Ph.D Thesis

Ph.D StudentLokshin Olga
SubjectMicro-Structural Characterization of the Skin
Constitutive Properties
DepartmentDepartment of Applied Mathematics
Supervisor PROFESSOR EMERITUS Yoram Lanir


The mechanical behavior of skin are of interest in several disciplines of clinical research and care, such as plastic surgery, the design of incision, skin transplantation, wound healing and dermatology.

Experimental studies with skin demonstrate anisotropy and non-linearity of stress-strain relationship, and two different aspects of time-dependent mechanical behavior: viscoelasticity, and preconditioning. While the nonlinearity and viscoelasticity of the skin have been studied extensively, the effects of preconditioning, although widely recognized, have hardly been dealt with.

The present work incorporates the above properties into constitutive equations of skin through the stochastic-structural approach (Lanir, 1983). The following assumptions are made: the tissue response is the sum of contributions of its constituents (e.g., collagen fibers, elastin fibers and amorphous ground substance); the fibers deform affinely; elastin and collagen fibers possess only tensile stiffness; the elastin network consists of straight viscoelastic fibers; the collagen network consists of viscoelastic fibers which are non-uniformly undulated; collagen preconditioning is due to increase in fibers gage length.

Two data sets were used as bases for parameters estimation and model analysis: uni-axial data of Eshel and Lanir (2001), and biaxial data of Lanir and Fung (1974). The model parameters were estimated to “best fit” the data using Genetic Algoritm search. Reliability of the estimation procedure was validated by applying it on simulated data with added random noise.

The results exhibit excellent fit to data and very good predictive power of response characteristics under protocols not used to estimate parameters. These results are thus consistent with the following notions: while collagen preconditioning is associated with increase in the gage length, in elastin the reference length is preserved, and preconditioning is manifested as Mullins effect (strain softening); the elastin response is predominant at low strains and still significant at high strain; collagen contribution is predominant at high strains. Additional conclusions from the biaxial investigation are: under biaxial stretch, the level of matrix hydrostatic pressure is low but significant for model-to-data fit; the waviness distribution of collagen fibers varies with the fibers direction, and in each direction, it changes during preconditioning; the orientation distribution of both fibers is bimodal. 

The present results indicate that reliable characterization of the skin mechanical response must include the effect of preconditioning, in addition to the non-linear and viscoelastic aspects. Assigning these three properties to the skin fibers in the framework of a structural model produces reliable material laws for the skin.