低温手术过程中的数值仿真及其损伤机理的研究
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摘要
肿瘤作为人类健康的头号杀手,目前肿瘤的治疗依然没有被攻克。近年来,据世界卫生组织报告,全球范围内每年都有近千万人死于各种癌症。低温手术技术以其微创性,靶向性,成本低,恢复快等优势,越来越多的被应用于各种癌症的临床治疗。然而,目前低温手术并没有成为肿瘤治疗的常规疗法,更多时候是作为肿瘤治疗的一种替代疗法。究其原因主要有以下几个方面：
◆当肿瘤较大或者肿瘤附近有大血管网存在时,低温手术的冷冻效率往往比较低,不能彻底的杀死全部的病变组织,从而造成术后复发率较高的问题；
◆低温手术临床实施时缺乏对冷刀杀伤范围的实时监测,对低温手术方案的杀伤能力也缺乏精准的预测；
◆对于低温下癌细胞的响应以及癌细胞低温下损伤机理的研究和认识还不够深刻。
鉴于目前低温手术存在的上述问题,本文应用有限元方法求解了低温手术过程中热显著性血管和热显著性血管网络与生物组织之间的共轭传热问题；结合胞内冰成核理论,提出利用胞内冰成核率(PIF)作为低温手术杀伤效率的评价准则；实验研究了Hela细胞低温下胞内冰成核的现象,完成了研究细胞低温响应所需的低温下NaCL-DMSO-H2O三元溶液粘度的测试工作。
具体来说,本研究主要包含以下几个方面：
●本文成功把单调迎风格式的有限元方法应用于低温手术过程中大血管与生物组织间共轭传热问题的数值求解；基于分形理论构造了一个热显著性血管树形网络,完成了该血管网络与组织共轭传热问题的数值求解,并讨论了热显著性血管网络对于传统低温手术和纳米低温手术冷冻效率的影响。结果显示：血管网络对于传统低温手术方案和纳米低温手术方案都有明显的加热效应,这种血管网络的加热效应在纳米低温手术中表现的更为明显。
●本文基于胞内冰成核理论,计算了低温手术过程中肿瘤内部胞内冰成核率(PIF)的发展情况。提出利用PIF作为评价低温手术效率的准则。本文利用PIF分析了热显著性血管网络影响下的传统低温手术和纳米低温手术的杀伤效率,结果表明：在大血管网络存在时,纳米低温手术能够更有效的杀死肿瘤组织,同时也说明,利用PIF来衡量低温手术的效率是可行的,方便的。
●本文利用低温显微镜系统实验研究了癌细胞在不同降温速率胞内冰的成核现象；使用胞内冰成核方程对胞内冰成核实验数据进行数值拟合,得到了计算癌细胞胞内冰成核所必须的热力学成核参数,动力学成核参数等生理参数；利用低温水浴系统和旋转粘度计测量了NaCL-DMSO-H2O三元溶液从室温到-40℃下的粘度数据,为深入研究细胞失水和细胞胞内冰成核提供了数据支持。
总的来说,本文对于低温手术方案的精准数值预测做了有益的探索。本文所开展的低温下癌细胞的胞内冰成核研究和NaCL-DMSO-H2O三元溶液粘度的测试,为进一步研究低温下细胞的损伤机理提供了数据支持,填补了相关的空白。
Cancer, as the number one killer of human health, still not been overcome. In recent years, according to the reports of the World Health Organization, there are nearly ten million people died of various cancers each year in worldwide. Cryosurgery is a physical therapy of tumor treatment which has obviously advantages compare to the routine therapy of tumor (such as radiotherapy, chemotherapy, surgical removal). The main advantages of cryosurgery include minimally invasive, relatively painless, less blood loss, short recovery time, and little expense etc. Cryosurgery is becoming more and more popular in tumor treatment with its important advantage. For all that, the technical still cannot be regarded as a conventional therapy of tumor treatment, but as an alternative to the traditional therapies in clinical. Currently, the main challenges in cryosurgery include:
When the tumor is larger or the tumor nearby one large vascular network, cryosurgery cannot completely kill all of the diseased tissue because of insufficient cooling and resulting in a higher recurrence rate in clinical.
It lacked the real-time monitor technology in the clinical implementation of cryosurgery and the prediction of cryosurgery program is still not accurate enough;
The responses and the injury mechanism of cancer cells during freezing still not be profoundly understand.
In view of these challenges, the significant thermal effects of vascular network during cryosurgery were numerically studied in this paper; the probability of intracellular ice nucleation (PIF) in tumor regions were also computed; the intracellular ice formation behaviors of Hela and the viscosity of physiological solution during freezing were experimental studied in this paper.
Specifically, this work consists of the following aspects:
The heat exchange between thermal significant vascular and biological tissue during cryosurgery were numerically solved based on the monotone streamlines upwind finite element method. A3D vascular network was constructed according to the fractal theory, then the conjugate heat transfer problem between vascular network and biological tissue during cryosurgery were successfully solved here. The results indicated that:the thermal effects of vascular network were obvious both in conventional cryosurgery and Nano-cryosurgery and the heating efficiency of vascular was higher in the Nano-cryosurgery procedure.
·The PIF in tumor region both during conventional cryosurgery and Nano-cryosurgery were computed based on the intracellular ice nucleation theory. This work proposed to use PIF as the criteria to evaluate the efficiency of cryosurgery procedure. The efficiency of the conventional cryosurgery and the Nano-cryosurgery effected by vascular network were analyzed using PIF in this study. The results suggested that:compared to conventional cryosurgery, the killing efficiency for the tumor cells was significantly improved in Nano-cryosurgery and using PIF to evaluate the efficiency of cryosurgery is feasible and convenient.
·The intracellular ice nucleation of Hela were experimental investigated using cryomicroscope in different cooling rate. The thermodynamics and kinetic nucleation parameters of Hela were obtained by fitting the intracellular ice nucleation equations to the experimental data. In this paper, the viscosity of physiological solution was measured in different temperature and an empirical formula was presented to predict the viscosity of physiological solution.
To sum up, this paper made an useful exploration to the accurate numerical prediction of cryosurgery. The investigates of intracellular ice nucleation of Hela and the viscosity of physiological solution are an enrichment and accumulation of experimental data for further study the dehydration and intracellular ice nucleation of tumor cells.
◆当肿瘤较大或者肿瘤附近有大血管网存在时,低温手术的冷冻效率往往比较低,不能彻底的杀死全部的病变组织,从而造成术后复发率较高的问题；
◆低温手术临床实施时缺乏对冷刀杀伤范围的实时监测,对低温手术方案的杀伤能力也缺乏精准的预测；
◆对于低温下癌细胞的响应以及癌细胞低温下损伤机理的研究和认识还不够深刻。
鉴于目前低温手术存在的上述问题,本文应用有限元方法求解了低温手术过程中热显著性血管和热显著性血管网络与生物组织之间的共轭传热问题；结合胞内冰成核理论,提出利用胞内冰成核率(PIF)作为低温手术杀伤效率的评价准则；实验研究了Hela细胞低温下胞内冰成核的现象,完成了研究细胞低温响应所需的低温下NaCL-DMSO-H2O三元溶液粘度的测试工作。
具体来说,本研究主要包含以下几个方面：
●本文成功把单调迎风格式的有限元方法应用于低温手术过程中大血管与生物组织间共轭传热问题的数值求解；基于分形理论构造了一个热显著性血管树形网络,完成了该血管网络与组织共轭传热问题的数值求解,并讨论了热显著性血管网络对于传统低温手术和纳米低温手术冷冻效率的影响。结果显示：血管网络对于传统低温手术方案和纳米低温手术方案都有明显的加热效应,这种血管网络的加热效应在纳米低温手术中表现的更为明显。
●本文基于胞内冰成核理论,计算了低温手术过程中肿瘤内部胞内冰成核率(PIF)的发展情况。提出利用PIF作为评价低温手术效率的准则。本文利用PIF分析了热显著性血管网络影响下的传统低温手术和纳米低温手术的杀伤效率,结果表明：在大血管网络存在时,纳米低温手术能够更有效的杀死肿瘤组织,同时也说明,利用PIF来衡量低温手术的效率是可行的,方便的。
●本文利用低温显微镜系统实验研究了癌细胞在不同降温速率胞内冰的成核现象；使用胞内冰成核方程对胞内冰成核实验数据进行数值拟合,得到了计算癌细胞胞内冰成核所必须的热力学成核参数,动力学成核参数等生理参数；利用低温水浴系统和旋转粘度计测量了NaCL-DMSO-H2O三元溶液从室温到-40℃下的粘度数据,为深入研究细胞失水和细胞胞内冰成核提供了数据支持。
总的来说,本文对于低温手术方案的精准数值预测做了有益的探索。本文所开展的低温下癌细胞的胞内冰成核研究和NaCL-DMSO-H2O三元溶液粘度的测试,为进一步研究低温下细胞的损伤机理提供了数据支持,填补了相关的空白。
Cancer, as the number one killer of human health, still not been overcome. In recent years, according to the reports of the World Health Organization, there are nearly ten million people died of various cancers each year in worldwide. Cryosurgery is a physical therapy of tumor treatment which has obviously advantages compare to the routine therapy of tumor (such as radiotherapy, chemotherapy, surgical removal). The main advantages of cryosurgery include minimally invasive, relatively painless, less blood loss, short recovery time, and little expense etc. Cryosurgery is becoming more and more popular in tumor treatment with its important advantage. For all that, the technical still cannot be regarded as a conventional therapy of tumor treatment, but as an alternative to the traditional therapies in clinical. Currently, the main challenges in cryosurgery include:
When the tumor is larger or the tumor nearby one large vascular network, cryosurgery cannot completely kill all of the diseased tissue because of insufficient cooling and resulting in a higher recurrence rate in clinical.
It lacked the real-time monitor technology in the clinical implementation of cryosurgery and the prediction of cryosurgery program is still not accurate enough;
The responses and the injury mechanism of cancer cells during freezing still not be profoundly understand.
In view of these challenges, the significant thermal effects of vascular network during cryosurgery were numerically studied in this paper; the probability of intracellular ice nucleation (PIF) in tumor regions were also computed; the intracellular ice formation behaviors of Hela and the viscosity of physiological solution during freezing were experimental studied in this paper.
Specifically, this work consists of the following aspects:
The heat exchange between thermal significant vascular and biological tissue during cryosurgery were numerically solved based on the monotone streamlines upwind finite element method. A3D vascular network was constructed according to the fractal theory, then the conjugate heat transfer problem between vascular network and biological tissue during cryosurgery were successfully solved here. The results indicated that:the thermal effects of vascular network were obvious both in conventional cryosurgery and Nano-cryosurgery and the heating efficiency of vascular was higher in the Nano-cryosurgery procedure.
·The PIF in tumor region both during conventional cryosurgery and Nano-cryosurgery were computed based on the intracellular ice nucleation theory. This work proposed to use PIF as the criteria to evaluate the efficiency of cryosurgery procedure. The efficiency of the conventional cryosurgery and the Nano-cryosurgery effected by vascular network were analyzed using PIF in this study. The results suggested that:compared to conventional cryosurgery, the killing efficiency for the tumor cells was significantly improved in Nano-cryosurgery and using PIF to evaluate the efficiency of cryosurgery is feasible and convenient.
·The intracellular ice nucleation of Hela were experimental investigated using cryomicroscope in different cooling rate. The thermodynamics and kinetic nucleation parameters of Hela were obtained by fitting the intracellular ice nucleation equations to the experimental data. In this paper, the viscosity of physiological solution was measured in different temperature and an empirical formula was presented to predict the viscosity of physiological solution.
To sum up, this paper made an useful exploration to the accurate numerical prediction of cryosurgery. The investigates of intracellular ice nucleation of Hela and the viscosity of physiological solution are an enrichment and accumulation of experimental data for further study the dehydration and intracellular ice nucleation of tumor cells.
引文
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[1]Gage AA, Baust JG. Cryosurgery for tumors. J Am Coll Surgeons.2007;205:342-56.
[2]Gage AA, Baust JG. Cryosurgery-A review of recent advances and current issues. Cryoletters. 2002;23:69-78.
[3]Deng ZS, Liu J. Numerical study of the effects of large blood vessels on three-dimensional tissue temperature profiles during cryosurgery. Numer Heat Tr a-Appl.2006;49:47-67.
[4]Yan JF, Liu J. Nanocryosurgery and its mechanisms for enhancing freezing efficiency of tumor tissues. Nanomed-Nanotechnol.2008;4:79-87.
[5]Liu J, Yan JF, Deng ZS. Nano-cryosurgery:A basic way to enhance freezing treatment of tumor. Proceedings of the Asme International Mechanical Engineering Congress and Exposition 2007, Vol 2.2008:87-94.
[6]Liu J, Deng ZS. Nano-Cryosurgery:Advances and Challenges. J Nanosci Nanotechno. 2009;9:4521-42.
[7]Rabin Y. Key issues in bioheat transfer simulations for the application of cryosurgery planning. Cryobiology.2008;56:248-50.
[8]Deng ZS, Liu J. Effect of configuration between cryoprobe and large blood vessels on the tissue freezing during cryosurgery. P Ann Int leee Embs.2005:490-3.
[9]Brooks AN, Hughes TJR. Streamline Upwind Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations. Comput Method Appl M.1982;32:199-259.
[10]Mizukami A. An Implementation of the Streamline-Upwind Petrov-Galerkin Method for Linear Triangular Elements. Comput Method Appl M.1985;49:357-64.
[11]Mizukami A, Hughes TJR. A Petrov-Galerkin Finite-Element Method for Convection-Dominated Flows-an Accurate Upwinding Technique for Satisfying the Maximum Principle. Comput Method Appl M.1985;50:181-93.
[12]Peters A. Nonsymmetrical Cg-Like Schemes and the Finite-Element Solution of the Advection-Dispersion Equation. Int J Numer Meth Fl.1993;17:955-74.
[13]Rice JG, Schnipke RJ. A Monotone Streamline Upwind Finite-Element Method for Convection-Dominated Flows. Comput Method Appl M.1985;48:313-27.
[14]Pennes HH. Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm. J Appl Physiol.1948;1:93-122.
[15]Liu ZF, Zhao G, Cheng YH, Gao DY. Heating Effect of Thermally Significant Blood Vessels in Perfused Tumor Tissue during Cryosurgery. J Mech Med Biol.2012;12.
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[1]Kalda J. Fractal Model of Blood Vessel System. Fractals.1993;1:191-7.
[2]Gabrys E, Rybaczuk M, Kedzia A. Fractal models of circulatory system. Symmetrical and asymmetrical approach comparison. Chaos Soliton Fract.2005;24:707-15.
[3]吕永钢杨.血管网分形研究进展.化工学报.2010；61：7.
[4]张燕乐,张欣欣.基于模拟血管树以及改进Pennes方程的生物传热模型.热科学与技术.2006；5：7.
[5]Zamir M. On fractal properties of arterial trees. J Theor Biol.1999;197:517-26.
[6]Davis JM, Pozrikidis C. Numerical Simulation of Unsteady Blood Flow through Capillary Networks. B Math Biol.2011;73:1857-80.
[7]Shi J, Chen ZQ, Shi MH. Simulation of heat transfer of biological tissue during cryosurgery based on vascular trees. Appl Therm Eng.2009;29:1792-8.
[8]Bhardwaj N, Gravante G, Strickland AD, Ahmad F, Dormer J, Dennison AR, et al. Cryotherapy of the liver:A histological review. Cryobiology.2010;61:1-9.
[9]Zamir M. Optimality principles in arterial branching. J Theor Biol.1976;62:227-51.
[10]Zamir M. Three-dimensional aspects of arterial branching. J Theor Biol.1981;90:457-76.
[11]Schreiner W, Neumann F, Neumann M, End A, Muller MR. Structural quantification and bifurcation symmetry in arterial tree models generated by constrained constructive optimization. J Theor Biol.1996;180:161-74.
[12]Yan JF, Liu J. Nanocryosurgery and its mechanisms for enhancing freezing efficiency of tumor tissues. Nanomed-Nanotechnol.2008;4:79-87.
[13]Liu J, Deng ZS. Nano-Cryosurgery:Advances and Challenges. J Nanosci Nanotechno. 2009;9:4521-42.
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[2]Zhao G, Luo DW, Gao DY. Universal model for intracellular ice formation and its growth. Aiche J.2006;52:2596-606.
[3]Borel Rinkes IH, Toner M, Sheeha SJ, Tompkins RG, Yarmush ML. Long-term functional recovery of hepatocytes after cryopreservation in a three-dimensional culture configuration. Cell Transplant.1992;1:281-92.
[4]Diller KR. Intracellular freezing:effect of extracellular supercooling. Cryobiology. 1975;12:480-5.
[5]Diller KR. Intracellular freezing of glycerolized red cells. Cryobiology.1979;16:125-31.
[6]Leibo SP, McGrath JJ, Cravalho EG. Microscopic observation of intracellular ice formation in unfertilized mouse ova as a function of cooling rate. Cryobiology.1978;15:257-71.
[7]Mazur P. The role of intracellular freezing in the death of cells cooled at supraoptimal rates. Cryobiology.1977;14:251-72.
[8]Mazur P. Freezing of living cells:mechanisms and implications. Am J Physiol. 1984;247:C125-42.
[9]McGrath JJ, Cravalho EG, Huggins CE. An experimental comparison of intracellular ice formation and freeze-thaw survival of HeLa S-3 cells. Cryobiology.1975; 12:540-50.
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[19]Hubel A, Toner M, Cravalho EG, Yarmush ML, Tompkins RG. Intracellular Ice Formation during the Freezing of Hepatocytes Cultured in a Double Collagen Gel. Biotechnol Progr.1991;7:554-9.
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[1]Gage AA, Baust JG. Cryosurgery for tumors. J Am Coll Surgeons.2007;205:342-56.
[2]Gage AA, Baust JG. Cryosurgery-A review of recent advances and current issues. Cryoletters. 2002;23:69-78.
[3]Deng ZS, Liu J. Numerical study of the effects of large blood vessels on three-dimensional tissue temperature profiles during cryosurgery. Numer Heat Tr a-Appl.2006;49:47-67.
[4]Yan JF, Liu J. Nanocryosurgery and its mechanisms for enhancing freezing efficiency of tumor tissues. Nanomed-Nanotechnol.2008;4:79-87.
[5]Liu J, Yan JF, Deng ZS. Nano-cryosurgery:A basic way to enhance freezing treatment of tumor. Proceedings of the Asme International Mechanical Engineering Congress and Exposition 2007, Vol 2.2008:87-94.
[6]Liu J, Deng ZS. Nano-Cryosurgery:Advances and Challenges. J Nanosci Nanotechno. 2009;9:4521-42.
[7]Rabin Y. Key issues in bioheat transfer simulations for the application of cryosurgery planning. Cryobiology.2008;56:248-50.
[8]Deng ZS, Liu J. Effect of configuration between cryoprobe and large blood vessels on the tissue freezing during cryosurgery. P Ann Int leee Embs.2005:490-3.
[9]Brooks AN, Hughes TJR. Streamline Upwind Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations. Comput Method Appl M.1982;32:199-259.
[10]Mizukami A. An Implementation of the Streamline-Upwind Petrov-Galerkin Method for Linear Triangular Elements. Comput Method Appl M.1985;49:357-64.
[11]Mizukami A, Hughes TJR. A Petrov-Galerkin Finite-Element Method for Convection-Dominated Flows-an Accurate Upwinding Technique for Satisfying the Maximum Principle. Comput Method Appl M.1985;50:181-93.
[12]Peters A. Nonsymmetrical Cg-Like Schemes and the Finite-Element Solution of the Advection-Dispersion Equation. Int J Numer Meth Fl.1993;17:955-74.
[13]Rice JG, Schnipke RJ. A Monotone Streamline Upwind Finite-Element Method for Convection-Dominated Flows. Comput Method Appl M.1985;48:313-27.
[14]Pennes HH. Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm. J Appl Physiol.1948;1:93-122.
[15]Liu ZF, Zhao G, Cheng YH, Gao DY. Heating Effect of Thermally Significant Blood Vessels in Perfused Tumor Tissue during Cryosurgery. J Mech Med Biol.2012;12.
[16]陶文铨.数值传热学(第二版).西安交通大学出版社.2003.
[17]Shemirani F, Jambunathan K. Conservative Monotone Streamline Upwind Formulation Using Simplex Elements. Int J Numer Meth Fl.1992;14:1245-57.
[18]Sheu TWH, Tsai SF, Wang MMT. A monotone multidimensional upwind finite element method for advection diffusion problems. Numer Heat Tr B-Fund.1996;29:325-44.
[1]Kalda J. Fractal Model of Blood Vessel System. Fractals.1993;1:191-7.
[2]Gabrys E, Rybaczuk M, Kedzia A. Fractal models of circulatory system. Symmetrical and asymmetrical approach comparison. Chaos Soliton Fract.2005;24:707-15.
[3]吕永钢杨.血管网分形研究进展.化工学报.2010；61：7.
[4]张燕乐,张欣欣.基于模拟血管树以及改进Pennes方程的生物传热模型.热科学与技术.2006；5：7.
[5]Zamir M. On fractal properties of arterial trees. J Theor Biol.1999;197:517-26.
[6]Davis JM, Pozrikidis C. Numerical Simulation of Unsteady Blood Flow through Capillary Networks. B Math Biol.2011;73:1857-80.
[7]Shi J, Chen ZQ, Shi MH. Simulation of heat transfer of biological tissue during cryosurgery based on vascular trees. Appl Therm Eng.2009;29:1792-8.
[8]Bhardwaj N, Gravante G, Strickland AD, Ahmad F, Dormer J, Dennison AR, et al. Cryotherapy of the liver:A histological review. Cryobiology.2010;61:1-9.
[9]Zamir M. Optimality principles in arterial branching. J Theor Biol.1976;62:227-51.
[10]Zamir M. Three-dimensional aspects of arterial branching. J Theor Biol.1981;90:457-76.
[11]Schreiner W, Neumann F, Neumann M, End A, Muller MR. Structural quantification and bifurcation symmetry in arterial tree models generated by constrained constructive optimization. J Theor Biol.1996;180:161-74.
[12]Yan JF, Liu J. Nanocryosurgery and its mechanisms for enhancing freezing efficiency of tumor tissues. Nanomed-Nanotechnol.2008;4:79-87.
[13]Liu J, Deng ZS. Nano-Cryosurgery:Advances and Challenges. J Nanosci Nanotechno. 2009;9:4521-42.
[1]Toner M. Nucleation of ice crystals inside biological cells. ADVANCED IN LOW-TEMPERATURE BIOLOGY:A Research Annual.1993;2:1-51.
[2]Zhao G, Luo DW, Gao DY. Universal model for intracellular ice formation and its growth. Aiche J.2006;52:2596-606.
[3]Borel Rinkes IH, Toner M, Sheeha SJ, Tompkins RG, Yarmush ML. Long-term functional recovery of hepatocytes after cryopreservation in a three-dimensional culture configuration. Cell Transplant.1992;1:281-92.
[4]Diller KR. Intracellular freezing:effect of extracellular supercooling. Cryobiology. 1975;12:480-5.
[5]Diller KR. Intracellular freezing of glycerolized red cells. Cryobiology.1979;16:125-31.
[6]Leibo SP, McGrath JJ, Cravalho EG. Microscopic observation of intracellular ice formation in unfertilized mouse ova as a function of cooling rate. Cryobiology.1978;15:257-71.
[7]Mazur P. The role of intracellular freezing in the death of cells cooled at supraoptimal rates. Cryobiology.1977;14:251-72.
[8]Mazur P. Freezing of living cells:mechanisms and implications. Am J Physiol. 1984;247:C125-42.
[9]McGrath JJ, Cravalho EG, Huggins CE. An experimental comparison of intracellular ice formation and freeze-thaw survival of HeLa S-3 cells. Cryobiology.1975; 12:540-50.
[10]Shabana M, McGrath JJ. Cryomicroscope investigation and thermodynamic modeling of the freezing of unfertilized hamster ova. Cryobiology.1988;25:338-54.
[11]Asahina E. Intracellular freezing and frost resistance in egg-cells of the sea urchin. Nature. 1961;191:1263-5.
[12]Morris GJ, Mcgrath JJ. Intracellular Ice Nucleation and Gas Bubble Formation in Spirogyra. Cryo-Lett.1981;2:341-&.
[13]Rasmussen DH, Macaulay MN, Mackenzie AP. Supercooling and Nucleation of Ice in Single Cells. Cryobiology.1975;12:328-39.
[14]Mathias SF, Franks F, Trafford K. Nucleation and growth of ice in deeply undercooled erythrocytes. Cryobiology.1984;21:123-32.
[15]Toner M, Cravalho EG, Karel M, Armant DR. Cryomicroscopic Analysis of Intracellular Ice Formation during Freezing of Mouse Oocytes without Cryoadditives. Cryobiology.1991;28:55-71.
[16]Myers SP, Pitt RE, Lynch DV, Steponkus PL. Characterization of Intracellular Ice Formation in Drosophila-Melanogaster Embryos. Cryobiology.1989;26:472-84.
[17]Toner M, Cravalho EG, Karel M. Thermodynamics and Kinetics of Intracellular Ice Formation during Freezing of Biological Cells. J Appl Phys.1990;67:1582-93.
[18]Toner M, Cravalho EG, Armant DR. Water Transport and Estimated Transmembrane Potential during Freezing of Mouse Oocytes. J Membrane Biol.1990;115:261-72.
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