An Invariant-Based Damage Model for Human and Animal Skins
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Abstract
Constitutive modelling of skins that account for damage effects is important to provide insight for various clinical applications, such as skin trauma and injury, artificial skin design, skin aging, disease diagnosis, surgery, as well as comparative studies of skin biomechanics between species. In this study, a new damage model for human and animal skins is proposed for the first time. The model is nonlinear, anisotropic, invariant-based, and is based on the Gasser–Ogden–Holzapfel constitutive law initially developed for arteries. Taking account of the mean collagen fibre orientation and its dispersion, the new model can describe a wide range of skins with damage. The model is first tested on the uniaxial test data of human skin and then applied to nine groups of uniaxial test data for the human, swine, rabbit, bovine and rhino skins. The material parameters can be inversely estimated based on uniaxial tests using the optimization method in MATLAB with a root mean square error ranged between 2.15% and 12.18%. A sensitivity study confirms that the fibre orientation dispersion and the mean fibre angle are among the most important factors that influence the behaviour of the damage model. In addition, these two parameters can only be reliably estimated if some histological information is provided. We also found that depending on the location of skins, the tissue damage may be brittle controlled by the fibre breaking limit (i.e., when the fibre stretch is greater than 1.13–1.32, depending on the species), or ductile (due to both the fibre and the matrix damages). The brittle damages seem to occur mostly in the back, and the ductile damages are seen from samples taken from the belly. The proposed constitutive model may be applied to various clinical applications that require knowledge of the mechanical response of human and animal skins.
Keywords
Skin Damage Fibre orientation Fibre orientation dispersion Constitutive model Inverse problemIntroduction
The human skin not only has important protective functions against mechanical trauma such as friction, impact, pressure, cutting and shearing, but also plays a vital role in active thermo-regulation, wound-healing, and acts as the nonslip intermediate surface when one grips, lifts, or presses.10 The skin consists of three layers: the epidermis, the dermis, and subcutaneous tissues. The epidermis is the top renewable layer of 0.1–1.5 mm thickness. The dermis is the middle layer with 1–4 mm thickness,46 which has two sub-layers: the papillary layer and the reticular layer. The dermis consists of 77% collagen and 4% elastin (fat-free dry weight),55 vasculature, nerve bundles, hair follicles, veins and sweat glands. The subcutaneous tissue is underneath the dermis and with fat to store energy for the body.
The skin is in tension in normal physiological conditions and its tension level depends on individual maturation and aging, wound healing state, dysfunction or diseases such as the Ehlers–Danlos syndrome.5,37,57 Studying biomechanical property of human skin is useful in cosmetic product development, plastic surgery, surgical practice and skin disease pathology as well as artificial skin design.
Despite many experimental studies, to date, there is a lack of mathematical constitutive models for describing the highly nonlinear and anisotropic skin behaviour due to damage. Such constitutive laws are essential for understanding skin mechanics after trauma and injury, as well as for applications such as artificial skin design, skin aging, disease diagnosis, and surgical treatment. In this contribution, we aim to develop such a model for the first time, which can describe the biomechanical properties of damaged human and animal skins.
Skin Histology and Constitutive Models
Skin Histology
A detailed microscopy study17 showed that there are at least three collagen layers inside the dermis of human skin: a thin superficial layer with fine bundles of collagen, a middle layer, which makes up most of the dermal bulk, and a deep layer of fibres linking the skin to the superficial fascia. Changes from a stretch mainly occur in the middle layer, suggesting it is the major load-bearer.17 When relaxed, collagen fibres are un-stretched and wavy; under an extension, the collagen fibres are individually straightened until all of these are recruited.17 In human skin, the collagen fibres in the unstressed dermis layer are grouped in large and small bundles and there are connective fine and thread-like fibrils between them.50
Constitutive Models for the Skin
Ridge and Wright first proposed a one-dimensional exponential and power function load-extension models for animal skin41 using uniaxial load-extension tests of the human abdomen and foreman skins.40,41 3D isotropic models were developed by using modified Mooney-Rivlin strain energy function for animal skin in Refs. 28,52,58 and human skin in Ref. 24.
Although there are no damage models specifically for the skin, various damage models for other soft tissues have been developed; namely, for the porcine carotid,15 the human anterior rectus sheath,31 the vaginal tissue,6 and the human thoracic and abdominal aortas.56 For human atherosclerotic arteries, a cohesive fracture model was proposed to allow cracks to develop when the tensile strength reaches the maximum damage criterion.12 Other fibre and matrix structure-based strain energy functions, e.g.,19 have also been extended to include damage in Ref. 53,54 and other references shown in Ref. 26.
A New Constitutive Model for Skin Damage
- (1)
Specify the ranges of all the material parameters;
- (2)
Normalise the parameters, and generate the initial guesses;
- (3)
Set up the working variables, the error tolerance for the lsqnonlin function (10^{−8}), the minimum and the maximum step changes of the variables (10^{−4} and 10^{−3}), and the maximum number of the iterations (2 × 10^{4});
- (4)
Calculate the objective function and update parameters by making use of the trust-region-reflective algorithm embedded in MATLAB;
- (5)
If the objective function value is larger than the tolerance, go back to (4);
- (6)
If any parameters are on a boundary, extend the boundary and go back to (2);
- (7)
Use the optimal parameters in the model and compute the Cauchy stress at a stretch;
- (8)
Output the model results, and compare with the experimental data.
We confirm that all the test data used in this paper are from the published references provided,2,23,29,33,35,44,51 and we have not harvested, handled and tested any tissues from cadavers and animals for the purpose of the paper.
Results
Choice of Parameters
To select the suitable parameters for our damage model we use the uniaxial data for the human skin harvested from various locations on the back of a cadaver, presented by Fig. 10 in Ref. 33. Following Ref. 33 we note that κ = 0.1404 and β = 41° were measured in this particular test. To check if we could inversely identify these parameters from the uniaxial tests only, we run five different cases: in case A, we consider the original GOH model without damage and fix κ = 0.1404 and β = 41° as the measured values. In cases B–E, we use the damage model Eq. (2), but in case B we keep κ = 0.1404 fixed, in case C, we keep β = 41° fixed, in case D we keep both κ = 0.1404 and β = 41° fixed, and in case E, we don’t fix any parameters.
Estimated material parameters for Cases A–E.
Parameters | Results in Ref. 33 | A | B | C | D | E |
---|---|---|---|---|---|---|
μ (MPa) | 2.01 × 10^{−1} | 1.50 × 10^{−3} | 1.51 × 10^{−1} | 1.47 × 10^{−1} | 1.52 × 10^{−1} | 6.11 × 10^{−1} |
k_{1} (MPa) | 24.53 | 26.38 | 15.10 | 14.72 | 15.25 | 61.13 |
k_{2} | 1.33 × 10^{−1} | 3.58 | 23.30 | 22.91 | 23.23 | 42.62 |
β (°) | 41.00 | 41.00 | 40.90 | 41.00 | 41.00 | 25.99 |
κ | 1.40 × 10^{−1} | 1.40 × 10^{−1} | 1.40 × 10^{−1} | 1.36 × 10^{−3} | 1.40 × 10^{−1} | 3.10 × 10^{−1} |
m | N/A | N/A | 3.46 | 3.30 | 3.15 | 4.19 |
ζ | N/A | N/A | 3.26 | 3.27 | 3.23 | 3.28 |
n | N/A | N/A | 6.30 | 6.33 | 6.33 | 7.12 |
ξ | N/A | N/A | 1.10 | 1.11 | 1.10 | 1.06 |
ɛ (%) | N/A | 11.73 | 4.47 | 4.49 | 4.50 | 3.25 |
In case E, all the material parameters are inversely estimated. This case gives the best curve fitting. However, the fitted parameters are significantly different to the measured values. In other words, it is difficult to estimate both the fibre angle and dispersion accurately using the uniaxial tests alone. Indeed, for most of the cases studied below, information from histology examination is required and a damage model must be used. Since case A shows that even with the measured parameters, using the GOH model without damage does not yield good agreement with the experiment. Even with a damage model, we also need to fix either (β or κ) as in case B or C, or both as in case D, to obtain the best agreement with the experiment.
Application to Skins with Damage
We now apply the damage model to a number of other experimental data obtained for animal and human skins. Unfortunately, we do not have direct histology data for these samples, but a range of κ = [0.1009, 0.1675] was given for the human skin.33 Hence, we have to inversely estimate both β and κ. First, we consider the swine skin (case F) in Ref. 29. We also consider the uniaxial tests by Ankersen et al., for samples harvested from the back (case G), and belly (case H), of an 8-month-old swine.2 Finally, we consider a foetal calf back skin test51 (case I), samples measured from the human back skin35 (case J), and samples measured from rhino back skin dermis44 (case K).
In cases F, G, H, I and K, the specimens were harvested from the body, so we choose the spine to be the reference of the mean fibre orientation. However, for case J, the Langer’s line is used as in Ref. 35. We are able to estimate all the parameters for cases H and J from the uniaxial tests for the fibre dispersion parameter κ ∈ [0, 1/3]. For cases F, G, I and K, however, a good curve fitting is achieved only when we constrain the value of κ in a narrow range [0.1009, 0.1675].33 This confirms the importance of the histology input in the model.
Estimated material parameters for cases F–K.
Species | Swine | Bovine | Human | Rhino | ||
---|---|---|---|---|---|---|
Case | F | G | H | I | J | K |
Strain rate in tests (s^{−1}) | 2500 | 1.00 × 10^{−2} | 1.00 × 10^{−2} | 3.00 × 10^{−2} | 1.2 × 10^{−2} | 2.20 × 10^{−1} |
μ (MPa) | 1.95 × 10^{−2} | 4.98 × 10^{−2} | 3.39 × 10^{−1} | 1.18 | 5.02 × 10^{−1} | 3.17 × 10^{−1} |
k_{1} (MPa) | 9.57 × 10^{−1} | 4.97 | 39.96 | 12.92 | 50.22 | 285.67 |
k_{2} | 56.33 | 2.88 | 7.66 × 10^{−1} | 1.624 × 10^{−1} | 1.53 | 216.27 |
β (°) | 42.63 | 47.98 | 5.20 × 10^{−3} | 40.31 | 6.96 × 10^{−2} | 46.02 |
κ | 1.68 × 10^{−1} | 1.68 × 10^{−1} | 2.70 × 10^{−1} | 1.01 × 10^{−1} | 2.84 × 10^{−1} | 1.68 × 10^{−1} |
m | 2.36 | 4.45 | 1.19 | 1.39 | 1.80 | 2.87 |
ζ | 3.11 | 3.83 | 3.11 | 3.27 | 3.73 | 3.03 |
n | 4.49 | 6.13 | 24.30 | 47.15 | 56.02 | 3.71 |
ξ | 1.06 | 1.26 | 1.12 | 1.26 | 1.14 | 1.03 |
ɛ (%) | 2.46 | 12.18 | 7.01 | 6.95 | 8.02 | 2.15 |
Sensitivity Analysis and Tissue Breaking Criterion
Figure 7 also shows that the magnitudes of the partial derivatives increase sharply at the stretches corresponding to the turning points of the stress-stretch curves when damage occurs. From the parameters optimization procedure, we know that the parameters that have larger magnitudes of partial derivative can be determined more accurately than those with smaller values. Hence, the group-I parameters are easier to determine than these in the group-II.
We note that the fibre angle is more aligned in the specimen 1 tension direction than that of the specimen 2. Therefore, the fibres are less stretched in the specimen 2. Hence to reach the fibre break limit, a much greater displacement is required for the specimen 2. As a result, there is a possibility that the matrix breaks earlier than the fibres. This may explain the change of rank of the parameter list in (7).
Sensitivity ranking of parameters in terms of gradients of strain energy function for Cases B, F–K.
Case | Specimen | Ranking | Break |
---|---|---|---|
B | 1 | ξ > κ > β > k_{2} | No |
2 | ξ > κ > β > ζ | ||
F | 1 | ξ > κ > β > ζ | No |
2 | ξ > κ > ζ > β | ||
G | 1 | ξ > κ > k_{2} > β | Yes |
2 | ξ > κ > k_{2} > β | ||
H | 1 | κ > ξ > k_{2} > ζ | Yes |
2 | ξ > κ > k_{1} > β | ||
I | 1 | k_{2} > β > κ > ξ | Yes |
2 | k_{2} > β > κ > ξ | ||
J | 1 | κ > ξ > k_{2} > ζ | Yes |
2 | ξ > κ > β > k_{1} | ||
K | 1 | ξ > κ > β > ζ | No |
2 | ξ > κ > β > ζ |
In cases B, F, H, J and K, ζ also appears on the list, presumably because the specimens in these cases were significantly stretched and thus induced the matrix damage also. If the matrix damage is significant in the soft tissue, as shown by cases H and J in Fig. 6, we refer to this as the ductile break. This is opposed to the brittle break where the fibres are damaged first.
Discussion
In our damage model for animal and human skins, the material parameters are inversely estimated based on two orthogonal uniaxial tests. We have found that it is difficult to estimate the mean collagen fibre angle and dispersion parameter from the uniaxial data alone.
The sensitivity analysis shows that the mean fibre angle and the dispersion parameter are among the most significant parameters. In general, histological information is required to estimate these two parameters accurately. Indeed, our results show that if one of these two parameters can be measured, or if the range of the dispersion parameter can be provided, then the rest of the parameters can be found so that the model results match the experimental stress-stretch data. Unfortunately, except,21,33 many experimental studies on skins did not perform histological examinations of collagen orientation and dispersion.
Human and animal skins are viscoelastic since the stress-stretch curves change with the strain rate.29^{,}45 Our model is based on the hyperelastic material assumption. Hence, the estimated fibre parameters agreed with the histological observations only at the lower strain rate. For example, the mean fibre angle and dispersion parameter optimized based on the two uniaxial stress-stretch curves at the strain rate of 0.012 s^{−1} are in agreement with the parameters observed histologically for human skin.33 For rat skin, the strain rate threshold that the constitutive response of skin starts to be rate dependent is 0.1–0.3 s^{−1}.45 Unfortunately, such a threshold of strain rate has not been established for human skin.
The specimens in cases G, I and J were harvested from swine, bovine and human backs, but the specimens in case H was from swine belly. For cases G, I, and J the fibre break limit remains the same in the uniaxial tests of specimen 1 and 2. This implies that the tissue damage is due to the fibre breaks, i.e., these tissues have the brittle break. In case H, however, the fibre break limit occurs at different fibre stretches in the two specimens. This suggests that the damage also occurred in the matrix as otherwise the damage should occur at the same fibre stretch. This type of damage is ductile.
We also plot the Cauchy stresses against a different fibre stretch measure, \( \sqrt {I_{4} } \), and the matrix stretch measure, I_{1}. However, neither \( \sqrt {I_{4} } \) or I_{1} remains constant in cases G, H, I and J. Therefore, these two invariants are not suitable for use as a breaking criterion.
Although this is the first invariant-based damage model applied to animal and human skins, the limitations of our study are also worth mentioning. Our current model parameters are estimated using the uniaxial test data, since there are very few bi-axial damage tests reported. Nevertheless the model could be better validated with the multi-axial tests in future.
Notably, neglecting viscosity when modelling damage in soft tissues might be a non-admissible over-estimation.14 It has been shown that animal skin exhibits plastic deformation and Mullins effect under a cyclic load.32 These have not been included in our model. In addition, due to the lack of experimental data, we have also omitted the effect of the residual stress in the model. The bundles of collagen fibres twist and extend to the next deeper observational plane in a helical manner, thus a 3D network is found in rat skins.39 The 3D network structure is yet to be considered in the modelling of the skin. Finally, in our work, the skin is modelled as a single layer model. However, the skin has multiple layers.7 This should be accounted for in future work.
Conclusion
We have proposed a new damage model for animal and human skins by modifying the Gasser–Ogden–Holzapfel strain energy function for arterial tissues. This new model describes the softening/damage effects using the Volokh-type power functions and consists of three parameters for the matrix and six parameters for the collagen fibres. The material parameters can be inversely determined based on the uniaxial test data using the optimization method in MATLAB. The model is successfully applied to a variety of skins of swine, human, rabbit and bovine, and results match the experimental stress-stretch curves well. Our sensitivity study confirms that the fibre orientation dispersion parameter, κ, the mean fibre angle, β, are the most important factors that influence the damage model. In addition, these two parameters can only be reliably determined if some histological information for one for these is provided. We also found that depending on the location of skins; the tissue damage may be brittle (i.e., mostly controlled by the fibre breaking limit), or ductile (due to both the fibre and the matrix damages). Finally, we illustrate that the fibre stretch, which is dependent on the fibre dispersion, is the best parameter for use as the fibre breaking limit.
Notes
Funding
This work is supported by the Scottish Funding Council (Interface Food & Drink) the EPSRC IAA (EP/K503903/1) of the University of Glasgow, and the EPSRC grant (EP/N014642/1).
Conflict interests
The authors have no conflicts of interest.
Ethical approval
Not required.
References
- 1.Alexander, H., and T. H. Cook. Accounting for natural tension in the mechanical testing of human skin. J. Invest. Dermatol. 69:310–314, 1977.CrossRefPubMedGoogle Scholar
- 2.Ankersen, J., A. E. Birkbeck, R. D. Thomson, and P. Vanezis. Puncture resistance and tensile strength of skin stimulants. Proc. Inst. Mech. Eng. Part H 213:493–501, 1999.CrossRefGoogle Scholar
- 3.Belkoff, S. M., and R. C. Haut. A structural model used to evaluate the changing microstructure of maturing rat skin. J. Biomech. 24:711–720, 1991.CrossRefPubMedGoogle Scholar
- 4.Bischoff, J. E., E. M. Arruda, and K. Grosh. Finite element modelling of human skin using anisotropic, nonlinear elastic constitutive model. J. Biomech. 33:645–652, 2000.CrossRefPubMedGoogle Scholar
- 5.Byers, P. H., K. Holbrook, B. McGillivray, P. M. MacLeod, and R. B. Lowry. Clinical and ultrastructure heterogeneity of Type IV Ehlers-Danlos Syndrome. Hum. Genet. 47:141–150, 1979.CrossRefPubMedGoogle Scholar
- 6.Calvo, B., E. Pena, P. Martins, T. Mascarenhas, M. Doblaré, R. M. Natal Jorge, and A. Ferreira. On modelling damage process in vaginal tissue. J. Biomech. 42(5):642–651, 2009.CrossRefPubMedGoogle Scholar
- 7.Ciarletta, P., and M. B. Amar. Papillary networks in the dermal-epidermal junction of skin: a biomechanical model. Mech. Res. Commun. 42:68–75, 2012.CrossRefGoogle Scholar
- 8.Cox, H. T. The cleavage lines of the skin. Br. J. Surg. 29:234–240, 1941.CrossRefGoogle Scholar
- 9.Dick, J. C. The tension and resistance to stretching of human skin and other membranes, with results from a series of normal and edematous cases. J. Physiol. 112:102–113, 1951.CrossRefPubMedPubMedCentralGoogle Scholar
- 10.Edwards, C., and R. Marks. Evaluation of biomechanical properties of human skin. Clin. Dermatol. 13:375–380, 1995.CrossRefPubMedGoogle Scholar
- 11.Evans, S. L., and C. A. Holt. Measuring the mechanical properties of human skin in vivo using digital image correlation and finite element modelling. J. Strain Anal. 44:337–345, 2009.CrossRefGoogle Scholar
- 12.Ferrara, A., and A. Pandolfi. Numerical modelling of fracture in human arteries. Comput. Methods Biomech. Biomed. Eng. 11(5):553–567, 2008.CrossRefGoogle Scholar
- 13.Flynn, C., A. Taberner, and P. Nielsen. Mechanical characterisation of in vivo human skin using 3D force-sensitive micro-robot and finite element analysis. Biomech. Model. Mechanobiol. 10:27–38, 2011.CrossRefPubMedGoogle Scholar
- 14.Forsell, C., and T. C. Gasser. Numerical simulation of the failure of ventricular tissue due to deep penetration: the impact of constitutive properties. J. Biomech. 44:45–51, 2011.CrossRefPubMedGoogle Scholar
- 15.Garcia, A., M. A. Martinez, and E. Peña. Determination and modeling of the inelasticity over the length of the porcine carotid artery. J. Biomech. Eng. 135(3):031004, 2013.CrossRefGoogle Scholar
- 16.Gasser, T. C., R. W. Ogden, and G. A. Holzapfel. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3:15–35, 2006.CrossRefPubMedGoogle Scholar
- 17.Gibson, T., R. M. Kendi, and J. E. Craik. The mobile micro-architectures of dermal collagen. Br. J. Surg. 52:764–770, 1965.CrossRefPubMedGoogle Scholar
- 18.Groves, R. B., S. A. Coulman, J. C. Birchall, and S. L. Evans. An anisotropic, hyperelastic model for skin: experimental measurements, finite element modelling and identification of parameters for human and murine skin. J. Mech. Behav. Biomed. Mater. 18:167–180, 2013.CrossRefPubMedGoogle Scholar
- 19.Holzapfel, G. A., T. C. Gasser, and R. Ogden. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elast. Phys. Sci. Solids 61(1–3):1–48, 2000.Google Scholar
- 20.Jor, J. W. Y., M. P. Nash, P. M. F. Nielsen, and P. J. Hunter. Estimating material parameters of a structurally based constitutive relation for skin mechanics. Biomech. Model. Mechanobiol. 10:767–778, 2010.CrossRefPubMedGoogle Scholar
- 21.Jor, J. W. Y., P. M. F. Nielsen, M. P. Nash, and P. J. Hunter. Modelling collagen fibre orientation in porcine skin based upon confocal laser scanning microscopy. Skin Res. Technol. 17:149–159, 2011.CrossRefPubMedGoogle Scholar
- 22.Lanir, Y., and Y. C. Fung. Two-dimensional mechanical properties of rabbit skin-I experimental system. J. Biomech. 7:29–34, 1974.CrossRefPubMedGoogle Scholar
- 23.Lanir, Y., and Y. C. Fung. Two-dimensional mechanical properties of rabbit skin-II experimental results. J. Biomech. 7:171–182, 1974.CrossRefPubMedGoogle Scholar
- 24.Lapeer, R. J., P. D. Gasson, and V. Karri. Simulating plastic surgery: from human skin tensile tests, through hyperelastic finite element models to real-time haptics. Prog. Biophys. Mol. Biol. 103:208–216, 2010.CrossRefPubMedGoogle Scholar
- 25.Larrabee, W. F., and D. Sutton. A finite element model of skin deformation II: an experimental model of skin deformation. Laryngoscope 96:406–412, 1986.PubMedGoogle Scholar
- 26.Li, W. Damage models for soft tissues: a survey. J. Med. Biol. Eng., 2016, in press.Google Scholar
- 27.Li, W. G., J. Going, N. A. Hill, and X. Y. Luo. Breaking analysis of artificial elastic tubes and human artery. Int. J. Appl. Mech. 5:55–66, 2013.CrossRefGoogle Scholar
- 28.Liang, X., and S. A. Boppart. Biomechanical properties of in vivo human skin from dynamic optical coherence elastography. IEEE Trans. Biomed. Eng. 57:953–959, 2010.CrossRefPubMedGoogle Scholar
- 29.Lim, J., J. Hong, W. W. Chen, and T. Weerasooriya. Mechanical response of pig skin under dynamic tensile loading. Int. J. Impact Eng. 38:130–135, 2011.CrossRefGoogle Scholar
- 30.Mahmud, J., C. Holt, S. Evans, N. F. A. Manan, and M. Chizari. a parametric study and simulations in quantifying human skin. Proc. Eng. 41:1580–1586, 2012.CrossRefGoogle Scholar
- 31.Martins, P., E. Peña, R. M. Jorge, A. Santos, L. Santos, T. Mascarenhas, and B. Calvo. Mechanical characterization and constitutive modelling of the damage process in rectus sheath. J. Mech. Behav. Biomed. Mater. 8:111–122, 2012.CrossRefPubMedGoogle Scholar
- 32.Munoz, M. J., J. A. Bea, J. F. Rodriguez, I. Ochoa, J. Grasa, A. Perez, P. del Palomar, P. Zaragoza, R. Osta, and M. Doblare. An experimental study of the mouse skin behaviour: damage and inelastic aspects. J. Biomech. 41:93–99, 2008.CrossRefPubMedGoogle Scholar
- 33.Ni Annaidh, A., K. Bruyere, M. Destrade, M. D. Gilchrist, C. Maurini, M. Ottenio, and G. Saccomandi. Automated estimation of collagen fibre dispersion in the dermis and its contribution to the anisotropic behaviour of skin. Ann. Biomed. Eng. 40:1666–1678, 2012.CrossRefPubMedGoogle Scholar
- 34.Ni Annaidh, A., K. Bruyere, M. Destrade, M. D. Gilchrist, and M. Ottenio. Characterization of the anisotropic mechanical properties of excised human skin. J. Mech. Behav. Biomed. Mater. 5:139–148, 2012.CrossRefPubMedGoogle Scholar
- 35.Ni Annaidh, A., M. Ottenio, K. Bruyere, M. Destrade, and M. D. Gilchrist. Mechanical properties of excised human skin. Proceedings of the 6th World Congress of Biomechanics (WCB 2010). Singapore, August 1–6, 2010.Google Scholar
- 36.Pailler-Mattei, C., S. Bec, and H. Zahouani. In vivo measurements of the elastic mechanical properties of human skin by indentation tests. Med. Eng. Phys. 30:599–606, 2008.CrossRefPubMedGoogle Scholar
- 37.Pope, F. M., G. R. Martin, J. R. Lichtenstein, R. Penttinen, B. Gerson, D. W. Rowe, and V. A. McKusick. Patients with Ehlers–Danlos syndrome type IV lack type III collagen. Proc. Natl. Acad. Sci. USA 72:1314–1316, 1975.CrossRefPubMedPubMedCentralGoogle Scholar
- 38.Reihsner, R., B. Balogh, and E. J. Menzel. Two-dimensional elastic properties of human skin in terms of an incremental model at the in vivo configuration. Med. Eng. Phys. 4:304–313, 1995.CrossRefGoogle Scholar
- 39.Ribeiro, J. F., E. H. M. dos Anjos, M. L. Mello, and B. de Campos Vidal. Skin collagen fiber molecular order: a pattern of distributional fiber orientation as assessed by optical anisotropy and image analysis. PLoS One 8:e54724, 2013. doi:10.1371/journal.pone.0054724.CrossRefPubMedPubMedCentralGoogle Scholar
- 40.Ridge, M. D., and V. Wright. The rheology of skin. Br. J. Dermatol. 77:635–649, 1965.CrossRefGoogle Scholar
- 41.Ridge, M. D., and V. Wright. Mechanical properties of skin: a bioengineering study of skin structure. J. Appl. Physiol. 21:1602–1606, 1966.PubMedGoogle Scholar
- 42.Ridge, M. D., and V. Wright. The directional effects skin. J. Invest. Dermatol. 46:341–346, 1966.CrossRefPubMedGoogle Scholar
- 43.Schneider, D. C., T. M. Davison, and A. M. Nahum. In vitro biaxial stress-strain response of human skin. Arch. Otolaryngol. 110:329–333, 1984.CrossRefPubMedGoogle Scholar
- 44.Shadwick, R. E., A. P. Russell, and R. F. Lauff. The structure and mechanical design of rhinoceros dermal armour. Philos. Trans. R. Soc. Lond. B 337:419–428, 1992.CrossRefGoogle Scholar
- 45.Shergold, O. A., N. A. Fleck, and D. Radford. The uniaxial stress versus strain response of pig skin and silicon rubber at low and high strain rates. Int. J. Impact Eng. 32:1384–1402, 2006.CrossRefGoogle Scholar
- 46.Silver, F. H., L. M. Siperko, and G. P. Seehra. Mechanobiology of force transduction in dermal tissue. Skin Res. Technol. 9:3–23, 2003.CrossRefPubMedGoogle Scholar
- 47.Tepole, A. B., A. K. Gosain, and E. Kuhl. Computational modelling of skin: using stress profiles as predictor for tissue necrosis in reconstructive surgery. Comput. Struct. 143:32–39, 2014.CrossRefPubMedPubMedCentralGoogle Scholar
- 48.Tonge, T. K., L. S. Atlan, L. M. Voo, and T. D. Nguyen. Full-field bulge test for planar anisotropic tissues: part I—experimental methods applied to human skin tissue. Acta Biomater. 9:5913–5923, 2013.CrossRefPubMedGoogle Scholar
- 49.Tonge, T. K., L. S. Atlan, L. M. Voo, and T. D. Nguyen. Full-field bulge test for planar anisotropic tissues: part II—a thin shell method for determining material parameters and comparison of two distribution fiber modelling approaches. Acta Biomater. 9:5926–5942, 2013.CrossRefPubMedGoogle Scholar
- 50.Tregear, R. T. The mechanical properties of skin. J. Soc. Cosmet. Chem. 20:467–477, 1969.Google Scholar
- 51.Ventre, M., M. Padovani, A. D. Covington, and P. A. Netti. Composition, structure and physical properties of foetal calf skin. Proceedings of IULTCS-EUROCONGRESO, Istanbul, Turkey, May 2006.Google Scholar
- 52.Veronda, D. R., and R. A. Westmann. Mechanical characterization of skin-finite deformation. J. Biomech. 3:111–124, 1970.CrossRefPubMedGoogle Scholar
- 53.Volokh, K. Prediction of arterial failure based on a microstructural bi-layer fiber–matrix model with softening. J. Biomech. 41(2):447–453, 2008.CrossRefPubMedGoogle Scholar
- 54.Volokh, K. Modeling failure of soft anisotropic materials with application to arteries. J. Mech. Behav. Biomed. Mater. 4(8):1582–1594, 2011.CrossRefPubMedGoogle Scholar
- 55.Weinstein, G. D., and R. J. Boucek. Collagen and elastin of human dermis. J. Invest. Dermatol. 35:227–229, 1960.CrossRefPubMedGoogle Scholar
- 56.Weisbecker, H., D. M. Pierce, P. Regitnig, and G. A. Holzapfel. Layer-specific damage experiments and modeling of human thoracic and abdominal aortas with non-atherosclerotic intimal thickening. J. Mech. Behav. Biomed. Mater. 12:93–106, 2012.CrossRefPubMedGoogle Scholar
- 57.Yen, J. L., S. P. Lin, M. R. Chen, and D. M. Niu. Clinical features of Ehlers-Danlos Syndrome. J. Formos. Med. Assoc. 105:475480, 2006.Google Scholar
- 58.Zhou, B., F. Xu, C. Q. Chen, and T. J. Lu. Strain rate sensitivity of skin tissue under thermomechanical loading. Philos. Trans. R. Soc. A 368:679–690, 2014.CrossRefGoogle Scholar
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