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

Generalized thermomechanical interaction in two-dimensional skin tissue using eigenvalues approach

The aim of this work is to analytically study the thermo-mechanical response of two-dimensional skin tissues when subjected to instantaneous heating. A complete understanding of the heat transfer process and the associated thermal and mechanical effects on the patient's skin tissues is critical to ensuring the effective applications of thermal therapy techniques and procedures. The surface boundary of the half-space undergoes a heat flux characterized by an exponentially decaying pulse, while maintaining a condition of zero traction. The utilization of Laplace and Fourier transformations is employed, and the resulting formulations are then applied to human tissues undergoing regional hyperthermia treatment for cancer therapy. To perform the inversion process for Laplace and Fourier transforms, a numerical programming method based on Stehfest numerical inverse method is employed. The findings demonstrate that blood perfusion rate and thermal relaxation time significantly influence all the analyzed distributions. Numerical findings suggest that thermo-mechanical waves propagate through skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model.

Simulating radiofrequency ablation of hepatocellular carcinomas proximal to bare area of liver

PURPOSE

To numerically assess the significance of dextrose 5% in water (D5W) thermo-protection during radiofrequency ablation (RFA) of hepatocellular carcinomas (HCCs) located near the 'bare area of liver'.

MATERIAL AND METHODS

This study utilises quasi-anatomical structures extracted from CT images. A multi-tine electrode, deployed inside the extracted organs and operated under temperature-controlled mode was used as the source of ablation. Geometrically, D5W was modelled around the 'bare area' and sandwiched between the liver and diaphragm. RFA at different sites relative to the 'bare area' was simulated to answer when to consider modelling D5W.

RESULTS

For targets near the edge of 'bare area' and at 0.5 mm gap (between the electrode and the 'bare area'), ignoring D5W and using ground conditions could result in underestimation of ablation volume by almost 25%. The importance of D5W becomes negligible for ablations near the centre of the 'bare area'.

CONCLUSIONS

Consideration of D5W during RFA of HCCs proximal to the 'bare area' can significantly influence the ablation outcome, especially when ablation is performed near the edge of the 'bare area'.

Directional ablation in radiofrequency ablation using a multi-tine electrode functioning in multipolar mode: An in-silico study using a finite set of states

PURPOSE

To analyse the feasibility of directional ablation using a multi-tine electrode.

METHODS

A multi-tine electrode capable of operating in multipolar mode has been used to study the directional ablation. In addition to the basic design, similar to commercially available FDA approved multi-tine electrode, tines have been insulated from each other inside the probe base and tip using a thin insulating material of thickness 0.25 mm. A cylindrical single-compartment model of size 6 cm × 6 cm has been used to model normal liver tissue. The temperature-controlled radiofrequency ablation has been employed to maintain the tine-tips at different temperatures. Electro-thermal simulations have been performed by using a commercial multi-physics software package based on finite element methods. To make this study feasible a new approach to predict the ablations have been proposed and used in this study.

RESULTS

Asymmetric ablation zone with up to 5 mm difference in ablation boundary between the intended and non-intended direction has been observed along the transverse direction. Reduction in ablation up to 5 mm along the axial direction in comparison to the monopolar mode has also been observed.

CONCLUSION

Multi-tine electrode modified to operate in multipolar mode can create directional ablations of different shapes and can be used to target position and shape specific tumours.

RF-energised intracoronary guidewire to enhance bipolar ablation of the interventricular septum: in-silico feasibility study

PURPOSE

Although bipolar radiofrequency (RF) ablation (RFA) is broadly used to eliminate ventricular tachycardias in the interventricular septum wall, it can fail to create transmural lesions in thick ventricular walls. To solve this problem, we explored whether an RF-energised guidewire inserted into the ventricular wall would enhance bipolar RFA in the creation of transmural lesions through the ventricular wall.

METHODS

We built three-dimensional computational models including two irrigated electrodes placed on opposing sides of the interventricular septum and a metal guidewire inserted into the septum. Computer simulations were conducted to compare the temperature distributions obtained with two ablation modes: bipolar mode (RF power delivered between both irrigated electrode) and time-division multiplexing (TDM) technique, which consists of activating the bipolar mode for 90% of the time and applying RF power between the guidewire and both irrigated electrodes during the remaining time.

RESULTS

The TDM technique was the most suitable in terms of creating wider lesions through the entire ventricular wall, avoiding the hour-glass shape of thermal lesions associated with the bipolar mode. This was especially apparent in the case of thick walls (15 mm). Furthermore, the TDM technique was able to create transmural lesions even when the guidewire was displaced from the midplane of the wall.

CONCLUSIONS

An RF-energised guidewire could enhance bipolar RFA by allowing transmural lesions to be made through thick ventricular walls. However, the safety of this new approach must be assessed in future pre-clinical studies, especially in terms of the risk of stenosis and its clinical impact.

Relation between denaturation time measured by optical coherence reflectometry and thermal lesion depth during radiofrequency cardiac ablation: Feasibility numerical study

BACKGROUND/OBJECTIVE

Radiofrequency (RF) catheter ablation is a minimally invasive medical procedure used to thermally destroy the focus of cardiac arrhythmias. Novel optical techniques are now being integrated into RF catheters in order to detect the changes in tissue properties. Loss of birefringence due to fiber denaturation at around 70°C is related to changes in accumulated phase retardation and can be measured by polarization-sensitive optical coherence reflectometry (PS-OCR). Since irreversible thermal lesions are produced when the tissue reaches 50°C, our goal was to seek the mathematical relationship between both isotherms.

MATERIALS AND METHODS

A two-dimensional model based on a coupled electric-thermal problem was built and solved using the finite element method. The model consisted of cardiac tissue, blood, and a non-irrigated electrode with a sensor embedded in its tip to maintain a specific target electrode temperature. Computer simulations were conducted by varying the tissue characteristics. Lesion depth was estimated by the 50°C isotherm, while the denaturation time (TD) was taken as the time at which the 70°C isotherm reached a depth of 0.75 mm (which corresponds to the optical depth reached by PS-OCR technology).

RESULTS

A strong correlation (R²  > 0.83) was found between TD and lesion depth and an even stronger correlation (R² > 0.96) was found between TD and the time required to achieve a specific lesion depth. For instance, the ablation time required to ensure a minimum lesion depth of 3 mm was 1.33 × TD + 3.93 × seconds.

CONCLUSIONS

The computer results confirmed the strong relationship between denaturation time and lesion depth and suggest that measuring denaturation time by PS-OCR could provide information on the ablation time required to reach a specific lesion depth. Lasers Surg. Med. 50:222-229, 2018. © 2017 Wiley Periodicals, Inc.

A methodology for constraining power in finite element modeling of radiofrequency ablation

Radiofrequency ablation (RFA) is a minimally invasive thermal therapy for the treatment of cancer, hyperopia, and cardiac tachyarrhythmia. In RFA, the power delivered to the tissue is a key parameter. The objective of this study was to establish a methodology for the finite element modeling of RFA with constant power. Because of changes in the electric conductivity of tissue with temperature, a nonconventional boundary value problem arises in the mathematic modeling of RFA: neither the voltage (Dirichlet condition) nor the current (Neumann condition), but the power, that is, the product of voltage and current was prescribed on part of boundary. We solved the problem using Lagrange multiplier: the product of the voltage and current on the electrode surface is constrained to be equal to the Joule heating. We theoretically proved the equality between the product of the voltage and current on the surface of the electrode and the Joule heating in the domain. We also proved the well-posedness of the problem of solving the Laplace equation for the electric potential under a constant power constraint prescribed on the electrode surface. The Pennes bioheat transfer equation and the Laplace equation for electric potential augmented with the constraint of constant power were solved simultaneously using the Newton-Raphson algorithm. Three problems for validation were solved. Numerical results were compared either with an analytical solution deduced in this study or with results obtained by ANSYS or experiments. This work provides the finite element modeling of constant power RFA with a firm mathematical basis and opens pathway for achieving the optimal RFA power.

A review of radiofrequency ablation: Large target tissue necrosis and mathematical modelling

Radiofrequency ablation (RFA) is an effective clinical method for tumour ablation with minimum intrusiveness. However, the use of RFA is mostly restricted to small tumours, especially those <3cm in diameter. This paper discusses the state-of-the-art of RFA, drawn from experimental and clinical results, for large tumours (i.e. ⩾3cm in diameter). In particular, the paper analyses clinical results related to target tissue necrosis (TTN) and mathematical modelling of the RFA procedure to understand the mechanism whereby the TTN is limited to under 3cm with RFA. This paper also discusses a strategy of controlling of the temperature of target tissue in the RFA procedure with the state-of-art device, which has the potential to increase the size of TTN. This paper ends with a discussion of some future ideas to solve the so-called 3-cm problem with RFA.

Computer modelling of an impedance-controlled pulsing protocol for RF tumour ablation with a cooled electrode

PURPOSE

To develop computer models to mimic the impedance-controlled pulsing protocol implemented in radiofrequency (RF) generators used for clinical practice of radiofrequency ablation (RFA), and to assess the appropriateness of the models by comparing the computer results with those obtained in previous experimental studies.

METHODS

A 12-min RFA was modelled using a cooled electrode (17G, 3 cm tip) inserted in hepatic tissue. The short (transverse) diameter of the coagulation zone was assessed under in vivo (with blood perfusion (BP) and considering clamping) and ex vivo (at 21 °C) conditions. The computer results obtained by programming voltage pulses were compared with current pulses.

RESULTS

The differences between voltage and current pulses were noticeable: using current instead of voltage allows larger coagulation zones to be created, due to the higher energy applied by current pulses. If voltage pulses are employed the model can accurately predict the number of roll-offs, although the waveform of the applied power is clearly not realistic. If current voltages are employed, the applied power waveform matches well with those reported experimentally, but there are significantly fewer roll-offs. Our computer results were overall into the ranges of experimental ones.

CONCLUSIONS

The proposed models reproduce reasonably well the electrical-thermal performance and coagulation zone size obtained during an impedance-controlled pulsing protocol.

Experimental measurement of microwave ablation heating pattern and comparison to computer simulations

INTRODUCTION

For computational models of microwave ablation (MWA), knowledge of the antenna design is necessary, but the proprietary design of clinical applicators is often unknown. We characterised the specific absorption rate (SAR) during MWA experimentally and compared to a multi-physics simulation.

METHODS

An infrared (IR) camera was used to measure SAR during MWA within a split ex vivo liver model. Perseon Medical's short-tip (ST) or long-tip (LT) MWA antenna were placed on top of a tissue sample (n = 6), and microwave power (15 W) was applied for 6 min, while intermittently interrupting power. Tissue surface temperature was recorded via IR camera (3.3 fps, 320 × 240 resolution). SAR was calculated intermittently based on temperature slope before and after power interruption. Temperature and SAR data were compared to simulation results.

RESULTS

Experimentally measured SAR changed considerably once tissue temperatures exceeded 100 °C, contrary to simulation results. The ablation zone diameters were 1.28 cm and 1.30 ± 0.03 cm (transverse), and 2.10 cm and 2.66 ± -0.22 cm (axial), for simulation and experiment, respectively. The average difference in temperature between the simulation and experiment were 5.6 °C (ST) and 6.2 °C (LT). Dice coefficients for 1000 W/kg SAR iso-contour were 0.74 ± 0.01 (ST) and 0.77 (± 0.03) (LT), suggesting good agreement of SAR contours.

CONCLUSION

We experimentally demonstrated changes in SAR during MWA ablation, which were not present in simulation, suggesting inaccuracies in dielectric properties. The measured SAR may be used in simplified computer simulations to predict tissue temperature when the antenna geometry is unknown.

Numerical analysis of the relationship between the area of target tissue necrosis and the size of target tissue in liver tumours with pulsed radiofrequency ablation

PURPOSE

Radiofrequency ablation (RFA) is currently restricted to the treatment of target tissues with a small size (<3 cm in diameter). To overcome this problem with RFA, some phenomena need to be understood first. The study presented in this paper investigated the relationship between the area of target tissue necrosis (TTN) and the size of target tissue in pulsed radiofrequency ablation (PRFA).

MATERIALS AND METHODS

Liver tumour, one of the common targets of RFA in clinical practice, was used as the target tissue in this study. Two types of pulsed RF power supply methods (half-square and half-sine) and three target tissues with different sizes (25 mm, 30 mm and 35 mm in diameter) were studied using finite element modelling. The finite element model (FEM) was validated by using an in vitro experiment with porcine liver tissue. The first roll-off occurrence or 720 s, whichever occurs first, was chosen as the ablation termination criterion in this study.

RESULTS

For each target tissue size, the largest TTN area was obtained using the maximum voltage applied (MVA) without roll-off occurrence. In this study, target tissues with a 25 mm diameter can be ablated cleanly but target tissues with 30-mm and 35-mm failed to be ablated.

CONCLUSIONS

The half-square PRFA could achieve a larger TTN area than the half-sine PRFA. The MVA decreases with an increase in the target tissue diameter in both the half-square PRFA and the half-sine PRFA. The findings of this study are in agreement with the clinical results that lesions (≥ 3 cm in diameter) have less favourable results from RFA.

Mechanics and spiral formation in the rat cornea

During the maturation of some mammals such as mice and rats, corneal epithelial cells tend to develop into patterns such as spirals over time. A better understanding of these patterns can help to understand how the organ develops and may give insight into some of the diseases affecting corneal development. In this paper, a framework for explaining the development of the epithelial cells forming spiral patterns due to the effect of tensile and shear strains is proposed. Using chimeric animals, made by combining embryonic cells from genetically distinguishable strains, we can observe the development of patterns in the cornea. Aggregates of cell progeny from one strain or the other called patches form as organs and tissue develop. The boundaries of these patches are fitted with logarithmic spirals on confocal images of adult rat corneas. To compare with observed patterns, we develop a three-dimensional large strain finite element model for the rat cornea under intraocular pressure to examine the strain distribution on the cornea surface. The model includes the effects of oriented and dispersed fibrils families throughout the cornea and a nearly incompressible matrix. Tracing the directions of critical strain vectors on the cornea surface leads to spiral-like curves that are compared to the observed logarithmic spirals. Good agreement between the observed and numerical curves supports the proposed assumption that shear and tensile strains facilitate sliding of epithelial cells to develop spiral patterns.

Measurement of the anisotropic thermal conductivity of the porcine cornea

Accurate thermal models for the cornea of the eye support the development of thermal techniques for reshaping the cornea and other scientific purposes. Heat transfer in the cornea must be quantified accurately so that a thermal treatment does not destroy the endothelial layer, which cannot regenerate, and yet is responsible for maintaining corneal transparency. We developed a custom apparatus to measure the thermal conductivity of ex vivo porcine corneas perpendicular to the surface and applied a commercial apparatus to measure thermal conductivity parallel to the surface. We found that corneal thermal conductivity is 14% anisotropic at the normal state of corneal hydration. Small numbers of ex vivo feline and human corneas had a thermal conductivity perpendicular to the surface that was indistinguishable from the porcine corneas. Aqueous humor from ex vivo porcine, feline, and human eyes had a thermal conductivity nearly equal to that of water. Including the anisotropy of corneal thermal conductivity will improve the predictive power of thermal models of the eye.

Review of the mathematical functions used to model the temperature dependence of electrical and thermal conductivities of biological tissue in radiofrequency ablation

PURPOSE

Although theoretical modelling is widely used to study different aspects of radiofrequency ablation (RFA), its utility is directly related to its realism. An important factor in this realism is the use of mathematical functions to model the temperature dependence of thermal (k) and electrical (σ) conductivities of tissue. Our aim was to review the piecewise mathematical functions most commonly used for modelling the temperature dependence of k and σ in RFA computational modelling.

MATERIALS AND METHODS

We built a hepatic RFA theoretical model of a cooled electrode and compared lesion dimensions and impedance evolution with combinations of mathematical functions proposed in previous studies. We employed the thermal damage contour D63 to compute the lesion dimension contour, which corresponds to Ω = 1, Ω being local thermal damage assessed by the Arrhenius damage model.

RESULTS

The results were very similar in all cases in terms of impedance evolution and lesion size after 6 min of ablation. Although the relative differences between cases in terms of time to first roll-off (abrupt increase in impedance) were as much as 12%, the maximum relative differences in terms of the short lesion (transverse) diameter were below 3.5%.

CONCLUSIONS

The findings suggest that the different methods of modelling temperature dependence of k and σ reported in the literature do not significantly affect the computed lesion diameter.