Skip to main content
Log in

Modeling lung tissue dynamics and injury under pressure and impact loading

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

A nonlinear viscoelastic model for the lung is implemented and evaluated for high-rate loading. Principal features of the model include a closed-cell approximation of the bulk compressibility accounting for air inside the lung and a damage-injury component by which local trauma is induced by cumulative normalized internal energy and amplified by gradients of energy density. The latter feature is adapted for use in standard numerical (i.e., explicit finite element) simulations in terms of the local rate of strain energy density and the longitudinal wave speed. Injury predictions for direct loading of a block of extracted lung material, rather than the entire thorax, via pressure pulses are in reasonably close agreement with experimental observations for an extracted rabbit lung: a threshold applied pressure exists above which edema is observed experimentally, correlating with low but non-negligible damage in the numerical results. Responses to impact by cylindrical and spherical projectiles are also interrogated. Penetration depths are comparable to those observed experimentally, as is drastically increasing damage with increasing impact velocity. Damage initiates and propagates from the impact surface, with local severity of injury decreasing with distance from the impact zone, in agreement with some empirical evidence. The model predicts more severe local injury, relative to the aforementioned surface pressure loading, than what is observed experimentally. Possible reasons for the discrepancy are analyzed, and adjustments to the model, with caveats, are suggested accordingly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  • Birzle AM, Hobrack SMK, Martin C, Uhlig S, Wall WA (2019) Constituent-specific material behavior of soft biological tissue: experimental quantification and numerical identification for lung parenchyma. Biomech Model Mechanobiol 18:1383–1400

    Google Scholar 

  • Bowen IG, Fletcher ER, Richmond DR (1968) Estimate of man’s tolerance to the direct effects of air blast. Technical report, Lovelace Foundation for Medical Education and Research, Albuquerque NM

  • Butler JP, Lehr JL, Drazen JM (1987) Longitudinal elastic wave propagation in pulmonary parenchyma. J Appl Physiol 62:1349–1355

    Google Scholar 

  • Chen H, Wang Z, Ning X, Xu H, Xiao K (2001) Animal study on lung injury caused by simulant segmented shock waves. Clin J Traumatol 4:37–39

    Google Scholar 

  • Clayton JD (2017) Generalized Finsler geometric continuum physics with applications in fracture and phase transformations. Z Angew Math Phys 68:9

    MathSciNet  MATH  Google Scholar 

  • Clayton JD (2019) Nonlinear elastic and inelastic models for shock compression of crystalline solids. Springer, Cham

    MATH  Google Scholar 

  • Clayton JD (2020) Compatibility conditions from a Gram–Schmidt decomposition of deformation gradient in two dimensions. Mech Res Commun 104(103498):1–6

    Google Scholar 

  • Clayton JD, Freed AD (2019a) A continuum mechanical model of the lung. Technical report ARL-8859, Army Research Laboratory, Aberdeen Proving Ground, MD

  • Clayton JD, Freed AD (2019b) Viscoelastic-damage theory based on a QR decomposition of deformation gradient. Technical report ARL-8840, Army Research Laboratory, Aberdeen Proving Ground, MD

  • Clayton JD, Freed AD (2020a) A constitutive model for lung mechanics and injury applicable to static, dynamic, and shock loading. Mech Soft Mater 2(3):1–35

    Google Scholar 

  • Clayton JD, Freed AD (2020b) A constitutive framework for finite viscoelasticity and damage based on the Gram-Schmidt decomposition. Acta Mech (in press)

  • Clayton JD, Knap J (2016) Phase field modeling of coupled fracture and twinning in single crystals and polycrystals. Comput Methods Appl Mech Eng 312:447–467

    MathSciNet  MATH  Google Scholar 

  • Clayton JD, Banton RJ, Freed AD (2020) A nonlinear thermoelastic-viscoelastic continuum model of lung mechanics for shock wave analysis. In: AIP conference proceedings (in press)

  • Cooper GJ, Jonsson A (1997) Protection against blast injury. In: Cooper GJ, Dudley HAF, Gann DS, Little RA, Maynard RL (eds) Scientific foundations of trauma. Butterworth Heinemann, Oxford, pp 258–283

    Google Scholar 

  • Cooper GJ, Pearce BP, Sedman AJ, Bush IS, Oakley CW (1996) Experimental evaluation of a rig to simulate the response of the thorax to blast loading. J Trauma Acute Care Surg 40:38S–41S

    Google Scholar 

  • Cronin DS (2011) Model for pulmonary response resulting from high deformation rate loading. In: Proceedings of the 2011 international research council on biomechanics of injury (IRCOBI) conference, Krakow (Poland), pp 181–192

  • Davison L (2008) Fundamentals of shock wave propagation in solids. Springer, Berlin

    MATH  Google Scholar 

  • Denny E, Schroter RC (2006) A model of non-uniform lung parenchyma distortion. J Biomech 39:652–663

    Google Scholar 

  • Dewey JM (2010) The shape of the blast wave: studies of the Friedlander equation. In: Proceedings of the 21st international symposium on military aspects of blast and shock, Jerusalem (Israel),

  • D’yachenko AI, Manyuhina OV (2006) Modeling of weak blast wave propagation in the lung. J Biomech 39:2113–2122

    Google Scholar 

  • Freed AD (2017) A note on stress/strain conjugate pairs: explicit and implicit theories of thermoelasticity for anisotropic materials. Int J Eng Sci 120:155–171

    MathSciNet  MATH  Google Scholar 

  • Freed AD, Einstein DR (2012) Hypo-elastic moded for lung parenchyma. Biomech Model Mechanobiol 11:557–573

    Google Scholar 

  • Freed AD, Zamani S (2018) On the use of convected coordinate systems in the mechanics of continuous media derived from a QR factorization of F. Int J Eng Sci 127:145–161

    MathSciNet  MATH  Google Scholar 

  • Freed AD, Zamani S (2019) Elastic Kelvin-Poisson-Poynting solids described through scalar conjugate stress/strain pairs derived from a QR factorization of F. J Mech Phys Solids 129:278–293

    MathSciNet  Google Scholar 

  • Freed AD, Graverend JB, Rajagopal KR (2019) A decomposition of Laplace stretch with applications in inelasticity. Acta Mech 230:3423–3429

    MathSciNet  MATH  Google Scholar 

  • Friedlander FG (1946) The diffraction of sound pulses I. Diffraction by a semi-infinite plane. Proc R Soc Lond A 186:322–344

    MathSciNet  MATH  Google Scholar 

  • Fung Y-C (1967) Elasticity of soft tissues in simple elongation. Am J Physiol 213:1532–1544

    Google Scholar 

  • Fung Y-C (1975) Stress, deformation, and atelectasis of the lung. Circ Res 37:481–496

    Google Scholar 

  • Fung Y-C (1990) Biomechanics: motion, flow, stress, and growth. Springer, New York

    MATH  Google Scholar 

  • Fung Y-C, Patitucci P, Tong P (1978) Stress and strain in the lung. ASCE J Eng Mech 104:201–223

    Google Scholar 

  • Fung Y-C, Yen RT, Tao ZL, Liu SQ (1988) A hypothesis on the mechanism of trauma of lung tissue subjected to impact load. J Biomech Eng 110:50–56

    Google Scholar 

  • Gayzik FS, Hoth JJ, Daly M, Meredith JW, Stitzel JD (2007) A finite element-based injury metric for pulmonary contusion: investigation of candidate metrics through correlation with computed tomography. Stapp Car Crash J 51:189–209

    Google Scholar 

  • Gayzik FS, Hoth JJ, Stitzel JD (2011) Finite element-based injury metrics for pulmonary contusion via concurrent model optimization. Biomech Model Mechanobiol 10:505–520

    Google Scholar 

  • Gibbons MM, Dang X, Adkins M, Powell B, Chan P (2015) Finite element modeling of blast lung injury in sheep. J Biomech Eng 137:041002

    Google Scholar 

  • Grimal Q, Watzky A, Naili S (2002) A one-dimensional model for the propagation of transient pressure waves through the lung. J Biomech 35:1081–1089

    MATH  Google Scholar 

  • Grimal Q, Gama BA, Naili S, Watzky Al, Gillespie JW (2004) Finite element study of high-speed blunt impact on thorax: linear elastic considerations. Int J Impact Eng 30:665–683

    Google Scholar 

  • Grimal Q, Naili S, Watzky A (2005) A high-frequency lung injury mechanism in blunt thoracic impact. J Biomech 38:1247–1254

    Google Scholar 

  • Hajji MA, Wilson TA, Lai-Fook SJ (1979) Improved measurements of shear modulus and pleural membrane tension of the lung. J Appl Physiol 47:175–181

    Google Scholar 

  • Hallquist JO et al (2016a) LS-DYNA user’s manual R9.0. Livermore Software Technology Corporation, Livermore

    Google Scholar 

  • Hallquist JO et al (2016b) LS-DYNA theory manual R9.0. Livermore Software Technology Corporation, Livermore

    Google Scholar 

  • Holzapfel GA (1996) On large strain viscoelasticity: continuum formulation and finite element applications to elastomeric structures. Int J Numer Meth Eng 39:3903–3926

    MATH  Google Scholar 

  • Holzapfel GA, Simo JC (1996) A new viscoelastic constitutive model for continuous media at finite thermomechanical changes. Int J Solids Struct 33:3019–3034

    MATH  Google Scholar 

  • Hoppin FG, Lee GC, Dawson SV (1975) Properties of lung parenchyma in distortion. J Appl Physiol 39:742–751

    Google Scholar 

  • Hughes R, May AJ, Widdicombe JG (1959) Stress relaxation in rabbits’ lungs. J Physiol 146:85–97

    Google Scholar 

  • Humphrey JD, Vawter DL, Vito RP (1987) Pseudoelasticity of excised visceral pleura. J Appl Mech 109:115–120

    Google Scholar 

  • Jahed M, Lai-Fook SJ (1994) Stress wave velocity measured in intact pig lungs with cross-spectral analysis. J Appl Physiol 76:565–571

    Google Scholar 

  • Jahed M, Lai-Fook SJ, Bhagat PK, Kraman SS (1989) Propagation of stress waves in inflated sheep lungs. J Appl Physiol 66:2675–2680

    Google Scholar 

  • Lee GC, Frankus A (1975) Elasticity properties of lung parenchyma derived from experimental distortion data. Biophys J 15:481–493

    Google Scholar 

  • Lembo M (2017) On the determination of deformation from strain. Meccanica 52:2111–2125

    MathSciNet  MATH  Google Scholar 

  • Liu B, Wang Z, Leng H, Yang Z, Li X (1996) Relationship between the dynamic parameters and injury severity of chest subjected to impact. J Trauma 40:71–74

    Google Scholar 

  • McLellan AG (1976) Finite strain coordinates and the stability of solid phases. J Phys C: Solid State Phys 9:4083–4094

    Google Scholar 

  • Oldmixon EH, Hoppin FG (1989) Distribution of elastin and collagen in canine lung alveolar parenchyma. J Appl Physiol 67:1941–1949

    Google Scholar 

  • Ranunkel O, Guder F, Arora H (2019) Soft robotic surrogate lung. ACS Appl Bio Mater 2:1490–1497

    Google Scholar 

  • Regueiro RA, Zhang B, Wozniak SL (2014) Large deformation dynamic three-dimensional coupled finite element analysis of soft biological tissues treated as biphasic porous media. Comput Model Eng Sci 98:1–39

    MathSciNet  MATH  Google Scholar 

  • Rice DA (1983) Sound speed in pulmonary parenchyma. J Appl Physiol 54:304–308

    Google Scholar 

  • Sanborn B, Nie X, Chen W, Weerasooriya T (2013) High strain rate pure shear and axial compressive response of porcine lung tissue. J Appl Mech 80:011029

    Google Scholar 

  • Saraf H, Ramesh KT, Lennon AM, Merkle AC, Roberts JC (2007) Mechanical properties of soft human tissues under dynamic loading. J Biomech 40:1960–1967

    Google Scholar 

  • Shen W, Niu Y, Mattrey RF, Fournier A, Corbeil J, Kono Y, Stuhmiller JH (2008) Development and validation of subject-specific finite element models for blunt trauma study. J Biomech Eng 130:021022

    Google Scholar 

  • Simo JC (1987) On a fully three-dimensional finite-strain viscoelastic damage model: formulation and computational aspects. Comput Methods Appl Mech Eng 60:153–173

    MATH  Google Scholar 

  • Stitzel JD, Gayzik FS, Hoth JJ, Mercier J, Gage HD, Morton KA, Duma SM, Payne RM (2005) Development of a finite element-based injury metric for pulmonary contusion part I: model development and validation. Stapp Car Crash J 49:271–289

    Google Scholar 

  • Stuhmiller JH, Ho K, Vander Vorst MJ, Dodd KT, Fitzpatrick T, Mayorga M (1996) A model of blast overpressure injury to the lung. J Biomech 29:227–234

    Google Scholar 

  • Tao ZL, Fung YC (1987) Lungs under cyclic compression and expansion. J Biomech Eng 109:160–162

    Google Scholar 

  • Vawter DL (1980) A finite element model for macroscopic deformation of the lung. J Biomech Eng 102:1–7

    Google Scholar 

  • Vawter DL, Fung Y-C, West JB (1979) Constitutive equation of lung tissue elasticity. J Biomech Eng 101:38–45

    Google Scholar 

  • Yager D, Feldman H, Fung YC (1992) Microscopic vs. macroscopic deformation of the pulmonary alveolar duct. J Appl Physiol 72:1348–1354

    Google Scholar 

  • Yen RT, Fung YC, Ho HH, Butterman G (1986) Speed of stress wave propagation in lung. J Appl Physiol 61:701–705

    Google Scholar 

  • Yen RT, Fung YC, Liu SQ (1988) Trauma of lung due to impact load. J Biomech 21:745–753

    Google Scholar 

  • Zeng YJ, Yager D, Fung YC (1987) Measurement of the mechanical properties of the human lung tissue. J Biomech Eng 109:169–174

    Google Scholar 

  • Zhou H, Ma G (2010) Stress amplification effect of lung. Med Hypotheses 74:37–38

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. D. Clayton.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Clayton, J.D. Modeling lung tissue dynamics and injury under pressure and impact loading. Biomech Model Mechanobiol 19, 2603–2626 (2020). https://doi.org/10.1007/s10237-020-01358-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-020-01358-9

Keywords

Navigation