Skip to main content
SpringerLink
Log in

Effects of External and Internal Hyperthermia on LDL Transport and Accumulation Within an Arterial Wall in the Presence of a Stenosis

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Effects of hyperthermia on transport of low-density lipoprotein (LDL) through a stenosed arterial wall are analyzed comprehensively in the present work. The realistic and pertinent aspects of an arterial wall is represented by a multi-layer model, with a proper representation of the thickened intima region due to the atherosclerotic plaque formation. Effects of external and internal hyperthermia on LDL concentration levels are established along with the range of influence of these effects. Various modules of the current work are comprehensively compared with pertinent literature and are found to be in excellent agreement. The effects of external and internal hyperthermia as well as the load level and the axial location of the plaque formation on LDL transport and accumulation for a stenosed artery are established in this work.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14

Similar content being viewed by others

Abbreviations

A :

Area reduction of the stenosis (m2)

c :

LDL concentration (mol/m3)

\( \bar{c} \) :

Intima volume-averaged LDL normalized concentration

C :

Thermal capacity (J/kg K)

D :

LDL diffusivity (m2/s)

k :

First-order reaction coefficient (1/s)

k T :

Thermal-diffusion coefficient

K :

Hydraulic permeability (m2)

\( \overrightarrow {J} \) :

Mass flux (mol/m2 s)

L :

Length of the artery (m)

M :

Molecular weight (g/mol)

\( \vec{q} \) :

Heat flux (W/m2)

p :

Hydraulic pressure (mmHg)

r :

Radial coordinate (m)

R g :

Universal gas constant (J/mol K)

T :

Temperature (K)

u :

Velocity vector axial component (m/s)

v :

Velocity vector radial component (m/s)

\( \overrightarrow {V} \) :

Velocity vector (m/s)

z :

Axial coordinate (m)

z 0 :

Distance between center of the stenosis and its beginning (m)

z st :

Axial coordinate at the center of the stenosis (m)

α :

Thermal diffusivity (m2/s)

δ :

Minimum thickness of the stenosis normalized with lumen radius

ε :

Porosity

λ :

Thermal conductivity (W/m K)

μ :

Dynamic viscosity (kg/m s)

ρ :

Density (kg/m3)

σ :

Staverman reflection coefficient

0:

Entrance condition

eff:

Effective property

f:

Fluid (plasma) property

w:

Wall property

z:

Axial component

References

  1. Abraham, J. P., E. M. Sparrow, J. M. Gorman, J. R. Stark, and R. E. Kohler. A mass transfer model of temporal drug deposition in artery walls. Int. J. Heat Mass Tran. 58:632–638, 2013.

    Article  CAS  Google Scholar 

  2. Abraham, J. P., E. M. Sparrow, and R. D. Lovik. Unsteady, three-dimensional fluid mechanic analysis of blood flow in plaque-narrowed and plaque-free arteries. Int. J. Heat Mass Tran. 51:5633–5641, 2008.

    Article  Google Scholar 

  3. Abraham, J. P., J. R. Stark, J. M. Gorman, E. M. Sparrow, and R. Kohler. A model of drug deposition within artery walls. J. Med. Dev. 7:020902, 2013.

    Article  Google Scholar 

  4. Ai, L., and K. Vafai. A coupling model for macromolecule transport in a stenosed arterial wall. Int. J. Heat Mass Tran. 49:1568–1591, 2006.

    Article  CAS  Google Scholar 

  5. Alazmi, B., and K. Vafai. Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer. Int J. Heat Mass Tran. 44:1735–1749, 2001.

    Article  Google Scholar 

  6. Amiri, A., and K. Vafai. Analysis of dispersion effects and non-thermal equilibrium, non-Darcian, variable porosity incompressible flow through porous media. Int J. Heat Mass Tran. 37:939–954, 1994.

    Article  CAS  Google Scholar 

  7. Auer, M., R. Stollberger, P. Regitnig, F. Ebner, and G. A. Holzapfel. 3-D reconstruction of tissue components for atherosclerotic human arteries using ex vivo high-resolution MRI. IEEE T. Med. Imaging 25:345–357, 2006.

    Article  Google Scholar 

  8. Auer, M., R. Stollberger, P. Regitnig, F. Ebner, and G. A. Holzapfel. In vitro angioplasty of atherosclerotic human femoral arteries: analysis of the geometrical changes in the individual tissues using MRI and image processing. Ann. Biomed. Eng. 38:1276–1287, 2010.

    Article  PubMed  Google Scholar 

  9. Chapman, S., and T. G. Cowling. The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases. Cambridge: Cambridge University Press, p. 431, 1952.

    Google Scholar 

  10. Chung, S., and K. Vafai. Effect of the fluid-structure interactions on low-density lipoprotein transport within a multi-layered arterial wall. J. Biomech. 45:371–381, 2012.

    Article  PubMed  Google Scholar 

  11. Chung, S., and K. Vafai. Low-density lipoprotein transport within a multi-layered arterial wall: effect of the atherosclerotic plaque/stenosis. J. Biomech. 46:574–585, 2013.

    Article  PubMed  Google Scholar 

  12. Chung, S., and K. Vafai. Mechanobiology of low-density lipoprotein transport within an arterial wall-impact of hyperthermia and coupling effects. J. Biomech. 47:137–147, 2014.

    Article  PubMed  Google Scholar 

  13. Cilla, M., E. Peña, and M. A. Martinez. 3D computational parametric analysis of eccentric atheroma plaque: influence of axial and circumferential residual stresses. Biomech. Model. Mechanobiol. 11:1001–1013, 2012.

    Article  CAS  PubMed  Google Scholar 

  14. Cilla, M., E. Peña, and M. A. Martinez. Mathematical modelling of atheroma plaque formation and development in coronary arteries. J. R. Soc. Interface 11:20130866, 2014.

    Article  PubMed Central  PubMed  Google Scholar 

  15. Colton, C. K., S. Friedman, D. E. Wilson, and R. S. Lees. Ultrafiltration of lipoproteins through a synthetic membrane. Implications for the filtration theory of atherogenesis. J. Clin. Invest. 51:2472–2481, 1972.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  16. Cullen, S. A., and R. I. Hill. Aviation pathology and toxicology. In: Ethics and Mental Health: The Patient, Profession and Community, edited by D. J. Rainford, and D. P. Gradwell. Boca Raton: CRC Press, 2006, pp. 517–533.

    Google Scholar 

  17. Darcy, H. Les Fontaines Publiques de la Ville de Dijon. Exposition et Application des Principes à Suivre et des Formules à Employer dans les Questions de Distribution d’Eau. Paris: Victor Dalmont, 1856.

    Google Scholar 

  18. Duck, F. A. Physical Properties of Tissues: A Comprehensive Reference Book. San Diego: Academic Press Inc, p. 336, 1990.

    Google Scholar 

  19. Eslamian, M. Advances in thermodiffusion and thermophoresis (Soret effect) in liquid mixtures. FHMT 2:043001, 2011.

    Google Scholar 

  20. Finegold, J. A., P. Asaria, and D. P. Francis. Mortality from ischaemic heart disease by country, region, and age: statistics from World Health Organisation and United Nations. Int. J. Cardiol. 168:934–945, 2013.

    Article  PubMed Central  PubMed  Google Scholar 

  21. Gupta, P. K., J. Singh, and K. N. Rai. Numerical simulation for heat transfer in tissues during thermal therapy. J. Therm. Biol. 35:295–301, 2010.

    Article  Google Scholar 

  22. Hao, W., and A. Friedman. The LDL-hdl profile determines the risk of atherosclerosis: a mathematical model. PLoS ONE 9:e90497, 2014.

    Article  PubMed Central  PubMed  Google Scholar 

  23. Hossain, S. S., S. F. A. Hossainy, Y. Bazilevs, V. M. Calo, and T. J. R. Hughes. Mathematical modeling of coupled drug and drug-encapsulated nanoparticle transport in patient-specific coronary artery walls. Comput. Mech. 49:213–242, 2012.

    Article  Google Scholar 

  24. Huang, Y., D. Rumschitzki, S. Chien, and S. Weinbaum. A fiber matrix model for the filtration through fenestral pores in a compressible arterial intima. Am. J. Physiol. 272:H2023–H2039, 1997.

    CAS  PubMed  Google Scholar 

  25. Huysmans, M., and A. Dassargues. Review of the use of Péclet numbers to determine the relative importance of advection and diffusion in low permeability environments. Hydrogeol. J. 13:895–904, 2005.

    Article  Google Scholar 

  26. Jung, H., J. W. Choni, and C. G. Park. Asymmetric flows of non-Newtonian fluids in symmetric stenosed artery. Korea-Aust. Rheol. J. 16:101–108, 2004.

    Google Scholar 

  27. Kaazempur-Mofrad, M. R., S. Wada, J. G. Myers, and C. R. Ethier. Mass transport and fluid flow in stenotic arteries: axisymmetric and asymmetric models. Int. J. Heat Mass Tran. 48:4510–4517, 2005.

    Article  CAS  Google Scholar 

  28. Karner, G., and K. Perktold. Effect of endothelial injury and increased blood pressure on albumin accumulation in the arterial wall: a numerical study. J. Biomech. 33:709–715, 2000.

    Article  CAS  PubMed  Google Scholar 

  29. Karner, G., K. Perktold, and H. P. Zehentner. Computational modeling of macromolecule transport in the arterial wall. Comput. Methods Biomech. Biomed. Eng. 4:491–504, 2001.

    Article  Google Scholar 

  30. Katz, M. A. New formulation of water and macromolecular flux which corrects for non-ideality: theory and derivation, predictions, and experimental results. J. Theor. Biol. 112:369–401, 1985.

    Article  CAS  PubMed  Google Scholar 

  31. Kays, W. M., and M. E. Crawford. Convective Heat and Mass Transfer. New York: Mcgraw-Hill, p. 512, 1993.

    Google Scholar 

  32. Kedem, O., and A. Katchalsky. Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. Biochim. Biophys. Acta 27:229–246, 1958.

    Article  CAS  PubMed  Google Scholar 

  33. Keller, B., F. Clubb Jr., and G. Dubini. A review of atherosclerosis and mathematical transport models. In: IFMBE Proceedings, Vol. 36, edited by S. Vlad, and R. V. Ciupa. Berlin: Springer, 2011, pp. 338–343.

    Google Scholar 

  34. Kenjereš, S., and A. de Loor. Modelling and simulation of low-density lipoprotein transport through multi-layered wall of an anatomically realistic carotid artery bifurcation. J. R. Soc. Interface 11:20130941, 2014.

    Article  PubMed Central  PubMed  Google Scholar 

  35. Khakpour, M., and K. Vafai. Effects of gender-related geometrical characteristics of aorta-iliac bifurcation on hemodynamics and macromolecule concentration distribution. Int. J. Heat Mass Tran. 51:5542–5551, 2008.

    Article  Google Scholar 

  36. Khakpour, M., and K. Vafai. Critical assessment of arterial transport models. Int. J. Heat Mass Tran. 51:807–822, 2008.

    Article  CAS  Google Scholar 

  37. Khamdaengyodtai, P., K. Vafai, P. Sakulchangsatjatai, and P. Terdtoon. Effects of pressure on arterial failure. J. Biomech. 45:2577–2588, 2012.

    Article  PubMed  Google Scholar 

  38. Kiousis, D. E., T. C. Gasser, and G. A. Holzapfel. A numerical model to study the interaction of vascular stents with human atherosclerotic lesions. Ann. Biomed. Eng. 35:1857–1869, 2007.

    Article  PubMed  Google Scholar 

  39. Kolios, M. C., M. D. Sherar, and J. W. Hunt. Large blood vessel cooling in heated tissues: a numerical study. Phys. Med. Biol. 40:477–494, 1995.

    Article  CAS  PubMed  Google Scholar 

  40. Liu, X., Y. Fan, and X. Deng. Effect of the endothelial glycocalyx layer on arterial LDL transport under normal and high pressure. J. Theor. Biol. 283:71–81, 2011.

    Article  CAS  PubMed  Google Scholar 

  41. Mahjoob, S., and K. Vafai. Analytical characterization of heat transport through biological media incorporating hyperthermia treatment. Int. J. Heat Mass Tran. 52:1608–1618, 2009.

    Article  CAS  Google Scholar 

  42. Malvè, M., C. Serrano, E. Peña, R. Fernández-Parra, F. Lostalé, M. A. De Gregorio, and M. A. Martinez. Modelling the air mass transfer in a healthy and a stented rabbit trachea: CT-images, computer simulations and experimental study. Int. Commun Heat. Mass 53:1–8, 2014.

    Article  Google Scholar 

  43. Mandal, D. K., N. K. Manna, and S. Chakrabarti. Influence of different bell-shaped stenoses on the progression of the disease, atherosclerosis. J. Mech. Sci. Technol. 25:1933–1947, 2011.

    Article  Google Scholar 

  44. Meyer, G., R. Merval, and A. Tedqui. Effects of pressure-induced stretch and convection on low-density lipoprotein and albumin uptake in the rabbit aortic wall. Circ. Res. 79:532–540, 1996.

    Article  CAS  PubMed  Google Scholar 

  45. Misra, J. C., and G. C. Shit. Blood flow through arteries in a pathological state: a theoretical study. Int. J. Eng. Sci. 44:662–671, 2006.

    Article  Google Scholar 

  46. Olgac, U., V. Kurtcuoglu, and D. Poulikakos. Computational modeling of coupled blood-wall mass transport of LDL: effects of local wall shear stress. Am. J. Physiol. Heart Circ. Physiol. 294:H909–H919, 2008.

    Article  CAS  PubMed  Google Scholar 

  47. Platten, J. K. The Soret effect: a review of recent experimental results. J. Appl. Mech. 73:5–15, 2006.

    Article  CAS  Google Scholar 

  48. Prosi, M., P. Zunino, K. Perktold, and A. Quarteroni. Mathematical and numerical models for transfer of low-density lipoproteins through the arterial walls: a new methodology for the model set up with applications to the study of disturbed lumenal flow. J. Biomech. 38:903–917, 2005.

    Article  CAS  PubMed  Google Scholar 

  49. Rahman, M. A., and M. Z. Saghir. Thermodiffusion or Soret effect: historical review. Int. J. Heat Mass Tran. 73:693–705, 2014.

    Article  Google Scholar 

  50. Sáez, P., E. Peña, M. A. Martínez, and E. Kuhl. Computational modeling of hypertensive growth in the human carotid artery. Comput. Mech. 53:1183–1196, 2014.

    Article  PubMed Central  PubMed  Google Scholar 

  51. Seeley, B. D., and D. F. Young. Effect of geometry on pressure losses across models of arterial stenosis. J. Biomech. 9:447–448, 1976.

    Article  Google Scholar 

  52. Stangeby, D. K., and C. R. Ethier. Computational analysis of coupled blood-wall arterial LDL transport. J. Biomech. Eng. 124:1–8, 2002.

    Article  PubMed  Google Scholar 

  53. Stark, J. R., J. M. Gorman, E. M. Sparrow, J. P. Abraham, and R. E. Kohler. Controlling the rate of penetration of therapeutic drug into the wall of an artery by means of a pressurized balloon. J. Biomed. Sci. Eng. 6:527–532, 2013.

    Article  Google Scholar 

  54. Steiner, R. Laser-tissue interactions. In: Laser and IPL Technology in Dermatology and Aesthetic Medicine, edited by S. Karsai, and C. Raulin. Berlin: Springer Berlin Heidelberg, 2011.

    Google Scholar 

  55. Sun, N., R. Torii, N. B. Wood, A. D. Hughes, S. A. Thom, and X. Y. Xu. Computational modeling of LDL and albumin transport in an in vivo CT image-based human right coronary artery. J. Biomech. Eng. 131:021003, 2009.

    Article  PubMed  Google Scholar 

  56. Sun, N., N. B. Wood, A. D. Hughes, S. A. M. Thom, and X. Y. Xu. Effects of transmural pressure and wall shear stress on LDL accumulation in the arterial wall: a numerical study using a multilayered model. Am. J. Physiol. Heart Circ. Physiol. 292:H3148–H3157, 2007.

    Article  CAS  PubMed  Google Scholar 

  57. Tada, S., and J. M. Tarbell. Interstitial flow through the internal elastic lamina affects shear stress on arterial smooth muscle cells. Am. J. Physiol. Heart Circ. Physiol. 278:H1589–H1597, 2000.

    CAS  PubMed  Google Scholar 

  58. Tarbell, J. M. Mass transport in arteries and the localization of atherosclerosis. Annu. Rev. Biomed. Eng. 5:79–118, 2003.

    Article  CAS  PubMed  Google Scholar 

  59. Taylor, F., M. D. Huffman, A. F. Macedo, T. H. Moore, M. Burke, G. Davey Smith, K. Ward, and S. Ebrahim. Statins for the primary prevention of cardiovascular disease. Cochrane Database Syst. Rev. 1:CD004816, 2013.

    PubMed  Google Scholar 

  60. Vafai, K., and C. L. Tien. Boundary and inertia effects on flow and heat transfer in porous media. Int. J. Heat Mass Tran. 24:195–203, 1981.

    Article  CAS  Google Scholar 

  61. Wada, S., and T. Karino. Computational study on LDL transfer from flowing blood to arterial walls. In: Clinical Application of Computational Mechanics to the Cardiovascular System, edited by T. Yamaguchi. Tokyo: Springer Japan, 2000, pp. 157–173.

    Chapter  Google Scholar 

  62. Wakeham, W. A., A. Nagashima, and J. V. Sengers. Experimental Thermodynamics, Vol. III, Measurement of the Transport Properties of Fluids, Vol. III. Oxford: Blackwell Scientific Publications, 1991.

    Google Scholar 

  63. Xie, X., J. Tan, D. Wei, D. Lei, T. Yin, J. Huang, X. Zhang, J. Qiu, C. Tang, and G. Wang. In vitro and in vivo investigations on the effects of low-density lipoprotein concentration polarization and haemodynamics on atherosclerotic localization in rabbit and zebrafish. J. R. Soc. Interface 10:20121053, 2013.

    Article  PubMed Central  PubMed  Google Scholar 

  64. Yang, F., G. Holzapfel, C. Schulze-Bauer, R. Stollberger, D. Thedens, L. Bolinger, A. Stolpen, and M. Sonka. Segmentation of wall and plaque in in vitro vascular MR images. Int. J. Cardiovasc. Imaging 19:419–428, 2003.

    Article  PubMed  Google Scholar 

  65. Yang, N., and K. Vafai. Modeling of low-density lipoprotein (LDL) transport in the artery—effects of hypertension. Int. J. Heat Mass Tran. 49:850–867, 2006.

    Article  CAS  Google Scholar 

  66. Young, D. F., and F. Y. Tsai. Flow characteristics in models of arterial stenoses: I. Steady flow. J. Biomech. 6:395–410, 1973.

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The financial support by UniNA and Compagnia di San Paolo, through Programme STAR, is greatly appreciated.

Conflict of interest

There is no conflict of interest. This manuscript has not been submitted to anywhere else.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of California, Riverside, CA, 92521, USA

    Marcello Iasiello, Kambiz Vafai & Fatemeh Tavakkoli

  2. Dipartimento di Ingegneria Industriale, Università degli Studi di Napoli Federico II, P.le Tecchio, 80, Naples, 80125, Italy

    Marcello Iasiello, Assunta Andreozzi & Nicola Bianco

Authors
  1. Marcello Iasiello
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kambiz Vafai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Assunta Andreozzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nicola Bianco
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fatemeh Tavakkoli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kambiz Vafai.

Additional information

Associate Editor Estefanía Peña oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Iasiello, M., Vafai, K., Andreozzi, A. et al. Effects of External and Internal Hyperthermia on LDL Transport and Accumulation Within an Arterial Wall in the Presence of a Stenosis. Ann Biomed Eng 43, 1585–1599 (2015). https://doi.org/10.1007/s10439-014-1196-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-014-1196-0

Keywords

Search

Navigation