1 Introduction

Skin mechanics has been studied for several decades [1]. The medical field is interested in diagnosis, monitoring, and treating skin diseases [2], preventing excessive scar tissue formation [3], and facilitating fast wound healing in wound care [4, 5]. Biomechanics aims at characterizing mechanical properties to model skin deformation behavior, to provide criteria for developing artificial skin, or to simulate skin behavior in facial animations [6], skin wrinkling [7], analysis of congenital skin defects [8, 9], and personalized reconstructive surgery [10].

The multilayered anatomy of skin can be represented in corresponding biomechanical models and this leads to the requirement of determining layer specific constitutive equations [11]. Previous research provided a wide range of constitutive model formulations for skin, but to this day no generally accepted theory exists that translates microstructural tissue properties into corresponding model equations [12].

The comparability of models proposed in the literature is often limited due to significant differences in the representation of skin anatomy. Large discrepancies in predicted mechanical response are also linked with differences in the deformation modes considered for model development. In fact, model parameters are often determined based on data obtained from one specific experimental configuration. The range of validity of such parameter sets is inherently limited, in that an optimization may well reproduce the experiments for a particular loading condition but is likely to provide poor predictions for any generalized multiaxial, time dependent deformation state [13]. Skin literature presents several dedicated parameter identification schemes that combine a particular mechanical testing method with a skin model formulation representative of that experiment.

This review presents different procedures for skin characterization and associated model parameter identification schemes and discusses their limitations with regard to the development of a skin model of more general validity. The chapter briefly summarizes skin anatomy and outlines experimental methods suitable for a quantitative analysis of skin constituents at different length scales. We then describe common testing protocols for characterizing skin mechanical properties and outline corresponding structural and phenomenological models used for their analysis. Finally, we discuss inverse analysis procedures presented in skin literature addressing problems associated with the variability in experimental data, the contribution of individual skin layers, and the inherent coupling between model parameters.

2 Experimental Anatomy of Skin

The anatomy of skin has been studied extensively, and histochemical staining and dissection have led to a comprehensive description of cells and microstructure of individual skin layers; yet, to date the characterization of skin microstructure across spatial and temporal scales in its natural in vivo environment remains an active field of research. Many visualization techniques have been developed to study skin and its individual layers for a rich set of medically relevant applications and experimental investigations. Ultrasound and magnetic resonance imaging of skin at the organ level are common diagnostic tools in clinical practice and microscopy-based visualization methods are often used in research to study skin at the tissue and cellular level [14].

In view of skin modeling and the identification of corresponding parameters, it is relevant to differentiate between an anatomical description of skin and the actually experimentally observable microstructure with its associated properties [15]. Each imaging modality is generally limited to a specific length scale and it remains a major challenge to visualize skin anatomy in vivo from the organ level down to the cellular level [16].

In the following, we present a brief description of skin anatomy and summarize imaging modalities that visualize skin at the organ, tissue, and cellular level.

2.1 Anatomical Description

Figure 1 shows a representation of skin that consists of three main layers [18]: the outermost epidermis is typically 100 μm thick. The layer underneath, the dermis, is around 500 μm thick and consists of two sublayers: the papillary dermis and the reticular dermis. The deepest layer is the hypodermis with a thickness of around 1 mm. The actual size and microstructure of these individual layers varies with location in the body in order to provide optimal functionality, such as resilience in feet, grip in palms, and barrier function around the core body.

Fig. 1
figure 1

Representation of the anatomical structure of skin. Skin has functionally different layers that contribute to the overall mechano-biochemical properties of what is the largest organ in the human body. Full thickness skin, left image, generally consists of three layers: the epidermis, dermis, and hypodermis. The epidermis, right image, is the outermost barrier between body and environment, and consists of five sublayers. Adapted from [17]

Full size image

The epidermis protects the body against mechanical and microbacterial hazards and prevents the body from dehydration. The outermost layer, the stratum corneum, consisting of 5–10 layers of dead, keratin rich, and flat cells, represents a barrier impermeable to most biochemical and toxic compounds. The four additional layers underneath, often referred to as the viable or living epidermis, consist of cells that migrate from the dermal-epidermal junction and gradually die, whilst accumulating keratin and losing their nuclei. The dense cell layering gives the epidermis significant mechanical strength and often plays an important role in the response observed in skin tests.

The dermis is the load-bearing layer in skin and is richly perfused with blood and lymph vessels, and hosts nerve endings. Cutaneous appendages, including sensory receptors, glands, and hair follicles, reside in the dermis which is mostly made up of type I and III collagen. The papillary layer has ridges consisting of thin collagen fibers and provides nutrients to the dermal-epidermal junction. The reticular dermis consists of a dense matrix of collagen bundles and elastin which gives skin its characteristic elastic extensibility.

The hypodermis, the deepest skin layer, primarily serves as a shock absorbing and insulating layer with a location-dependence specialized microstructure. It is located between the dermis and the fascia, which is a thin but strong membrane of connective tissue that encapsulates bones, muscles, and other organs underneath the skin. Fibrous septa running through the hypodermis anchor the dermis to fascial membranes and provide some degree of shear stiffness to the superficial layers of skin. The hypodermis itself contains primarily adipocytes and consists mainly of fat lobules embedded in a loose collagen network.

2.2 Imaging Modalities

In-vivo imaging modalities may generally be categorized by the length scales they resolve and their ability to identify individual pathologies [19]. MRI and US resolve organ and tissue structures at a submillimeter scale [20] and provide a full-thickness representation of skin [21]. High resolution ultrasound [22] and magnetic resonance imaging (MRI) at the organ-level [20] is used to determine layer thicknesses in different body regions and is gaining importance in clinical examinations, due to increased resolution of superficial tissue layers like epidermis and dermis [23]. The echogenicity of individual structures across full-thickness skin is proving useful to diagnose and monitor cysts, scleroderma, and solid, malignant, or inflammatory lesions [24]. It is important to note, however, that individual layers visible in MRI and ultrasound images may differ from medical anatomy. In sonography, and visible in the second row of Fig. 2, skin is often separated into the hyperechoic epidermis, the subepidermal low echogenic band (SLEB) representing the papillary dermis, the dermal echogenic band (DEB) showing reticular dermis, and the mostly hypoechogenic subcutis.

Fig. 2
figure 2

High resolution magnetic resonance images of deformed skin in the forehead, top row; high resolution ultrasound images in facial regions, middle row. Each skin layer plays a particular role in providing skin its characteristic extensibility and region-specific mechanical response [25, 26]. Second harmonic generation visualizes the collagen network in excised skin samples: The bottom row shows collagen fibers undulated in the excised reference, and progressively aligned in approximated in vivo, and large deformation states [27]

Full size image

Imaging modalities that visualize skin features down to the cellular level are generally based on the reflective behavior of individual tissue constituents and use either light or lasers as a source for penetrating superficial skin layers [2]. Such non-invasive methods are limited to a penetration depth up to 1000 μm and are therefore primarily used for in vivo characterization of the epidermis and the dermis [28]. Most commonly used methods include reflectance confocal microscopy, optical coherence tomography (OCT), multi-photon microscopy, two-photon fluorescence, and second harmonic generation (SHG).

The characterization of the structural anatomy of the epidermis and dermis -and of the dermal collagen network in particular- is an active field of research [29]. The assembly of collagen fibers into a highly functional network provides skin tissue its characteristic viscoelastic and anisotropic response [30]. The literature reports a rich set of studies investigating microstructure with respect to skin architecture [31, 32], inflammatory and blistering conditions [33], fiber orientation [30, 34], bundle thickness [35], tissue remodeling and skin diseases [36], and cutaneous vasculature [28, 37]. Acute changes of these properties cause structural alterations that may result in reduced extensibility, damage, and patient discomfort [14, 38].

3 Quantification of Mechanical Properties of Skin

Literature provides a rich body of work that investigated the mechanical behavior of skin or individual dermal and subdermal layers [1]. The range of data presented, however, has not led to a complete or consistent description of mechanical skin properties, and the findings continue to show a significant dependence on the testing method used. The biophysical response of skin is just too complex for a single experiment-or the aggregate of experimental data- to fully uncover the mechanisms governing the in vivo relation between local forces and deformations as a function of relevant biomarkers. Thus far, mechanical and biochemical properties are collected at a temporal and spatial scale most relevant to each individual application in medicine, biomechanical engineering, or for cosmetic industry. A comprehensive representation of the hierarchical structure of skin requires investigating the mechanical response across all relevant length and time scales and formulating model equations that allow bridging these scales.

Biomechanical testing methods are generally categorized as either in vivo, in vitro, or ex vivo. They are suitable for the characterization of intact skin or individual layers thereof. Traditionally, skin testing focused on ex-vivo measurements of global force-displacement curves under different loading conditions; recent experiments combine full-field deformation analysis, or tracking of complex 3D deformation of tissue structures, combined with local force measurement. These rich data sets are used to inform skin models of increased complexity which reflect microstructural characteristics. Measurements in many locations across the body illustrate the variation in skin compliance with varying microstructure. One major open question is the rationalization of skin stiffness measurements across several length scales which have provided values ranging from kPa, e.g. [40], to several MPa, e.g. [41].

The most common in vivo and ex vivo measurement methods in skin testing are suction, indentation, and (multiaxial) extension tests (see Fig. 3) and are discussed in the following.

Fig. 3
figure 3

The most common skin testing methods are suction, indentation, extension, shear, and torsion testing. Experimental setups for each method vary significantly across literature. In recent years, full-field in vivo methods have emerged, enabling the characterization of intact skin in its physiological state. Images adapted from [39]

Full size image

3.1 Suction

Suction measurements are used to determine in vivo and in situ skin properties [1]. The negative pressure draws tissue into the probe opening where an optical system measures bulge height. The resulting relation between pressure and bulge height is directly related to the probe opening size and loading protocol. Most suction devices presented in literature use a 2–8 mm probe opening diameter and apply a negative suction pressure of up to 500mbars [11, 26]. Due to a wide range of possible loading profiles, suction measurements are particularly useful to determine the nonlinear, viscoelastic, and time- and location-dependent behavior of skin [11]. Immediate compliance, elastic recovery, creep, and permanent deformation are represented in corresponding parameters, which are used to quantify the influence of fatigue [42], ageing [43,44,45], sex [46], and body location [11, 26, 43, 46,47,48,49]. Commercially available devices, such as the Cutometer (Cutometer® MPA 580; Courage+Khazaka, Cologne, Germany), come with multiple probe types and a computer interface to prescribe customized loading protocols. Several custom-built devices apply the same principle and might have larger probe openings, like the Aspirator [11, 50], opening shapes [51], or include ultrasound imaging for a visualization of tissue deformation [52]. Although suction data are affected by significant variability, they demonstrate that skin properties vary across the body and are determined by local microstructure. Devices integrating the suction test with ultrasound imaging/optical coherence tomography visualize skin deformation during tissue loading [46, 53]. The results demonstrate that epidermis and dermis are tightly connected and are primarily responsible for skin’s local stiffness [6, 53]. Variable probe opening size allows for the recruitment of individual skin layers [11, 54]. Small probe opening size of around 2 mm recruit the most superficial layers of skin, i.e. epidermis and the papillary dermis, while larger opening diameters of about 6–8 mm involve deeper layers, including the reticular dermis as well as the hypodermis or SMAS (superficial musculo aponeurotic system) [26, 53]. Inverse methods, which will be discussed further below, suggest stiffness ratios between superficial and deep skin layers of up to three orders of magnitude difference [11, 53].

Measurements across the body have shown that regions with a loose hypodermis or fatty subcutis, i.e. jaw, cheek, and neck, tend to respond more elastically [26, 44] than regions with a dense dermal matrix that connects the deep fascia with superficial skin layers, i.e. hands, forearm, and forehead [11, 44]. In fact, the face is a representative region of the body for which functionally driven microstructure characteristics can be linked with differences in skin mechanics, with the forehead being stiffest, followed by the parotid region and the jaw [26].

Suction experiments have well-known limitations. First, the mechanical analysis is based on the simplifying assumption that skin is isotropic. In fact, given the circular opening of typical suction probes, it is impossible to characterize the anisotropic properties of skin from these tests. Second, the measured response is dominated by the characteristics of the superficial layers, while the influence of deeper layer diminishes with their distance from the surface, in particular for small probe openings. Third, the repeatability of suction measurements depends on accurate probe handling, especially for hand-held devices such as a the Cutometer. Repeated probe placement-including proper alignment of probe and skin and control of contact pressure are paramount to ensure reliable measurement results [55, 56]. The development of an experimental setup that minimizes movement between probe and skin surface and maintains constant contact pressure improved measurement results for multiple repetitions per measurement site and probe diameter size [11, 26].

3.2 Indentation

Indentation is another widely used in vivo testing method as it enables a non-invasive measurement. Unlike the suction method, indentation testing is restricted to flat body regions, such as the volar forearm or the calf [57, 58]. Direct mechanical interpretation of indentation tests is restricted to a linear analysis of the quasi-static or linear viscoelastic properties of skin. Combination of nonlinear analysis and an inverse scheme are necessary to inform more complex models [59]. A major challenge in indentation of soft biological tissues is the reliable identification of the initial contact point between indenter tip and skin surface during loading as well as the assessment of adhesion effects during unloading. Lastly, in-vivo indentation tests do not allow for a quantification of the anisotropic tissue response, since the unidirectional registration of force and displacement does not allow to detect a direction-dependent tissue response.

Indentation tests have shown that volar forearm skin softens with age and progressively loses elasticity, most likely due to microstructural changes in the dermis and hypodermis [58, 60, 61]. The same experimental setup was used to measure the dynamic response of superficial skin at an indentation depth of 200 ± 3 μm in a range of 10–60 Hz. At these low indentation depths, skin stiffness and viscosity were found to be frequency independent [57], which may suggest that the dermal matrix is not activated at a relevant length scale.

A more recent study investigated stiffness and viscosity in reconstructed skin [62]. A series of quasi-static, force-controlled indentation / creep experiments (including a hold time of 100 s after reaching a maximum indentation force of 0.5 mN) were conducted to assess differences in tissue properties at critical stages during the in vitro reconstruction of skin. It was found that skin substitutes stiffen significantly once keratinocytes are seeded on top of the reconstructed dermis to form an epidermal layer. This finding is very insightful in view of the generally accepted claim that skin stiffness is primarily originating from the dermis.

Atomic force microscopy (AFM) is an indentation-based measurement method and has been used to quantify the impact of hydration on the mechanical response of the stratum corneum and epidermis [60, 61]. Indentation depths of up to 200 nm are three orders of magnitude smaller than the previously described indentation tests and therefore capture the mechanical response at a much smaller length scale. General observations from studies using AFM are that scar tissue is generally stiffer than healthy skin [63] and that the Young’s modulus of stratum corneum is roughly twice as high as for the epidermis [64]. Latter study reported stiffness values in the range of 1–2 MPa in comparison to values reported for “skin” (varying due to age) between 5–10 kPa by [40, 57, 58]. Indentation experiments thus provide compelling evidence of the length scale influence on the mechanical properties of skin.

3.3 Skin Extension Tests

Skin extension tests have been used to characterize ex vivo mechanical properties of skin and individual layers thereof. Unlike suction and indentation, extension testing allows investigating the anisotropic response of skin as it relates to the Langer lines distributed across the body [65, 66]. Further, it is used to characterize the time and history dependent behavior of skin through monotonic and cyclic creep and relaxation experiments, e.g. [67].

In most studies, samples are cut from excised skin and clamped inside a uniaxial or multiaxial loading rig [41]. Inevitably, mechanical properties change upon excision and strongly depend on storage duration, storage conditions, and temperature. Sample preparation, often in the form of removing the epidermis as well as adipose tissue to isolate the dermal layer, represents a major interference with the physiological state of alive skin tissue [41, 68]. In fact, cutting away or peeling off of individual layers might damage the structural connections between individual layers. Extraction of skin from the body leads to the loss of in vivo multiaxial pre-tension, so that the peculiar in vivo tensioned configuration of collagen and elastin networks is lost thus leading to unphysiological stress-strain measurements.

Most skin extension studies interpret the experimental data on the basis of linear elasticity theory, extracting the slope of the linear regime of the overall nonlinear, J-shaped force-displacement curve [41, 69]. The most frequently reported parameters from uni- or multiaxial measurements are the ultimate tensile strength and the elastic modulus of the dermis [41]. Fewer studies derive non-linear model parameters through a finite element based inverse analysis [70]. Finite strain models usually require an inverse scheme to identify model parameters that match prediction and observation. Time-independent models are typically associated with quasi-static loading conditions, in the form of slow loading rates.

Flynn et al. [71] presented a setup to measure the three-dimensional force-displacement response of in vivo skin in multiple directions. The system captures the nonlinear and viscoelastic skin behavior at different measurement sites and allows to determine the anisotropic properties of skin by gradually changing the loading direction. As one of the few studies found in literature, the resulting data set is used to fit an anisotropic material model [72].

Recent studies were able to visualize local microstructural tissue deformation, often using Two-Photon Excited Fluorescence or second harmonic generation (SHG), while gradually loading the sample [29, 30]. Bancelin et al. [30] show that mice dermal collagen matrix undergoes three characteristic mechanisms in uniaxial tension experiments: (i) realignment of collagen fibers along the principal direction of stretch during the early loading phase; noticeable levels of stretch at low loads and low stiffness, (ii) tissue stiffening due to the recruitment of load bearing fibers aligned with the primary direction of loading, and (iii) a linear regime in the stress strain curve due to intra-and interfibrillar sliding in collagen fibers. Tissue loaded beyond its fracture point leads to widespread breakage of fibrils and their immediate recoil [70]. The distribution of fiber orientation is strongly coupled to the stiffness regime of the tissue and highlights the relevance of properly accounting for in vivo stress.

Pensalfini et al. [29] analyzed excised mice skin samples including a previously induced excisional wound. Uniaxial tension tests were performed to visualize the heterogeneity within the strain field of the wound region [29]. It was observed that skin tissue around the wound can be divided into mechanically distinct regions displaying microstructurally motivated stretch patterns. While skin in the core of the wound showed little extensibility, a highly compliant zone next to the wound accommodates the majority of tissue deformation. Concomitant histological analysis and SHG imaging demonstrated that the presence of the compliant region avoids the recruitment of newly deposited collagen fibers in the early phase of healing.

3.4 Other Testing Methods

Other, less common, skin testing methods include torsion testing, the bulge method, and static and dynamic shear load methods. Torsion experiments were among the earliest applied to characterize the in vivo response of skin [73, 74] and inspired the development of suction devices in later years. Bulge tests performed by [75] provided information on the macroscopic biaxial response of skin and reported stiffness values of around 11 MPa for the linear regime of the stress-strain curve; strikingly, a tenfold increase in skin stiffness was observed from the toe region to the linear regime with an average transition stretch value of 1.1. And lastly, full thickness shear measurements indicated a large variation of around 100% in the shear modulus depending on depth [76]. Epidermis was found to be almost two times stiffer than dermis in these large amplitude shear oscillatory tests, which is in contrast with the common claim that the mechanical response of the epidermis has negligible influence [53].

3.5 Summary

The review of experimental data on in vivo and ex vivo human skin highlights the complex nature of skin biophysics. Its mechanical behavior is nonlinear, viscoelastic, and anisotropic. Significant differences between in vivo and ex vivo measurements exist, and they might be linked with the level of in vivo tension of skin, which is difficult to quantify or reproduce in ex vivo settings. This poses a significant limitation, as most computational models assume a stress-free initial state. Knowledge of the physiological loading state of skin is relevant also for the assessment of the mechanical biocompatibility of tissue engineered skin substitutes and their scaffolds [27, 77].

4 Constitutive Modeling

Modeling of the mechanical behavior of skin has been the objective of biomechanics studies for several decades and remains an active field of research [1]. Given the highly complex mechanical response of individual skin structures as well as the interaction at the interface of sublayers, skin modeling requires not only the formulation of a material model, but a corresponding representation of skin anatomy as well. In most studies reported in literature, skin is homogenized into a single layer including epidermis, dermis, and potentially even hypodermis. Fewer studies apply a multilayered representation and differentiate between epidermis, papillary and reticular layer of dermis, and hypodermis or SMAS [11, 78].

The interpretation of experimental data using inverse analysis depends on the chosen mathematical description of the stress-strain relation, as well as on the anatomic reconstruction. Very often, application specific skin models are developed, such as e.g. for the simulation of skin response to cosmetic products [79], the role of skin in facial expressions or mastication [6, 7], or the prediction of scar tissue formation due to suture tension [80]. Chapter “Constitutive Modelling of Skin Mechanics” reviews constitutive model formulations for skin. In this section, we will briefly discuss the different type of material model equations, their parameters and how they relate to the inverse analysis of experimental data.

Early models focused on integrative strategies to represent the mechanical response of individual constituents of the extracellular matrix [81]. Such collagen-based models represent the degree of fibers undulation and its progressive reduction as the matrix deforms. Evidence based implementation of these models requires a thorough characterization of the microstructure for each sublayer of the skin. For most specific applications such level of detail is unknown, and experiments may not provide the information relevant to respective length scales and structures. Hence, most material models proposed in literature generally homogenize the tissues response and aim at reproducing the experimentally observed stress-strain curves [12]. Next to physically motivated formulations for structural models, commonly used constitutive models are often based on phenomenological parameters. A common assumption is that skin behaves as incompressible, although no experimental evidence was reported on this property. Corresponding measurements are needed, since recent findings indicates that interstitial fluid motion might lead to significant volume changes in soft collagenous tissues [82]. The most relevant model equations applied for the analysis of experiments on skin are listed below. Many of these material models include a large number of parameters which cannot be measured directly and require an inverse identification scheme, as will be discussed in the following section. Table 1 summarizes material models frequently found in skin literature.

Table 1 Common constitutive models, main model features, number of parameters m, and accompanying experiments to identify model parameters
Full size table

5 Parameter Identification Methods

Constitutive model parameter identification is a broad field of research and a variety of optimization schemes were proposed in the literature. Within the specific context of skin modeling, there are a few popular approaches that have proven useful for the identification of potentially large parameter sets. The following section provides a summary of these optimization schemes specific to skin models.

On the most abstract level, the choice of the appropriate optimization scheme depends on the availability of an analytical expression for the relation between stress and strain of the experiment providing the data. If skin is treated as a linear or nonlinear solid, such analytical solutions exists for all commonly applied loading conditions including uniaxial and planar biaxial tension/compression experiments [97]. Model parameters are then identified by a least-squares fit analysis which minimizes the sum of squared differences between the experimentally observed force-deformation (or stress-strain) curve and corresponding model predictions. These tests are usually performed on ex vivo or in vitro skin tissue samples. In vivo skin tissue measurements usually involve more complex deformation patterns for which no analytical expression exists. In these cases, the relation between material constants and experimental data is implicit and requires a numerical approach to determine a set of material parameters that minimizes the difference between the observed and predicted tissue response [11].

Optimization schemes minimize an objective function which may or may not explicitly depend on the model parameters. Two general classes of optimization algorithms exist: In one case, algorithms require an analytical or numerical evaluation of the objective function’s gradients in the model parameter space [98]; the second class are derivative-free methods and include so called simplex algorithms [99].

Derivative-free methods have proven most useful in skin mechanics because they provide robust schemes for multidimensional parameter spaces [97]. Most skin models discussed in chapter “Constitutive Modelling of Skin Mechanics” have a large number of model parameters and assume a geometrically and structurally complex representation of skin, and therefore require the use of heuristic search methods that are more likely to find a minimum of the objective function. Several implementations of derivative-free optimization schemes exist, and the fminsearch function in Matlab (The MathWorks Inc., Natick, Massachusetts, US) is widely used throughout skin literature. The fminsearch function uses the Nelder-Mead simplex algorithm [100, 101]: in an n-dimensional parameter space, the algorithm maintains n + 1 test points arranged as a simplex. The behavior of the objective function measured at each test point is used to extrapolate new test points and to replace those, that provide the worst response. Different strategies exist to update the test points and the algorithm will stop if the sample standard deviation of the objective function falls below a prescribed tolerance. As shown in Fig. 4, an initial parameter set is iteratively updated through an optimization algorithm, i.e. the fminsearch function, to minimize the error between experimental data and the associated numerical simulation. During each iteration, a finite element simulation is necessary to determine the model response based on the updated parameter set. The number of parameters, the number of simulations necessary per iteration, and the degree of coupling between parameters determine the required computation time and the uniqueness of the final parameter set.

Fig. 4
figure 4

Common implementation of inverse analysis algorithms (e.g. the fminsearch algorithm) for skin parameter identification schemes. The optimization scheme iteratively determines a model parameter set that minimizes the error between experimental data and the associated numerical simulation. During each iteration, a finite element simulation is necessary to predict the model response based on the updated parameter set

Full size image

Several groups working on skin mechanics have developed specialized optimization schemes, that range from a simultaneous fit of all model parameters to a sequential determination for individual layers and loading conditions. Weickenmeier et al. [11] performed suction experiments with varying probe opening diameters to recruit superficial and deeper skin layers individually. An initial sensitivity analysis of the accompanying multi-layered finite element skin model revealed strong coupling between material parameters as well as a significant influence of individual layers on the deformation field for different probe opening diameters. Sequential fitting of individual layers resulted in a stiffness ratio between the superficial and deep layer corresponding to two orders of magnitude difference [47]. The simultaneous fitting of superficial and deep material parameters using four different loading conditions to capture the instantaneous and transient response of skin, provided more homogeneous results [11] which seem more reasonable in view of previously reported ex-vivo mechanical analysis of dermal tissue and SMAS [67].

Hendrik and co-authors presented a series of suction based skin experiments and corresponding model parameter fits [52, 53, 102]. While initially working with a single layer model [53, 102] and later extending skin to a two-layer model, Hendrik et al. used a constrained nonlinear optimization function based on Sequential Quadratic Programming (SQP), to determine all material parameters in parallel. Their two-layer model predicted three orders of magnitude difference between superficial and deeper layers. This outcome is motivated by the finite element model implementation and the weight of individual measurement curves on the overall cost function.

Flynn and co-authors’ in vivo multi-axial skin loading device requires a finite element model for data analysis [96]. In a process similar to previously presented schemes, model parameters of a single layer skin model-including in vivo stress-are determined based on a nonlinear least-squares curve fitting algorithm. Based on the trust region method, a set of initial parameters is iteratively improved to minimize the error between experiment and model, while running a finite element simulation at each iteration to evaluate the model-based tissue response. Two different models were tested: an isotropic Ogden model [91] and the anisotropic Tong and Fung model [92]. The total number of parameters fit simultaneously were 4, 6, and 8, depending on the model formulation. The error function was calculated as the sum over all measurement directions and the in vivo stress level was used to represent the anisotropy of the tissue response. Jor et al. [103], using the same experimental setup, aimed at fitting a microstructurally motivated constitutive relation with 7 parameters.

With the emergence of experimental methods combining force measurements with video imaging of the accompanying deformation field, more elaborate and localized inversion schemes are presented in literature. The quantitative assessment of the heterogeneity of the deformation fields allows to determine material parameters at a local scale and are based on so called full-field methods. Avril et al. [104] presents an overview of corresponding inverse analysis schemes. In comparison to the above-mentioned methods, the new approaches solve the nonlinear elasticity equations based on the pointwise experimentally observed deformation field. This procedure allows using derivative-based methods, which are more reliable in that they are more likely to provide a global minimum. The associated increase in computational cost to evaluate the derivative of the objective function is often linked with the requirement of increased computational power.

6 Outlook

Skin is a complex biological system that is characterized by an intricate interplay between individual tissue layer and ECM components at different length scales. The interaction of the different components of the extracellular matrix and the different layers depends on the state of deformation imposed to the skin, with different mechanisms influencing in-plane tension, in-plane or out-of-plane shear, and skin bending. Although a large number of mechanical tests has been conducted, our understanding of full-thickness skin behavior remains incomplete. New integrative testing methods, i.e. simultaneous visualization of tissue and microstructure kinematics during mechanical response to a wide range of loading conditions, as well as the analysis of skin properties in relation to observable microstructural parameters, represent promising approaches to improve our understanding of skin mechanics.

The range of mechanical properties reported in literature and the dependence of the mechanical response on the testing method used continues to represent a major challenge in determining a universal description of skin mechanics. In this context, a specific problem is represented by the mismatch in stiffness reported for different tissue length scales interrogated in the different experiments. The quantification of in vivo stress represents another critical question in skin mechanics: As most computational models assume a test specific stress-free initial state, existing parameter sets proposed in literature are likely to grossly misrepresent the actual in-vivo response of skin tissue.

Anatomy based skin models used in parameter identification schemes will become more reliable as we continue to improve our understanding of the relation between local microstructure and mechanical response. Essential input will be obtained through in vivo and ex vivo application of full field methods and the associated model parameter identification procedures. The systematic combination of computer-based modeling and multiscale experimental data acquisition will facilitate the development of biomechanical and mechanobiological models with enhanced predictive capabilities. Improved understanding of skin biomechanics will allow future research to focus on highly relevant medical questions, such as impaired wound healing, skin suturing, reconstructive surgery, skin tissue engineering, as well as diagnosis and monitoring of specific skin diseases.