HETEROGENEOUS MECHANICS AND MECHANOBIOLOGYOF SKIN

The skin plays an important role in the human body, as it is the largest organ. It houses the sense of touch and provides mechanical protection. Computational models have commonly treated the skin as a thin homogeneous material or ignored the heterogeneities observed at the mesoscale when considering multiple layers. In this study we created finite element models of the representative volume elements (RVEs) of skin. The RVE included the three-dimensional variation of the interface in between the epidermis and dermis. Then a hair follicle was introduced into the model with an epithelium surrounding it. The rete ridges were approximated using a sinusoidal interface and do not affect the homogenized mechanical response of the RVE but did contribute to local stress concentrations especially at the valleys of the rete ridges. Due to the the skins anisotropy the stress profile is three-dimensional leading to high-stress bands connecting the valleys of the rete ridges through one type of saddle point. Under equi-biaxial loading the sinusoidal surface formed a second set of low-stress bands from the peaks of the rete ridges and the other class of saddle points. The heterogeneous stress pattern showed a switch in the stress jump across the interface. The average stress jump becomes lower with respect to the flat interface at increasing deformations. These features were also observed in tension and shear loading. The RVE with the hair follicle showed large strains concentrating at the epidermis adjacent to the hair follicle, at the epithelium right below the epidermis surrounding the hair follicle, and at the base or bulb of the hair follicle. In equi-biaxial and shear loading the regions of large strain near the hair follicle align with the presence of distinct mechanoreceptors in the skin expect for at the base region. This initial study highlights the importance of skin heterogeneities and its potential mechanophysiological role in the prevention of skin delamination and the sense of touch.

After showing how the rete ridges contribute to the stress behavior in the skin a question arose if the heterogenities change or are preserved in tissue expansion. Experimentally, it has been observed that upon repeated tissue expansion and growth, physiological rete ridge frequency is preserved. A 2D multilayered skin model was implemented in which each layer is able to grow in response to applied loading to recover the layer-specific homeostatic stretch.

Our hypothesis is that the mechanics of growing tissue is sufficient to explain secondary buckling and new rete ridge formation in tissue expansion and was supported by our simulations. In respect to parameters such as shear moduli, layer thicknesses, and homeostatic stretch of the different layers the process is robust. A stiffer epidermis with respect to the basal layer and a thicker epidermis suppress higher frequency features. After experiencing tissue expansion, new rete ridge valleys formed at the same locations that were originally peaks of the sinusoidal interface and the original valleys remained valleys. This observed pattern may have a connection to transient amplifying cells in the epidermis and the localization of stem cells. This study does not disregard the role of cell-cell signaling dynamics, but emphasizes the possibility of using simple rules of growing tissue to achieve robust geometric patterns even in the absence of complex regulatory networks.

Another aspect of skin multilayer modeling and heterogenities is having the appropriate constitutive model to describe each layer. Previous models have incorporated growth in isotropic models like Neo-Hookean and on the GOH anisotropic constitutive model. The GOH model is limited because it does not extrapolate well with its exponential and ignores microstructure. An alternative theory is constrained mixture theory which is very detailed but it is difficult to track all the mass fractions in all directions. Therefore in this study an anisotropic constitutive model with growth was developed considering how the collagen (fibers) in the dermis grow and deform based on an orientation and undulation distribution. It is an intermediate model to the other two theories which provides a balance to microstructure and detailed description. The results showed how the constitutive model does not only provide the stress on the model but also tracks the growth, elastic and total deformation from multiple orientations. The additional information gained provides a greater understanding on each fibers role on the deformation during tissue expansion making it a great intermediate anisotropic constitutive model to describe the dermis layer and other anisotropic growing soft tissue. The constitutive model was implemented in the finite element package called Abaqus to validate the analytical results. After the validation, the constitutive model was used on both 2D and 3D finite element models of different complexities under tissue expansion demonstrating its versatility and showing a lot of promise.

After a 2D tri-layer model with finite thicknesses was introduced to understand the formation of the rete ridges from buckling during tissue expansion an analytical model to predict when buckling occurs with different combinations of stiffness ratios and varying other parameters. Validation was done with a finite element model without perturbation fores to demonstrate how the buckling forms naturally with the parameters used. The results showed how buckling triggers when both the upper and lower stiffness ratios are less than one. Buckling does not trigger when the upper and lower stiffness ratios are greater than one. Buckling will sometimes trigger when there is a combination of stiffness ratios of greater and less than one. Other parameter variations were considered in the system which included the epidermis thickness and the initial loading of the epidermis and dermis. As the epidermis thickness decreased it increased the wavelength when buckling occurs or even stopped the interface from buckling. The results provide an understanding on how stiffness ratios increasing and the epidermis thinning from aging will diminish the rete ridge formation. Overall, each study conducted focuses on a different aspect of heterogenities in the skin which include incorporating the rete ridges in 3D and 2D multilayered skin models, how the rete ridges are formed and persevered, an anisotropic constitutive growth model for the dermis and ways to predict the rete ridge formation and how it changes with aging.