Source/Sink terms

The source/sink term can be derived by temporarily ignored the diffusion term:

Prevention of Lethal Osmotic Injury to Cells

ii. Transportation across cell membrane

the sum of the water, CPA and cell solid volumes:

further determined based on mass conservation:

equation will result in a finite difference scheme:

the 1st CV is followed by the Kth one. Thus

where *nc* is the number of cells in a CV.

Numerical Simulation

During Addition and Removal of Cryoprotective Agents: Theory and Technology 125

For the ternary system as considered in the present example, the mass transport across cell membrane can be described by the two-parameter formalism [2,3]. The total cell volume is

where the intracellular CPA volume can be determined as *i i V =VN s ss* . As soon as cell volume

*ei i*

With finite volume method, a fully implicit control volume integration of the governing

 e e e old eold 1 1 k 1 1 k1 1 , 2, , 1 *old*

where *a* is the coefficient and K is the total number of CV in the system. The subscript 'k' refers to the kth CV in the system and the superscript 'old' refers to the previous time level.

*<sup>V</sup> dt* , <sup>1</sup> *<sup>e</sup>*

The subscript '*k*-1' and '*k*+1' in equation (30) refer to the previous and next CVs along the *x* direction, respectively. Noting that the cell suspension flows circularly in the closed system,

> 2 1 <sup>1</sup> 22 1 1 <sup>1</sup> <sup>1</sup> *old e e e old eold K p CV K K c CV a a a SV a a a SV*

1 1 1 1 11 *old <sup>e</sup> e e old e old K Kp CV K KK <sup>K</sup> KK c CV <sup>K</sup> a a a SV a a a SV*

Here, the removal of glycerol from cryopreserved human red blood cells (RBCs) is discussed for an instance. For the ease of discussion, it is further restricted that blood volume keeps constant, i.e. ultrafiltrate flow rate keeps equal to diluent flow rate, although the presented system and model can adapt to more complicated situations. Besides, the concentration of NaCl in diluent and thawed blood are considered to be isotonic (0.29 Osmol/kg·water). In

 

*<sup>w</sup> <sup>p</sup> <sup>e</sup> w dV <sup>S</sup>*

(32)

(33)

 

 

 

(30)

*a a a SV a a a SV k K*

*k k k p CV k k k k k c CV <sup>k</sup> <sup>k</sup>*

Sc and Sp are the constant portion and gradient of the linearized source term:

*c e w dN <sup>S</sup>*

1 *<sup>e</sup>*

*e i s cs <sup>c</sup> dN n dN* , 0 *<sup>e</sup>*

and intracellular solute concentrations are calculated the values of *<sup>e</sup>*

*i i VV VV c w s cb* (27)

*w cw c c s <sup>c</sup> dV n dV n dV dV* (29)

  *<sup>c</sup> dN* and *<sup>e</sup>*

*<sup>n</sup> <sup>c</sup> dN* (28)

*<sup>V</sup> dt* (31)

*<sup>w</sup> <sup>c</sup> dV* can be

$$S = \frac{d\overline{\phi^{\epsilon}}}{dt} = \frac{d\left(N^{\epsilon}/V\_{w}^{\epsilon}\right)}{dt} = \frac{1}{V\_{w}^{\epsilon}}\overline{\frac{dN^{\epsilon}}{dt}} - \frac{\overline{\phi^{\epsilon}}}{V\_{w}^{\epsilon}}\overline{\frac{dV\_{w}^{\epsilon}}{dt}}\tag{20}$$

where *<sup>e</sup> N* and *<sup>e</sup> Vw* are the number of osmoles of solutes and water volume in extracellular solution, respectively. The overlines in the equation indicate the given deriving condition. The terms of *<sup>e</sup> dN* and *<sup>e</sup> dV* can be further specified as

$$
\overline{dN^{\varepsilon}} = dN^{\varepsilon} \Big|\_{d} - dN^{\varepsilon} \Big|\_{f} + dN^{\varepsilon} \Big|\_{c} \tag{21}
$$

$$
\overline{dV\_w^\epsilon} = dV\_w^\epsilon \Big|\_d - dV\_w^\epsilon \Big|\_f + dV\_w^\epsilon \Big|\_c \tag{22}
$$

where the subscripts "*d*", "*f*" and "*c*" refer to the effects of dilution, filtration and cell membrane transport, respectively. According to assumption (2), cell suspension inside the system can be equally divided into a finite number of control volumes (CVs), as shown in Fig.17B. For each CV, the values of the terms in the right hands of equation [21] and [22] can be determined as flows.

#### i. Dilution/filtration

According to assumption (3), when a CV is going through the diluting point, the extracellular solution will be diluted immediately. Considering the pure filtration method used in the system, it is also assumed that ultrafiltration happens only at a certain location (the filtrating point, shown in Fig.17A), and the ultrafiltrate has the same composition as the extracellular solution. Thus the values of *<sup>e</sup> <sup>w</sup> <sup>d</sup> dV* , *<sup>e</sup> d dN* , *<sup>e</sup> <sup>w</sup> <sup>f</sup> dV* and *<sup>e</sup> f dN* of each CV can be

determined as

$$
\begin{bmatrix}
\overline{dV\_w^{\varepsilon}}
\end{bmatrix}\_d = \begin{bmatrix}
\frac{Q\_b V\_{CV}}{Q\_b} & & \text{CV at the diluting point} \\
0 & & \text{CVs at the other locations}
\end{bmatrix} \tag{23}
$$

$$
\overline{dN^\epsilon}\Big|\_d = \overline{dV\_w^\epsilon}\Big|\_d \cdot \phi^d\tag{24}
$$

$$
\overline{\left| \overline{dV\_w^{\varepsilon}} \right|\_f} = \left| \frac{Q\_f V\_{\text{CV}}}{(Q\_b + Q\_d)(1 + \overline{V}\_s \phi\_s^{\varepsilon})} \right. \qquad \text{CV at the filtering point} \tag{25}
$$

$$
\overline{dN^{\epsilon}}\Big|\_{f} = \overline{dV^{\epsilon}\_{w}}\Big|\_{f} \cdot \phi^{\epsilon} \tag{26}
$$

where *Qf*, *Qb* and *Qd* are the flow rates of ultrafiltrate, cell suspension and diluent, *ϕd* is the solute concentration in diluent, *<sup>e</sup> <sup>s</sup>* is the extracellular CPA concentration, *Vs* is the partial molar volume of the CPA, and *V*CV is the volume of a CV, respectively.

#### ii. Transportation across cell membrane

124 Current Frontiers in Cryobiology

*d d dN V <sup>N</sup> dV <sup>S</sup> dt dt dt dt V V*

where *<sup>e</sup> N* and *<sup>e</sup> Vw* are the number of osmoles of solutes and water volume in extracellular solution, respectively. The overlines in the equation indicate the given deriving condition.

*ee e e*

*ee e e*

where the subscripts "*d*", "*f*" and "*c*" refer to the effects of dilution, filtration and cell membrane transport, respectively. According to assumption (2), cell suspension inside the system can be equally divided into a finite number of control volumes (CVs), as shown in Fig.17B. For each CV, the values of the terms in the right hands of equation [21] and [22] can

According to assumption (3), when a CV is going through the diluting point, the extracellular solution will be diluted immediately. Considering the pure filtration method used in the system, it is also assumed that ultrafiltration happens only at a certain location (the filtrating point, shown in Fig.17A), and the ultrafiltrate has the same composition as the

> *<sup>w</sup> <sup>d</sup> dV* , *<sup>e</sup>*

*d CV*

*f CV*

*Q V*

molar volume of the CPA, and *V*CV is the volume of a CV, respectively.

*Q V*

*d dN* , *<sup>e</sup>*

0 CVs at the other locations

0 CVs at the other locations

*<sup>s</sup>* is the extracellular CPA concentration, *Vs* is the partial

CV at the filtrating point ( )(1 )

*e ed <sup>w</sup> d d dN dV*

*e ee <sup>w</sup> f f dN dV*

where *Qf*, *Qb* and *Qd* are the flow rates of ultrafiltrate, cell suspension and diluent, *ϕd* is the

CV at the diluting point

*<sup>w</sup> <sup>f</sup> dV* and *<sup>e</sup>*

*f*

(24)

(26)

*dN* of each CV can be

(23)

(25)

The terms of *<sup>e</sup> dN* and *<sup>e</sup> dV* can be further specified as

be determined as flows. i. Dilution/filtration

determined as

extracellular solution. Thus the values of *<sup>e</sup>*

*e*

*w b d*

*<sup>e</sup> <sup>e</sup> <sup>w</sup> b d ss <sup>f</sup>*

*dV QQ V*

 

solute concentration in diluent, *<sup>e</sup>*

*dV Q* 

<sup>1</sup> *e e <sup>e</sup> e e <sup>e</sup> <sup>w</sup> <sup>w</sup>*

*e e w w*

 (20)

*<sup>d</sup> <sup>f</sup> <sup>c</sup> dN dN dN dN* (21)

*ww w w <sup>d</sup> <sup>f</sup> <sup>c</sup> dV dV dV dV* (22)

For the ternary system as considered in the present example, the mass transport across cell membrane can be described by the two-parameter formalism [2,3]. The total cell volume is the sum of the water, CPA and cell solid volumes:

$$V\_c = V\_w^i + V\_s^i + V\_{cb} \tag{27}$$

where the intracellular CPA volume can be determined as *i i V =VN s ss* . As soon as cell volume and intracellular solute concentrations are calculated the values of *<sup>e</sup> <sup>c</sup> dN* and *<sup>e</sup> <sup>w</sup> <sup>c</sup> dV* can be further determined based on mass conservation:

$$\left. \begin{array}{c} d\mathcal{N}\_s^e \right|\_{\mathcal{C}} = -\mathfrak{n}\_c d\mathcal{N}\_s^i \quad d\mathcal{N}\_n^e \Big|\_{\mathcal{C}} = 0 \end{array} \tag{28}$$

$$\left.dV\_w^{\varepsilon}\right|\_c = -n\_c dV\_w^i = -n\_c \left(dV\_c - dV\_s^i\right) \tag{29}$$

where *nc* is the number of cells in a CV.

#### Numerical Simulation

With finite volume method, a fully implicit control volume integration of the governing equation will result in a finite difference scheme:

$$\left[a\_{k-1} + a\_{k+1} + a\_k^{\text{old}} - \left(S\_p V\_{\text{CV}}\right)\_k\right] \mathfrak{g}\_k^{\text{c}} = a\_{k-1} \mathfrak{g}\_{k-1}^{\text{c}} + a\_{k+1} \mathfrak{g}\_{k+1}^{\text{c}} + a\_k^{\text{old}} \mathfrak{g}\_k^{\text{cold}} + \left(S\_c V\_{\text{CV}}\right)\_k, k = 2, \dots, K-1 \tag{50}$$

where *a* is the coefficient and K is the total number of CV in the system. The subscript 'k' refers to the kth CV in the system and the superscript 'old' refers to the previous time level. Sc and Sp are the constant portion and gradient of the linearized source term:

$$S\_c = \frac{1}{V\_w^{\epsilon}} \overline{dN^{\epsilon}} \quad S\_p = -\frac{1}{V\_w^{\epsilon}} \overline{dV\_w^{\epsilon}}\tag{31}$$

The subscript '*k*-1' and '*k*+1' in equation (30) refer to the previous and next CVs along the *x* direction, respectively. Noting that the cell suspension flows circularly in the closed system, the 1st CV is followed by the Kth one. Thus

$$\left[a\_K + a\_2 + a\_1^{old} - \left(S\_p V\_{CV}\right)\_1\right] \phi\_1^\epsilon = a\_K \phi\_K^\epsilon + a\_2 \phi\_2^\epsilon + a\_1^{old} \phi\_1^{cold} + \left(S\_c V\_{CV}\right)\_1 \tag{32}$$

$$\left[\left(a\_{K-1} + a\_1 + a\_K^{old} - \left(S\_p V\_{CV}\right)\_K\right)\right] \phi\_K^\epsilon = a\_{K-1} \phi\_{K-1}^\epsilon + a\_1 \phi\_1^\epsilon + a\_K^{old} \phi\_K^{\epsilon \
abla} + \left(S\_c V\_{CV}\right)\_K \tag{33}$$

Here, the removal of glycerol from cryopreserved human red blood cells (RBCs) is discussed for an instance. For the ease of discussion, it is further restricted that blood volume keeps constant, i.e. ultrafiltrate flow rate keeps equal to diluent flow rate, although the presented system and model can adapt to more complicated situations. Besides, the concentration of NaCl in diluent and thawed blood are considered to be isotonic (0.29 Osmol/kg·water). In

Prevention of Lethal Osmotic Injury to Cells

During Addition and Removal of Cryoprotective Agents: Theory and Technology 127

Fig. 18. Simulated glycerol concentration variation and cell volume excursion in CV1

Venous human blood was collected from healthy, adult blood donors in the Red Cross Transfusion Center of Heifei. For each donor, up to 200ml whole blood was collected into CPDA-1 anticoagulant solution in PVC plastic bag, and stored for up to 24 hours at 4°C. Then it was centrifuged at 1615×g for 4 minutes, and the platelets, leukocytes and plasma

Each of the RBC suspensions was transferred into a 400-ml plastic bag, and then it was glycerolized by 57.1% w/v glycerol solution with a volume ratio of 2:1 (glycerol to blood) to achieve a final glycerol concentration about 40% (w/v) and a hematocrit of 25%-30%. Subsequently the blood bag was covered by PE foam sheet (thickness: 5mm) and then placed into a metal box (size: 200mm×150mm×20mm). After 30 minutes of equilibrium, the metal box was transferred to a -80°C freezer (MDF-U52V, SANYON, Japan) and the RBC suspension was frozen gradually. After cryopreservation in the freezer for 2~7 days, the RBC suspension was

Each unit of the thawed blood was deglycerolized with the dilution-filtration system as shown in Fig. 16, and the operation protocol was theoretically optimized. A typical experimental conditions ( *<sup>0</sup> Vb* = 200ml, *<sup>0</sup> h* = 30%, *<sup>0</sup> Ms* = 6.28 Osmol/kg·water) was studied first to reveal the general law. To evaluate the effect of each operation parameter, different protocols were applied respectively. Fig.19 shows that time cost is significantly reduced but maximum cell volume grows directly along with diluent flow rate increases, i.e. the washing efficiency can be

taken out and thawed in a 37°C water bath for about 10 minutes with gentle agitating.

(initially at the diluting point) during a dilution-filtration process.

were removed to produce a hematocrit of 75±5 percent.

**Experiments** 

this manner, the basic variables for a simulation consist of the experimental conditions (including the initial blood volume ( *<sup>0</sup> Vb* ), hematocrit ( *<sup>0</sup> <sup>h</sup>* ), and the concentrations of CPA ( *<sup>0</sup> Ms* ) in extra/intracellular solution) as well as the operation parameters (including the flow rates of blood (*Qb*) and diluent (*Qd*)). The initial values of the other parameters in the model can be determined as

$$V\_{CV}^{0} = V\_{b}^{0} \;/\; K \tag{35}$$

$$V\_c^0 = V\_{iso} + V\_s M\_s^0 (V\_{iso} - V\_{cb}) \tag{36}$$

$$m\_c^0 = V\_{CV}^0 h^0 \;/\; V\_c^0 \tag{37}$$

where *V*iso is the isotonic volume of RBC. When terming the CV at the diluting point (x=0) when t=0 as the 1st CV (CV1), the initial location of each CV can be allocated. Then the values of *<sup>e</sup> dN* and *<sup>e</sup> dV* for each CV can be calculated according to equations [21]-[31]. By alternatively calculating the source terms and solving the linearized governing equation, the concentration variation of extra-/intracellular solution as well as the responding cell volume excursion can be simulated. A typical process is shown in Fig.18, in which *<sup>0</sup> Vb* = 200ml, *<sup>0</sup> h* = 30%, *<sup>0</sup> Ms* = 6.28 Osmol/kg·water (approximately 40% w/v), *Qb*=200ml/min, and *Qd*= 25ml/min.

To quantitatively evaluate the effect of an operation protocol, the maximum cell volume and the total time cost (to a final glycerol concentration below 10g/L (Brecher, 2002)) of the removing process can be taken as criteria for cell recovery rate and removing efficiency, respectively. Then the optimal protocol can be found out by applying different operation parameters to the given experimental conditions and comparing the simulated results. Hereinafter, the diffusion coefficients of glycerol and NaCl in water were set to be 5.43×10- 10 m2/s and 14.41×10-10 m2/s, respectively (Ternstorm et al, 1996). The parameters about the dilution -filtration system and RBC membrane are also specified as listed in Table 4 and Table 5. These parameters may be different in various applications and systems.


Table 4. Structural parameters of the dilution-filtration system used in the calculation


a From literature (Papanek, 1978);

Table 5. Membrane parameters of human RBC used in the calculation

Fig. 18. Simulated glycerol concentration variation and cell volume excursion in CV1 (initially at the diluting point) during a dilution-filtration process.

### **Experiments**

126 Current Frontiers in Cryobiology

this manner, the basic variables for a simulation consist of the experimental conditions (including the initial blood volume ( *<sup>0</sup> Vb* ), hematocrit ( *<sup>0</sup> <sup>h</sup>* ), and the concentrations of CPA ( *<sup>0</sup> Ms* ) in extra/intracellular solution) as well as the operation parameters (including the flow rates of blood (*Qb*) and diluent (*Qd*)). The initial values of the other parameters in the model

where *V*iso is the isotonic volume of RBC. When terming the CV at the diluting point (x=0) when t=0 as the 1st CV (CV1), the initial location of each CV can be allocated. Then the values of *<sup>e</sup> dN* and *<sup>e</sup> dV* for each CV can be calculated according to equations [21]-[31]. By alternatively calculating the source terms and solving the linearized governing equation, the concentration variation of extra-/intracellular solution as well as the responding cell volume excursion can be simulated. A typical process is shown in Fig.18, in which *<sup>0</sup> Vb* = 200ml, *<sup>0</sup> h* = 30%, *<sup>0</sup> Ms* = 6.28 Osmol/kg·water (approximately 40% w/v), *Qb*=200ml/min, and *Qd*=

To quantitatively evaluate the effect of an operation protocol, the maximum cell volume and the total time cost (to a final glycerol concentration below 10g/L (Brecher, 2002)) of the removing process can be taken as criteria for cell recovery rate and removing efficiency, respectively. Then the optimal protocol can be found out by applying different operation parameters to the given experimental conditions and comparing the simulated results. Hereinafter, the diffusion coefficients of glycerol and NaCl in water were set to be 5.43×10- 10 m2/s and 14.41×10-10 m2/s, respectively (Ternstorm et al, 1996). The parameters about the dilution -filtration system and RBC membrane are also specified as listed in Table 4 and

**Sections Inner volume Effective area From the outlet of blood bag to the diluting point** 5ml 1.25×10-5 m2 **From the diluting point to the filtrating point** 5ml 1.25×10-5 m2 **From the filtration point to the outlet of hemofilter** 85ml 5×10-4 m2 **From the outlet of hemofilter to the inlet of blood bag** 5ml 1.25×10-5 m2 **Blood bag** Variable 5×10-3 m2 Table 4. Structural parameters of the dilution-filtration system used in the calculation

Table 5. These parameters may be different in various applications and systems.

**Surface area of RBC(***Ac***)** 135 ×10-12 m2 a **Hydraulic permeability of cell membrane (***Lp***)** 1.74 ×10-12 m/Pa/s a **Isotonic volume of RBC (***V***iso)** 98.3 ×10-18 m3 a **Solid volume of RBC (***Vcb***)** 0.283 ×*Viso* <sup>a</sup> **Glycerol permeability to cell membrane (***Ps***)** 6.61 ×10-8 m/s a

Table 5. Membrane parameters of human RBC used in the calculation

0 0 *V VK CV b* / (35)

0 00 0 *n Vh V c CV c* / (37)

0 0( ) *V V VM V V c iso s s iso cb* (36)

can be determined as

25ml/min.

a From literature (Papanek, 1978);

Venous human blood was collected from healthy, adult blood donors in the Red Cross Transfusion Center of Heifei. For each donor, up to 200ml whole blood was collected into CPDA-1 anticoagulant solution in PVC plastic bag, and stored for up to 24 hours at 4°C. Then it was centrifuged at 1615×g for 4 minutes, and the platelets, leukocytes and plasma were removed to produce a hematocrit of 75±5 percent.

Each of the RBC suspensions was transferred into a 400-ml plastic bag, and then it was glycerolized by 57.1% w/v glycerol solution with a volume ratio of 2:1 (glycerol to blood) to achieve a final glycerol concentration about 40% (w/v) and a hematocrit of 25%-30%. Subsequently the blood bag was covered by PE foam sheet (thickness: 5mm) and then placed into a metal box (size: 200mm×150mm×20mm). After 30 minutes of equilibrium, the metal box was transferred to a -80°C freezer (MDF-U52V, SANYON, Japan) and the RBC suspension was frozen gradually. After cryopreservation in the freezer for 2~7 days, the RBC suspension was taken out and thawed in a 37°C water bath for about 10 minutes with gentle agitating.

Each unit of the thawed blood was deglycerolized with the dilution-filtration system as shown in Fig. 16, and the operation protocol was theoretically optimized. A typical experimental conditions ( *<sup>0</sup> Vb* = 200ml, *<sup>0</sup> h* = 30%, *<sup>0</sup> Ms* = 6.28 Osmol/kg·water) was studied first to reveal the general law. To evaluate the effect of each operation parameter, different protocols were applied respectively. Fig.19 shows that time cost is significantly reduced but maximum cell volume grows directly along with diluent flow rate increases, i.e. the washing efficiency can be

Prevention of Lethal Osmotic Injury to Cells

During Addition and Removal of Cryoprotective Agents: Theory and Technology 129

after thawing to that after washing (Valeri et al, 2001). Residual glycerol concentration in the washed blood was measured by a glycerol assay kit (K-GCROL, Megazyme®) and a

Fig. 20. Variations of glycerol clearance (real line and left Y-axis) and maximum cell volume

A total number of ten units of blood were cryopreserved and deglycerolized by the dilutionfiltration method, and the results are shown in Table 6. The residual glycerol concentration (5.57±2.81 g/L, n=10) is obviously lower than the standard value (10g/L) indicated by American association of blood banking (AABB). During the optimization of the operation procedures, the maximum cell volume constraints was critically applied (1.35×Viso) for the best of cell recovery, and thus the deglycerolizing efficiency is limited. However, each of the unit was processed within an hour, which is similar to the automatic centrifuging method (Valeri et al, 2001). The cell count recovery rate is 91.19±3.57% (n=10). Comparing to the reported methods (Diafiltration method: 70% (Castino et al, 1996), dialysis method, no in vitro data was presented (Ding et al, 2007, 2010), manual centrifuging method: >80% (Brecher, 2002), and automatic centrifuging method 89.4±3.0% (Valeri et al, 2001)), the

(dash line and right Y-axis) with glycerol concentation as a paramter.

recovery rate indicates an obviously advantage of our method in cell safety.

**2.4 Results** 

spectrophotometer (756MC UV-VIS, Scientific Instrument®, Shanghai, China).

improved by applying higher diluent flow rate but more hemolysis may be induced. Thus the diluent flow rate has to be carefully selected to achieve the optimal result. Comparatively, the effect of blood flow rate is not so complicated. Increasing of blood flow rate has little effect on glycerol clearance, but helps to reduce the maximum cell volume excursion.

Fig. 19. Variations of time cost (real line and left Y-axis) and maximum cell volume (dash line and right Y-axis) with blood or diluent flow rates as parameters.

On the other hand, the effect of the operation parameters is also highly related to the blood conditions, especially the glycerol concentration. As shown in Fig.20, the same operation protocol (*Qb*=200 ml/min and *Qd* =20ml/min) is applied to several different conditions, in which *<sup>0</sup> Vb* =200ml, *<sup>0</sup> h* =30%, and *<sup>0</sup> Ms* varies from 0.56 Osmol/kg·water (5% w/v) to 6.28 Osmol/kg·water (40% w/v). When the glycerol concentration decreases, both the glycerol clearance and the maximum cell volume are reduced (glycerol clearance is defined here as the difference of initial and final numbers of osmoles of glycerol in blood over time cost). This phenomenon indicates us that along with the glycerol concentration drops during washing, diluent flow rate can be continuously increased to speed up the process without inducing extra cell volume excursion.

Based on the analysis above, it can be concluded that to achieve the optimal deglycerolization it is important to: a) use a low diluent flow rate at first, and stepwise increase it as CPA concentration drops; b) always use a high blood flow rate. The detailed operation parameters of the optimal protocol can be found out by the theoretical model with some practical constraints. During the in-vitro experiments, operation protocol for each unit was optimized theoretically according to the specific experimental conditions as well as the following constraints: maximum cell volume: 1.35 times of the isotonic volume (*V*iso) of RBCs; maximum flow rate of pumps: 200 ml/min and maximum ultrafiltrate flow rate of hemofilter: 40 ml/min. The value of upper cell volume level was conservatively selected in order to achieve the best cell recovery rate, although the washing efficiency may be limited.

Samples were taken before and after deglycerolization. Cell count and hematocrit were measured by a hematology Analyzer (Ac·T diff II TM, Beckman COULTER®) The Freeze-Thaw-Wash (FTW) cell count recovery rates were calculated by comparing the total cell counts after thawing to that after washing (Valeri et al, 2001). Residual glycerol concentration in the washed blood was measured by a glycerol assay kit (K-GCROL, Megazyme®) and a spectrophotometer (756MC UV-VIS, Scientific Instrument®, Shanghai, China).

Fig. 20. Variations of glycerol clearance (real line and left Y-axis) and maximum cell volume (dash line and right Y-axis) with glycerol concentation as a paramter.

#### **2.4 Results**

128 Current Frontiers in Cryobiology

improved by applying higher diluent flow rate but more hemolysis may be induced. Thus the diluent flow rate has to be carefully selected to achieve the optimal result. Comparatively, the effect of blood flow rate is not so complicated. Increasing of blood flow rate has little effect on

Fig. 19. Variations of time cost (real line and left Y-axis) and maximum cell volume (dash

On the other hand, the effect of the operation parameters is also highly related to the blood conditions, especially the glycerol concentration. As shown in Fig.20, the same operation protocol (*Qb*=200 ml/min and *Qd* =20ml/min) is applied to several different conditions, in which *<sup>0</sup> Vb* =200ml, *<sup>0</sup> h* =30%, and *<sup>0</sup> Ms* varies from 0.56 Osmol/kg·water (5% w/v) to 6.28 Osmol/kg·water (40% w/v). When the glycerol concentration decreases, both the glycerol clearance and the maximum cell volume are reduced (glycerol clearance is defined here as the difference of initial and final numbers of osmoles of glycerol in blood over time cost). This phenomenon indicates us that along with the glycerol concentration drops during washing, diluent flow rate can be continuously increased to speed up the process without

Based on the analysis above, it can be concluded that to achieve the optimal deglycerolization it is important to: a) use a low diluent flow rate at first, and stepwise increase it as CPA concentration drops; b) always use a high blood flow rate. The detailed operation parameters of the optimal protocol can be found out by the theoretical model with some practical constraints. During the in-vitro experiments, operation protocol for each unit was optimized theoretically according to the specific experimental conditions as well as the following constraints: maximum cell volume: 1.35 times of the isotonic volume (*V*iso) of RBCs; maximum flow rate of pumps: 200 ml/min and maximum ultrafiltrate flow rate of hemofilter: 40 ml/min. The value of upper cell volume level was conservatively selected in order to achieve the best cell recovery rate, although the washing efficiency may be limited. Samples were taken before and after deglycerolization. Cell count and hematocrit were measured by a hematology Analyzer (Ac·T diff II TM, Beckman COULTER®) The Freeze-Thaw-Wash (FTW) cell count recovery rates were calculated by comparing the total cell counts

line and right Y-axis) with blood or diluent flow rates as parameters.

inducing extra cell volume excursion.

glycerol clearance, but helps to reduce the maximum cell volume excursion.

A total number of ten units of blood were cryopreserved and deglycerolized by the dilutionfiltration method, and the results are shown in Table 6. The residual glycerol concentration (5.57±2.81 g/L, n=10) is obviously lower than the standard value (10g/L) indicated by American association of blood banking (AABB). During the optimization of the operation procedures, the maximum cell volume constraints was critically applied (1.35×Viso) for the best of cell recovery, and thus the deglycerolizing efficiency is limited. However, each of the unit was processed within an hour, which is similar to the automatic centrifuging method (Valeri et al, 2001). The cell count recovery rate is 91.19±3.57% (n=10). Comparing to the reported methods (Diafiltration method: 70% (Castino et al, 1996), dialysis method, no in vitro data was presented (Ding et al, 2007, 2010), manual centrifuging method: >80% (Brecher, 2002), and automatic centrifuging method 89.4±3.0% (Valeri et al, 2001)), the recovery rate indicates an obviously advantage of our method in cell safety.

Prevention of Lethal Osmotic Injury to Cells

approach (see Figures 12 and 13).

glycerol.

During Addition and Removal of Cryoprotective Agents: Theory and Technology 131

FMS removal of 1.0 M glycerol from spermatozoa were predicted and shown to be acceptable procedures which minimize osmotic injury. From calculations, the minimum or maximum cell volumes after each step of FVS addition or removal were shown to be unequal, some of which may exceed the lower or upper volume limits of the cells. In contrast, from calculations, the minimum or maximum cell volumes after each step of FMS addition or removal of glycerol were shown to be relatively even (Figures 12 and 13). For a fixed number of steps, the minimum or maximum of cell volume excursion during glycerol addition or removal using the FMS approach is much smaller than that using the FVS

In the example, it was postulated that the sperm osmotic injury as a function of cell volume excursion must be determined to predict the optimal glycerol addition and removal procedures. However, the definition and determination of 'sperm injury' is dependent upon the assays used. In the example, sperm motility was used as a standard of sperm viability because of its relatively high sensitivity to osmotic changes and the requirement of sperm motility for functional viability. If sperm membrane integrity was chosen as the endpoint to evaluate the sperm viability, as shown in Figure 7, different osmotic tolerance limits would be obtained. One can readily repeat the same procedures to predict the extent to which spermolysis is caused by the different glycerol addition/removal procedures used in the example, based on the information provided in Figure 5. For example, it was found (Figure 7) that >85% of spermatozoa maintained membrane integrity when they were returned to isotonic condition after having been exposed to anisosmotic conditions ranging from 90 and 700 mOsmol. The corresponding sperm volume excursion range was 0.7-2.1 times the isotonic sperm volume (Figure 9). From Figures 12 and 13, it can be seen that a one-step addition and one-step removal of 1.0 M glycerol would result in a minimum relative sperm volume of 0.72 and maximum volume of 1.68 respectively, which did not exceed the sperm volume excursion range 90.7-2.1 times relative volume) for maintaining >85% sperm membrane integrity. Based on this information, one can predict that the majority (>85%) of spermatozoa would maintain membrane integrity even using one-step addition and one-step removal of

A dilution-filtration system for removing CPAs from cryopreserved cell suspension was also introduced here. The system realized continuous processing of cell suspension and the dilution & filtration were conducted simultaneously, thus it can achieve much better efficiency than traditional multi-step centrifuging methods. Moreover, dilution in the system is conducted to cell suspension flow in tubing but not whole suspension in container, thus the mixing process should be much rapider and then the osmotic

A theoretical model was established to simulate the specific process. Based on the model, cell volume excursion and the variation of CPA concentration during the dilutionfiltration process can be simulated. Theoretical analysis indicates the operation parameters, especially the flow rate of diluent, are critical for the dilution-filtration method. In the previous studies concerning removing CPAs with hollow fibers (Castino et al, 1996; Arnaud et al 2003; Ding et al, 2007, 2010 ), only the protocols with constant flow rates were discussed. However, it was found to be difficult to balance the requirements in removing efficiency and cell safety. This problem also exists in the presented dilution-

disequilibrium during dilution can be significantly reduced.


Table 6. *In-vitro* experiments of deglycerolization with dilution-filtration method
