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Multiphysics computation of thermal tissue damage as a consequence of electric power absorption

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Abstract

Electrically induced tissue damage is a coupled phenomenon in multiphysics. Conducting electricity produces heat and this increases the temperature. The soft tissue like skin, organs, brain, or muscles is burnt under successive heating. This damage is modeled by using a damage parameter with a corresponding evolution law above a threshold temperature. Electromagnetism, thermomechanics, and damage modeling creates a set of coupled and nonlinear field equations, by solving them with the aid of the finite element method, we compute a realistic example where the tissue absorbs the electric energy, converts to heat, and gets burnt due to the excessive temperature increase.

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References

  1. Abali BE (2016) Technical University of Berlin, Institute of Mechanics, Chair of Continuum Mechanics and Material Theory, Computational Reality. http://www.lkm.tu-berlin.de/ComputationalReality/. Accessed 11 Jan 2019

  2. Abali BE (2017) Computational reality, solving nonlinear and coupled problems in continuum mechanics. Advanced structured materials, vol 55. Springer, Singapore

    MATH  Google Scholar 

  3. Abali BE, Müller WH (2015) Numerical modeling of thermoelectric coupling. In: Elgeti S, Simon J-W (eds) Conference proceedings of the YIC GACM 2015, 3rd ECCOMAS young investigators conference, pp 1–4. Publication server of RWTH Aachen University

  4. Abali BE, Queiruga AF (2019) Theory and computation of electromagnetic fields and thermomechanical structure interaction for systems undergoing large deformations. J Comput Phys 394:200–231

    Article  MathSciNet  Google Scholar 

  5. Abali BE, Reich FA (2017) Thermodynamically consistent derivation and computation of electro-thermo-mechanical systems for solid bodies. Comput Methods Appl Mech Eng 319:567–595

    Article  MathSciNet  Google Scholar 

  6. Abali BE, Reich FA (2018) Verification of deforming polarized structure computation by using a closed-form solution. Contin Mech Thermodyn. https://doi.org/10.1007/s00161-018-0709-8

  7. Abali BE, Zohdi TI (2018) On the accuracy of reduced-order integrated circuit simulators for computing the heat production on electronic components. J Comput Electron 17(2):625–636

    Article  Google Scholar 

  8. Alnaes MS, Mardal K-A (2010) On the efficiency of symbolic computations combined with code generation for finite element methods. ACM Trans Math Softw 37(1):6

    Article  MathSciNet  MATH  Google Scholar 

  9. Altenbach H, Altenbach J, Kissing W (2018) Mechanics of composite structural elements. Springer, Berlin

    Book  Google Scholar 

  10. Bossavit A (1988) Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism. IEE Proc A Phys Sci Meas Instrum Manag Educ Rev 135(8):493–500

    Article  Google Scholar 

  11. Cheng L, Hannaford B (2015) Finite element analysis for evaluating liver tissue damage due to mechanical compression. J Biomech 48(6):948–955

    Article  Google Scholar 

  12. Ciarlet P Jr, Zou J (1999) Fully discrete finite element approaches for time-dependent Maxwell’s equations. Numer Math 82(2):193–219

    Article  MathSciNet  MATH  Google Scholar 

  13. Cooper MA (1995) Emergent care of lightning and electrical injuries. Semin Neurol 15:268–278

    Article  Google Scholar 

  14. Cushing TA, Wright RK (2009) Electrical injuries. Emergency medicine web site. Available at: http://emedicine.medscape.com/article/770179-overview

  15. Demkowicz L (2006) Computing with HP-adaptive finite elements: one and two dimensional elliptic and Maxwell problems, vol 1. CRC Press, Boca Raton

    Book  Google Scholar 

  16. Eswaran SK, Bayraktar HH, Adams MF, Gupta A, Hoffmann PF, Lee DC, Papadopoulos P, Keaveny TM (2007) The micro-mechanics of cortical shell removal in the human vertebral body. Comput Methods Appl Mech Eng 196(31–32):3025–3032

    Article  MATH  Google Scholar 

  17. Fontanarosa PB (1993) Electrical shock and lightning strike. Ann Emerg Med 22(2):378–387

    Article  Google Scholar 

  18. Freitas RA (1999) Nanomedicine, volume I: basic capabilities, vol 1. Landes Bioscience, Georgetown

    Google Scholar 

  19. Fung YC (1967) Elasticity of soft tissues in simple elongation. Am J Physiol Leg Content 213(6):1532–1544

    Article  Google Scholar 

  20. Fung YC (1983) On the foundations of biomechanics. J Appl Mech 50(4b):1003–1009

    Article  Google Scholar 

  21. Gatewood MOK, Zane RD (2004) Lightning injuries. Emerg Med Clin 22(2):369–403

    Article  Google Scholar 

  22. Gillette A, Rand A, Bajaj C (2016) Construction of scalar and vector finite element families on polygonal and polyhedral meshes. Comput Methods Appl Math 16(4):667–683

    Article  MathSciNet  MATH  Google Scholar 

  23. Giorgio I, Andreaus U, Lekszycki T, Corte AD (2017) The influence of different geometries of matrix/scaffold on the remodeling process of a bone and bioresorbable material mixture with voids. Math Mech Solids 22(5):969–987

    Article  MathSciNet  MATH  Google Scholar 

  24. GNU Public (2007) Gnu general public license. http://www.gnu.org/copyleft/gpl.html. Accessed 11 Jan 2019

  25. Henriques FC Jr, Moritz AR (1947) Studies of thermal injury: I. The conduction of heat to and through skin and the temperatures attained therein. A theoretical and an experimental investigation. Am J Pathol 23(4):530

    Google Scholar 

  26. Holzapfel GA, Ogden RW (2009) Biomechanical modelling at the molecular, cellular and tissue levels, vol 508. Springer, Berlin

    Book  Google Scholar 

  27. Humphrey JD (2013) Cardiovascular solid mechanics: cells, tissues, and organs. Springer, Berlin

    Google Scholar 

  28. Hutter K (1975) On thermodynamics and thermostatics of viscous thermoelastic solids in the electromagnetic fields. A Lagrangian formulation. Arch Ration Mech Anal 58(4):339–368

    Article  MathSciNet  MATH  Google Scholar 

  29. Kachanov L (1986) Introduction to continuum damage mechanics, vol 10. Springer, Berlin

    Book  MATH  Google Scholar 

  30. Lance A (2018) https://grabcad.com/library/hand-export-from-3dmax-to-solidworks-1. Accessed 11 Jan 2019

  31. Lederer W, Kroesen G (2005) Emergency treatment of injuries following lightning and electrical accidents. Der Anaesthesist 54(11):1120–1129

    Article  Google Scholar 

  32. Li J (2009) Numerical convergence and physical fidelity analysis for Maxwell’s equations in metamaterials. Comput Methods Appl Mech Eng 198(37):3161–3172

    Article  MathSciNet  MATH  Google Scholar 

  33. Logg A, Mardal KA, Wells GN (2011) Automated solution of differential equations by the finite element method, the FEniCS book. Lecture notes in computational science and engineering, vol 84. Springer, Berlin

    Google Scholar 

  34. Lorenz L (1867) On the identity of the vibrations of light with electrical currents. Lond Edinb Dublin Philos Mag J Sci 34(230):287–301

    Article  Google Scholar 

  35. Moritz A, Moritz AR, Henriques FC Jr (1947) Studies of thermal injury: II. The relative importance of time and surface temperature in the causation of cutaneous burns. Am J Pathol 23(5):695

    Google Scholar 

  36. Nédélec J-C (1980) Mixed finite elements in R3. Numer Math 35(3):315–341

    Article  MathSciNet  MATH  Google Scholar 

  37. Niyonzima I, Jiao Y, Fish J (2019) Modeling and simulation of nonlinear electro-thermo-mechanical continua with application to shape memory polymeric medical devices. Comput Methods Appl Mech Eng 350:511–534

    Article  MathSciNet  Google Scholar 

  38. Oliphant TE (2007) Python for scientific computing. Comput Sci Eng 9(3):10–20

    Article  Google Scholar 

  39. Pearce J (2018) Irreversible tissue thermal alterations: skin burns, thermal damage and cell death. Theory Appl Heat Transf Hum 2:553–590

    Article  Google Scholar 

  40. Placidi L, Barchiesi E (2018) Energy approach to brittle fracture in strain-gradient modelling. Proc R Soc A Math Phys Eng Sci 474(2210):20170878

    Article  MathSciNet  MATH  Google Scholar 

  41. Queiruga AF, Zohdi TI (2016) Formulation and numerical analysis of a fully-coupled dynamically deforming electromagnetic wire. Comput Methods Appl Mech Eng 305:292–315

    Article  MathSciNet  MATH  Google Scholar 

  42. Raviart PA, Thomas JM (1977) A mixed finite element method for 2-nd order elliptic problems. In: Galligani I, Magenes E (eds) Mathematical aspects of finite element methods. Lecture notes in mathematics, vol 606. Springer, Berlin, Heidelberg, pp 292–315

  43. Sapareto SA, Dewey WC (1984) Thermal dose determination in cancer therapy. Int J Radiat Oncol* Biol* Phys 10(6):787–800

    Article  Google Scholar 

  44. Stephen A, Adams CA, Cioffi WG (2012) Electrical injury-high-voltage current. In: Vincent JL, Hall JB (eds) Encyclopedia of intensive care medicine. Springer, Berlin, Heidelberg, pp 820–822

    Google Scholar 

  45. Wright NT (2015) Quantitative models of thermal damage to cells and tissues. In: Heat transfer and fluid flow in biological processes, pp 59–76. Elsevier

  46. Xu F, Lu TJ, Seffen KA (2008) Biothermomechanics of skin tissues. J Mech Phys Solids 56(5):1852–1884

    Article  MathSciNet  MATH  Google Scholar 

  47. Zohdi TI (2014) Modeling electrical power absorption and thermally-induced biological tissue damage. Biomech Model Mechanobiol 13(1):115–121

    Article  MathSciNet  Google Scholar 

  48. Zohdi TI, Abali BE (2018) Modeling of power transmission and stress grading for corona protection. Comput Mech 62(3):411–420

    Article  MathSciNet  MATH  Google Scholar 

  49. Zohdi TI (2018) Finite element primer for beginners. Springer, Berlin

    Book  MATH  Google Scholar 

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Acknowledgements

B. E. Abali’s work was partly supported by a Grant from the Daimler and Benz Foundation.

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Authors and Affiliations

  1. Institute of Mechanics, Technische Universität Berlin, Berlin, Germany

    B. Emek Abali

  2. Department of Mechanical Engineering, University of California, Berkeley, USA

    Tarek I. Zohdi

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  1. B. Emek Abali
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  2. Tarek I. Zohdi
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Correspondence to B. Emek Abali.

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Abali, B.E., Zohdi, T.I. Multiphysics computation of thermal tissue damage as a consequence of electric power absorption. Comput Mech 65, 149–158 (2020). https://doi.org/10.1007/s00466-019-01757-5

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