Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Engineering with Computers
Published in: Engineering with Computers 5/2022

07-10-2022 | Original Article

A novel fully adaptive truly explicit time-marching methodology for the solution of hyperbolic bioheat conduction models

Authors: Lucas Ruffo Pinto, Delfim Soares Jr., Webe João Mansur

Published in: Engineering with Computers | Issue 5/2022

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this work, a truly explicit time-marching methodology is discussed for the time-domain solution for heat propagation considering the dual-phase-lag (DPL) bioheat model. The proposed technique considers self-adjustable time integration parameters, and it is approached together with automated calculations of domain decomposition and subcycling, providing a very versatile fully adaptive solution algorithm. The discussed domain decomposition procedure automatically divides the domain model into different subdomains (according to the properties of the discretized problem), in which different time-step values are applied, enabling more efficient (yet stable) explicit analyses. Expressions for the adaptive time integration parameters of the method and for the critical time steps of the subdomains of the model are presented and discussed. At the end of the paper, benchmark and applied examples are studied, showing the excellent performance of the proposed approach and the great effectiveness of the discussed fully adaptive formulation.
previous article Data-driven modeling of the mechanical behavior of anisotropic soft biological tissue
next article Enhanced grasshopper optimization algorithm using elite opposition-based learning for solving real-world engineering problems

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Minkowycz WJ, Sparrow EM, Murthy JY, Abraham JP (2007) Handbook of Numerical Heat Transfer, 2nd edn. Wiley, New Jersey
2.
Liu J, Xu LX (2000) Boundary information based diagnostics on the thermal states of biological bodies. Int J Heat Mass Transf 43(16):2827–39MATHCrossRef
3.
Torvi DA, Dale JD (1994) A finite element model of skin subjected to a flash fire. J Biomech Eng 116(3):250–5CrossRef
4.
Dai W, Yu H, Nassar R (2004) A fourth-order compact finite-difference scheme for solving a 1-D pennes’ bioheat transfer equation in a triple-layered skin structure. Numer Heat Transf, B: Fundam 46(5):447–61CrossRef
5.
Chan CL (1992) Boundary element method analysis for the bioheat transfer equation. J Biomech Eng 113(4):358–65CrossRef
6.
Tzou DY. A unified field approach for heat conduction from macro- to microscales. J. Heat Transfer. 1995;117.
7.
Liu J, Chen X, Xu LX (1999) New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating. IEEE Trans Biomed Eng. 46(4):420–8CrossRef
8.
Özen Ş, Helhel S, Çerezci O (2008) Heat analysis of biological tissue exposed to microwave by using thermal wave model of bio-heat transfer (TWMBT). Burns 34(1):45–49CrossRef
9.
Liu KC (2008) Thermal propagation analysis for living tissue with surface heating. Int J Therm Sci. 47(5):507–513CrossRef
10.
Xu F, Seffen KA, Lu TJ (2008) Non-Fourier analysis of skin biothermomechanics. Int J Heat Mass Transf 51(9–10):2237–2259MATHCrossRef
11.
Loureiro FS, Wrobel LC, Mansur WJ (2012) Solution of hyperbolic bioheat transfer problems by numerical Green’s functions: the ExGA-linear θ method. J Braz Soc Mech Sci Eng 34(4):459–468CrossRef
12.
Cattaneo C (1958) A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Compte Rendus. 247(4):431MATH
13.
Vernotte P (1961) Some possible complications in the phenomena of thermal studies. Compete Rendus 252:2190–2191
14.
Tzou DY (2014) Macro- to microscale heat transfer: the lagging behavior, 2nd edn. John wiley & sons, New JerseyCrossRef
15.
Askarizadeh H, Ahmadikia H (2015) Analytical study on the transient heating of a two-dimensional skin tissue using parabolic and hyperbolic bioheat transfer equations. Appl Math Model 39(13):3704–20MathSciNetMATHCrossRef
16.
Hobiny AD, Abbas IA (2020) Nonlinear analysis of dual-phase lag bio-heat model in living tissues induced by laser irradiation. J Therm Stress 43(4):503–511CrossRef
17.
Jasiński M, Majchrzak E, Turchan L (2016) Numerical analysis of the interactions between laser and soft tissues using generalized dual-phase lag equation. Appl Math Model 40(2):750–62MathSciNetMATHCrossRef
18.
Zhang Q, Sun Y, Yang J (2021) Thermoelastic behavior of skin tissue induced by laser irradiation based on the generalized dual-phase lag model. J Therm Biol 100:103038CrossRef
19.
Zhou H, Li P, Zuo W, Fang Y (2020) Dual-phase-lag thermoelastic damping models for micro/nanobeam resonators. Appl Math Model 79:31–51MathSciNetMATHCrossRef
20.
Liu L, Zheng L, Chen Y (2018) Macroscopic and microscopic anomalous diffusion in comb model with fractional dual-phase-lag model. Appl Math Model 62:629–637MathSciNetMATHCrossRef
21.
Shah FA, Awana MI (2020) A computational wavelet method for solving dual-phase-lag model of bioheat transfer during hyperthermia treatment. Comput Math Methods 2(4):e1095MathSciNetCrossRef
22.
Kumar M, Rai KN, Rajeev. (2020) A study of fractional order dual-phase-lag bioheat transfer model. J Therm Biol 93:102661CrossRef
23.
Fahmy MA (2021) A new boundary element algorithm for a general solution of nonlinear space-time fractional dual-phase-lag bio-heat transfer problems during electromagnetic radiation. Case Stud Therm Eng. 25:100918CrossRef
24.
Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis. Dover Publications INC, New YorkMATH
25.
Zienkiewicz O, Taylor R, Zhu JZ (2013) The Finite Element Method: its Basis and Fundamentals, 7th edn. Elsevier, AmsterdamMATH
26.
Soares D (2021) Three novel truly-explicit time-marching procedures considering adaptive dissipation control. Eng Comput 38:3251–3268CrossRef
27.
Pinto LR, Soares D, Mansur WJ (2021) Elastodynamic wave propagation modelling in geological structures considering fully-adaptive explicit time-marching procedures. Soil Dyn Earthq Eng 150:106962CrossRef
28.
Gravouil A, Combescure A (2001) Multi-time-step explicit - implicit method for non-linear structural dynamics. Int J Numer Methods Eng 50(1):199–225MATHCrossRef
29.
Dujardin G, Lafitte P (2016) Asymptotic behaviour of splitting schemes involving time-subcycling techniques. IMA J Numer Anal 36(4):1804–1841MathSciNetMATHCrossRef
30.
Soares D, Mansur WJ, Lima DL (2007) An explicit multi-level time-step algorithm to model the propagation of interacting acoustic-elastic waves using finite element/finite difference coupled procedures. CMES Comput Model Eng Sci. 17(1):19MathSciNetMATH
31.
Hulbert GM, Chung J (1996) Explicit time integration algorithms for structural dynamics with optimal numerical dissipation. Comput Methods Appl Mech Eng. 137(2):1785–188MathSciNetMATHCrossRef
32.
Noh G, Bathe KJ (2013) An explicit time integration scheme for the analysis of wave propagations. Comput Struct 129:178–193CrossRef
33.
Soares D (2021) A multi-level explicit time-marching procedure for structural dynamics and wave propagation models. Comput Methods Appl Mech Eng 375:1136MathSciNetMATHCrossRef
34.
Soares D (2021) A novel single-step explicit time-marching procedure with improved dissipative, dispersive and stability properties. Comput Methods Appl Mech Eng 386:114077MathSciNetMATHCrossRef
35.
Pennes HH (1998) Analysis of tissue and arterial blood temperatures in the resting human forearm. J Appl Physiol 85(1):5–34CrossRef
36.
Nazmdeh H, Vahabi M, Nazari MA (2021) Finite element modeling of Non-Fourier heat transfer in a cancerous tissue with an injected fat layer during hyperthermia treatment. J Therm Biol 100:103073CrossRef
37.
Figueiredo AAA, Nascimentodo JG, Malheiros FC, Silva Ignacioda LH, Fernandes HC, Guimaraes G (2019) Breast tumor localization using skin surface temperatures from a 2D anatomic model without knowledge of the thermophysical properties. Comput Methods Programs Biomed 172:65–77CrossRef
38.
Paruch M (2020) Mathematical modeling of breast tumor destruction using fast heating during radiofrequency ablation. Materials 13(1):136CrossRef
39.
Soares D, Wrobel LC (2018) Solution of hyperbolic bioheat conduction models based on adaptive time integrators. Finite Elem Anal Des 149:1–14MathSciNetCrossRef
40.
PDQ Adult Treatment Editorial Board. (2002) Breast Cancer Treatment During Pregnancy (PDQ®): Patient Version. In: PDQ Cancer Information Summaries. National Cancer Institute, US
41.
Roetzel W, Xuan Y (1998) Transient response of the human limb to an external stimulus. Int J Heat Mass Transf 41(1):221–239MATHCrossRef
42.
Feldmann A, Wili P, Maquer G, Zysset P (2018) The thermal conductivity of cortical and cancellous bone. Eur Cells Mater 35:25–33CrossRef
43.
Karmani S (2006) The thermal properties of bone and the effects of surgical intervention. Curr Orthop. 20(1):52–58CrossRef
44.
Liu KC, Chen HT (2009) Analysis for the dual-phase-lag bio-heat transfer during magnetic hyperthermia treatment. Int J Heat Mass Transf 52(5–6):1214–1222MATH
Metadata
Title
A novel fully adaptive truly explicit time-marching methodology for the solution of hyperbolic bioheat conduction models
Authors
Lucas Ruffo Pinto
Delfim Soares Jr.
Webe João Mansur
Publication date
07-10-2022
Publisher
Springer London
Published in
Engineering with Computers / Issue 5/2022
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-022-01739-x

Other articles of this Issue 5/2022

Engineering with Computers 5/2022 Go to the issue

Original Article

Correlating tau pathology to brain atrophy using a physics-based Bayesian model

Original Article

A finite element based optimization algorithm to include diffusion into the analysis of DCE-MRI

Original Article

FORNITS : a flexible variable step size non-iterative co-simulation method handling subsystems with hybrid advanced capabilities

Original Article

The design and application of a diffusion tensor informed finite-element model for exploration of uniaxially prestressed muscle architecture in magnetic resonance imaging

Original Article

IFOSMONDI Co-simulation Algorithm with Jacobian-Free Methods in PETSc

Original Article

An ABAQUS® plug-in for generating virtual data required for inverse analysis of unidirectional composites using artificial neural networks