Association between foot thermal responses and shear forces during turning gait in young adults

Background The human foot typically changes temperature between pre and post-locomotion activities. However, the mechanisms responsible for temperature changes within the foot are currently unclear. Prior studies indicate that shear forces may increase foot temperature during locomotion. Here, we examined the shear-temperature relationship using turning gait with varying radii to manipulate magnitudes of shear onto the foot. Methods Healthy adult participants (N = 18) walked barefoot on their toes for 5 minutes at a speed of 1.0 m s−1 at three different radii (1.0, 1.5, and 2.0 m). Toe-walking was utilized so that a standard force plate could measure shear localized to the forefoot. A thermal imaging camera was used to quantify the temperature changes from pre to post toe-walking (ΔT), including the entire foot and forefoot regions on the external limb (limb farther from the center of the curved path) and internal limb. Results We found that shear impulse was positively associated with ΔT within the entire foot (P < 0.001) and forefoot (P < 0.001): specifically, for every unit increase in shear, the temperature of the entire foot and forefoot increased by 0.11 and 0.17 °C, respectively. While ΔT, on average, decreased following the toe-walking trials (i.e., became colder), a significant change in ΔT was observed between radii conditions and between external versus internal limbs. In particular, ΔT was greater (i.e., less negative) when walking at smaller radii (P < 0.01) and was greater on the external limb (P < 0.01) in both the entire foot and forefoot regions, which were likely explained by greater shear forces with smaller radii (P < 0.0001) and on the external limb (P < 0.0001). Altogether, our results support the relationship between shear and foot temperature responses. These findings may motivate studying turning gait in the future to quantify the relationship between shear and foot temperature in individuals who are susceptible to abnormal thermoregulation.

114 experience greater shear forces compared to the internal limb (limb closer to the center of the 115 curved path), due to a greater force needed to orient the body towards the turning direction 116 (Orendurff et al., 2006). Turning at a sharper angle (i.e., smaller radius) may in turn result in 117 higher mediolateral forces to orient the body in a new path.

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The purpose of this study was to investigate the thermal response of the foot to varying 119 magnitudes of shear forces during barefoot curved-path walking. The study utilized toe-walking 120 during continuous turning with varying radii as a means of influencing the differing magnitude 121 of shear forces encountered at the forefoot region (metatarsal-phalangeal joints and toes). Due to 122 the mechanical requirement of the task, greater shear forces were expected when turning with a 123 smaller radius, and greater shear was expected on the external foot compared to the internal foot 124 (Orendurff et al., 2006). It was hypothesized that the foot temperature increase would be related 125 to a greater shear force. It was also hypothesized that the external foot, due to greater shear 126 forces, would experience higher temperature increase compared to the internal foot.

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To determine the contribution of contact time with the floor relative to stride time (duty 215 factor), a full gait cycle was needed and thus a previously established method for determining 216 heel strike and toe-off based on target pattern recognition was used (Stanhope et al., 1990). The 217 impulse from the ML and AP vectors of the ground reaction force (normalized to body weight) 218 as well as the resultant of these two vectors were analyzed for both limbs using Visual 3D 219 software (C-Motion, Germantown, MD) by utilizing the local coordinate system affixed to each 220 foot. The impulse from the resultant shear forces was calculated by integrating the entire time 221 series over the stance phase. Shear impulse was extrapolated to the entirety of the walking trial 222 (5 minutes). In order to extrapolate the shear data, duty factor (i.e., ratio of floor contact time to 223 stride) from each participant was multiplied by the total time to estimate the total time spent in 224 the stance phase for each radius condition. The product of shear impulse per step and estimated 225 floor contact time was used to gather accumulated shear impulse per five minutes of walking.

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One participant was omitted from the study as technical difficulties prevented the 227 collection of their kinetic and kinematic data. Due to this difficulty, all statistical analyses were 228 performed on 18 participants (9 females and 9 males).

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We analyzed additional variables that could affect ∆T, including work done by the foot, 231 free moment, and baseline temperatures. A unified deformable power analysis was utilized to 232 calculate the power contributions of all structures distal to the hindfoot (i.e., entire foot) 233 (Takahashi et al., 2012;Takahashi et al., 2017). Mechanical work done by the foot was 234 determined by integrating the distal-to-hindfoot power with respect to time during stance. The 235 free moment angular impulse was calculated by integrating the free moment of the force plate 236 during the stance. Free moment was normalized by body weight x height (Creaby and Dixon, 237 2008;Holden and Cavanagh, 1991;Milner et al., 2006), and distal-to-hindfoot power was 238 normalized by body mass. Foot mechanical work and free moment angular impulse were 239 extrapolated to the entirety of the walking trial (5 minutes).

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After completing all of the walking trials, the participants performed additional walking 241 trials to quantify foot contact area, which is required to estimate shear stress (defined as the peak 242 resultant shear force over the contact area with the ground). The contact area was gathered by 243 capturing a thermal foot imprint using the thermal imaging camera. The foot imprints were 244 placed on top of a leather cloth-back material by having the participants walk on their toes an 245 additional lap on the curved path for each foot and each radius. To create a clear contrast 246 difference between the foot thermal imprint and leather material, participants had their feet 247 passively warmed using warm water (~40 °C). After the participant had their feet dried, they 248 were asked to walk barefoot on their toes over the curved path containing the leather material for 249 one lap for each radius. A custom MATLAB code was utilized to gather the average contact 250 area. Briefly, the code reads the temperature data from individual pixels within the FLIR thermal 251 image and sets a threshold gradient between the leather material and foot thermal imprint to 252 detect the area of the forefoot in contact with the leather material. During post-processing, we 253 discovered that some participants' feet did not create a clear temperature gradient, most likely 254 since the ground contact time was not long enough for the leather material to accumulate heat 255 from the foot. With this technical difficulty, only ten participants were analyzed for the stress 256 data.

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To analyze differences in shear impulse and ∆T of entire foot and forefoot across radii 259 conditions and limbs, two-way repeated-measures ANOVA was performed in SPSS (IBM, 260 Armonk, NY). When a significant main effect was found, Fishers' least significant difference 261 method was used for pair-wise comparisons. Data were reported as means and standard deviations. 262 Statistical significance was defined as α < 0.05.

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A linear mixed effects (LME) model analysis was performed in R (R Core Team, 2019) 264 using the extrapolated data to determine the shear-thermal relationship. Although more simple 265 statistical tests (e.g. repeated measures ANOVA) are usually enough, more complex structures 266 require more complex models (Zuur et al., 2009). The LME model allows for multiple fixed 267 effects in addition to controlling for non-independence among data points (by utilizing 268 participants as a random effect). The statistical model was able to determine whether potential 269 confounding variables could potentially influence foot temperature.

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A hierarchical approach was used to test for significance, where all potential confounding 271 factors and factors of interest were initially included within the model. Terms were removed 272 from the final model when non-significance was yielded. A likelihood ratio test was performed 273 on two models to determine the effect of each variable. That is, the temperature data were 274 analyzed by comparing a full model as a function of the fixed effects as well as the random 275 effects to a reduced model (subtraction of fixed effects) to determine whether the fixed effect 276 improved upon the model. Additionally, the coefficient of determination was determined to 277 quantify the goodness-of-fit of the fixed effects. The variance explained (R 2 ) reported here were 278 calculated according to Nakagawa et al., (2012 Shapiro Wilk's test was performed to check for normality of residuals (entire foot model : 285 P = 0.40, forefoot model: P = 0.60). Homoscedasticity and linearity were confirmed visually via 286 a residual plot. Independence of the data was accounted for by having participants input as a 287 random effect into the statistical model.
308 Effect of radius/limb on temperature pre (baseline) and post walking
322 Effect of radius condition/limb on foot temperature change from pre and post walking (∆T)

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Factors significantly affecting foot temperature were included within the final linear 340 mixed effects model. Significant fixed effects affecting the final model included extrapolated 341 shear impulse and gender. Participants were utilized as a random effect within the model. Shear 342 impulse affected entire foot ∆T (χ2(1)= 20.23, P < 0.0001), increasing temperature by about 0.11 343 ± 0.10 °C for every unit of shear impulse normalized to body weight (Eqn 1) (Fig. 5). Shear 344 impulse also affected forefoot ∆T (χ2(1)= 17.23, P < 0.0001), increasing temperature by about 345 0.17 ± 0.16 °C for every unit increase of shear (Eqn 2). 348 For the final model (temperature as a function of shear impulse and gender), the 349 coefficient of determination for the fixed effects were: marginal R 2 = 0.32 for the entire foot and 350 marginal R 2 =0.24 for the forefoot region. The coefficients of determination for the random 351 effects were: conditional R 2 = 0.83 for the entire foot and conditional R 2 = 0.81 for the forefoot 352 region. When analyzing the two shear components separately during turning, AP impulse was a 353 significant predictor of entire foot ∆T (P = 0.03) but not forefoot ∆T (P = 0.10). The ML impulse 354 was a significant predictor of entire foot ∆T (P < 0.0001) and forefoot ∆T (P < 0.0001). The limb 355 side was not a significant predictor of entire foot ∆T (P = 0.85) nor forefoot ∆T (P = 0.46).

[Insert Figure 5 near here]
357 Effect of baseline temperature on changes in foot temperature (∆T) 358 An additional mixed model was used to examine the effect of baseline temperatures on 359 ∆T, where significant fixed effects included extrapolated shear impulse, gender, and baseline 360 temperature. Participants were utilized as a random effect within the model. Even with the 361 inclusion of baseline temperatures, shear impulse continued to be a significant predictor of ∆T. 362 Within the entire foot, shear impulse significantly (χ2(1)= 19.48, P < 0.0001) increased 363 temperature by about 0.07 ± 0.06 °C for every unit of shear impulse normalized to body weight 364 (Eqn 3). Shear impulse also affected forefoot ∆T (χ2(1)= 23.03, P < 0.0001), increasing 365 temperature by about 0.12 ± 0.10 °C for every unit of shear (Eqn 4). When accounting for baseline temperature, the coefficient of determination for the fixed 369 effects were: marginal R 2 = 0.84 for the entire foot and marginal R 2 =0.81 for the forefoot region. 370 When accounting for baseline temperature, the coefficients of determination for the random 371 effects were: conditional R 2 = 0.94 for the entire foot and conditional R 2 = 0.96 for the forefoot 372 region.

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To analyze the effect of potential confounding factors on foot temperature change, a 375 hierarchical approach was utilized (i.e., factors were removed when non-significance was 376 detected). The fixed factors analyzed were: net work, free moment, lab surface temperature, limb 377 side, gender, and extrapolated shear impulse. Participants were utilized as a random effect within 378 the model. Additionally, the effect of shear stress on foot temperature was analyzed separately 379 utilizing significant factors (i.e., including gender as a fixed factor as well).

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Net work distal to the hindfoot was not a significant predictor of ∆T within the entire foot 381 (P = 0.87) nor in the forefoot (P = 0.36) (Fig. S3). Free moment angular impulse was also not a 382 significant predictor of entire foot ∆T (P = 0.47) nor forefoot ∆T (p = 0.56) (Fig. S4). Shear 383 stress measured within the forefoot (N = 10) was a significant predictor of entire foot ∆T (P < 384 0.01) and forefoot ∆T (P = 0.01).

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Gender was a significant predictor of ∆T where males had a lower estimated entire foot 386 ∆T relative to females (χ2(1)= 6.36, P = 0.01). Within the entire foot, the pre and post 387 temperature values for females were 25.67 ± 1.14 °C and 25.47 ± 0.96 °C, respectively, and the 388 values for males were 26.86 ± 2.78 °C and 25.52 ± 1.62 °C, respectively. Likewise, males had a    The experimental setup involved pre-and post-temperature measurements (Fig. 1A) as participants (n=18) walked on their toes along a curved path with varying radii (Fig. 1B).
The order of the radii conditions (1.0, 1.5, and 2.0 m) was randomized for each participant.     Fig. 2A) and post- (Fig. 2B) temperature measurements. The outlines (manually traced for visualization) represent the areas to gather the entire foot (white) and forefoot (gray) temperature. To create a contrast difference between the foot and background temperature, a cold towel was placed above the subject's leg (no contact between towel and limb) before taking the thermal image.
PeerJ reviewing PDF | (2020:06:49818:1:1:NEW 13 Oct 2020) Manuscript to be reviewed   The anteroposterior (AP) (Fig. 3A) and mediolateral (ML) (Fig. 3B) components of the ground reaction forces (time-normalized to stance phase) were utilized to gather resultant shear impulse extrapolated to the 5 minute walking trial for each limb within each radii condition for all subjects (n=18) (Fig. 3C). AP and ML forces are relative to the coordinate system of each foot, where medial forces on the external limb and lateral forces on the internal limb indicate forces directed towards the center of the radii, respectively. The resultant shear impulse was greater within the external limb compared to the internal limb (p < 0.0001, denoted by an asterisk) and greater as the radii condition decreased (p < 0.0001, denoted by a + symbol) (Fig. 2C).