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Research Papers

A Nonlinear Viscoelastic Model for Adipose Tissue Representing Tissue Response at a Wide Range of Strain Rates and High Strain Levels

[+] Author and Article Information
Hosein Naseri

Mechanics and Maritime Sciences,
Chalmers University of Technology,
Gothenburg SE-412 96, Sweden
e-mail: hosein.naseri@chalmers.se

Håkan Johansson

Mechanics and Maritime Sciences,
Chalmers University of Technology,
Gothenburg SE-412 96, Sweden
e-mail: Hakan.Johansson@chalmers.se

Karin Brolin

Mechanics and Maritime Sciences,
Chalmers University of Technology,
Gothenburgkarin SE-412 96, Sweden
e-mail: brolin@chalmers.se

1Corresponding author.

Manuscript received May 30, 2017; final manuscript received October 9, 2017; published online February 12, 2018. Assoc. Editor: Thao (Vicky) Nguyen.

J Biomech Eng 140(4), 041009 (Feb 12, 2018) (8 pages) Paper No: BIO-17-1230; doi: 10.1115/1.4038200 History: Received May 30, 2017; Revised October 09, 2017

Finite element human body models (FEHBMs) are nowadays commonly used to simulate pre- and in-crash occupant response in order to develop advanced safety systems. In this study, a biofidelic model for adipose tissue is developed for this application. It is a nonlinear viscoelastic model based on the Reese et al.'s formulation. The model is formulated in a large strain framework and applied for finite element (FE) simulation of two types of experiments: rheological experiments and ramped-displacement experiments. The adipose tissue behavior in both experiments is represented well by this model. It indicates the capability of the model to be used in large deformation and wide range of strain rates for application in human body models.

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References

Hardy, W. N. , Howes, M. K. , Kemper, A. R. , and Rouhana, S. W. , 2015, “ Impact and Injury Response of the Abdomen,” Accidental Injury, Springer, New York, pp. 373–434. [CrossRef]
Jehle, D. , Gemme, S. , and Jehle, C. , 2012, “ Influence of Obesity on Mortality of Drivers in Severe Motor Vehicle Crashes,” Am. J. Emerg. Med., 30(1), pp. 191–195. [CrossRef] [PubMed]
Shi, X. , Cao, L. , Reed, M. P. , Rupp, J. D. , and Hu, J. , 2015, “ Effects of Obesity on Occupant Responses in Frontal Crashes: A Simulation Analysis Using Human Body Models,” Comput. Methods Biomech. Biomed. Eng., 18(12), pp. 1280–1292. [CrossRef]
Desapriya, E. , Giulia, S. , Subzwari, S. , Peiris, D. C. , Turcotte, K. , Pike, I. , Sasges, D. , and Hewapathirane, D. S. , 2014, “ Does Obesity Increase the Risk of Injury or Mortality in Motor Vehicle Crashes? A Systematic Review and Meta-Analysis,” Asia-Pac. J. Public Health, 26(5), pp. 447–460. [CrossRef] [PubMed]
Rouhana, S. W. , 2002, “ Biomechanics of Abdominal Trauma,” Accidental Injury, Springer, New York, pp. 405–453.
Iwamoto, M. , Kisanuki, Y. , Watanabe, I. , Furusu, K. , Miki, K. , and Hasegawa, J. , 2002, “ Development of a Finite Element Model of the Total Human Model for Safety (THUMS) and Application to Injury Reconstruction,” International Research Council on Biomechanics of Injury Conference (IRCOBI), Munich, Germany, Sept. 18–20, pp. 31–42. http://www.ircobi.org/wordpress/downloads/irc0111/2002/Session1/1.2.pdf
Mendoza-Vazquez, M. , Davidsson, J. , and Brolin, K. , 2015, “ Construction and Evaluation of Thoracic Injury Risk Curves for a Finite Element Human Body Model in Frontal Car Crashes,” Accid. Anal. Prev., 85, pp. 73–82. [CrossRef] [PubMed]
Brolin, K. , Östh, J. , Svensson, M. , Sato, F. , Ono, K. , Linder, A. , and Kullgren, A. , 2015, “ Aiming for an Average Female Virtual Human Body Model for Seat Performance Assessment in Rear-End Impacts,” The 24th International Technical Conference on the Enhanced Safety of Vehicles (ESV), Gothenburg, Sweden, June 8–11, Paper No. 15-0247 http://publications.lib.chalmers.se/publication/220923-aiming-for-an-average-female-virtual-human-body-model-for-seat-performance-assessment-in-rear-end-im.
Tiwari, G. , and Mohan, D. , 2016, Transport Planning and Traffic Safety Making Cities, Roads, and Vehicles Safer, CRC Press, Boca Raton, FL, p. 362.
Nusholtz, G. S. , Kaiker, P. S. , Huelke, D. F. , and Suggitt, B. R. , 1985, “ Thoraco-Abdominal Response to Steering Wheel Impacts,” SAE Paper No. 851737.
Cavanaugh, J. M. , Nyquist, G. W. , Goldberg, S. J. , and King, A. I. , 1986, “ Lower Abdominal Tolerance and Response,” SAE Paper No. 861878.
Miller, M. A. , 1989, “ The Biomechanical Response of the Lower Abdomen to Belt Restraint Loading,” J. Trauma Acute Care Surg., 29(11), pp. 1571–1584. [CrossRef]
Foster, C. D. , Hardy, W. N. , Yang, K. H. , King, A. I. , and Hashimoto, S. , 2006, “ High-Speed Seatbelt Pretensioner Loading of the Abdomen,” Stapp Car Crash J., 50, pp. 27–51. https://www.ncbi.nlm.nih.gov/pubmed/17311158
Hardy, W. N. , Schneider, L. W. , and Rouhana, S. W. , 2001, “ Abdominal Impact Response to Rigid-Bar, Seatbelt, and Airbag Loading,” Stapp Car Crash J., 45, pp. 1–32. https://www.ncbi.nlm.nih.gov/pubmed/17458738 [PubMed]
Viano, D. C. , 1989, “ Biomechanical Responses and Injuries in Blunt Lateral Impact,” SAE Paper No. 892432.
Ruan, J. S. , El-Jawahri, R. , Barbat, S. , and Prasad, P. , 2005, “ Biomechanical Analysis of Human Abdominal Impact Responses and Injuries Through Finite Element Simulations of a Full Human Body Model,” Stapp Car Crash J., 49, pp. 343–366. https://www.ncbi.nlm.nih.gov/pubmed/17096281
Geerligs, M. , Peters, G. W. , Ackermans, P. A. , Oomens, C. W. , and Baaijens, F. , 2008, “ Linear Viscoelastic Behavior of Subcutaneous Adipose Tissue,” Biorheology, 45(6), pp. 677–688. [PubMed]
Geerligs, M. , Peters, G. W. , Ackermans, P. A. , Oomens, C. W. , and Baaijens, F. P. , 2010, “ Does Subcutaneous Adipose Tissue Behave as an (Anti-)Thixotropic Material?,” J. Biomech., 43(6), pp. 1153–1159. [CrossRef] [PubMed]
Comley, K. , and Fleck, N. , 2012, “ The Compressive Response of Porcine Adipose Tissue From Low to High Strain Rate,” Int. J. Impact Eng., 46, pp. 1–10. [CrossRef]
Gefen, A. , and Haberman, E. , 2007, “ Viscoelastic Properties of Ovine Adipose Tissue Covering the Gluteus Muscles,” ASME J. Biomech. Eng., 129(6), pp. 924–930. [CrossRef]
Sommer, G. , Eder, M. , Kovacs, L. , Pathak, H. , Bonitz, L. , Mueller, C. , Regitnig, P. , and Holzapfel, G. A. , 2013, “ Multiaxial Mechanical Properties and Constitutive Modeling of Human Adipose Tissue: A Basis for Preoperative Simulations in Plastic and Reconstructive Surgery,” Acta Biomater., 9(11), pp. 9036–9048. [CrossRef] [PubMed]
Comley, K. , and Fleck, N. A. , 2010, “ A Micromechanical Model for the Young's Modulus of Adipose Tissue,” Int. J. Solids Struct., 47(21), pp. 2982–2990. [CrossRef]
Bilston, L. E. , Liu, Z. , and Phan-Thien, N. , 2001, “ Large Strain Behaviour of Brain Tissue in Shear: Some Experimental Data and Differential Constitutive Model,” Biorheology, 38(4), pp. 335–345. https://content.iospress.com/articles/biorheology/bir113 [PubMed]
El Sayed, T. , Mota, A. , Fraternali, F. , and Ortiz, M. , 2008, “ Biomechanics of Traumatic Brain Injury,” Comput. Methods Appl. Mech. Eng., 197(51), pp. 4692–4701. [CrossRef]
Hrapko, M. , Van Dommelen, J. , Peters, G. , and Wismans, J. , 2006, “ The Mechanical Behaviour of Brain Tissue: Large Strain Response and Constitutive Modelling,” Biorheology, 43(5), pp. 623–636. https://content.iospress.com/articles/biorheology/bir436 [PubMed]
Brands, D. , Peters, G. , and Bovendeerd, P. , 2004, “ Design and Numerical Implementation of a 3-D Non-Linear Viscoelastic Constitutive Model for Brain Tissue During Impact,” J. Biomech., 37(1), pp. 127–134. [CrossRef] [PubMed]
Brands, D. W. , Bovendeerd, P. H. , and Wismans, J. , 2002, “ On the Potential Importance of Non-Linear Viscoelastic Material Modelling for Numerical Prediction of Brain Tissue Response: Test and Application,” Stapp Car Crash J., 46, pp. 103–121. https://www.ncbi.nlm.nih.gov/pubmed/17096221
Hrapko, M. , Van Dommelen, J. , Peters, G. , and Wismans, J. , 2009, “ On the Consequences of Non Linear Constitutive Modelling of Brain Tissue for Injury Prediction With Numerical Head Models,” Int. J. Crashworthiness, 14(3), pp. 245–257. [CrossRef]
Darvish, K. , and Crandall, J. , 2001, “ Nonlinear Viscoelastic Effects in Oscillatory Shear Deformation of Brain Tissue,” Med. Eng. Phys., 23(9), pp. 633–645. [CrossRef] [PubMed]
Davidsson, J. , and Risling, M. , 2015, “ Characterization of the Pressure Distribution in Penetrating Traumatic Brain Injuries,” Front. Neurol., 6(51), pp. 1–12. [PubMed]
Mihai, L. A. , Chin, L. , Janmey, P. A. , and Goriely, A. , 2015, “ A Comparison of Hyperelastic Constitutive Models Applicable to Brain and Fat Tissues,” J. R. Soc., Interface, 12(110), p. 20150486. [CrossRef]
Franceschini, G. , Bigoni, D. , Regitnig, P. , and Holzapfel, G. A. , 2006, “ Brain Tissue Deforms Similarly to Filled Elastomers and Follows Consolidation Theory,” J. Mech. Phys. Solids, 54(12), pp. 2592–2620. [CrossRef]
Bilston, L. E. , Liu, Z. , and Phan-Thien, N. , 1997, “ Linear Viscoelastic Properties of Bovine Brain Tissue in Shear,” Biorheology, 34(6), pp. 377–385. [CrossRef] [PubMed]
Nicolle, S. , Lounis, M. , Willinger, R. , and Palierne, J.-F. , 2005, “ Shear Linear Behavior of Brain Tissue Over a Large Frequency Range,” Biorheology, 42(3), pp. 209–223. https://content.iospress.com/articles/biorheology/bir351 [PubMed]
Reese, S. , and Govindjee, S. , 1998, “ A Theory of Finite Viscoelasticity and Numerical Aspects,” Int. J. Solids Struct., 35(26–27), pp. 3455–3482. [CrossRef]
Bonet, J. , and Wood, R. D. , 1997, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, New York.
Bathe, K.-J. , 2006, Finite Element Procedures, Massachusetts Institute of Technology, Cambridge, MA.
Bathe, K.-J. , Ramm, E. , and Wilson, E. L. , 1975, “ Finite Element Formulations for Large Deformation Dynamic Analysis,” Int. J. Numer. Methods Eng., 9(2), pp. 353–386. [CrossRef]
Bathe, K.-J. , and Baig, M. M. I. , 2005, “ On a Composite Implicit Time Integration Procedure for Nonlinear Dynamics,” Comput. Struct., 83(31), pp. 2513–2524. [CrossRef]
Bathe, K.-J. , and Noh, G. , 2012, “ Insight Into an Implicit Time Integration Scheme for Structural Dynamics,” Comput. Struct., 98–99, pp. 1–6. [CrossRef]
Tanner, R. I. , 2000, Engineering Rheology, Vol. 52, Oxford University Press, Oxford, UK.
Naseri, H. , Johansson, H. , and Brolin, K. , 2016, “ Modeling the Mechanical Behavior of Adipose Tissue,” 29th Nordic Seminar on Computational Mechanics (NSCM-29), Gothenburg, Sweden, Oct. 26–28, p. 4. http://publications.lib.chalmers.se/records/fulltext/247689/local_247689.pdf
Pipkin, A. C. , 2012, Lectures on Viscoelasticity Theory, Vol. 7, Springer Science & Business Media, New York.

Figures

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Fig. 1

Schematic illustration of characterizing adipose tissue response in the unknown region specified by a question mark based on known regions A and B

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Fig. 2

(a) Generalized Maxwell model and (b) schematic representation of the multiplicative decomposition of the deformation gradient tensor F [35]. Fv is inelastic part of F which transfers the initial configuration to the intermediate configuration. Then Fe, elastic part of F, transfers the intermediate configuration to the current configuration.

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Fig. 3

Schematic illustration of ramped displacement experiment at constant shear strain and different rates [18]

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Fig. 4

The FE model for adipose tissue samples and its four node quadrilateral element in cylindrical coordinates

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Fig. 5

The effect of inertia with increasing ω from a to b in a typical virtual rotational rheometer test [42]. The used parameters: μe=0.6 kPa,μv(1,2,3,4,5)={2,4,7,13,20}kPa,t⋆(1,2,3,4,5)={4500,600,28,10,4} s,nc=1.75 and τc = 30 kPa.

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Fig. 6

The first calibration approach: frequency sweep results: model fit for ω = {1, 10, 100} and model prediction for the remaining frequency responses in the frequency sweep experiment

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Fig. 7

The first calibration approach: model prediction of adipose tissue response in the ramped displacement test: (a) ε˙=1 s−1 and (b) ε˙=0.1 s−1

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Fig. 8

The second calibration approach: (a) model fit for ε˙=1 s−1, (b) model prediction for ε˙=0.1 s−1, and (c) model prediction for ε˙=0.01 s−1

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Fig. 9

The second calibration approach: model prediction for the frequency sweep test

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Fig. 10

The third calibration approach: model prediction for the frequency sweep test

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Fig. 11

The third calibration approach: (a) model fit for the ε˙=1 s−1, (b) model prediction for the ε˙=0.1 s−1, and (c) model prediction for the ε˙=0.01 s−1

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Fig. 12

Adipose tissue response at high strain rates and large deformation: solid lines are test data from Ref. [19] and dashed lines are model prediction from different calibration approaches

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