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.

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

The objective of this study was to compare three different heat transfer models for radiofrequency ablation of in vivo liver tissue using a cooled electrode and three different voltage levels. The comparison was between the simplest but less realistic Pennes' equation and two porous media-based models, i.e. the Local Thermal Non-Equilibrium (LTNE) equations and Local Thermal Equilibrium (LTE) equation, both modified to take into account two-phase water vaporization (tissue and blood). Different blood volume fractions in liver were considered and the blood velocity was modeled to simulate a vascular network. Governing equations with the appropriate boundary conditions were solved with Comsol Multiphysics finite-element code. The results in terms of coagulation transverse diameters and temperature distributions at the end of the application showed significant differences, especially between Pennes and the modified LTNE and LTE models. The new modified porous media-based models covered the ranges found in the few in vivo experimental studies in the literature and they were closer to the published results with similar in vivo protocol. The outcomes highlight the importance of considering the three models in the future in order to improve thermal ablation protocols and devices and adapt the model to different organs and patient profiles.

Numerical analysis of the pulsating heat source effects in a tumor tissue.

BACKGROUND AND OBJECTIVES: Hyperthermia treatment is nowadays recognized as the fourth additional cancer therapy technique following surgery, chemotherapy, and radiation; it is a minimally or non-invasive technique which involves fewer complications, a shorter hospital stay, and fewer costs. In this paper, pulsating heat effects on heat transfer in a tumor tissue under hyperthermia are analyzed. The objective of the paper is to find and quantify the advantages of pulsatile heat protocols under different periodical heating schemes and for different tissue morphologies. METHODS: The tumor tissue is modeled as a porous sphere made up of a solid phase (tissue, interstitial space, etc.) and a fluid phase (blood). A Local Thermal Non-Equilibrium (LTNE) model is employed to consider the local temperature difference between the two phases. Governing equations with the appropriate boundary conditions are solved with the finite-element code COMSOL Multiphysics®. The pulsating effect is modeled with references to a cosine function with different frequencies, and such different heating protocols are compared at equal delivered energy, i. e. different heating times at equal maximum power. RESULTS: Different tissue properties in terms of blood vessels sizes and blood volume fraction in tissue (porosity) are investigated. The results are shown in terms of tissue temperature and percentage of necrotic tissue obtained. The most powerful result achieved using a pulsating heat source instead of a constant one is the decreasing of maximum temperature in any considered case, even reaching about 30% lower maximum temperatures. Furthermore, the evaluation of tissue damage at the end of treatment shows that pulsating heat allows to necrotize the same tumoral tissue area of the non-pulsating heat source. CONCLUSIONS: Modeling pulsating heat protocols in thermal ablation under different periodical heating schemes and considering different tissues morphologies in a tumor tissue highlights how the application of pulsating heat sources allows to avoid high temperature peaks, and simultaneously to ablate the same tumoral area obtained with a non-pulsating heat source. This is a powerful result to improve medical protocols and devices in thermal ablation of tumors.

Modeling Heat Transfer in Tumors: A Review of Thermal Therapies.

It is quite challenging to describe heat transfer phenomena in living systems because of the involved phenomena complexity. Indeed, thermal conduction and convection in tissues, blood perfusion, heat generation due to metabolism, complex vascular structure, changing of tissue properties depending on various conditions, are some of the features that make hard to obtain an accurate knowledge of heat transfer in living systems for all the clinical situations. This theme has a key role to predict accurately the temperature distribution in tissues, especially during biomedical applications, such as hyperthermia treatment of cancer, in which tumoral cells have to be destroyed and at the same time the surrounding healthy tissue has to be preserved. Moreover, the lack of experimentation in this field, due to ethical reasons, makes bioheat models even more significant. The first simple bioheat model was developed in 1948 by Pennes (J Appl Physiol 1:93-122, 1948) but it has some shortcomings that make the equation not so accurate. For this reason, over the years it has been modified and more complex models have been developed. The purpose of this review is to give a clear overview of how the bioheat models have been modified when applied in various hyperthermia treatments of cancer.