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Flow Constraint and Loading Rate Effects on Prosthetic Liner Material and Human Tissue Mechanical Response

Steven J. Covey, PhD, PE
Joshua Muonio
Glenn M. Street, PhD

ABSTRACT

The compressive mechanical properties of four prosthetic liner materials (urethane, two silicones, and a thermoplastic elastomer) were compared to human muscle as a function of geometric flow constraint and loading rate. Loading rate effects on calcaneal heel pad were also measured. The mechanical properties evaluated were from force-displacement data obtained during material tests and included stiffness, the percentage of energy absorbed, and residual displacement (or thinning) 8 seconds after unloading. The geometric flow constraint involved a 25.4-mm diameter piston pushed into an 11.5-mm deep cylindrical cavity with radial piston/cylinder clearances of 0.8 mm, 1.55 mm, and 3.2 mm. The haversine waveform load-controlled tests increased the load from 50 N to 550 N in 10.0, 1.0, and 0.2 seconds; loading rates of 0.1 Hz, 1.0Hz, and 5.0 Hz. The variation of test parameters had a large and mixed effect on the different materials. The average stiffnesses for each material over all geometries and loading rates were as follows: urethane, 537 N/mm; silicone A, 442 N/mm; human muscle, 394 N/mm; thermoplastic elastomer, 220 N/mm; heel pad, 134 N/mm; and silicone B, 99 N/mm. The average percentages of energy absorbed were as follows: human muscle, 90%; silicone A, 74%; urethane, 71%; heel pad, 59%; thermoplastic elastomer, 56%; and silicone B, 41%. The average residual displacements were as follows: urethane, 0.23 mm; silicone A one layer, 0.43 mm; silicone B, 0.47 mm; thermoplastic elastomer, 0.66 mm; silicone A two layers, 0.74 mm; human muscle, 1.09 mm; and heel pad, 1.6 mm. Impact tests were also performed that involved dropping a 4.45 N mass 151 mm onto the liner materials placed on a piezoelectric sensor. The 820 N impact force without liner materials was decreased to 186 N with muscle, 258 N with urethane or two layers of silicone A, 268 N with a thin layer of heel pad, and 309 N for the thermoplastic elastomer. A single layer of silicone A and the silicone B material both ripped repeatedly during impact testing. Using standard material selection methods, urethane appears to be the optimal prosthetic liner material by offering the unique combination of best response (via highest stiffness), best impact protection (via lowest impact forces), and least thinning (via least residual displacement 8 seconds after unloading). The preliminary data reported here suggests that the differences in comfort reported by amputees who have used multiple liner material types are justified.

Key Words: Urethane, silicone, thermoplastic elastomer, stiffness, energy, residual strain, impact, strain rates, compression, human tissues

Introduction

A few researchers^1,2 have compared the compressive mechanical properties and friction levels of various prosthetic liner materials. Few have compared the compressive properties of the liner materials to human tissue, even though biotissue responses are available.³ None have presented how the compressive properties of the liner might be affected by tighter geometric confinement in the socket, which reduces the ability of the material to flow under stress. Data that show how the rate at which the load is applied affects mechanical properties has also been lacking. It is well known that geometric constraint and loading rate can drastically alter the mechanical response of most materials. Accurate finite element models of the liner interface require this information. In this work, the compressive response of four liner materials and human muscle tissue are compared for varying geometric constraints and loading rates. Calcaneal heel pad response at various loading rates is also provided.

Materials and Methods

Material Details

Four common liner materials, urethane (Custom Liner, TEC Interface Systems, Waite Park, MN), a thermoplastic elastomer (Alpha Cushion Liner, Ohio Willow Wood Company, Mount Sterling, OH), silicone A (Ice Ross Comfort, Ossur Prosthetics Orthotics, 110 Reykjavik, Iceland), and silicone B (Easy Liner, Alps South Corporation, St. Petersburg, FL) were evaluated at a thickness of approximately 7 mm. Even though attempts were made to obtain a similar thickness, the average thickness varied from 6.94 mm to 9.17 mm because of the normal variations found in commercial products. The actual specimen thickness values can be found in Table 1 . Because the silicone A material is thinner than the others are, tests were performed on a single thin layer and on two layers stacked together to obtain a thickness similar to the other liner materials. The thermoplastic elastomer and silicone A materials were tested as received with a thin polymeric cover material attached and material side up in the fixture. For the two layers test of silicone A, the cover material on the top layer was removed to better simulate the other materials that were tested with just one cover. Material durometers (Shore 00) varied from 29 for the thermoplastic elastomer to 51 for the urethane. This range of durometer from 29 to 51 is almost identical to the spread found in the midsole materials used in running shoes.^4,5Table 1 provides the thickness, diameter, and durometer information.

All liner materials were manufactured in the last quarter of 1998 and were obtained commercially or were of commercial quality. The muscle sample was removed from the gastrocnemius (calf) muscle of a 72-year-old female whose height was 1.6 meters high and weighed 64 kg. The external sheath of the muscle was retained on the sample. The calcaneal heel pad was from the same cadaver as the muscle and was left intact for initial testing. Subsequent tests removed first the skin and then the skin plus a thin layer roughly 3.6 mm (0.14 inch) in thickness from the heel pad.

Experimental Details

Mechanical Testing

The mechanical testing was performed in load control on an Instron Model 8500 servohydraulic test system (Instron Corporation, Canton, MA). The test system is closed loop via direct digital control and allows data acquisition of the force versus displacement profiles while testing. Data acquisition was performed using an Omega Tempbook66 (Omega Products, Stamford, CT) at typical rates of 50 points/second during a time interval that started with the test and allowed at least 8 seconds of data after the load was returned to 50 N. To decrease the noise in the data, 50 points of data were collected and averaged for each of the 50 points/second stored to disk. The force was measured using a 100 kN load cell that had its calibration verified at much lower forces. Displacement was measured using a strain-gage-based axial extensometer with 25 mm gage and 12.5 mm travel. Hydraulic grips were used to hold the test fixtures.

Fixtures

The test fixture used to measure the effect of flow constraint and strain rate on the liner materials and muscle mechanical response was an aluminum cylinder and piston with various clearances between the piston and cylinder wall (Figure 1 ). For all cases, the piston was 25.4 mm in diameter by 16.7 mm long. The diameter of the cylinder was 27 mm, 28.5 mm, or 31.8 mm, resulting in radial cylinder wall/piston clearances of 0.8 mm, 1.55 mm, and 3.2 mm, respectively. These die clearances were chosen to simulate the range of values encountered in the actual socket/liner environment. It is believed that the range of radial clearances used here spans those actually occurring for well and poor fitting liners. The cylinders were 9.4 mm, 12.4 mm, and 11.6 mm deep for the small, medium, and large die clearances, respectively. Talcum powder was applied on all liner material surfaces before testing.

The calcaneal heel pad was tested using a separate fixture because containment testing was not performed. The cadaver foot was removed from the lower leg at the tibial-talar joint. Soft tissue on the medial and lateral aspects of the calcaneous was removed, leaving the heel pad intact but exposing it for testing. The foot was anchored with a U-shaped steel bracket that fit over the superior, and medial and lateral sides of the calcaneous. Two 8-mm diameter pins were threaded through the lateral wall of the bracket and a third 8-mm pin through the medial wall of the bracket. One end of each pin was tapered 45 degrees to a sharp point. The points were driven 3 mm into the medial and lateral sides of the calcaneous, and the talus rested against the top wall of the bracket. An 11.8-mm (0.464-inch) diameter shaft, welded on the top wall of the bracket and centered over the mid-talus, was positioned in the bottom jaw of the Instron. In all cases, the force to the calcaneal heel pad was applied with the 25.4-mm diameter aluminum piston from the containment testing pressing directly onto the heel pad.

Force Levels

The compressive force level used was a 50 N preload with an additional 500 N applied via a one-cycle haversine waveform. This maximum force of 550 N corresponds to a stress of approximately 1.1 MPa for a 25.4-mm diameter specimen compressed with flat compression platens. This stress of 1.1 MPa is four times higher than the 0.25 MPa measured for walking⁶ but lower than the 1.5 MPa measured during running.⁷ Many of the 5 Hz tests obtained peak forces of less than 550 N because the material test system did not have adequate hydraulic capacity. However, the engineering results obtained, such as stiffness, percentage of absorbed energy, and residual displacements, are still of value in comparing the material responses.

Loading Rates

One-cycle haversine loading rates of 0.1 Hz, 1.0 Hz, and 5.0 Hz were used to simulate an amputee loading the liner material at low, moderate, and high activity levels. The force was increased from 50 N to 550 N in 10 seconds, 1.0 seconds, and 0.2 seconds, for the 0.1 Hz, 1.0 Hz, and 5.0 Hz tests, respectively (Figure 2 ). The 5.0 Hz tests, with the associated 0.1 seconds from low to maximum force, is representative of the loading rates measured elsewhere for runners.⁸ Because the same specimen was used for the three different loading rates, a consistent testing sequence was followed. The materials were tested first at 5.0 Hz, then 1.0 Hz, and finally at 0.1 Hz with adequate time between tests for any material flow required to return to original shape. It is believed that any order effect is small because of the time between tests, which was approximately 90 seconds. This sequence was chosen to simplify the servogain selection process. After each test, the muscle and heel pad was returned to their original shapes by manual manipulation.

Mechanical Properties

Modulus, or slope of the stress-strain curve, is a very common material property, but its magnitude is strain-dependent for materials with a nonlinear stress-strain response such as these liner material polymers. Typical references to polymeric material modulus values, such as 150 modulus (the slope of the tangent at a strain of 150%), were not used in this work because the tests performed were fixture geometry, specimen geometry, and material dependent. During deformation, the stress state is multiaxial and not well defined, so computation of a stress value is less meaningful.

Friction between the liner material and the fixture accounts for a portion of the applied load; hence, the entire applied load is not going into the deformation of the specimen. For example, powdered urethane specimens were previously compressed using 25.4-mm diameter flat aluminum compression platens with the same 550 N haversine loading at 1 Hz. The stiffness of the urethane decreased by a factor of two as specimen thickness increased from approximately 2 mm to 4 mm. However, very little change in stiffness was observed for specimens thicker than approximately 4 mm (Figure 3 ). This friction stiffening is fairly common in mechanical design and can be explained by the fact that for a thinner specimen, friction is far more effective at preventing flow not only in the region of the surface contact but also near the center of the material. A thicker material, on the other hand, can still flow out at its center because the frictional force is less active so far from the surface.

From the force and displacement data between 225 N and 250 N, the slope during loading was used to determine the stiffness at an average load of 237 N, hereafter referred to as the 237stiffness. The 237stiffness is the slope (or tangent) of the force-displacement curve at a load of 237 N. The 237stiffness was used to provide a method for determining the material stiffness for all materials and consistently excludes peculiarities such as sudden slope changes from specimen thinning or 5 Hz tests that did not obtain a 550 N peak load. As the 237stiffness increases, so does the firmness of the material. Although comfort is directly dependent on stiffness, whether a higher or lower stiffness is better depends on a number of other factors.

The area under and enclosed by the force-displacement curves was used to compute the percentage of energy absorbed as compared to the total energy applied, hereafter referred to as the percentage of energy absorbed. This computation was performed in a spreadsheet by integrating the force as a function of displacement using the trapezoidal rule of integration. Typically, the 0.1 Hz, 1.0 Hz, and 5.0 Hz tests used approx 250, approx 37, and approx 16 integration points, respectively. Because of the fairly weak nonlinearity of these curves, it is believed that these numbers of integration points provided accurate results. The integrated areas compared well to those computed by manual methods (graphically counting squares). As the percentage of energy absorbed increases, the material is absorbing a larger fraction of the energy applied and begins to feel more like "running on sand." In theory, the lower the energy absorbed, the less work would be required for a runner to complete a given race using that material. However, the magnitude of this effect is negligible when compared to the overall energy change of running.⁴ Consequently, higher energy absorption is more important because the material is more effective at shielding the athlete's body from impact forces.

The residual displacement is the decrease of the specimen thickness, or specimen thinning, approximately 8 seconds after unloading. As useful and interesting as the residual displacements are, they do not address the fact that some of the tests did not obtain a 550 N load or that some of the specimens actually had a much larger maximum displacement during testing than others because of a lower stiffness. Consequently, the ratio of residual displacement 8 seconds after the test to the maximum displacement during the test will also be presented. This ratio is identical to the residual strain 8 seconds after unloading to the maximum strain during testing and is hereafter referred to as the residual strain ratio and will be given as a percentage. As the residual displacement and residual strain ratio increases, so does the plastic "set" or "thinning," and the material can be expected to exhibit degraded behavior on subsequent loadings. Therefore, the lower the residual displacement and residual strain ratio, the better.

Although the responses of the cadavered human muscle and calcaneal heel pad, especially the residual displacements, are not considered representative of living tissue because of the lack of restorative blood flow, they are presented for comparison. When a cadaver-to-living-tissue mechanical response correction (or mapping) factor becomes available, these data will then be more useful.

Impact Testing

Protecting the body from impact is a major concern. Impact tests were performed by dropping a 4.45 N weight 151 mm onto each of the liner materials of Table 1 while resting on a three-axis, 10 kN piezoelectric transducer. The Kistler (Kistler Instrument Corporation, Amherst, NY) model 9275A transducer was used in conjunction with Kistler model 5004 amplifiers using an output of 500 N per volt and 3.69 calibration factor. Output of the piezoelectric transducer was verified using calibrated dead weights. The data acquisition method and equipment was similar to that described above using the Omega-TempBook/66. Each test was repeated three times and the measured peak impact forces were averaged.

The velocity at impact for a 151 mm drop, computed using standard techniques, is 1.72 m/sec. This impact velocity of 1.72 m/sec is 69 times larger than the maximum velocity used during the material tests; a displacement of 5 mm in 0.2 seconds for the 5 Hz loading rate corresponds to an average velocity of 25 mm/sec or 0.025 m/sec. The liner material properties, if tested at this 1.72 m/sec impact loading rate, would likely be very different than reported here for the 0.1 Hz, 1.0 Hz, and 5.0 Hz loading rates. The flat, circular steel impact body weighed 4.45 N and was 12.7 mm (0.5 inch) thick and had a 47.625 mm (1.875 inch) radius. The impact area was the 12.7-mm dimension edge by a width that depended on the depth of penetration into the liner material and the weight radius of curvature, which was 47.625 mm (1.875 inches). The depth of penetration was not recorded.

Typical impact analysis methods can be used to predict the impact force for dropping a 4.45 N weight a distance of 151 mm with no liner materials. An impact force of 820 N was measured without liner materials inserted. The energy at impact was equal to the weight times the distance dropped, or 670 N-mm. This impact energy of 670 N-mm applied during the impact test compares well to the average 448 N-mm applied during compression testing.

Results

Each of the six materials (human muscle, urethane, thermoplastic elastomer, silicone A thick, silicone A thin, and silicone B) were tested at three different loading rates (0.1 Hz, 1.0 Hz, and 5.0 Hz) for three different radial clearances (0.8 mm, 1.55 mm, and 3.2 mm), so that a total of 54 550 N haversine tests were performed on the muscle tissue and liner materials. The calcaneal heel pad had another nine tests at three different loading rates (0.1 Hz, 1.0 Hz, and 5.0 Hz) for three different conditions (intact, skin removed, and skin plus one layer removed). So a total of 63 tests were performed. For each test, three mechanical properties of interest were computed: 237stiffness, percentage of energy absorbed, and residual displacements. Thus, for 63 tests and three properties each, 189 data points result. Rather than providing all 63 force-displacement curves, only the calculated mechanical properties, shown using 21 graphs with 9 data points per graph, will be presented. However, the entire force-displacement curve will be used to demonstrate general trends or other results of interest as necessary. Average impact forces from dropping a 4.45 N weight 151 mm onto the liner materials and human tissues will also be given.

General Comparisons

Urethane Responses for All Tests

The effect of loading rate and geometric constraint is quite large for these types of materials. The general trend can be represented by the urethane results. The variation in urethane's force-displacement curves for the differing geometric constraints and loading rates is striking (Figure 4 ). The stiffness increases over an order of magnitude from 151 N/mm for the 0.8 mm die clearance, 5.0 Hz test to 1563 N/mm for the 3.2 mm, 0.1 Hz test. The general shape of the area enclosed by the curve (the percentage of energy absorbed) also changes for the various test conditions. The percentage of energy absorbed for urethane had a minimum value of 65% for the 3.2 mm, 5.0 Hz test and a maximum value of 77% for the 0.8 mm, 1.0 Hz test. The maximum displacement decreases by an order of magnitude considering the maximum displacement of 0.34 mm for the 0.8 mm, 5.0 Hz test and 3.32 mm for the 3.2 mm, 0.1 Hz test. Finally, the residual displacement 8 seconds after the test decreases from 0.4 mm for the 3.2 mm, 0.1 Hz test to 0.06 mm for the 0.8 mm, 5.0 Hz test.

The 3.2 mm clearance die loaded at 5.0 Hz reached a peak force of only approximately 350 N whereas the 0.8 mm, 5.0 Hz test reached the full 550 N peak force. This difference occurred because the tighter geometric constraint of the 0.8 mm fixture decreased the amount of liner material flow and the associated maximum displacement. The geometric constraint of the 0.8 mm clearance increased the stiffness enough that the peak load could be obtained. The hydraulic actuator could supply adequate hydraulic oil to meet the 550 N load for the 0.8 mm, 5.0 Hz test but not the 3.2 mm, 5.0 Hz test. Consequently, the 350 N peak force was the maximum possible for this material under these loading conditions using this material test system.

Material Responses for the 1.55 mm, 1.0 Hz Tests

For the 1.55 mm, 1.0 Hz (medium clearance, medium frequency) tests, a wide variety of force-displacement curves was observed (Figure 5 ). The silicone B material, having the lowest 237stiffness (93 N/mm), had the most displacement (4.16 mm) but the least energy absorbed (31%). The human muscle had the least displacement (1.8 mm), the greatest 237stiffness (291 N/mm), and the most energy absorbed (88%). The linearity of the urethane and silicone A compares well with that of the human muscle and the calcaneal heel pad. Although the heel pad and silicone B 237stiffness are similar, the heel pad remains fairly linear after 237 N whereas the silicone B increases exponentially thereafter. The load magnitude at which an exponential increase in load is observed for the silicone B material (approximately 350 N) suggests that 350 N is probably beyond the maximum desirable load because the subsequent increased stiffness would likely cause discomfort for the amputee.

Summarized Comparisons

Stiffness

The value of 237stiffness varied from 56 N/mm for silicone B at a 0.1 Hz load rate and 3.6 mm clearance to 1563 N/mm for urethane for 5.0 Hz and 0.8 mm clearance (Figures 6a , 6b , 6c , 6d , 6e , 6f , and 6g ). The average 237stiffness for all geometric constraints and loading rates was as follows: silicone B, 99 N/mm; intact calcaneal heel pad, 134 N/mm; thermoplastic elastomer, 220 N/mm; human muscle, 394 N/mm; two layers of silicone A, 409 N/mm; one layer of silicone A, 475 N/mm; and urethane, 537 N/mm. All the stiffness data can be found in Table 2 . In general, the stiffness showed little difference for the 1.55 and 3.2 mm radial clearances but a greater than five-fold increase for the 0.8 mm clearance for urethane and silicone A. If only the 3.2 mm and 1.55 mm clearance (lower constraint) tests are used, the average stiffness of one layer of silicone A (268 N/mm) is actually higher than that of the urethane (209 N/mm). The average 134 N/mm 237stiffness obtained here for intact calcaneal heel pad is somewhat lower than the 296 N/mm stiffness reported elsewhere for intact, cadavered calcaneal heel pad.³ In that work, a higher stiffness should be expected because the platen contacting the heel pad was just over twice the diameter (and hence six times the contact area) of the piston used here.

The stiffness for human muscle increased by a little more than a factor of two with increasing constraint. In general, the stiffness increased with loading rate from a negligible amount for the thermoplastic elastomer material to an increase of approximately 1.75 times that for urethane and muscle. A decrease in stiffness with increase in loading rate was observed for two layers of the silicone A material. The small increase in stiffness for one layer of silicone A (469 N/mm) when compared to two layers of silicone A (409 N/mm) was a surprise considering the thickness differed by a factor of two.

Energy Absorbed

The ratio of energy absorbed to total energy varied from 17% for silicone B at a 1.0 Hz load rate and 1.55 mm clearance to 95% for muscle at 0.1 Hz and 0.8 mm clearance (Figures 7a , 7b , 7c , 7d , 7e , 7f , and 7g ). The average percentage of energy absorbed for all loading rates and geometric constraints was silicone B, 41%; thermoplastic elastomer, 56%; urethane, 71%; silicone A, 75%; and muscle had the highest average percentage of energy absorbed, 90%. The unconstrained, intact heel pad absorbed 59% of the applied energy. It is important to note that the heel pad was not in the geometrically constraining fixture and direct comparisons of the percentage of absorbed energy to the other results here are difficult. All of the energy data can be found in Table 3 . The percentage of energy absorbed for urethane, 71%, compares well with the 67% and 77% observed for intact cadavered and in vivo calcaneal heel pads, respectively.³ The lower percentage of energy absorbed by the heel pad (59%) in this work may be attributable to the fact that the piston used here had about one sixth the contact area of that used in the reference. In general, the percentage of energy absorbed tended to increase with flow constraint but there are many exceptions. For the various loading rates and the 1.55 mm constraint, the percentage of energy absorbed varied from only 67% to 75% for urethane and from 17% to 40% for silicone B.

There are no general trends of the energy absorbed with loading rate as some materials increased, others remained constant, and yet others decreased. For example, although the silicone B shows a decrease in absorbed energy from 69% to 36% for the 0.8 mm fixture for an increase in loading rate from 0.1 Hz to 5.0 Hz, the thermoplastic elastomer shows an increase from 32% to 54% for the 1.55 mm with increase in loading rate from 1.0 Hz to 5.0 Hz. Two layers of the silicone A material with 3.2 mm clearance die shows the smallest absorbed energy change from 77% at 1.0 Hz to 73% at 5.0 Hz.

Residual Displacement

The decrease in specimen thickness, or specimen "thinning," as measured 8 seconds after unloading, varies from a low of 0.06 mm for the urethane material at 0.8 mm die clearance and 1.0 Hz loading rate to a high of 2.47 mm for the thermoplastic elastomer at 1.55 mm clearance and 0.1 Hz. Urethane had by far the lowest overall amount of thinning. The average amount of thinning observed for each material type for all constraints and loading rates was as follows: urethane, 0.23 mm; silicone A one layer, 0.43 mm; silicone B, 0.47 mm; thermoplastic elastomer, 0.66 mm; silicone A two layers, 0.74 mm; and human muscle, 1.09 mm. The average residual displacement for the intact heel pad was 1.60 mm. Again, the lack of restorative blood flow renders these human tissue residual displacements almost meaningless. All the displacement data can be found in Table 4 . For all materials the maximum displacement during testing decreases with increased loading rate. For all materials, except the thermoplastic elastomer, the maximum displacement during testing increases with increased radial clearance. For the thermoplastic elastomer, the 1.55 mm clearance actually exhibited a larger maximum displacement than the 3.2 mm clearance. Urethane shows the general trend of decreasing maximum displacements with increasing loading rate and flow constraint quite well (Figure 8a ). Because the maximum force achieved for most of the 5.0 Hz tests was well below 550 N (for the urethane it was approximately 350 N), the maximum displacement during testing should be less at 5.0 Hz even if the stiffness does not increase with loading rate.

For all materials, the residual displacement eight seconds after the test decreases with increased loading rate. However, although the residual displacement decreases with increasing radial clearance for urethane (Figure 8b ) and two layers of silicone A, the 1.55 mm clearance residual displacement is actually minimum for silicone B and maximum for the thermoplastic elastomer. Although both the maximum displacements and residual displacements decrease with loading rate for urethane, the maximum displacements decrease more rapidly. Consequently, the residual strain ratio, the ratio of the residual displacement 8 seconds after unloading to the maximum displacement during testing, actually increases as a function of loading rate for urethane (Figure 8c ).

The residual strain ratio varied from approximately 2% for silicone B at a 1.0 Hz load rate and 3.2 mm clearance to 50% for the thermoplastic elastomer at 0.1 Hz and 1.55 mm clearance (Figures 9a , 9b , 9c , 9d , 9e , 9f , and 9g ). Silicone B had the lowest average residual strain ratio of 12%; urethane was next at 14%, and the thermoplastic elastomer had an average residual strain ratio of 20%. Two layers of silicone A had the highest residual strain ratio with an average value of 38%. Cadavered human muscle and heel pad had average residual strain ratios of 76% and 51%, respectively. In general, the residual strain ratio increased with geometric constraint (smaller clearance), but not always. Urethane demonstrated the least variation in residual strain ratio with both geometric constraint (from 17% to 22%) and loading rate (from 11% to 23%). Whereas two layers of silicone A showed a 1.6 times change in residual strain ratio (from 26% to 42%) with geometric constraint at 1.0 Hz, the thermoplastic elastomer had a 7.4 times change (from 7% to 52%) with loading rate for the 1.55 mm clearance.

Impact Testing

The impact tests indicate that all the liner materials significantly reduce the impact force. With no material, the impact force measured after dropping a 4.45 N weight a distance of 151 mm was 820 N. The average measured impact forces were as follows: no material, 820 N; thermoplastic elastomer, 309 N; two layers of sectioned calcaneal heel pad 7.87 mm (0.31 inch) thick, 268 N; urethane, 257 N; two layers of the silicone A, 257 N; and muscle, 185 N. The impact forces of silicone B and one layer of silicone A were 257 N and 463 N, respectively, but both liners repeatedly ripped during testing. Table 5 summarizes the impact data.

Discussion

Understanding the mechanical response of a prosthetic liner in a socket environment is a difficult task. Although the preliminary data, summarized in Table 6 as average values for all loading rates and geometric constraints, may be useful toward that end, other factors are also important. For example, the coefficient of friction between the prosthetic liner material and human tissue and between the prosthetic liner material and the socket/sheath is also a major factor. Some excellent work has appeared recently on this topic.^1,2 Finally, even if all of these issues were understood, a definition of comfort that is valid for all amputees may be the most elusive of all. Amputees who have used multiple liner material types report a large difference in liner feel. The data presented here supports these comments. Furthermore, the prosthetic liner material selection method of feeling the prosthetic material is unreliable because stiffness, percentage of energy absorbed, and residual displacement depend on geometric flow constraint and loading rate.

Durability of the prosthetic liner material is an entirely different issue and is complicated by the fact that the current material testing standards for textiles, rubbers, and polymers do not adequately address the major factors directly responsible for liner life. Issues like multiaxial stress states, friction levels, geometric flow constraints, and the ratio of "sliding" to "rolling" contacts are not even mentioned, yet almost certainly dictate the durability of the liner. Other researchers⁹ have shown that for simple compression, an open cell polyurethane foam is superior at maintaining properties when compared to other orthotic materials used in therapeutic footwear. The current work focuses on selected liner material properties with the understanding that they correlate with amputee comfort. A manuscript to be submitted elsewhere focuses on the durability issue.

Stiffness

The prosthetic liner material stiffness is important for two reasons. First, the higher the stiffness, the more critical is the socket design and liner fit. A stiff liner material, such as urethane and one layer of silicone A, when poorly fitted, will have a greater tendency to cause patient discomfort and/or damage to the liner. The increased material stiffness localizes the forces applied during use and can increase the stress level in both the liner and the tissue. The second reason prosthetic liner material stiffness is important is response. All else being equal, a stiffer material will have a quicker response for the patient. A stiffer material may be more desirable for patients with high activity levels.

For metals, durometer (or hardness) is correlated with strength. For the four liner materials tested here and other polymeric materials, durometer better correlates with stiffness. For example, urethane, silicone A, and the thermoplastic elastomer had average durometers (Table 1 ) of 50, 44, and 31 with average stiffnesses (Table 6 ) of 537, 409, and 220 N/mm, respectively. However, although silicone B and the thermoplastic elastomer both had average durometers of approximately 31, their average stiffness differed by more than a factor of two. Another part of this work to be presented elsewhere shows that there is no correlation between durometer and tear strength for these liner materials or for chemistry variations within a class of materials.

Energy Absorbed and Impact

From a material selection perspective, there are two important issues associated with the percentage of energy absorbed. The first issue is that the higher the percentage of energy absorbed, the more work the amputee must do while using the product. For example, all else being equal, a runner would expend more energy using a liner with a higher percentage of energy absorbed. However, the energy dispersed by the liner material itself is a very small fraction of the overall energy consumed during locomotion. What this means is that although the average percentage of energy absorbed of the silicone B material is about half that of the silicone A material, the silicone A material may be only a fraction of 1% more efficient in a race.⁴ The second, most important, issue is that the higher the percentage of energy absorbed, the lower the impact force experienced by the amputee, and hence the greater the comfort. The results support the correlation between increasing percentage of energy absorbed and decreasing impact force.

Residual Displacement

Residual displacement is probably the easiest test result to use in developing criteria to specify an optimal liner material. The lower the residual displacement and residual strain ratio are, the better. Urethane (0.23 mm) had less than half of the average residual displacement of any other material of comparable thickness (silicone B, 0.47 mm) and less than one-third the value of two layers of silicone A (0.74 mm). The silicone B material (12%) and urethane (14%) had the lowest values of residual strain ratio whereas thermoplastic elastomer had 20% and two layers of silicone A (37%) had the highest residual strain ratio.

Liner Material Evaluation

The ideal prosthetic liner material should provide a good response (high stiffness), protection from impact, and have minimal change in thickness during use. It may also be desirable for the liner material to possess mechanical properties similar to the biotissues it is replacing. Urethane, with the highest average stiffness of 537 N/mm, would provide a much better response than, say, silicone B, which had an average stiffness of 99 N/mm. This does not mean, however, that stiffer is always better because for many structures, increased stiffness comes at the high price of increased impact forces. Surprisingly, urethane offers the unique combination of highest stiffness (for best response) and lowest impact forces (for best protection). The second stiffest material, one layer of silicone A with an average stiffness of 469 N/mm, had almost twice the residual displacement of urethane and tore repeatedly during impact testing. Both urethane and two layers of silicone A offer the best impact protection by reducing the 820 N force without a liner material to 258 N. However, two layers of silicone A had the worst residual displacement of all liner materials tested.

Urethane offers the lowest average residual displacement at almost half that of the next lowest value (0.23 mm for urethane vs. 0.43 mm for one layer of silicone A) and the second lowest residual strain ratio (0.14 mm for urethane vs. 0.12 mm for silicone B). However, silicone B had the lowest average stiffness and tore repeatedly during impact testing. Urethane best matches the stiffness response of the human muscle for all geometric flow constraints and loading rates, although it is somewhat stiffer than muscle for the 0.8 mm clearance. The thermoplastic elastomer best matches the stiffness and energy of the calcaneal heel pad but has poor impact protection and becomes too stiff at high loads.

Using standard material selection methods, urethane appears to be the optimal prosthetic liner material by offering the unique combination of best response (via highest stiffness), best impact protection (via lowest impact forces), and least thinning (via least residual displacement 8 seconds after unloading). However, the higher stiffness may make it more difficult to obtain a good fit with urethane.

Conclusion

The compressive mechanical properties of four prosthetic liner materials (urethane, two silicones, and a thermoplastic elastomer) were compared to human muscle as a function of geometric flow constraint and loading rate. Loading rate effects were also evaluated for calcaneal heel pad. The mechanical properties evaluated were from force-displacement data obtained during testing and included stiffness, percentage of energy absorbed, and the residual displacement 8 seconds after unloading. The geometric flow constraint involved a 25.4 mm piston pushed into a 11.5 mm deep cylinder with radial piston/cylinder clearances of 0.8 mm, 1.55 mm, and 3.2 mm. The haversine waveform load-controlled tests increased the load from 50 N to 550 N in 10.0, 1.0, and 0.2 seconds (loading rates of 0.1 Hz, 1.0 Hz, and 5.0 Hz). Impact tests were also performed by dropping a 4.45 N weight 151 mm onto the liner material positioned on a piezoelectric sensor.

Based on the results, the following conclusions can be made:

• For a given material, the mechanical response is generally strongly dependent on the geometric flow constraint and loading rate. Although there are many exceptions, in general, stiffness increased with flow constraint and loading rate, the percentage of energy absorbed increases with flow constraint but varies with loading rate, and the residual displacement decreases with increasing geometric constraint and/or increasing loading rate.
• For a given geometric flow constraint and loading rate, the mechanical response of each liner material and human tissue is very different.
• Although the material stiffnesses varied with each test condition, the average values were as follows: urethane, 537 N/mm; one layer of silicone A, 475 N/mm; two layers of silicone A, 409 N/mm; human muscle, 394 N/mm; thermoplastic elastomer, 220 N/mm; calcaneal heel pad, 134 N/mm; and silicone B, 99 N/mm.
• Although the material percentages of absorbed energy varied with each test condition, the average values were as follows: human muscle, 90%; two layers of silicone A, 75%; urethane, 71%; calcaneal heel pad, 59%; thermoplastic elastomer, 56%; and silicone B, 41%.
• Although the liner material residual displacements 8 seconds after unloading varied with each test condition, the average values were as follows: urethane, 0.23 mm; one layer of silicone A, 0.43 mm; silicone B, 0.47 mm; thermoplastic elastomer, 0.66 mm; two layers of silicone A, 0.74 mm; human muscle, 1.09 mm; and calcaneal heel pad, 1.60 mm.
• A 820 N impact force without use of liner materials was decreased to 185 N using the muscle tissue, 258 N using urethane and two layers of silicone A, 268 N using two thin sections of heel pad, and 309 N using thermoplastic elastomer. Silicone B and one layer of silicone A both ripped repeatedly during impact testing.
• Using standard material selection methods, urethane appears to be the optimal prosthetic liner material by offering the unique combination of best response (via highest stiffness), best impact protection (via lowest impact forces), and least thinning (via least residual displacement eight seconds after unloading).
• The prosthetic liner material selection method of "feeling" the prosthetic material is unreliable because stiffness, percentage of energy absorbed, and residual displacement all depend on geometric flow constraint and loading rate.
• The preliminary data reported here suggests that the difference in comfort reported by amputees who have used multiple liner material types is justified.

Acknowledgements

This work was supported, in part, by funding provided by TEC Interface Systems. Credit for the idea to test the effect of geometric flow constraint belongs to Carl Caspers of TEC Interface Systems.

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