(31f) Contemporary Modeling and Analysis of Human Blood Rheology

Evan Ousley, Tyler Helton, Michael Deegan, Jesse Hudgins, Matthew Armstrong

Department of Chemistry and Life Science, United States Military Academy,

West Point, NY 10996

The State of Contemporary Modeling and Analysis of Human Blood Rheology

Recent work modeling the rheological behavior of blood indicates that blood has all of the hallmark features of a complex material, including shear-thinning, viscoelastic behavior, a yield stress and thixotropy. After decades of modeling steady state blood data, and the development of steady state models, like the Casson, Carreau-Yasuda, Herschel-Bulkley, etc. the advancement and evolution of blood modeling to transient flow conditions now has a renewed interest [11,12]. Using published data by Sousa et al. and Moreno et al. [2,3,7] we show and compare modeling efforts with the simple models [1-3]. We first show the strengths of the simple models, then discuss potential weaknesses.

This effort is followed with an evolution into using models that can handle the transient flow conditions to include fitting to published step-up/step-down experiments [1] and Large Amplitude Oscillatory Shear (LAOS) flow [2]. The family of models that can handle the transient flows involve the recently published Modified Delaware Thixotropic Model (MDTM), the Apostolidis Thixotropic Blood Model and the Bautista-Monero-Puig Model (BMP) [5,9,13]. We fist discuss the development of the scalar, structure parameter evolution models and we compare fitting results with all of these published models and transient data [1]. In addition we propose an new term for, similar to what has been used in MDTM, for the Apostolidis model using a structural viscosity term, that has the potential to also be used in a more viscoelastic mode if necessary [4,9]. The new term is compared to the original model, and the BMP model to demonstrate its effectiveness.

Lastly we demonstrate a novel approach to analyzing transient blood data by incorporating the novel Series of Physical Phenomena (SPP) framework [6]. Recent work with blood using LAOS has shown that its unique rheological signature can be used as a psuedo- “fingerprint” [13-17], able to clearly show and delineate elastic and viscous regions of the LAOS cycle. Applying large amplitude oscillatory shear (LAOS) to complex fluids induces nonlinear rheological responses, that, with proper LAOS analysis technique, can be used to sensitively probe the underlying microstructure and its dynamics. With this analysis strategy we show how to interpret transient human blood data in a meaningful way by looking at relative elastic and viscous contributions, Cole-Cole plots, and the torsion and curvature plots [6]. This is done with both the Bureau et al. published step up and step down data, as well as the recently published LAOS data by Sousa et al. [1,2]. Together these contemporary blood analysis techniques are shown, with a view to improved modeling, and experimental techniques moving forward. All of the data are fit to respective models with using a recently published parallel tempering algorithm [10].

Reference

[1] Bureau et al. Biorheology (1980).

[2] Sousa et al. Biorheology (2013).

[3] Moreno et al. Korea-Australia Rheology Journal (2015).

[4] Apostolidis et al. J. Rheol. (2015).

[5] Bautista et al. JNNFM (1999).

[6] S. Rogers. Rheol. Acta. (2017). DOI 10.1007/s00397-017-1008-1.

[7] Tomaiuolo et al. Rheol. Acta (2016).

[8] Ewoldt, R. and G.H. McKinley. Rheol. Acta. (2017).

[9] M. J. Armstrong, A. N. Beris, S. Rogers, N. J. Wagner,J. Rheol. 60, 433 (2016).

[10] M. J. Armstrong, A. N. Beris, N. J. Wagner, AIChE Journal (2016).

[11] Bessonov et al. Math. Model. Nat. Phenom. 11(1) (2016).

[12] Merrill, E. Physiological Reviews 49(4) (1969).

[13] C.J. Dimitriou, R.H. Ewoldt and G.H. McKinley. J. Rheol. 571(1), 27-70.

[14] B.C. Blackwell and R.H. Ewoldt. JNNFM 227, (2016) 80-89.

[15] B.C. Blackwell and R.H. Ewoldt. JNNFM 208-209, (2014) 27-41.

[16] R.H. Ewoldt and N.A. Bharadwaj. Rheol. Acta. (2013) 52:201-219.

[17] N.A. Bharadwaj and R.H. Ewoldt. J.Rheol. 59(2), (2015) 557-592.