**3. RBC deformability and blood microcirculation**

The RBC deformability can influence blood microcirculation since viscosity and flow can be significantly changed by the viscoelastic properties of RBCs.

## **3.1. Blood viscosity**

Viscosity of liquid characterizes its resistance to flow under certain deforming force, especially shear stress. Under laminar flow conditions where particles move parallel to adjacent neighbors with minimal turbulence, the fluidity is classified by the dependence of viscosity to shear strain or shear stress: (1) Newtonian fluid, if the viscosity is independent of shear stress or shear strain so that shear stress is linearly proportional to shear strain, (2) non-Newtonian fluid whose viscosity either decrease (shear-thinning) or increase (shearthickening) depending on the changes of shear stress (Merrill,1969).

Blood is non-Newtonian fluid which exhibits shear-thinning behavior. Blood viscosity decreases at high shear stress due to the deformation of RBCs, while it increases at low shear stress because RBCs aggregate with each others and form stacked coin structure, called rouleaux (Shiga, Maeda et al.,1990). For normal blood at 37°C, blood viscosity at high shear rate (100~200 s-1) is measured as 4 ~ 5 cP, while it increases rapidly up to 10 cP as shear stress decreases less than 10 s-1 (Rand, Lacombe et al.,1964).

Whole blood is a two-phase liquid consisting of a liquid medium (plasma) and formed elements such as RBCs, white blood cells, and platelets. Thus, its viscosity is mainly determined by (1) viscous properties of plasma, (2) the fraction of RBCs in the blood (hematocrit, normal range is 42 – 47%), and (3) viscoelastic properties of the formed elements.

**Figure 3.** (a) Apparent viscosity of blood as a function of shear rates. (b) Hematocrit effects on blood as a function of shear rates. Modified, with permission, from (Somer and Meiselman,1993; Baskurt,2007)


#### **3.2. Blood flow in microcirculation**

172 Blood Cell – An Overview of Studies in Hematology

**2.4. Mathematical models and simulations** 

 *~* 0.06 – 0.6 *µ*Ns/m. The 2-D surface viscosity of RBC membranes has been

*2D* (Waugh,1982). The diffusion constant of membrane-bound proteins can be

measured by several experiments. Tether experiments performed on model membrane systems, where cytoskeleton structure was absent, obtained a resultant upper bound of 5×10-

used to calculate the membrane viscosity (Saffman and Delbrück,1975). Using this method, the 2-D membrane viscosity values of RBC membranes have been reported in the range of (0.5-14)x10-9 Ns/m with various technqiues including fluorescence photobleaching recovery (Golan and Veatch,1980), fluorescence photo-bleaching technique (Kapitza and Sackmann, 1980), and restriction of the lateral motion of membrane embedded proteins (Tsuji and

Using mathematical models, the mechanics of the membrane cortex structures has been simulated. Using a worm-like-chain model with surface and bending energy, the forcedisplancement relations for the spectrin network of RBCs have been described (Discher, Boal et al.,1998; Dubus and Fournier,2006). The viscoelastic properties of the RBC membrane was described using an effective continuum membrane model that simulates a finitethickess 2-D continuum plane model with in-plane shear modulus and bending modulus (Dao, Lim et al.,2003). Recently developed numerical models accurately describes the

complex viscoelastic properties of RBCs deformabilty (Fedosov, Caswell et al.,2010).

The RBC deformability can influence blood microcirculation since viscosity and flow can be

Viscosity of liquid characterizes its resistance to flow under certain deforming force, especially shear stress. Under laminar flow conditions where particles move parallel to adjacent neighbors with minimal turbulence, the fluidity is classified by the dependence of viscosity to shear strain or shear stress: (1) Newtonian fluid, if the viscosity is independent of shear stress or shear strain so that shear stress is linearly proportional to shear strain, (2) non-Newtonian fluid whose viscosity either decrease (shear-thinning) or increase (shear-

Blood is non-Newtonian fluid which exhibits shear-thinning behavior. Blood viscosity decreases at high shear stress due to the deformation of RBCs, while it increases at low shear stress because RBCs aggregate with each others and form stacked coin structure, called rouleaux (Shiga, Maeda et al.,1990). For normal blood at 37°C, blood viscosity at high shear rate (100~200 s-1) is measured as 4 ~ 5 cP, while it increases rapidly up to 10 cP as shear stress

**3. RBC deformability and blood microcirculation** 

significantly changed by the viscoelastic properties of RBCs.

thickening) depending on the changes of shear stress (Merrill,1969).

decreases less than 10 s-1 (Rand, Lacombe et al.,1964).

*µ* ~ 1-10 *µ*N/m,

<sup>3</sup> *µ*N·s/m for

Ohnishi,1986).

**3.1. Blood viscosity** 

Microcirculation transports blood to the small vessels in the vasculature embedded within organs. The arterial side of vessels in the microcirculation, surrounded by smooth muscle cells, has the inner diameter of ~ 10 – 100 μm. Capillaries, parts of the microcirculation, have only one RBC thick, having the diameter of ~ 5 – 10 μm. Blood flow in microcirculation has low Reynold number and thus it is governed by Stoke's law (Baskurt,2007). Flow dynamics in microcirculation requires deep consideration of (1) fluid dynamics in capillaries, (2) interaction between formed elements with vessel walls, and (3) the structure and network of microvessels. Blood flow in microcirculation is not only determined by the geometric features of blood vessels and hydrostatic blood pressure, but also affected by the rheological properties. RBC deformability can significantly alter blood flow in microcirculation (Chien, 1987). The reduction in RBC deformability under certain physiological or pathological conditions results into the retardation of blood-flow thourgh the microcirculation, which plays important roles in the stages of peripheral vascular insufficiency (Reid, Dormandy et al.,1976); reduced RBC deformability in sickle cell disease and malaria results into occlusions in the microcirculation.

#### **4. Measurement techniques for individual RBCs**

#### **4.1. Micropipette aspiration**

Micropipette aspiration techniques have been extensively used to measure the mechanical properties of RBC membranes (Evans and La Celle,1975; Shiga, Maeda et al.,1990; Hochmuth, 2000). Micropipette aspiration uses a glass micropipette, having inner diameter of 1~3 μm, to apply negative pressure onto RBC membranes. When negative pressure is applied, RBC membrane is aspirated into the micropipette and the amount of aspiration depends on the viscoelastic properties of cell membrane. Detailed measurement techniques vary depending on the mechanical property of interest (Fig. 4): (1) measuring pressure necessary to aspirate the membrane when the aspirated distance is equal to the radius of the pipette; (2) measuring the ratio between aspirated length of membrane and the radius of the pipette in given pressure; (3) measuring pressure required to aspirate whole RBC inside the micropipette (Evans,1973; Evans and La Celle,1975). The area expansion modulus of RBC membranes can be measured by using micropipette aspiration based on Eq. (1); the measured value for *K* for normal RBCs at room temperature was 450 mN/m (Evans and Waugh, 1977). In order to measure the shear modulus of RBC membranes, the second method (Fig. 4b) can be used and the shear modulus *µ* of the RBCs can be related to the aspirated length (or "tongue length") of membrane *Dp* as,

$$D\_p \mid R\_p \sim pR\_p \mid \mu\_\prime \tag{6}$$

Measurement Techniques for Red Blood Cell Deformability: Recent Advances 175

Micropipette asperation technique can measure the bending elastic modulus *B* of RBC membranes (Evans,1983; Shiga, Maeda et al.,1990). The value for *B* depends directly on the magitude of the aspiration pressure when RBCs start to buckle and inversely on the pipette area; measuring negative pressure with varying radius of the pipette can measure *B* of RBCs. The measured value for *B* was 43.5 *kBT* (Evans,1983). By measuring the time for recovering original shape from releasing negative pressure, the 2-D viscosity of RBC

Atomic force microscopy (AFM) is a tip-scanning technique that images topographies of materials in atomic or molecular scale (Binnig, Quate et al.,1986). It uses a cantilever with a sharp tip as a probe. Depending on the amount of force to apply or sensitivity, diverse tip shapes are used such as triangular, parabolic, or cylindrical shapes (Weisenhorn, Khorsandi et al.,1993). As a tip scans over a sample with physical contact, the vertical motion of the tip is monitored by photodiodes which precisely detect small changes in laser beam position reflected from the tip. As shown in Figs. 5a-b, the topographic images of RBCs can be obtained in high spatial resolution; cytoskeleton structure of membrane can even be

**Figure 5.** AFM measures RBC topography and deformability. (A) Topogram of normal RBCs. (B) Detailed texture of the RBC membrane surface. (C) Indentation depth measurement. (D) Different force-

Since AFM can apply forces to sample surfaces at the nN scales, it can measure mechanical properties of soft materials such as RBCs. The displacement of the stage required for the same deflection of the tip is different between solid- and soft-materials, from which applied forces can be calibrated. For a parabola-shaped or a spherical tip having the radius of curvature *R*c, the indentation depth *z* relates an applied force *F* and a relative Young's

(). <sup>3</sup>

*Rc F Ez* (7)

versus-indentation depth curves of RBCs in various conditions: a. anisocytosis; s. hereditary spherocytosis; d. G6PD deficiency; and n. normal condition. Reproduced, with permission, from

(c) (d)

membranes can also be obtained by Eq. (5).

revealed (Kamruzzahan, Kienberger et al.,2004).

10 µm 3 µm

modulus *E\** (Weisenhorn, Khorsandi et al.,1993):

The relative Young's modulus *E\** is defined as:

\* 3/2 <sup>4</sup>

(Kamruzzahan, Kienberger et al.,2004; Dulinska, Targosz et al.,2006)

**4.2. Atomic force microscopy** 

(a) (b)

where *Rp* is the radius of the micropipette, *p* is the applied pressure (Evans,1973; Chien, Sung et al.,1978). Using micropipette aspiration, the value for *µ* was measured as 91.7 *µ*N/m (Evans, Mohandas et al.,1984).

**Figure 4.** Various methods for micropipette aspiration. (A) Measuring pressure *P* to aspirate the distance same with the micropipette radius. (B) Measuring the ratio between the aspirated length of membrane *D* and the micropipette radius at a certain negative pressure. (C) Measuring pressure *Pt* necessary to aspirate a whole RBC into the pipette. Reproduced, with permission, from (Evans and La Celle,1975)

Micropipette asperation technique can measure the bending elastic modulus *B* of RBC membranes (Evans,1983; Shiga, Maeda et al.,1990). The value for *B* depends directly on the magitude of the aspiration pressure when RBCs start to buckle and inversely on the pipette area; measuring negative pressure with varying radius of the pipette can measure *B* of RBCs. The measured value for *B* was 43.5 *kBT* (Evans,1983). By measuring the time for recovering original shape from releasing negative pressure, the 2-D viscosity of RBC membranes can also be obtained by Eq. (5).

#### **4.2. Atomic force microscopy**

174 Blood Cell – An Overview of Studies in Hematology

**4. Measurement techniques for individual RBCs** 

aspirated length (or "tongue length") of membrane *Dp* as,

**(A) (B) (C)**

*µ*N/m (Evans, Mohandas et al.,1984).

La Celle,1975)

in the microcirculation.

**4.1. Micropipette aspiration** 

1987). The reduction in RBC deformability under certain physiological or pathological conditions results into the retardation of blood-flow thourgh the microcirculation, which plays important roles in the stages of peripheral vascular insufficiency (Reid, Dormandy et al.,1976); reduced RBC deformability in sickle cell disease and malaria results into occlusions

Micropipette aspiration techniques have been extensively used to measure the mechanical properties of RBC membranes (Evans and La Celle,1975; Shiga, Maeda et al.,1990; Hochmuth, 2000). Micropipette aspiration uses a glass micropipette, having inner diameter of 1~3 μm, to apply negative pressure onto RBC membranes. When negative pressure is applied, RBC membrane is aspirated into the micropipette and the amount of aspiration depends on the viscoelastic properties of cell membrane. Detailed measurement techniques vary depending on the mechanical property of interest (Fig. 4): (1) measuring pressure necessary to aspirate the membrane when the aspirated distance is equal to the radius of the pipette; (2) measuring the ratio between aspirated length of membrane and the radius of the pipette in given pressure; (3) measuring pressure required to aspirate whole RBC inside the micropipette (Evans,1973; Evans and La Celle,1975). The area expansion modulus of RBC membranes can be measured by using micropipette aspiration based on Eq. (1); the measured value for *K* for normal RBCs at room temperature was 450 mN/m (Evans and Waugh, 1977). In order to measure the shear modulus of RBC membranes, the second method (Fig. 4b) can be used and the shear modulus *µ* of the RBCs can be related to the

/ ~ /, *D R pR pp p*

where *Rp* is the radius of the micropipette, *p* is the applied pressure (Evans,1973; Chien, Sung et al.,1978). Using micropipette aspiration, the value for *µ* was measured as 91.7

**Figure 4.** Various methods for micropipette aspiration. (A) Measuring pressure *P* to aspirate the distance same with the micropipette radius. (B) Measuring the ratio between the aspirated length of membrane *D* and the micropipette radius at a certain negative pressure. (C) Measuring pressure *Pt* necessary to aspirate a whole RBC into the pipette. Reproduced, with permission, from (Evans and

(6)

Atomic force microscopy (AFM) is a tip-scanning technique that images topographies of materials in atomic or molecular scale (Binnig, Quate et al.,1986). It uses a cantilever with a sharp tip as a probe. Depending on the amount of force to apply or sensitivity, diverse tip shapes are used such as triangular, parabolic, or cylindrical shapes (Weisenhorn, Khorsandi et al.,1993). As a tip scans over a sample with physical contact, the vertical motion of the tip is monitored by photodiodes which precisely detect small changes in laser beam position reflected from the tip. As shown in Figs. 5a-b, the topographic images of RBCs can be obtained in high spatial resolution; cytoskeleton structure of membrane can even be revealed (Kamruzzahan, Kienberger et al.,2004).

**Figure 5.** AFM measures RBC topography and deformability. (A) Topogram of normal RBCs. (B) Detailed texture of the RBC membrane surface. (C) Indentation depth measurement. (D) Different forceversus-indentation depth curves of RBCs in various conditions: a. anisocytosis; s. hereditary spherocytosis; d. G6PD deficiency; and n. normal condition. Reproduced, with permission, from (Kamruzzahan, Kienberger et al.,2004; Dulinska, Targosz et al.,2006)

Since AFM can apply forces to sample surfaces at the nN scales, it can measure mechanical properties of soft materials such as RBCs. The displacement of the stage required for the same deflection of the tip is different between solid- and soft-materials, from which applied forces can be calibrated. For a parabola-shaped or a spherical tip having the radius of curvature *R*c, the indentation depth *z* relates an applied force *F* and a relative Young's modulus *E\** (Weisenhorn, Khorsandi et al.,1993):

$$F = \frac{4\sqrt{R\_c}}{3} E^\* \left(\Lambda z\right)^{3/2}.\tag{7}$$

The relative Young's modulus *E\** is defined as:

$$\frac{1}{E\_1} = \frac{1 - \gamma\_1^2}{E\_1} + \frac{1 - \gamma\_2^2}{E\_2} \cong \frac{1 - \gamma\_1^2}{E\_1} \text{ for } E\_1 << E\_{2'} \tag{8}$$

Measurement Techniques for Red Blood Cell Deformability: Recent Advances 177

= 1064 nm) with maximum power of ~ 605 mW, corresponding

Since optical tweezers can apply forces at the pN level, it has been employed for measuring the deformability of RBCs. Measurements of the mechanical properties of RBCs with optical tweezers can be done either by applying optical force to microspheres attached to RBCs (Henon, Lenormand et al.,1999; Dao, Lim et al.,2003) or stretching RBCs by diverging beams from opposite directions (Guck, Ananthakrishnan et al.,2001). In the former approach, two silica beads are attached to the opposite sides of a RBC, then these beads are trapped with a

maximum optical force is 80 pN (Henon, Lenormand et al.,1999). The change in the projected diameter of the RBC in response of optical force is converted to shear modulus of the RBC using mathematical membrane models. The shear modulus of discotic RBCs were measured as ~ 10 μN/m (Dao, Lim et al.,2003). Using optical twezers system with a high power laser, the shear modulus values of RBCs under large deformation (corresponding to 400 pN) was measured as 11-18 μN/m while initial values were 19-30 μN/m, showing hyperelastic constitutive response (Lim, Dao et al.,2004). Optical stretcher, a variant of optical tweezers, uses two diverging laser beams from opposite directions (Guck, Ananthakrishnan et al.,2001). Linear momentum changes by two laser beams apply stretching force to the RBC along the optical axis, and the RBC deformations under varying optical force are measured from which mechnical properties are retrieved. Optical tweezers can also be used for detecting membrane fluctuation dynamics of RBCs by imposing a

Magnetic twisting cytometry (MTC) applies both static and oscillating magnetic field to ferromagnetic microbeads attached to the surface of cell membrane (Wang, Butler et al.,1993). Depending on the applied magnetic field, the microbeads exhibit both translational and rotational motion, which applies torques to the cell membrane. The motion of beads is recorded by a CCD camera, and the stiffness *G*' and loss modulus *G* of the membrane can be obtained by analyzing the displacement of bead in response to applied torque. By varying oscillating frequency (0.1 to 100 Hz) and the magnitude of applied magnetic field (~ 1 - 10 Gauss), the stiffness and loss modulus of RBC membranes are measured at different

**Figure 7.** Magnetic Twisting Cytometry (a) Bright field and (b) Scanning electron microscopy images of RBCs with ferromagnetic beads attached. (c) Principles of magnetic twisting cytometry. Reproduced,

driving frequencies (Puig-de-Morales-Marinkovic, Turner et al.,2007).

**(a) (b) (c)**

with permission, from (Puig-de-Morales-Marinkovic, Turner et al.,2007)

Nd:YAG laser beam (

deformation (Yoon, Kotar et al.,2011).

**4.4. Magnetic twisting cytometry** 

where *E1, E2, 1*, and *<sup>2</sup>* are the Young's moduli and Poisson ratios for the simple and the tip, respectively. Since typical value of *E2* (~150 GPa for Si3N4 tip) is much greater than that of biological samples (1 ~ 100 kPa), the rightmost equation is valid for biological samples (Radmacher,1997). The Poisson ratio is 0.5 for a perfectly incompressible and elastic material deformed elastically; the Poisson ratio of soft tissues varies with 0.490 ~ 0.499 (Fung,1993). Young's moduli of RBCs at various pathophysiological conditions have been measured using AFM. Young's moduli of healthy RBCs have been obtained to be is 4.4 ± 0.6 kPa (Dulinska, Targosz et al.,2006). RBCs from hereditary spherocytosis, thalassemia (Dulinska, Targosz et al.,2006) and diabetes mellitus (Fornal, Lekka et al.,2006), and sickle cell traits (Maciaszek and Lykotrafitis,2011) have measured.

#### **4.3. Optical tweezers**

Optical tweezers use highly focused laser beams that transfer linear or angular momentum of light, in order to optically trap μm- and nm-sized dielectric spherical particles (Ashkin, 1970). Light refraction at a sample induces linear momentum change, resulting into trapping forces (Fig. 6). High numerical aperture (NA) objective lens is used to generate a tightly focused optical trap, and its trapping force is governed by the refractive indices of sample and surrounding medium, laser power, and sample size; optical force to trap particles much smaller than laser wavelength can be described by Rayleigh scattering theory, while trapping samples much larger than laser wavelength belongs to Mie scattering regime (Ashkin, Dziedzic et al.,1986; Svoboda and Block,1994). Optical tweezers have been widely used in many fields such as biophysics and soft matter sciences, where manipulation of μm sized particles (e.g. cells or microspheres) with a small force (pN scale) is required (Grier, 2003; Lee and Grier,2007).

**Figure 6.** Principles of optical tweezers. (A) Laser beam with gradual intensity transfers linear momentum to a microsphere to escape from the beam center. (B) Focused Gaussian beam exerts trapping force. (c) Deformation of a RBC by exerting various optical forces to microspheres attached on the RBC membrane. The change of diameter *D* in response of optical force *F* is converted to shear modulus of the RBC. Modified, with permission, from (Svoboda and Block,1994; Henon, Lenormand et al.,1999).

Since optical tweezers can apply forces at the pN level, it has been employed for measuring the deformability of RBCs. Measurements of the mechanical properties of RBCs with optical tweezers can be done either by applying optical force to microspheres attached to RBCs (Henon, Lenormand et al.,1999; Dao, Lim et al.,2003) or stretching RBCs by diverging beams from opposite directions (Guck, Ananthakrishnan et al.,2001). In the former approach, two silica beads are attached to the opposite sides of a RBC, then these beads are trapped with a Nd:YAG laser beam ( = 1064 nm) with maximum power of ~ 605 mW, corresponding maximum optical force is 80 pN (Henon, Lenormand et al.,1999). The change in the projected diameter of the RBC in response of optical force is converted to shear modulus of the RBC using mathematical membrane models. The shear modulus of discotic RBCs were measured as ~ 10 μN/m (Dao, Lim et al.,2003). Using optical twezers system with a high power laser, the shear modulus values of RBCs under large deformation (corresponding to 400 pN) was measured as 11-18 μN/m while initial values were 19-30 μN/m, showing hyperelastic constitutive response (Lim, Dao et al.,2004). Optical stretcher, a variant of optical tweezers, uses two diverging laser beams from opposite directions (Guck, Ananthakrishnan et al.,2001). Linear momentum changes by two laser beams apply stretching force to the RBC along the optical axis, and the RBC deformations under varying optical force are measured from which mechnical properties are retrieved. Optical tweezers can also be used for detecting membrane fluctuation dynamics of RBCs by imposing a deformation (Yoon, Kotar et al.,2011).

#### **4.4. Magnetic twisting cytometry**

176 Blood Cell – An Overview of Studies in Hematology

(Maciaszek and Lykotrafitis,2011) have measured.

where *E1, E2,* 

*1*, and 

**4.3. Optical tweezers** 

2003; Lee and Grier,2007).

**Gradient Profile**

**Light in Light in**

(a) (b) (c)

**Dielectric Sphere**

**Momentum Change Momentum Change**

**out in Δ**

**Figure 6.** Principles of optical tweezers. (A) Laser beam with gradual intensity transfers linear momentum to a microsphere to escape from the beam center. (B) Focused Gaussian beam exerts trapping force. (c) Deformation of a RBC by exerting various optical forces to microspheres attached on the RBC membrane. The change of diameter *D* in response of optical force *F* is converted to shear modulus of the RBC. Modified, with permission, from (Svoboda and Block,1994; Henon, Lenormand et al.,1999).

**dim ray bright ray focus**

**out in Δ**

**Light out Light out**

222 121 \* 1 2 12 1

 

*E EE E*

<sup>1</sup> <sup>111</sup> for , *E E*

respectively. Since typical value of *E2* (~150 GPa for Si3N4 tip) is much greater than that of biological samples (1 ~ 100 kPa), the rightmost equation is valid for biological samples (Radmacher,1997). The Poisson ratio is 0.5 for a perfectly incompressible and elastic material deformed elastically; the Poisson ratio of soft tissues varies with 0.490 ~ 0.499 (Fung,1993). Young's moduli of RBCs at various pathophysiological conditions have been measured using AFM. Young's moduli of healthy RBCs have been obtained to be is 4.4 ± 0.6 kPa (Dulinska, Targosz et al.,2006). RBCs from hereditary spherocytosis, thalassemia (Dulinska, Targosz et al.,2006) and diabetes mellitus (Fornal, Lekka et al.,2006), and sickle cell traits

Optical tweezers use highly focused laser beams that transfer linear or angular momentum of light, in order to optically trap μm- and nm-sized dielectric spherical particles (Ashkin, 1970). Light refraction at a sample induces linear momentum change, resulting into trapping forces (Fig. 6). High numerical aperture (NA) objective lens is used to generate a tightly focused optical trap, and its trapping force is governed by the refractive indices of sample and surrounding medium, laser power, and sample size; optical force to trap particles much smaller than laser wavelength can be described by Rayleigh scattering theory, while trapping samples much larger than laser wavelength belongs to Mie scattering regime (Ashkin, Dziedzic et al.,1986; Svoboda and Block,1994). Optical tweezers have been widely used in many fields such as biophysics and soft matter sciences, where manipulation of μm sized particles (e.g. cells or microspheres) with a small force (pN scale) is required (Grier,

(8)

**5 µm**

*<sup>2</sup>* are the Young's moduli and Poisson ratios for the simple and the tip,

Magnetic twisting cytometry (MTC) applies both static and oscillating magnetic field to ferromagnetic microbeads attached to the surface of cell membrane (Wang, Butler et al.,1993). Depending on the applied magnetic field, the microbeads exhibit both translational and rotational motion, which applies torques to the cell membrane. The motion of beads is recorded by a CCD camera, and the stiffness *G*' and loss modulus *G* of the membrane can be obtained by analyzing the displacement of bead in response to applied torque. By varying oscillating frequency (0.1 to 100 Hz) and the magnitude of applied magnetic field (~ 1 - 10 Gauss), the stiffness and loss modulus of RBC membranes are measured at different driving frequencies (Puig-de-Morales-Marinkovic, Turner et al.,2007).

**Figure 7.** Magnetic Twisting Cytometry (a) Bright field and (b) Scanning electron microscopy images of RBCs with ferromagnetic beads attached. (c) Principles of magnetic twisting cytometry. Reproduced, with permission, from (Puig-de-Morales-Marinkovic, Turner et al.,2007)

The torsional stiffness modulus is independent of frequency, whose value is ~ 10-3 Pa/nm at sinusoidal magnetic field of 1 G, while the loss modulus increases as frequency increases; these values correspond to the bending moduli in the range of 0.2 - 0.8 pN·μm and the shear moduli in the range of 6-12 μN/m (Puig-de-Morales-Marinkovic, Turner et al.,2007). MTC technique also revealed dramatic increases in the stiffness of malaria-infected RBC at the febrile temperature (41°C) (Marinkovic, Diez-Silva et al.,2009).

Measurement Techniques for Red Blood Cell Deformability: Recent Advances 179

et al.,2010). Several alterations in the deformability of RBCs have been studied using DPM, including the effects of ATP (Park, Best et al.,2010; Ben-Isaac, Park et al.,2011), the nonlinear behavior of RBC deformability in response to different osmotic pressure (Park, Best et al., 2011), and malaria egress mechanism (Chandramohanadas, Park et al.,2011). Employing spectroscopic quantitative phase imaging, cytoplasmic Hb concentration that is tightly related to the cytoplasmic viscosity, can also be simultaneously quantified (Park, Yamauchi et al.,2009; Jang, Jang et al.,2012). In addition, polarization-sensitive quantitative phase microscopy will be potentially used for the study of sickle cell disease and its implications to

Dyanmic light scattering signals provide rheological information about RBCs (Tishler and Carlson, 1987; Amin, Park et al.,2007). Although dynamic light scattering have been extensively used in combination with ektacytometry, it provides averaged signals from

Fourier transform light scattering (FTLS) provides both static and dynamic light scattering signal from individual cells. Light field, measured by quantitative phase microscopy or digital holographic microscopy, contains both amplitude and phase information, and thus far-field light scattering pattterns can be directly calculated by numerically propagating the measured field – technically applying Fourier transformation (Ding, Wang et al.,2008). FTLS technique can provide both morphological and rheological information about individual biological cells. By analyzing dynamic light scattering signals measured by FTLS, one can qualitatively access the membrane surface tension and viscosity of individual RBCs (Park, Diez-Silva et al.,2010). Due to its capability of measuring light scattering signals from individual cells with high signal-to-noise ratio, FTLS has been employed to study several pathophysiological effects to the deformabiltiy of RBCs, including malaria infection (Park, Diez-Silva et al.,2010), depletion of ATP (Park, Best-Popescu et al.,2011), and sickle cell

Blood viscometer measures the viscosity of blood over a wide range of shear rates. Blood viscometer controls either shear stress or shear rate of blood using rational objects. Stresscontrolled blood viscometer applys a constant torque which corresponds to constant rotational speed in a well-designed rotational rheometer. In a rate-controlled system, applied torque is controlled by a stress-sensing device so that a constant rotational speed is achieved. Viscometers can be classified by the cylinder shape: a concentric cylinder, a cone

Cylinder-type viscometer uses two concentric cylinders: a rotational inner cup and a stationary outer cylinder. Time-independent shear rate can be precisely measured by

many RBCs. Thus it is difficult to access the deformability of individual RBCs.

RBC deformability (Kim, Jeong et al.,2012).

**4.6. Dynamic light scattering** 

disease (Kim, Higgins et al.,2012).

**5. Measurement techniques for blood rheology** 

**5.1. Blood viscometer and ektacytometry** 

plate, and a parallel plate viscometer (Fig. 9).

## **4.5. Quantitative phase imaging**

Quantitaitve phase imaging technqiues measure the electric field, i.e. amplitude and phase images whereas conventional brightfield microscopy only images light intensity (Fig. 8) (Popescu, 2011). Employing the principle of laser interference, electric field information of target sample is modulated onto intereferograms recorded by a CCD camera. By using appropriate field retrieval algorithms, the field information can be retrieved from the measured holograms (Debnath and Park, 2011). Typical interferogram and quantitative phase image of a RBC are shown in Fig. 8b-c. Quantitative phase imaging techniques can measuring dynamic membrane fluctuations of RBCs (Popescu, Ikeda et al.,2005; Popescu, Park et al.,2008; Park, Best et al.,2011) as well as cellular dry-mass (Popescu, Park et al.,2008). Dynamic membrane fluctuation, consisting of submicron displacement of the membrane, has a strong correlation with deformability of RBCs and can be altered by biochemical changes in protein level (Waugh and Evans,1979). By measuring membrane fluctuation of RBCs, bending modulus and tension factor of RBCs were calcualated (Popescu, Ikeda et al., 2006).

**Figure 8.** Quantitative phase imaging. (A) Schematic of the principle of quantitative phase imaging. (B) Measured interferogram and (C) retrieved phase image of a RBC using quantitative phase imaging. Reproduced, with permission, from (Park, Best et al.,2011).

Diffraction phase microscopy (DPM), a highly stable technique for quantitative phase imaging, has been widely used for investigating the deformability of RBCs. Employing common-path laser interferometry, DPM provides full-field quantitative phase imaging with unprecedented stability (Park, Popescu et al.,2006; Popescu, Ikeda et al.,2006). DPM measured spatiotemporal coherency in dynamic membrane fluctuations (Popescu, Park et al.,2007), shear modulus for the RBCs invaded with malaria-inducing parasite *Plasmodium falcifarum* (*Pf*-RBCs) (Park, Diez-Silva et al.,2008), and effective viscoelastic properties of RBCs (Wang, Ding et al.,2011). Recently, integrated with a mathematical model, DPM provide the mechanical properties of individual RBCs from membrane fluctuations: shear modulus, bending modulus, area expansion modulus, and cytoplasmic viscosity (Park, Best et al.,2010). Several alterations in the deformability of RBCs have been studied using DPM, including the effects of ATP (Park, Best et al.,2010; Ben-Isaac, Park et al.,2011), the nonlinear behavior of RBC deformability in response to different osmotic pressure (Park, Best et al., 2011), and malaria egress mechanism (Chandramohanadas, Park et al.,2011). Employing spectroscopic quantitative phase imaging, cytoplasmic Hb concentration that is tightly related to the cytoplasmic viscosity, can also be simultaneously quantified (Park, Yamauchi et al.,2009; Jang, Jang et al.,2012). In addition, polarization-sensitive quantitative phase microscopy will be potentially used for the study of sickle cell disease and its implications to RBC deformability (Kim, Jeong et al.,2012).

#### **4.6. Dynamic light scattering**

178 Blood Cell – An Overview of Studies in Hematology

**4.5. Quantitative phase imaging** 

2006).

**(a)**

febrile temperature (41°C) (Marinkovic, Diez-Silva et al.,2009).

The torsional stiffness modulus is independent of frequency, whose value is ~ 10-3 Pa/nm at sinusoidal magnetic field of 1 G, while the loss modulus increases as frequency increases; these values correspond to the bending moduli in the range of 0.2 - 0.8 pN·μm and the shear moduli in the range of 6-12 μN/m (Puig-de-Morales-Marinkovic, Turner et al.,2007). MTC technique also revealed dramatic increases in the stiffness of malaria-infected RBC at the

Quantitaitve phase imaging technqiues measure the electric field, i.e. amplitude and phase images whereas conventional brightfield microscopy only images light intensity (Fig. 8) (Popescu, 2011). Employing the principle of laser interference, electric field information of target sample is modulated onto intereferograms recorded by a CCD camera. By using appropriate field retrieval algorithms, the field information can be retrieved from the measured holograms (Debnath and Park, 2011). Typical interferogram and quantitative phase image of a RBC are shown in Fig. 8b-c. Quantitative phase imaging techniques can measuring dynamic membrane fluctuations of RBCs (Popescu, Ikeda et al.,2005; Popescu, Park et al.,2008; Park, Best et al.,2011) as well as cellular dry-mass (Popescu, Park et al.,2008). Dynamic membrane fluctuation, consisting of submicron displacement of the membrane, has a strong correlation with deformability of RBCs and can be altered by biochemical changes in protein level (Waugh and Evans,1979). By measuring membrane fluctuation of RBCs, bending modulus and tension factor of RBCs were calcualated (Popescu, Ikeda et al.,

**(b) (c)**

**Figure 8.** Quantitative phase imaging. (A) Schematic of the principle of quantitative phase imaging. (B) Measured interferogram and (C) retrieved phase image of a RBC using quantitative phase imaging.

Diffraction phase microscopy (DPM), a highly stable technique for quantitative phase imaging, has been widely used for investigating the deformability of RBCs. Employing common-path laser interferometry, DPM provides full-field quantitative phase imaging with unprecedented stability (Park, Popescu et al.,2006; Popescu, Ikeda et al.,2006). DPM measured spatiotemporal coherency in dynamic membrane fluctuations (Popescu, Park et al.,2007), shear modulus for the RBCs invaded with malaria-inducing parasite *Plasmodium falcifarum* (*Pf*-RBCs) (Park, Diez-Silva et al.,2008), and effective viscoelastic properties of RBCs (Wang, Ding et al.,2011). Recently, integrated with a mathematical model, DPM provide the mechanical properties of individual RBCs from membrane fluctuations: shear modulus, bending modulus, area expansion modulus, and cytoplasmic viscosity (Park, Best

Reproduced, with permission, from (Park, Best et al.,2011).

20 pixels 1.5um

[rad]

0 0.5 1 1.5 2 2.5 Dyanmic light scattering signals provide rheological information about RBCs (Tishler and Carlson, 1987; Amin, Park et al.,2007). Although dynamic light scattering have been extensively used in combination with ektacytometry, it provides averaged signals from many RBCs. Thus it is difficult to access the deformability of individual RBCs.

Fourier transform light scattering (FTLS) provides both static and dynamic light scattering signal from individual cells. Light field, measured by quantitative phase microscopy or digital holographic microscopy, contains both amplitude and phase information, and thus far-field light scattering pattterns can be directly calculated by numerically propagating the measured field – technically applying Fourier transformation (Ding, Wang et al.,2008). FTLS technique can provide both morphological and rheological information about individual biological cells. By analyzing dynamic light scattering signals measured by FTLS, one can qualitatively access the membrane surface tension and viscosity of individual RBCs (Park, Diez-Silva et al.,2010). Due to its capability of measuring light scattering signals from individual cells with high signal-to-noise ratio, FTLS has been employed to study several pathophysiological effects to the deformabiltiy of RBCs, including malaria infection (Park, Diez-Silva et al.,2010), depletion of ATP (Park, Best-Popescu et al.,2011), and sickle cell disease (Kim, Higgins et al.,2012).
