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DOI: 10.1148/radiol.2362040965
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(Radiology 2005;236:495-502.)
© RSNA, 2005

Experimental Studies

Radiofrequency Ablation: Importance of Background Tissue Electrical Conductivity—An Agar Phantom and Computer Modeling Study1

Stephanie A. Solazzo, BA, Zhengjun Liu, MD, S. Melvyn Lobo, MD, Muneeb Ahmed, MD, Andrew U. Hines-Peralta, MD, Robert E. Lenkinski, PhD and S. Nahum Goldberg, MD

1 From the Minimally-Invasive Tumor Therapy Laboratory, Department of Radiology, Beth Israel Deaconess Medical Center, Harvard Medical School, 1 Deaconess Rd, WCC 308B, Boston, MA 02215. Received June 1, 2004; revision requested August 9; revision received September 20; accepted October 20. Supported by a grant from the National Cancer Institute, National Institutes of Health, Bethesda, Md (RO1-CA87992-01A1). Address correspondence to S.N.G. (e-mail: sgoldber{at}caregroup.harvard.edu).


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 References
 
PURPOSE: To determine whether radiofrequency (RF)-induced heating can be correlated with background electrical conductivity in a controlled experimental phantom environment mimicking different background tissue electrical conductivities and to determine the potential electrical and physical basis for such a correlation by using computer modeling.

MATERIALS AND METHODS: The effect of background tissue electrical conductivity on RF-induced heating was studied in a controlled system of 80 two-compartment agar phantoms (with inner wells of 0.3%, 1.0%, or 36.0% NaCl) with background conductivity that varied from 0.6% to 5.0% NaCl. Mathematical modeling of the relationship between electrical conductivity and temperatures 2 cm from the electrode (T2cm) was performed. Next, computer simulation of RF heating by using two-dimensional finite-element analysis (ETherm) was performed with parameters selected to approximate the agar phantoms. Resultant heating, in terms of both the T2cm and the distance of defined thermal isotherms from the electrode surface, was calculated and compared with the phantom data. Additionally, electrical and thermal profiles were determined by using the computer modeling data and correlated by using linear regression analysis.

RESULTS: For each inner compartment NaCl concentration, a negative exponential relationship was established between increased background NaCl concentration and the T2cm (R2 = 0.64–0.78). Similar negative exponential relationships (r2 > 0.97%) were observed for the computer modeling. Correlation values (R2) between the computer and experimental data were 0.9, 0.9, and 0.55 for the 0.3%, 1.0%, and 36.0% inner NaCl concentrations, respectively. Plotting of the electrical field generated around the RF electrode identified the potential for a dramatic local change in electrical field distribution (ie, a second electrical peak ["E-peak"]) occurring at the interface between the two compartments of varied electrical background conductivity. Linear correlations between the E-peak and heating at T2cm (R2 = 0.98–1.00) and the 50°C isotherm (R2 = 0.99–1.00) were established.

CONCLUSION: These results demonstrate the strong relationship between background tissue conductivity and RF heating and further explain electrical phenomena that occur in a two-compartment system.

© RSNA, 2005


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 References
 
The potential benefits of using minimally invasive image-guided radiofrequency (RF) tumor ablation (ie, coagulating a tumor with short-duration heating [<15 minutes] by directly applying temperatures >50°C with needle electrodes) to treat a wide range of focal tumors in the liver, kidney, bone, breast, and lung include reduced morbidity and mortality compared with those stemming from standard surgical resection and the ability to treat patients who are not eligible for surgery and have no other effective therapeutic options (1,2). Yet, despite rapid adoption of this technique, a lack of fundamental knowledge about tissue-energy interactions and incomplete system optimization and characterization have resulted in the clinical reality of investigators being unable to consistently achieve the desired goal of complete and/or predictable ablation. For example, even with multiple treatment sessions, depending on the tumor type and organ, complete ablation is achieved in only 60%–90% of tumors 3–5 cm in diameter (3–6).

In addition to the well-known negative effects of tissue perfusion on RF ablation efficacy (7–9), the bio-heat and electrostatic equations governing RF-tissue interactions predicts that the electrical conductivity of the tissue is important in determining overall RF ablation efficacy (10,11). Along these lines, we have been able to define the surface response contour for the effects of alteration of local electrical conductivity on RF heating for normal liver, and we have used this effect to dramatically increase tumor ablation in vivo in animals by injecting NaCl around an inserted RF electrode prior to ablation (12–14). More recently, Ahmed et al (15) have also substantiated the importance of the background tumor environment by demonstrating significant differences in tumor destruction when performing RF ablation in the same tumor type in the kidney, lung, and breast. These results were found to be independent of blood flow and correlated with the overall electrical impedance of the RF ablation system. On the basis of these results, we hypothesized that RF-induced heating is directly correlated with background tissue electrical conductivity. Thus, the purpose of our study was to determine whether RF-induced heating can be correlated with background electrical conductivity in a controlled experimental phantom environment mimicking different background tissue electrical conductivities and to determine the potential electrical and physical basis for such a correlation by using computer modeling.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 References
 
Overview of Experimental Design
Initially, the effect of background tissue electrical conductivity on RF-induced heating was studied in a controlled system of agar phantoms. Mathematical modeling of the relationship between background tissue electrical conductivity and RF heating at a defined 2 cm from the electrode (T2cm) was performed. Next, computer simulation of RF heating was performed by using a two-dimensional finite-element analysis program (ETherm). Parameters were selected to most closely approximate those of our model system. Resultant heating, in terms of both the T2cm and the distance of defined thermal isotherms (45°–60°C) from the electrode surface, was calculated. Computer-generated T2cm values were then compared with experimentally, empirically derived data. Once this validation of the computer model was established, electrical and thermal profiles were calculated from our computer modeling data. Electrical data—most notably the maximum electrical peak at a distance from the electrode—were then correlated with thermal profiles.

Phantom Experiments
Phantom construction.—Two-compartment agar phantoms were constructed to simulate an inner tumor surrounded by background tissue (Fig 1), as previously described (13). Briefly, agar phantoms were made by heating a solution of 5% agar, 3% sucrose, and the designated concentration of NaCl (0.06%, 0.1%, 0.13%, 0.2%, 0.25%, 0.3%, 0.5%, 1.0%, or 5.0%) (all from Fisher Scientific, Fairlawn, NJ) in one liter of distilled deionized water (resistivity, >1.8e–7 {Omega} · cm at 25°C) at 90°C. This solution was allowed to solidify in standardized 1.5-L cylindrical Pyrex beakers to a temperature of 8°C for at least 6 hours prior to use to ensure solidification. To form an inner well compartment, a cylindrical rod with a diameter of 2 cm was inserted to a depth of 6 cm within the phantom before refrigeration. After refrigeration, the cylindrical rod was removed and well depth was measured. The phantoms were allowed to sit until they were at room temperature (20°–25°C) to ensure that they were at the same baseline temperature as the water bath.



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  		Figure 1. Experimental apparatus. An internally cooled RF electrode (white arrow) has been inserted into a NaCl gel–filled well within an agar phantom. The RF electrode has been placed in a saline bath at a fixed distance from the grounding pad (G). Thermocouple probes (solid black arrows) have been inserted to measure temperature. An acrylic guide (open arrow) ensures proper positioning of the thermocouple. The RF generator and a temperature measurement device can be seen in the background.

 
The effect of outer electrical conductivity on RF-induced heating was studied by comparing the heating curves of three different NaCl concentrations placed in the inner well. The central wells of the agar phantoms were filled with a solution of 0.25% agar, 3% sucrose, and the designated NaCl concentration (0.3%, 1.0%, 36.0% [all from Fisher Scientific]) in 1 L of distilled deionized water (resistivity, >1.8e–7 {Omega} · cm at 25°C) at 90°C. The solution was allowed to cool to room temperature prior to use. To ensure experimental validity, at least three trials were performed for the 0.3% and 1.0% NaCl inner well concentrations (10 outer concentrations times two inner concentrations times three trials equals 60) and 20 trials were performed for the 36.0% NaCl concentration, for a total sample size of 80 agar phantoms.

RF application.—RF was applied by a single author (S.A.S.) with a 500-kHz monopolar RF generator (CC-1; Radionics, Burlington, Mass) that was capable of delivering 2000 mA (into 35–65-{Omega} load impedances). Phantoms were placed on their bases in room-temperature water (25°C) so that the water bathed the lower 7 cm of the phantom. The RF electrode was inserted vertically to a depth of 3 cm in the center of the well. The electrical circuit was completed by submerging a standardized 12.5 x 8-cm metal grounding pad (Radionics) into the water. To standardize background conductivity, the water was titrated accordingly with NaCl until an impedance of 70 {Omega} was reached. Internally cooled 17-gauge RF electrodes (CC-1020; Radionics) with a 2-cm tip exposure delivered RF for 12 minutes (16). Electrode tip temperatures were maintained at 10°–15°C during RF application by perfusing the electrode with 0°C water.

RF current was slowly ramped to 2000 mA (the generator output current limit) over a period of 5 minutes in order to prevent boiling or overflowing of the runny agar in the central well. The current limit of 2000 mA was chosen on the basis of the actual limitations of commercial generators, including the generator used in the agar phantom experiments. RF current remained at 2000 mA for the duration of the 12-minute experiment. The amount of RF power deposited, as well as impedance, was recorded every minute.

Temperature measurement.—Phantom temperatures were measured (by S.A.S.) at defined distances from the RF electrode with a series fluoroptic thermometer (Model 3100; Luxtron, Santa Clara, Calif) with a fiber diameter of 250 mm and a total diameter of 0.5 mm. Temperature sensor distance from the electrode was maintained by an acrylic stabilizing block placed above the phantom. Temperature sensors were adjusted along the z-axis (parallel to the electrode) within the first 3 minutes and during the 8th minute of RF energy deposition to monitor the maximum temperature. Baseline measurements of temperature, current, power, and overall system impedance were recorded every 60 seconds for the entirety of the 12-minute RF application. Final temperature measurements at 20 mm were used for further analysis.

Computer Modeling
Given the complexity of the family of numeric solutions needed to solve the electrostatic equations (17–21), finite-element analysis was performed (by Z.L.) instead of analytic solutions. Comparative temperature profiles were created by using computer simulation of the Pennes bio-heat equation (ETherm) (17,22). To allow for comparison with phantom data, profiles were created assuming zero perfusion and parameter values were chosen to reflect the experimental conditions. Computer-simulated profiles were created for a distance of 20 mm away from a 2-cm electrode (T2cm) with a maximum current output of 2000 mA.

The selection of electrical conductivity parameters for the inner 1-cm radius, 2-cm diameter compartment and the background tissue were based on empirical determination of electrical conductivity at room temperature for our agar-NaCl substances in the absence of RF energy application. Electrical conductivity was measured at 0 Hz by using the AR 20 PH/Conductivity meter (Fisher Scientific). Results are listed in the Table. These values were modified according to published observations (24) to account for changes in conductivity in the presence of high (500-kHz) RF. Dynamic modulation of the electrical conductivity as a function of temperature was incorporated into our modeling on the basis of results of prior studies that documented an approximate 2% increase in electrical conductivity per degree celsius (23). A thermal conductivity of 0.75 W/(m · °C) and a specific heat of 4200 J/(kg · °C) were selected on the basis of results of previous studies (R. Mahajan, unpublished data and oral communication, July 2, 2003) (25). Given that the experimental system required 5 minutes of ramping of energy to reach maximum current, we based temperature profiles on a 7- rather than 12-minute ablation in order to accurately model the effective duration of heating. Resultant heating, in terms of both the T2cm and the distance of defined thermal isotherms (45°–60°C) from the electrode surface, was calculated.


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  		Electrical Conductivity of NaCl Solutions

 
Statistical Analysis
For comparison of experimental and computer modeling data, regression analysis between phantom and computer-generated data was performed (A.U.H. and S.N.G.) by using linear and higher-order models. Nonlinear curve fitting of both agar-phantom and computer-simulated data was performed (Origin 6.1; Microcal Software, Northampton, Mass). The relationship between the T2cm and the outer NaCl concentration (while the inner NaCl concentration was kept constant) was plotted by using various power and exponential decay functions. Results of graph fitting of experimental and simulated data were compared to assess data similarity and accuracy of the predicted values.

The finite-element ETherm model permits the recording of the RF electrical field as it distributes around the RF electrode and throughout the two-compartment system. Additionally, it generates similar thermal profiles for specified times during the RF ablation. Accordingly, initial electrical field data and thermal profiles at the conclusion of the ablation were recorded. These were analyzed and compared by using regression analysis, as described above.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 References
 
Phantom Studies
For all experiments, generator output achieved a maximum of 2000 mA without pulsing. For each inner compartment NaCl concentration, a negative exponential relationship was established between increased background NaCl concentration and temperature measured 2.0 cm from the electrode (Fig 2). Lower inner NaCl concentrations resulted in higher temperatures. R2 values were 0.64, 0.66, and 0.78 for the 0.3%, 1.0%, and 36.0% inner compartment NaCl concentrations, respectively.



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  		Figure 2. Graph of all experimental data from the agar phantoms depicts effect of background tissue conductivity on RF heating. Negative exponential relationships between temperature and background NaCl concentration are seen for each different inner compartment NaCl concentration. T2cm(°C) represents the temperature 2.0 cm from the electrode 12 minutes into RF ablation.

 
Computer Simulation
Negative exponential relationships between increase in background electrical conductivity and heating 2.0 cm from the electrode were observed. An r2 of greater than 0.97% was identified for each of the three inner electrical conductivities (Fig 3). However, despite tight fits, each inner compartment conductivity produced its own curve. Negative exponential relationships for temperature and background conductivity were also seen for computer-generated isotherms. Again, best correlation was dependent on the specified isotherm, with lower powers (ß) observed for low-temperature isotherms.



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  		Figure 3a. Results of computer-simulated RF heating. (a) Graph shows effect of background heating [{sigma}(O)] in siemens (S) per meter on T2cm for three different inner conductivities [{sigma}(I)]. (b) Graph shows radius of several isotherms generated around the inner compartment that had an inner conductivity of 1.7 siemen/m and demonstrates the distance at which various thermal isotherms can be found in relation to the midpoint of the RF electrode. Both T2cm and the isotherms follow a negative power function based on the inner and outer electrical conductivity.

 


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  		Figure 3b. Results of computer-simulated RF heating. (a) Graph shows effect of background heating [{sigma}(O)] in siemens (S) per meter on T2cm for three different inner conductivities [{sigma}(I)]. (b) Graph shows radius of several isotherms generated around the inner compartment that had an inner conductivity of 1.7 siemen/m and demonstrates the distance at which various thermal isotherms can be found in relation to the midpoint of the RF electrode. Both T2cm and the isotherms follow a negative power function based on the inner and outer electrical conductivity.

 
Correlation between Computer and Experimental Data
Excellent correlation between two of the computer simulations and the experimentally generated data were observed. Indeed, the correlations (r2) between the computer and experimental data were 0.9, 0.9, and 0.55 for the 0.3%, 1.0%, and 36.0% NaCl inner compartment concentrations, respectively, with all computer-generated data falling within one standard deviation for the 0.3% and 1.0% inner NaCl concentrations (Fig 4). The average error of temperature was 3.0°C ± 2.2 (standard deviation), with a maximum error of 8.2°C. On a percentage basis, average error was 6.6% ± 6.0.



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  		Figure 4. Comparison of experimental and computer-generated data. Background electrical conductivity (normalized in terms of a relative {sigma} based on data in the Table) is compared with T2cm for three inner compartment NaCl concentrations. Left: 0.3% NaCl (inner conductivity [{sigma}(I)], 1.7 siemen [S]/meter). Middle: 1.0% NaCl (inner conductivity, 4.5 siemen/m). Right: 36.0% NaCl (inner conductivity, 45 siemen/m). The error bars for experimental data represent standard deviations. For the 0.3% and 1.0% inner compartment NaCl concentrations, most data points fall within a single standard deviation. The curves represent the power function expressing the experimental data.

 
Electrical Profiles
Plotting of the electrical field generated around the RF electrode in the presence of varied electrical background conductivity identified the potential for a dramatic local change in electrical field distribution occurring at the interface between the two media. This manifested as a second electrical peak, or "E-peak," particularly in conditions of high electrical background conductivity and low inner conductivity (Fig 5). This E-peak had effects on thermal distribution throughout the heated region, as a tight correlation between the amplitude of the secondary E-peak and the outer background conductivity for each of the three inner conductivities was observed (r2 > .98 for each) (Fig 6). Accordingly, tight linear correlations between the secondary E-peak and heating 2 cm from the electrode (Fig 6), as well as between the secondary E-peak and the 50°C thermal isotherm, were established (Fig 6).



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  		Figure 5a. (a) Graph shows electrical field distributions and temperatures around an RF electrode for two-compartment RF ablation. For all three cases, the electrical conductivity of the 1.0-cm-radius inner compartment [{sigma}(I)] is held constant at 4.5 siemen (S)/m (or 1.0% NaCl). When the background tissue conductivity [{sigma}(O)] is equivalent to that of the inner compartment at 4.5 siemen/m, there is a smooth continuous decrease in the electrical field distribution around the electrode (green line with open symbols). However, with decreasing background electrical conductivity, a second electrical field peak (arrow) is identified at the interface between the inner and outer electrical conductivity boundaries. This increased electrical field distribution is associated with increasing temperatures (as shown by the curves with solid symbols). (b) In this graph, for the magenta curves, the inner compartment electrical conductivity has been maximized at 45 siemen/m, whereas the outer background conductivity has been minimized at 0.2 siemen/m. This causes the secondary interface electrical peak to nearly double in intensity, at a cost of reducing the inner electrical conductivity peak (a phenomenon requiring further study). This shift in electrical energy distribution alters the thermal profile, as demonstrated by a much shorter but much wider thermal distribution. (c) In this graph, there is reversal of the electrical conductivity parameters so that outer conductivity is markedly elevated compared with inner compartment conductivity. This results in a negative inflection at the interface between the compartments that reduces temperature deeper in the tissue. For all graphs, open data points represent the electrical field, whereas the solid data points represent the temperature distribution.

 


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  		Figure 5b. (a) Graph shows electrical field distributions and temperatures around an RF electrode for two-compartment RF ablation. For all three cases, the electrical conductivity of the 1.0-cm-radius inner compartment [{sigma}(I)] is held constant at 4.5 siemen (S)/m (or 1.0% NaCl). When the background tissue conductivity [{sigma}(O)] is equivalent to that of the inner compartment at 4.5 siemen/m, there is a smooth continuous decrease in the electrical field distribution around the electrode (green line with open symbols). However, with decreasing background electrical conductivity, a second electrical field peak (arrow) is identified at the interface between the inner and outer electrical conductivity boundaries. This increased electrical field distribution is associated with increasing temperatures (as shown by the curves with solid symbols). (b) In this graph, for the magenta curves, the inner compartment electrical conductivity has been maximized at 45 siemen/m, whereas the outer background conductivity has been minimized at 0.2 siemen/m. This causes the secondary interface electrical peak to nearly double in intensity, at a cost of reducing the inner electrical conductivity peak (a phenomenon requiring further study). This shift in electrical energy distribution alters the thermal profile, as demonstrated by a much shorter but much wider thermal distribution. (c) In this graph, there is reversal of the electrical conductivity parameters so that outer conductivity is markedly elevated compared with inner compartment conductivity. This results in a negative inflection at the interface between the compartments that reduces temperature deeper in the tissue. For all graphs, open data points represent the electrical field, whereas the solid data points represent the temperature distribution.

 


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  		Figure 5c. (a) Graph shows electrical field distributions and temperatures around an RF electrode for two-compartment RF ablation. For all three cases, the electrical conductivity of the 1.0-cm-radius inner compartment [{sigma}(I)] is held constant at 4.5 siemen (S)/m (or 1.0% NaCl). When the background tissue conductivity [{sigma}(O)] is equivalent to that of the inner compartment at 4.5 siemen/m, there is a smooth continuous decrease in the electrical field distribution around the electrode (green line with open symbols). However, with decreasing background electrical conductivity, a second electrical field peak (arrow) is identified at the interface between the inner and outer electrical conductivity boundaries. This increased electrical field distribution is associated with increasing temperatures (as shown by the curves with solid symbols). (b) In this graph, for the magenta curves, the inner compartment electrical conductivity has been maximized at 45 siemen/m, whereas the outer background conductivity has been minimized at 0.2 siemen/m. This causes the secondary interface electrical peak to nearly double in intensity, at a cost of reducing the inner electrical conductivity peak (a phenomenon requiring further study). This shift in electrical energy distribution alters the thermal profile, as demonstrated by a much shorter but much wider thermal distribution. (c) In this graph, there is reversal of the electrical conductivity parameters so that outer conductivity is markedly elevated compared with inner compartment conductivity. This results in a negative inflection at the interface between the compartments that reduces temperature deeper in the tissue. For all graphs, open data points represent the electrical field, whereas the solid data points represent the temperature distribution.

 


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  		Figure 6a. Graphs show correlation of E-peaks (the second electrical field peak identified at the interface between inner and outer compartments of varied electrical conductivity) to tissue temperatures during RF ablation. (a) For this comparison of E-peak to temperatures at a fixed 2 cm from the electrode, there is divergence of the slopes of the linear correlation. (b) For this comparison of E-peak to the 50°C isotherm, the slopes converge. This difference can be attributed to the complex heating patterns generated during RF ablation in a system that has two or more compartments of varied electrical conductivity (Fig 5). S = siemen, {sigma}(I) = inner conductivity.

 


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  		Figure 6b. Graphs show correlation of E-peaks (the second electrical field peak identified at the interface between inner and outer compartments of varied electrical conductivity) to tissue temperatures during RF ablation. (a) For this comparison of E-peak to temperatures at a fixed 2 cm from the electrode, there is divergence of the slopes of the linear correlation. (b) For this comparison of E-peak to the 50°C isotherm, the slopes converge. This difference can be attributed to the complex heating patterns generated during RF ablation in a system that has two or more compartments of varied electrical conductivity (Fig 5). S = siemen, {sigma}(I) = inner conductivity.

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
References
 
This work demonstrates the strong relationship between background tissue conductivity and RF heating. Thus, this work confirms the previous hypothesis stated by Ahmed et al (14) that differences in RF efficacy from organ type to organ type may be due, in part, to differences in background tissue conductivity. This has important clinical implications, as these results add further impetus to the need for optimizing RF ablation parameters for different tissues of widely varying electrical conductivities. For example, whereas bone and lung have relatively low electrical conductivity (0.1 siemen/m at RF ablation frequencies) compared with liver (0.3–0.5 siemen/m), other organs that are increasingly being treated with RF ablation, such as the kidney, have much higher values (0.9 siemen/m) (24–26).

Our study results further demonstrate the utility of performing two-dimensional finite computer model simulation of the electrostatic and bio-heat equations as they apply to the clinical application of RF tumor ablation. Indeed, a tight correlation with small residual errors (approximately 6%) was seen, confirming the robustness of this model. Not only was this computer simulation capable of confirming and validating our experimental observations, but the use of this platform enabled the generation of additional clinically relevant information, including the zones encompassed by clinically relevant isotherms of 60°C (the temperature required for instantaneous protein denaturation and tissue coagulation [27,28]), 50°C (the standard ablation isotherm that produces coagulation in 4–6 minutes [1]), and 45°C (an isotherm at which coagulation may be achieved with hyperthermic adjuvants such as liposomal doxorubicin [29]).

Computer modeling also helped us establish the physical basis for the phenomenon observed (ie, the negative exponential relationship between increasing background tissue electrical conductivity and tissue heating). By plotting the electrical field for our simulations, we were able to identify a secondary electrical field peak at the interface between two materials of differing electrical conductivities. This was most pronounced in the presence of an accentuated difference in electrical conductivity between inner compartment (ie, tumor) and background electrical conductivity. Our data show that these electrical peaks are the primary determinant of the nonlinear temperature profiles generated, as manifested by the tight correlations between this E-peak and temperatures 2 cm from the electrode and at the 50°C isotherm, where appropriate. This secondary E-peak likely also accounts for the dramatic increases in thermal heating in the presence of highly concentrated NaCl injections and the altered temperature profiles observed in those conditions (12,13). It may also account for the "edge effects" of increased temperature observed by Ahmed et al (14), who observed 5°–15°C temperature rises at the interface of NaCl-injected canine venereal sarcomas (which had very high electrical conductivity) and surrounding low-conductivity fatty tissue.

Analysis of the electrical field data provided further insights into RF tissue heating that may ultimately be used to clinical advantage. Most notably, the graphs comparing the E-peak with temperatures at a fixed 20 mm from the electrode (T2cm) were divergent, whereas convergent slopes were identified for the E-peak versus the 50°C isotherm. This suggests a complex interaction between the geometry of the heating and the electrical and thermal conductivity of the tissues that results in nonlinear heating profiles around an RF electrode. Further work is therefore necessary to elucidate these interactions and determine the higher-order mathematical functions that govern this complex behavior. This also underscores the need to determine actual heating profiles deep in the tissue, because, depending on the situation, a single point temperature will potentially not predict other temperatures either closer or further from the electrode. Nevertheless, these results suggest that, with judicious use of NaCl injection, it may ultimately be possible to modulate electrical conductivity to achieve beneficially altered heating profiles, including less near-field tissue boiling and deeper tissue heating.

Excellent correlations were achieved between computer modeling and experimental data for the lower inner compartment conductivities of 0.3% and 1.0%. Nevertheless, a weaker correlation was achieved for the 36% NaCl inner compartment conductivity. This poor correlation may be due to errors in measurement (given the low temperatures achieved in these conditions) or to calculational assumptions used in our computer modeling. For example, additional parameters, such as potential changes in thermal conductivity with heating (30), may play a greater role in conditions with high inner conductivity. It is also possible that the high gradient of NaCl in the inner compartment diffused by osmosis into the outer portions of the phantom during the experiment and our computer model did not take into account these physical changes. Regardless, these imperfections highlight the need for further study to better elucidate relevant electrical and thermal parameters during RF ablation.

Substantial additional work defining the relative importance of electrical conductivity for RF ablation is required. Future work will include better characterization and definition of the relationship between the secondary electrical peak and thermal profiles. Given that both inner and outer electrical conductivity affect the E-peak and resultant heating, this will include characterizing the relationship and interaction between these two conductivities. Furthermore, the influence of the radius of the inner compartment, which is known to influence efficacy of RF heating in conditions of altered inner electrical conductivity (ie, in the presence of NaCl injection) (12–14), will need to be studied. It is known that the electrical field around the electrode decreases with distance from the electrode according to the Coulomb law, and we therefore hypothesize that the reduction in heating caused by expanded radii of the inner compartments can be attributed to a reduction in the magnitude of the secondary E-peak resulting from an increased distance from the electrode.

It must also be noted that all of our experiments were performed with essentially constant RF current as maximum generator output was achieved. Lobo et al (13), however, have demonstrated that different mathematical functions govern thermal tissue heating when generator output is held constant versus when generator output is increased. Given the results of Lobo et al, further studies that take into account possible increases in current that are enabled by the increase in local electrical conductivity will need to be performed. Our work also points out the need for accurate measurements of electrical conductivity for various tissues and tumors. However, many of these values (and how these values change with high temperatures) are incompletely characterized for the electrical frequencies used for RF ablation, so more research is required. Last, the interaction between the effects of electrical conductivity and other factors that can alter tissue heating, such as blood flow (7–9), will need to be studied.

Although static phantoms and computer modeling that limits the number of active variables are useful for establishing the relationship between a given variable and tissue heating, our study had several key limitations that prevent immediate translation of this theoretical work into a clinically useful predictive model. These include the use of a phantom whose simulated tissue parameters, including electrical conductivity, may be different from the parameters encountered in many situations in clinical practice and the fact that we performed the study in the absence of blood flow, a primary determinant of RF ablation efficacy (7–9). Additionally, for the phantoms, temperatures were only measured at one point. Given these facts, further in vivo experimentation is likely required to better delineate interaction between the two variables of blood flow and electrical conductivity and to quantify the magnitude of the effect likely seen in the clinic.

Practical applications: Our experimental phantom and computer modeling studies demonstrate the strong relationship between background tissue conductivity and RF heating and further explain electrical phenomena that occur in a two-compartment system. Specifically, a secondary E-peak that influences tissue heating was predicted with computer modeling. Given the importance of background tissue conductivity, our results underscore the need for understanding which clinical conditions (such as those involved in performing ablation in different organs of varied electrical conductivities) have appreciable clinical effects on RF ablation efficacy so that optimized clinical efficacy can be predicted. Thus, both tumor and tissue type may need to be considered in devising RF ablation algorithms. It is likely that for some tumors and tissues, current ablation algorithms optimized for the liver may ultimately be shown to be less than ideal. Our results also help explain why and in which conditions NaCl injection around an electrode can have beneficial or detrimental effects on RF ablation efficacy.


   FOOTNOTES
 

Abbreviations: RF = radiofrequency

Authors stated no financial relationship to disclose.

Author contributions: Guarantor of integrity of entire study, S.N.G.; study concepts, S.N.G., Z.L., S.M.L., M.A., R.E.L.; study design, S.N.G., Z.L., R.E.L.; literature research, S.N.G.; experimental studies, S.A.S., Z.L.; data acquisition, S.A.S., Z.L., M.A., A.U.H.; data analysis/interpretation, S.N.G., S.A.S., Z.L.; statistical analysis, S.N.G., S.A.S., Z.L.; manuscript preparation, S.N.G., S.A.S., Z.L., A.U.H.; manuscript definition of intellectual content, S.N.G., Z.L., S.M.L., M.A.; manuscript editing, S.N.G., M.A.; manuscript revision/review and final version approval, all authors


   References
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 References
 

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S. A. Solazzo, M. Ahmed, Z. Liu, A. U. Hines-Peralta, and S. N. Goldberg
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