Changes in the three-dimensional microscale topography of human skin with aging impact its mechanical and tribological behavior

Human skin enables interaction with diverse materials every day and at all times. The ability to grasp objects, feel textures, and perceive the environment depends on the mechanical behavior, complex structure, and microscale topography of human skin. At the same time, abrasive interactions, such as sometimes occur with prostheses or textiles, can damage the skin and impair its function. Previous theoretical and computational efforts have shown that skin’s surface topography or microrelief is crucial for its tribological behavior. However, current understanding is limited to adult surface profiles and simplified two-dimensional simulations. Yet, the skin has a rich set of features in three dimensions, and the geometry of skin is known to change with aging. Here we create a numerical model of a dynamic indentation test to elucidate the effect of changes in microscale topography with aging on the skin’s response under indentation and sliding contact with a spherical indenter. We create three different microrelief geometries representative of different ages based on experimental reports from the literature. We perform the indentation and sliding steps, and calculate the normal and tangential forces on the indenter as it moves in three distinct directions based on the characteristic skin lines. The model also evaluates the effect of varying the material parameters. Our results show that the microscale topography of the skin in three dimensions, together with the mechanical behavior of the skin layers, lead to distinctive trends on the stress and strain distribution. The major finding is the increasing role of anisotropy which emerges from the geometric changes seen with aging.

The contours of the 11 component of the Green-Lagrange strain in Figure S2 show much less influence from microrelief changes or changes of SC properties between wet and dry conditions compared to Figure S1 or Figure 3 in the main text. Indeed, the indentation step mostly affects the normal strain component or the first principal strain. Similarly, Figure S3 shows that the shear strain component is minimally affected by the changes in microrelief or changes in SC properties. Nevertheless, Figure S2 does show that the microrelief leads to strain concentration around the microscale features, mostly in the epidermis, which might be important for improving understanding of epidermis mechanosensing.

Green Lagrange Strain components plotted across the thickness
The main text shows the E 33 and E13 Components of the Green-Lagrange plotted across the skin thickness right underneath the indenter for the different age topographies and different SC condition (wet or dry) (Figure 4). In the supplement we present these components as well as the first principal Green-Lagrange strain E 1 , in different positions: right underneath the indenter apex, R/2 and R from indenter apex. Results are for the 50-60 years old topography. A minor variation in the trend is observed between dry (dashes) and wet (solid line) SC conditions. The main noticeable difference among the dermal stiffness is the E13 component in dermis zone. Figure S4 50-60 years-old topography E33, E13 and E1 plotted across the skin thickness for in three different positions underneath the indenter. Blue, green and red correspond to underneath indenter apex, R/2 and R away from the center respectively. The solid line represents the wet SC case and dashes are for the dry SC simulations.

E33 Green Lagrange Strain component and surface stress during indenter movement
The main text shows the maximum principal stress at the skin surface when the indenter moves in the anatomical directions 1 which corresponds to the lateral axis. Figure S5 shows the maximum principal stress when the indenter moves in the directions given by the primary skin lines 3 and 4 . Similar to the discussion in the main text, the skin microrelief becomes more anisotropic with aging, which leads to an increasingly anisotropic stress profile at the surface as the skin interacts with the indenter. Figure S5 Maximum principal stress contours for three different skin age topographies, for the displacement directions U3 and U4 given by the primary skin lines. The results correspond to: a) wet SC b) dry SC material properties.

E33 Green Lagrange Strain component and surface stress under intermediate SC mechanical properties
The values for SC mechanical properties considered in the main text are at the extremes of the values reported in the literature. Therefore, we expected that our results in the main text would reflect these extreme conditions. To further confirm that an intermediate SC stiffness [E=100 MPa] would show an intermediate response with respect to our main results, we ran additional simulations in the 30-40 years-old topography. Figure S6 show the contours of E33 Green Lagrange Strain component for all SC conditions and figure S7 the maximum shear at the top surface. As expected, this intermediate SC stiffness leads to results in between wet and dry conditions reported in the main text.

Regression for skin friction as a function of model parameters
As indicated in eq. (2), we perform a simple multi-linear regression of the global coefficient of friction in terms of the parameters of the model. The corresponding R functions are results are illustrated here. As can be seen from the results, only the direction of indenter movement with respect to the skin microrelief lines show statistical significance for the global coefficient of friction, whereas neither age nor SC properties led to statistically significant results. A second linear regression was then performed, ignoring all parameters except for direction. These results are shown in Table S2.

Mesh convergence
To verify that the mesh density was accurate we performed a mesh refinement analysis and found that increasing the mesh by a factor of 1.5 resulted in small variations of the stress features. In particular, the maximum shear stress shown in Figure S8 only increases by 0.8% with the 50% increase in mesh elements. The simulations are already computationally demanding with the coarse mesh which consists of approximately 350,000 hex elements. Figure S8 Mesh convergence analysis for Max Shear stress τmax of skin flat topography. The mesh is based on Preview Butterfly 2D 120,150,175 elements in x and y direction for 3.5 mm square ROI.