Effect of collagen degradation on the mechanical behavior and wrinkling of skin

Chronological skin aging is a complex process that is controlled by numerous intrinsic and extrinsic factors. One major factor is the gradual degradation of the dermal collagen fiber network. As a step toward understanding the mechanistic importance of dermal tissue in the process of aging, this study employs analytical and multiscale computational models to elucidate the effect of collagen fiber bundle disintegration on the mechanical properties and topography of skin. Here, human skin is modeled as a soft composite with an anisotropic dermal layer. The anisotropy of the tissue is governed by collagen fiber bundles with varying densities, average fiber alignments, and normalized alignment distributions. In all finite element models examined, collagen fiber bundle degradation results in progressive decreases in dermal and full-thickness composite stiffness. This reduction is more profound when collagen bundles align with the compression axis. Aged skin models with low collagen fiber bundle densities under compression exhibit notably smaller critical wrinkling strains and larger critical wavelengths than younger skin models, in agreement with in vivo wrinkling behavior with age. The propensity for skin wrinkling can be directly attributable to the degradation of collagen fiber bundles, a relationship that has previously been assumed but unsubstantiated. While linear-elastic analytical models fail to capture the postbuckling behavior in skin, nonlinear finite element models can predict the complex bifurcations of the compressed skin with different densities of collagen bundles.

Figure 1

Structural properties of heterogeneous and anisotropic human skin and their dependency on age. (a) Histological section of full-thickness human skin tissue annotated with the different skin layers. The hypodermis layer is not included. The scale bar denotes 200 μm. (b) The percentage of area occupied (AO) by collagen in the reticular dermis as a function of age. AO is representative of the density of collagen bundles and is characterized by quantifying the ratio of the area occupied by bundles to the total area of the matrix. Panel (b) has been modified from Ref. [5] and used with permission from Wiley.

Figure 2

Collagen distribution and orientation in a skin sample. (a) Horizontal transverse cross section of skin in the reticular dermal layer, parallel to the skin surface, displaying tortuous collagen fiber bundles. The scale bar denotes 200 μm. (b) Histogram of collagen fiber bundle directionality from panel (a) using the directionality tool in fiji [109, 110, 111]. (Blue curve) Least square best-fit Gaussian distribution (mean: 21.03°, standard deviation: 23.17°) to the histogram revealing normally distributed collagen orientations. An angle of 0° denotes alignment in panel (a) along the long axis of the scale bar with positive angles increasing in a counterclockwise direction.

Figure 3

Schematic of the three-layer skin model which consists of the stratum corneum (SC), viable epidermis layer (VE), and dermal layer (DE). $E_{\mathrm{SC}},$ $E_{\mathrm{VE}}$, $E_{\mathrm{DE}}$, ${\vartheta }_{\mathrm{SC}}$, ${\vartheta }_{\mathrm{VE}}$, ${\vartheta }_{\mathrm{DE}}$, $h_{\mathrm{SC}}$, $h_{\mathrm{VE}}$, and $h_{\mathrm{DE}}$ are Young's modulus of SC, Young's modulus of VE, Young's modulus of DE, Poisson's ratio of SC, Poisson's ratio of VE, Poisson's ratio of DE, the thickness of SC, the thickness of VE, and the thickness of DE, respectively. (a) Mode I: wrinkling of a composite beam (SC and VE combined) on a single layer substrate (DE). (b) Mode II: wrinkling of the stiff top layer (SC) on a composite substrate (VE and DE combined).

Figure 4

Probability density of bundles’ angles for models with distributions that are (a) horizontal, (b) 15°, (c) 30°, (d) 45°, (e) 60°, and (f) random. A 2D finite element model (g) of the dermal layer with randomly distributed collagen bundles at random angles. The layer is filled with 80% collagen bundles $(\mathrm{AO}=80\%)$. Blue depicts the soft matrix. The collagen bundles have not been rendered to the actual diameter to make visualization easier.

Figure 5

A 2D dynamic finite element model of the skin with randomly distributed collagen bundles at random angles. The dermal layer is filled with 80% collagen bundles. Blue, gray, red, and green depict the ground substance, collagen bundles, viable epidermis, and SC, respectively. The collagen bundles have not been rendered to the actual diameter to make visualization easier.

Figure 6

Von Mises stress distribution (MPa) within a dermal tissue model subjected to a strain of $\varepsilon =0.1$. Dermal tissue models exhibit (a) 80% and (b) 50% AOs for average collagen orientation aligned with the loading axis and (c) 80% and (d) 50% collagen fiber densities with 60° distributions of collagen orientations. (e) Axial stress distribution in the collagen fibers for the cases with 0° and 60° orientations in two different collagen densities under $\varepsilon =0.1$ compressive strain.

Figure 7

(a) Variation of equivalent elastic modulus of the dermal layer during the aging process according to the different orientations of collagen bundles. (b) Variation of equivalent elastic modulus of the dermal layer by the decrease in AO by aging. AO is the ratio of the area occupied by bundles to the total area of the matrix.

Figure 8

The critical strains of the two wrinkling modes for different $E_{\mathrm{SC}}$ and $E_{\mathrm{VE}}$ values. (a), (c), (e) are the critical strain curves for both of the wrinkling modes, and (b), (d), (f) are the wrinkling mode region plots. The values of the Young's modulus of the substrate for (a), (c), and (e) are 0.030 (MPa), 0.115 (MPa), and 0.200 (MPa), respectively. Plots (b), (d), and (f) are the corresponding mode regions of (a), (c), and (e), respectively.

Figure 9

(a), Variation of critical wrinkling strain with $h_{\mathrm{VE}}/h_{\mathrm{SC}}$, $E_{\mathrm{VE}}/E_{\mathrm{SC}}$, $E_{\mathrm{DE}}/E_{\mathrm{SC}}$; (b) variation of normalized critical wavelength (${\lambda }_c/h_{\mathrm{SC}}$) with $h_{\mathrm{VE}}/h_{\mathrm{SC}}$, $E_{\mathrm{VE}}/E_{\mathrm{SC}}$, $E_{\mathrm{DE}}/E_{\mathrm{SC}}$. Wrinkling mode region plots for (c) $h_{\mathrm{VE}}/h_{\mathrm{SC}}=2$, (d) $h_{\mathrm{VE}}/h_{\mathrm{SC}}=3.5$, and (e) $h_{\mathrm{VE}}/h_{\mathrm{SC}}=5$.

Figure 10

Critical wavelength vs AO (ratio of the area occupied by bundles to the total area of the matrix) for various orientations of bundles.

Figure 11

Critical strain vs AO (ratio of the area occupied by bundles to the total area of the matrix) for various orientations of bundles.

Figure 12

Wrinkled skin under 30% compressive strain with 0° orientation and with (a) 80% AO and (b) 50% AO inside the dermal layer. (c) Comparison between the profiles of the wrinkles after deformation.

Figure 13

Variation of (a) $R_a$ (average roughness) and (b) $R_q$ (root mean square roughness) in cases with different orientations and with 80% and 50% AOs in the dermal layer. The unit of $R_a$ and $R_q$ is mm.