基于动态光热作用模型的激光诱导肿瘤间质热疗中的参数选择

建立了描述温控加热方式下激光诱导肿瘤间质热疗过程中动态光热作用的二维圆柱坐标下的数学模型,采用基于网格的蒙特卡罗方法数值模拟热疗过程中激光能量在非均质生物组织内的传输过程,基于Pennes生物传热方程和Arrhen ius方程数值求解组织内的温度场和热损伤体积的变化。通过数值模拟的方法分析了激光波长、激光功率、温控范围等因素对激光诱导肿瘤间质热疗中热损伤体积的影响。数值模拟的结果表明,通过选择合适的治疗参数,可以得到各种不同大小的热疗区域。本文的结果和结论对于临床治疗方案的制定具有一定的理论指导意义。     

Perfused phantom models of microwave irradiated tissue

The theoretical basis, practical design considerations, and prototype testing of a perfused model suitable for simulation studies of microwave heated tissue are presented. A parallel tube heat exchanger configuration is used to simulate the internal convection effects of blood flow. The global thermal response of the phantom, on a scale of several tube spacings, is shown theoretically to be nearly identical to that predicted by Pennes' bioheat equation, which is known to give a reasonable representation of tissue under many conditions. A parametric study is provided for the relationships between the tube size, spacing and material properties and the simulated perfusion rate. A prototype with a physiologically reasonable perfusion rate was tested using a typical hyperthermia applicator. The measured thermal response of the phantom compares favorably with the numerical solution of the bioheat equation under the same irradiation conditions. This similarity sheds light on the unexpected success of the bioheat equation for modeling the thermal response of real tissue.     

MicroCT image based simulation to design heating protocols in magnetic nanoparticle hyperthermia for cancer treatment

ObjectivesThe objective is to design heating protocols to completely damage PC3 tumors after a single magnetic nanoparticle hyperthermia session with minimal collateral thermal damage, based on microCT image generated tumor and mouse models.MethodsTumor geometries and volumetric heat generation rate distributions that are generated from microCT scans in our previous study are imported into COMSOL 4.3® multiphysics for heat transfer simulations and heating protocol design using the Arrhenius damage model. Then, parametric studies are performed to evaluate how significantly the infusion rate affects the protocol design and its resulted collateral thermal damage.ResultsThe simulated temperature field in the generated tumor geometry and volumetric heat generation rate distribution are reasonable and correlates well with the amount of the total thermal energy deposited into the tumors. The time needed for complete thermal damage is determined to be approximately 12 min or 25 min if one uses the Arrhenius integral Ω equal to 1 or 4 as the damage threshold, when the infusion rate is 3 μL/min. The heating time increases 26% or 91% in the higher infusion rate groups of 4 or 5 μL/min, respectively. Collateral thermal damage to the surrounding tissue is also assessed. Although the two larger infusion rate groups can still cause thermal damage to the entire tumor, the collateral thermal damage would have exceeded the design criterion of 5%, while the assessment criterion is acceptable only in the infusion rate group of 3 μL/min. Based on the results of this study, we identify an injection strategy and heating protocols to be implemented in future animal experiments to evaluate treatment efficacy for model validation.     

A study on thermal damage during hyperthermia treatment based on DPL model for multilayer tissues using finite element Legendre wavelet Galerkin approach

Hyperthermia is a process that uses heat from the spatial heat source to kill cancerous cells without damaging the surrounding healthy tissues. Efficacy of hyperthermia technique is related to achieve temperature at the infected cells during the treatment process. A mathematical model on heat transfer in multilayer tissues in finite domain is proposed to predict the control temperature profile at hyperthermia position. The treatment technique uses dual-phase-lag model of heat transfer in multilayer tissues with modified Gaussian distribution heat source subjected to the most generalized boundary condition and interface at the adjacent layers. The complete dual-phase-lag model of bioheat transfer is solved using finite element Legendre wavelet Galerkin approach. The present solution has been verified with exact solution in a specific case and provides a good accuracy. The effect of the variability of different parameters such as lagging times, external heat source, metabolic heat source and the most generalized boundary condition on temperature profile in multilayer tissues is analyzed and also discussed the effective approach of hyperthermia treatment. Furthermore, we studied the modified thermal damage model with regeneration of healthy tissues as well. For viewpoint of thermal damage, the least thermal damage has been observed in boundary condition of second kind. The article concludes with a discussion of better opportunities for future clinical application of hyperthermia treatment.     

An analytical study on the thermal effects of cryosurgery on selective cell destruction

The aim of cryosurgery is to kill cells within a closely defined region maintained at a predetermined low temperature. To effectively kill cells, it is important to be able to predict and control the cooling rate over some critical range of temperatures and freezing states in order to regulate the spatial extent of injury during any freeze-thaw protocol. The objective of manipulating the freezing parameters is to maximize the destruction of cancer cells within a defined spatial domain while minimizing cryoinjury to the surrounding healthy tissue. An analytical model has been developed to study the rate of cell destruction within a liver tumor undergoing a freeze-thaw cryosurgical process. Temperature transients in the tumor undergoing cryosurgery have been quantitatively investigated. The simulation is based on solving the transient bioheat equation using the finite volume scheme for a single or multiple-probe geometry. Simulated results show good agreement with experimental data obtained from in vivo clinical study. The calibrated model has been employed to study the effects of different freezing rates, freeze-thaw cycle(s), and multi-probe freezing on cell damage in a liver tumor. The effectiveness of each treatment protocol is estimated by generating the cell survival-volume signature and comparing the percentage of cell damaged within the ice-ball. Results from the model show that employing freeze-thaw cycles has the potential to enhance cell destruction within the cancerous tissue. Results from this study provide the basis for designing an optimized cryosurgical protocol which incorporates thermal effects and the extent of cell destruction within tumors.     

Theoretical analysis of thermal damage in biological tissues caused by laser irradiation

A bioheat transfer approach is proposed to study thermal damage in biological tissues caused by laser radiation. The laser light propagation in the tissue is first solved by using a robust seven-flux model in cylindrical coordinate system. The resulting spatial distribution of the absorbed laser energy is incorporated into the bioheat transfer equation for solving temperature response. Thermal damage to the tissue is assessed by the extent of denatured protein using a rate process equation. It is found that for the tissue studied, a significant protein denaturation process would take place when temperature exceeds about 53 degrees C. The effects of laser power, exposure time and beam size as well as the tissue absorption and scattering coefficients on the thermal damage process are examined and discussed. The laser conditions that cause irreversible damage to the tissue are also identified.     

Osmotic modification of thermal damage in Escherichia coli bacteria at various pH values of the media

A study was made of the influence of media with different osmotic pressure on cell survival and on optic density of supernatants from Escherichia coli B/r and E. coli Bs-1 cell suspensions heated under different pH values of media. Hyperthermia induced cell death accompanied with the loss of optically active (lambda = 260 nm) material. Both cell damage effects were increased in acid and alkaline conditions, compared to neutral condition of heating. Hypertonic media results in a decrease in thermic cell death and loss of cell substances. Under this condition, the protection influence of high osmotic pressure was seen to increase significantly in acid and alkaline conditions of heating, compared to neutral condition. It has been proposed that a higher thermal damage of microorganisms in acid and alkaline beating conditions and protection influence of hypertonic media, especially expressed in acid and alkaline medium, is caused to a great extent by the status of osmotic cell homeostasis.     

A parametric study of thermal therapy of skin tissue

A thermal therapy for cancer in skin tissue is numerically investigated using three bioheat conduction models, namely Pennes, thermal wave and dual-phase lag models. A laser is applied at the surface of the skin for cancer ablation, and the temperature and thermal damage distributions are predicted using the three bioheat models and two different modeling approaches of the laser effect. The first one is a prescribed surface heat flux, in which the tissue is assumed to be highly absorbent, while the second approach is a volumetric heat source, which is reasonable if the scattering and absorption skin effects are of similar magnitude. The finite volume method is applied to solve the governing bioheat equation. A parametric study is carried out to ascertain the effects of the thermophysical properties of the cancer on the thermal damage. The temperature distributions predicted by the three models exhibit significant differences, even though the temperature distributions are similar when the laser is turned off. The type of bioheat model has more influence on the predicted thermal damage than the type of modeling approach used for the laser. The phase lags of heat flux and temperature gradient have an important influence on the results, as well as the thermal conductivity of the cancer. In contrast, the uncertainty in the specific heat and blood perfusion rate has a minor influence on the thermal damage.     

Studies on the three-dimensional temperature transients in the canine prostate during transurethral microwave thermal therapy

Thermal therapy of benign prostatic hyperplasia requires accurate prediction of the temperature distribution induced by the heating within the prostatic tissue. In this study, the Pennes bioheat transfer equation was used to model the transient heat transfer inside the canine prostate during transurethral microwave thermal therapy. Incorporating the specific absorption rate of microwave energy in tissue, a closed-form analytical solution was obtained. Good agreement was found between the theoretical predictions and in-vivo experimental results. Effects of blood perfusion and the cooling at the urethral wall on the temperature rise were investigated within the prostate during heating. The peak intraprostatic temperatures attained by application of 5, 10, or 15 W microwave power were predicted to be 38 degrees C, 41 degrees C, and 44 degrees C. Results from this study will help optimize the thermal dose that can be applied to target tissue during the therapy.     

Analytical study on bioheat transfer problems with spatial or transient heating on skin surface or inside biological bodies

Several closed form analytical solutions to the bioheat transfer problems with space or transient heating on skin surface or inside biological bodies were obtained using Green's function method. The solutions were applied to study several selected typical bioheat transfer processes, which are often encountered in cancer hyperthermia, laser surgery, thermal comfort analysis, and tissue thermal parameter estimation. Thus a straightforward way to quantitatively interpret the temperature behavior of living tissues subject to constant, sinusoidal, step, point or stochastic heatings etc. both in volume and on boundary were established. Further solution to the three-dimensional bioheat transfer problems was also given to illustrate the versatility of the present method. Implementations of this study to the practical problems were addressed.     

Thermal models for microwave hazards and their role in standards development

We consider the thermal response of the body to radiofrequency (RF) energy, with emphasis on partial-body exposure, to assess potential thermal hazards. The thermal analysis is based on Pennes' bioheat equation. In this model, the thermal response is governed by two time constants. One (τ₁) pertains to heat convection by blood flow and is (for physiologically normal perfusion rates) on the order of 3 min. The second (τ₂) characterizes heat conduction, and varies as the square of a distance that characterizes the spatial extent of the heating. We examine three idealized cases. The first is a region of tissue with an insulated surface, subject to irradiation with an exponentially decreasing SAR, which models a large surface area of tissue exposed to microwaves. The second is a region of tissue in contact with a hemispherical electrode that passes current into it, which models exposure from contact with a conductor. The third is a region of tissue with an insulated surface, subject to heating from a dipole located close to it. In all three cases, we estimate the maximum steady-state temperature increase as a function of the relevant electrical and thermal parameters and the thresholds for thermal hazard. We conclude that thermal models are a potentially fruitful but underutilized means of analyzing thermal hazards from RF fields. A quantitative analysis of such hazards enables the development of data-based uncertainty factors, which can replace arbitrary “safety factors” in developing exposure limits. Finally, we comment on the need to marry quantitative modeling of data and risk assessment, and to incorporate contemporary approaches to risk assessment into RF standards development. Bioelectromagnetics 20:52–63, 1999. © 1999 Wiley-Liss, Inc.     

Prediction of the extent of thermal damage in the cornea during conductive keratoplasty

Conductive keratoplasty (CK) is a sub-ablative thermal therapy used to treat hyperopia and presbyopia. In this study, a 3-D finite element model of the cornea was developed to predict the transient temperature distributions and the resultant thermal damage fields in the cornea during simulated CK procedures. The model incorporated collagen denaturation and vaporization of water as well as ablation-induced thermal/electrical contact loss. The effects of the radiofrequency power applied on the electrode and the duration of the treatment on the extent of thermal damage in the tissue were examined and compared with the previously published experimental results on human cornea. It was shown that with clinical settings (60% power and 0.6 s treatment duration), the temperature maximum near the tip of the radiofrequency probe exceeded the temperature for vaporization. The results also indicated that the increase in the treatment duration had a much more significant effect on the size of the thermally modified region than increased radiofrequency power (as verified by the experimental results). The model predictions matched the experimental results well and showed the feasibility of using simulations to optimize thermal treatment of the cornea.     

A new model of thermal inactivation and its application to clonogenic survival data for WiDr human colonic adenocarcinoma cells

Based on the analysis of clonogenic survival data for human colonic adenocarcinoma cells (WiDr) after a single heating, a new model is proposed to describe cell survival after hyperthermia quantitatively. The effects of heat are explained as heat-induced cell damage assuming a first-order (single-hit) and a second-order (cumulative damage) process. Thus cell survival at a specified temperature can be described by the linear-quadratic (LQ) model. The proposed model is based on an alternative definition of the (single) thermal dose, given as the (normalized) product of heating time and a specified nonlinear function of the increase in temperature (relative to a threshold temperature) to be interpreted as the thermal dose rate. In further analogy to the modeling of the effects of low-dose-rate radiation, an inherent capacity of the cells to repair sublethal damage is assumed, and these effects are quantified by the usual g factor measuring incomplete repair effects. The model defines thermal dose-response and isoeffect dose relationships, enabling a direct (i. e. single-step) analysis of the available thermal response data. Additionally, the analysis of our data based on heating times in the range from 0 to 360 min and temperatures from 41 to 46 degrees C and covering a broad spectrum of different densities of cells seeded for colony formation did not yield any evidence of the existence of a breaking point usually derived from Arrhenius plots based on the single-hit, multitarget model and the Arrhenius equation. The model includes no specific assumptions describing the development of thermotolerance, which can be assumed to be negligible under our experimental conditions. The proposed thermal dose-response model correlates satisfactorily with the in vitro survival data for WiDr adenocarcinoma cells.     

Uncertainty analysis for temperature prediction of biological bodies subject to randomly spatial heating

An analytical solution to the Pennes bioheat transfer equation in three-dimensional geometry with practical hyperthermia boundary conditions and random heating was obtained in this paper. Uncertainties for the predicted temperatures of tissues due to approximate parameters were studied based on analyzing one-dimensional heat transfer in the biological bodies subject to a spatially decay heating. Contributions from each of the thermal parameters such as heat conductivity, blood perfusion rate, and metabolic rate of the tissues, the scattering coefficient and the surface power flux of the heating apparatus were compared and the uncertainty limit for temperature distribution in this case was estimated. The results are useful in a variety of clinical hyperthermia and biological thermal parameter measurement.     

Evaluation of microwave hyperthermia applicators.

Hyperthermia has been used in conjunction with radiation and chemotherapy for cancer treatment. When using electromagnetic heating, applicators are critical components in contact with or in proximity to patients and can be the determining factor for effective and safe treatment. Tissue absorption of electromagnetic energy is determined by many factors. Three cases are shown to illustrate the complexity of microwave heating: 1) The BSD MA-151 applicator has good center heating on a muscle-only phantom as shown in the operation manual. When fat slabs of 0.25, 0.5, 1, and 2 cm thick were added, two hot spots near the periphery of the applicator were evident on all fat surfaces, exposed at 631 MHz. At 915 MHz, the heating was elongated on the surface of the models with 0.25- and 2-cm fat, and two hot spots were observed on the 0.5- and 1-cm fat surfaces. 2) Heating patterns of the Clini-Therm applicators on a muscle-only phantom, as indicated in the operations guide, are elliptical with their major axes perpendicular to the electric field. However, when a bolus is used, the elliptical pattern is parallel to the E field. 3) Heating patterns in cylindrical structures were studied with inhomogeneous models of limbs. Arm and thigh models consisting of fat, bone, and muscle material were heated with Clini-Therm L, M, and MS applicators at 915 MHz. In addition to the geometric effect, the results indicated that placing the applicators with E field parallel to the long axis of cylindrical structures can minimize required power, produce less heating of fats and reduce stray radiation. In conclusion, to apply penetrating microwave or other RF fields for tissue heating, one must simulate the clinical exposure conditions as closely as possible to obtain useful heating patterns.     

Evaluation of the effectiveness of transurethral radio frequency hyperthermia in the canine prostate: temperature distribution analysis

The heating pattern of a transurethral radio frequency (RF) applicator and its induced steady-state temperature field in the prostate during transurethral hyperthermia treatment were investigated in this study. The specific absorption rate (SAR) of the electromagnetic energy was first quantified in a tissue-equivalent gel phantom. It was used in conjunction with the Pennes bioheat transfer equation to model the steady-state temperature field in prostate during the treatment. Theoretical predictions were compared to in vivo temperature measurements in the canine prostate and good agreement was found to validate the model. The prostatic tissue temperature rise and its relation to the effect of blood perfusion were analyzed. Blood perfusion is found to be an important factor for removal of heat especially at the higher RF heating level. To achieve a temperature above 44 degrees C within 10 percent of the prostatic tissue volume, the minimum RF power required ranges from 5.5 W to 36.4 W depending on the local blood perfusion rate (omega = 0.2-1.5 ml/gm/min). The corresponding histological results from the treatment suggest that to obtain better treatment results, either higher RF power level or longer treatment time (> 180 minutes) is necessary. This is consistent with the predictions from the theoretical model developed in this study.     

Cellular ATP content of heated Chinese hamster ovary cells

Hyperthermia at either 41.5 or 45 degrees C with variable heating times to reduce cell survival up to three orders of magnitude did not decrease significantly cellular ATP content when measured either immediately or up to 7 hr after a heat treatment. Similarly, cellular ATP content was not significantly reduced with step-down heating, precooling prior to hyperthermia, or thermotolerance induction. The data suggest that heat-induced depletion of intracellular ATP content is not a critical factor in the thermal death of cells heated under normal culture conditions.     

Comparative study of shortwave heating patterns in phantoms with polyethylene and silk partitions

Specific absorption rate (SAR) and effective depths of heating patterns induced by a shortwave, pancake diathermy applicator in fat-muscle phantom are measured. Midplane partitions of polyethylene and silk screen with and without contact chemicals are used. Thermographically obtained SAR data show nearly the same value for silk-screen partitions with and without contact chemicals and slightly lower values with polyethylene partitions, provided that the partition midplanes are tightly pressed against each other. Thermometry data indicate that for low-power exposures the major error in thermographic measurements obtained after termination of heating is due to thermal diffusion and not evaporative cooling in the opened midplane of the phantom.     

Numerical study to establish relationship between coagulation volume and target tip temperature during temperature-controlled radiofrequency ablation

The present study aims at proposing a relationship between the coagulation volume and the target tip temperature in different tissues (viz., liver, lung, kidney, and breast) during temperature-controlled radiofrequency ablation (RFA). A 20-min RFA has been modelled using commercially available monopolar multi-tine electrode subjected to different target tip temperatures that varied from 70°C to 100°C with an increment of 10°C. A closed-loop feedback proportional-integral-derivative (PID) controller has been employed within the finite element model to perform temperature-controlled RFA. The coagulation necrosis has been attained by solving the coupled electric field distribution, the Pennes bioheat and the first-order Arrhenius rate equations within the three-dimensional finite element model of different tissues. The computational study considers temperature-dependent electrical and thermal conductivities along with the non-linear piecewise model of blood perfusion. The comparison between coagulation volume obtained from the numerical and in vitro experimental studies has been done to evaluate the aptness of the numerical models. In the present study, a total of 20 numerical simulations have been performed along with 12 experiments on tissue-mimicking phantom gel using RFA device. The study revealed a strong dependence of the coagulation volume on the pre-set target tip temperature and ablation time during RFA application. Further, the effect of target tip temperature on the applied input voltage has been studied in different tissues. Based on the results attained from the numerical study, statistical correlations between the coagulation volume and treatment time have been developed at different target tip temperatures for each tissue.