regions where bones lie near the surface (e.g. hand joints, fingertip dorsum, etc), where the tissue structure is thin, are of particular interest in clinical diagnosis and treatment of dermal pathologies such as scleroderma5. As an example, consider a simple estimate of the combined thickness of skin and tissues (~3 mm; ~2 mm for the skin and ~1 mm for the underlying tissues) in the fingertip joint near the nail plate for a volunteer subject (Supplementary Fig. 20)46,47. Measurements with EMM sensors yield VS of 27.1 μV (D = 3 mm) and 18.2 μV (D = 1.5 mm), corresponding to modulus values of (1) 316 kPa for the skin layer, and (2) 67 kPa for inner tissues at this region of the body (red in Figure 5G and Supplementary Fig. 19b). These results agree with those determined using conventional approaches45,48. These findings demonstrate that a combined set of EMM sensors with appropriate D allow modulus characterization for multilayer biological targets with different thicknesses, across a wide range that involves not only bulk geometries (deep tissue scale) but also near-surface regions (superficial depth).
Interconnected arrays of devices for spatial mapping of modulus. Multiple EMM sensors can be used separately, as described above, or they can be configured into arrays, as show in Figure 6. Here, Fig. 6a presents a photograph of a collection of strain sensors printed onto a polymer substrate before interconnection (fabrication procedures appear in Methods), highlighting mechanical flexibility (Supplementary Fig. 21) for wrapping areas of interest across the body, as shown on the back in Fig. 6b (volunteer subject, age of 32, male). Fig. 6c presents a schematic illustration of a 4 × 4 array of this type (4 columns, 4 rows, area of ~100 cm2, thickness of system as ~2.5 mm) after assembly of vibratory actuators (Supplementary Fig. 22). Fig. 6d summarizes an equivalent circuit diagram of the system. Interconnection to multiplexers allows rapid readout of signals from each unit cell in a time sequence controlled by a data acquisition (DAQ) system that features a minimal number of addressing wires, with capabilities for defining the frequencies and amplitudes of input voltages to each EMM sensor via a function generator (Tektronix) as a power supply (Supplementary Fig. 23). Details appear in Methods.
The resulting multiplexed system can perform fast mapping of elastic modulus on curved, soft surfaces of tissues under quasi-static conditions. As an example, Fig. 6e shows results from measurements of elastic modulus across the back (Fig. 6b) during relaxed (left) and tensed states (right) associated with muscle contraction. Here, the actuator array (50 Hz; 5 V, Sine-wave) produces signals from the underlying sensor array. Each unit cell corresponds to an elastic modulus value determined from an individual EMM sensor with a corresponding spatial resolution of ~1.5 cm2. Stretching the trapezius muscle (red frame in Fig. 6e) of the back in the tensed condition (right of Fig. 6e) leads to spatial variations of increased modulus associated with activation of this targeted muscle group. Specifically, the average modulus for the tensed condition corresponds to ~430 kPa, compared to ~310 kPa for relaxed state, consistent with expectation and recent literature49.