Fundamental solutions to the bioheat equation and their application to magnetic fluid hyperthermia

Reaction-diffusion study of electron-beam-induced contamination growth

A time-dependent reaction-diffusion model was elaborated to better understand the dynamical growth of contamination on surfaces illuminated by an electron beam. The goal of this work was to fully describe the flow of hydrocarbon molecules, denoted as contaminants, and their polymerization in the irradiated area with the number of parameters reduced to a minimum necessary. It was considered that the diffusion process of contaminants is driven by the gradient of their surface density generated by the impact of a circular homogeneous electron beam. The contribution of the residual gas atmosphere in the instrument was described by the tendency to reestablish the initial equilibrium surface density of contaminants before irradiation. The four unknown parameters of the model, the electron interaction cross-section, the diffusion coefficient, the initial surface density of contaminants, and the frequency of the supply of contaminants from the residual gas atmosphere were determined by comparing the modeled contamination growth with experimental results. The experiments were designed such that the influence of the single parameters could be unequivocally separated. To follow the dynamical evolution of the system and to generate time-resolved distinct experimental data, successive contamination measurements were performed at short time intervals up to 20 min. The local height and shape of the grown contamination were quantified by evaluating high-angle annular dark-field (HAADF) scanning-transmission- electron-microcopy (STEM) image intensities and corresponding Monte-Carlo simulations. Our model also applies to nonhomogeneous initial conditions like the reduced local surface density of contaminants after previous beam-showering. The dynamic analyses of this process might provide hints regarding the relative size of the contaminant molecules and also indicate some measures for the reduction of contamination growth.

Patient-specific temperature distribution prediction in laser interstitial thermal therapy: single-irradiation data-driven method

Laser interstitial thermal therapy (LITT) is popular for treating brain tumours and epilepsy. The strict control of tissue thermal damage extent is crucial for LITT. Temperature prediction is useful for predicting thermal damage extent. Accurately predictingin vivobrain tissue temperature is challenging due to the temperature dependence and the individual variations in tissue properties. Considering these factors is essential for improving the temperature prediction accuracy.Objective. To present a method for predicting patient-specific tissue temperature distribution within a target lesion area in the brain during LITT.Approach. A magnetic resonance temperature imaging (MRTI) data-driven estimation model was constructed and combined with a modified Pennes bioheat transfer equation (PBHE) to predict patient-specific temperature distribution. In the PBHE for temperature prediction, the individual specificity and temperature dependence of thermal tissue properties and blood perfusion, as well as the individual specificity of optical tissue properties were considered. Only MRTI data during one laser irradiation were required in the method. This enables the prediction of patient-specific temperature distribution and the resulting thermal damage region for subsequent ablations.Main results. Patient-specific temperature prediction was evaluated based on clinical data acquired during LITT in the brain, using intraoperative MRTI data as the reference standard. Our method significantly improved the prediction performance of temperature distribution and thermal damage region. The average root mean square error was decreased by 69.54%, the average intraclass correlation coefficient was increased by 37.5%, the average Dice similarity coefficient was increased by 43.14% for thermal damage region prediction.Significance. The proposed method can predict temperature distribution and thermal damage region at an individual patient level during LITT, providing a promising approach to assist in patient-specific treatment planning for LITT in the brain.

Towards optimal thermal distribution in magnetic hyperthermia

A linear combination of spherically symmetric heat sources is shown to provide optimal stationary thermal distribution in magnetic hyperthermia. Furthermore, such spatial location of heat sources produces suitable temperature distribution in biological medium even for assemblies of magnetic nanoparticles with a moderate value of specific absorption rate (SAR), of the order of 100-150 W/g. We also demonstrate the advantage of using assemblies of spherical magnetic nanocapsules consisting of metallic iron nanoparticles covered with non magnetic shells of sufficient thickness in magnetic hyperthermia. Based on numerical simulation we optimize the size and geometric structure of biocompatible spherical capsules in order to minimize the influence of strong magneto-dipole interaction between closely spaced nanoparticles. It is shown that assembly of capsules can provide sufficiently high SAR values of the order of 250-400 W/g at moderate amplitudes H0 = 50-100 Oe and frequencies f = 100-200 kHz of alternating magnetic field, being appropriate for application in clinics.

A Computational Study on Magnetic Nanoparticles Hyperthermia of Ellipsoidal Tumors

The modelling of magnetic hyperthermia using nanoparticles of ellipsoid tumor shapes has not been studied adequately. To fill this gap, a computational study has been carried out to determine two key treatment parameters: the therapeutic temperature distribution and the extent of thermal damage. Prolate and oblate spheroidal tumors, of various aspect ratios, surrounded by a large healthy tissue region are assumed. Tissue temperatures are determined from the solution of Pennes’ bio-heat transfer equation. The mortality of the tissues is determined by the Arrhenius kinetic model. The computational model is successfully verified against a closed-form solution for a perfectly spherical tumor. The therapeutic temperature and the thermal damage in the tumor center decrease as the aspect ratio increases and it is insensitive to whether tumors of the same aspect ratio are oblate or prolate spheroids. The necrotic tumor area is affected by the tumor prolateness and oblateness. Good comparison is obtained of the present model with three sets of experimental measurements taken from the literature, for animal tumors exhibiting ellipsoid-like geometry. The computational model enables the determination of the therapeutic temperature and tissue thermal damage for magnetic hyperthermia of ellipsoidal tumors. It can be easily reproduced for various treatment scenarios and may be useful for an effective treatment planning of ellipsoidal tumor geometries.

Fractal Pennes and Cattaneo-Vernotte bioheat equations from product-like fractal geometry and their implications on cells in the presence of tumour growth

In this study, the Pennes and Cattaneo-Vernotte bioheat transfer equations in the presence of fractal spatial dimensions are derived based on the product-like fractal geometry. This approach was introduced recently, by Li and Ostoja-Starzewski, in order to explore dynamical properties of anisotropic media. The theory is characterized by a modified gradient operator which depends on two parameters: R which represents the radius of the tumour and R0 which represents the radius of the spherical living tissue. Both the steady and unsteady states for each fractal bioheat equation were obtained and their implications on living cells in the presence of growth of a large tumour were analysed. Assuming a specific heating/cooling by a constant heat flux equivalent to the metabolic heat generation in the tissue, it was observed that the solutions of the fractal bioheat equations are robustly affected by fractal dimensions, the radius of the tumour growth and the dimensions of the living cell tissue. The ranges of both the fractal dimensions and temperature were obtained, analysed and compared with recent studies. This study confirms the importance of fractals in medicine.

Non-Heating Alternating Magnetic Field Nanomechanical Stimulation of Biomolecule Structures via Magnetic Nanoparticles as the Basis for Future Low-Toxic Biomedical Applications

The review discusses the theoretical, experimental and toxicological aspects of the prospective biomedical application of functionalized magnetic nanoparticles (MNPs) activated by a low frequency non-heating alternating magnetic field (AMF). In this approach, known as nano-magnetomechanical activation (NMMA), the MNPs are used as mediators that localize and apply force to such target biomolecular structures as enzyme molecules, transport vesicles, cell organelles, etc., without significant heating. It is shown that NMMA can become a biophysical platform for a family of therapy methods including the addressed delivery and controlled release of therapeutic agents from transport nanomodules, as well as selective molecular nanoscale localized drugless nanomechanical impacts. It is characterized by low system biochemical and electromagnetic toxicity. A technique of 3D scanning of the NMMA region with the size of several mm to several cm over object internals has been described.

Magnetic Resonance-Guided High-Intensity Focused Ultrasound Ablation of Uterine Fibroids-Efficiency Assessment with the Use of Dynamic Contrast-Enhanced Magnetic Resonance Imaging and the Potential Role of the Administration of Uterotonic Drugs

OBJECTIVE

The assessment of the usefulness of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) when qualifying patients with uterine fibroids (UFs) for magnetic resonance-guided high-intensity ultrasound (MR-HIFU).

MATERIAL AND METHODS

This retrospective, single center study included 283 women who underwent DCE-MRI and were treated with MR-HIFU. The patients were divided according to non-perfused volume (NPV) as well as by the type of curve for patients with a washout curve in the DCE-MRI study and patients without a washout curve. The studied women were assessed in three groups according to the type of uterotonics administered. Group A (57 patients) received one dose of misoprostol/diclofenac transvaginally and group B (71 patients) received oxytocin intravenously prior to the MR-HIFU procedure. The remaining 155 women (group C) were treated with the traditional non-drug enhanced MR-HIFU procedure.

RESULTS

The average NPV value was higher in no washout group, and depended on the uterotonics used.

CONCLUSIONS

We demonstrated a correlation between dynamic contrast enhancement curve types and the therapeutic efficacy of MR-HIFU. Our results suggest that DCE-MRI has the potential to assess treatment outcomes among patients with UFs, and patients with UFs that present with a washout curve may benefit from the use of uterotonic drugs. More studies are required to draw final conclusions.

Self-Assembly of Magnetic Nanoparticles in Ferrofluids on Different Templates Investigated by Neutron Reflectometry

In this article we review the process by which magnetite nanoparticles self-assemble onto solid surfaces. The focus is on neutron reflectometry studies providing information on the density and magnetization depth profiles of buried interfaces. Specific attention is given to the near-interface "wetting" layer and to examples of magnetite nanoparticles on a hydrophilic silicon crystal, one coated with (3-Aminopropyl)triethoxysilane, and finally, one with a magnetic film with out-of-plane magnetization.

Feasibility of removable balloon implant for simultaneous magnetic nanoparticle heating and HDR brachytherapy of brain tumor resection cavities

AIM

Hyperthermia (HT) has been shown to improve clinical response to radiation therapy (RT) for cancer. Synergism is dramatically enhanced if HT and RT are combined simultaneously, but appropriate technology to apply treatments together does not exist. This study investigates the feasibility of delivering HT with RT to a 5-10mm annular rim of at-risk tissue around a tumor resection cavity using a temporary thermobrachytherapy (TBT) balloon implant.

METHODS

A balloon catheter was designed to deliver radiation from High Dose Rate (HDR) brachytherapy concurrent with HT delivered by filling the balloon with magnetic nanoparticles (MNP) and immersing it in a radiofrequency magnetic field. Temperature distributions in brain around the TBT balloon were simulated with temperature dependent brain blood perfusion using numerical modeling. A magnetic induction system was constructed and used to produce rapid heating (>0.2°C/s) of MNP-filled balloons in brain tissue-equivalent phantoms by absorbing 0.5 W/ml from a 5.7 kA/m field at 133 kHz.

RESULTS

Simulated treatment plans demonstrate the ability to heat at-risk tissue around a brain tumor resection cavity between 40-48°C for 2-5cm diameter balloons. Experimental thermal dosimetry verifies the expected rapid and spherically symmetric heating of brain phantom around the MNP-filled balloon at a magnetic field strength that has proven safe in previous clinical studies.

CONCLUSIONS

These preclinical results demonstrate the feasibility of using a TBT balloon to deliver heat simultaneously with HDR brachytherapy to tumor bed around a brain tumor resection cavity, with significantly improved uniformity of heating over previous multi-catheter interstitial approaches. Considered along with results of previous clinical thermobrachytherapy trials, this new capability is expected to improve both survival and quality of life in patients with glioblastoma multiforme.

Therapeutic evaluation of magnetic hyperthermia using Fe3O4-aminosilane-coated iron oxide nanoparticles in glioblastoma animal model

Objective:

To evaluate the potential of magnetic hyperthermia using aminosilane-coated superparamagnetic iron oxide nanoparticles in glioblastoma tumor model.

Methods:

The aminosilane-coated superparamagnetic iron oxide nanoparticles were analyzed as to their stability in aqueous medium and their heating potential through specific absorption rate, when submitted to magnetic hyperthermia with different frequencies and intensities of alternating magnetic field. In magnetic hyperthermia in vitro assays, the C6 cells cultured and transduced with luciferase were analyzed by bioluminescence in the absence/presence of alternating magnetic field, and also with and without aminosilane-coated superparamagnetic iron oxide nanoparticles. In the in vivo study, the measurement of bioluminescence was performed 21 days after glioblastoma induction with C6 cells in rats. After 24 hours, the aminosilane-coated superparamagnetic iron oxide nanoparticles were implanted in animals, and magnetic hyperthermia was performed for 40 minutes, using the best conditions of frequency and intensity of alternating magnetic field tested in the in vitro study (the highest specific absorption rate value) and verified the difference of bioluminescence before and after magnetic hyperthermia.

Results:

The aminosilane-coated superparamagnetic iron oxide nanoparticles were stable, and their heating capacity increased along with higher frequency and intensity of alternating magnetic field. The magnetic hyperthermia application with 874kHz and 200 Gauss of alternating magnetic field determined the best value of specific absorption rate (194.917W/g). When these magnetic hyperthermia parameters were used in in vitro and in vivo analysis, resulted in cell death of 52.0% and 32.8%, respectively, detected by bioluminescence.

Conclusion:

The magnetic hyperthermia was promissing for the therapeutical process of glioblastoma tumors in animal model, using aminosilane-coated superparamagnetic iron oxide nanoparticles, which presented high specific absorption rate.

Temperature-controlled power modulation compensates for heterogeneous nanoparticle distributions: a computational optimization analysis for magnetic hyperthermia

Purpose:

To study, with computational models, the utility of power modulation to reduce tissue temperature heterogeneity for variable nanoparticle distributions in magnetic nanoparticle hyperthermia.

Methods:

Tumour and surrounding tissue were modeled by elliptical two- and three-dimensional computational phantoms having six different nanoparticle distributions. Nanoparticles were modeled as point heat sources having amplitude-dependent loss power. The total number of nanoparticles was fixed, and their spatial distribution and heat output were varied. Heat transfer was computed by solving the Pennes’ bioheat equation using finite element methods (FEM) with temperature-dependent blood perfusion. Local temperature was regulated using a proportional-integral-derivative (PID) controller. Tissue temperature, thermal dose and tissue damage were calculated. The required minimum thermal dose delivered to the tumor was kept constant, and heating power was adjusted for comparison of both the heating methods.

Results:

Modulated power heating produced lower and more homogeneous temperature distributions than did constant power heating for all studied nanoparticle distributions. For a concentrated nanoparticle distribution, located off-center within the tumor, the maximum temperatures inside the tumor were 16% lower for modulated power heating when compared to constant power heating. This resulted in less damage to surrounding normal tissue. Modulated power heating reached target thermal doses up to nine-fold more rapidly when compared to constant power heating.

Conclusions:

Controlling the temperature at the tumor-healthy tissue boundary by modulating the heating power of magnetic nanoparticles demonstrably compensates for a variable nanoparticle distribution to deliver effective treatment.

Magnetic hyperthermia therapy for the treatment of glioblastoma: a review of the therapy's history, efficacy and application in humans

Hyperthermia therapy (HT) is the exposure of a region of the body to elevated temperatures to achieve a therapeutic effect. HT anticancer properties and its potential as a cancer treatment have been studied for decades. Techniques used to achieve a localised hyperthermic effect include radiofrequency, ultrasound, microwave, laser and magnetic nanoparticles (MNPs). The use of MNPs for therapeutic hyperthermia generation is known as magnetic hyperthermia therapy (MHT) and was first attempted as a cancer therapy in 1957. However, despite more recent advancements, MHT has still not become part of the standard of care for cancer treatment. Certain challenges, such as accurate thermometry within the tumour mass and precise tumour heating, preclude its widespread application as a treatment modality for cancer. MHT is especially attractive for the treatment of glioblastoma (GBM), the most common and aggressive primary brain cancer in adults, which has no cure. In this review, the application of MHT as a therapeutic modality for GBM will be discussed. Its therapeutic efficacy, technical details, and major experimental and clinical findings will be reviewed and analysed. Finally, current limitations, areas of improvement, and future directions will be discussed in depth.

Self-Assembled Layering of Magnetic Nanoparticles in a Ferrofluid on Silicon Surfaces

This article describes the three-dimensional self-assembly of monodisperse colloidal magnetite nanoparticles (NPs) from a dilute water-based ferrofluid onto a silicon surface and the dependence of the resultant magnetic structure on the applied field. The NPs assemble into close-packed layers on the surface followed by more loosely packed ones. The magnetic field-dependent magnetization of the individual NP layers depends on both the rotational freedom of the layer and the magnetization of the adjacent layers. For layers in which the NPs are more free to rotate, the easy axis of the NP can readily orient along the field direction. In more dense packing, free rotation of the NPs is hampered, and the NP ensembles likely build up quasi-domain states to minimize energy, which leads to lower magnetization in those layers. Detailed analysis of polarized neutron reflectometry data together with model calculations of the arrangement of the NPs within the layers and input from small-angle scattering measurements provide full characterization of the core/shell NP dimensions, degree of chaining, arrangement of the NPs within the different layers, and magnetization depth profile.

Commentary on the clinical and preclinical dosage limits of interstitially administered magnetic fluids for therapeutic hyperthermia based on current practice and efficacy models

We offer a critique of what constitutes a suitable dosage limit, in both clinical and preclinical studies, for interstitially administered magnetic nanoparticles in order to enable therapeutic hyperthermia under the action of an externally applied alternating magnetic field. We approach this first from the perspective of the currently approved clinical dosages of magnetic nanoparticles in the fields of MRI contrast enhancement, sentinel node detection, iron replacement therapy and magnetic thermoablation. We compare this to a simple analytical model of the achievable hyperthermia temperature rise in both humans and animals based on the interstitially administered dose, the heating and dispersion characteristics of the injected fluid, and the strength and frequency of the applied magnetic field. We show that under appropriately chosen conditions a therapeutic temperature rise is achievable in clinically relevant situations. We also show that in such cases it may paradoxically be harder to achieve the same therapeutic temperature rise in a preclinical model. We comment on the implications for the evidence-based translation of hyperthermia based interventions from the laboratory to the clinic.

Mathematical and numerical analysis of thermal distribution in cancerous tissues under the local heat therapy

The main purpose of this study is to investigate the thermal behavior of living tissues in the presence of spatial external heat source. An effort has been made to formulate the mathematical model to study the temperature distribution in in vivo tissues of the human body. The mathematical formulation is governed by bio-heat equation together with appropriate initial, boundary and interface conditions. The solution of the model was carried out using variational finite element method and computational simulations. The model describes the exchange of heat between the internal biological tissues and other surrounding media. The effect of external heat source under different conditions of atmospheric temperature and as a local hyperthermic method provides an important information to the temperature regulation in biological tissues under normal and malignant conditions. Thermal fluctuations at the targeted regions were obtained with respect to various time-dependent heating sources and scattering coefficients. The results obtained may be helpful for clinical purposes especially in the treatment of cancerous tumors through radiotherapy and other local hyperthermic approaches.

Towards nanomedicines of the future: Remote magneto-mechanical actuation of nanomedicines by alternating magnetic fields

The paper describes the concept of magneto-mechanical actuation of single-domain magnetic nanoparticles (MNPs) in super-low and low frequency alternating magnetic fields (AMFs) and its possible use for remote control of nanomedicines and drug delivery systems. The applications of this approach for remote actuation of drug release as well as effects on biomacromolecules, biomembranes, subcellular structures and cells are discussed in comparison to conventional strategies employing magnetic hyperthermia in a radio frequency (RF) AMF. Several quantitative models describing interaction of functionalized MNPs with single macromolecules, lipid membranes, and proteins (e.g. cell membrane receptors, ion channels) are presented. The optimal characteristics of the MNPs and an AMF for effective magneto-mechanical actuation of single molecule responses in biological and bio-inspired systems are discussed. Altogether, the described studies and phenomena offer opportunities for the development of novel therapeutics both alone and in combination with magnetic hyperthermia.

A model evaluation study for treatment planning of laser-induced thermal therapy

A cross-validation analysis evaluating computer model prediction accuracy for a priori planning magnetic resonance-guided laser-induced thermal therapy (MRgLITT) procedures in treating focal diseased brain tissue is presented. Two mathematical models are considered. (1) A spectral element discretisation of the transient Pennes bioheat transfer equation is implemented to predict the laser-induced heating in perfused tissue. (2) A closed-form algorithm for predicting the steady-state heat transfer from a linear superposition of analytic point source heating functions is also considered. Prediction accuracy is retrospectively evaluated via leave-one-out cross-validation (LOOCV). Modelling predictions are quantitatively evaluated in terms of a Dice similarity coefficient (DSC) between the simulated thermal dose and thermal dose information contained within N = 22 MR thermometry datasets. During LOOCV analysis, the transient model's DSC mean and median are 0.7323 and 0.8001 respectively, with 15 of 22 DSC values exceeding the success criterion of DSC ≥ 0.7. The steady-state model's DSC mean and median are 0.6431 and 0.6770 respectively, with 10 of 22 passing. A one-sample, one-sided Wilcoxon signed-rank test indicates that the transient finite element method model achieves the prediction success criteria, DSC ≥ 0.7, at a statistically significant level.

Magnetic particle hyperthermia--a promising tumour therapy?

We present a critical review of the state of the art of magnetic particle hyperthermia (MPH) as a minimal invasive tumour therapy. Magnetic principles of heating mechanisms are discussed with respect to the optimum choice of nanoparticle properties. In particular, the relation between superparamagnetic and ferrimagnetic single domain nanoparticles is clarified in order to choose the appropriate particle size distribution and the role of particle mobility for the relaxation path is discussed. Knowledge of the effect of particle properties for achieving high specific heating power provides necessary guidelines for development of nanoparticles tailored for tumour therapy. Nanoscale heat transfer processes are discussed with respect to the achievable temperature increase in cancer cells. The need to realize a well-controlled temperature distribution in tumour tissue represents the most serious problem of MPH, at present. Visionary concepts of particle administration, in particular by means of antibody targeting, are far from clinical practice, yet. On the basis of current knowledge of treating cancer by thermal damaging, this article elucidates possibilities, prospects, and challenges for establishment of MPH as a standard medical procedure.

Comparison of a single optimized coil and a Helmholtz pair for magnetic nanoparticle hyperthermia

Magnetic nanoparticles in a tumor can induce therapeutic heating when energized by an alternating magnetic field from a current-carrying coil outside the body. We analyzed a single-turn, air-core coil carrying a filamentary current to quantify the power absorbed by: a) magnetic nanoparticles at depth in tissue and b) superficial tissue in response to induced eddy currents; we defined this quotient as power ratio (PR). Given some limit on the eddy current heating tolerated by an alert patient, maximizing the PR maximizes the power absorbed in the tumor; all else being equal, this increases the thermal dose delivered to the tumor. The mean eddy current heating rate tolerated in four clinical studies we reviewed equaled 12.5 kW/m (3). We differentiated our analytical expression for PR with respect to the radius of the coil to find the value of radius that maximizes PR. Under reasonable simplifying assumptions, the optimal value of coil radius equaled 1.187 times the depth of the nanoparticle target below the body surface. We also derived the PR of two coils surrounding the body configured as a Helmholtz pair. We computed PR for combinations of nanoparticle depths below the surface and axial locations with respect to the coils. At depths less than 4.6 cm, the optimized single coil had a higher PR than that of the Helmholtz pair and furthermore produced less total ohmic heating within the coil. These results were independent of driving frequency, nanoparticle concentration, tissue electrical conductivity, and magnetic nanoparticle heating rate, provided the latter is assumed to be proportional to the product of frequency and the square of the local magnetic field. This paper supports the clinical application of current-carrying coils to deliver efficacious hyperthermia therapy to tumors injected with magnetic nanoparticles.

Effect of magnetic nanoparticle heating on cortical neuron viability

PURPOSE

Superparamagnetic iron oxide nanoparticles are currently approved for use as an adjunctive treatment to glioblastoma multiforme radiotherapy. Radio frequency stimulation of the nanoparticles generates localised hyperthermia, which sensitises the tumour to the effects of radiotherapy. Clinical trials reported thus far are promising, with an increase in patient survival rate; however, what are left unaddressed are the implications of this technology on the surrounding healthy tissue.

METHODS AND MATERIALS

Aminosilane-coated iron oxide nanoparticles suspended in culture medium were applied to chick embryonic cortical neuron cultures. Cultures were heated to 37 °C or 45 °C by an induction coil system for 2 h. The latter regime emulates the therapeutic conditions of the adjunctive therapy. Cellular viability and neurite retraction was quantified 24 h after exposure to the hyperthermic events.

RESULTS

The hyperthermic load inflicted little damage to the neuron cultures, as determined by calcein-AM, propidium iodide, and alamarBlue® assays. Fluorescence imaging was used to assess the extent of neurite retraction which was found to be negligible.

CONCLUSIONS

Retention of chick, embryonic cortical neuron viability was confirmed under the thermal conditions produced by radiofrequency stimulation of iron oxide nanoparticles. While these results are not directly applicable to clinical applications of hyperthermia, the thermotolerance of chick embryonic cortical neurons is promising and calls for further studies employing human cultures of neurons and glial cells.

Study of the one dimensional and transient bioheat transfer equation: multi-layer solution development and applications

In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multiphysics v4.1©.

An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle

This study analytically analyzes the changes in the temperature profile of a homogenous and isotropic medium having the same thermal parameters as a muscular tissue, due to the heat released by a single magnetic nanoparticle (MNP) to its surroundings when subject to different magnetic field profiles. Exploring the temperature behavior of a heated MNP can be very useful predicting the temperature increment of it immediate surroundings. Therefore, selecting the most effective magnetic field profile (MFP) in order to reach the necessary temperature for cancer therapy is crucial in hyperthermia treatments. In order to find the temperature profile caused by the heated MNP immobilized inside a homogenous medium, the 3D diffusive-heat-flow equation (DHFE) was solved for three different types of boundary conditions (BCs). The change in the BC is caused by the different MF profiles (MFP), which are analyzed in this article. The analytic expressions are suitable for describing the transient temperature response of the medium for each case. The analysis showed that the maximum temperature increment surrounding the MNP can be achieved by radiating periodic magnetic pulses (PMPs) on it, making this MFP more effective than the conventional cosine profile.

The ability of different areas of the skin to absorb heat from a locally applied heat source: the impact of diabetes

BACKGROUND

When heat is applied to the skin, heat is conducted away because of the latent heat transfer properties of the skin and an increase in skin circulation, but little attention has been paid to the heat transfer properties of skin in different areas of the body and in people with diabetes. research design: Thirty subjects in the age range of 20-75 years had a thermode (44°C) applied to the skin of their arm, leg, foot, and back for 6 min to assess the heat transfer characteristics of skin in these four areas of the body. Skin blood flow and skin temperature were monitored over the 6-min period.

RESULTS

For the younger subjects, blood flow was not statistically different in response to heat in three areas of the body, starting at less than 200 flux measured by a laser Doppler imager and ending at approximately 1,200 flux after heat exposure. The foot had higher resting blood flow and higher blood flow in response to heat. Temperature and the rate of rise of temperature were also not different in any of the areas. The heat added to raise temperature, however, varied by body region. The arm required the least, whereas the leg and foot required the most. For the older group and subjects with diabetes, the heat required for any region of the body was much less to achieve the same increase in skin temperature, and blood flows were also much less; the subjects with diabetes showed the least blood flow and required the fewest calories to heat the skin. Whereas the foot required the greatest number of calories to heat the tissue in younger and older subjects, in subjects with diabetes, the foot took proportionally fewer calories.

CONCLUSION

Thus, specific areas of the body are damaged more by diabetes than other areas.

The contribution of skin blood flow in warming the skin after the application of local heat; the duality of the Pennes heat equation

As predicted by the Pennes equation, skin blood flow is a major contributor to the removal of heat from an external heat source. This protects the skin from erythema and burns. But, for a person in a thermally neutral room, the skin is normally much cooler than arterial blood. Therefore, if skin blood flow (BF) increases, it should initially warm the skin paradoxically. To examine this phenomenon, 10 young male and female subjects participated in a series of experiments to examine the contribution of skin blood flow in the initial warming the skin after the application of local heat. Heat flow was measured by the use of a thermode above the brachioradialis muscle. The thermode was warmed by constant temperature water at 44°C entering the thermode at a water flow rate of 100 cm(3)/min. Skin temperature was measured by a thermistor and blood flow in the underlying skin was measured by a laser Doppler imager in single point mode. The results of the experiments showed that, when skin temperature is cool (31-32°C), the number of calories being transferred to the skin from the thermode cannot account for the rise in skin temperature alone. A significant portion of the rise in skin temperature is due to the warm arterialized blood traversing the skin from the core areas of the body. However, as skin temperature approaches central core temperature, it becomes less of a heat source and more of a heat sync such that when skin temperature is at or above core temperature, the blood flow to the skin, as predicted by Pennes, becomes a heat sync pulling heat from the thermode.