Allometric scaling of skin thickness, elasticity, viscoelasticity to mass for micro-medical device translation: from mice, rats, rabbits, pigs to humans

Abstract

Emerging micro-scale medical devices are showing promise, whether in delivering drugs or extracting diagnostic biomarkers from skin. In progressing these devices through animal models towards clinical products, understanding the mechanical properties and skin tissue structure with which they interact will be important. Here, through measurement and analytical modelling, we advanced knowledge of these properties for commonly used laboratory animals and humans (~30 g to ~150 kg). We hypothesised that skin's stiffness is a function of the thickness of its layers through allometric scaling, which could be estimated from knowing a species' body mass. Results suggest that skin layer thicknesses are proportional to body mass with similar composition ratios, inter- and intra-species. Experimental trends showed elastic moduli increased with body mass, except for human skin. To interpret the relationship between species, we developed a simple analytical model for the bulk elastic moduli of skin, which correlated well with experimental data. Our model suggest that layer thicknesses may be a key driver of structural stiffness, as the skin layer constituents are physically and therefore mechanically similar between species. Our findings help advance the knowledge of mammalian skin mechanical properties, providing a route towards streamlined micro-device research and development onto clinical use.

Figure 1

Representative cryo histological cross sections of upper skin specimens: (a) mouse – flank, (b) rat – flank, (c) rabbit – flank, (d) large pig – ear (e) human – abdomen, at three magnification levels (i) 4x, (ii) 10x and (iii) 40x. (f) Measured skin strata thicknesses based on histology plotted against species mass. Horizontal error bars show SD of mass and vertical error bars show SD of measured thicknesses.

Figure 2

(a) Representative examples of two-term Prony series fitted to raw data showing the spread of raw data and curve fits. (b) Representative example of fitted two-term Prony series on one set of human in vivo data illustrating noticeable oscillations caused by heartbeats and small body movements of volunteers (first 10 s shown). Curves were still able to fit to the raw data as shown. (c) Mean force-time response of skin during a step-load over the first ten seconds of all species. (d) Mean and SD of force-relaxation curves for each species shown individually.

Figure 3

(a) Representative examples of raw data fitted to Ogden model. (b) Representative example of force-displacement curves when measuring human in vivo illustrating cyclical vibration caused by volunteers. (c) Mean force-displacement curves from all indents. (d) Mean force-displacement fitted to Ogden model normalised to 10% strain for all species with SD in shaded region. Note that y-axes have different scales. (e) Elastic moduli experimental trends shown vs. indentation tip radii with individual data points. (f) Elastic moduli shown vs. body mass.

Figure 4

(a) Analytical model estimation of the elastic moduli against tip radii. (b) Approximate share of structural modulus of SC, VE and dermis for each species and tip size estimated from the analytical model using Equation 14. (c) Elastic moduli shows vs. body mass, for tip sizes used experimentally in this study and also estimates down to the cellular scale.