In vivo measurements of the elastic mechanical properties of human skin by indentation tests

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Medical Engineering & Physics 30 (2008) 599–606

In vivo measurements of the elastic mechanical properties of human skin by indentation tests C. Pailler-Mattei a,b,∗ , S. Bec a , H. Zahouani a a

Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Syst`emes, UMR-CNRS 5513, France b Universit´ e Lyon 1, ISPB, EA 4169, Lyon F-69003, France Received 7 March 2007; received in revised form 15 June 2007; accepted 18 June 2007

Abstract Knowledge about the human skin mechanical properties is essential in several domains, particularly for dermatology, cosmetic or to detect some cutaneous pathology. This study proposes a new method to determine the human skin mechanical properties in vivo using the indentation test. Usually, the skin mechanical parameters obtained with this method are influenced by the mechanical properties of the subcutaneous layers, like muscles. In this study, different mechanical models were used to evaluate the effect of the subcutaneous layers on the measurements and to extract the skin elastic properties from the global mechanical response. The obtained results demonstrate that it is necessary to take into account the effect of the subcutaneous layers to correctly estimate the skin Young’s modulus. Moreover, the results illustrate that the variation of the measured Young’s modulus at low penetration depth cannot be correctly described with usual one-layer mechanical models. Thus a two-layer elastic model was proposed, which highly improved the measurement of the skin mechanical properties. © 2007 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Biomechanics; Human skin; Mechanical properties; Tissue engineering; Thin layer; Young’s modulus

1. Introduction Human skin is the main organ of protection of the body against the external environment. One of its most essential functions is the protection against external mechanical aggressions, which is ensured by a reversible deformation of its structure. Human skin is a living complex material, composed of several heterogeneous layers [1–5]. It is mainly composed of three layers: epidermis, dermis, and hypodermis which is an extremely viscous and soft layer. The dermis consists in a network of collagen with interspersed elastic fibres, and lymphatic elements, all covered by an epidermal layer of partially keratinized cells that are progressively dehydrated during their migration to the outer surface. The thickness of each skin layers varies as a function of age, body zone or hydration [6].

∗ Corresponding author at: Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Syst`emes, UMR-CNRS 5513, 36 Avenue Guy de Collongue, 69134 Ecully Cedex, France. Tel.: +33 4 72 18 62 91; fax: +33 4 78 43 33 83. E-mail address: [email protected] (C. Pailler-Mattei).

Mechanical testing of human skin presents considerable challenges in different domains. For example, measuring human skin mechanical properties contributes to quantification of effectiveness of dermatologic products or detection of skin diseases. To evaluate the skin mechanical properties, different non-invasive techniques have been developed. The most commonly used methods are based on the measurement of suction [7,8], torsion [9,10] and traction [11]. Other experimental methods can be used to measure the skin mechanical behaviour like extensometry [12–14], or elastic wave propagation [15,16]. However, the data obtained with these methods are mainly descriptive [8] and often very different, depending on the experimental conditions. In the literature, the Young’s modulus of the skin, E, varies between 0.42 MPa and 0.85 MPa for torsion tests [17], 4.6 MPa and 20 MPa for tensile tests [18] and between 0.05 MPa and 0.15 MPa for suction tests [7,8]. The main disadvantage of all these methods is that they modify the skin’s natural state of stress as the experimental device has to be fixed to the skin all along the test. As a consequence, the measured values of mechanical properties might be affected, and it is very difficult to estimate

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and extract the prestress value induced by the mechanical devices. The indentation method is not commonly used to measure the skin mechanical properties, although it permits to obtain the skin mechanical properties, in normal direction, without prestressing the skin before the test [19,20]. Moreover, it permits to determine the bulk and surface properties of the cutaneous surface, which reflect the physico-chemical properties of the skin/indenter interface [21,22]. The aim of this paper is to describe the skin mechanical behaviour using indentation tests. First, indentation curves obtained on skin are described. It is proposed to neglect the viscous part of the skin response, in order to assimilate the human skin mainly to an elastic material. In the second part, the Young’s modulus of the skin is estimated using different models. These models account for the combined mechanical response of the skin (one-layer composed of dermis and hypodermis) and the substrate (subcutaneous tissues). Finally, the experimental results show that it is necessary to develop a two-layer elastic model in order to better describe the variation of the measured Young’s modulus versus penetration depth, particularly at low penetration.

2. Experimental details 2.1. Indentation device An original light load indentation device has been developed to study in vivo the mechanical properties of human skin [22]. The penetration depth, δ, of a rigid indenter is recorded as a function of the applied normal force, FN , during a loading/unloading experiment. In this study, the indentation tests are performed in controlled displacement mode. The z-displacement is obtained by using National Instrument displacement table and controlled by a displacement sensor (Fig. 1(a)). The maximum displacement during the loading–unloading cycle can reach about 15 mm with a resolution of 10 ␮m and the experimental device offers a wide range of indenting velocities from 5 ␮m/s to 1500 ␮m/s. In the following, the indentation tests were realised for

a constant indentation speed δ˙ = 400 ␮m/s. The indenter used in this study is a conical steel indenter, with a half angle α = 45◦ . The height of the conical indenter is 10 mm, which is higher than its maximum penetration depth into the skin. 2.2. Method Static indentation tests permit to determine the reduced Young’s modulus, E*, of the tested material, by the measurement of the normal contact stiffness, kz , which is the slope of the initial portion of the unloading curve, kz = (dFN /dδ)|FN =FN max [23]. For a bulk material in contact with an axisymmetric rigid indenter, when no sliding occurs, the normal stiffness is linked to the reduced Young’s modulus by [24]: √ π kz ∗ √ E = (1) 2 A where A is the projected contact area. E* is defined as (1/E∗ ) = (1 − ν12 /E1 ) + (1 − ν22 /E2 ) with E1 , ν1 and E2 , ν2 the respective Young’s modulus and Poisson’s ratio of the steel indenter and the indented material. In this study, since E1 (steel)  E2 (skin), it can be assumed that E* is the reduced Young’s modulus of the indented material, (1/E∗ ) ≈ (1 − ν22 /E2 ). For indentation with a conical indenter, the elastic penetration, δ, is related to the contact radius, a, of the projected contact area (A = πa2 ) by δ = (π/2a) tan((π/2) − α) [25], thus Eq. (1) becomes: π  π kz E∗ = tan −α (2) 4 δ 2 2.3. Materials The indentation tests have been carried out on the inner forearm zone of Caucasian men (Fig. 1(b)). This location is easily accessible, relatively flat and less disturbed by the natural movements of the body. At this part, the epidermis is thin, less than 80 ␮m [6] and the thickness of the hypodermis, about 0.8 mm, is lower than the thickness of

Fig. 1. Skin tribometer device: (a) schematic representation of the indentation device; (b) indentation system and positioning of the subject’s arm. The tests were realised on the inner forearm.

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the dermis, between 1.2 mm and 1.5 mm [8]. Therefore, the contribution of the epidermis to the mechanical response of the skin was neglected [8] and the total response was the composite response of the dermis and hypodermis. Thereafter, as we cannot directly measure the thickness of the skin on the inner forearm, we will assume that the average thickness of the skin (dermis + hypodermis) at this part is approximately 2 mm, as already observed in the literature [8]. However, the thickness effect will be discussed later in this paper. In order to reduce the influence of ageing, on the skin mechanical properties [26] the mechanical tests have been performed on 10 men about 30 years old. All indentation tests were repeated five times for each subject. The tests have been made, in afternoon, in ambient air, at temperature, T, 22 ◦ C < T < 24 ◦ C, and humidity rate, HR , 20% < HR < 30%, and there is no surface treatment on skin before the tests.

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Using Eq. (3) and considering the measured values (FN max , δmax ) at maximum load, a theoretical elastic curve for conical indentation was obtained (Fig. 2). The experimental and theoretical curves are comparable even if they are not exactly superimposed. The contact stiffness, kz , measured from the experimental curve is approximately 24 N/m and the reduced measured Young’s modulus, E*, is around 12.5 kPa. From the theoretical elastic curve obtained using Eq. (3), the reduced Young’s modulus, E*, is 13.7 kPa, and the corresponding contact stiffness value, kz , is 26 N/m. Experimental and theoretical contact stiffness and Young’s modulus values are comparable, which justifies the elastic hypothesis used in the following. The complex multi-layer structure of the human skin contributes to the explanation of the observed slight difference between the experimental and theoretical curves. 3.2. Skin Young’s modulus

3. Results and discussion 3.1. Analysis of skin indentation curves A representative indentation curve obtained on human skin in vivo is presented in Fig. 2. This curve is reversible and the hysteresis, due to the dissipated energy in the material [27], is very low. Plastic behaviour was not observed: there is no residual print onto the skin surface, and no measurable plastic depth (Fig. 2). As a consequence, in this load range, human skin can be considered to be mainly an elastic material [21,28,29]. The relation FN = f(δ) for elastic material indented by a conical indenter was given by [25,30]: FN =

2 E∗ δ2 π tan((π/2) − α)

(3) 3.2.2. Estimation of the skin Young’s modulus using different mechanical models The skin is analysed like a thin soft layer (including dermis + hypodermis) onto a rigid substrate, the muscle. In the

25 Experimental curve Theoretical elastic curve

0.022

15

10

dF kz = N dδ

5

FN =F Nmax

0 0

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400

600

800

1000

1200

1400

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Pentration depth (µm) Fig. 2. Indentation curve obtained on the inner forearm of subject 1 (indentation speed δ˙ = 400 ␮m/s) and theoretical elastic curve for a conical indenter (α = 45◦ ). From the experimental curve, using the slope of the unloading curve, the measured contact stiffness is kz ≈ 24 N/m and the reduced measured Young’s modulus is around E* = 12.5 kPa. From the theoretical elastic curve which intercepts the experimental curve at the maximum load (1500 ␮m, 20 mN), the reduced Young’s modulus is E* = 13.7 kPa.

Global apparent measured Young's modulus (MPa)

Normal load (mN)

20

3.2.1. Experimental data The variation of the apparent reduced Young’s modulus, E*, versus penetration depth, δ, for the 10 subjects is reported in Fig. 3. For all subjects, the apparent reduced Young’s modulus globally increases with penetration depth. In order to facilitate the interpretation of the results, the mechanical behaviour of subject 1, which approximately corresponds to a mean mechanical behaviour among the 10 persons (Fig. 3), was chosen to illustrate the analysis. The increase of the apparent reduced Young’s modulus, E*, versus penetration depth, δ (Fig. 3), can be attributed to the multi-layered structure of the skin and shows the influence of the subcutaneous tissues, like the muscles. Thus, in vivo, the skin cannot be analysed like an elastic half space, but rather like an elastic soft thin layer on a rigid substrate.

Subject 8 Subject 4

0.02

Subject 6

Subject 1

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0.014 Subject 7

0.012 0.01 0.008 0

Subject 5 Subject 9 Subject 10

1

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Penetration depth (mm) Fig. 3. Variation of the global apparent reduced Young’s modulus of the skin vs. penetration depth for the 10 subjects (indentation speed δ˙ = 400 ␮m/s). Apparent Young’s modulus for subject 1 corresponds to some mean behaviour (full line).

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literature, muscle shear modulus value ranges from 12 kPa to 24 kPa [31–33]. Assuming linear elasticity and a Poisson’s ratio value 0.25 < ν < 0.5, the reduced Young’s modulus of the muscle, E*, is then between 32 kPa and 96 kPa. As a consequence, the muscle is more rigid than the skin, which explains that the measured Young’s modulus increases versus penetration depth (Fig. 3). Indentation of an elastic thin layer on a rigid substrate was extensively studied in the literature [34–38]. The loading–unloading behaviour is a complex function of the elastic properties of both the thin layer and the substrate and several models have been proposed to extract the intrinsic thin layer properties from the global measurements. In the present study, three different models were used to estimate the Young’s modulus,Ef∗ , of the skin: the Bec/Tonck model [36,39], the Song/Pharr model [37], which is an extension of the Gao model [35] and the Perriot/Barthel model [38]. For the Bec/Tonck model, the measured global stiffness, kz , is a function of the reciprocal sum of the thin layer stiffness (skin), kf = πa2 Ef∗ /e, and the substrate’s stiffness (muscle), ks = 2ES∗ a, where e is the total thickness of the skin (e ≈ 2 mm), a is the contact radius between skin and indenter and Ef∗ and ES∗ are respectively the reduced Young’s modulus of the layer and substrate. To ensure correct boundary conditions, the expression of the two stiffnesses are rewritten using two polynomial functions f1 (a) and f2 (a), chosen in the form 1 + Can [36] (with C and n polynomial variables). It gives the following equation: e 1 1 = + kz f1 (a)πa2 Ef∗ f2 (a)2aES∗

(6)

These boundary conditions are as follows: (a) The thin layer behaves like a bulk material when the contact radius is very small compared to the thin layer thickness (a  e). (b) If the thin layer and substrate have the same elastic properties, the global stiffness must be equal to the substrate stiffness ks .

For elastic isotropic solids, the shear modulus, G, and the Young’s modulus, E, or the reduced Young’s modulus, E*, are linked by G=

(1 − ν2 )E∗ E = 2(1 + ν) 2(1 + ν)

As a consequence, it is possible to explain Eq. (7) versus Young’s moduli, which gives the following equation: 1 (1 − νS )(1 − νf ) = E∗ [1 − (1 − I1 )νf − I1 νS ]   (1 − I0 )(1 + νS ) I0 (1 + νf ) × + ∗ ES∗ (1 − νS2 ) Ef (1 − νf2 )

In the Song/Pharr model, substrate and layer Poisson’s ratio values are needed. These values are chosen to be νs = νf = ν and 0.35 < ν < 0.5, because it is consistent with hypothesis for the soft tissue [5,8,40]. For the Perriot/Barthel model, the apparent reduced Young’s modulus is defined by E∗ = Ef∗ +

where I0 and I1 are weighting functions, depending on the contact radius, the thickness of the layer and the Poisson’s ratio. Gf and Gs are the shear moduli, νf and νs are the Poisson’s ratio, with the subscripts “s” and “f” referring respectively to the substrate and the layer. The effective compliance, Ceff , is defined by Ceff = (1 − ν/G) [34].

ES∗ − Ef∗ 1 + (ex0 /a)n

(9)

where x0 and n are parameters which vary with the modulus mismatch β = ES∗ /Ef∗ [38]. In this study, both the Young’s modulus value, ES∗ , of the substrate (muscle) and the Young’s modulus value of the skin, Ef∗ , are unknown. So, in order to estimate the skin Young’s modulus, the mismatch ratio β = ES∗ /Ef∗ was assumed and introduced in Eqs. (6), (8), and (9). The β value was chosen in the range 2 < β < 100. The effect of the different β values is discussed later. The variation of the apparent reduced Young’s modulus, E*, and the skin Young’s modulus, Ef∗ , versus penetration depth, δ, for the three models are reported in Fig. 4, for subject 1. The results are given for β = 10 and for a total thickness Apparent measured Young's modulus Perriot/Barthel Bec/Tonck Song/Pharr (ν ν=0.35 = ) Song/Pharr (ν=0.5) ν

Young's Modulus (MPa)

0.02

Calculations lead to f1 (a) = f2 (a) = 1 + (2e/πa). The Song/Parr model derives from the Gao model. Contrary to the Gao model, it can be used for modulus mismatch larger than two between the thin layer and substrate. It is based on the analysis of the effective compliance, Ceff , of the thin layer/substrate system, which is given by the following equation:   1 (1 − νS )(1 − νf ) 1 (7) Ceff = + I0 (1 − I0 ) [1 − (1 − I1 )νf − I1 νS ] GS Gf

(8)

0.015

0.01

0.005 0

1

2

3

4

5

Penetration depth (mm) Fig. 4. Estimation of the skin Young’s modulus, Ef∗ , using different mechanical elastic models. The results are given for β = 10 and for e = 2 mm. The total displacement δ = 3.14 mm, pointed out on the graph, corresponds to a penetration into the skin equal to its thickness (2 mm). For the Song/Pharr model, νs = νf = ν = 0.35 and νs = νf = ν = 0.5. For the Perriot/Barthel model, β = 10 leads to x0 = 5.36 and n = 1.18. The apparent measured Young’s modulus is the mean Young’s modulus measured on the subject 1.

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(b) 0.025 Apparent measured Young's modulus E*f, for e=1 mm E*f, for e=2 mm E*f, for e=3 mm

0.02

Young's modulus (MPa)

Young's modulus (MPa)

(a) 0.025

0.015 0.01 0.005

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Apparent measured Young's modulus E*f, for β =2 E*f, for β =10 E*f, for β =100

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a/e

Penetration depth (mm)

Fig. 5. Variation of the estimated skin Young’s modulus, Ef∗ : (a) with the Bec/Tonck model vs. penetration depth and for different skin thicknesses; (b) with the Bec/Tonck model vs. a dimensionless number, a/e, for different ratio β (with e = 2 mm). For the conical indenter with α = 45◦ , a/e = 1 corresponds to a penetration into the skin equal to its thickness. The apparent reduced Young’s modulus was measured on the subject 1.

3.2.3. Influence of thickness and mismatch values The variation of the estimated Young’s modulus of the skin, Ef∗ , versus skin thickness, e (Fig. 5(a)) and versus β mismatch (Fig. 5(b)) was then analysed. The estimated skin Young’s modulus was obtained with the Bec/Tonck model because it is easy to use (all models give similar results). It first shows that the calculated skin Young’s modulus depends on the skin thickness value (Fig. 5(a)). This was expected because as e → ∞, then E∗ → Ef∗ (low substrate effect) or as e → 0 then Ef∗ and E* differ significantly. However, in the relevant thickness range, the calculated skin Young’s modulus, Ef∗ , slightly changes: Ef∗ ≈ 5 kPa for e = 1 mm and for e = 3 mm, Ef∗ ≈ 8 kPa. As a consequence, the thickness effect is low in the range of thickness used. The effect of the ratio β = ES∗ /Ef∗ was also studied (Fig. 5(b)). For 2 < β < 10, the Young’s modulus of the skin, Ef∗ , significantly changes. On the other hand, for β > 10, the calculation of the skin Young’s modulus is not influenced by β value. Similar results were obtained with the Perriot/Barthel model, where the coefficients x0 and n change as a function of β. 3.3. Comparison between the measured and the theoretical apparent Young’s modulus values To go further, the theoretical apparent Young’s modulus, ∗ , was calculated and compared with the measured one. Eth Using the Bec/Tonck model, the expression for the theoretical

apparent Young’s modulus is given by ∗ = Eth

1 + (2e/πa) E∗ (1/β) + (2e/πa) f

(10)

∗ is the apparent Eq. (10) is deduced from Eq. (6), where Eth ∗ reduced Young’s modulus, Eth = kz /2a [24,41]. The variation of the theoretical apparent Young’s modulus, ∗ , versus a/e is reported Fig. 6. It is calculated with an averEth age skin Young’s modulus, Ef∗ = 6.5 kPa and β ≈ 12, which are the optimum parameters. For a/e > 0.5 the measured and theoretical apparent Young’s moduli are rather comparable. For a/e < 0.5, the difference between the calculated and the measured apparent Young’s modulus is significant, it reaches 70% for a/e ≈ 0.2. Assuming that the skin behaves like a homogenous layer is thus not really appropriate to describe the elastic response of the skin at small penetration depth. In the following, a refinement of the model is proposed.

3.3.1. The two-layer model For a/e < 0.5, the apparent measured Young’s modulus, E*, decreases as the penetration depth increases, revealing the composite structure of the skin itself, composed of dermis and hypodermis. In order to account for this structure in 0.025

Young's modulus (MPa)

value e = 2 mm. The measured apparent Young’s modulus increases from 10 kPa to 18 kPa, as a function of penetration depth. As Regards to the skin Young’s modulus value, all models give similar results: for penetration depths higher than 1.5 mm, the skin Young’s modulus, Ef∗ , is almost constant and ranges between 4.5 kPa and 8 kPa (Fig. 4). These values are in the same order of magnitude as literature values obtained by indentation [19,28], which are around 1–6 kPa. The value of the skin Young’s modulus, Ef∗ , is two to four times lower than the value of the measured apparent Young’s modulus. Finally, we note that the different values of skin Poisson’s ratio used for Song/Pharr model do not change significantly compared to the values of calculated skin Young’s modulus.

Apparent measured Young's modulus Theoretical apparent Young's modulus 0.02

0.015

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a/e Fig. 6. Variation of the apparent measured Young’s modulus and the theoretical apparent Young’s modulus vs. a/e (with e = 2 mm). The theoretical Young’s modulus is determined with the Bec/Tonck model for a reduced skin Young’s modulus Ef∗ = 6.5 kPa and for β = 12.3. The ratio a/e = 1, pointed out on the graph, corresponds to a penetration into the skin equal to its thickness.

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Fig. 7. Mechanical equivalent model for two thin layers on half space (substrate). The mechanical model is equivalent to an assembly of three springs, with different stiffnesses, k1 , k2 , ks , connected in series. E1∗ and E2∗ are respectively the Young’s modulus of the dermis and hypodermis. ES∗ , is the Young’s modulus of the subcutaneous tissues (muscle). e1 is the thickness of the dermis and e2 is the thickness of the hypodermis and a is the contact radius between the indenter and the material.

(a) If E1∗ = E2∗ = ES∗ , then (1/kz ) = (1/2aES∗ ). (b) If E1∗ = E2∗ = ES∗ , then the system is equivalent to one thin layer (Young’s modulus Ef∗ = E1∗ = E2∗ ), of thickness e = e1 + e2 , on a substrate. (c) If E2∗ = ES∗ and E1∗ = E2∗ , then the system is equivalent to one thin layer (Young’s modulus E1∗ ) of thickness e1 , on a substrate (Young’s modulus ES∗ = E2∗ ). It gives the following equation: 1 e1 e2 1 = + + ∗ ∗ 2 2 kz f1 (a)πa E1 f2 (a)πa E2 f3 (a)2aES∗ Calculations lead to 2e1 , f1 (a) = 1 + πa



f2 (a) =

2e1 1+ πa



(12)

2(e1 + e2 ) 1+ πa



and 2(e1 + e2 ) πa Eq. (12) can thus be written as a function of the apparent measured reduced Young’s modulus, E*, with E* = kz /2a: f3 (a) = 1 +

E∗ = E1∗ E2∗ ES∗

π2 a2 E1∗ E2∗

0.025

Young's modulus (MPa)

the apparent Young’s modulus measurement, the Bec/Tonck model was refined by considering two thin layers on a substrate (two-layer model). The surface layer is the dermis, the intermediate layer is the hypodermis and the substrate is the subcutaneous tissues. The equivalent mechanical model is obtained by considering three springs, with different stiffnesses, k1 , k2 , ks , connected in series (Fig. 7). By analogy with the Bec/Tonck one-layer model, the measured global stiffness, kz , corresponds to the reciprocal sum of the stiffnesses of the two layers (k1 = πa2 E1∗ /e1 and k2 = πa2 E2∗ /e2 ) and the substrate (ks = 2ES∗ a). The parameters e1 and e2 are respectively the thickness of the surface layer and the intermediate layer. E1∗ , E2∗ and ES∗ are respectively the reduced Young’s modulus of the surface layer, intermediate layer and substrate (Fig. 7). Three polynomial functions f1 (a), f2 (a) and f3 (a) have been introduced in the expression to ensure correct boundary conditions, as follows:

Measured apparent Young's modulus Calculated Young's modulus, with the one-layer model Calculated Young's modulus, with the two-layers model

0.02

0.015

0.01

0.005

0

1

2

3

4

5

Penetration depth (mm) Fig. 8. Variation of the measured apparent Young’s modulus and calculated Young’s modulus, with Bec/Tonck extended models (one-layer model and two-layer model) vs. penetration depth. The calculated Young’s modulus, for the two-layer model, is obtained with E1∗ = 35 kPa, E2∗ = 2 kPa, ES∗ = 80 kPa and e1 = 1.2 mm and e2 = 0.8 mm. The calculated Young’s modulus, for the one-layer model, is determined with Ef∗ = 6.5 kPa and for β = 12.3.

The apparent Young’s modulus of the two-layer system was calculated using Eq. (13) with the following parameters (Fig. 8): • Dermis: E1∗ = 35 kPa and e1 = 1.2 mm, the reduced Young’s modulus used for the dermis is in good correlation with the literature [28]. • Hypodermis: E2∗ = 2 kPa and e2 = 0.8 mm. • Muscle: ES∗ = 80 kPa. With these realistic parameters, the agreement between the calculated and measured Young’s modulus curves is significantly improved until a penetration depth equal to the skin’s thickness. The two-layer mechanical model permits to describe the decrease of the Young’s modulus measured at low penetration depth, by separating the contributions of the dermis and the hypodermis. Such a model is more appropriate to account for the influence of each skin layer on the global skin mechanical response. At higher penetration depth, the observed difference may be explained by the complex nature of the substrate which is not really

πa2 + πa(4e1 + 2e2 ) + 2e1 (2e1 + 2e2 ) + 2πa(e1 ES∗ E2∗ + e2 ES∗ E1∗ + e1 E1∗ E2∗ ) + 2e1 ES∗ E2∗ (2e1 + 2e2 )

(13)

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a semi-infinite half space and also by compression of the hypodermis between the dermis and the muscle. 4. Conclusion To measure the human skin mechanical properties, an original indentation device has been developed, specifically dedicated to the measurement of soft material mechanical properties. In this study, human skin was assumed to behave elastically in the considered load range. The measured apparent reduced Young’s modulus of the skin globally increases versus penetration depth, because of the complex structure of the skin in vivo. In order to simplify the study, it was proposed to consider the skin like an elastic soft thin layer on a rigid substrate. Human skin was assumed to be composed of only two layers: dermis and hypodermis, because the epidermis was not supposed to influence the global mechanical behaviour. To extract an average value for the Young’s modulus of the skin from the apparent Young’s modulus, which includes the elastic response of the subcutaneous muscle, three different mechanical models were used. All models give an average value of the skin Young’s modulus between 4.5 kPa and 8 kPa, these values are in good agreement with the literature [19,21,28]. Comparison between the theoretical and measured apparent Young’s modulus shows a difference at low penetration depths. A refinement of the model, obtained by considering two layers in order to separate dermis and hypodermis contributions is than proposed. It permitted to account for the observed decrease of properties and to correctly describe the elastic behaviour of the skin up to a penetration depth equal to its thickness. Realistic values for the Young’s modulus of each layer that constitutes the skin are thus obtained. Conflict of interest None. References [1] Barbenel JC, Evans JH. The time-dependent mechanical properties of skin. J Invest Dermatol 1977;69:318–20. [2] Pereira JM, Mansour JM, Davis BR. Dynamic measurement of the viscoelastic properties of skin. J Biomech 1991;24:157–62. [3] Reihsner R, Balogh B, Menzel EJ. Two-dimensional elastic properties of human skin in terms of an incremental model at the in vivo configuration. Med Eng Phys 1995;17:304–13. [4] Wu JZ, Dong RG, Smutz WP, Schopper AW. Modeling of timedependent force response of fingertip to dynamic loading. J Biomech 2003;36:383–92. [5] Kathyr F, Imberdis C, Vescovo P, Varchon D, Lagarde JM. Model of the viscoelastic behaviour of skin in vivo and study of anisotropy. Skin Res Technol 2004;10:93–103. [6] Agache P. Physiologie de la peau et exploitations fonctionnelles cutan´ees. Paris: Editions M´edicales Internationales; 2000.

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