To develop the target material, a polymer substrate was selected, sensor sensitivity to magnetic material concentration and material thickness were tested and optimum values selected, and then material properties, sensitivity, error from applied compression, and durability of the new material were characterized.
We sought to develop a ferrous target made up of a polymer substrate seeded with iron powder. The basis for using iron powder is that it was demonstrated effective previously in development of a ferrous sheath [22 (
link)]. The sensing element, which may be placed either on or within the wall of the prosthetic socket [19 (
link),21 (
link)], is a coil antenna of diameter 32.0 mm and thickness 0.15 mm made using flexible circuit technology [13 (
link)]. A surface-mounted capacitor is affixed to the antenna. This sensing element is wired to an inductive sensing chip (LDC1614, Texas Instruments, Dallas, TX, USA) so that when it is powered the inductor and capacitor operate as an LC tank oscillator. The magnetically permeable target near the sensor reinforces the inductor and lowers the sensor’s oscillation frequency in a distance-dependent manner. Therefore, changes in sensor frequency measured by the inductive sensing chip are a sensitive measure of the distance between the antenna and the magnetically permeable target. The sensor is calibrated in the socket using spacers of known thickness [14 (
link)].
Outside of woven forms, most thermoplastics are not flexible or elastic enough to match the properties of prosthetic liners and thus serve as the polymer substrate. Three potential exceptions are thermoplastic vulcanizates (TPV), thermoplastic polyurethanes (TPU), and thermoplastic elastomers (TPE). TPVs are fully cross-linked ethylene propylene diene terpolymer (EPDM)/polyolefin phase (PP) compounds. TPUs are thermoplastic elastomers consisting of linear segmented block copolymers composed of hard and soft segments. TPEs are copolymers that can be a mixture of polymers. They have both thermoplastic and elastomeric properties. These polymers mimic the mechanical behavior of elastomers while retaining the ability to be heated and molded. TPEs encompass a much broader range of elasticities than the others; TPVs and TPUs fall at the stiff end of the TPE tensile elasticity spectrum. Samples of both TPV and TPU polymers were tested to see if their properties could be modified sufficiently to achieve the range of desired liner elasticity. Preliminary test results showed that at the highest plasticizer loading possible, which would create the lowest stiffness material, samples from both TPV and TPU groups remained beyond the high end of the stiffness range of most elastomeric liners (tensile stiffness >309 kPa) [23 (
link)]. Thus, TPV and TPU materials were not considered further, and TPEs were selected for development in the present study.
Three TPEs were considered. The first material, 4044, is a SEEPS (styrene–ethylene–ethylene/propylene–styrene) polymer. The second material, 2063, is a SPS (styrene–propylene–styrene) polymer. The third material, an alloy, is made from two different SBS (styrene–butylene–styrene) polymers. The styrene content of each polymer and the average molecular weight of the chains are the most influential factors that determine polymer strength. Different midblock chemistries affect the amount of plasticizer the polymer can absorb and thus its elasticity, but of equal importance a variety of chemistries provide a good chance of finding a suitable adhesive for bonding the target to the elastomer or fabric backing of a typical prosthetic liner product. Preliminary testing demonstrated 4044 the most promising of these three polymers in that it demonstrated compressive and tensile elasticities within the desired range for this application.
Ferrous target samples of thickness ranging from 0.50 to 1.00 mm were fabricated for testing. To make the samples, light mineral oil was mixed with Septon 4044 (Kurarary America, Pasadena, TX, USA), placed on a hotplate, and stirred until it congealed. Iron powder was added, the material mixed, and then placed into the base of a mold (coated with a release agent) that had venting channels (
Figure 2). Three molds were used, of heights 0.50, 0.75, and 1.00 mm. A top plate was loaded with weights to compress the viscous polymer so that excess polymer was forced out through the venting channels. The mold was allowed to cool, and the material was removed and cut into 50.8 mm diameter samples for testing.
A high iron concentration compared with a low iron concentration will induce a stronger signal from the inductive sensor but will increase cost and may also increase the tensile elasticity of the target. In prior efforts developing a polyurethane-based target within a prosthetic sheath fabric, we found that a concentration of 75% to 83% produced an appropriate sensitivity [22 (
link)]. In the present study using the TPE polymer, three iron concentrations were evaluated (75%, 77%, and 85% by weight). It was expected that the highest concentration (85%) would approach saturation of the signal, thus experience minimal error from compressive stress compared with the lower concentrations.
To characterize sensitivity of the inductive sensor to targets of different iron concentration, a testing jig was used (
Figure 3). The jig allowed the inductive sensor antenna to be positioned above a target sample at a known height, recorded using a height gauge (570–312, Mitutoyo, Aurora, IL, USA) with resolution of 0.01 mm. The antenna was adjusted in incremental steps, 0.25 mm for distances up to 2.00 mm, and 1.00 mm for distances between 2.00 mm and 15.00 mm.
A thinner magnetic target is preferable since it occupies less volume in the socket and is thus less disruptive to prosthesis users. Thicknesses of 0.50, 0.75, and 1.00 mm were tested.
To characterize sensitivity of the inductive sensor to target thickness, the testing jig shown in
Figure 3 was used. Data points were concentrated at low distance so as to obtain an accurate sensitivity reading in the high sensitivity region of the calibration curve and to ensure the 0.00 mm distance was well defined. The antenna was adjusted in incremental steps, 0.05 mm for distances up to 0.60 mm, 0.25 mm for distances between 0.60 mm and 2.00 mm, and 1.00 mm for distances above 2.00 mm but less than 15.00 mm.
Compression testing was conducted using procedures similar to those described previously for testing prosthetic liners [23 (
link)]. A material testing machine was used (Instron 5944, Norwood, MA, USA). Samples were of dimension 19.0 mm diameter. Synthetic lubricant (Outlast, C & C Synthetics, Mandeville, LA, USA) was applied to the target material samples to reduce friction. Samples were cyclically preconditioned for 15 minutes from 0 to 250 kPa at a rate of 100% strain per second and then re-lubricated before the test. They were then compressed to 60% strain at a rate of 150% strain per second. Tests were conducted until two cycles of repeatable stress strain response were achieved.
Measured engineering stress was converted to true stress under the assumption of material incompressibility. Compressive elasticity (CE) was calculated as the tangent modulus between 10% and 40% strain [23 (
link)]. Three samples were tested, and the overall CE was the arithmetic mean of the three of them.
Tensile testing was conducted using procedures similar to those described previously for testing prosthetic liners [23 (
link)]. Samples of target material of dimension 170.0 mm × 31.3 mm were adhered at the ends of a custom test fixture equipped with linear slide rails to accommodate the changing thickness in the sample during the test. The two halves of the jig were installed using parallel blocks to ensure the sample was properly aligned. The sample was pulled at a displacement rate of 30 mm/s until a 60% strain was achieved. The sample was allowed to rest for 20 minutes and then the test was rerun. Testing was repeated until two consistent results were achieved.
Engineering stress was converted to true stress using the assumption of incompressibility. From the resulting stress strain plot, the slope of the tangent line to the curve between strains of 10% and 40% was calculated. The slope of this line was the tensile elasticity for each sample. Three samples were tested, and the overall tensile elasticity was the arithmetic mean of the three of them.
Volumetric elasticity testing was conducted similar to that described previously for liner testing [23 (
link)]. Samples 10.0 mm in diameter and 1.0 mm thick were coated with synthetic lubricant and placed in a 10.0 mm diameter well. Six samples were stacked in the well to achieve a thickness comparable to prosthetic liners tested previously (approximately 6.0 mm). The plunger of the tensile testing machine was lowered into the well and compressed the specimen at 0.1 percent strain per second up to 500 kPa compression. Tests were conducted until two cycles of repeatable stress strain response were achieved. Using the highest loads tested, the line tangent to the linear region was calculated and the slope reported as the volumetric elasticity (VE).
Using the VE and CE values for each sample, we calculated the Poisson ratio using Hooke’s law and the definition of Poisson ratio:
Evaluations were conducted to characterize sensor sensitivity to compressive stress. A base with a cutout space was used to isolate the antenna and keep it at a consistent distance from the target (2.0 mm) during testing (
Figure 4). A 1.6 mm-thick plate of quartz glass (elasticity of 72 GPa) was placed on top of the base to minimize deformation of the support jig. Testing machine load and displacement data (Instron 5944, Norwood, MA, USA) were collected simultaneously with sensor data.
A 50.8 mm diameter target material sample was centered above the antenna. Preliminary testing demonstrated that samples tended to stick to the platen during testing, thus a thin layer of synthetic lubricant was applied to the sample. Six pre-conditioning cycles from 10 kPa to 425 kPa were applied. The crosshead rate was 30 mm/s during loading and unloading. A pressure of 425 kPa was held for 15 s during each cycle. Addition of the lubricant introduced a “toe” region to the material property curve at pressures below 25 kPa. Lubricant was squeezed out from between the platen and test sample. Therefore, after preconditioning, the pressure was stepped from 25 kPa to 425 kPa in 40 kPa increments and held for 15 s at each pressure.
Durability testing was conducted using a fabric–polymer–fabric stack-up so that the 0.50 mm-thick polymer target did not fold over itself when the test sample was worn in the shoe of an able-bodied person. The stack-up was made in a two-step process. First, a 0.50 mm-thick sample of the ferrous polymer was overlaid onto a 0.60 mm-thick sheet of nylon spandex (FLNS, Seattle Fabrics, Inc., Seattle, WA, USA). This construct was placed in a mold and heated to mechanically bond together. This process was repeated on the opposite surface with a second layer of fabric so as to sandwich the 0.50 mm-thick ferrous polymer sample between the two fabric sheets. Samples of 50.8 mm diameter were punched out of the finished stack-up. These samples were affixed to the silicone elastomer from a prosthetic liner using silicone adhesive (Sil-Poxy, Smooth-On, Inc., Macungie, PA, USA). The elastomer from the liner was 63.5 mm in diameter and 2.30 mm in thickness (
Figure 5).
One testing sample was worn in each shoe under the metatarsal region of the foot by a 65.7 kg male for 14 days. A smart phone step counter was used to monitor the number of steps during the test period. Over 14 days, the mean step count was 2,123 steps/day. Calibration tests were performed before the sample was worn (pre-wear) and were repeated at 1d, 3d, 7d, 10d and 14d of wear. The elastomeric liner material affixed to the sample plastically compressed over time, which was accounted for in calibration by shifting the zero position of the sample by the reduced thickness.
Weathersby E.J., Gurrey C.J., McLean J.B., Sanders B.N., Larsen B.G., Carter R., Garbini J.L, & Sanders J.E. (2019). Thin Magnetically Permeable Targets for Inductive Sensing: Application to Limb Prosthetics. Sensors (Basel, Switzerland), 19(18), 4041.
