Determination of the 3D temperature distribution during ferromagnetic hyperthermia under the influence of blood flow

A numerical simulation of tissue heating during thermo-seed ferromagnetic hyperthermia was performed to determine the temperature distribution of treated tumor tissues under the influence of three large blood vessels at different locations. The effects of the blood velocity waveform, blood vessel size, Curie point of the thermo-seeds and the thermo-seed number on temperature distributions were analyzed. The results indicate that the existence of a blood vessel inside the tumor has a significant cooling effect on the temperature distribution in a treated tumor tissue, which is enhanced with an increase in blood velocity. However, the pulsatile blood flow does not have apparently different effects on the outcomes of uniformly heating target tissues in comparison with the steady blood flow during the hyperthermia process. It is also concluded that a higher Curie point temperature and an increase in the number of thermo-seeds can result in profound increases in the temperature variations of the tumor tissue. In addition, tissue-equivalent phantom experiments were conducted to confirm the cooling effects of the blood vessels, and to validate the effectiveness and accuracy of the proposed heat transfer model for the ferromagnetic hyperthermia.     

Temperature difference between the body core and arterial blood supplied to the brain during hyperthermia or hypothermia in humans

 A vascular heat transfer model is developed to simulate temperature decay along the carotid arteries in humans, and thus, to evaluate temperature differences between the body core and arterial blood supplied to the brain. Included are several factors, including the local blood perfusion rate, blood vessel bifurcation in the neck, and blood vessel pairs on both sides of the neck. The potential for cooling blood in the carotid artery by countercurrent heat exchange with the jugular veins and by radial heat conduction to the neck surface was estimated. Cooling along the common and internal carotid arteries was calculated to be up to 0.87 °C during hyperthermia by high environmental temperatures or muscular exercise. This model was also used to evaluate the feasibility of lowering the brain temperature effectively by placing ice pads on the neck and head surface or by wearing cooling garments during hypothermia treatment for brain injury or other medical conditions. It was found that a 1.1 °C temperature drop along the carotid arteries is possible when the neck surface is cooled to 0 °C. Thus, the body core temperature may not be a good indication of the brain temperature during hyperthermia or hypothermia. Received: 10 January 2002 / Accepted: 7 May 2002 This research was supported by a UMBC Summer Faculty Fellowship.     

Predicting effects of blood flow rate and size of vessels in a vasculature on hyperthermia treatments using computer simulation

Background

Pennes Bio Heat Transfer Equation (PBHTE) has been widely used to approximate the overall temperature distribution in tissue using a perfusion parameter term in the equation during hyperthermia treatment. In the similar modeling, effective thermal conductivity (K_eff) model uses thermal conductivity as a parameter to predict temperatures. However the equations do not describe the thermal contribution of blood vessels. A countercurrent vascular network model which represents a more fundamental approach to modeling temperatures in tissue than do the generally used approximate equations such as the Pennes BHTE or effective thermal conductivity equations was presented in 1996. This type of model is capable of calculating the blood temperature in vessels and describing a vasculature in the tissue regions.

Methods

In this paper, a countercurrent blood vessel network (CBVN) model for calculating tissue temperatures has been developed for studying hyperthermia cancer treatment. We use a systematic approach to reveal the impact of a vasculature of blood vessels against a single vessel which most studies have presented. A vasculature illustrates branching vessels at the periphery of the tumor volume. The general trends present in this vascular model are similar to those shown for physiological systems in Green and Whitmore. The 3-D temperature distributions are obtained by solving the conduction equation in the tissue and the convective energy equation with specified Nusselt number in the vessels.

Results

This paper investigates effects of size of blood vessels in the CBVN model on total absorbed power in the treated region and blood flow rates (or perfusion rate) in the CBVN on temperature distributions during hyperthermia cancer treatment. Also, the same optimized power distribution during hyperthermia treatment is used to illustrate the differences between PBHTE and CBVN models. K_eff (effective thermal conductivity model) delivers the same difference as compared to the CBVN model. The optimization used here is adjusting power based on the local temperature in the treated region in an attempt to reach the ideal therapeutic temperature of 43°C. The scheme can be used (or adapted) in a non-invasive power supply application such as high-intensity focused ultrasound (HIFU). Results show that, for low perfusion rates in CBVN model vessels, impacts on tissue temperature becomes insignificant. Uniform temperature in the treated region is obtained.

Conclusion

Therefore, any method that could decrease or prevent blood flow rates into the tumorous region is recommended as a pre-process to hyperthermia cancer treatment. Second, the size of vessels in vasculatures does not significantly affect on total power consumption during hyperthermia therapy when the total blood flow rate is constant. It is about 0.8% decreasing in total optimized absorbed power in the heated region as γ (the ratio of diameters of successive vessel generations) increases from 0.6 to 0.7, or from 0.7 to 0.8, or from 0.8 to 0.9. Last, in hyperthermia treatments, when the heated region consists of thermally significant vessels, much of absorbed power is required to heat the region and (provided that finer spatial power deposition exists) to heat vessels which could lead to higher blood temperatures than tissue temperatures when modeled them using PBHTE.     

Improved preferential tumor hyperthermia with regional heating and systemic blood cooling: a balanced heat transfer method

Absorption of power in large body volumes can occur with some approaches used for hyperthermia treatment of cancer. A systemic heat absorption rate exceeding the heat dissipation rate can lead to systemic temperature elevation that limits the magnitude and duration of application of power and hence the degree of preferential tumor temperature rise. We describe a hyperthermia approach consisting of regional electromagnetic power absorption and extracorporeal blood cooling with regulation of both systemic heat absorption and dissipation rates ("balanced heat transfer"). A test of this approach in five dogs with nonperfused tumor models demonstrated intratumoral temperatures greater than 42 degrees C, while systemic temperature remained at 33 degrees C and visceral temperatures within the heated region equilibrated between 33 and 42 degrees C. Solutions of the bioheat transfer equation were obtained for a simplified model with a tumor perfusion rate lower than surrounding normal tissue perfusion rate. In this model, the use of arterial blood temperatures less than 37 degrees C allowed higher power densities to be used, for given normal tissue temperatures, than when arterial temperature was greater than or equal to 37 degrees C. As a result, higher intratumoral temperatures were predicted. Control of arterial blood temperature using extracorporeal cooling may thus (1) limit systemic temperature rise produced by regional heating devices and (2) offer a means of improving intratumoral temperature elevations.     

A Three-Dimensional Finite Element Analysis of Heat Transfer in the Forearm

The finite element method was used to analyze heat transfer within a section of the forearm while exposed to different ambient conditions and with different metabolic states. The three-dimensional model accounts for the different material properties of bone, muscle and blood and incorporates a single artery-vein pair for counter-current heat exchange. The geometry of the model was developed from anatomical cross-sectional images of the forearm. The model was used to determine the effects or rest vs. exercise, free vs. forced surface convection and 0 degrees C vs. -20 degrees C external temperatures. The results of the model were compared to experimental data and the model exhibits qualitatively correct behaviour. This model can be used to study hyperthermia, burns and cryogenic freezing of tissue.     

Temperature evolution in tissues embedded with large blood vessels during photo-thermal heating

During laser-assisted photo-thermal therapy, the temperature of the heated tissue region must rise to the therapeutic value (e.g., 43 °C) for complete ablation of the target cells. Large blood vessels (larger than 500 micron in diameter) at or near the irradiated tissues have a considerable impact on the transient temperature distribution in the tissue. In this study, the cooling effects of large blood vessels on temperature distribution in tissues during laser irradiation are predicted using finite element based simulation. A uniform flow is assumed at the entrance and three-dimensional conjugate heat transfer equations in the tissue region and the blood region are simultaneously solved for different vascular models. A volumetric heat source term based on Beer–Lambert law is introduced into the energy equation to account for laser heating. The heating pattern is taken to depend on the absorption and scattering coefficients of the tissue medium. Experiments are also conducted on tissue mimics in the presence and absence of simulated blood vessels to validate the numerical model. The coupled heat transfer between thermally significant blood vessels and their surrounding tissue for three different tissue-vascular networks are analyzed keeping the laser irradiation constant. A surface temperature map is obtained for different vascular models and for the bare tissue (without blood vessels). The transient temperature distribution is seen to differ according to the nature of the vascular network, blood vessel size, flow rate, laser spot size, laser power and tissue blood perfusion rate. The simulations suggest that the blood flow through large blood vessels in the vicinity of the photothermally heated tissue can lead to inefficient heating of the target.     

A 3D thermal model to analyze the temperature changes of digits during cold stress and predict the danger of frostbite in human fingers

The existing computational models of frostbite injury are limited to one and two dimensional schemes. In this study, a coupled thermo-fluid model is applied to simulate a finger exposed to cold weather. The spatial variability of finger-tip temperature is compared to experimental ones to validate the model. A semi-realistic 3D model for tissue and blood vessels is used to analyze the transient heat transfer through the finger. The effect of heat conduction, metabolic heat generation, heat transport by blood perfusion, heat exchange between tissues and large vessels are considered in energy balance equations. The current model was then tested in different temperatures and air speeds to predict the danger of frostbite in humans for different gloves. Two prevalent gloves which are commonly used in cold climate are considered for investigation. The endurance time and the fraction of necrotic tissues are two main factors suggested for obtaining the response of digit tissues to different environmental conditions.     

A Three-Dimensional Finite Element Analysis of Heat Transfer in the Forearm

Abstract

The finite element method was used to analyze heat transfer within a section of the forearm while exposed to different ambient conditions and with different metabolic states. The three-dimensional model accounts for the different material properties of bone, muscle and blood and incorporates a single artery-vein pair for counter-current heat exchange. The geometry of the model was developed from anatomical cross-sectional images of the forearm. The model was used to determine the effects or rest vs. exercise, free vs. forced surface convection and 0°C vs. — 20 °C external temperatures. The results of the model were compared to experimental data and the model exhibits qualitatively correct behaviour. This model can be used to study hyperthermia, burns and cryogenic freezing of tissue.     

A thermal model of the human body exposed to an electromagnetic field

The human body was modeled by numerical procedures to determine the thermal response under varied electromagnetic (EM) exposures. The basic approach taken was to modify the heat transfer equations for man in air to account for thermal loading due to the energy absorbed from the EM field. The human body was represented in an EM model by a large number of small cubical cells of tissue, and the energy density was determined for each cell. This information was then analyzed by a thermal response model consisting of a series of two-dimensional transient conduction equations with internal heat generation due to metabolism, internal convective heat transfer due to blood flow, external interaction by convection and radiation, and cooling of the skin by sweating and evaporation. This model simulated the human body by a series of cylindrical segments. The local temperature at 61 discrete locations as well as the thermoregulatory responses of vasodilatation and sweating were computed for a number of EM field intensities and two frequencies, one near whole-body resonance.     

A review on numerical modeling for magnetic nanoparticle hyperthermia: Progress and challenges

Recent progress in nanotechnology has advanced the development of magnetic nanoparticle (MNP) hyperthermia as a potential therapeutic platform for treating diseases. Due to the challenges in reliably predicting the spatiotemporal distribution of temperature in the living tissue during the therapy of MNP hyperthermia, critical for ensuring the safety as well as efficacy of the therapy, the development of effective and reliable numerical models is warranted. This article provides a comprehensive review on the various mathematical methods for determining specific loss power (SLP), a parameter used to quantify the heat generation capability of MNPs, as well as bio-heat models for predicting heat transfer phenomena and temperature distribution in living tissue upon the application of MNP hyperthermia. This article also discusses potential applications of the bio-heat models of MNP hyperthermia for therapeutic purposes, particularly for cancer treatment, along with their limitations that could be overcome.     

Conditions for equivalency of countercurrent vessel heat transfer formulations.

Previous models of countercurrent blood vessel heat transfer have used one of two, different, equally valid but previously unreconciled formulations, based either on: (1) the difference between the arterial and venous vessels' average wall temperatures, or (2) the difference between those vessels' blood bulk fluid temperatures. This paper shows that these two formulations are only equivalent when the four, previously undefined, "convective heat transfer coefficients" that are used in the bulk temperature difference formulation (two coefficients each for the artery and vein) have very specific, problem-dependent relationships to the standard convective heat transfer coefficients. (The average wall temperature formulation uses those standard coefficients correctly.) The correct values of these bulk temperature difference formulation "convective heat transfer coefficients" are shown to be either: (1) specific functions of (a) the tissue conduction resistances, (b) the standard convective heat transfer coefficients, and (c) the independently specified bulk arterial, bulk venous and tissue temperatures, or (2) arbitrary, user defined values. Thus, they are generally not equivalent to the standard convective heat transfer coefficients that are regularly used, and must change values depending on the blood and tissue temperatures. This dependence can significantly limit the convenience and usefulness of the bulk temperature difference formulations.     

Paradox: increased blood perfusion to the face <Emphasis Type="BoldItalic">enhances</Emphasis> protection against frostbite while it <Emphasis Type="BoldItalic">lowers</Emphasis> wind chill equivalent temperatures

A model of facial heat exchange in cold and windy environments is presented. The tissue is depicted as a hollow cylinder and the model includes heat conduction and heat transport by blood circulation from the warmer core. A steady-state solution facilitating the estimation of wind chill equivalent temperature (WCET) as a function of the effective wind velocity, air temperature and blood perfusion rate was obtained. The results quantify and demonstrate the elevation of skin temperatures caused by increased flow of warmer blood from the inner core to the face. Elevated facial temperatures, while enhancing protection against frostbite and other cold-related injuries, also increase heat loss to the colder environment. Paradoxically, such elevated facial temperatures cause WCETs, as estimated by the prevailing definition, to attain lower rather than higher values, indicating, in fact, increased risk of frostbite. The results of this study should be useful in understanding and quantifying the effects of blood perfusion in protection against cold-related injuries. They should also be considered in the re-evaluation and re-formulation of the concept of wind chill, which has been a useful cold weather indicator for decades.     

Three-dimensional steady-state temperature distribution about cylinders and discs

The steady-state temperature distribution about heat sources possessing axial symmetry is presented in two cases, the right circular source cylinder and the cylindrical column of thin circular source discs of random orientation. In both cases, the source strength is assumed to decrease exponentially from the one end of the cylinder to the other. Application of the results to the problem of optically produced burns, such as the retinal burn obtained in sun-gazing, is discussed. A brief comparison is made of the steady-state model with that employed in studies of transient temperature distributions in systems with time-dependent source strengths.     

A new fundamental bioheat equation for muscle tissue--part II: Temperature of SAV vessels

In this study, a new theoretical framework was developed to investigate temperature variations along countercurrent SAV blood vessels from 300 to 1000 microm diameter in skeletal muscle. Vessels of this size lie outside the range of validity of the Weinbaum-Jiji bioheat equation and, heretofore, have been treated using discrete numerical methods. A new tissue cylinder surrounding these vessel pairs is defined based on vascular anatomy, Murray's law, and the assumption of uniform perfusion. The thermal interaction between the blood vessel pair and surrounding tissue is investigated for two vascular branching patterns, pure branching and pure perfusion. It is shown that temperature variations along these large vessel pairs strongly depend on the branching pattern and the local blood perfusion rate. The arterial supply temperature in different vessel generations was evaluated to estimate the arterial inlet temperature in the modified perfusion source term for the s vessels in Part I of this study. In addition, results from the current research enable one to explore the relative contribution of the SAV vessels and the s vessels to the overall thermal equilibration between blood and tissue.     

The effects of some physical factors on the production of hyperthermia by ultrasound in neoplastic tissues

Summary A one-dimensional and a three-dimensional computer model have been built in order to study the importance of blood flow and ultrasonic absorption in tissues during local hyperthermia. The decreased blood flow in the interior of certain tumours and possibly the increased ultrasonic absorption of the malignant tissue in some cases may cause selectively higher temperatures inside the tumours though the heat input is the same as in the surrounding tissues. Also, the vasodilation of blood vessels in normal tissues as a response to heat causes a therapeutically useful temperature difference. These blood flow differences can lead to enhanced effects during sonication to produce hyperthermia in the tumour. The inhomogenity of blood flow in the tumour causes a non-uniform temperature distribution leaving the well-perfused cells in the advancing front at a much lower temperature than the cells in the necrotic centre. Thus, the combination of local hyperthermia with radio-and chemotherapy seems to offer the most attractive means of destroying malignant tissue.     

Investigation of thermal distribution for pulsed laser radiation in cancer treatment with nanoparticle-mediated hyperthermia

In this paper, we have simulated the efficacy of gold/gold sulfide (GGS) nanoshells in NIR laser hyperthermia to achieve effective targeting for tumor photothermal therapy. The problem statement takes into account the heat transfer with the blood perfusion through capillaries, and pulsed laser irradiation during the hyperthermia. Although previous researchers have used short laser pulses (nanosecond and less), in order to prevent heat leakage to the neighbor tissues, we have examined the effect of millisecond pulses, as the extent of the target volume to which hyperthermia is induced is usually larger and also the lasers with this specification are more available. A tumor with surrounding tissue was simulated in COMSOL software (a finite element analysis, solver and simulation software) and also in a phantom made of agarose and intralipid. The tumor was irradiated by 10, 20 and 30 laser pulses with durations of 15, 50 and 200 ms and fluences of 20, 40 and 60 J/cm². Experimental tests performed on a phantom prove the ability of the applied numerical model to capture the temperature distribution in the target tissue. We have shown that our simulation permits prediction of treatment outcome from computation of thermal distribution within the tumor during laser hyperthermia using GGS nanoshells and millisecond pulsed laser irradiation. The advantage of this simulation is its simplicity as well as its accuracy. Although, to develop the model completely for a given organ and application, all the parameters should be estimated based on a real vasculature of the organ, physiological conditions, and expected variation in those physiological conditions for that application in the organ.     

Investigation of the influence of blood flow rate on large vessel cooling in hepatic radiofrequency ablation.

Radiofrequency (RF) ablation using high-frequency current has become an important treatment method for patients with non-resectable liver tumors. Tumor recurrence is associated with tissue cooling in the proximity of large blood vessels. This study investigated the influence of blood flow rate on tissue temperature and lesion size during monopolar RF ablation at a distance of 10 mm from single 4- and 6-mm vessels using two different approaches: 1) an ex vivo blood perfusion circuit including an artificial vessel inserted into porcine liver tissue was developed; and 2) a finite element method (FEM) model was created using a novel simplified modeling technique for large blood vessels. Blood temperatures at the inflow/outflow of the vessel and tissue temperatures at 10 and 20 mm from the electrode tip were measured in the ex vivo set-up. Tissue temperature, blood temperature and lesion size were analyzed under physiological, increased and reduced blood-flow conditions. The results show that changes in blood flow rate in large vessels do not significantly affect tissue temperature and lesion size far away from the vessel. Monopolar ablation could not produce lesions surrounding the vessel due to the strong heat-sink effect. Simulated tissue temperatures correlated well with ex vivo measurements, supporting the FEM model.     

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.