Mathematical Models to Assess Foot–Ground Interaction

An Analytical Model to Predict Foot Sole Temperature: Implications to Insole Design for Physical Activity in Sport and Exercise

Foot sole temperature, besides its importance in thermal comfort, can be considered an important factor in identifying tissue injuries due to heavy activities or diseases. Hyperthermia, which is a raise in the foot temperature, increases the risk of diabetic ulcers considerably. In this study, a model is proposed to predict the foot sole temperature with acceptable accuracy. This model for the first time considers both the thermal and mechanical properties of the shoe sole, the intensity of the activity, the ambient condition, and sweating, which are involved in the thermal interaction between the sole of the foot and footwear. Furthermore, the proposed model provides the opportunity to estimate the contributions of different parameters in foot thermal regulation by describing the interaction of activity, duration, and intensity as well as sweating in influencing the foot sole temperature. In doing so it takes into account the relative importance of heat capacitance and the thermal conductivity. The results of this study revealed that sweating is not as effective in cooling the ball area of the foot while it is the principal contributor to thermal regulation in the arch area. The model also showed the importance of trapped air in keeping the foot warm, especially in cold conditions. Based on the simulation results, in selecting the shoe sole, and in addition to the conductivity, the thermal capacity of the sole of the shoe needs to be considered. The developed analytical model allowed the investigation of the contribution of all the involved parameters in foot thermal regulation and has shown that a different foot temperature can be achieved when the amount of material versus air is changed in the insole design. This can have practical implications in the insole design for a variety of conditions such as hypo and hyper-thermia in physical activities in sports and exercise settings.

Biomechanical Effects of Plastic Heel Cup on Plantar Fasciitis Patients Evaluated by Ultrasound Shear Wave Elastography

The plastic heel cup has been adopted to treat plantar heel problems for years. However, its mechanisms and biomechanical effects are yet to be fully understood. The purpose of this study was to investigate the effects of the plastic heel cup on the microchamber and macrochamber layers of the heel pad by comparing the stiffness (in terms of the shear wave speed) and thickness of these two layers with and without a plastic heel cup during static standing. Fifteen patients with unilateral plantar fasciitis were recruited. The shear wave speed and thickness of the microchamber and microchamber layers of each symptomatic heel pad during standing measured by ultrasound shear wave elastography were compared between conditions with and without a plastic heel cup. It was found that a plastic heel cup reduced the shear wave speed of the microchamber layer to 55.5% and increased its thickness to 137.5% compared with the condition without a plastic heel cup. For the microchamber layer, the shear wave speed was reduced to 89.7%, and thickness was increased to 113.6% compared with the condition without a plastic heel cup. The findings demonstrate that a plastic heel cup can help to reduce the stiffness and increase the thickness for both layers of the heel pad during standing, suggesting that the mechanism of a plastic heel cup, and its resulting biomechanical effect, is to reduce the internal stress of the heel pad by increasing its thickness through confinement.

Diabetes Status is Associated With Plantar Soft Tissue Stiffness Measured Using Ultrasound Reverberant Shear Wave Elastography Approach

INTRODUCTION

The purpose of this study was to investigate the association between the mechanical properties of plantar soft tissue and diabetes status.

METHOD

51 (M/F: 21/30) participants with prediabetes onset (fasting blood sugar [FBS] level > 100 mg/dL), age >18 years, and no lower limb amputation were recruited after ethical approval was granted from Pontificia Universidad Catolica del Peru ethical review board. Ultrasound reverberant shear wave elastography was used to assess the soft tissue stiffness at the 1st metatarsal head (MTH), 3rd MTH, and the heel at both feet.

RESULTS

Spearman's rank-order correlation (rho) test indicated a significant (P < .05) positive correlations between FBS level and the plantar soft tissue shear wave speed at the 1st MTH: rho = 0.402 (@400 Hz), rho = 0.373 (@450 Hz), rho = 0.474 (@500 Hz), rho= 0.395 (@550 Hz), and rho = 0.326 (@600 Hz) in the left foot and rho = 0.364 (@450 Hz) in the right foot. Mann-Whitney U test indicated a significantly (P < .05) higher shear wave speed in the plantar soft tissue with the following effect sizes (r) at the 1st MTH of the left foot at all tested frequencies: r = 0.297 (@450 Hz), r = 0.345 (@500 Hz), r = 0.322 (@550 Hz), and r = 0.275 (@600 Hz), and at the 1st MTH of right foot r = 0.286 (@400 Hz) in diabetes as compared with the age and body mass index matched prediabetes group.

CONCLUSION

An association between fasting blood sugar level and the stiffness of the plantar soft tissue with higher values of shear wave speed in diabetes versus prediabetes group was observed. This indicated that the proposed approach can improve the assessment of the severity of diabetic foot complications with potential implications in patient stratification.

Plantar Soft Tissue Characterization Using Reverberant Shear Wave Elastography: A Proof-of-Concept Study

Plantar soft tissue stiffness provides relevant information on biomechanical characteristics of the foot. Therefore, appropriate monitoring of foot elasticity could be useful for diagnosis, treatment or health care of people with complex pathologies such as a diabetic foot. In this work, the reliability of reverberant shear wave elastography (RSWE) applied to plantar soft tissue was investigated. Shear wave speed (SWS) measurements were estimated at the plantar soft tissue at the first metatarsal head, the third metatarsal head and the heel from both feet in five healthy volunteers. Experiments were repeated for a test-retest analysis with and without the use of gel pad using a mechanical excitation frequency range between 400 and 600 Hz. Statistical analysis was performed to evaluate the reliability of the SWS estimations. In addition, the results were compared against those obtained with a commercially available shear wave-based elastography technique, supersonic imaging (SSI). The results indicate a low coefficient of variation for test-retest experiments with gel pad (median: 5.59%) and without gel pad (median: 5.83%). Additionally, the values of the SWS measurements increase at higher frequencies (median values: 2.11 m/s at 400 Hz, 2.16 m/s at 450 Hz, 2.24 m/s at 500 Hz, 2.21 m/s at 550 Hz and 2.31 m/s at 600 Hz), consistent with previous reports at lower frequencies. The SWSs at the plantar soft tissue at the first metatarsal head, third metatarsal head and heel were found be significantly (p<0.05) different, with median values of 2.42, 2.16 and 2.03 m/s, respectively which indicates the ability of the method to differentiate between shear wave speeds at different anatomical locations. The results indicated better elastographic signal-to-noise ratios with RSWE compared to SSI because of the artifacts presented in the SWS generation. These preliminary results indicate that the RSWE approach can be used to estimate the plantar soft tissue elasticity, which may have great potential to better evaluate changes in biomechanical characteristics of the foot.

A new approach to modelling the ground reaction force from a runner

The impact force experienced by a runner when his/her foot makes contact with the ground has been the subject of much research. This force is called the ground reaction force (GRF), and has been measured by several groups. In parallel with this, mathematical models have been developed to simulate GRFs in order to investigate various effects on this, such as the parameters of the human body and types of running shoe soles. Lumped parameter models have been developed by several researchers with limited success, because they are either constrained to model translational motion, or become complicated if they include rotational motion. This paper proposes a new approach based on modes of vibration, which encompasses the simplicity of the lumped parameter approach, without the motion constraints. The GRF is decomposed into contributions due to the various vibration modes of the system. To achieve this, a linear system is required, so a Zener model, which is used to model viscoelastic materials, is employed as the ground reaction model. The modal modelling approach is described in detail using established lumped parameter models used to predict the GRF. It is then applied to four experimental data sets from the literature, where it is shown that at most three modes are required to model GRF data accurately. Two of these modes are oscillatory modes and one is a non-oscillatory exponentially decaying mode. In general, it is shown that the modal model can capture the dynamics of each measured GRF independently of speed and running style.

A mathematical model to investigate heat transfer in footwear during walking and jogging

Foot temperature during activities of daily living affects the human performance and well-being. Footwear thermal characteristics affect the foot temperature inside the shoe during activities of daily living. The temperate at the sole of the foot (plantar temperature) is influenced by different thermal properties such as heat capacity, heat diffusivity, and thermal conductivity of the shoe sole in addition to its mechanical properties. Hence the purpose of this study was to propose a method to allow investigating the effect of footwear thermal characteristics on the foot temperature during activities of daily living, like walking or jogging. The transient heat transfer between the foot and the ground was studied to drive the governing equation for heat transfer modelling in footwear and to predict foot sole temperature during walking, and jogging. Different thermo-mechanical properties of shoe sole, as well as geometrical parameters, were investigated. The proposed model showed to be able to adequately predict the plantar temperature at the ball of the foot when compared to the results from experimental measurements. Finally, using the proposed method, the thermal behaviour of two different shoes with two different sole materials EVA08 and EVA12 were compared. It was shown that heat capacity as compared to the thermal conductivity of the shoe sole is more effective in reducing the plantar temperature increase in short term. The proposed method proved to be able to accurately predict the thermal behaviour of shoes and can provide a tool to predict footwear thermal comfort.

Identification of PIEZO1 polymorphisms for human bone mineral density

Bone mineral density (BMD) is a key indicator for diagnosis and treatment for osteoporosis; the reduction of BMD could increase the risk of osteoporotic fracture. It was very recently found that Piezo1 mediated mechanically evoked responses in bone and further participated in bone formation in mice. Here, we performed cross phenotype meta-analysis for human BMD at lumbar spine (LS), femoral neck (FN), distal radius/forearm (FA) and heel and screened out 14 top SNPs for PIEZO1, these SNPs were overlapped with putative enhancers, DNase-I hypersensitive sites and active promoter flanking regions. We found that the signal of the best SNP rs62048221 was mainly from heel ultrasound estimated BMD (-0.02 SD per T allele, P = 8.50E-09), where calcaneus supported most of the mechanical force of body when standing, walking and doing physical exercises. Each copy of the effect allele T of SNP rs62048221 was associated with a decrease of 0.0035 g/cm² BMD (P = 4.6E-27, SE = 0.0003) in UK Biobank data within 477,760 samples. SNP rs62048221 was located at the enhancer region (HEDD enhancer ID 2331049) of gene PIEZO1, site-directed ChIP assays in human mesenchymal stem cells (hMSCs) showed significant enrichment of H3K4me1 and H3K27ac in this region, luciferase assays showed that rs62048221 could significantly affect the activity of the enhancer where it resides. Our results first suggested that SNP rs62048221 might mediate the PIEZO1 expression level via modulating the activity of cis-regulatory elements and then further affect the BMD.

Development of a Subject-Specific Foot-Ground Contact Model for Walking

Computational walking simulations could facilitate the development of improved treatments for clinical conditions affecting walking ability. Since an effective treatment is likely to change a patient's foot-ground contact pattern and timing, such simulations should ideally utilize deformable foot-ground contact models tailored to the patient's foot anatomy and footwear. However, no study has reported a deformable modeling approach that can reproduce all six ground reaction quantities (expressed as three reaction force components, two center of pressure (CoP) coordinates, and a free reaction moment) for an individual subject during walking. This study proposes such an approach for use in predictive optimizations of walking. To minimize complexity, we modeled each foot as two rigid segments-a hindfoot (HF) segment and a forefoot (FF) segment-connected by a pin joint representing the toes flexion-extension axis. Ground reaction forces (GRFs) and moments acting on each segment were generated by a grid of linear springs with nonlinear damping and Coulomb friction spread across the bottom of each segment. The stiffness and damping of each spring and common friction parameter values for all springs were calibrated for both feet simultaneously via a novel three-stage optimization process that used motion capture and ground reaction data collected from a single walking trial. The sequential three-stage process involved matching (1) the vertical force component, (2) all three force components, and finally (3) all six ground reaction quantities. The calibrated model was tested using four additional walking trials excluded from calibration. With only small changes in input kinematics, the calibrated model reproduced all six ground reaction quantities closely (root mean square (RMS) errors less than 13 N for all three forces, 25 mm for anterior-posterior (AP) CoP, 8 mm for medial-lateral (ML) CoP, and 2 N·m for the free moment) for both feet in all walking trials. The largest errors in AP CoP occurred at the beginning and end of stance phase when the vertical ground reaction force (vGRF) was small. Subject-specific deformable foot-ground contact models created using this approach should enable changes in foot-ground contact pattern to be predicted accurately by gait optimization studies, which may lead to improvements in personalized rehabilitation medicine.

In-vivo viscous properties of the heel pad by stress-relaxation experiment based on a spherical indentation

Identifying the viscous properties of the plantar soft tissue is crucial not only for understanding the dynamic interaction of the foot with the ground during locomotion, but also for development of improved footwear products and therapeutic footwear interventions. In the present study, the viscous and hyperelastic material properties of the plantar soft tissue were experimentally identified using a spherical indentation test and an analytical contact model of the spherical indentation test. Force-relaxation curves of the heel pads were obtained from the indentation experiment. The curves were fit to the contact model incorporating a five-element Maxwell model to identify the viscous material parameters. The finite element method with the experimentally identified viscoelastic parameters could successfully reproduce the measured force-relaxation curves, indicating the material parameters were correctly estimated using the proposed method. Although there are some methodological limitations, the proposed framework to identify the viscous material properties may facilitate the development of subject-specific finite element modeling of the foot and other biological materials.