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Nano-cryosurgery and its mechanisms for enhancing freezing efficiency

Nano-cryosurgery and its mechanisms for enhancing freezing efficiency
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  • Available online at Nanomedicine: Nanotechnology, Biology, and Medicine 4 (2008) 79 – 87 Original Article: Oncology Nanomedicine Nanocryosurgery and its mechanisms for enhancing freezing efficiency of tumor tissues Jing-Fu Yan, PhD (C), a Jing Liu PhD, BS, BE a,b,⁎ a Cryogenics Laboratory, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, China b Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, ChinaAbstract We proposed for the first time a surgical term, the nanocryosurgery, for efficient tumor treatment through combining the theories of cyrosurgery and nanotechnology. Simulations were performed on the combined phase change bioheat transfer problems in a single cell level and its surrounding tissues, to explicate the difference of transient temperature response between conventional cyrosugery and nanocyrosurgery. According to theoretical interpretation and existing experimental measurements, intentional loading of nanoparticles with high thermal conductivity into the target tissues can lower the final temperature significantly, increase the maximum freezing rate, and enlarge the ice volume obtained in the absence of nanoparticles. In addition, introduction of nanoparticle- enhanced freezing could also make conventional cyrosurgery more flexible in many aspects such as artificially interfering in the size, shape, image and direction of iceball formation. The concepts of nanocyrosurgery may offer new opportunities for future tumor treatment. © 2008 Elsevier Inc. All rights reserved.Key words: Nanocryosurgery; Bioheat transfer; Cryoinjury; Ice nucleation; Tumor treatmentBackground alternative to traditional therapies. Accompanied with modern imaging technology, the field of cryosurgery has Cryosurgery is a technique that uses freezing to destroy in fact been widely extended since its early stage.1-3undesired tissues. This therapy is becoming popular However, in many clinical cases it has been found thatbecause of its important clinical advantages. Besides freezing alone could not completely destroy the targetedbeing less invasive than traditional surgical resection, it tumor; moreover, there is always a high recurrence rateminimizes pain, bleeding, and other complications of with follow-up surveys. 4,5 From the viewpoint ofsurgery, is less expensive than other treatments, and cryomedical engineering,6 the major reason concerns therequires a much shorter recovery time and hospital stay. freezing rate, which does not produce a massive iceAlthough it still cannot be regarded as a routine method of nucleation in tumor cells, especially at the edge of thecancer treatment, cryosurgery is developing rapidly as an tumor; thus the procedure cannot guarantee complete lethality to all of the tumor. Consequently, a major concern in conventional cryosurgery is to avoid insuffi- cient freezing between multiple cryoprobes and to Received 11 March 2007; accepted 13 November 2007. maximize the freezing efficiency so as to enhance killing No conflict of interest was reported by the authors of this paper. of the target tumor. This research is partially supported by the National Natural Science If cryosurgery is to be successful, freezing efficiencyFoundation of China under Grants 50575219 and 50325622. ⁎Corresponding author: Cryogenics Laboratory, Technical Institute of should be guaranteed by introducing adjuvant approaches.Physics and Chemistry, Chinese Academy of Sciences, Beijing 100080, Belonging to the same category of physical therapy,China. modern hyperthermia combined with advanced nanotech- E-mail address: (J. Liu). nique exemplifies such endeavors. The newly developed1549-9634/$ – see front matter © 2008 Elsevier Inc. All rights reserved.doi:10.1016/j.nano.2007.11.002 Please cite this article as: J.-F. Yan, J. Liu, Nanocryosurgery and its mechanisms for enhancing freezing efficiency of tumor tissues. Nanomedicine: NBM 2008;4:79 - 87, doi:10.1016/j.nano.2007.11.002
  • 80 J.-F. Yan, J. Liu / Nanomedicine: Nanotechnology, Biology, and Medicine 4 (2008) 79–87 Figure 1. Schematic illustration of computational domain loaded with nanoparticles during cryosurgery (not to scale).magnetic nanohyperthermia, which takes full advantage of Moreover, because the particulate suspension can beelectromagnetic heating effects and powerful thermo- locally injected and distributed into the region of interest asosmosis, offers some attractive possibilities in tumor desired,21 it is available to provide accurate killing on thetherapy.7-12 Moreover, the ability to treat cancer by nanoscale by means of nanocryosurgery. As is well known,targeted delivery through angiogenesis or some antineo- freezing affects biological systems at both nanoscaleplastic drug, especially using hyperthermia-introduced (molecular) and microscale (cellular) levels, which maynanoparticles, has also been reported to show a good bring about changes in structure, composition, water and fattreatment effect.13-15 Inspired by such curative trends in content, and salinity of tissues.3,22 High concentrations ofhyperthermia, we propose a new modality in cryosurgery, nanoparticles combined with freezing might enhance suchnamed nanocryosurgery, and offer our preliminary results harmful effects. Although a series of studies23-25 have beenin this article. published on the toxicological effect of nanoparticles, the potential toxicity to normal tissues with targeted injection of particles could be prevented through appropriate choice ofMethods particle type and careful control of injection time, procedure, and dose of particulate suspension. Thus far, itBasic principle of nanocryosurgery is clear that some candidate particles like the iron oxide This physical therapy is combined with advanced magnetite (Fe3O4) and gold (Au), have good biologicalnanotechnologies. Its basic principle is to introduce a compatibility and have been widely used in clinics.functional solution with nanoparticles into the target Meanwhile, using nanoparticles to deliver antineoplastictissues (Figure 1), which then serves to maximize freezing drugs or angiogenesis to damage target tumors has alsoheat transfer, increase the probability of intracellular ice proved feasible for tumor treatment. For instance, Bischofformation (PIF), and regulate iceball formation orientation. and colleagues15 proposed a novel method using AuNanoparticles with high thermal conductivity allow nanoparticle-assisted tumor necrosis factor-α delivery incryosurgery to take full advantage of the enhanced heat combination with hyperthermia, which significantly delayedconduction effects and their ability to serve as nucleation tumor growth, reducing both tumor cell survival rate andseeds. As was recently realized, liquids containing metallic tumor blood perfusion. All of these working media andor nonmetallic solid nanoparticles show an increase in techniques can also be used in nanocryosurgery.thermal conductivity compared with that of the base Furthermore, the iceball growth during cryosurgery canliquid. 16,17 This can also be true when applied to be artificially controlled by asymmetrically injectingnanocryosurgery, where addition of metal nanoparticles nanoparticle solution into the targeted tissues, thus makinginto the wet biological environment will increase the tissue cryosurgery more flexible. It is often difficult to produce anconductivity, which in turn results in significant freezing optimal cryolesion area using conventional cryosurgicaleffects. Meanwhile, according to the theory of ice technique because of the irregular shape of the tumor.nucleation, it will be seen that massive loading of However, when using injected nanoparticles the growthnanoparticles in tumor cells is bound to induce more state of ice crystals can be efficiently modified as desired.efficient heterogeneous nucleation as ice seeds, which to In nanocryosurgery one can regulate growth direction andsome extent guarantees a higher PIF, the main reason for orientation of an iceball, thus permitting good conformationcell death in cryosurgery.18-20 of the cryosurgery to the tumor outline.
  • J.-F. Yan, J. Liu / Nanomedicine: Nanotechnology, Biology, and Medicine 4 (2008) 79–87 81 process based on three different conditions. Nano-silver was added in a phantom gel as case 1, and carbon nanotubes as case 2, whereas the original phantom gel was referred as the reference sample. From the curve it can be seen that the freezing rate at the target position where nanoparticle solutions were locally injected was evidently increased. Generally, if the freezing process does not endure long enough, it could lead to a “dead region” representing insufficient freezing between two cryoprobes (as indicated by red dotted lines in Figure 2). Clearly, with the help of nanoparticle-enhanced freezing, such dead regions could be successfully prevented. In other words, the possibility of insufficient freezing will be decreased substantially. To evaluate the capacity for controlling the size, shape, and direction of the iceball formation by injecting nanoparticle solutions with specific thermal properties intoFigure 2. Transient temperature response of selected position with different the target tissues, we had adopted a medical infraredinjection samples during same freezing process. thermometer to map the temperature profile over the whole surface above the freezing area.18 In a typical test, different volumes of particulate solution were considered. As thermal images indicated, different doses of injecting solution have Finally, introduction of nanoparticles into target tissues resulted in varied magnitudes of iceball formation, whichcould improve image contrast and offer a better image indicates that the appropriate particulate solution couldguidance for the cryosurgical operation.26 In this respect, effectively regulate the tumor-killing area via directionalsome imaging magnetic nanoparticles27 such as Fe3O4, 20– freezing.30 nm in diameter, have been found to increase the resolutionand contrast of several commonly used imaging techniques Bioheat transfer modelin minimally invasive therapy such as magnetomotive Nanoparticle-aided cryosurgery can produce a predictableoptical coherence tomography or magnetic resonance improvement of temperature response on the target tissue andimaging. Fluorescent nanoparticles are also used as image cell. Because the present study focuses only on the freezingprobes to image and monitor thermal lesion of tissue during effect of a single tumor cell when different kinds ofthermal therapies so as to guarantee an accurate treatment.28 nanoparticles have already been injected in or outside theSuch characteristics of nanoparticles can increase the cell membranes, the computational domain can be simplifiedcurative tumor-killing effect and decrease local recurrence and depicted in Figure 1, which is divided into two parts:rate as well. Therefore, when nanotechnology meets intracellular and extracellular areas. For simplicity, acryosurgery, the treatment efficiency of conventional spherical coordinate system in one dimension was used.cryosurgery is expected to be significantly improved. Calculations of heat transfer are based on the widely acceptedExperimental findings for nanocryosurgery bioheat model proposed by Pennes,29 which is widely used in the description of the tissue freezing process. Several experiments already performed in our laboratory In the intracellular medium the bioheat equation ishave demonstrated the significant effect of nanoparticles in expressed as follows:enhancing the process of freezing biological tissues.According to the typical temperature response curves of AT 1 A2 ðrT Þ C ¼ ki d d þ Qm : ð1Þpork tissue during the freezing process with one liquid At r Ar2nitrogen–based cryoprobe,21 it has been shown that thelowest temperature for injecting nanoparticles (30 mL 5% In the extracellular medium the effect of blood perfusionw/w particulate suspension) can reach –115°C at a location should be included, and the bioheat equation reads as:5 mm distant from the probe, which is much lower than its AT 1 A2 ðrT Þcounterpart case of no injection. The latter case achieves C ¼ ko d d þ xb Cb ðTa À T Þ þ Qm ð2Þ At r Ar2only a lowest temperature of –75°C at the same position andunder the same freezing conditions. This was a result of the where T is the temperature, Cb and ωb are the heat capacityenhanced heat conduction due to the addition of metal and the blood perfusion of biological tissues, respectively; kinanoparticles into tissues. Presented in Figure 2 is a newly and ko are intracellular and extracellular thermal conductiv-obtained transient temperature response of the selected ity, respectively; C is heat capacity of biomaterial includingposition (at the midpoint between two liquid nitrogen the contribution of the loaded nanoparticles; Qm is thecryoprobes spaced 2 cm apart) during the same freezing metabolic heat generation, and Ta is arterial temperature.
  • 82 J.-F. Yan, J. Liu / Nanomedicine: Nanotechnology, Biology, and Medicine 4 (2008) 79–87Table 1 areas, the thermal conductivity for the treated object can bePhysical properties of biological tissues and nanoparticles30-32 depicted, respectively, as follows:Items Units Values kp þ 2kf t À 2gðkf t À kp ÞThermal conductivity of frozen tissue, kft W/m °C 2 kf ¼ kf t d : ð3Þ kp þ 2kf t þ gðkf t À kp ÞThermal conductivity of unfrozen tissue, kut W/m °C 0.5Thermal conductivity of Al2O3, kp W/m °C 39.7Heat capacity of Al2O3, Cp J/m °C 2.82 × 106 kp þ 2kut À 2gðkut À kp Þ ku ¼ kut d ð4ÞThermal conductivity of Fe3O4, kp W/m °C 7.1 kp þ 2kut þ gðkut À kp ÞHeat capacity of Fe3O4, Cp J/m °C 3.2 × 106 As for thermal capacity, considering the energy equationThermal conductivity of Au, kp W/m °C 297.73 for a two-component (biology part and nanoparticle part)Heat capacity of Au, Cp J/m3 °C 2.21 × 106 system of biomaterial, the volume fraction of particleused inThermal conductivity of PTFE, kp W/m °C 0.2 Equations (3) and (4) is introduced. Then the thermalHeat capacity of PTFE, Cp J/m °C 2.13 × 106 capacity can be defined as follows:Thermal conductivity of diamond, kp W/m °C 2000 Cf ¼ Cf t dð1 À gÞ þ Cp d g ð5ÞHeat capacity of diamond, Cp J/m °C 1.4 × 106Heat capacity of frozen tissue, Cft J/m °C 2 × 106Heat capacity of blood, Cb J/m °C 3.6 × 106 Cu ¼ Cut dð1 À gÞ þ Cp d g ð6ÞHeat capacity of unfrozen tissue, Cut J/m °C 3.6 × 106 here, subscripts f and u represent frozen and unfrozenLatent heat, L J/m °C 250 × 106 mixture, respectively. Subscripts ft and ut mean frozen andTemperature of lower phase change, Tl K 265.15 unfrozen tissues, respectively. Subscript p stands for the loaded particles.Temperature of upper phase change, Tu K 272.15 Based on Equations (1) and (2), a unified equation, whichTemperature of outside boundary, Tp K 77 can be applied to frozen, partially frozen, and unfrozen tissueArterial temperature, Ta K 310.15 regions, can be written by introducing effective heat capacity. Because the phase change of real biological tissue does not take place at a specific temperature but within a temperature range, it is reasonable to substitute a large effective heat The mathematical model used here is based on four capacity over a temperature range (Tml, Tmu) for the latent heat,principal assumptions: (1) The effect of cell deformation due where Tml and Tmu are, respectively, the lower and upper phaseto freezing is neglected, and the transmembrane temperature transition temperatures of the tissue. For brevity, the derivationdifference is also omitted for simplicity. (2) Both the target and definition of effective thermal capacity, effective thermalcell and its surrounding tumor area are regarded as an ideal conductivity, effective metabolic heat generation, and effectivesphere, and the media inside or outside the cell as blood perfusion are not repeated here. Readers are referred tohomogeneous and are treated as one-dimensional. (3) The Deng and Liu29 for more details.thermal properties of nanoparticles are treated as tempera-ture-independent. (4) The injected nanoparticles are alltreated as ideal spheres. Results Because the Hamilton-Crosser (H-C) model is the Simulation resultsclassical theory to predict thermal conductivity of nanofluidsthat has been applied in the field of particles-tissue Considering the typical characteristic size of biological cellsinteraction resulting from hyperthermia, in this study it is as between 5 and 20 μm, the radius of a tumor cell is taken herealso used for calculating the thermal conductivities of objects as 10 μm. It is assumed further that the distance between thecomposed of biomaterials and nanoparticles. Another reason cell center and the boundary of the calculation domain isto use the H-C model is that it can simply but effectively 30 μm. For simplification, only the first boundary conditiondescribe the macroscale thermal conductivity of nanoparti- was considered, namely to suppose that T = 77 K at the edge ofcle-tissue mixtures without considering the size effect of the calculation domain. For much more complicated situationsnanoparticles, which, according to our previous experimen- the present method is still applicable. In addition, the initialtal results, does not play a distinct role in increasing the temperature in the calculation domain is set as T = 310.15 K.macroscale thermal conductivity. The theoretical model was simulated using the finite Considering phase change phenomena during cryosur- element method. Typical properties for biological tissue30,31gery, the effective heat capacity method is adopted to as well as different kinds of particles32 are listed in Table 1 insimultaneously solve the heat transfer in frozen and unfrozen the following simulations. Considering that the size effect ofareas. According to the H-C model, in frozen and unfrozen nanoparticles is neglected with the H-C model and has
  • J.-F. Yan, J. Liu / Nanomedicine: Nanotechnology, Biology, and Medicine 4 (2008) 79–87 83Figure 3. Freezing temperature responses at the core of the studied cell for different nanoparticle loading situations where the volume fraction of particles isdistributed uniformly by η = 1%. within the cell interior and outside the cell by η = 2% (A), η = 10% (B), and η = 20% (C), respectively. (D) Temperature profilealong the radius direction at 0.5 ms with different concentrations of nano-Al2O3.minimal influence on the macroscale thermal conductivity as exceeding that of gold by fivefold, it is noted that if itsmentioned, standard thermal property values for particles are volumetric loads are not high enough there is almost noused instead. differential cooling effect with nanogold. Therefore, choos- Presented in Figure 3, A–C are the temperature responses ing an optimal concentration with appropriate particles isat the core of a cell during freezing for the situations loading crucial to maximize the effects of cryosurgery with minimumwith different kinds of nanoparticles when their volume cost. In addition, with the increase of volume fractions infractions are η = 1% in the cell and η = 2%, η = 10%, and tumor cells, the influence induced by particles becomesη = 20% outside the cell, respectively. Figure 3, D shows the stronger and more apparent. Figure 3, D shows that thetemperature profile along the radius direction at 0.5 ms temperature of a tumor cell core with a 20% volume fractionwith different concentrations of nano-Al2O3. It can be seen of nano-Al2O3 could decrease to 82 K at 0.5 ms, whereas itthat different kinds and concentrations of nanoparticles have could only reach 107 K with 2% volumetric loads. However,different influences on the freezing rate in the cell. A large it still can be observed that the freezing enhancementvolume fraction of nanoparticles with high thermal con- induced by a 2% volume fraction of nano-Al2O3 is evident inductivity could evidently increase the freezing rate of the comparison with the case without loading nanoparticles (6 Kcell. On the contrary, particles with low thermal conductivity temperature difference in core of cell at 0.5 ms). As can becould decrease the freezing rate. As shown from Figure 3, seen in Figure 3, D, the calculated values are in good accordA–C, at the same volume fraction, polytetrafluoroethylene with the currently available experimental data.21(PTFE) and diamond play a much more significant role in To better quantify the freezing rate of a cell loaded withaffecting the freezing rate than other candidate particles. This nanoparticles, Figure 4, A–C, corresponding to the samecan be attributed to their lowest and highest thermal situations in Figure 3, A–C, presents the freezing rateconductivity, respectively. However, from Figure 3, A–C it response at the core of the cell, with maximum freezing rateswas shown that at one volume fraction there would be a specifically marked on the curve. At the same time, anlimitation on the increase in freezing rate when using average temperature-decreasing rate at the core of the cell Zparticles with larger thermal conductivity. That is, concen- 1 s AT can be defined as PB ¼ dt, where τ is the freezingtrations correlate closely with thermal conductivities of s 0 Atparticles in the contribution to freezing enhancement. For time. Here the total freezing time is calculated as 1 ms,instance, although diamond has a thermal conductivity because the freezing procedure tends to be relatively stable
  • 84 J.-F. Yan, J. Liu / Nanomedicine: Nanotechnology, Biology, and Medicine 4 (2008) 79–87Figure 4. Freezing-rate response at the core of the cell, where the maximum rate was marked. Here, A to C correspond to Figure 3, A–C, respectively. D, Averagetemperature decreasing rate at the core of the cell with various particle loading fractions and particle types.after that. The results are illustrated in Figure 4, D for various Au is used and η = 20% outside the cell compared with thecases. An interesting result can be found in Figure 4, A–C no-particle case. Therefore, from the above discussion it isthat at the same concentration of particles, the time of clear that nanocryosurgery could produce stronger freezingmaximum freezing rate occurs in accordance with the order effects than that of conventional cryosurgery, especially withof thermal conductivity. Diamond, with greatest thermal regard to the maximum freezing rate. Such influence is veryconductivity, results in the earliest maximum freezing rate, important in a large extent to enhance killing of tumor tissueswhereas PTFE results in the last one. However, it seems that the during cryosurgery.actual value of the maximum freezing rate has no clear Nucleation mechanism of nanocryosurgerycorrelation with the kinds and volume fractions of particles. Asshown from Figure 4, A–C, the maximum freezing rate of Au From the above heat transfer simulation it can be seen thatcould reach 3.37 × 106 K/s and 4.12 × 106 K/s when the the maximum freezing rate could be substantially improvedfraction volume outside the cell is 0.02 and 0.2, respectively, when nanoparticles are introduced. However, this is still notwhereas the maximum freezing rate will only reach 3.09 × the complete story, because the temperature decrease alone106 K/s when its fraction volume is 0.1. Meanwhile, it can also does not necessarily represent that the tumor cell has becomebe seen that when η = 20%, the best thermal conductivity necrotic. Besides their influence on freezing speed, nano-particles (diamond) do not necessarily guarantee reaching a particles also play an important role in inducing icemaximum freezing rate, as reflected by Figure 4, C. Therefore, nucleation, which is critical in determining the final cellone can conclude that the maximum freezing rate not only damage. As will be illustrated in the following, usingdepends on the thermal conductivities but also on the volume nanoparticles as seeds, the heterogeneous nucleation ratefraction and other thermal properties such as density, heat could be significantly improved. Such an improvementcapacity, and latent heat. As for the average freezing rate in results in a higher PIF, leading to a lethal effect on tumor cells.Figure 4, D, it demonstrates effectively that the better thermal In a classical homogeneous nucleation theory, theconductivity and the larger volume fraction it has, the higher standard Gibbs free energy of formation (ΔGi) of a clustervalue of average freezing rate it could reach. It can be of phase β (ice) containing i molecules from its mother phasefound that the maximum average freezing rate reaches α is given by:33about 2.33 × 105 K/s when diamond is used and η = 20%outside the cell, and the increasing magnitude attains about DGi ¼ ivb DGi þ ð36pÞ1=3 i2=3 rab ðvb Þ2=3 ð7Þ2.5% compared with the PTFE state. Likewise, the maximum where ΔGt is the Gibbs free-energy difference between αmagnitude of maximum freezing rate can reach 76% when and β phase per volume, vβ is the molecular volume of phase
  • J.-F. Yan, J. Liu / Nanomedicine: Nanotechnology, Biology, and Medicine 4 (2008) 79–87 85 Figure 5. The influence of particle size and volume fractions upon nucleation effectiveness at different temperatures.β, and σαβ is the interfacial free energy per unit area. 8prabMaximizing ΔGi with respect to i and assuming closely DGiT ¼ f ðg; xÞ ð12Þ 3ðDGt Þ2packed water molecules, one can obtain the followingrelationships for the critical cluster: here, x is defined as x = Rn/r*, Rn is the radius of the particle.  3 η = cosθ, in which θ is the wrapping angle. Because it is T 32p rab 2rabi ¼À b ; or rT ¼ À ð8Þ assumed that particles in the cell are in the state of perfect 3v DGt DGt humidification, that is θ = 0 and η = 1. Therefore, f (η,x) canand the following relationship for ΔGi*: be expressed as follows35: 16p ðrab Þ3DGi* ¼ ð9Þ f ðn; xÞ ¼ 1 " 3 ðDGt Þ2       # 1Àx 3 3 xÀ1 xÀ1 3 þ þx 2À3 þwhere r* is the radius of the critical cluster. g g g Considering both diffusion barrier ΔGi′ and nucleation   xÀ1barrier ΔGi*, nucleation rate Jhom reads as34: þ 3x2 À1     g nl kT DGi V DGi T ð13ÞJhom ¼ exp À exp À ð10Þ h kT kT where, g = (1+x2-2x)1/2.where h is Plancks constant, k the Boltzmann constant, and As is well known, the heterogeneous nucleation rate Jhetn1 molecules per unit volume of mother phase. can be defined as: When nanoparticles are introduced as seeds and uni-    formly distributed throughout the target tissue or cell, the n0 kT DGi V DGiT Jhet ¼ 4pR2 exp À n exp À ð14Þheterogeneous nucleation will play a leading role. According h kT kTto heterogeneous nucleation theory, r * and ΔGi* are where n0 is number of water molecules contacting therespectively given by: particle surface per unit area. If homogeneous nucleation is the main process in the no- 2rabrT ¼ À ð11Þ particle case, whereas heterogeneous nucleation is the main DGt process in particle case, under the same temperature
  • 86 J.-F. Yan, J. Liu / Nanomedicine: Nanotechnology, Biology, and Medicine 4 (2008) 79–87condition, the nucleation rate ratio that implies the influence biological compatibility. Particle sizes less than 10 μm areof particles on ice nucleation can be obtained as follows: normally considered sufficiently small to permit effective ! delivery to the site of the tumor, either via encapsulation in a n0d 4pR2 8prab  ab 2  larger moiety or suspension in a carrier fluid. Introduction ofJhet =Jhom ¼ n exp 2ðr Þ À f ð1; xÞ : n1 3kT ðDGt Þ2 nanoparticles into the target would effectively increase the nucleation rate at a high temperature threshold. In this case, a ð15Þ cryoprobe with only a moderate freezing capability may Because of the lack of experimental data, in this study we work well for treating the tumor.assume that r* = 1 nm, σαβ = 2 mJ/m2 ,ΔGt = -1E103 T Although a complete understanding of nanocryosurgery n0d 4pR2n is presently not yet available, this study offers a preliminary(273.15-T), = 1-η, and Figure 5 quantitatively outline of the new therapys promising future. Such a n1depicts the influence of particle size and volume fractions surgical protocol could overcome the limitations of conven-upon nucleation effectiveness. From the calculation as given tional cryosurgery in many respects and offers a much higherin Figure 5, A–D, it can be seen that once nanoparticles are maximum freezing rate as well as possibilities of iceloaded into the cell, the heterogeneous nucleation rate would nucleation. It can also be helpful and flexible for an adaptivebe significantly high at the beginning of the freezing process tumor treatment as well as in vivo medical imaging. In anin comparison with the no-particle case, which implies that ideal scenario, a minimally invasive and safe freezingnanocryosurgery could result in cell death at a relatively high therapy could be guaranteed. Future efforts should betemperature threshold. In addition, if particle size exceeds directed toward both the fundamental mechanisms as wellthe radius of the critical cluster, its influence on ice as clinical issues of the new conceptual nanocryosurgery.nucleation does not change. However, it is interesting tonote that particles with low volume fraction can increase the Referencesnucleation rate much more than the ones with high volumefraction. This is a contradiction when considering freezing 1. Rubinsky B. Cryosurgery: advances in the application of lowenhancement. 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