Compressive Material Properties of Plantar Soft Tissue
Orthoses and shoe insoles have been designed with specialized shape and material properties for maximal comfort and optimal foot bone control. However, this process has occurred largely in the absence of material property data on the natural cushioning that the plantar soft tissue offers. Enhanced understanding of the regional tissue material properties of the plantar soft tissue may alter design constraints and motivate advanced orthotic design. Additionally, the methods employed in this study could be used to explore the effects of aging and diabetes on the plantar soft tissue. Understanding how these conditions effect the plantar soft tissue may lead to new treatment options, such as orthoses that are impedance matched with the plantar soft tissue.
Furthermore, a validated computational model of the foot can be a useful tool in investigating potential outcomes before investing in cadaveric studies that are often technically difficult, time-intensive, and expensive. A model can provide additional insight by determining quantities often not obtainable by measurement in cadaveric experiments, such as internal stresses and strains. Accurate model predictions are, in part, dependent on accurate material models. However, the material properties of the plantar soft tissue have not been fully investigated.
Previous mechanical testing research on the plantar soft tissue has concentrated on the heel pad and has, for the most part, been structural rather than material in nature. The subcalcaneal structural tests were either in vivo impact tests14 or ex vivo servohydraulic material testing machine experiments.5,6 The ex vivo tests resulted in lower percent energy absorption (29–33% versus 73–99%), less deformation (2.1 mm versus 8.5–11.3 mm) and increased stiffness (12.0 × 105 N/m versus 1.0 × 105–1.75 × 105 N/m). Aerts et al.7 noted that the in vivo tests failed to isolate the heel pad from the lower extremity. They performed testing protocols with a pendulum and an Instron materials testing machine on isolated heel pads to ensure similar experimental conditions. These protocols resulted in:
However, four of the five feet tested were from subjects between 50–80 years of age with peripheral vascular disease and the experiments were all done at room temperature. Age,3,810 diabetes,11,12 and temperature (i.e., the melting point of adipose tissue)13 may affect the plantar soft tissue properties. Thus, it is not clear whether Aerts et al.’s data are representative of healthy plantar soft tissue. Furthermore, these experiments were structural, not material, in nature.
One study has quantified the compressive material properties of the subcalcaneal tissue.14 They demonstrated that the plantar soft tissue behaves in an isotropic manner and developed an analytical model for the soft tissue that incorporates hyperelastic and viscoelastic characteristics. This research represents the first compressive material property data published on the plantar soft tissue. However, they only tested heel pad tissue from older feet (age 61–99) of unknown vascular condition and experiments were conducted at room temperature.
In summary, mechanical testing of the plantar soft tissue has primarily consisted of structural tests on the heel pad, with only one material properties study. Furthermore, potentially confounding factors are not always considered. The purpose of this study was to control for temperature, age, and diabetes (vascular condition), while quantifying the material properties of the plantar soft tissue at six locations beneath the:
Specimens were obtained from 11 fresh frozen cadaveric feet (36.4 ± 8.4 years, range 21–46 years, 801 ± 125 N) from eight non-diabetic donors, which were purchased from the International Institute for the Advancement of Medicine or the National Disease Research Interchange. Institutional Review Board approval was obtained for this study from the Human Subjects Division at the University of Washington. Sagittal plane X-rays were taken for each foot and examined for abnormalities. Each foot was thawed in a plastic bag in a warm water bath for an hour prior to dissection. Specimens were acquired from the six locations of interest (Figure 1). The plantar soft tissue was dissected free from the bone, cut into two cm × 2 cm specimens with a razor blade punch, and a scalpel was used to remove the skin. The order in which the specimens were tested was randomized to minimize any effect that time between dissection and testing may have. Samples were stored on ice until immediately prior to testing.
The specimen was placed between two smooth stainless steel platens attached to a Bose ElectroForce 3400 materials testing machine in an environmental chamber (Figure 2a). The top platen was lowered until a force of approximately 0.5 N was detected. The corresponding distance between the platens was the initial thickness of the tissue. The chamber was covered with an acrylic lid and sealed with plastic wrap (Figure 2b). By using a Techne water bath and a heater, hot moist air was circulated to keep the specimen at 35° C and near 100% humidity. The target load (20% body weight) was based on normative ground reaction force and contact area data,15 specimen cross-sectional area and cadaveric weight. In load control, the specimen underwent ten 1-Hz sine waves from 10 N to the target load. The displacement at the target load was noted as the target displacement.
Using displacement control, a stress relaxation experiment (unconfined compression) was performed. Ten 1-Hz sine waves were used to precondition the specimen to the target displacement. The tissue was compressed to the target displacement over a period of 0.1 s and held at a constant strain for 300 s. The tissue was allowed to recover for at least 5 minutes between tests. Data were sampled at a rate of 1024 Hz.
To test the tissue frequency dependence, we conducted a series of three triangle waves (unconfined compression) to the target displacement at frequencies of 10, 1, 0.1, 0.01, and 0.005 Hz. Data were sampled at 1024 Hz for the 10 Hz triangle waves and at 128 Hz for the lower frequencies.
The relaxation curves were normalized by the peak force value and were fit to the quasi-linear viscoelastic (QLV) theory16 with a least squares regression by using Wavemetrics Igor Pro. The QLV theory, which assumes that the spatial characteristics (i.e., the elastic response, σ(e)(ε)) and the temporal characteristics (i.e., the reduced relaxation response, G(t)) are independent, is described with the following equation:
where σ is the stress and ε is the strain. The elastic function was defined as:17
where A and B are the elastic constants. The form of the reduced relaxation response is as follows:
where S(τ) represented the relaxation spectrum, where:
where c1 is the amplitude of the viscous effects, and τ1 and τ2 represent the time values corresponding to the frequency limits of the relaxation spectrum.
For quantitative analyses, each individual stress relaxation curve was fit. An analysis of variance (ANOVA) was used to determine if the QLV parameters differed between testing areas. To qualitatively compare the six areas, the relaxation data for all trials for each location were averaged together. The QLV coefficients for each area were then averaged and used to generate representative plots of ‘‘dummy’’ average data, which were overlain with actual average data for each location.
From the triangle data, we obtained the modulus (the slope of the curve after the inflection point) and energy loss (the area between the loading and unloading curves). Because there were repeated measures within subjects, linear mixed effects models were used to determine the relationship of stress, modulus, and energy loss within the region of the foot and the frequency. Models of modulus and energy loss were also adjusted for force. Post hoc multiple comparison tests were done by using the Sidak or Tukey method, with statistical significance set at p = 0.05.
For the QLV data, the dummy data created from the mean coefficients for each area was nearly coincident with the average data for each of the six locations (Figures 3 and 4), indicating that averaging the coefficients for each location was a good approximation of the average data.
The long-term relaxation constant, τ2, was significantly larger for the subcalcaneal (20,090 s) than the other areas except for the fifth submetatarsal specimens (15,360 s, Table 1). No significant differences were found for the other parameters (τ1, c, A, or B). However, the two areas, the lateral submidfoot and the third submetatarsal, with the largest viscous damping amplitude (c) also experienced, as expected, the most relaxation (Figures 3 and 4).
Table 1: The coefficients from the QLV fit of the six areas of interest.
*Significantly different from all areas accept the fifth metatarsal.
All areas exhibited a non-linear stress–strain response for all frequencies, with an extended toe region up to approximately 30% strain (Figure 5).
There were significant differences in the stress between all locations, with the subcalcaneal (89.5 ± 4.0 kPa) having the highest values and the third submetatarsal (70.3 ± 4.0 kPa) having the lowest values (Figure 6a). The fifth submetatarsal (83.3 ± 4.0 kPa) and lateral submidfoot (75.3 ± 4.0 kPa) were also significantly different from each other. The stress increased with frequency, with the 0.005 Hz (62.0 ± 4.0 kPa) and 10 Hz (117.3 ± 5.3 kPa) data significantly different from all others, and 1 Hz (66.0 ± 4.0 kPa) significantly different from all but 0.1 Hz (74.0 ± 4.0 kPa, Figure 6b). Note that we present our results according to test frequency (0.005–10 Hz) rather than strain rate (s−1) because while test frequency (i.e., the frequency of the input triangle waves) remained constant, the strain rate was dependent on the thickness and target displacement of each specimen. The corresponding strain rates (s−1) were (average ± standard deviation): 0.006 ± 0.001, 0.012 ± 0.002, 0.108 ± 0.020, 1.057 ± 0.194, and 10.8 ± 2.190.
The subcalcaneal location (0.83 ± 0.03 MPa) had a significantly larger modulus than the other five locations (ranging from 0.67 ± 0.03 to 0.74 ± 0.03 MPa, Figure 7a). The modulus was also significantly higher at 1 Hz (0.75 ± 0.03 MPa) and at 10 Hz (1.03 ± 0.03 MPa, Figure 7b).
Energy loss also varied significantly across locations, with the subcalcaneal location having the least energy loss (36.0 ± 3.0%), followed by the fifth submetatarsal (43.0 ± 3.0%), and then the remaining areas (ranging from 47.0 ± 3.0% to 51.0 ± 3.0%, Figure 8a). The energy loss also significantly increased at higher frequencies of 1 Hz (48.0 ± 3.0%) and 10 Hz (63.0 ± 3.0%, Figure 8b).
The differences (increased stress, increased modulus and decreased energy loss) demonstrated between the subcalcaneal tissue and the other tissues can also be seen in a representative stress versus strain plot (Figure 9).
The subcalcaneal tissue was found to have an increased relaxation time compared to the other areas. The subcalcaneal tissue was also found to have an increased modulus and decreased energy loss compared to the other areas. Across all areas, the modulus and energy loss increased for the 1 and 10 Hz tests compared to the other testing frequencies. This study was the first to generate material properties for all areas of the plantar soft tissue, demonstrating that the subcalcaneal tissue is different than the other plantar soft tissue areas. These data will have implications for foot computational modeling efforts and potentially for orthotic pressure reduction devices.
To read the full project description, please see:
The Compressive Material Properties of the Plantar Soft Tissue. Ledoux WR, Blevins JJ, J Biomech. 2007;40(13):2975-81. Epub 2007 Apr 12.
This work was supported in part by the Department of Veterans Affairs, Rehabilitation Research & Development Service Grant nos. A2362P and A2661C. The authors would also like to thank Jane Shofer, M.S. for the statistical analysis and David J. Nuckley, Ph.D. for contributing to this article.
William R. Ledoux, Ph.D.