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Beneficial Effects of Freezing Rate Determined

by Indirect Thermophysical Calculation on CellViability in Cryopreserved Tissues

Dong-Wook Han

Department of Medical Engineering, Yonsei University College of Medicine,Seoul, Korea

Han-Ki Park and Young Hwan Park

Cardiovascular Research Institute, Yonsei University College of Medicine,Seoul, Korea

Taek-Soo Kim and Woong-Sub Yoon

Propulsion-Combustion Laboratory, College of Mechanical Engineering,

Yonsei University, Seoul, Korea

Jeong Koo Kim

Department of Biomedical Engineering, College of Biomedical Science andEngineering, Inje University, Gimhae, Korea

Jong-Chul Park

Department of Medical Engineering andBrain Korea 21 Project for Medical Science,

Yonsei University College of Medicine, Seoul, Korea

Abstract: Many types of mammalian cells, such as sperm, blood, embryos, etc.,have been successfully cryopreserved for the last few decades, while no optimalmethod for the cryopreservation of mammalian tissues or organs has been estab-lished, showing a poor survival after thawing with a low recovery of function. Inthis study, the freezing rate was determined by indirect thermodynamic calcu-lation, and its potential effect on the cryoprotection of human saphenous veins

and tissue-engineered bones was investigated. The vein segments were frozen

Artificial Cells, Blood Substitutes, and Biotechnology, 34: 205221, 2006

CopyrightQTaylor & Francis Group, LLC

ISSN: 1073-1199 print/1532-4184 online

DOI: 10.1080/10731190600581742

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according to the calculated freezing rate, using rate-controlled freezing devices,with a freezing solution composed of 10% dimethylsulphoxide and 20% fetal

bovine serum in RPMI 1640 media. The efficacy of indirect calculation wasassessed by the cell viability measured using fluorescence double-staining meth-ods. The results indicated that the freezing rate determined by indirect calculationsignificantly (P

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whether they give enhanced protection in terms of cellular viability. Onewas the direct calculation method, where many parameters, such as thethermophysical characteristics of all components, latent heat of fusion,area, density and volume, etc., should be considered. Because this kindof calculation was very sophisticated, some variables could not bedetermined. The other was the indirect calculation method, where HSVand TEB were frozen using a previously constructed freezing rate, andthen the actual freezing rates of both tissues were determined. Finally,the freezing rate was modified by several calculation steps, includingpolynomial regression analysis and time constant, thermal responseand inverse chamber temperature calculations.

MATERIALS AND METHODS

Preparations of Human Saphenous Vein

Using the methods described previously [810], HSV segments wereharvested from 20 patients undergoing arterial bypass graft surgery.The segments containing the branches were excluded from the testing,

as it was impossible to achieve a precise cell viability measurement as wellas homogeneous freezing.

Cell Cultures and Conditions

The mouse pre-osteoblasts (MC3T3-E1) were obtained from the RIKENCell Bank (Tsukuba Sciences City, Japan). The normal rat osteoblasts(NROs) were isolated from neonatal (

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a 0.1 g=mL viscous polymer solution was prepared by dissolving the poly-mer in chloroform (Sigma). The solution was precipitated in cold ethanoland homogenated with sodium chloride salt particles followed by freeze-drying. The MC3T3-E1 cells were seeded at the initial density of 2 105

cells=scaffold and then cultured into the PLGA scaffolds for 5 to 7 daysprior to freezing.

Using the previously described method [12,13], a composite of 980C-heated carbonate apatite (CAp), produced by a solution-precipitationmethod, and type I atelocollagen (AtCol), extracted from bovine tailskins, were grafted onto poly-L-lactic acid (PLLA; Polysciences Inc.,Warrington, PA) scaffolds (12 mm diameter and 3 mm thickness). Toincrease the collagen fibrillar cross-links, the fabricated scaffolds wereirradiated by ultraviolet rays (wave length 254 nm) at 4C for 4h. TheNROs (initial seeding density, 1105 cells=scaffold) were cultured ontothe CAp-AtCol-PLLA scaffolds for 7 days prior to freezing.

Thermophysical Modeling and Calculation

Lumped Thermal Capacity Model

If a system undergoing a transient thermal response to a heat transferprocess has a nearly uniform temperature, small differences of tempera-ture within the system can be ignored. Changes in the internal energyof the system can then be specified in terms of the changes in the assumeduniform temperature of the system. This approximation is called thelumped thermal capacity model [14]. This model was adopted for thenumerical modeling of the cooling process of tissue samples. Althoughthe model is only applicable to a small sample able to be considered ashaving a uniform temperature, it enables a first-order ordinary differen-tial equation for the sample temperature,Ts, as a function of time, t, to beobtained. This equation is:

dTs

Ts Tf

1

tcdt 1

whereTfis the freezing chamber temperature, tcqVc=hcA[s] is the timeconstant of the process, where q is the sample density, V the samplevolume, c the sample specific heat, and hc the heat transfer coefficientaveraged over the sample surface area, A.

Direct Thermophysical Calculation

208 D. W. Han et al.

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steps: (a) inputting thermophysical properties of a tissue sample whoseideal freezing rate is being sought; (b) inputting the freezing chambertemperature profile, where the change in the sample temperature willbe simulated; (c) calculating Ts using the lumped thermal capacity modelduring the cooling process before the freezing process; (d) calculating Tsduring the freezing process; and (e) calculatingTs using the lumped ther-mal capacity model during the cooling process after the freezing process.Difficulty in obtaining the exact thermophysical properties of each sam-ple, however, renders the direct thermophysical calculation inefficient.Most of all, the exact thermophysical properties are essential for step(d). Figure 1 shows the comparison between the experimental freezingrates and the calculated freezing rates using the direct thermophysicalcalculation for the HSV (A) and TEB (B).

Indirect Thermophysical Calculation

To make up for the shortcoming of the direct thermophysical calculation,and thus calculate the ideal freezing rate without inputting the respectivethermophysical properties of each sample, the indirect thermophysicalcalculation was employed in this study. This was derived from the ideathattc can be regarded as a function ofTs in a particular freezing cham-ber. Given the tc Ts diagram calculated and organized from a freezingexperiment on a tissue sample, the various thermal responses of the sam-ple to diverse freezing rates in the chamber can be simulated withoutknowing the respective thermophysical properties of the sample.

The algorithm of the indirect thermophysical calculation is described,with the demonstration of the calculation method on HSV and TEB, asfollows. First, experimentally freezing the tissue samples for which the

ideal freezing rate is being sought. Second, reading the Ts; tand Tf; tcoordinates from the experimental result at 1.0-second intervals oft, usinga polynomial regression analysis. Third, calculating tcby substituting thecoordinates values obtained from the previous step into the above Eq. (1)and constructing the tc Ts diagram, as shown in Figure 2. The freezingprocess within the sample can be understood indirectly by analyzing thediagram, even though the complex thermophysical aspect of the freezingprocess is not considered in the indirect thermophysical calculation. Forexample, the freezing point of the sample can be inferred from the fact that

the phase change in the sample happens most actively at the sample tem-perature where the time constant is a maximum. Fourth, inputting the

Cryoprotection Using Freezing Rate by Thermodynamic Calculation 209

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Along with its simplicity in simulating the thermal response of thesample, the inverse calculation of the chamber temperature is another

advantage of the indirect thermophysical calculation. The indirect ther-mophysical calculation can simulate the chamber temperature profile

Figure 1. The comparison between the experimental freezing rate and the calcu-lated freezing rate using the direct thermophysical calculation for the HSV (A)and TEB (B).


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Freezing and Thawing

The rate-controlled freezing protocol determined by the indirect ther-mophysical calculation was applied to the vein segments, as shown in

Figure 3(B). By inserting a stopcock into a lumen, an extremity ofthe vessel was closed and tied. In a freezing solution composed of

Figure 2. Thetc Ts diagrams of the chamber temperature for the HSV (A) andthe TEB (B).


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The cell-cultured scaffolds were also frozen using the freezing ratesshown in Figures 1(B) and 4. The final volume, including medium,serum, DMSO and scaffolds, was 3.6 ml. Cryogenic vials (Corning CostarCorp., Cambridge, MA) were used for freezing. After 1 week of storage,the vials were removed from the liquid N2and thawed quickly in a waterbath at 37C.

Cell Viability Measurement

The fluorescence double-staining method, combined with flow cytometry

(FCM; FACSCalibur, BD Biosciences Immunocytometry Systems, SanJose, CA) was used to determine the cellular viability of the cryopre-served vein segments. By enzymatic digestion with solution containingcollagenase 1A (250 units=ml; Sigma) and trypsin (2.5 mg=ml; Sigma)mixed 2:1 by volume, all vascular cells, including endothelial cells(ECs), were obtained. As described in previous studies [810], 0.004%Griffonia simplicifolia agglutinin-fluorescein isothiocyanate (GSA-FITC;MP Biomedicals, Aurora, OH), mixed with 2 mM CaCl2 and 2mMMgCl2in phosphate-buffered saline (PBS, pH 7.4) and 20 mM propidium

iodide (PI; Sigma), were added to a dissociated cell suspension containing1 105 cells=ml. The GSA-FITC=PI double-stained cells were detectedby FCM, and the unstained dissociated cells were regarded as the non-frozen control. The data obtained were analyzed with CellQuest software,written in MacApp (BD Biosciences Immunocytometry Systems), andplotted as dot plots and histograms.

Similarly, the cell-cultured scaffolds were washed twice with PBS andtrypsinized. The cell precipitates were obtained by centrifugation at200g and then re-suspended in PBS. As described previously [15],

2 mM 5(6)-carboxyfluorescein diacetate (cFDA; Sigma) and 20mM PI(Sigma) were added to the suspension containing 1 105 cells=ml andanalyzed by the above-mentioned FCM.

Statistical Analysis

All variables were tested in three independent cultures for each experi-ment, and each experiment was repeated twice (n 6). The students

t-test was used to detect the influence of the freezing rate, as determinedby the indirect thermodynamic calculation, on the cellular viability, and


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RESULTS

Freezing Rates Determined by Direct Thermophysical Calculation

For the HSV [Fig. 1(A)] and TES [Fig. 1(B)], the experimental freezingrates and the calculated freezing rates using the direct thermophysical cal-culation could be respectively obtained. Although both the rates wouldappear to be clearly similar to each other in their shapes, there werefound to be subtle differences attributed to many hypotheses and limitsto exact thermophysical calculation in the direct calculation methods.

Freezing Rates Determined by Indirect Thermophysical Calculation

Figure 2 showed the inverse operation of the time constant by the indirectthermophysical calculation. The phase changes in the HSV (A) and theTEB (B) in the freezing process occurred at about 7.9C and 4.8C,respectively. These results suggest that the time constants from experi-mental data may be different according to the size (volume) and thethermal properties of the samples. Moreover, the inverse calculation of

the chamber temperature allowed the temperature of a sample to changeas intended. As shown in Figure 3(A), however, the rate of the chambertemperature change should be infinitely large in order to obtain the lineartemperature response of the sample. This phenomenon might be imposs-ible to happen in nature and, if possible, it would take infinite time to doso. The freezing rate for the HSV in a 180 ml freezing bag was determinedby the inverse calculation as shown in Figure 3(B) and that for the TEB ina 3.6 ml cryogenic vial was shown in Figure 4.

Cryoprotection of HSV and TEB Using Freezing Rates Determined

by Thermodynamic Calculations

Freezing the HSV according to the freezing rate determined by directthermophysical calculation resulted in a significant (P

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with NROs. It was revealed that the TEB frozen using the freezing ratedetermined by the direct calculation showed an appreciable decrease incell viability compared with the non-frozen control [Fig. 5(B)]. About

22% and 27% decreases in the cell viability of PLGA scaffolds withMC3T3-E1 cells and CAp-AtCol-PLLA scaffolds with NROs were

Figure 5. The cellular viability of the cryopreserved HSV (A) and TEB (B),according to the freezing rates determined by direct or indirect thermophysicalcalculations.


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significant (P

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In conclusion, a significant difference between cellular viabilities in the

HSVs frozen using the freezing rates determined by the direct and indirect

thermophysical calculations would have been expected because the freez-

ing rate was applied to the vessels on a large scale. It might be suggested

that this program will be helpful in easily finding the ideal freezing rate.

However, there was no difference in cellular viabilities of the TEBs, which

postulated to result from the small volume of the freezing material, the

scaffolds containing cellular component.

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