Annals of Biomedical Engineering, Vol. 36, No. 1, January 2008 ( 2007) pp. 86–101 DOI: 10.1007/s10439-007-9383-x Thermal Injury Prediction During Cryoplasty Through In Vitro Characterization of Smooth Muscle Cell Biophysics and Viability SARAVANA KUMAR BALASUBRAMANIAN,1 RAMJI T. VENKATASUBRAMANIAN,1 ARJUN MENON,2 and JOHN C. BISCHOF1,2,3 1 Department of Mechanical Engineering, University of Minnesota, 1100 Mechanical Engineering, 111 Church Street, Minneapolis, MN 55455, USA; 2Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN 55455, USA; and 3Department of Urologic Surgery, University of Minnesota, Minneapolis, MN 55455, USA (Received 22 February 2007; accepted 13 September 2007; published online 18 October 2007) propagate. This is reflected by the change in the predicted IIF parameters when a gap junction inhibitor was added and tested in monolayer (Xo ¼ 58:1
108 (1/m2 s)); jo = 2.1 · 109 K5). SMC viability was affected by the model system (lower viability in attached systems), the thermal conditions and the biophysics. For e.g., IIF is lethal to cells and SMC viability was verified to be the least in fibrin TE (most % IIF) and the most in suspensions (least % IIF) at all cooling rates. Using the results from the fibrin TE (suggested as the best in vitro system to mimic a restenosis environment), conservative estimates of injury regimes in the artery during cryoplasty is predicted. The results can be used to suggest future optimizations and modifications during cryoplasty and also to design future in vivo studies. Abstract—Restenosis in peripheral arteries is a major health care problem in the United States. Typically, 30–40% of angioplasties result in restenosis and hence alternative treatment techniques are being actively investigated. Cryoplasty, a novel technique involving simultaneous stretching and freezing of the peripheral arteries (e.g., femoral, iliac, popliteal) using a cryogen-filled balloon catheter, has shown the potential to combat restenosis. However, evaluation of the thermal and biophysical mechanisms that affect cellular survival during cryoplasty is lacking. To achieve this, the thermal history in arteries was predicted for different balloon temperatures using a thermal model. Cellular biophysical responses (water transport (WT) and intracellular ice formation (IIF)) were then characterized, using in vitro model systems, based on the thermal model predictions. The thermal and biophysical effects on cell survival were eventually determined. For this study, smooth muscle cells (SMC) isolated from porcine femoral arteries were used in suspensions and attached in vitro systems (monolayer and fibrin gel). Results showed that for different balloon temperatures, the thermal model predicted cooling rates from 2200 to 5
C/ min in the artery. Biophysical parameters (WT & IIF) were higher for SMCs in attached systems as compared to suspensions. The ‘‘combined’’ fit WT parameters for SMCs in suspension (at 5, 10, and 25
C/min) are Lpg = 0.12 lm/ (min atm) and ELp = 24.1 kcal/mol. Individual WT parameters for SMCs in attached cell systems at higher cooling rates are approximately an order of magnitude higher compared to suspensions (e.g., at 130
C/min, WT parameters in monolayer and fibrin TE systems are Lpg = 18.6, 19.4 lm/(min atm) and ELp = 112, 127 kcal/mol, respectively). Similarly, IIF parameters assessed at 130
C/min are higher for SMCs in attached systems than suspensions (Xo = 1.1, 354, 378 (· 108 (1/m2 s)) and jo = 1.6, 1.8, 2.1 (· 109 K5) for suspensions, monolayer, and fibrin TE, respectively). One possible reason for the differences in IIF kinetics was verified to be the presence of gap junctions, which facilitate cell–cell connections through which ice can Keywords—Restenosis, Cryoplasty, Smooth muscle cells, Biophysics, Viability, Thermal modeling. INTRODUCTION The most common types of vascular disease in the peripheral arteries (i.e., PAD) are blocked arteries due to fatty deposits that affected about 8–12 million people in the United States in 2006.4 Endovascular techniques such as percutaneous transluminal angioplasty (PTA) are used to treat PAD. However, typically 30–40% of angioplasties result in restenosis.3,43 This occurs because PTA causes substantial injury to the vessel wall during dilation of the arterial blockage. This disrupts not only the plaque but also the endothelium, the internal elastic lamina, and the media, which can lead to aggressive proliferation of SMCs resulting in neointimal hyperplasia or restenosis.39 To offset these drawbacks, alternative treatment procedures for PAD are being actively investigated.9 Drugcoated stents have been introduced as an option over PTA. However, there are durability issues associated with the treatment (e.g., material sloughing, restenosis Address correspondence to John C. Bischof, Department of Mechanical Engineering, University of Minnesota, 1100 Mechanical Engineering, 111 Church Street, Minneapolis, MN 55455, USA. Electronic mail: bischof@tc.umn.edu 86 0090-6964/08/0100-0086/0  2007 Biomedical Engineering Society Thermal Injury Prediction During Cryoplasty over time, etc.).46 This suggests the need for continued research and development in restenosis treatments. One new and promising method is the use of freezing to treat stenotic vessels (cryoplasty) involving controlled freezing of the affected artery using a cryogen-filled balloon catheter. The choice of the cryogen includes liquid N2, Freon, nitrous oxide, CO2 gas, and in certain cases saline solution mixed with ethanol.31 Freezing of the stenotic vessel can help predict the survival of the proliferating SMCs and also prevent elastic recoil of the artery, which could result in restenosis.31 Other advantages of freezing include maintenance of ECM structure,33 the minimally invasive approach and lack of coagulation effects, i.e., thermal fixation.12 Recently, a thermal model analyzing the temperature distribution in arteries during cryoplasty was reported.38 Though relevant, assumption of constant thermal properties for tissues during freezing will affect predicted temperatures and cooling rates. Thus, there is still a lack of clear understanding of the extent and distribution of thermal injury during freezing in arteries that limits the informed use of cryoplasty. The use of freezing for the treatment of tumors in various tissues and organs has been well documented in the literature.13,14,25 The interpretation of results during freezing is limited by the choice of the model system (i.e., in vitro or in vivo). In vivo models are complicated since freezing results in both cellular- and host-mediated (vascular and immunological) injury.11,43 Though in vivo animal models are ultimately needed to demonstrate the efficacy of the treatment, the proper in vitro model system can help elucidate the mechanism of freeze injury.18In vitro models are simple to handle and provide a basic understanding of the cellular biophysical responses during freezing. The effects of freezing in the arterial system have been reported using both in vivo and in vitro systems. Reported effects of direct freezing using in vivo systems include early arterial cell loss, late intimal hyperplasia, and increased collagen production for a 10-week postfreeze study using the rabbit iliac artery model.11 Also, recovery of microvascular perfusion and endothelial cell injury was reported for a 7-day post-freeze study using myocardial cryothermia in rats.28 However, there is a lack of quantitative information linking freezing effects to direct cell injury. To address this, tissue and cellular level studies have been reported for arterial cells. Previous cellular freezing studies in monolayer have shown that endothelial cells are more resistant to freezing and have increased proliferation post-freeze/ thaw as compared to SMCs.27 Additionally, the biophysics of freezing was quantified for microvascular endothelial cells in suspensions in an effort to under- 87 stand the mechanisms of freeze injury.7 Different in vitro model systems were also used to study the freezing effects on SMCs from different animal cell lines including rat, pig, and human SMCs. It was concluded that porcine SMCs behave similarly to human SMCs on freezing.16 In spite of these, the mechanisms of freeze injury (cellular/molecular) during freezing and the appropriate thermal thresholds are still not completely understood. An attempt to quantify molecular mechanisms of injury was reported for human SMCs and endothelial cell suspensions. Necrotic injury and to a lesser extent apoptotic cell injury were observed at temperatures below -20
C and between -5 & -15
C, respectively.47 Further challenges then involve quantifying the thermal, biophysical, and molecular events (mechanisms) responsible for cell injury during freezing. The aim of the current study is to quantify and predict the thermally driven mechanisms of injury (biophysics) during freezing that affect cell survival. A thermal model is first used to predict temperature distribution in femoral and popliteal arteries (two common targets) during freezing. Based on these predictions, in vitro model systems are then employed to characterize the cellular biophysics. The model systems studied include suspensions (simplest), monolayer (cell–cell interactions), and fibrin TE (tissue-like environment with cell–cell and cell–ECM interactions). The variable parameters of the study are the model system, the cooling rate, the end temperature, and the time post-freeze/thaw. Results from the thermal model and the viability are then used to obtain conservative estimates of thermal injury regimes in the artery. THEORETICAL MODEL Thermal Model The energy equation, modified to account for phase change using the enthalpy method,22,24 was used to predict the thermal history of the artery during freezing. Similar use of the model was reported for a variety of tissue systems as reviewed recently.21 The governing partial differential equation is given by:   1@ @T @H kr ð1Þ ¼q r @r @r @t In Eq. (1), H is the volumetric enthalpy, k is the thermal conductivity (W/m K) and q the density (kg/ m3). The tissue was considered frozen for all T < Ts, unfrozen for all T > Tl, and a mushy zone considered for Ts < T < Tl where Ts = -40
C and Tl = -0.53
C. The thermal properties used in the model, outside the mushy zone, are listed in Table 1. 88 BALASUBRAMANIAN et al. TABLE 1. Thermal properties used in the model. Property kl ks Cl Cs ql qs L Values Units 0.6 2.24 + 5.975 · 10-3 · (-T)1.156 4100 7.16(T-273.15) + 138 999 921 210 W/m K W/m K J/kg K J/kg K kg/m3 kg/m3 kJ/kg Tissue properties from previously reported studies22 were assumed to be true for arteries. The latent heat of artery was calculated based on the assumption that the 60–65% of the tissue was water and the non-water portion did not contribute to the latent heat. Calculation of the thermal properties and enthalpy inside the mushy zone has been discussed elsewhere.24,45 Briefly, the thermal properties and the enthalpy in the mushy zone were calculated as follows: Xi ¼ Xs þ fðTÞ  ðXl  Xs Þ fðTÞ ¼ Ts T Ts Tl 1 1
 ð2aÞ ð2bÞ where Xs and Xl are the thermal property or enthalpy at Ts and Tl, respectively and f(T) the release pattern describing the relation between temperature and the unfrozen tissue within the mushy zone. An Euler forward one-dimensional finite difference analysis with time step of 10-5 s and element size of 0.025 mm was constructed and run to solve the thermal model.17 The results were additionally verified using finite element analysis (ANSYS 10.0, Canonsburg, PA). The thermal model predicted the temperature distribution in geometries corresponding to femoral and popliteal arteries. Figure 1 depicts the arterial geometry modeled and the boundary conditions imposed. A lumen radius of 3 mm for popliteal and 5.5 mm for femoral artery was used while the arterial thickness was assumed to be 2 mm for both the arteries.6,42 The thermal properties described in Table 1 were used for both. The arteries were assumed to be perfectly cylindrical and the heat transfer was assumed to be radial. Cryoplasty involves freezing of the artery to approximately -15 to -20
C for about 60 s.51 Thus, a constant boundary temperature of -15
C and -20
C was separately applied for each case at the inner artery wall for a time of 60 s. The entire artery was assumed to be at an initial temperature of 37
C. Both femoral and popliteal arteries are surrounded by blood-perfused muscle fibers. Assuming that the blood flow in the surrounding tissues would maintain the outer arterial wall temperature at 37
C, a constant temperature boundary condition was imposed at the FIGURE 1. Artery geometry used in the thermal model for the prediction of temperature distribution during cryoplasty. The geometrical dimensions and the imposed boundary conditions for the thermal model are listed. outer wall. In another case, as an extreme situation, the surrounding tissues were included in the model and a constant temperature (37
C) boundary condition imposed at 15.5 mm from the lumen center. The surrounding tissues were also assigned the same thermal properties as the arteries. It is expected that an in vivo situation would fall in between the two boundary conditions described. Water Transport Model The WT model used in this study was developed for cells in suspension.34 The WT parameters obtained for several cell types have been recently reviewed.21 Briefly, during freezing, the osmotic balance across the cell membrane is affected by the solute concentration in the extracellular space. Equation (3) models the WT across the cell membrane to achieve chemical equilibrium. dV Lp A ¼ ðDpÞ dT B Lp ¼ Lpg exp    ELp 1 1  T Tref R ð3Þ ð4Þ In Eq. (3), V is the cell volume (lm3); T is the absolute temperature (K); Tref is the reference temperature (273.15 K); A is the cell surface area (lm2); R is the universal gas constant (8.314 J/mol K); B is the cooling rate (
C/min); and Dp is the osmotic pressure difference across the cell membrane, which can be calculated as shown elsewhere.34 Variation in the cell membrane permeability (Lp) is modeled using an Thermal Injury Prediction During Cryoplasty Arrhenius relationship32 (Eq. 4). Here, Lpg is the membrane hydraulic permeability at Tref (lm/min atm) and ELp is the activation energy for water transport (kcal/mol). A detailed discussion of the assumptions made in the above equations has been given elsewhere.35,37,40 Intracellular Ice Formation (IIF) Model The IIF model used in this study, based on classical nucleation theory, was developed by Toner et al.49 for cells in suspension. The IIF parameters obtained for a variety of cell types has recently been reviewed.21 For a thermodynamic system composed of identical biological cells, the probability of IIF (PIF) by surface catalyzed nucleation (SCN) is given: 3 2 ZT 7 6 1 PIFscn ¼ 1  exp 4 ð5Þ AIscn dT5 B Tseed In Eq. (5), Tseed is the ice seeding temperature (K) and I is the crystal nucleation frequency given as:   jscn ð6Þ Iscn ¼ Xscn exp  DT2 T3 1 2 where X and j are the kinetic (1/m s) and thermodynamic (K5) heterogeneous nucleation parameters, respectively and DT ¼ T  Tf (K) is the degree of undercooling of the cytoplasm where Tf is the equilibrium freezing temperature of the cytoplasm. While both the WT and IIF models were used to predict cellular response to freeze/thaw in monolayer and fibrin TE, it should be understood that these models were not designed to account for cell–cell and cell– ECM interactions. 89 37
C and 5% CO2 for 3–4 days before either experimentation or splitting. Before experiments, SMCs were trypsinized (0.5 mL) to remove them from the tissue culture flask (0.05% Trypsin/0.53 mM EDTA). The cells were then centrifuged at 500 · g for 7 min and the cell concentration was measured using a hemocytometer. It was observed that SMCs show a 10–20% decrease in viability between passages 4 and 5 immediately after freeze/thaw (<1 h) at different cooling rates to an end temperature of -20
C (data not shown). Hence, a single cell passage (passage 4) was maintained in all experiments for consistency of results. Monolayer Preparation SMCs in monolayer were prepared on sterilized coverslips (12 mm diameter, Fisher Scientific, Hampton, NH) and cultured in a Petri dish covered with 10 mL of media (cell concentration of 2 · 105 cells/ mL). The cells were incubated at 37
C and 5% CO2 for 4 days to allow them to proliferate before experimentation. Fibrin Tissue Equivalent (TE) Preparation Bovine fibrinogen was mixed with cell solution and bovine thrombin at a ratio of 4:1:1 at room temperature. The final cell concentration in the mixture was 2 · 105 cells/mL. Ten microliters of the solution was plated on a 12-mm-diameter tissue culture-treated glass cover slip and incubated at 37
C for 1 h to allow it to gel. Cell media (3 mL) was then added and the fibrin TE was incubated for 4 days prior to experimentation. Cryomicroscope Setup and Cooling Protocol MATERIALS AND METHODS Smooth Muscle Cells (SMCs) Culture The SMCs used for the experiments were isolated from adult pig femoral arteries as described elsewhere.16,20 Briefly, the arteries were cut into small pieces, placed in a Petri dish and covered with media to allow SMCs to migrate from the tissue to the dish and grow. The cell media contained Dulbecco’s modified Eagle medium (DMEM) (Gibco, Grand Island, NY) supplemented with 10% fetal bovine serum (FBS), 1% penicillin–streptomycin, and 1% L-Glutamine. The cells were grown in 75-cm2 T-flasks and incubated at 1 scn X is dependent on a variety of other parameters including viscosity (g) and cell surface area (A). Please see other references for a complete description.48 Controlled freezing of the samples was carried out on the Linkam Scientific conduction type cryostage (Linkam Corporation, UK). An Olympus BX50 fluorescent microscope (Tokyo, Japan) was used to observe freezing. Details on the cryomicroscope setup are discussed elsewhere.5,7 In brief, samples were mounted on a quartz crucible with a coverslip on top for freezing in the cryomicroscope. The freezing protocol included temperature decrease at 10
C/min to -2
C when ice was seeded (Tseed) using a chilled needle at the edge of the sample, temperature increase to -0.6
C (Tfreeze for media) and then progressive decrease at the desired cooling rate to the desired temperature end point. Instrumentation error in temperature measurement was less than 0.1
C for all controlled cooling rates. The cells were thawed back to room temperature at 130
C/min. 90 BALASUBRAMANIAN et al. Water Transport and IIF Suspensions Cellular volumetric changes during freezing were measured at cooling rates of 5, 10, and 25
C/min for suspensions. The data was averaged for n ‡ 15 cells at each of these cooling rates. The projected cell area was measured manually using Image-Pro Plus software (Media Cybernetics, Silver Spring, MD). Briefly, the projection of the outer cell membrane was traced three times and averaged for a particular cell at a specific temperature. Only cells that maintained their spherical shape during freezing were included in the final analysis. The osmotically inactive cell volume (Vb) was determined using a Boyle–Van’t Hoff plot as described previously.5,7 Individual WT parameters at 5, 10, and 25
C/min were obtained by fitting the experimental data using the theoretical model. A ‘‘combined’’ fit parameter was then obtained by fitting all three experimental data sets simultaneously into the theoretical model.7 The accuracy of the ‘‘combined’’ fit was verified by comparing predicted WT data to the experimental data set at 10
C/min. The kinetics of IIF for cells in suspension was determined for a range of cooling rates (130, 100, 75, and 50
C/min). IIF was characterized by the sudden ‘‘darkening’’ or opaque ‘‘flashing’’ in the cells at a particular temperature that indicated the formation of large ice crystals. PIF in cells was defined to be the ratio of the cumulative number of cells exhibiting IIF to the total number of cells in the sample population. Data from n > 50 cells were pooled to obtain the final IIF kinetics for each group. 130
C/min, an important assumption for the initial fit of the IIF parameters. It should be noted that both the WT and the IIF models were developed for cell suspensions. Hence, WT and IIF for attached cell systems should be used with the caveat that the model does not account for cell–cell or cell–ECM effects. One important change in attached model systems is the possibility of gap junction-mediated intercellular IIF. This tends to increase the rates of IIF. To check this, SMCs in monolayer were treated with 10 mM of gap junction inhibitor carbenoxolone disodium (Sigma-Aldrich Co., St Louis, MO) as previously reported.15,41 Cell Viability Analysis Cell viability was assessed at four different time points: immediately (<1 h), 3, 24, and 72 h after freeze/thaw using Hoechst 33342 (Sigma, St. Louis, MO) and propidium iodide (PI) (Molecular Probes, Eugene, OR). The control and frozen/thawed cells were incubated for 30 min in cell media with Hoechst and PI at 1:1000 and 5:1000 assay-media ratio, respectively. The samples were then placed on a microslide, coverslipped, and analyzed under the cryomicroscope. Hoechst stains all cells whereas PI stains only dead (membrane compromised) cells. Three to five fields with 30–40 cells per field were counted for every model system. Cell viability is reported in terms of ‘‘percent’’ viability defined as: Percent viability (%) ¼ Total number of live cells
100 Total number of cells Monolayer and Fibrin TE Numerical Model for Biophysical Parameter Estimation IIF in the attached model systems was assessed exactly as in suspensions above. However, it was not possible to obtain similar direct quantitative measurements of WT in attached cell systems (monolayer and fibrin TE). To circumvent this problem, WT parameters were predicted from the analysis of the IIF data at slower rates where WT is present as done previously.5 Briefly, IIF nucleation parameters were determined at 130
C/min from the experimental IIF data assuming minimal cellular water transport. These parameters were then assumed constant for all cooling rates irrespective of WT (i.e., same at 50, 75, and 100
C/min). A coupled IIF–WT equation was then used with WT parameters selected to best fit the IIF data. In brief, despite assignment of constant IIF parameters, the IIF kinetics shift at lower cooling rates due to WT. These WT parameters were then used to verify that cell volume decrease is minimal (£5%) at The experimental data was fit to the previously given equations to determine WT and IIF parameters. The Marquardt optimization scheme8 was used as previously described in Toner et al.49 Briefly, it minimizes the variance between the experimental data (yi) and the theoretical fit/data (yfit,i) and maximizes the R2 value of the fit as represented by Eq. (7).
2 P yi  yfit;i 2 ð7Þ R ¼1 P ðyi  yÞ2 Theoretical predictions for WT in cell suspensions are generally reported in two ways: theoretical value at a particular cooling rate and a ‘‘combined’’ fit parameter obtained by fitting of the complete dehydration data from all cooling rates as previously described.44 Accuracy of fit (WT ‘‘combined’’ fit and IIF parameters) was ascertained by comparing the Thermal Injury Prediction During Cryoplasty experimental data at a new rate, which is not part of the fitted data, to the predicted behavior from the biophysical parameters obtained. Statistics Viability data are represented as mean ± standard deviation of at least three samples. Student’s t-test was used to determine significant differences with a minimum confidence level of p < 0.05. RESULTS Thermal Model The temperature distribution in the artery vs. radial distance was estimated using the finite difference model. For a constant boundary temperature condi- 91 tion (Fig. 1), the ice ball edge grew up to approximately half the arterial thickness (~1 mm) in each case. For example, in the femoral artery, for a constant boundary temperature of -20
C at the inner wall (ri = 5.5 mm), the iceball is predicted to grow to r = 6.7 mm within 12 s. Cooling rate at different radial locations in the artery is determined from the slope of the temperature variation over the first 15–20 s as transients at any location reduces significantly after that time point (Fig. 2b). For the popliteal artery, the estimated cooling rates range from 2500 to 5
C/min at different radial locations. Table 2 provides information on end temperatures and cooling rates predicted at different locations within the artery for different initial balloon temperatures. In addition to the different conditions listed in Table 2, thermal response during constant boundary condition at ro = 15.5 mm (extreme case) is studied. Figure 2c describes FIGURE 2. Thermal history of femoral artery (r = 5.5 mm) wall during cryoplasty. (a) Temperature within the artery as a function of radial distance for different times. (b) Temperature as a function of time at different locations. (c) Temperature as a function of radial distance during the extreme case (i.e., constant boundary condition (37 °C) at ro = 15.5 mm). 92 BALASUBRAMANIAN et al. TABLE 2. Summary of the thermal injury following cryoplasty in the (a) femoral and (b) popliteal artery model. (a) Femoral artery r (mm) 5.9 BT (
C) (@ r = 5.5 mm) -15 -20 IBE (mm) 6.6 6.7 6.3 6.6 5.9 CR (
C/min) 530 400 100 190 6.3 6.6 ET (
C) – 90 -10 -14 -5 -8 0 -3 3.3 3.6 4.0 NZ (mm) AZ (mm) 5.5–5.9 5.5–6.2 5.8–6.6 6.2–6.7 NZ (mm) AZ (mm) 3–3.3 3–3.6 3.3–4 3.6–4.2 (b) Popliteal artery r (mm) 3.3 BT (
C) (@ r = 5.5 mm) -15 -20 IBE (mm) 4.0 4.2 3.6 4.0 CR (
C/min) 2300 2500 220 380 ET (
C) – 80 -11 -15 -7 -10 0 -4 BT: Balloon temperature (
C), r: radius (mm), IBE: Ice ball edge (mm), NZ: Necrotic zone (mm), AZ: Apoptotic zone (mm), CR: Cooling Rate (
C/min), and ET: End Temperature (
C). the temperature vs. radial distance at different times during the extreme case. In vivo thermal history is expected to be captured in between the two extreme cases considered in the thermal model. While the initial cooling rates did not change significantly, sub-zero temperatures are predicted in the entire artery and the ice ball edge grew beyond the artery wall. The thermal information is used to construct the in vitro biophysics study and also quantify the biophysics in different regimes of the artery. Biophysics Water Transport WT parameters, Lpg and ELp, are estimated from previously established theoretical models (Eqs. 3 and 4). The mean diameter of SMCs is estimated to be 11.1 ± 2.2 lm for n = 76 cells at room temperature. Hence, initial cell volume (Vo) is calculated to be 716.2 ± 5.6 lm3. Also, the osmotically inactive cell volume fraction (Vb) for SMCs is determined to be 0.24Vo using Boyle Von’t Hoff plot. Figure 3 depicts the dehydration biophysics of SMCs in suspension during freezing. Cell volumetric changes are depicted as a function of temperature at 5, 10, and 25
C/min. The biophysical parameters for WT at 5 and 25
C/min (Figs. 3a and 3b) are estimated as previously described and given in Table 3. The ‘‘combined fit’’ parameters are estimated to be Lpg = 0.12 lm/min atm and ELp = 24.1 kcal/mol. Using these, the dehydration response at 10
C/min is predicted and compared to the experimental results in Fig. 3c. A good correlation (R2 = 0.96) is obtained between the predicted and the experimental data. For SMCs in monolayer and fibrin TE, the WT parameters are estimated as described previously and included in Table 5. Intracellular Ice Formation (IIF) IIF kinetics are studied at cooling rates of 130, 100, 75, and 50
C/min. Figures 4(a–c) depict the variation of maximum cumulative fraction of IIF with cooling rate for each model system. In all the model systems, the maximum cumulative fraction of IIF increases with an increase in the cooling rate as expected. The incidence of IIF for SMCs in attached states is higher as compared to suspensions. For example, at 130
C/min, SMCs in monolayer and fibrin TE exhibit 100% IIF whereas only 46% of SMCs form IIF in suspensions. Additionally, a difference in the IIF kinetics is observed between SMCs in attached state vs. suspension. Figure 5 depicts the IIF kinetics at 130
C/min for all model systems studied. Ice propagates faster among cells in the attached states as compared to cells in suspension. SMCs in monolayer were treated with gap junction inhibitor carbenoxolone disodium and the resultant IIF kinetics is studied. The IIF kinetics change significantly in the presence of the inhibitor (Fig. 5) as determined from the IIF kinetics (Table 4). The values indicate that the kinetics of the process is slower (Xo = 58.1 vs. 354) as compared to a normal monolayer of cells. A comparison of the experimental vs. predicted values of IIF fraction is performed using the biophysical parameters estimated previously. For cells in suspension, the combined fit WT parameters and IIF Thermal Injury Prediction During Cryoplasty 93 FIGURE 3. Normalized volume as a function of temperature for SMCs in suspension for a cooling rate of (a) 5 °C/min, (b) 25 °C/ min, and (c) 10 °C/min. Dark circles indicate experimental data (n = 10–30 cells) and error bars indicate standard deviation. Solid lines represent the theoretical fit (a, b) obtained by fitting the experimental data to the water transport model and the predicted volume change from the estimated ‘‘combined fit’’ parameters (c). TABLE 3. Water transport parameters (Lpg and ELp) for SMCs in suspension (both individual and combined fit parameters) at 5, 10, and 25 °C/min. Cooling rate (
C/min) 5 10 25 Combined fit Viability Effect of End Temperature 2 Lpg (lm/min atm) ELp (kcal/mol) R 0.13 0.28 0.20 0.12 45.2 54.2 32.5 24.1 0.99 0.99 0.99 0.96 parameters at 130
C/min were used for the predictions. For monolayer and fibrin TE systems, the biophysical parameters estimated at 130
C/min were used for IIF predictions. Using these parameters, a comparison of the cumulative incidences of IIF is obtained as shown in Figs. 4(a–c). The goodness of fit (R2), defined by Eq. (7), is calculated between the theoretical and predicted fit and reported in Table 4 for all model systems. Cell viability shows a 10–20% variation between passages 4 and 5 for SMCs in suspension at different cooling rates to an end temperature of -20
C immediately after freeze/thaw (data not shown). To maintain consistency, all experiments were performed using SMCs from passage 4. Figure 6 shows the effect of end temperature on SMC viability in a monolayer and a fibrin TE at 3 h post-freeze/thaw. The viability drops as cooling rate increases and end temperature decreases in most cases. In the monolayer (Fig. 6a), for an end temperature of -10
C, 81% of the SMCs are viable at a cooling rate of 130
C/min whereas only 37% of the SMCs survive to an end temperature of -20
C. Similarly, for the fibrin TE model system (Fig. 6b), 3% of the cells survive freeze/thaw to an end temperature of -20
C at a cooling rate of 130
C/min. 94 BALASUBRAMANIAN et al. FIGURE 4. Maximum cumulative fraction of IIF as a function of cooling rates to end temperature -20 °C for SMCs in (a) suspension, (b) monolayer, and (c) fibrin TE. Dark circles represent the experimental data, open circles represent the predicted data fit at the corresponding cooling rates, and the solid line represents the curve fit for the predicted data fit. Goodness of fit between the experimental and predicted fits is reported in Table 4. The fibrin TE exhibits inverted U-shape viability vs. cooling rate dependence during freezing. Figure 8 compares the cooling rate effect on cell viability (to 20
C) across model systems. Cell survival is observed to be the highest for SMCs in suspension and lowest in the fibrin TE at all rates (except 10
C/min). Effect of Time Post-Freeze/Thaw FIGURE 5. A comparison of the IIF kinetics during freezing of SMCs in suspension, monolayer, fibrin tissue equivalent, and monolayer with gap junction inhibitor carbenoxolone disodium at a cooling rate of 130 °C/min to end temperature of -20 °C. For SMCs in attached states, cell viability varies with time after freeze/thaw (3, 24, and 72 h) to an end temperature of -10
C as shown in Fig. 7. For the monolayer, viability decreases between 3 and 24 h (93 and 86% survival at 50
C/min) post-freeze/thaw but a slight increase is observed at 72 h post-freeze/thaw (91% at 50
C/min) (including control samples). A typical inverted U response of viability vs. cooling rate is observed at all time points of study for the fibrin TE (Fig. 7b). SMC viability is least at 72 h post-freeze/ thaw and maximum at 3 h post-freeze/thaw (except at Thermal Injury Prediction During Cryoplasty 95 TABLE 4. Estimates for the kinetic (j) and thermodynamic (X) nucleation parameters for SMCs in suspension, monolayer, monolayer with gap junction inhibitor carboxolene disodium, and fibrin tissue equivalent at a cooling rate of 130 °C/min. Xo
108 (1/m2 s) jo · 10-9 (K5) R2 (130
C/min) R2 (fit) (5–130
C/min) Model system Suspension Monolayer Monolayer (with gap junction inhibitor carboxolene disodium) Fibrin TE 1.13 354 58.1 378 1.6 1.8 2.1 2.1 0.98 0.99 0.99 0.98 0.30 0.94 – 0.95 R2 (fit) represents the goodness of fit between experimental incidence of IIF to cumulative IIF in a cell population over a cooling rate range for each of the model system represented in Fig. 4. TABLE 5. Water transport parameters (Lpg and ELp) for SMCs in monolayer and fibrin TE at different cooling rates. Fibrin TE Monolayer Cooling rate (
C/min) 130 100 50 Lpg (lm/min atm) ELp (kcal/mol) R2 Lpg (lm/min atm) 18.6 17.4 18 112 98 121 0.93 0.98 0.94 19.4 19.4 17.1 100
C/min where no statistical significance is found in the difference between the 3 and 72 h time points). Cell regeneration/proliferation after freeze/thaw is not observed in the fibrin TE or other systems except for control sample at 24 h in the fibrin TE. Correlation of Biophysics and Viability A correlation was sought between the cellular biophysics and the viability observed. Figure 9 shows the experimental IIF results along with the observed viability changes as a function of cooling rate for SMCs in all model systems to an end temperature of -20
C. In all cases, cell viability decreases as the fraction of IIF and the cooling rate increases. Cell viability is maximal when IIF is minimal in the model system and vice versa. Hence, suspensions exhibited maximum cell survival and minimum IIF (53% survival and 46% IIF at 130
C/min) whereas fibrin TE had the least cell survival and maximum IIF (3% survival and 100% IIF at 130
C/min). DISCUSSION Choice of Model System In vitro model systems have been used to help assess the effectiveness of freezing on SMCs within an arterial system with the ultimate goal of treating intimal hyperplasia (restenosis). The results from the study may help suggest mechanistically based modifications to the cryoplasty protocol for future in vivo studies. In this study, an in vitro assessment of freezing injury and the mechanisms responsible for it (cellular/molecular) ELp (kcal/mol) 127 118 127 R2 0.97 0.94 0.95 were studied. The biophysical mechanisms of cell injury are quantified using different model systems including suspensions, monolayer, and fibrin TE. Cell suspensions provide a basic understanding of the freezing effects on biophysics and viability. However, additional effects to injury due to cell–cell and cell– ECM interactions need to be probed. This was analyzed using monolayer and fibrin TE model systems in the current work. Additionally, since fibrin is a part of the restenotic arterial wall, it may represent an improved in vitro system over cell suspensions to quantify freeze/thaw injury during cryoplasty. The molecular mechanisms behind freeze injury, due to apoptosis and necrosis, have been previously reported for SMC and endothelial cell suspensions.47 Future work will focus on quantifying molecular mechanisms of injury for cells in tissue systems. Comparison of Model Systems Cells exhibit differential biophysical and injury response (e.g., Chinese hamster, AT-1 tumor cells) to freezing depending on whether they are in an attached system or in suspension.1,23,25 The biophysical response is verified in Fig. 5 where IIF biophysics is clearly model system dependent. Suspensions exhibit the lowest fraction of IIF as compared to SMCs in attached systems at all cooling rates. The reason for the differential IIF response to freeze/thaw is hypothesized to due to cell–cell or cell–ECM interactions prevalent among cells in the attached systems and absent in cell suspensions. Acker et al.1,2 have shown that cell–cell interactions promote IIF through intercellular pathways (gap junctions) present in monolayers. In the 96 BALASUBRAMANIAN et al. FIGURE 6. The effect of end temperature (-10 and -20 °C) on SMCs at different cooling rates determined 3 h post-thaw in (a) monolayer and (b) fibrin TE. Statistical analysis is done using Student’s t-test with p < 0.05. FIGURE 7. The effect of time post-thaw (3, 24, and 72 h) on SMC viability at different cooling rates to an end temperature of -10 °C in (a) monolayer and (b) fibrin TE. Statistical analysis is done using Student t-test with p < 0.05. current study, the effect of gap junctions on the IIF kinetics was tested in monolayer using gap junction blocker carbenoxolone disodium. Figure 5 also compares the difference in the IIF kinetics for SMCs in monolayer in the presence and absence of the gap junction blocker. Though 100% of SMCs exhibited IIF in both cases, the kinetics in the presence of the gap junction blocker tended more towards a typical cell suspension response than a monolayer response. Modification of this pathway of IIF injury by further thermal or chemical (i.e. gap junction inhibition) intervention may be possible in the arterial wall. Figure 8 demonstrates the effect of the model system on cell viability with respect to cooling rate to an end temperature of -20
C. SMCs in suspension exhibited higher viabilities post-freeze/thaw as compared to SMCs in monolayer or fibrin TE (least in fibrin TE). Grassl et al.16 reported similar differences in viability post-freeze/thaw for SMCs in collagen TE vs. suspensions. They used a directional solidification stage (DSS) to freeze SMCs in suspension and a cryoprobe for the collagen TE system. Statistically significant differences in SMC viability were reported for end temperatures of -11 (25%) and -35
C (<1%) in the collagen TE. The present study observes viability results of 87% and 75% at end temperatures -10
C and -20
C, respectively at 10
C/min in the fibrin TE. This is likely due to the differences in the model Thermal Injury Prediction During Cryoplasty FIGURE 8. A comparison of the viability vs. cooling rate response during freezing SMCs in suspension, monolayer, and fibrin TE determined 3 h post-thaw to an end temperature of 20 °C. systems themselves and also in the freezing setup. Grassl et al. used a cryoprobe (directional freezing) for the collagen TE and we used a Linkam cryostage, which is equiaxial and non-directional freezing stage, for the fibrin TE. Figure 9 correlates maximum cumulative fraction of IIF at different cooling rates to the SMC viability in the attached (monolayer and fibrin TE) vs. the non-attached system (suspensions). SMC viability is lower and IIF is higher in the attached state as compared to suspensions at all cooling rates. This may be a consequence of the cell–cell and cell– ECM interactions that enhance IIF and thereby reduce cell viability for the thermal conditions imposed. Thermal and Biophysical Responses The thermal model predicts initial cooling rates ranging from 2500 to 5
C/min in the artery. Table 2 (panels a and b) summarizes the initial cooling rates, the end temperatures, and the location of the ice ball edge for the given boundary conditions in the models. In general, results from the thermal model and the biophysics suggest that IIF is dominant in regions close to the lumen whereas both IIF and dehydration occur in the remaining sub-zero arterial regions. It should, however, be noted that the thermal properties used in the model are based on values reported for other tissues22 due to unavailability of porcine artery thermal properties. Care should therefore be taken when interpreting the model predictions. As discussed previously, IIF kinetics (Table 4) is dependent on the model system. The thermodynamic and kinetic parameters determined were found to be 97 higher for SMCs in monolayer and fibrin TE as compared to SMCs in suspensions (Table 4). This is in agreement with observations reported previously for hepatocytes52 and human dermal fibroblasts.5 Differences were also observed in the dehydration response of SMCs in suspension as compared to SMCs in attached systems (Table 5). The WT parameters determined for SMCs in attached systems are higher as compared to suspensions. This is also in agreement with previous results reported for hepatocytes in a collagen sandwich52 and human dermal fibroblasts in a collagen/fibrin TE.5 Care should be taken in the interpretation of these results since biophysical models developed for individual cells are being used for predicting responses in tissue like systems.34,49 However, these models are still useful in highlighting possible effects of cell–cell and cell–ECM interactions on the biophysical responses. Recently mathematical models have been proposed to account for intercellular mechanisms of IIF29,30 However, these models were developed for controlled micropatterned layer of hepatocytes where an individual cell was in contact with two neighboring cells. Unfortunately, the use of these models is currently not possible in most tissues wherein random multi-cell connections occur. Further developments in the field are needed to more accurately model and predict WT and IIF in tissues. Viability Responses The current study establishes that cell viability is affected by the model system, the cooling rate, the end temperature, and the time post-freeze/thaw. Previous studies have shown an inverted U relation between viability vs. cooling rate for different cell types (e.g., lymphocytes, red blood cells, ova).36 Solution effects injury is hypothesized to dominate at slower cooling rates whereas intracellular ice is predominant at higher cooling rates.36,50 This inverted U shape dependence was observed during freezing SMCs in fibrin TE (Fig. 8) whereas the response of cells in suspension and monolayer were predicted to be the right hand limb (i.e., IIF), at 3 h time post-freeze/thaw, of the inverted U-shaped curve since cooling rates lower than 5
C/ min were not studied. The effect of end temperature on cell viability has also been extensively studied. Previous parametric studies using AT-1 tumor cells and ELT-3 uterine leiomyoma tumor cells established that end temperature and hold time are important parameters influencing cell viability.10,45 In general, lower end temperatures result in increased cell injury. This trend is observed while freezing SMCs in all the model systems studied (Fig. 6) and it is most pronounced in the fibrin TE as compared to the other model systems. 98 BALASUBRAMANIAN et al. FIGURE 9. A correlation between the cumulative fraction of IIF and viability at different cooling rates during freezing SMCs in (a) suspension, (b) monolayer, and (c) fibrin TE to an end temperature of -20 °C. Studies on the effect of time post-freeze/thaw were also performed to quantify viability and proliferation response of SMCs in the attached state. Grassl et al. reported that SMCs did not proliferate in a collagen TE16 as had previously been suggested elsewhere.48 However, they observed cell proliferation in the control samples of fibrin TE system16 which is in agreement with this study (Fig. 7b). Cell viability was observed to drop after 24 h (especially for fibrin TE) suggesting the possibility of molecular pathways that may upregulate apoptosis. Tatsutani et al. reported apoptosis in SMC and endothelial cells for 30–120 s exposure between -5 and -15
C at 1 h post-freeze/ thaw47 using in vitro model systems (suspension). Hollister et al. reported apoptosis in prostate tumor cell lines 24–72 h after freeze/thaw26 whereas Hanai et al. reported apoptosis in human colon carcinoma cells within 8 h after freeze/thaw.19 The injury pathways and time periods for apoptosis is highly debated and needs to be addressed as a longer-term (i.e., many hours or days) injury mechanism post-cryoplasty. Additionally, apoptosis under in vivo conditions will also be affected by vascular and immunological responses to applied thermal insults. Injury Prediction Based on the thermal history, the biophysical mechanisms and the viability outcomes as discussed previously, conservative estimates of injury regimes with the artery are predicted (Table 2 and Fig. 10). Since the fibrin TE model is hypothesized to be the best in vitro model to study restenosis, thermal and biophysical effects are linked to cell survival to predict injury regimes. From our results and previous studies,47 we define temperature regimes and cooling rates that may result in necrotic or apoptotic cell injury. Necrotic injury is defined to occur in regimes experiencing 100% IIF and 20% viability and a cooling rate greater than 50
C/min (dominated by IIF). Apoptosis is defined to occur in regimes experiencing 50% or less IIF, 0 to -10
C and a cooling rate less than 50
C/min (as experienced closer to the ice ball edge). Regions close to the inner arterial wall or to the cryoplasty Thermal Injury Prediction During Cryoplasty 99 FIGURE 10. The thermal injury regimes during cryoplasty (with balloon temperature of -20 °C) in a femoral artery as predicted using the thermal model and the in vitro studies on SMC biophysics and viability. Regions of both necrosis and apoptosis are predicted. For further information on the regimes, please refer to Table 2. balloon experience a lower end temperature (~-20
C) and a high cooling rate (>130
C/min) and hence are presumed to have higher necrotic injury. The thermal injury was higher as expected when a lower balloon temperature (-20
C) was used. Figure 10 summarizes the different injury regimes, using the ANSYS model, in a femoral artery of 11-mm lumen diameter when the balloon temperature was maintained at -20
C. Table 2 summarizes the predicted necrotic and apoptotic injury regimes for the femoral and popliteal artery due to freezing. When a constant temperature boundary condition was applied at radial distance of 15.5 mm (Fig. 2c), the ice ball edge and the injury zones are expected to extend beyond the artery wall. This study is useful in predicting possible temperature regimes that can yield higher necrotic or apoptotic cell injury by modifying the thermal conditions imposed. Arteries occlude when rapidly frozen to -80
C and apoptosis and necrosis are reported for balloon temperatures of -20
C and -10
C11,47 under in vitro conditions. Balloon temperatures in between -80
C and -20
C may be looked into as options to enhance cell injury post-cryoplasty. The results of the study may be used in further optimization of the cryoplasty protocol and in designing in vivo studies. CONCLUSIONS The goal of the current study was to assess the thermal and the biophysical effects of freezing on SMC survival using different in vitro model systems. It was established that both the biophysics and the viability is affected by the model system and the thermal conditions. Cell–cell and cell–ECM contact plays a crucial role in enhancing IIF and affecting cell viability. Gap junctions are important in promoting increased IIF in cells in monolayer. Conservative estimates of thermal injury regimes in peripheral arteries were predicted using the results of the study. The study provides insights into possible optimization/modification of cryoplasty protocol and in designing future in vivo studies. 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