A numerical model was developed to study heat transfer process during freezing of biological tumors. Two different cryosurgical systems, Endocare cryoprobe and novel combined cryosurgery and hyperthermia system, were investigated using the multidimensional, finite element method (FED) developed in Ansys (V7.0) by us recently. The tissues were modeled as nonideal materials, the thermophysical properties of which were temperature dependent. The enthalpy method was applied to solve the highly nonlinear problem. It was found that for the same initial/boundary conditions and the same target tissues, the novel combined cryosurgery and hyperthermia system could supply the target tissue an approximate cooling rate, a much lower minimal temperature, a much greater warming rate, and a much greater thermal gradient as compared with the Endocare cryoprobe system. The numerical simulation results indicated that the novel combined cryosurgery and hyperthermia system could provide an excellent curative effect in the corresponding cryotherapy.

A modified analytical and experimental method using differential scanning calorimeter (DSc) was applied to determine the cell water transport properties of human erythrocytes during the freezing process. Using DSC, samples containing human erythrocyte cell suspensions of human erythrocytes with different cytocrits were cooled to -40 degrees C at slow cooling rates WC/min) after nucleation. It was shown that latent heat release from one unit mass of the cell suspension was a linear function of cytocrits (cell numbers), with a temperature-dependent slope and intercept. Based on the theoretical model, cell volumes were calculated from the slope and intercept at corresponding temperatures. Cell water transport properties (I-pg/E-a) were next calculated by curve fitting of the cell volume change during the freezing process. The results revealed that, for human erythrocyte, L-pg (T-r = 273.15 K) is 0.10 +/- 0.01 mu m/min . atm and E-a is 279.1 +/- 0.7 kJ/mol at the cooling rate of 5 degrees C/min. For comparison, both DSC and cryomicroscopic experiments were performed on Saccharomyces cerevisia cells (cooling rate 10 degrees C/min): results of DSC experiments showed that L-pg (T-r = 293.15 K) is (6.6 +/- 0.1) X 10(-2) mu m/min - atm and E-a is 66.6 +/- 0.2 kJ/mol; results of cryomicroscope experiments showed that L-pg (T-r = 293.15 K) is (6.7 +/- 0.2) X 10(-2) mu m/min atm and Ea is 68.3 +/- 0.2 kJ/mol. These data are comparable, and in agreement with cryomicroscope experiments from independent investigators. The theoretical model and the DSC experimental procedure provide a verifiable approval to the determination of cell membrane transport properties at low temperatures and under the freezing conditions.

Biological metabolism in living cells dramatically diminishes at low temperatures, a fact that permits the long-term cryopreservation of cells and tissues for either scientific research or medical applications (eg, blood transfusion, transplantation of cells and organs, artificial insemination, in vitro fertilization, etc.). However, there is an apparent contradiction between the purpose of preservation and experimental findings that the cryopreservation process itself can kill cells and tissues. The challenge to cells and tissues during cryopreservation is not their ability to endure storage at very low temperatures (below–80 C); rather it is the potential lethal factors existing in the four major cryopreservation procedures; ie, the addition of cryoprotective agents (CPAs) to cells and tissues before cooling, the cooling process (to a low temperature for storage), the warming process (after storage at low temperatures), and the removal of the CPAs from the cells and tissues after warming. These potential lethal factors include at least the following:

Cryosurgery has been recently accepted as a treatment option for eradicating undesirable tissues, especially tumor tissues, due to its minimally invasive nature and low hospitalization needs. A multidimensional, finite element analysis (FEA) for the cooling, holding and rewarming processes of biological tissues during cryosurgery is presented. The tissues were treated as non-ideal materials with temperature dependent thermophysical properties. The enthalpy method has been applied to solve the non-linear problem. The influence of heating effect due to blood flow and metabolism was studied, and furthermore, the effect of pre-injecting solutions with particular thermal properties into the target tissues was also numerically studied. It was found that the heat source term due to blood flow and metabolism in the bioheat transfer equation has a significant influence on the thermal and thermal gradient histories of the target tissues, and that the method of injection of solutions with particular thermal properties into the target tissues before cryosurgery may be a possible way to optimize the treatment process. However, in vitro experiments have not fully supported this viewpoint.

An electromagnetic (EM) heating system is developed to achieve the rapid and uniform warming of cryopreserved biomaterials. Using the heating system, a rectangular resonant cavity is excited in TE101 mode at frequencies near 434 MHz. In experiments, a spherical phantom of biomaterial with a diameter of 36 mm is placed at the center of the cavity. The phantom is first cooled down to about -80 degrees C within the cavity and then thawed by EM absorption. Results show that EM warming can produce much higher warming rate than conventional water-bath warming method. The spatial temperature distribution in the phantom during EM warming is also more uniform than that during the water-bath warming.

A multidimensional, finite element analysis (FEA) for the freezing, holding, rewarming and heating processes of biological tissues during the cryosurgery process of the new Combined Cryosurgery/Hyperthermia System is presented to theoretically test its validity. The tissues are treated as nonideal materials freezing over a temperature range, and the thermophysical properties of which are temperature dependent. The enthalpy method is applied to solve the highly nonlinear problem. It was found that when the same boundary condition and the same target tissue presented, the novel Cryosurgery/Hyperthermia System could supply the target tissue an approximative cooling rate, a much lower minimal temperature, a much greater warming rate, and a much greater thermal gradients compared with that of the simplified Endocare system. The numerical simulation indicates that the novel combined cryosurgery and hyperthermia system can provide an excellent curative effect in the corresponding cryotherapy. And the most attractive feature of this FEA framework is that it can be easily mastered by the surgeon without in-depth theory of heat transfer to analyze the cryosurgery process beforehand due to the friendly GUI (graphical user interface) of Ansys software.

The intracellular ice volume (IIV) term, Vice(c,T), is introduced into the classical water transport model developed by P. Mazur so that the modified model is capable of predicting cell volumetric change even after intracellular ice formation (IIF). By coupling the modified P. Mazur's model, ice nucleation, and the diffusion-limited ice growth theory, the new model describing IIF and the growth of the intracellular ice (IIG) is developed based on J. O. M. Karlsson's work in 1994. The new model could be used to predict IIF, IIG, the final volumetric fraction of the intracellular ice, and the size distribution of the intracellular ice crystals. The major advantage of the new model is that it can provide reasonable intracellular information for both high cryoprotective agent (CPA) and low CPA concentrations without “Avrami correction”. The new model is then used to study the effect of cooling rate and initial CPA concentration on IIF and IIG. Three interesting phenomena, “hydration of salt ions (Na+ and Cl−)”, “crustaceous vitrification”, and “local vitrification” are presented, and their effects on IIF and IIG are studied in detail. It is found that all three of these factors have significant influences on the predicted critical cooling rate for the vitrification of the intracellular solution. © 2006 American Institute of Chemical Engineers AIChE J, 2006

An iteration algorithm is presented to obtain the electromagnetic field distribution and the temperature pattern for arbitrary shaped samples when they are in free space and inside cavities. The iteration involves solving the electromagnetic wave equation and the heat transfer equation alternatively. The electromagnetic solver models the cavity with quadrangle patches and the dielectric tissue by hexahedrons. Hence it can be used to simulate realistic microwave re-warming and heating processes, and provides an accurate and effective tool for virtual experiments, through which we can analyze the heating pattern and the heating rate as functions of sample's size, shape, and electric and heat conduction properties. The similar simulation can be performed using the FDTD method. Our preliminary comparison shows that the integral equation method has higher efficiency than the FDTD method for this example. These simulations are essential to determine what kind of cavity and what control process can lead to a desired heating pattern and re-warming history

A theoretical analysis of inlet and outlet effects on mass transfer performance of hemodialyzers is presented. In the theory, a dual-porous-medium model is applied to simulate the flow fields of blood and dialysate, and the blood conservation equations are coupled to the dialysate conservation equations through the modified Kedem-Katchalsky equations. The results show that blood and dialysate fluid fields are interactional. Blood only flows along fibers, and dialysate flows perpendicular to the fibers near the inlet and outlet ports and parallel to fibers between ports. For the given dialysate boundary conditions, the even inlet velocity of blood is beneficial to mass transfer. For the given blood boundary conditions, the high velocity of dialysate causes mass transfer performance to deviate badly from ideal countercurrent situation due to the effects of inlet and outlet.

The novel differential scanning calorimetry method as a technique for determining human red cell volume during freezing process has been reexamined and has been shown to provide a final erythrocyte volume to be 53% of its isotonic value after freezing from 0 to -40 degrees C. A new type of electronic particle counter (Multisizer 3, Beckman Coulter Inc., USA) was used to measure cell volume changes in response to equilibration in anisotonic media, and which gave out an equilibrated volume to be 57% of cell isotonic value in solution of 3186 mOsm. Both of these results indicate that 34-40% of intracellular water is trapped and is unavailable for participation in osmotic shifts. These findings are consistent with the published data that at least 20-32% (v/v) of the isotonic cell water is retained within RBCs. Then the application of trapped water in both simulation of freezing models and freezing-drying control was pointed out.

通过数值模拟人工肾4种不同放置方式(水平放置透析液进出口朝上、水平放置透析液进出口朝下、竖直放置血流向上、竖直放置血流向下)时尿素的传质情况,定性考察了重力场对透析性能的影响,获得了各种放置情况下尿素的三维浓度场和清除率.模拟结果显示,重力场对人工肾传质影响显著.在重力的影响下,竖直放置血流向上尿素清除率最高,水平放置透析液进出口朝上清除率次之.

使用新颖的差示扫描量热仪方法测定了人类红细胞从0 ℃冷冻至-40℃这一过程终结时的体积值,为等渗体积的53%.使用一种新型的颗粒粒度及计数分析仪(MultisizerTM 3,Beckman CoulterInc,USA)测定了人类红细胞在各种非等渗溶液中的平衡体积,溶液渗透压增加至3186 mOsm(mol·kg-1水),红细胞的最终体积值为等渗体积的57%.两种实验方法均表明大约34%～40%的红细胞胞内水被束缚在细胞内,不能参与渗透性迁移.实验结果和文献结论"至少20%～32%的等渗胞内水被保留在红细胞内"相符.基于这一实验结果,改进了传统的细胞冷冻模型,并使用改进后的模型预测冷冻过程中红细胞在不同降温速率下的体积变化过程.随后对这一结果在细胞低温冷冻保存和冻干保存中的应用进行了探讨.

给出了一种利用差示扫描量热仪(DSC)间接测定在冷冻过程中细胞体积变化的理论模型,并且以此为基础设计了一套实验方案. 为了验证这一方法的正确性,分别使用差示扫描量热仪和颗粒粒度及计数分析仪(EPC)两种方法测定了平衡冷冻过程中人红细胞(RBC)的体积变化,两者结果相符. 将压积比已知的等渗细胞悬浮液(0.9% NaCl 溶液+人红细胞)从-0.53℃分别降温至 -1, -1.53, -2.53, -3.53, -4.53, -5.53, -7.53, -9.53℃,使用DSC测定该平衡冷冻过程中所释放的热量. 平衡降温至-1, -1.53, -2.53, -3.53, -4.53, -5.53, -7.53, -9.53℃温度下细胞的无量纲化体积由理论模型相应的方程计算得出. 使用新型EPC测定了人RBC在不同质量渗摩尔浓度下的 NaCl 溶液中的体积. 假定温度对细胞平衡体积的影响相对渗透压而言可以忽略, 则通过NaCl-H2O二元溶液的相图可以获得不同温度下NaCl溶液的质量渗摩尔浓度(通过质量百分比浓度换算得到). 进而,使用DSC方法得到的平衡降温过程中RBC的体积变化可以与使用EPC方法的测量结果相互验证.

The novel differential scanning calorimetry method for determining trapped water volume of human red blood cell during freezing process has been reexamined. Results show that the final erythrocyte volume is 53% of its isotonic volume after freezing to -40degreesC. An electronic particle counter (Multisizer(TM) III, Beckman Coulter Inc., USA) was used to measure cell volume changes in response to hypertonic solution. Using this approach, when extracellular solution. was 3186 mOsm, the equilibrium cell volume was found to be 57% of its isotonic value. Both results indicate that 34%-40% of intracellular water is trapped and cannot respond to osmotic difference between intra- and extracellular solution. These findings are consistent with the published data: at least 20% -32% of the isotonic cell water volume is retained within RBCs during freezing. Some applications of the values of trapped water are addressed.

Determination of thermal conductivity of cryoprotectant solutions is required in modeling and predicting cooling/warming conditions for optimal cryopreservation of cells and tissues. A needle-like "heat probe" was developed to measure the thermal conductivity in this study. The heat probe was inserted into a medium (e.g., a cryopreservation solution, a cell suspension, or a soft tissue) with unknown thermal conductivity. A constant voltage from an electrical power source was applied to the probe, while a digital Ampere meter was used to measure the change of electrical current in the probe as a function of ambient medium temperature change caused by heating (heat is generated in the probe when a current runs through the probe). The electrical current change was monitored and recorded by a computer. By analyzing/modeling the heat transfer between the probe and the surrounding medium, a relationship between the thermal conductivity of the medium and the measured current was derived and used to determine the thermal conductivity of the medium. Using this technique, thermal conductivity values of cryoprotectant solutions, human blood, and blood–glycerol mixture were determined as a function of temperature and cryoprotectant concentration. From this study, the "heat probe" method was shown to be accurate, minimally invasive and practical.

In this research, continuum theory. (macroscopic enthalpy model) for multi-component phase change was applied to study the freezing process of bulk sample (cell suspension in a flat blood bag), coupled with the investigation of microscopic mass transfer across cell membrane. Numerical simulation results indicated that distributions of temperature and solute concentration inside the sample are not uniform during the cooling process. As a consequence, the degrees of cell dehydration are different at various locations.

The determination of the temperature dependent thermal conductivity inside an infinite region with a constant linear heat source at the center is investigated, Assuming the material has a known constant thermal diffusivity, the heat conduction problem is linearised by employing the. Kirchhoff transformation. The analytical solution of this inverse heat conduction problem has been developed by applying H ankel transformation and the corresponding inversion transformation. Based on the solution, the temperature dependent thermal conductivity can be obtained by measuring the temperature profile at an arbitrary space location. (C) 2003 Elsevier Science Ltd.

Using a continuum model for multi-component phase change system, the freezing of cell suspension in a ternary solution, H2O-NaCl-CPA (cryoprotective agent) inside a flat bag is investigated numerically in this study. The temperature and phase change history, intracellular water loss, and the volume change of the cells at different locations inside cell suspension are calculated. Numerical results reveal that although the sample boundary is cooled at a constant rate, different locations inside the sample experienced different temperature changes and cooling rates. The highest cooling rates occur at internal locations. The cell volume change is location-dependent.