## 2 Methods for Evaluation of Erythrocyte Deformability
### Visometric Methods for Evaluation of RBC Deformability  
Blood viscosity is a key factor influencing blood flow in both large and small vessels, but its role differs depending on vessel size [5]: In large arteries (macroversels), in which vessel diameter far exceeds RBC size, blood viscosity directly affects flow resistance, assuming a constant diameter. In capillaries (microversels), in which RBCs are nearly the same size as the lumen, blood does not behave as a uniform fluid, and the concept of viscosity--especially as measured by standard viscometers--becomes less straightforward.  
Accordingly, in microcirculation, other factors such as hematocrit (Ht), RBC aggregation, RBC deformability, and plasma protein levels must be directly considered, especially since microvascular hematocrit is typically lower than the levels in venous blood samples used for in vitro viscosity testing.  
Additionally, elevated whole-blood viscosity (WBV) can increase mechanical stress on vessel walls, potentially damaging endothelial cells and promoting inflammation, thus contributing to vascular dysfunction.  
[PERSON] et al. [22] present a comprehensive review of the visualization and measurement of blood cells flowing in microfluidic systems, focusing on blood rheology and its implications for personalized medicine. This work highlights the importance of hemorheological properties, such as blood viscosity, red blood cell (RBC) deformability, and aggregation, in diagnosing and managing metabolic and blood-related diseases like diabetes, hypertension, and malaria.  
A review by [PERSON] et al. [23] explores the mechanical properties of red blood cell (RBC) membranes and their impacts on blood flow and rheology, from both numerical and experimental perspectives. The authors note the following key point in their study: the unique structure of RBC membranes--notably their lack of a nucleus and simple composition--makes them ideal for modeling and analysis. The review emphasizes the advances in microfluidic technologies that enable precise in vitro assessments of RBC membrane elasticity, hemodynamics, and hemorheology. Experimentally, the authors used microfluidic methods to measure blood viscosity, and to analyze how RBC aggregation and erythrocyte concentration influence whole-blood rheological properties. Overall, the study showcases how microfluidics offers powerful tools for investigating the biomechanics of RBCs and their role in blood flow regulation.  
RBC deformability and aggregation can be quantified using experimental blood viscosity data. Based on the blood viscosity experimental data, the RBC deformability (Tk) index, characterizing erythrocyte deformability [24], and the erythrocyte aggregation (IAE) index, characterizing the erythrocyte aggregation, can be calculated as described below.  
The Tk index is used to characterize erythrocyte deformability and is calculated using the following Formula (1) [24].  
\[Tk=\frac{\eta_{r}^{0.4}-1}{\eta_{r}^{0.4}*Ht} \tag{1}\]  
where \(\eta_{r}\) is the relative viscosity; (\(\eta_{r}=\eta_{bl}/\eta_{pl}\)), \(\eta_{bl}\) is the apparent dynamic blood viscosity at shear rate 94.5 s\({}^{-1}\) and \(\eta_{pl}\) is plasma viscosity at the same shear rate, and Ht, % is the hematocrit [2]. This suggests that the Tk index is a useful metric for assessing how changes in RBC deformability influence blood viscosity, especially under low shear flow conditions.  
The IAE index (not further detailed here) represents erythrocyte aggregation.