Skip to main content
SpringerLink
Log in

Parallel Computer Simulations of Heat Transfer in Biological Tissues

  • Chapter
Book cover Parallel Computing

Abstract

Parallel computer simulation of heat transfer in parts of the human body is described. Realistic geometric models and tissues with different thermodynamic properties are analyzed. The principal steps of the computer simulations, including mathematical and geometric modeling, domain discretization, numerical solution, validation of simulated results, and visualization, are described. An explicit finite difference method for the inhomogeneous computational domain has been developed and tested on the diffusion equation. The bio-heat equation, which incorporates heat conduction, heat transfer between blood and tissues and heat production by metabolism, was used in our analysis. Because of significant calculation complexity, a parallel simulation code was also implemented.

Domain decomposition and communication with messages have been selected in the parallel implementation of the explicit finite difference method. Mapping of the computational domain on the parallel computer was addressed, followed by theoretical performance analysis of the proposed parallel algorithm. The implementation of all simulation steps is shown in detail for the simulation of the steady-state temperature and its evolution in time for a human knee exposed to external conditions and to topical cooling. The results have been validated by experimental measurements. Execution time was measured on a computing cluster with different numbers of processors and compared with theoretical expectations. It is shown that parallel computer simulations can be of great use in medicine, either for planning surgery or for evaluating doctrines of medical treatment. The chapter concludes with a summary of the results and a list of relevant references from the research field.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. L. Martino, C. A. Johnson, E. B. Suh, et al., Parallel computing in biomedical-research, Science 265 (1994) 902–908.

    Article  Google Scholar 

  2. R. Rook, S. Dost, The use of smoothed particle hydrodynamics for simulating crystal growth from solution, Int J Eng Sci 45 (2007) 75–93.

    Article  MathSciNet  Google Scholar 

  3. Y. Aggarwal, B. M. Karan, B. N. Das, R. K. Sinha, Computer simulation of heat transfer in different tissue layers of body extremities under heat stress in deep anesthetic condition, JMed Syst 32 (2008) 283–90.

    Article  Google Scholar 

  4. M. Šterk, R. Trobec, Biomedical simulation of heat transfer in a human heart, J Chem Inf Mod 45 (2005) 1558–1563.

    Article  Google Scholar 

  5. T. Liszka, J. Orkisz, The finite difference method at arbitrary irregular grids and its application in applied mechanics, Comput Struct 11 (1980) 83–95.

    Article  MATH  MathSciNet  Google Scholar 

  6. K. T. Danielson, R. A. Uras, M. D. Adley, S. Li, Large-scale application of some modern CSM methodologies by parallel computation, Adv Eng Softw 31 (2000) 501–509.

    Article  MATH  Google Scholar 

  7. C. Hirsch, Numerical Computation of Internal and External Flows: Fundamentals of Computational Fluid Dynamics, Butterworth-Heinemann (2007).

    Google Scholar 

  8. A. Lipej, Optimization method for the design of axial hydraulic turbines, Proc Inst Mech Eng A – J Power Energy 218 (2004) 43–50.

    Article  Google Scholar 

  9. A. Horvat, M. Leskovar, B. Mavko, Comparison of heat transfer conditions in tube bundle cross-flow for different tube shapes, Int J Heat Mass Transfer 49 (2007) 1027–1038.

    Article  Google Scholar 

  10. L. F. Richardson, Weather Prediction by Numerical Process, Dover Publications, New York (1965).

    Google Scholar 

  11. B. Urban, D. Janežič, Symplectic molecular dynamics simulations on specially designed parallel computers, J Chem Inf Modell 45 (2005) 1600–1604.

    Article  Google Scholar 

  12. P. Bernardi, M. Cavagnaro, S. Pisa, E. Piuzzi, Specific absorption rate and temperature elevation in a subject exposed in the far-field of radio-frequency sources operating in the 10-900- MHz range, IEEE Trans Biomed Eng 50 (2003) 295–304.

    Article  Google Scholar 

  13. M. Depolli, V. Avbelj, R. Trobec, Computer-simulated alternative models of U-wave genesis, J Cardiovasc Electrophysiol 19 (2008) 84–89.

    Google Scholar 

  14. R. Trobec, B. Slivnik, B. Gersak, T. Gabrijelčič, Computer simulation and spatial modelling in heart surgery, Comput Biol Med 28 (1998) 393–403.

    Article  Google Scholar 

  15. M. J. Ackerman, The visible human project, Proc IEEE 86 (1998) 504–511.

    Article  Google Scholar 

  16. O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, Elsevier Butterworth-Heinemann (2005).

    MATH  Google Scholar 

  17. M. Šterk, R. Trobec, Meshless solution of a diffusion equation with parameter optimization and error analysis, Eng Anal Bound Elem 32 (2007) 567–577.

    Google Scholar 

  18. V. Nguyen, T. Rabczuk, S. Bordas, M. Duflot, Meshless methods: a review and computer implementation aspects, Math Comput Simul 79 (2008) 763–813.

    Article  MATH  MathSciNet  Google Scholar 

  19. M. T. Heath, Scientific Computing: An Introductory Survey, 2nd Ed., McGraw-Hill (2002).

    Google Scholar 

  20. S. G. Akl, Parallel Computation: Models and Methods, Prentice Hall, New Jersey (1997).

    Google Scholar 

  21. A. Sulistio, U. Cˇ ibej, S. Venugopal, B. Robicˇ, R. Buyya, A toolkit for modelling and simulating data Grids: an extension to GridSim, Concurr Comput Pract Exp 20 (2008) 1591–1609.

    Article  Google Scholar 

  22. I. Rozman, M. Šterk, J. Močnik, B. Robič, R. Trobec, Performance measurements of computing networks, Scalable Comput Pract Exp 9 (2008) 143U˝ –150.

    Google Scholar 

  23. A. A. C. Braga, Technical aspects of beowulf cluster construction, Quimica Nova 26 (2003) 401–406.

    Google Scholar 

  24. U. Borštnik, M. Hodošček, D. Janežič, Improving the performance of molecular dynamics simulations on parallel clusters, J Chem Inf Comput Sci 44 (2004) 359–364.

    Google Scholar 

  25. R. Trobec, U. Borštnik, D. Janežič, Communication performance of d-meshes in molecular dynamics simulation, J Math Chem DOI 10.1007/s10910-008-9423-2.

    Google Scholar 

  26. K. L. Knight, Cryotherapy: Theory, Technique and Physiology, Chatanooga Corporation, Chattanooga (1985).

    Google Scholar 

  27. S. S. Martin, K. P. Spindler, J.W. Tarter, K. Detwiler, H. A. Petersen, Cryotherapy: an effective modality for decreasing intraarticular temperature after knee arthroscopy, Am J Sports Med 29 (2001) 288–291.

    Google Scholar 

  28. S. S. Martin, K. P. Spindler, J. W. Tarter, K. Detwiler, H. A. Petersen, Accelerated rehabilitation after anterior cruciate ligament reconstruction, Am J Sports Med 18 (1990) 292–299.

    Article  Google Scholar 

  29. W. Grana, Cold modalities, in: J. C. DeLee and D. Drez (Eds.), Orthopaedic Sports Medicine, Principles and Practice, WB Saunders, Philadelphia (1994).

    Google Scholar 

  30. W. C. McMaster, S. Liddle, T. R.Waugh, Laboratory evaluation of various cold therapy modalities, Am J Sports Med 6 (1978) 291–294.

    Article  Google Scholar 

  31. D. H.Silverthorn, Human Physiology, An Integrated Approach, Prentice-Hall, New Jersey (2001).

    Google Scholar 

  32. H. H. Pennes, Analysis of tissue and arterial blood temperature in the resting human forearm, J Appl Physiol 1 (1948) 93–122.

    Google Scholar 

  33. H. F. Bowman, E. G. Cravalho, M. Woods, Theory, measurement, and application of thermal properties of biomaterials, Annu Rev Biophys Bioeng 4 (1975) 43–80.

    Article  Google Scholar 

  34. C. K. Charny, Mathematical models of bioheat transfer, in: Y.I. Cho (Ed.), Advances in Heat Transfer, Academic Press, New York (1992).

    Google Scholar 

  35. H. Barcroft, O. G. Edholm, Temperature and blood flow in the human forearm, J Physiol 104 (1946) 366–376.

    Google Scholar 

  36. M. B. Ducharme, W. P. VanHelder, M. W. Radomski, Tissue temperature profile in the human forearm during thermal stress at thermal stability, J Appl Physiol 71 (1991) 1973–1978.

    Google Scholar 

  37. E. H. Wissler, Pennes’ 1948 paper revisited, J Appl Physiol 85 (1998) 35–41.

    Google Scholar 

  38. R. Trobec, M. Šterk, S. AlMawed, M. Veselko, Computer simulation of topical knee cooling, Comput Biol Med 38 (2008) 1076–1083.

    Article  Google Scholar 

  39. S. Karthik, A. D. Grayson, A. Y. Oo, et al., A survey of current myocardial protection practices during coronary artery bypass grafting, Ann Roy Coll Surg 86 (2004) 413–415.

    Article  Google Scholar 

  40. C. L. Olin, I. E. Huljebrant, Topical cooling of the heart – a valuable adjunct to cold cardioplegia, Scand J Thorac Card 41 (1993) 55–58.

    Google Scholar 

  41. P. Trunk, B. Gersak, R. Trobec, Topical cardiac cooling – computer simulation of myocardial temperature changes, Comput Biol Med 33 (2003) 203–214.

    Article  Google Scholar 

  42. G. B. Pollard, Lectures on Partial Differential Equations, Wiley, New York (1964).

    Google Scholar 

  43. M. N. Özisik, Finite Difference Methods in Heat Transfer, CRC Press, Boca Raton (1994).

    MATH  Google Scholar 

  44. S. J. Owen, A survey of unstructured mesh generation technology, in: Proceedings of 7th International Meshing Roundtable, Sandia National Laboratories (1998), pp. 239–267.

    Google Scholar 

  45. T. Rabczuk, S. Bordas, G. Zi, A three-dimensional meshfree method for continuous crack initiation, nucleation and propagation in statics and dynamics, Comput Mech 40 (3) (2007) 473–495.

    Article  MATH  Google Scholar 

  46. M. Thuné, Straightforward partitioning of composite grids for explicit difference methods, Parallel Comput 17 (1991) 665–672.

    Article  MATH  MathSciNet  Google Scholar 

  47. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, London (1959).

    Google Scholar 

  48. P. Trunk, R. Trobec, B. Gersak, Measurement of porcine heart temperatures, Pflügers Arch 440 (2000) R132–R133.

    Article  Google Scholar 

  49. G. Golub, J. M. Ortega, Scientific Computing – An Introduction with Parallel Computing, Academic Press Inc., Boston (1993).

    MATH  Google Scholar 

  50. M. Vajteršic, Algorithms for Elliptic Problems, Efficient Sequential and Parallel Solvers, Kluwer Academic Publishers (1993).

    Google Scholar 

  51. H. A. van der Vorst, BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems, SIAM J Sci Stat Comput 13 (1992) 631–644.

    Article  MATH  Google Scholar 

  52. R. Barrett, M. Berry, T. F. Chan, et al., Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia (1994).

    Google Scholar 

  53. M. Šterk, R. Trobec, Parallel performance of a multigrid poisson solver, in: Proceedings of Second International Symposium on Parallel and Distributed Computing, IEEE Computer Soc (2003), pp. 238–243.

    Google Scholar 

  54. C. Shen, J. Zhang, Parallel two level block ILU preconditioning techniques for solving large sparse linear systems, Parallel Comput 28 (2002) 1451–1475.

    Article  MATH  MathSciNet  Google Scholar 

  55. R. Trobec, M. Šterk, B. Robič, Computational complexity and parallelization of the meshless ocal Petrov-Galerkin method, Comput Struct 87 (2009) 81–90.

    Article  Google Scholar 

  56. J. W. Mitchell, G. E. Myers, An analytical model of the counter-current heat exchange phenomena, Biophys J 8 (1968) 897–911.

    Article  Google Scholar 

  57. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing, Cambridge University Press, Cambridge (1986).

    MATH  Google Scholar 

  58. M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford (1987).

    MATH  Google Scholar 

  59. D. Janežič, M. Praprotnik, Molecular dynamics integration time step dependence of the split integration symplectic method on system density, J Chem Inf Comput Sci 43 (2003) 1922–1927.

    Google Scholar 

  60. I. Kuščer, A. Kodre, Mathematik in Physik und Technik, Springer Verlag, Berlin (1993).

    MATH  Google Scholar 

  61. M. Praprotnik, M. Šterk, R. Trobec, Inhomogeneous heat-conduction problems solved by a new explicit finite difference scheme, Int J Pure Appl Math 13 (2004) 275–291.

    MATH  MathSciNet  Google Scholar 

  62. M. B. Ducharme, P. Tikuisis, In vivo thermal conductivity of the human forearm tissues, J Appl Physiol 70 (1991) 2682–2690.

    Google Scholar 

  63. P. Tikuisis, M. B. Ducharme, Finite-element solution of thermal conductivity of muscle during cold water immersion, J Appl Physiol 70 (1991) 2673–2681.

    Google Scholar 

  64. The visible human project, United States National Library of Medicine, http www.nlmnih.gov/research/visible/getting_data.html;

  65. M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI – The Complete Reference, The MIT Press, Cambridge (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Communication Systems, Jožef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia

    Roman Trobec

Authors
  1. Roman Trobec
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roman Trobec .

Editor information

Editors and Affiliations

  1. Dept. Communication Systems, Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia

    Roman Trobec

  2. Department of Computer Sciences, University of Salzburg, Jakob–Haringer Str. 2, 5020 Salzburg, Austria

    Marián Vajteršic  & Peter Zinterhof  & 

  3. Mathematical Institute Department of Informatics, Slovak Academy of Sciences, Dúbravská 9, 840 00 Bratislava, Slovakia

    Marián Vajteršic

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Trobec, R. (2009). Parallel Computer Simulations of Heat Transfer in Biological Tissues. In: Trobec, R., Vajteršic, M., Zinterhof, P. (eds) Parallel Computing. Springer, London. https://doi.org/10.1007/978-1-84882-409-6_11

Download citation

  • DOI: https://doi.org/10.1007/978-1-84882-409-6_11

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84882-408-9

  • Online ISBN: 978-1-84882-409-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation