A thermal based RBC Aggregation model for two-phase blood flow

Erke Aribas; M. Serdar Celebi

Korea-Australia Rheology Journal, Vol.32, No.2, 121-136, May, 2020

DOI10.1007/s13367-020-0011-8 Export Citation

A thermal based RBC Aggregation model for two-phase blood flow

Erke Aribas^†, and M. Serdar Celebi

Department of Computational Science and Engineering, Istanbul Technical University, Korea

E-mail:

Creating a reliable and accurate Red Blood Cell (RBC) aggregation model for small and midsize arteries and veins is still an active research subject with more in focus with a multi-scale approach including mesoscale effects. Better understanding the RBC aggregation requires a multi-phase and multi-scale approach for simulating blood with Newtonian and non-Newtonian parts. In our proposed work, viscosity, shear rates, phase distributions and volume fractions with a range of hematocrit levels of RBC are calculated using the depletion interaction theory for two-phase blood flow simulation and compared with the numerical and experimental data in literature. In addition, thermal effects are modeled using energy equations and changes in RBC aggregation are studied with respect to thermal variations. Two-phase fluid-fluid model is used including inter-phase momentum exchange. A new shape factor is proposed for the coupling effects on drag and lift forces. Finally, total interaction energy of RBCs, hematocrit levels of blood at varying temperatures and effects of temperature on viscosity and relative apparent viscosity are computed at varying shear rates and compared with the existing data in literature.

Keywords:plasma;RBC;aggregation;depletion model;thermal effects;two-phase blood flow;shear rate;viscosity;hematocrit level

[References]

Al-Taweel AM, Madhavan S, Podila K, Koksal M, Troshko A, Gupta YP, European Conference on Mixing, 495 2006.
Aribas E, Celebi MS, The 2nd Symposium on Multiscale, Multiphysics and Turbulent flow Simulations, ICNAAM, 15th International Conference of Numerical Analysis and Applied Mathematics, 2018.
Arkin H, Xu LX, Holmes KR, IEEE T. Bio-Med. Eng., 41, 97 (1994)
Arkin H, Xu LX, Holmes KR, IEEE T. Bio-Med. Eng., 41, 97 (1994)
Baskurt O, Neu B, Meiselman HJ, Red Blood Cell Aggregation, 2011.
Baskurt OK, Gelmont D, Meiselman HJ, Am. J. Respir. Crit. Care. Med., 157, 421 (1998)
Brooks DE, Goodwin JE, Seaman GV, J. Appl. Phycol., 28, 172 (1970)
Charny CK, Levin RL, J. Biomech. Eng., 111, 263 (1989)
Chien S, Annu. Rev. Physiol., 49, 177 (1987)
Chung TH, Wu SH, Yao M, Lu CW, Lin YS, Hung Y, Mou CY, Chen YC, Huang DM, Biomaterials, 28, 2959 (2007)
Craciunescu OI, Clegg ST, J. Biomech. Eng., 123, 500 (2001)
Cinar Y, Senyol AM, Duman K, Am. J. Hypertens., 14, 433 (2001)
Dong RG, Effective mass and damping of submerged structures, 1978.
Dufaux J, Quemada D, Mills P, Rev. Phys. Appl., 15, 1367 (1980)
Enwald H, Peirano E, Almstedt AE, Int. J. Multiph. Flow, 22(S), 21 (1996)
Fischer TM, Stohr-Lissen M, Schmid-Schonbein H, Science, 202, 894 (1978)
Gijsen FJH, Allanic E, Van de Vosse FN, Janssen JD, J. Biomech., 32, 705 (1999)
Jung J, Hassanein A, Med. Eng. Phys., 30, 91 (2008)
Jung J, Hassanein A, Lyczkowski RW, Ann. Biomed. Eng., 34, 393 (2006)
Jung J, Lyczkowski RW, Panchal CB, Hassanein A, J. Biomech., 39, 2064 (2006)
Legendre D, Magnaudet J, J. Fluid Mech., 368, 81 (1998)
Mandal M, World J. Pharm. Pharm. Sci., 5, 2165 (2016)
Massoudi M, Kim J, Antaki JF, Int. J. Nonlin. Mech., 47, 506 (2012)
Mazumdar J, Biofluid Mechanics, 2015.
Neu B, Meiselman HJ, Biophys. J., 83, 2482 (2002)
O'Rourke MF, Nichols WW, experimental and clinical principles, Hodder Arnold London, 2005.
Pennes HH, J. Appl. Phycol., 1, 93 (1948)
Piskin S, Aribas E, Celebi MS, 5th European conference on computational fluid dynamics, 2010.
Piskin S, Celebi MS, Comput. Biol. Med., 43, 717 (2013)
Roache PJ, J. Fluids Eng., 116, 405 (1994)
Schmid-Schonbein H, Wells R, Science, 165, 288 (1969)
Secomb RW, Pries AR, C. R. Phys., 14, 470 (2013)
Sphaier LA, Su J, Cotta RM, Kulacki FA, Handbook of thermal science and engineering, 2017.
Shih TC, Horng TL, Huang HW, Ju KC, Huang TC, Chen PY, Ho YJ, Lin WL, Int. J. Heat Mass Transf., 55(13-14), 3763 (2012)
Srivastava VP, Srivastava R, Comput. Mater. Sci., 58, 227 (2009)
Tomiyama A, Multiphas. Sci. Tech., 10, 369 (1998)
Wojnarowski J, Efficiency of Engineering Education in XX Century, Ukraine, Donetsk, 2001.
Yilmaz F, Gundogdu MY, Korea-Aust. Rheol. J., 20(4), 197 (2008)
Yilmaz F, Gundogdu MY, Korea-Aust. Rheol. J., 21(3), 161 (2009)
Young T, Philos. Trans. R. Soc. Lond. B., 98, 164 (1808)

[1] Al-Taweel AM, Madhavan S, Podila K, Koksal M, Troshko A, Gupta YP, European Conference on Mixing, 495 2006.

[2] Aribas E, Celebi MS, The 2nd Symposium on Multiscale, Multiphysics and Turbulent flow Simulations, ICNAAM, 15th International Conference of Numerical Analysis and Applied Mathematics, 2018.

[3] Arkin H, Xu LX, Holmes KR, IEEE T. Bio-Med. Eng., 41, 97 (1994)

[4] Arkin H, Xu LX, Holmes KR, IEEE T. Bio-Med. Eng., 41, 97 (1994)

[5] Baskurt O, Neu B, Meiselman HJ, Red Blood Cell Aggregation, 2011.

[6] Baskurt OK, Gelmont D, Meiselman HJ, Am. J. Respir. Crit. Care. Med., 157, 421 (1998)

[7] Brooks DE, Goodwin JE, Seaman GV, J. Appl. Phycol., 28, 172 (1970)

[8] Charny CK, Levin RL, J. Biomech. Eng., 111, 263 (1989)

[9] Chien S, Annu. Rev. Physiol., 49, 177 (1987)

[10] Chung TH, Wu SH, Yao M, Lu CW, Lin YS, Hung Y, Mou CY, Chen YC, Huang DM, Biomaterials, 28, 2959 (2007)

[11] Craciunescu OI, Clegg ST, J. Biomech. Eng., 123, 500 (2001)

[12] Cinar Y, Senyol AM, Duman K, Am. J. Hypertens., 14, 433 (2001)

[13] Dong RG, Effective mass and damping of submerged structures, 1978.

[14] Dufaux J, Quemada D, Mills P, Rev. Phys. Appl., 15, 1367 (1980)

[15] Enwald H, Peirano E, Almstedt AE, Int. J. Multiph. Flow, 22(S), 21 (1996)

[16] Fischer TM, Stohr-Lissen M, Schmid-Schonbein H, Science, 202, 894 (1978)

[17] Gijsen FJH, Allanic E, Van de Vosse FN, Janssen JD, J. Biomech., 32, 705 (1999)

[18] Jung J, Hassanein A, Med. Eng. Phys., 30, 91 (2008)

[19] Jung J, Hassanein A, Lyczkowski RW, Ann. Biomed. Eng., 34, 393 (2006)

[20] Jung J, Lyczkowski RW, Panchal CB, Hassanein A, J. Biomech., 39, 2064 (2006)

[21] Legendre D, Magnaudet J, J. Fluid Mech., 368, 81 (1998)

[22] Mandal M, World J. Pharm. Pharm. Sci., 5, 2165 (2016)

[23] Massoudi M, Kim J, Antaki JF, Int. J. Nonlin. Mech., 47, 506 (2012)

[24] Mazumdar J, Biofluid Mechanics, 2015.

[25] Neu B, Meiselman HJ, Biophys. J., 83, 2482 (2002)

[26] O'Rourke MF, Nichols WW, experimental and clinical principles, Hodder Arnold London, 2005.

[27] Pennes HH, J. Appl. Phycol., 1, 93 (1948)

[28] Piskin S, Aribas E, Celebi MS, 5th European conference on computational fluid dynamics, 2010.

[29] Piskin S, Celebi MS, Comput. Biol. Med., 43, 717 (2013)

[30] Roache PJ, J. Fluids Eng., 116, 405 (1994)

[31] Schmid-Schonbein H, Wells R, Science, 165, 288 (1969)

[32] Secomb RW, Pries AR, C. R. Phys., 14, 470 (2013)

[33] Sphaier LA, Su J, Cotta RM, Kulacki FA, Handbook of thermal science and engineering, 2017.

[34] Shih TC, Horng TL, Huang HW, Ju KC, Huang TC, Chen PY, Ho YJ, Lin WL, Int. J. Heat Mass Transf., 55(13-14), 3763 (2012)

[35] Srivastava VP, Srivastava R, Comput. Mater. Sci., 58, 227 (2009)

[36] Tomiyama A, Multiphas. Sci. Tech., 10, 369 (1998)

[37] Wojnarowski J, Efficiency of Engineering Education in XX Century, Ukraine, Donetsk, 2001.

[38] Yilmaz F, Gundogdu MY, Korea-Aust. Rheol. J., 20(4), 197 (2008)

[39] Yilmaz F, Gundogdu MY, Korea-Aust. Rheol. J., 21(3), 161 (2009)

[40] Young T, Philos. Trans. R. Soc. Lond. B., 98, 164 (1808)