人体前臂软组织活体力学性质研究
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摘要
人体皮肤、肌肉等软组织的力学性质是诸多研究领域的基础,尤其在互动可视注射模拟,微创外科治疗,皮肤病学、美容化妆、量化医药产品效力及皮肤病检测等方面有着举足轻重的作用。
如今,压凹痕实验被广泛应用于软组织材料的弹塑性力学行为研究。人体的皮肤是一个复杂的多层复合材料,具有和其他生物软组织相同的力学性质,即非线性、超弹性、粘弹性和各向异性等。但传统的压痕实验也有其自身的局限性,虽然可以通过自动控制设备来得到探头的总体压痕深度,但并不能由此确定每层的变形位移。因此,在传统实验方法的基础上,我们提出一种结合断层扫描技术(Magnetic Resonance Imaging)的方法来弥补传统压痕实验方法的不足,使其具有更广泛的应用性。
本文提出了一种结合传统的压痕实验方法和MRI技术来测量人体皮下层和肌肉层非线性力学性质的实验方法。为此,我们利用MRI断层扫描图像建立了皮肤-皮下-肌肉-骨头复合体的三维有限元模型作为整个前臂组织的简化模型。通过静态压痕实验和MRI图像的原始数据确定了材料本构方程的超弹性参数,并利用上述模型验证了该过程,此时只把皮下-肌肉视为弹性材料而忽略了其粘弹性力学特征的影响。另外,我们通过测量动态荷载下前臂接触反力随时间变化的响应来确定不同的加载速率对整个软组织结构率相关性行为的影响。结果显示,整个结构的初始接触力随着载荷速率的增加而不断增大,此时模型所有软组织都视为非线性弹性和粘弹性,其中粘弹性特征通过应力松弛函数的Prony级数来表示。总体来说,本文的研究内容可分为以下几个部分:
压痕实验及实验结果整理。实验部分主要介绍压痕实验的建立方法,包括压痕部位的绑定,压痕设备的安装,前臂部位的影像定位,以及实验过程中的加载等。实验结果整理部分,包括对断层图像中各个软组织层变形位移的测量,静态压痕实验中压痕深度的确定以及动态松弛实验中力位移数据的整理。
断层图像三维重建。由于理想的生物组织模型在外部形态和内部结构方面都与真实结构存在着巨大的差异,从而大大降低了模拟计算的可信度,导致整个研究的结果出现错误。基于上述原因,我们通过医学图像处理软件Simplewar-ScanIP对断层扫描图像进行了真实结构的三维重建,大大提升了计算模型的精确度和可信度。
各软组织层力学性质的描述。将上述整理的力位移数据通过弹性接触理论的关系获得皮下层和肌肉层的超弹性材料参数,再将所有的软组织层视为非线性超弹性和粘弹性来研究不同加载速率对整个结构粘弹性响应的影响,其中材料的粘弹性参数全部来自于文献中的数据。
有限元仿真模拟。将上述三维重建的实体模型划分网格后转化为可用于后续计算分析的有限元模型,将力学参数赋予表皮-皮下-肌肉-骨头分层结构的复合体,来模拟其非线性超弹性和粘弹性力学特征,通过模拟结果和实验结果的对比来验证参数的合理性。
Characterization of the human skin-muscle complex mechanical properties is essential in several research domains, particularly for interactive virtual needle insertion simulation, minimally invasive surgical training, dermatology, cosmetic, and quantification of effectiveness of dermatologic products and detection of skin diseases.
Indentation testing is a widely used technique to characterize the elastoplastic properties of soft tissues. Especially, human skin is a complex and multi-layered material which has common mechanical behavior of non-linear, hyperelasticity, anisotropic like muscle and other biological soft tissue. But traditional indentation also has its own limits, the indentation depth of indenter can be measured by automatic equipment, but for multi-layered composite material like skin, we can’t directly determine the deformed displacement of the single layer, so we present a method combined with MRI technique improving this traditional experiment for widely use.
In this paper we present a method combined traditional indentation test with MRI technique to in vivo quantify the nonlinear mechanical behavior of the subcutaneous and muscle layer. To achieve this a MRI scan based three-dimensional (3D) finite element (FE) model of skin-muscle-bone complex as simplified representation of the whole forearm was developed, we determine the material hyperelastic parameters by static indentation test with MRI raw data, and the proposed multi-layered FE model which neglect the viscous part of the skin response, in order to assimilate the human skin mainly to an elastic material is presented to verify this process. Then , the force versus time response of forearm under dynamic loading condition was measured to quantify how different loading rates affect the whole structure’s time-dependent behavior, the results showed that the initial contact force in the whole model were increased for increasing applied loading rate. Meanwhile, all the soft-tissue layers were assumed to be nonlinearly elastic and viscoelastic, the viscoelastic behavior of the soft-tissue layers was simulated using the stress-relaxation function based on the Prony series, and the FE solution shows a good agreement with the corresponding experimental force data. Generally speaking, the thesis can be described as follows:
Indentation test setup and data collection. Experimental setup mainly includes contact region bind, equipment fixed, local part position, load etc. Data collection includes measurement of layer deformation displacement, indentation depth and force versus displacement data of stress-relaxation test.
Three-dimensional reconstruction of MRI images. Because of the great differences between ideal model and real structure will mislead the result, we reconstruction the model by image processing soft ware-Simpleware, highly improved the quality of computation model
Characterization of soft tissue mechanical properties. we determine the subcutaneous and muscle layer material parameter by elastic contact theory. Then, all the layers are assumed to be hyperelastic and viscoelastic to study how the different strain rates affect the whole structure’s viscoelactic behavior, here, all the visco parameters were obtained from the public references.
The finite element simulation . The proposed multi-layered model was meshed by Simpleware-Scan FE module for further finite element analysis. All the parameters are assigned to this cutaneous-subcutaneous-bone complex to simulate the hyperelastic and viscoelastic behavior, then compared with the tests results to verify this process.
如今,压凹痕实验被广泛应用于软组织材料的弹塑性力学行为研究。人体的皮肤是一个复杂的多层复合材料,具有和其他生物软组织相同的力学性质,即非线性、超弹性、粘弹性和各向异性等。但传统的压痕实验也有其自身的局限性,虽然可以通过自动控制设备来得到探头的总体压痕深度,但并不能由此确定每层的变形位移。因此,在传统实验方法的基础上,我们提出一种结合断层扫描技术(Magnetic Resonance Imaging)的方法来弥补传统压痕实验方法的不足,使其具有更广泛的应用性。
本文提出了一种结合传统的压痕实验方法和MRI技术来测量人体皮下层和肌肉层非线性力学性质的实验方法。为此,我们利用MRI断层扫描图像建立了皮肤-皮下-肌肉-骨头复合体的三维有限元模型作为整个前臂组织的简化模型。通过静态压痕实验和MRI图像的原始数据确定了材料本构方程的超弹性参数,并利用上述模型验证了该过程,此时只把皮下-肌肉视为弹性材料而忽略了其粘弹性力学特征的影响。另外,我们通过测量动态荷载下前臂接触反力随时间变化的响应来确定不同的加载速率对整个软组织结构率相关性行为的影响。结果显示,整个结构的初始接触力随着载荷速率的增加而不断增大,此时模型所有软组织都视为非线性弹性和粘弹性,其中粘弹性特征通过应力松弛函数的Prony级数来表示。总体来说,本文的研究内容可分为以下几个部分:
压痕实验及实验结果整理。实验部分主要介绍压痕实验的建立方法,包括压痕部位的绑定,压痕设备的安装,前臂部位的影像定位,以及实验过程中的加载等。实验结果整理部分,包括对断层图像中各个软组织层变形位移的测量,静态压痕实验中压痕深度的确定以及动态松弛实验中力位移数据的整理。
断层图像三维重建。由于理想的生物组织模型在外部形态和内部结构方面都与真实结构存在着巨大的差异,从而大大降低了模拟计算的可信度,导致整个研究的结果出现错误。基于上述原因,我们通过医学图像处理软件Simplewar-ScanIP对断层扫描图像进行了真实结构的三维重建,大大提升了计算模型的精确度和可信度。
各软组织层力学性质的描述。将上述整理的力位移数据通过弹性接触理论的关系获得皮下层和肌肉层的超弹性材料参数,再将所有的软组织层视为非线性超弹性和粘弹性来研究不同加载速率对整个结构粘弹性响应的影响,其中材料的粘弹性参数全部来自于文献中的数据。
有限元仿真模拟。将上述三维重建的实体模型划分网格后转化为可用于后续计算分析的有限元模型,将力学参数赋予表皮-皮下-肌肉-骨头分层结构的复合体,来模拟其非线性超弹性和粘弹性力学特征,通过模拟结果和实验结果的对比来验证参数的合理性。
Characterization of the human skin-muscle complex mechanical properties is essential in several research domains, particularly for interactive virtual needle insertion simulation, minimally invasive surgical training, dermatology, cosmetic, and quantification of effectiveness of dermatologic products and detection of skin diseases.
Indentation testing is a widely used technique to characterize the elastoplastic properties of soft tissues. Especially, human skin is a complex and multi-layered material which has common mechanical behavior of non-linear, hyperelasticity, anisotropic like muscle and other biological soft tissue. But traditional indentation also has its own limits, the indentation depth of indenter can be measured by automatic equipment, but for multi-layered composite material like skin, we can’t directly determine the deformed displacement of the single layer, so we present a method combined with MRI technique improving this traditional experiment for widely use.
In this paper we present a method combined traditional indentation test with MRI technique to in vivo quantify the nonlinear mechanical behavior of the subcutaneous and muscle layer. To achieve this a MRI scan based three-dimensional (3D) finite element (FE) model of skin-muscle-bone complex as simplified representation of the whole forearm was developed, we determine the material hyperelastic parameters by static indentation test with MRI raw data, and the proposed multi-layered FE model which neglect the viscous part of the skin response, in order to assimilate the human skin mainly to an elastic material is presented to verify this process. Then , the force versus time response of forearm under dynamic loading condition was measured to quantify how different loading rates affect the whole structure’s time-dependent behavior, the results showed that the initial contact force in the whole model were increased for increasing applied loading rate. Meanwhile, all the soft-tissue layers were assumed to be nonlinearly elastic and viscoelastic, the viscoelastic behavior of the soft-tissue layers was simulated using the stress-relaxation function based on the Prony series, and the FE solution shows a good agreement with the corresponding experimental force data. Generally speaking, the thesis can be described as follows:
Indentation test setup and data collection. Experimental setup mainly includes contact region bind, equipment fixed, local part position, load etc. Data collection includes measurement of layer deformation displacement, indentation depth and force versus displacement data of stress-relaxation test.
Three-dimensional reconstruction of MRI images. Because of the great differences between ideal model and real structure will mislead the result, we reconstruction the model by image processing soft ware-Simpleware, highly improved the quality of computation model
Characterization of soft tissue mechanical properties. we determine the subcutaneous and muscle layer material parameter by elastic contact theory. Then, all the layers are assumed to be hyperelastic and viscoelastic to study how the different strain rates affect the whole structure’s viscoelactic behavior, here, all the visco parameters were obtained from the public references.
The finite element simulation . The proposed multi-layered model was meshed by Simpleware-Scan FE module for further finite element analysis. All the parameters are assigned to this cutaneous-subcutaneous-bone complex to simulate the hyperelastic and viscoelastic behavior, then compared with the tests results to verify this process.
引文
1 S. P. DiMaio, S. E. Salcud. Simulated interactive needle inredon. In Tenfh Symposium on Haptic lnterj'oces for Mrfual Emimnmenr and Telropemtor Syrrem. WG351. IEEE, 2W2
2 N. Abolhassani, R. Patel, M. Moallem. Needleinsertion into soft tissue: A survey. Medical Engineering & Physics, 2007, (5):413~431
3 D. Lürding, Y. Baar, Ulrike, Hanstter. Application of Transversely Isotropic Materials to Multi-layer Shell Elements Undergoing Finite Rotations and Large Strains International Journal of Solids and Structures, 2001, (12):943~950
4 T.Johansson, P. Meier, R. Blickhan. A Finite-Element Model for the Mechanical Analysis of Skeletal Muscles. Journal of Theoretical, 2000, (9)
5 M. Kaua, V. Dual, G. Szikdy, M. Bajka. Inverse Finite Element Charanerhtion of Soft Tissues with Aspintion Experiments. Medical Image Analysis, 2002, 6(3):275~287
6 M. P. Ottensmeyer, A. E. Kerdok, R. D. Howe, S. L. Dawson. The Effects of Testing Environment on the Viscoelastic Properties of Soft Tissues. In: Proceedings of the International Symposium on Medical Simulation, 2004: 9~18
7 A. Manduca, T. E. Oliphant, M. A. Dresner, J. L. Mahowald, S. A. Kruse, E. Amromin, J. P. Felmlee, J. F. Greenleaf, R. L. Ehman. Magnetic Resonance Elastography Non Invasive Mapping of Tissue Elasticity. Medical Image Analysis, 2001, 5(4): 237~254
8 A. Weiss, B. N. Maker, S. Govindjee. Finite Element Implementation of Incompressible, Isotropic hyperelasticity. Computer Methods in Applied Mechanics and Engineering, 1996, 8(15):107~128
9 P. Agache, Physiologie de la peau et Explorations Fonctionnelle Scutanees, Collection Explorations Fonctionnelles Humaines, Editions Medicales Internationales. Technique&Documentation, 2000 :1850~1861
10 F. Tognella, A. Mainar, C. Vanhoutte, F. Goubel. A Mechanical Device for Studying Mechanical Properties of Human Muscles in Vivo. Journal ofBiomechanics, 1997, 30(10):1077~1080
11 J. L. Gennissona, C. Cornub, S. Cathelinea, M. Finka, P. Porterob. Human muscle hardness assessment during incremental isometric contraction using transient elastography. Journal of Biomechanics, 2005, (38): 1543~1550
12 P. Mattei, H. Zahouani. Study of Adhesion Strengthsand Mechanical Properties of Human Skin in Vivo. Journal of Adhesion Science and Technology, 2004, (18):17391758
13 E. M. H. Bosboom, M. K. C. Hesselink, C. W. J. Oomens, C. V. C. Bouten, M. R. Drost, F. P. T. Baaijens. Passive Transverse Mechanical Properties of Skeletal Muscle under in Vivo Compression. Journal of Biomechanics, 2001, 34(10): 1365~1368
14 M. Zhang, A. R. Turner-Smith, V. C. Roberts. The Reaction of Skin and Soft Tissue to Shear Forces Applied Externally to the Skin Surface. Proceedings of the Institution of Mechanical Engineers, 1994, 208 :217~222
15 C.C. Van Donkelaar, P. J. B. Willems, A. M. M. Muijtjen, M. R. Drost. Skeletal muscle transverse strain during isometric contraction at different lengths. Journal of Biomechanics, 1999, (32):755~762
16 C. W. J. Oomens, D. H. VanCampen, H. J. Grootenboer, L. J. DeBoer. Experimental and theoretical Compression on Porcine Skin, Biomechanics: Current Interdisciplinary Research. Selected Proceedings of Meetings of European Society of Biomechanics, 1984: 227~232
17 C. W. J. Oomens, D. H. VanCampen, H. J. Grootenboer. A Mixture Approach to the Mechanics of Skin. Journal of Biomechanics, 1987, 20(9):877~885
18 J. Asserin, H. Zahouani, P. Humbert, V. Couturaud, D. Mougin. Measurement of the Friction Coefficient of the Human Skin in Vivo. Quantification of the Cutaneous Smoothness Colloids and Surfaces. Biointerfaces, 2000, (19):1~12
19 F. Khatyr, C. Imberdis, P. Vescovo, D. Varchon, J. M. Lagarde. Model of The Viscoelastic Behaviour of Skin in Vivo and Study of Anisotropy. Skin Research and Technology, 2004, 10 (2): 96
20 V. Retel, P. Vescovo, E. Jacquet, D. Varchon, B. Burtheret. Non-linear Model of Skin Mechanical Behavior Analysis with Finite Element Method. Skin Research and Technology, 2001, (7): 152~158
21 E. Samur, M. Sedef, C. Basdogan, L. Avtan, O. Duzgun. A RoboticNndenter for Minimally Invasive Characterization of Soft Tissues. International Congress Series, 2005, (5): 713~718
22 Tran, F. Charleux, M. Rachik, A. Ehrlacher, M.C. Hobatho. IN Vivo Characterization of the Mechanical Properties of Human Skin and Passive Muscle. Journal of Biomechanics, 2008, 41(7):29
23 F. M. Hendriks, D. Brokken, C. W. J. Oomens, D. L. Bader, F. P. T. Baaijens. The Relative Contributions of Different Skin Layers to The Mechanical Behavior of Human Skin in Vivo Using Suction Experiments. Medical Engineering & Physics, 2006, 28(3):259~266
24 S. Diridollou, M. Berson, V. Vabre, D. Black, B. Karlsson, F. Auriol, et al. An in Vivo Method for Measuring Mechanical Properties of The Skin Using Ultrasound. Ultrasound Medical Biology, 1998, 24:215~24
25 E. Samur, M. Sedef, C. Basdogan, L. Avtan, O. Duzgun. A Robotic Indenter for Minimally Invasive Measurement and Characterization of Soft Tissue Response. Medical Image Analysis, 2007, 11(4): 361~373
26 A. Delalleau, G. Josse, J. M. Lagarde, H. Zahouani, J. M. Bergheau. Characterization of The Mechanical Properties of Skin Byinverse Analysis Combined with The Indentation Test, 2006
27 A. Manduca, T. E. Oliphant, M. A. Dresner, J. L. Mahowald, S. A. Kruse, E. Amromin, J. P. Felmlee, J. F. Greenleaf, R. L. Ehman. Magnetic resonance elastography: Non-Invasive Mapping of Tissue ElasticityMedical Image Analysis, 2001, 5(4):37~54
28 L. J. Wu. Nonlinear Finite Element Analysis for Musculoskeletal Biomechanics of Medial and Lateral Plantar Longitudinal Arch of Virtual Chinese Human After Plantar ligamentous Structure Failures Clinical Biomechanics, 2007, 22(2):221~229
29 P. Agache. Physiologie de la Peau et Exploitations Fonctionnelles Cutan′ees. Editions M′edicales Internationales, 2000
30 Warren, B. D. Jenne, T. Wang. Charcterization of The Lower Limb Soft Tissues In Pedstrian Finite Element Models. General Motors Research & Development, 2005
31 S. Majumder, A. Roychowdhury, S. Pal. Simulation of Hip Fracture in Sideways Fall Using A 3D Finite Element Model of Pelvis-Femur–SoftTissue Complex with Simplified Representation of Whole Body. Medical Engineering & Physics, 2007, 31(1)
32 S. Diridollou, V. Vabre, L. Berson, L. Vaillant, D. Black, JM. Lagarde, et al. Skin Ageing: Changes of Physical Properties of Human Skin In Vivo. Int J Cosmet Science, 2001, 23:353~362
33 O. H. Yeoh. Some Forms of the Strain Energy for Rubber . Rubber Chemical and Technology, 1993 ,66(5) : 711～754
34 E. H. Lee, J. R. M. Radok. The Contact Problem for Viscoelastic Bodies. Journal of Applied Mechanics, 1960, 27: 438~444
35 E. Samur, M. Sedef, C. Basdogan, L. Avtan, O. Duzgun. A Robotic Indenter for Quantification of Soft Tissues. International Congress Series, 2006, 28(4):235~240
36 S. M. Harrison, M. B. Bush, P. E. Petros. A pinch Elastometer for Soft Tissue. Medical Engineering & Physics, 2007, 29(3):307~315
37 J. Z. Wu, R. G. Dong. Analysis of the Point Mechanical Impedance of Finger pad in Vibration. Medical Engineering and Physics, 2006, 28(8): 816~826
38 E. M. H. Bosboom, M. K. C. Hesselink, C. W. J. Oomens, C. V. C. Bouten, M. R. Drost, F. P. T. Baaijens. Passive Transverse Mechanical Properties of Skeletal Muscle under in Vivo Compression. Journal of Biomechanics, 2001, 34(10): 1365~1368
39 H. Yamada. Strength of Biological Materials. Baltimore: Williams and Wilkins Co, 1970
2 N. Abolhassani, R. Patel, M. Moallem. Needleinsertion into soft tissue: A survey. Medical Engineering & Physics, 2007, (5):413~431
3 D. Lürding, Y. Baar, Ulrike, Hanstter. Application of Transversely Isotropic Materials to Multi-layer Shell Elements Undergoing Finite Rotations and Large Strains International Journal of Solids and Structures, 2001, (12):943~950
4 T.Johansson, P. Meier, R. Blickhan. A Finite-Element Model for the Mechanical Analysis of Skeletal Muscles. Journal of Theoretical, 2000, (9)
5 M. Kaua, V. Dual, G. Szikdy, M. Bajka. Inverse Finite Element Charanerhtion of Soft Tissues with Aspintion Experiments. Medical Image Analysis, 2002, 6(3):275~287
6 M. P. Ottensmeyer, A. E. Kerdok, R. D. Howe, S. L. Dawson. The Effects of Testing Environment on the Viscoelastic Properties of Soft Tissues. In: Proceedings of the International Symposium on Medical Simulation, 2004: 9~18
7 A. Manduca, T. E. Oliphant, M. A. Dresner, J. L. Mahowald, S. A. Kruse, E. Amromin, J. P. Felmlee, J. F. Greenleaf, R. L. Ehman. Magnetic Resonance Elastography Non Invasive Mapping of Tissue Elasticity. Medical Image Analysis, 2001, 5(4): 237~254
8 A. Weiss, B. N. Maker, S. Govindjee. Finite Element Implementation of Incompressible, Isotropic hyperelasticity. Computer Methods in Applied Mechanics and Engineering, 1996, 8(15):107~128
9 P. Agache, Physiologie de la peau et Explorations Fonctionnelle Scutanees, Collection Explorations Fonctionnelles Humaines, Editions Medicales Internationales. Technique&Documentation, 2000 :1850~1861
10 F. Tognella, A. Mainar, C. Vanhoutte, F. Goubel. A Mechanical Device for Studying Mechanical Properties of Human Muscles in Vivo. Journal ofBiomechanics, 1997, 30(10):1077~1080
11 J. L. Gennissona, C. Cornub, S. Cathelinea, M. Finka, P. Porterob. Human muscle hardness assessment during incremental isometric contraction using transient elastography. Journal of Biomechanics, 2005, (38): 1543~1550
12 P. Mattei, H. Zahouani. Study of Adhesion Strengthsand Mechanical Properties of Human Skin in Vivo. Journal of Adhesion Science and Technology, 2004, (18):17391758
13 E. M. H. Bosboom, M. K. C. Hesselink, C. W. J. Oomens, C. V. C. Bouten, M. R. Drost, F. P. T. Baaijens. Passive Transverse Mechanical Properties of Skeletal Muscle under in Vivo Compression. Journal of Biomechanics, 2001, 34(10): 1365~1368
14 M. Zhang, A. R. Turner-Smith, V. C. Roberts. The Reaction of Skin and Soft Tissue to Shear Forces Applied Externally to the Skin Surface. Proceedings of the Institution of Mechanical Engineers, 1994, 208 :217~222
15 C.C. Van Donkelaar, P. J. B. Willems, A. M. M. Muijtjen, M. R. Drost. Skeletal muscle transverse strain during isometric contraction at different lengths. Journal of Biomechanics, 1999, (32):755~762
16 C. W. J. Oomens, D. H. VanCampen, H. J. Grootenboer, L. J. DeBoer. Experimental and theoretical Compression on Porcine Skin, Biomechanics: Current Interdisciplinary Research. Selected Proceedings of Meetings of European Society of Biomechanics, 1984: 227~232
17 C. W. J. Oomens, D. H. VanCampen, H. J. Grootenboer. A Mixture Approach to the Mechanics of Skin. Journal of Biomechanics, 1987, 20(9):877~885
18 J. Asserin, H. Zahouani, P. Humbert, V. Couturaud, D. Mougin. Measurement of the Friction Coefficient of the Human Skin in Vivo. Quantification of the Cutaneous Smoothness Colloids and Surfaces. Biointerfaces, 2000, (19):1~12
19 F. Khatyr, C. Imberdis, P. Vescovo, D. Varchon, J. M. Lagarde. Model of The Viscoelastic Behaviour of Skin in Vivo and Study of Anisotropy. Skin Research and Technology, 2004, 10 (2): 96
20 V. Retel, P. Vescovo, E. Jacquet, D. Varchon, B. Burtheret. Non-linear Model of Skin Mechanical Behavior Analysis with Finite Element Method. Skin Research and Technology, 2001, (7): 152~158
21 E. Samur, M. Sedef, C. Basdogan, L. Avtan, O. Duzgun. A RoboticNndenter for Minimally Invasive Characterization of Soft Tissues. International Congress Series, 2005, (5): 713~718
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23 F. M. Hendriks, D. Brokken, C. W. J. Oomens, D. L. Bader, F. P. T. Baaijens. The Relative Contributions of Different Skin Layers to The Mechanical Behavior of Human Skin in Vivo Using Suction Experiments. Medical Engineering & Physics, 2006, 28(3):259~266
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