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Research Papers

# Experimental and Numerical Evaluation of Small-Scale Cryosurgery Using Ultrafine CryoprobeOPEN ACCESS

[+] Author and Article Information
Junnosuke Okajima

Institute of Fluid Science,
Tohoku University,
2-1-1 Katahira, Aoba-ku,
Sendai, Miyagi 980-8577, Japan
e-mail: okajima@pixy.ifs.tohoku.ac.jp

Atsuki Komiya

Institute of Fluid Science,
Tohoku University,
2-1-1 Katahira, Aoba-ku,
Sendai, Miyagi 980-8577, Japan
e-mail: komy@pixy.ifs.tohoku.ac.jp

Shigenao Maruyama

Institute of Fluid Science,
Tohoku University,
2-1-1 Katahira, Aoba-ku,
Sendai, Miyagi 980-8577, Japan
e-mail: maruyama@ifs.tohoku.ac.jp

1Corresponding author.

Manuscript received February 14, 2014; final manuscript received July 3, 2014; published online July 24, 2014. Assoc. Editor: Calvin Li.

J. Nanotechnol. Eng. Med 4(4), 040906 (Jul 24, 2014) (5 pages) Paper No: NANO-14-1011; doi: 10.1115/1.4027988 History: Received February 14, 2014; Revised July 03, 2014

## Abstract

The objective of this work is to experimentally and numerically evaluate small-scale cryosurgery using an ultrafine cryoprobe. The outer diameter (OD) of the cryoprobe was 550 μm. The cooling performance of the cryoprobe was tested with a freezing experiment using hydrogel at 37 °C. As a result of 1 min of cooling, the surface temperature of the cryoprobe reached −35 °C and the radius of the frozen region was 2 mm. To evaluate the temperature distribution, a numerical simulation was conducted. The temperature distribution in the frozen region and the heat transfer coefficient was discussed.

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## Introduction

Cryosurgery is a surgical treatment that utilizes the frozen phenomena of the biological tissue for removing undesirable tissue. The advantages of cryosurgery are minimal invasiveness, low bleeding, and short recovery period [1]. The cryoprobe is the cooling equipment used during cryosurgery. A conventional cryoprobe is 3–8 mm in diameter and is classified into two types, depending on the cooling method used. One type of cryoprobe utilizes the boiling heat transfer of liquid nitrogen [2]. This cryoprobe can generate an extremely low temperature condition; however, the complexity of the system is increased by the necessity for vacuum insulation to maintain the liquid nitrogen. The other type utilizes the Joule–Thompson expansion of high pressure gas as a heat transfer mechanism [3,4] and employs several types of refrigerants [5]. The main drawback of this type of cryoprobe is the low heat transfer coefficient, which prevents the surface temperature of the cryoprobe from reaching the refrigerant temperature inside the cryoprobe [6].

Some cryoprobes have succeeded commercially, such as Accuprobe by Cryomedical Science [7], CRYOcare by ENDOcare [8], ERBOKRYO by ERBE [9], CryoHit by Galil Medical [10], and SurgiFrost by CryoCath Technologies [11] conventional cryoprobes are 3–8 mm in diameter making it difficult to treat small lesions, such as pigments on the skin, wrinkles around the eyes, and early breast cancer.

To reduce invasiveness, several cryoprobes have been proposed. Takeda et al. [12] developed the Peltier cryoprobe. In this cryoprobe, the electric current supplied to the Peltier module can be varied to control the surface temperature of the cooling section precisely. Aihara et al. [13] developed a long, slender, and flexible cryoprobe with vacuum insulation; in this cryoprobe, the boiling heat transfer of an impinging jet using liquid nitrogen was used as the heat transfer mechanism. In addition, Maruyama et al. [14] developed a flexible cryoprobe using the Peltier effect; this cryoprobe consists of a flexible plastic tube. Further, miniaturized cryoprobes of approximately 1 mm in diameter have been researched by Benita and Conde [15] and Zhang et al. [16]. However, the cooling power of these cryoprobes was insufficient because of a low heat transfer rate, which in turn is due to the large surface area to volume ratio. Therefore, an efficient heat transfer mechanism is required.

To overcome this problem, the authors have studied phase change heat transfer in a coaxial small double tube [17] and developed an ultrafine cryoprobe with boiling heat transfer in a microchannel [18]. The OD of the cryoprobe is 550 μm. The ultrafine cryoprobe may realize cryosurgery for small lesions with minimum invasiveness or in blood vessels using catheters. Against the small lesions, it is expected that the treatment time will be shortened. The objective of this study is to evaluate the applicability of the ultrafine cryoprobe for cryosurgery in small areas. Both experiments and numerical simulations were conducted, and the heat transfer characteristics of the ultrafine cryoprobe were evaluated.

## Ultrafine Cryoprobe and Experimental System

Figure 1 shows the concept of the ultrafine cryoprobe. The ultrafine cryoprobe consists of an inner tube and an outer tube. The inner tube has a 0.15 mm OD and a 0.07 mm inner diameter (ID), and the outer tube has a 0.55 mm OD and 0.30 mm ID. Both tubes are made of stainless steel. HFC-23, which is alternative Freon with normal boiling point of −82.1 °C, was used as a refrigerant. HFC-23 was transported to the inner tube in the liquid state.

The inner tube plays the role of a capillary for depressurization. A large pressure drop occurs in the inner tube and the temperature of the refrigerant decreases causing the refrigerant to expand at the exit of the inner tube. The refrigerant then converts to two-phase flow and the outer tube is subsequently cooled. The advantages of this cooling system are as follows:

1. (1)The refrigerant can be transported from the reservoir to the cooling section eliminating the need for a complex insulation system like the liquid nitrogen cryoprobe.
2. (2)The ultrafine cryoprobe is cooled by boiling heat transfer which has a higher heat transfer coefficient than that of a Joule–Thomson cryoprobe.

Figure 2 shows the experimental apparatus, which consists of a HFC-23 tank, a precooler, several valves, and the cooling section. By using the precooler, HFC-23 was transported at subcooled state to avoid two-phase instability. The measurements were conducted by T-type thermocouples, a pressure gauge, and a thermal mass flowmeter. The locations of each sensor are denoted in Fig. 2. T-type thermocouples were soldered on the cryoprobe surface (TC1, TC2) as shown in Fig. 2. In addition, the refrigerant temperatures of the inlet (TC3) and outlet (TC4) of the cryoprobe were measured by ϕ1 mm sheathed T-type thermocouples. Instead of biological tissue, water gelated with 0.1 wt.% agar was used as a tissue phantom to simulate the biological tissue given that the thermophysical properties of biological tissue are similar to those of water. The effect of natural convection can be neglected due to gelatinization.

Prior to the experiment, the air in the experimental apparatus was evacuated by a vacuum pump. The HFC-23 tank was kept at room temperature. The precooler was cooled by ice water. The vapor of HFC-23 from the tank passed through the precooler and HFC-23 condensed from vapor to liquid phase. Hence, the conditions of the refrigerant at inlet of the cryoprobe were subcooled and the pressure was 4.2 MPa. Before starting the experiment, valve 2 was opened to release the pressure inside the cryoprobe. The hydrogel was maintained at 37 °C in a constant temperature bath. To begin the experiment, the cryoprobe was inserted into the hydrogel and the experiment was started by opening valve 1. The progress of frozen region was recorded by a video camera. The size of frozen region was measured by image processing software. After the experiment, a scale was photographed for the calibration of length.

In this experiment, the cooling duration was 60 s. This cryosurgery using the ultrafine cryoprobe targets the treatment of small lesion. Therefore, the treatment time can be shortened and the initial cooling performance is important for the ultrafine cryoprobe.

## 2D Axisymmetric Freezing Model

To calculate the transient freezing phenomena, the enthalpy method [19,20] is applied to the heat conduction equation which is expressed asDisplay Formula

(1)$∂H∂t=1r∂∂r(k(T)r∂T∂r)+∂∂z(k(T)∂T∂z)$

where H [J/m3] is enthalpy. The relationship between temperature and enthalpy is given in Fig. 3. Enthalpy is calculated by

where $ρ$ [kg/m3], cp [J/(kg·K)], and T'[K] are the density, the specific heat, and the dummy variable for integration, respectively. To accommodate for phase change phenomena, it is assumed that phase change starts at the upper phase change temperature, Tml, and ends at the lower phase change temperature, Tms, and the release of the latent heat occurs proportionally to the temperature during phase change. The phases were judged based on the temperature of each grid. The fraction of the unfrozen region is defined asDisplay Formula

(3)$fUF={0T≤TmsHρFLTms

where fUF [-] and L [J/kg] are the fractions of the unfrozen region and the latent heat for solidification, respectively. The thermal conductivity in the partially frozen region kmix was calculated as a weighted mean of the frozen and unfrozen regions using the fraction of the unfrozen region, expressed asDisplay Formula

(4)$kmix=(1-fUF)kU+fUFkUF$

Figure 4 shows the calculation domain and its size was 20 mm × 20 mm. The convective heat transfer was given to the upper side as the boundary condition. The heat transfer coefficient was calculated using the correlation of the natural convection from flat horizontal plate. The ambient temperature was 25 °C which is the temperature at experimental room. The boundary conditions on other sides were adiabatic condition. To be consistent with the experimental conditions, the surface temperature of the cooling section was given by the experimental data as the boundary condition. The temperature distribution on the area where the experimental data were given was assumed to be uniform. The material of the ultrafine cryoprobe was assumed to be stainless steel and heat conduction in the tip was considered. The other side of the calculation domain is the adiabatic condition. The thermophysical properties of pure water and pure ice are provided to the tissue phantom as listed in Table 1. It was assumed that the phase change starts at 0 °C and ends at −0.5 °C to maintain the stability of the calculation [21].

Equation (1) was discretized by the finite volume method. Time evolution was calculated by the fully implicit method. The calculation progressed with the satisfaction of the relationship between temperature and enthalpy, as shown in Fig. 3.

## Results and Discussion

Figure 5 shows the time variation in the surface temperature of the cryoprobe. As shown in Fig. 5, the surface temperature in the frozen region was maintained at about −35 °C. The thermocouple located outside of the hydrogel indicated −50 °C after 15 s. Prior to t = 15 s, unstable variation of the surface temperature was observed. This phenomenon could be caused by insufficient subcooling of the refrigerant at the inlet. The vapor phase was mixed at the inlet, and the vapor flow caused the degradation of heat transfer. At 15 s, the surface temperature outside of the hydrogel suddenly decreased as the liquid refrigerant was supplied to the cryoprobe. In addition, the temperature measured outside the hydrogel can be considered as the fluid temperature because of the low thermal conductivity of air.

Figure 6 shows the time variation of the frozen region. Here, the radius of frozen region was measured at the surface. The radius of the frozen region reached about 2.5 mm in 60 s. Therefore, this cryoprobe can be used to freeze biological tissue locally. In spite of the assumption that the surface temperature of the cryoprobe is uniform, the results show good agreement with each other. As time elapses, the difference is larger. The nonuniformity of the surface temperature should affect this difference. Figure 7 shows snapshots of the frozen region at 30 s obtained by experiment and calculation. As shown in these figures, the shapes of frozen region were similar to each other. The difference in the shapes was mainly at the tip of the cryoprobe. The cooling performance of the tip is strongly affected by the exit position of the inner tube and the thermal conductivity of the tip section.

Figure 8 shows the temperature distribution around the ultrafine cryoprobe at 30 s. In the current study, hydrogel was considered as the tissue phantom, and, therefore, the freezing point was 0 °C. However, the freezing point of biological tissue is known to be from −1 °C to −8° C [22]. Therefore, the frozen region in the biological tissue is smaller than that of pure water. Furthermore, reaching a temperature of −20 °C is one of the conditions for necrosis [23]. As shown in Fig. 8, the area at −20 °C is located only near the cryoprobe surface. Therefore, the freezing and thawing cycle, which is the other condition for necrosis, is required for cryosurgery using ultrafine cryoprobes.

The heat flux and heat transfer coefficient are estimated to evaluate the thermal characteristics of the ultrafine cryoprobe during cryosurgery. The heat flux can be calculated from the temperature distribution in Fig. 8. However, the heat transfer coefficient of the refrigerant flow inside the ultrafine cryoprobe is estimated considering the temperature distribution in the wall of the cryoprobe. 1D axisymmetric heat conduction in the wall at steady-state is expressed asDisplay Formula

(5)$ksrddr(rdTdr)=0$

Here, the steady-state heat conduction equation was used because the heat conduction process in stainless steel is much faster than that in hydrogel. The boundary conditions can be written asDisplay Formula

(6)$-ksdTdr|r=ro=-q$

(7)$-ksdTdr|r=ri=h[Tsat-T(ri)]$

where Tsat denotes the saturation temperature. Here, in Fig. 5, the measured temperature outside the hydrogel (TC2) can be considered as the refrigerant temperature because of the low thermal conductivity of air. Hence, the saturation temperature is assumed as the measured temperature outside the hydrogel shown in Fig. 5. As shown in Fig. 5, the both temperatures of TC1 and TC2 became stable. On the other hand, before 15 s, the temperature of TC1 was fluctuated. The cause of fluctuation may be the high vapor quality flow due to insufficient subcooling by the precooler. Therefore, this assumption is valid after 15 s, as shown in Fig. 5. Solving these equations, the heat transfer coefficient, h, can be expressed asDisplay Formula

(8)$h=qrori[Tsurf-Tsat-qrokslnrori]-1$

Here, the heat flux q was calculated from the result of numerical simulation.

Figure 9 shows the time variation of heat flux on an ultrafine cryoprobe positioned at TC1. At the early stage of cooling, the heat flux was −50 kW/m2, which is a smaller value than that after 8 s. In addition, the value of heat flux became stable after 15 s. Therefore, the heat transfer mode was completely different from that after 15 s. After the first 15 s, the value of heat flux changed from −200 kW/m2 to −150 kW/m2.

Figure 10 shows the time variation of the local heat transfer coefficient of refrigerant flow in an ultrafine cryoprobe positioned at the surface of the hydrogel. Because of the assumption of the saturation temperature in this study, the values before 15 s are not reliable. As shown in Fig. 10, this cryoprobe had a constant heat transfer coefficient of approximately 20 kW/(m2·K) during freezing.

## Conclusion

This paper describes the evaluation of the heat transfer characteristics during freezing by experiments and numerical simulation. The results obtained are as follows:

1. (1)A freezing experiment using hydrogel was conducted. The surface temperature in the frozen region was maintained at about −35 °C. The radius of frozen region reached about 2.5 mm in 60 s.
2. (2)The experimental and numerical results of the time variation of the frozen region were in agreement.
3. (3)The temperature distribution around the ultrafine cryoprobe was evaluated. The area at −20 °C, which is one of the conditions for necrosis, occurs only near the cryoprobe surface. Therefore, the freezing and thawing cycle, which is other condition for necrosis, is required for cryosurgery using an ultrafine cryoprobe.
4. (4)The heat flux and heat transfer coefficients were estimated from the numerical simulation. At the early stage of cooling, the heat flux was −50 kW/m2. Afterward, the heat flux was stable and ranged from −200 kW/m2 to −150 kW/m2. Moreover, this cryoprobe had a constant heat transfer coefficient of approximately 20 kW/(m2·K) during freezing.

In order to shorten the treatment time, the inlet condition of refrigerant is important to avoid the initial instability of the heat flux. To keep the cooling with high heat flux, the refrigerant at inlet should be subcooled enough.

## Acknowledgements

J. Okajima has received support from Grant-in-Aid for Young Scientists (B) [25820054] from the Japan Society for the Promotion of Science.

Nomenclature
• cp =

specific heat capacity (J/(kg·K))

• fUF =

fraction of unfrozen region, dimensionless

• h =

heat transfer coefficient (W/(m2·K))

• H =

enthalpy (J/m3)

• k =

thermal conductivity (W/(m·K))

• L =

latent heat of solidification (J/kg)

• q =

heat flux (W/m2)

• r =

• T =

temperature ( °C)

• z =

coordinate (m)

• $ρ$ =

density (kg/m3)

Subscripts
• F =

frozen region

• i =

inner tube

• mix =

partially frozen region

• o =

outer tube

• s =

stainless steel, surface

• UF =

unfrozen region

## References

Bischof, J., Christov, K., and Rubinsky, B., 1993, “A Morphological-Study of Cooling Rate Response in Normal and Neoplastic Human Liver-Tissue-Cryosurgical Implications,” Cryobiology, 30(5), pp. 482–492. [PubMed]
Popken, F., Seifert, J. K., Engelmann, R., Dutkowski, P., Nassir, F., and Junginger, T., 2000, “Comparison of Iceball Diameter and Temperature Distribution Achieved With 3-Mm Accuprobe Cryoprobes in Porcine and Human Liver Tissue and Human Colorectal Liver Metastases in Vitro,” Cryobiology, 40(4), pp. 302–310. [PubMed]
Coleman, R. B., and Richardson, R. N., 2005, “A Novel Closed Cycle Cryosurgical System,” Int. J. Refrig., 28(3), pp. 412–418.
Forest, V., Peoc'h, M., Campos, L., Guyotat, D., and Vergnon, J.-M., 2006, “Benefit of a Combined Treatment of Cryotherapy and Chemotherapy on Tumour Growth and Late Cryo-Induced Angiogenesis in a Non-Small-Cell Lung Cancer Model,” Lung Cancer, 54(1), pp. 79–86. [PubMed]
Fredrickson, K., Nellis, G., and Klein, S., 2006, “A Design Method for Mixed Gas Joule–Thomson Refrigeration Cryosurgical Probes,” Int. J. Refrig., 29(5), pp. 700–715.
Hewitt, P. M., Zhao, J., Akhter, J., and Morris, D. L., 1997, “A Comparative Laboratory Study of Liquid Nitrogen and Argon Gas Cryosurgery Systems,” Cryobiology, 35(4), pp. 303–308. [PubMed]
Seifert, J. K., Gerharz, C. D., Mattes, F., Nassir, F., Fachinger, K., Beil, C., and Junginger, T., 2003, “A Pig Model of Hepatic Cryotherapy. In Vivo Temperature Distribution During Freezing and Histopathological Changes,” Cryobiology, 47(3), pp. 214–226. [PubMed]
Rewcastle, J. C., Sandison, G. A., Saliken, J. C., Donnelly, B. J., and McKinnon, J. G., 1999, “Considerations During Clinical Operation of Two Commercially Available Cryomachines,” J. Surg. Oncol., 71(2), pp. 106–111. [PubMed]
Popken, F., Land, M., Bosse, M., Erberich, H., Meschede, P., Konig, D. P., Fischer, J. H., and Eysel, P., 2003, “Cryosurgery in Long Bones With New Miniature Cryoprobe: An Experimental in Vivo Study of the Cryosurgical Temperature Field in Sheep,” Eur. J. Surg. Oncol., 29(6), pp. 542–547. [PubMed]
Tacke, J., Adam, G., Haage, P., Sellhaus, B., Großkortenhaus, S., and Günther, R. W., 2001, “MR-Guided Percutaneous Cryotherapy of the Liver: In Vivo Evaluation With Histologic Correlation in an Animal Model,” J. Magn. Reson. Imaging, 13(1), pp. 50–56. [PubMed]
Doll, N., Meyer, R., Walther, T., and Mohr, F. W., 2004, “A New Cryoprobe for Intraoperative Ablation of Atrial Fibrillation,” Ann. Thorac. Surg., 77(4), pp. 1460–1462. [PubMed]
Takeda, H., Maruyama, S., Okajima, J., Aiba, S., and Komiya, A., 2009, “Development and Estimation of a Novel Cryoprobe Utilizing the Peltier Effect for Precise and Safe Cryosurgery,” Cryobiology, 59(3), pp. 275–284. [PubMed]
Aihara, T., Kim, J.-K., Suzuki, K., and Kasahara, K., 1993, “Boiling Heat Transfer of a Micro-Impinging Jet of Liquid Nitrogen in a Very Slender Cryoprobe,” Int. J. Heat Mass Transfer, 36(1), pp. 169–175.
Maruyama, S., Nakagawa, K., Takeda, H., Aiba, S., and Komiya, A., 2008, “The Flexible Cryoprobe Using Peltier Effect for Heat Transfer Control,” J. Biomech. Sci. Eng., 3(2), pp. 138–150.
Bénita, M., and Condé, H., 1972, “Effects of Local Cooling Upon Conduction and Synaptic Transmission,” Brain Res., 36(1), pp. 133–151. [PubMed]
Zhang, J.-X., Ni, H., and Harper, R. M., 1986, “A Miniaturized Cryoprobe for Functional Neuronal Blockade in Freely Moving Animals,” J. Neurosci. Methods, 16(1), pp. 79–87. [PubMed]
Okajima, J., Komiya, A., and Maruyama, S., 2010, “Boiling Heat Transfer in Small Channel for Development of Ultrafine Cryoprobe,” Int. J. Heat Fluid Flow, 31(6), pp. 1012–1018.
Okajima, J., Maruyama, S., Takeda, H., Komiya, A., and Sangkwon, J., 2010, “Cooling Characteristics of Ultrafine Cryoprobe Utilizing Convective Boiling Heat Transfer in Microchannel,” Proceedings of the 14th IHTC, Washington DC, Aug. 8–13, Vol. 1, pp. 297–306.
Voller, V. R., and Swaminathan, C. R., 1993, “Treatment of Discontinuous Thermal Conductivity in Control-Volume Solutions of Phase-Change Problems,” Numer. Heat Transfer, Part B, 24(2), pp. 161–180.
Swaminathan, C. R., and Voller, V. R., 1992, “A General Enthalpy Method for Modeling Solidification Processes,” MTB, 23(5), pp. 651–664.
Okajima, J., Takeda, H., Komiya, A., and Maruyama, S., 2008, “Possibility of Micro-Cryosurgery Utilizing Cooling Needle,” Proceedings of 16th International Conference on Mechanics in Medicine and Biology, Pittsburgh, PA, July 23–25.
Deng, Z.-S., and Liu, J., 2005, “Numerical Simulation of Selective Freezing of Target Biological Tissues Following Injection of Solutions With Specific Thermal Properties,” Cryobiology, 50(2), pp. 183–192. [PubMed]
Gage, A. A., and Baust, J., 1998, “Mechanisms of Tissue Injury in Cryosurgery,” Cryobiology, 37(3), pp. 171–186. [PubMed]
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## References

Bischof, J., Christov, K., and Rubinsky, B., 1993, “A Morphological-Study of Cooling Rate Response in Normal and Neoplastic Human Liver-Tissue-Cryosurgical Implications,” Cryobiology, 30(5), pp. 482–492. [PubMed]
Popken, F., Seifert, J. K., Engelmann, R., Dutkowski, P., Nassir, F., and Junginger, T., 2000, “Comparison of Iceball Diameter and Temperature Distribution Achieved With 3-Mm Accuprobe Cryoprobes in Porcine and Human Liver Tissue and Human Colorectal Liver Metastases in Vitro,” Cryobiology, 40(4), pp. 302–310. [PubMed]
Coleman, R. B., and Richardson, R. N., 2005, “A Novel Closed Cycle Cryosurgical System,” Int. J. Refrig., 28(3), pp. 412–418.
Forest, V., Peoc'h, M., Campos, L., Guyotat, D., and Vergnon, J.-M., 2006, “Benefit of a Combined Treatment of Cryotherapy and Chemotherapy on Tumour Growth and Late Cryo-Induced Angiogenesis in a Non-Small-Cell Lung Cancer Model,” Lung Cancer, 54(1), pp. 79–86. [PubMed]
Fredrickson, K., Nellis, G., and Klein, S., 2006, “A Design Method for Mixed Gas Joule–Thomson Refrigeration Cryosurgical Probes,” Int. J. Refrig., 29(5), pp. 700–715.
Hewitt, P. M., Zhao, J., Akhter, J., and Morris, D. L., 1997, “A Comparative Laboratory Study of Liquid Nitrogen and Argon Gas Cryosurgery Systems,” Cryobiology, 35(4), pp. 303–308. [PubMed]
Seifert, J. K., Gerharz, C. D., Mattes, F., Nassir, F., Fachinger, K., Beil, C., and Junginger, T., 2003, “A Pig Model of Hepatic Cryotherapy. In Vivo Temperature Distribution During Freezing and Histopathological Changes,” Cryobiology, 47(3), pp. 214–226. [PubMed]
Rewcastle, J. C., Sandison, G. A., Saliken, J. C., Donnelly, B. J., and McKinnon, J. G., 1999, “Considerations During Clinical Operation of Two Commercially Available Cryomachines,” J. Surg. Oncol., 71(2), pp. 106–111. [PubMed]
Popken, F., Land, M., Bosse, M., Erberich, H., Meschede, P., Konig, D. P., Fischer, J. H., and Eysel, P., 2003, “Cryosurgery in Long Bones With New Miniature Cryoprobe: An Experimental in Vivo Study of the Cryosurgical Temperature Field in Sheep,” Eur. J. Surg. Oncol., 29(6), pp. 542–547. [PubMed]
Tacke, J., Adam, G., Haage, P., Sellhaus, B., Großkortenhaus, S., and Günther, R. W., 2001, “MR-Guided Percutaneous Cryotherapy of the Liver: In Vivo Evaluation With Histologic Correlation in an Animal Model,” J. Magn. Reson. Imaging, 13(1), pp. 50–56. [PubMed]
Doll, N., Meyer, R., Walther, T., and Mohr, F. W., 2004, “A New Cryoprobe for Intraoperative Ablation of Atrial Fibrillation,” Ann. Thorac. Surg., 77(4), pp. 1460–1462. [PubMed]
Takeda, H., Maruyama, S., Okajima, J., Aiba, S., and Komiya, A., 2009, “Development and Estimation of a Novel Cryoprobe Utilizing the Peltier Effect for Precise and Safe Cryosurgery,” Cryobiology, 59(3), pp. 275–284. [PubMed]
Aihara, T., Kim, J.-K., Suzuki, K., and Kasahara, K., 1993, “Boiling Heat Transfer of a Micro-Impinging Jet of Liquid Nitrogen in a Very Slender Cryoprobe,” Int. J. Heat Mass Transfer, 36(1), pp. 169–175.
Maruyama, S., Nakagawa, K., Takeda, H., Aiba, S., and Komiya, A., 2008, “The Flexible Cryoprobe Using Peltier Effect for Heat Transfer Control,” J. Biomech. Sci. Eng., 3(2), pp. 138–150.
Bénita, M., and Condé, H., 1972, “Effects of Local Cooling Upon Conduction and Synaptic Transmission,” Brain Res., 36(1), pp. 133–151. [PubMed]
Zhang, J.-X., Ni, H., and Harper, R. M., 1986, “A Miniaturized Cryoprobe for Functional Neuronal Blockade in Freely Moving Animals,” J. Neurosci. Methods, 16(1), pp. 79–87. [PubMed]
Okajima, J., Komiya, A., and Maruyama, S., 2010, “Boiling Heat Transfer in Small Channel for Development of Ultrafine Cryoprobe,” Int. J. Heat Fluid Flow, 31(6), pp. 1012–1018.
Okajima, J., Maruyama, S., Takeda, H., Komiya, A., and Sangkwon, J., 2010, “Cooling Characteristics of Ultrafine Cryoprobe Utilizing Convective Boiling Heat Transfer in Microchannel,” Proceedings of the 14th IHTC, Washington DC, Aug. 8–13, Vol. 1, pp. 297–306.
Voller, V. R., and Swaminathan, C. R., 1993, “Treatment of Discontinuous Thermal Conductivity in Control-Volume Solutions of Phase-Change Problems,” Numer. Heat Transfer, Part B, 24(2), pp. 161–180.
Swaminathan, C. R., and Voller, V. R., 1992, “A General Enthalpy Method for Modeling Solidification Processes,” MTB, 23(5), pp. 651–664.
Okajima, J., Takeda, H., Komiya, A., and Maruyama, S., 2008, “Possibility of Micro-Cryosurgery Utilizing Cooling Needle,” Proceedings of 16th International Conference on Mechanics in Medicine and Biology, Pittsburgh, PA, July 23–25.
Deng, Z.-S., and Liu, J., 2005, “Numerical Simulation of Selective Freezing of Target Biological Tissues Following Injection of Solutions With Specific Thermal Properties,” Cryobiology, 50(2), pp. 183–192. [PubMed]
Gage, A. A., and Baust, J., 1998, “Mechanisms of Tissue Injury in Cryosurgery,” Cryobiology, 37(3), pp. 171–186. [PubMed]

## Figures

Fig. 1

Concept of the ultrafine cryoprobe

Fig. 2

Schematic of the experimental system

Fig. 3

Relationship between temperature and enthalpy for pure water

Fig. 4

Calculation domain

Fig. 5

Time variation of the surface temperature on the ultrafine cryoprobe

Fig. 6

Time variation of the frozen region at surface of the hydrogel

Fig. 7

Snapshots of the frozen region at 30 s obtained by (a) experiment and (b) calculation

Fig. 8

Temperature distribution around the ultrafine cryoprobe at 30 s

Fig. 9

Time variation of the heat flux on the ultrafine cryoprobe positioned at the surface of the hydrogel

Fig. 10

Time variation of local heat transfer coefficient for the refrigerant flow in the ultrafine cryoprobe positioned at the surface of the hydrogel

## Tables

Table 1 Thermophysical properties for the numerical simulation

## Discussions

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