Pennes' bioheat equation vs. porous media approach in computer modeling of radiofrequency tumor ablation

Advances in screening hyperthermic nanomedicines in 3D tumor models

Hyperthermic nanomedicines are particularly relevant for tackling human cancer, providing a valuable alternative to conventional therapeutics. The early-stage preclinical performance evaluation of such anti-cancer treatments is conventionally performed in flat 2D cell cultures that do not mimic the volumetric heat transfer occurring in human tumors. Recently, improvements in bioengineered 3D in vitro models have unlocked the opportunity to recapitulate major tumor microenvironment hallmarks and generate highly informative readouts that can contribute to accelerating the discovery and validation of efficient hyperthermic treatments. Leveraging on this, herein we aim to showcase the potential of engineered physiomimetic 3D tumor models for evaluating the preclinical efficacy of hyperthermic nanomedicines, featuring the main advantages and design considerations under diverse testing scenarios. The most recent applications of 3D tumor models for screening photo- and/or magnetic nanomedicines will be discussed, either as standalone systems or in combinatorial approaches with other anti-cancer therapeutics. We envision that breakthroughs toward developing multi-functional 3D platforms for hyperthermia onset and follow-up will contribute to a more expedited discovery of top-performing hyperthermic therapies in a preclinical setting before their in vivo screening.

Ultrasound-mediated nano-sized drug delivery systems for cancer treatment: Multi-scale and multi-physics computational modeling

Computational modeling enables researchers to study and understand various complex biological phenomena in anticancer drug delivery systems (DDSs), especially nano-sized DDSs (NSDDSs). The combination of NSDDSs and therapeutic ultrasound (TUS), that is, focused ultrasound and low-intensity pulsed ultrasound, has made significant progress in recent years, opening many opportunities for cancer treatment. Multiple parameters require tuning and optimization to develop effective DDSs, such as NSDDSs, in which mathematical modeling can prove advantageous. In silico computational modeling of ultrasound-responsive DDS typically involves a complex framework of acoustic interactions, heat transfer, drug release from nanoparticles, fluid flow, mass transport, and pharmacodynamic governing equations. Owing to the rapid development of computational tools, modeling the different phenomena in multi-scale complex problems involved in drug delivery to tumors has become possible. In the present study, we present an in-depth review of recent advances in the mathematical modeling of TUS-mediated DDSs for cancer treatment. A detailed discussion is also provided on applying these computational models to improve the clinical translation for applications in cancer treatment. This article is categorized under: Nanotechnology Approaches to Biology > Nanoscale Systems in Biology Therapeutic Approaches and Drug Discovery > Nanomedicine for Oncologic Disease.

Microwave ablation modeling with AMICA antenna: Validation by means a numerical analysis

BACKGROUND AND OBJECTIVES

Percutaneous microwave thermal ablation is based on electromagnetic waves that generate dielectric heating, and it is widely recognized as one of the mostly used techniques for tumor treatment. The aim of this work is to validate a predictive model capable of providing physicians with guidelines to be used during thermal ablation procedures avoiding collateral damage.

METHODS

A finite element commercial software, COMSOL Multiphysics, is employed to implement a tuning-parameter approach. Governing equations are written with reference to variable-porosity and Local Thermal Non-Equilibrium (LTNE) equations are employed. The simulations results are compared with available ex-vivo and in-vivo data with the help of regression analysis. For in-vivo data simulations, velocity vector modulus and direction are varied between 0.0007 and 0.0009 m/s and 90-270°, respectively, in order to use this parameter as a tuning one to simulate - and lately optimize with respect to the differences from experimental outcomes - all the possible directions of the blood flow with respect to the antenna, whose insertion angle is not registered in the dataset.

RESULTS

The model is validated using reference data provided by the manufacturer (AMICA), which is obtained from ex-vivo bovine liver. The model accurately predicts the size and shape of the ablated area, resulting in an overestimation lesser than 10 %. Additionally, predictive data are compared to an in-vivo dataset. The ablated volume is accurately predicted with a mean underestimation of 6 %. The sphericity index is calculated as 0.75 and 0.62 for the predictions and in-vivo data, respectively.

CONCLUSION

This study developed a predictive model for microwave ablation of liver tumors that showed good performance in predicting ablation dimensions and sphericity index for ex-vivo bovine liver and for in-vivo human liver data with the tuning technique. The study emphasizes the necessity for additional development and validation to enhance the accuracy and reliability of in-vivo application.

Effect of collision, size, and oscillation of RBCs on blood heat transfer in a bifurcated vessel

This study attempts to analyze the effect of red blood cells (RBCs) on blood heat transfer in a three-dimensional bifurcated vessel when treated with hyperthermia procedure. A two-phase granular model is used in this paper to study the various underlying factors that affect the flow dynamics of RBCs in a blood vessel. Separate cases are analyzed to study the effect of RBC size, RBC-RBC, and RBC-wall collision and oscillation on heat transfer in a three-dimensional bifurcated vessel under pulsatile flow condition. Blood temperature and transient Nusselt number are used as heat transfer representative parameters. A good agreement with the experimental results from the existing literature is observed when the numerical model used in this study is compared for accuracy. From this study, it has been found that an increase in the size of RBCs of a blood disorder patient can decrease the temperature of blood compared to a normal patient when subjected to hyperthermia treatment. A change in the nature of collision between RBCs does not affect the heat transfer of blood under pulsatile flow condition in a bifurcated vessel. Also, an increase in granular temperature or oscillation of RBCs slightly increases the blood temperature when exposed to thermal treatment.

Emprint Microwave Thermoablation System: Bridging Thermal Ablation Efficacy between Human Patients and Porcine Models through Mathematical Correlation

To investigate the in vivo ablation characteristics of a microwave ablation antenna in the livers of humans with tumors, a retrospective analysis of the ablation zones was conducted after applying Emprint microwave ablation systems for treatment. Percutaneous microwave ablations performed between January 2022 and September 2022 were included in this study. Subsequently, immediate post-ablation echography images were subjected to retrospective evaluation to state the long ablated diameter, short ablated diameter, and volume. The calculated ablation lengths and volume indices were then compared between in vivo and ex vivo results obtained from laboratory experiments conducted on porcine liver. The ex vivo data showed a good correlation between energy delivered and both increasing ablated dimensions (both p < 0.001) and volume (p < 0.001). The in vivo data showed a good correlation for dimensions (p = 0.037 and p = 0.019) and a worse correlation for volume (p = 0.142). When comparing ex vivo and in vivo data for higher energies, the ablated volumes grew much more rapidly in ex vivo cases compared to in vivo ones. Finally, a set of correlations to scale ex vivo results with in vivo ones is presented. This phenomenon was likely due to the absence of perfusion, which acts as a cooling system.

A 3D Approach Using a Control Algorithm to Minimize the Effects on the Healthy Tissue in the Hyperthermia for Cancer Treatment

According to the World Health Organization, cancer is a worldwide health problem. Its high mortality rate motivates scientists to study new treatments. One of these new treatments is hyperthermia using magnetic nanoparticles. This treatment consists in submitting the target region with a low-frequency magnetic field to increase its temperature over 43 °C, as the threshold for tissue damage and leading the cells to necrosis. This paper uses an in silico three-dimensional Pennes' model described by a set of partial differential equations (PDEs) to estimate the percentage of tissue damage due to hyperthermia. Differential evolution, an optimization method, suggests the best locations to inject the nanoparticles to maximize tumor cell death and minimize damage to healthy tissue. Three different scenarios were performed to evaluate the suggestions obtained by the optimization method. The results indicate the positive impact of the proposed technique: a reduction in the percentage of healthy tissue damage and the complete damage of the tumors were observed. In the best scenario, the optimization method was responsible for decreasing the healthy tissue damage by 59% when the nanoparticles injection sites were located in the non-intuitive points indicated by the optimization method. The numerical solution of the PDEs is computationally expensive. This work also describes the implemented parallel strategy based on CUDA to reduce the computational costs involved in the PDEs resolution. Compared to the sequential version executed on the CPU, the proposed parallel implementation was able to speed the execution time up to 84.4 times.

Magnetothermal-based non-invasive focused magnetic stimulation for functional recovery in chronic stroke treatment

Magnetic heat-based brain stimulation of specific lesions could promote the restoration of impaired motor function caused by chronic stroke. We delivered localized stimulation by nanoparticle-mediated heat generation within the targeted brain area via focused magnetic stimulation. The middle cerebral artery occlusion model was prepared, and functional recovery in the chronic-phase stroke rat model was demonstrated by the therapeutic application of focused magnetic stimulation. We observed a transient increase in blood-brain barrier permeability at the target site of < 4 mm and metabolic brain activation at the target lesion. After focused magnetic stimulation, the rotarod score increased by 390 ± 28% (p < 0.05) compared to the control group. Standardized uptake value in the focused magnetic stimulation group increased by 2063 ± 748% (p < 0.01) compared to the control group. Moreover, an increase by 24 ± 5% (p < 0.05) was observed in the sham group as well. Our results show that non-invasive focused magnetic stimulation can safely modulate BBB permeability and enhance neural activation for chronic-phase stroke treatment in the targeted deep brain area.

Effects of Pulsed Radiofrequency Source on Cardiac Ablation

Heart arrhythmia is caused by abnormal electrical conduction through the myocardium, which in some cases, can be treated with heat. One of the challenges is to reduce temperature peaks-by still guaranteeing an efficient treatment where desired-to avoid any healthy tissue damage or any electrical issues within the device employed. A solution might be employing pulsed heat, in which thermal dose is given to the tissue with a variation in time. In this work, pulsed heat is used to modulate induced temperature fields during radiofrequency cardiac ablation. A three-dimensional model of the myocardium, catheter and blood flow is developed. Porous media, heat conduction and Navier-Stokes equations are, respectively, employed for each of the investigated domains. For the electric field, solved via Laplace equation, it is assumed that the electrode is at a fixed voltage. Pulsed heating effects are considered with a cosine time-variable pulsed function for the fixed voltage by constraining the product between this variable and time. Different dimensionless frequencies are considered and applied for different blood flow velocity and sustained voltages. Results are presented for different pulsed conditions to establish if a reasonable ablation zone, known from the obtained temperature profiles, can be obtained without any undesired temperature peaks.

Heat distribution and the condition of hypothermia in the multi-layered human head: A mathematical model

The conduction, perfusion and metabolic heat generation based partial differential equation has been used to study the heat transfer in human head. The main objective of this study is to predict the temperature distribution at the multi-layered human head that results in hypothermic condition. The temperature profiles have been estimated at the interface points of brain, skull and scalp with respect to various parameters including atmospheric temperature, arterial temperature and metabolic heat generation. The variational finite element method and analytical method based on Laplace transform has been employed to establish the solution of the formulated model, and the resulting outcomes are illustrated graphically. Under cold exposure, the blood capillaries around scalp exchange core heat with the external cold environment and experience lowering in the tissue temperature of the blood in the scalp. It is reflected in the graphical view of the model that the prolonged exposure to cold transmits its effect into the deep brain capillaries, wherein the temperature gradually lowers down below the normal body temperature that results hypothermia and hence abnormal body homoeostasis.

Photothermal conversion and transfer in photothermal therapy: From macroscale to nanoscale

Photothermal therapy (PTT) is a promising alternative therapy for benign or even malignant tumors. To improve the selective heating of tumor cells, target-specific photothermal conversion agents are often included, especially nanoparticles. Meanwhile, some indirect methods by manipulating the radiation and heat delivery are also adopted. Therefore, to gain a clear understanding of the mechanism, and to improve the controllability of PTT, a few issues need to be clarified, including bioheat and radiation transfer, localized and collective heating of nanoparticles, etc. In this review, we provide an introduction to the typical bioheat transfer and radiation transfer models along with the dynamic thermophysical properties of biological tissue. On this basis, we reviewed the most recent advances in the temperature control methods in PTT from macroscale to nanoscale. Most importantly, a comprehensive introduction of the localized and collective heating effects of nanoparticle clusters is provided to give a clear insight into the mechanism for PPT from the microscale and nanoscale point of view.

Study of heat sink effect of blood in a bifurcated vessel

Thermal ablation treatment uses elevated (hyperthermia) or depressed (hypothermia) tissue temperature to destroy tumor cells. The efficacy and effectiveness of thermal ablation therapy is dependent on the tissue temperature which is significantly affected due to heat sink effect of blood flow near the infected site. In this study, Euler-Euler multiphase model is used to analyze the effect of plasma and RBC concentration on the heat sink effect of blood in a bifurcated vessel. This study is divided into two separate cases. First case refers to the study of heat sink effect produced by a tumor patient suffering from HVS (hyperviscosity syndrome) and a normal (without blood disorder) tumor patient during hyperthermia treatment. The second case analyses the effect of RBCs on blood heat transfer. Temperature distribution and transient Nusselt number, which are used to represent heat sink effect, are calculated and compared for different cases of blood disorders. From the results, it is found that a patient with HVS blood disorder produces a smaller heat sink effect during hyperthermia treatment compared to a normal tumor patient. Also, the level of RBC concentration in the blood stream has a minimal effect on heat transfer.

A computational framework to simulate the thermochemical process during thermochemical ablation of biological tissues

Thermochemical ablation (TCA) is a thermal ablation therapy that utilises heat released from acid-base neutralisation reaction to destroy tumours. This procedure is a promising low-cost solution to existing thermal ablation treatments such as radiofrequency ablation (RFA) and microwave ablation (MWA). Studies have demonstrated that TCA can produce thermal damage that is on par with RFA and MWA when employed properly. Nevertheless, TCA remains a concept that is tested only in a few animal trials due to the risks involved as the result of uncontrolled infusion and incomplete acid-base reaction. In this study, a computational framework that simulates the thermochemical process of TCA is developed. The proposed framework consists of three physics, namely chemical flow, neutralisation reaction and heat transfer. An important parameter in the TCA framework is the neutralisation reaction rate constant, which has values in the order of 10⁸ m³/(mol⋅s). The present study will demonstrate that since the rate constant impacts only the rate and direction of the reaction but has little influence on the extent of reaction, it is possible to replicate the thermochemical process of TCA by employing significantly smaller values of rate constant that are numerically tractable. Comparisons of the numerical results against experimental studies from the literature supports this. The aim of this framework is for researchers to advance and develop TCA to gain an in-depth understanding of the fundamental mechanisms of TCA and to develop a safe treatment protocol of TCA in the hope of advancing TCA into clinical trials.

Mathematical modeling of microwave liver ablation with a variable-porosity medium approach

BACKGROUND AND OBJECTIVES

Thermal ablation of tumors plays a key role to fight cancer, since it is a minimally invasive treatment which involves some advantages compared to surgery and chemotherapy, such as shorter hospital stays and consequently lower costs, along with minor side effects. In this context, computational modeling of heat transfer during thermal ablation is relevant to accurately predict the obtained ablation zone in order to avoid tumor recurrence risk caused by incomplete ablation, and the same time to save the surrounding healthy tissue. The aim of this work is to develop a more realistic porous media-based mathematical model to simulate a microwave thermal ablation (MWA) of an in vivo liver tumor surrounded by healthy tissue.

METHODS

The domain is made up of a spherical tumor bounded by a cylindrical healthy liver tissue. The simulated microwave antenna is a 14 G HS Amica-Gen Probe, and the supplied power of 60 W is applied for 300 s and 600 s. The model consists in coupling modified Local Thermal Non Equilibrium (LTNE) equations with the electromagnetic equations. The LTNE equations include a variable porosity function which fits the porosity changing from the tumor core to the rim based on experimental measures in in vivo cases. Moreover, four different blood vessels' uniform distributions are investigated to compare the effects of different vascularizations of the considered target tissue.

RESULTS

The results are shown in terms of temperature fields, ablation diameters and volumes based on the Arrhenius thermal damage model with 99% of cell death probability. The outcomes show a very good agreement with a clinical study on human patients with hepatocellular carcinoma using the same antenna and energy setting, when terminal arteries distribution is included.

CONCLUSIONS

In this work, an in vivo microwave ablation of liver tumor surrounded by healthy tissue is modeled with a variable-porosity medium approach based on experimental measures. The outcomes shown for distinct vascularizations underline the key relevance of modeling more and more accurately tumor MWA, by considering increasingly realistic features, avoiding tumor recurrence, and improving both medical protocols and devices.

A New Thermal Damage-Controlled Protocol for Thermal Ablation Modeled with Modified Porous Media-Based Bioheat Equation with Variable Porosity

Thermal ablation of tumors is a minimally invasive technique more and more employed in cancer treatments. The main shortcomings of this technique are, on the one hand, the risk of an incomplete ablation, and on the other hand, the destruction of the surrounding healthy tissue. In this work, thermal ablation of a spherical hepatocellular carcinoma tumor (HCC) surrounded by healthy tissue is modeled. A modified porous media-based bioheat model is employed, including porosity variability from tumor core to healthy tissue, following experimental in vivo measures. Moreover, three different protocols are investigated: a constant heating protocol, a pulsating protocol, and a new developed damage-controlled protocol. The proposed damage-controlled protocol changes the heating source from constant to pulsating according to the thermal damage probability on the tumor rim. The equations are numerically solved by means of the commercial software COMSOL Multiphysics, and the outcomes show that the new proposed protocol is able to achieve the complete ablation in less time than the completely pulsating protocol, and to reach tissue temperature on the tumor rim 10 °C smaller than the constant protocol. These results are relevant to develop and improve different patient-based and automated protocols which can be embedded in medical devices’ software or in mobile applications, supporting medical staff with innovative technical solutions.

RapidET: a MEMS-based platform for label-free and rapid demarcation of tumors from normal breast biopsy tissues

The rapid and label-free diagnosis of malignancies in ex vivo breast biopsy tissues has significant utility in pathology laboratories and operating rooms. We report a MEMS-based platform integrated with microchips that performs phenotyping of breast biopsy tissues using electrothermal sensing. The microchip, fabricated on a silicon substrate, incorporates a platinum microheater, interdigitated electrodes (IDEs), and resistance temperature detectors (RTDs) as on-chip sensing elements. The microchips are integrated onto the platform using a slide-fit contact enabling quick replacement for biological measurements. The bulk resistivity (ρ B ), surface resistivity (ρ S ), and thermal conductivity (k) of deparaffinized and formalin-fixed paired tumor and adjacent normal breast biopsy samples from N = 8 patients were measured. For formalin-fixed samples, the mean ρ B for tumors showed a statistically significant fold change of 4.42 (P = 0.014) when the tissue was heated from 25 °C to 37 °C compared to the adjacent normal tissue, which showed a fold change of 3.47. The mean ρ S measurements also showed a similar trend. The mean k of the formalin-fixed tumor tissues was 0.309 ± 0.02 W m-1 K-1 compared to a significantly higher k of 0.563 ± 0.028 W m-1 K-1 for the adjacent normal tissues. A similar trend was observed in ρ B, ρ S, and k for the deparaffinized tissue samples. An analysis of a combination of ρ B , ρ S , and k using Fisher's combined probability test and linear regression suggests the advantage of using all three parameters simultaneously for distinguishing tumors from adjacent normal tissues with higher statistical significance.

Heat Transfer in Biological Spherical Tissues during Hyperthermia of Magnetoma

Hyperthermia therapy is now being used to treat cancer. However, understanding the pattern of temperature increase in biological tissues during hyperthermia treatment is essential. In recent years, many physicians and engineers have studied the use of computational and mathematical models of heat transfer in biological systems. The rapid progress in computing technology has intrigued many researchers. Many medical procedures also use engineering techniques and mathematical modeling to ensure their safety and assess the risks involved. One such model is the modified Pennes bioheat conduction equation. This paper provides an analytical solution to the modified Pennes bioheat conduction equation with a single relaxation time by incorporating in it the (MGT) equation. The suggested model examines heat transport in biological tissues as forming an infinite concentric spherical region during magnetic fluid hyperthermia. To investigate thermal reactions caused by temperature shock, specifically the influence of heat generation through heat treatment on a skin tumor [AEGP9], the Laplace transformation, and numerical inverse transformation methods are used. This model was able to explain the effects of different therapeutic approaches such as cryotherapy sessions, laser therapy, and physical occurrences, transfer, metabolism support, and blood perfusion. Comparison of the numerical results of the suggested model with those in the literature confirmed the validity of the model's numerical results.

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.

Fluid–Structure Interaction and Non-Fourier Effects in Coupled Electro-Thermo-Mechanical Models for Cardiac Ablation

In this study, a fully coupled electro-thermo-mechanical model of radiofrequency (RF)-assisted cardiac ablation has been developed, incorporating fluid–structure interaction, thermal relaxation time effects and porous media approach. A non-Fourier based bio-heat transfer model has been used for predicting the temperature distribution and ablation zone during the cardiac ablation. The blood has been modeled as a Newtonian fluid and the velocity fields are obtained utilizing the Navier–Stokes equations. The thermal stresses induced due to the heating of the cardiac tissue have also been accounted. Parametric studies have been conducted to investigate the effect of cardiac tissue porosity, thermal relaxation time effects, electrode insertion depths and orientations on the treatment outcomes of the cardiac ablation. The results are presented in terms of predicted temperature distributions and ablation volumes for different cases of interest utilizing a finite element based COMSOL Multiphysics software. It has been found that electrode insertion depth and orientation has a significant effect on the treatment outcomes of cardiac ablation. Further, porosity of cardiac tissue also plays an important role in the prediction of temperature distribution and ablation volume during RF-assisted cardiac ablation. Moreover, thermal relaxation times only affect the treatment outcomes for shorter treatment times of less than 30 s.

A Computational Study on the Role of Parameters for Identification of Thyroid Nodules by Infrared Images (and Comparison with Real Data)

According to experts and medical literature, healthy thyroids and thyroids containing benign nodules tend to be less inflamed and less active than those with malignant nodules. It seems to be a consensus that malignant nodules have more blood veins and more blood circulation. This may be related to the maintenance of the nodule's heat at a higher level compared with neighboring tissues. If the internal heat modifies the skin radiation, then it could be detected by infrared sensors. The goal of this work is the investigation of the factors that allow this detection, and the possible relation with any pattern referent to nodule malignancy. We aim to consider a wide range of factors, so a great number of numerical simulations of the heat transfer in the region under analysis, based on the Finite Element method, are performed to study the influence of each nodule and patient characteristics on the infrared sensor acquisition. To do so, the protocol for infrared thyroid examination used in our university's hospital is simulated in the numerical study. This protocol presents two phases. In the first one, the body under observation is in steady state. In the second one, it is submitted to thermal stress (transient state). Both are simulated in order to verify if it is possible (by infrared sensors) to identify different behavior referent to malignant nodules. Moreover, when the simulation indicates possible important aspects, patients with and without similar characteristics are examined to confirm such influences. The results show that the tissues between skin and thyroid, as well as the nodule size, have an influence on superficial temperatures. Other thermal parameters of thyroid nodules show little influence on surface infrared emissions, for instance, those related to the vascularization of the nodule. All details of the physical parameters used in the simulations, characteristics of the real nodules and thermal examinations are publicly available, allowing these simulations to be compared with other types of heat transfer solutions and infrared examination protocols. Among the main contributions of this work, we highlight the simulation of the possible range of parameters, and definition of the simulation approach for mapping the used infrared protocol, promoting the investigation of a possible relation between the heat transfer process and the data obtained by infrared acquisitions.