A simple approach for adding thixotropy to an elasto-visco-plastic rheological model to facilitate structural interrogation of human blood


Blood is an important biofluid that plays a critical role in facilitating a range of body functions. Since blood is a non-Newtonian fluid, its viscosity is influenced by the shear rate/velocity and the microstructure level due to rouleaux and the size of the blood vessels it flows. In addition, the blood viscosity is also dependent on applied strain and the physiological parameters of the different blood components (i.e. cholesterol, hematocrit, fibrinogen concentration etc.). To this end, a thorough understanding of blood rheology is of great significance in diagnosing vascular-related disorders and modeling human blood rheological properties. Conventional models tried to understand the transient, elastic, plastic and viscous flow characteristics of blood. However, these models are limited as they are unable to effectively model the dynamics flow by changing the rheological properties simultaneously. They also fail to account for the structural breakdown and build-up during transient rheological flow due to their inability to accurately model the microstructure and viscosity changes caused by shear rate changes.

Generally, a dynamic state is characterized by two viscosities: pure solvent viscosity (plasma + individual red blood cells) and microstructure-based (rouleaux) viscosity. And distinguishing the contributions of these viscosities is critical in modeling viscosity variation in both changing shear rate and transient conditions. This has been the basis of the recent modification to enhance the accuracy and feasibility of the models. Recently, much progress has been achieved in the thixo-elasto-visco-plasticity (EVP) modeling. Various methods have been employed to test the feasibility of these models. Interestingly, thixotropic model improvements have been shown to improve the robustness of the methods used to test and validate the models for various suspensions, thus improving understanding of the microstructure of complex materials like human blood. Over the past decades, human blood rheology modeling has enabled researchers to identify the limitations of the existing thixotropy models to improve the rheology blood study.

Herein, a team of scientists from the United States Military Academy: Dr. Matthew Armstrong, Mr. Mathias Scully, Mr. Michael Clark, Mr. Trevor Corrigan, and Dr. Corey James demonstrated the modification and refinement of a simple elastic-viscous-plastic rheological model with an added thixotropic term for better modeling of the rheological flow of human blood. The modified framework, realized by adding the thixotropy to the EVP model, was used to accurately describe the transient effects of human blood with microstructure contained in the plasma. The main objective was to directly correlate the evolution of viscous and elastic properties to the structural predictions of the model for further testing and validation of the model’s feasibility and applicability. The results can significantly improve the accuracy of existing hemodynamics simulations The original research article is now published in the Journal of Non-Newtonian Fluid Mechanics.

The research team demonstrated the effectiveness of the presented framework in modeling and predicting the microstructure of human blood in both transient and steady-state conditions by representing the structure breakdown and built-up induced by the changes in the shear rate. Unlike the previous models that only modeled steady-state blood with 1 – 4 parameters, the proposed approach could effectively capture the stress during transient flow and the everchanging and evolving structure to determine the effects on structure from shear rate changes. The results demonstrated that the rheological behavior and properties of human blood could be obtained more effectively by including two sets of time scales for thixotropic and viscoelastic changes. Furthermore, it was worth noting that the addition of thixotropy to the EVP model was useful in determining the non-ideal physiological blood traits thanks to the deviation of the ideal values of the following parameters: yield stress and shear viscosity.

In summary, the study demonstrated the effectiveness of a simple approach comprising an EVP rheological model with an additional thixotropic parameter to predict and interpret the response of complex human blood to changes in shear rate with improved accuracy. The results demonstrated the contributions of thixotropy in enhancing the fitting and prediction accuracy of complex rheology flows with microstructure. The feasibility of the thixotropic features was successfully verified against other thixo-elasto-visco-plastic (TEVP) models. In a statement to Advances in Engineering, Dr. Matthew Armstrong, first and corresponding author explained their new study will contribute to a better collection of rheological data of human blood and more robust modeling. Moreover, with better blood flow predictions it will advance various applications including drug delivery, bypass surgery, and medical device design.

A simple approach for adding thixotropy to an elasto-visco-plastic rheological model to facilitate structural interrogation of human blood - Advances in Engineering

About the author

LTC Matthew Armstrong is an Associate Professor, and the Chemical Engineering Program Director, in the Department of Chemistry and Life Science at the United States Military Academy at West Point, NY where he oversees an ABET accredited program with a staff of 10+ faculty, and technicians, while supervising a research group of 3 – 6 soft matter researchers.  He earned his Ph.D. in Chemical Engineering from University of Delaware, and B.S. in Chemical Engineering from Rensselaer Polytechnic Institute. His research work is focused on interrogation of the microstructure of soft matter through thixo-elastic-visco-plastic modeling, rheology, light and neutron scattering along with global, stochastic optimization algorithms.


Armstrong, M., Scully, M., Clark, M., Corrigan, T., & James, C. (2021). A simple approach for adding thixotropy to an elasto-visco-plastic rheological model to facilitate structural interrogation of human bloodJournal of Non-Newtonian Fluid Mechanics, 290, 104503.

Go To Journal of Non-Newtonian Fluid Mechanics

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