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Experimental Studies |
1 From the Department of Radiology, Beth Israel Deaconess Medical Center, Harvard Medical School, 330 Brookline Ave, Boston, MA 02215. Supported by grants from the National Cancer Institute, National Institutes of Health, Bethesda, Md (RO1-CA87992–01A1), and Radionics/Tyco Healthcare, Burlington, Mass. Received November 19, 2002; revision requested February 6, 2003; revision received March 5; accepted May 27. Address correspondence to S.N.G. (e-mail: sgoldber@caregroup.harvard.edu).
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONREFERENCES |
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MATERIALS AND METHODS: Standardized 1-L 5% agar phantoms were constructed with central wells of varying volume that were filled with a protein-based polymer gel of varying NaCl concentration (0%–35%). RF ablation to the maximum system current output (2,000 mA) was applied to internally cooled 2-cm electrodes placed in the center of the gel wells. Remote thermometry was performed 20 mm from the electrode. Temperatures generated within the phantom were then used to model the response surface by using regression analysis. The generated model was then applied to previously published in vivo data to determine its applicability to a porcine liver tissue model. Statistical analyses included one-way analysis of variance to compare the temperatures reached with different NaCl concentrations and volumes with those reached without NaCl. In addition, modeled functions were evaluated for goodness of fit and the statistical significance of their coefficients.
RESULTS: NaCl volume and concentration had significant effects on RF-generated heating of the agar phantoms. The mean maximum temperature, 91.4oC ± 0.8 (SD), was reached with 3.5 mL of 10% NaCl gel. This was significantly higher than the mean temperature reached in phantoms containing 0% NaCl gel, 40.3oC ± 4.9 (P < .001). Heat increases to the maximum temperature correlated strongly with the deposited RF energy, with maximum temperatures limited by the current output of the RF generator. The response surface was defined by a generator energy–dependent region and a generator current–limited region, which were best modeled by a modified gamma-variate function and an exponential function, respectively (r2 = 0.92). This model correlated well with previously published in vivo data (r2 = 0.86).
CONCLUSION: Modulation of electrical conductivity has different effects on RF ablation response that are dependent on generator capabilities and the volume and concentration of NaCl pretreatment.
© RSNA, 2004
Index terms: Computers, simulation • Experimental study • Neoplasms, therapy, **.12992 • Radiofrequency (RF) ablation, **.1299
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONREFERENCES |
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RF tumor ablation involves the application of electromagnetic energy and can producetheoretically predictable tumor destruction on the basis of well-defined variables of the bio-heat equation (16). One approach under investigation for increasing RF ablation efficacy involves modulation of the biologic environment of treated tissues to potentiate conditions that promote heat deposition, conduction, and retention (17,18). Several investigators (17–20) have achieved increased RF heating by instilling NaCl solutions that alter the local electrical and/or thermal conductivity in the vicinity of the RF electrode. For example, Goldberg et al (21) demonstrated that pretreatment with NaCl solution in a porcine liver model can increase the coagulation diameter to as much as 7 cm, with results that are dependent on the volume and concentration of NaCl in, as of yet, incompletely characterized relationships. Subsequently, Ahmed et al (22) confirmed these findings in a canine visceral sarcoma model in which 6 mL of 38% NaCl was shown to enable increased and complete destruction of 5-cm tumors with a single RF application. Given this marked increased tissue destruction, these authors emphasized the importance of matching treatment to tumor size to prevent the undertreatment or overtreatment of tumors, which in some cases can damage critical adjoining structures.
Prior models of the temperature response surface have not incorporated the effects of NaCl pretreatment (23,24). Hence, an adequate relationship between either the volume of NaCl or the concentration of NaCl and RF-induced temperatures has not been determined. For this reason, the potentiating effects of NaCl on RF tissue coagulation cannot yet be used in a predictable and reproducible manner. In this study, we conducted a series of experiments to characterize the effects of volume and concentration of adjuvant NaCl pretreatment on RF ablation and to model these results to determine their applicability to in vivo systems.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONREFERENCES |
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Phantom Construction
Agar phantoms were constructed by heating a solution of 5% agar, 3% sucrose, and 0.075% NaCl (all from Fisher Scientific, Fairlawn, NJ) in 1 L of distilled deionized water (resistivity > 1.8e-7 
-cm at 25°C) at 90°C. This solution was allowed to solidify in standardized 1.5-L cylindrical glass beakers to a temperature of 8°C for at least 6 hours prior to use to ensure a consistent and uniform baseline temperature for the experiments. Prior to refrigeration of the phantoms, a cylindrical solid rod of a known diameter was inserted into the phantom center to a known depth of 7 cm. On retrieval of the phantoms from the 8°C refrigerated environment, the previously inserted cylindrical rod was removed and the diameter and depth of the created well were measured (by S.M.L.). By inserting cylindrical rods of varying diameters to a fixed depth, an array of phantoms with wells of varying diameters (0.43–2.54 cm) and consequently varying volumes (1–38 mL) was produced. The heights of the phantoms ranged from 10.0 to 10.4 cm, with a diameter of 11.3 cm.
The effect of altered electrical conductivity on RF-induced heating was studied by varying the NaCl volume and the NaCl concentration by filling the central well of the agar phantoms with the NaCl solution mixed into a protein-based polymer gel (ProSurg, Mountain View, Calif), also at 8°C. Seven volumes were used: 1.0, 2.0, 3.5, 8.0, 12.0, 22.0, and 38.0 mL. Nine concentrations were used: 0%, 0.9%, 2.5%, 5.0%, 7.5%, 10.0%, 15.0%, 24.0%, and 35.0%. To ensure experimental validity, at least three trials were performed for each set of variables studied: Seven volumes times nine concentrations in three trials each (189 samples) plus three trials performed with 0 mL of NaCl yielded a total of 192 samples.
RF Energy Deposition
The RF source used for the experiments was a 500-kHz monopolar RF generator (model CC-1; Radionics, Burlington, Mass) capable of delivering 2,000 mA (into 35–650- load impedances). The phantoms were placed on their bases in a 0.9% NaCl (normal saline) room-temperature (25°C) solution that bathed the lower 7 cm of the phantom. The RF electrode was placed vertically in the center of the gel-filled well to a depth of 4.8 cm. The electrical circuit was completed by way of a standardized 12.5 x 8.0-cm metal grounding pad (Radionics), which was also placed vertically in the bath (for 112 cm2 of grounding return surface area) 24 cm from the electrode (Fig 1). All experiments were performed at room temperature to ensure a uniform background temperature for all materials and reduce variability in the study.
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Pulsed high-current RF energy was applied for 20 minutes according to a previously designed algorithm that has been shown to maximize energy deposition and tissue coagulation (26). In addition, the RF current was adjusted to either the maximum generator output current, 2,000 mA, or until the gel began to boil and overflow from the well. Boiling of the gel was marked by impedance increases of greater than 10 ohm, at which point manual control was instituted to limit the current and thus prevent boiling and ensure the impedance stability of the gel. The amount of RF power deposited was recorded (by S.M.L. and K.S.A.) every 60 seconds during each 20-minute experiment.
Measurement of Phantom Heating
Temperatures within the phantoms were monitored at a fixed distance of 20 mm from the RF electrode by using 21-gauge thermocouple probes (Radionics). These probes had sufficient electromagnetic RF shielding and grounding properties so that their temperature measurements were not disturbed by RF energy interference (26). Positioning of temperature sensors at 20 mm from the electrode was ensured by using a homemade acrylic stabilizing device placed outside of the phantom. Additionally, the position of the temperature sensors within the phantoms was adjusted along the z axis, parallel to the electrode, during the initial 3 minutes of RF application to determine and monitor the maximal temperature.
Despite varied well diameters, the temperature 20 mm from the RF electrode was always measured outside of the gel-filled wells. Temperature, current, power, and overall system impedance were recorded at baseline and thereafter at 60-second intervals for the 20-minute duration of RF application (S.M.L.). Temperatures generated within the phantom, 20 mm from the RF electrode at the end of 20 minutes of RF energy application, were then used to model a surface response contour.
Statistical Analyses
Temperatures, which were measured 20 mm from the RF electrode, were subjected to routine univariate statistical analysis of each variable (ie, volume or concentration of the NaCl gel) while keeping the second variable fixed. One-way analysis of variance with the Dunnett test (P = .05, two-tailed test) was performed to compare the temperatures measured with different NaCl concentrations and volumes with those measured without NaCl. Subsequently, the measured temperatures were also subjected to analysis of variance, including multiple regression analysis with interactions to determine the influence of NaCl concentration and volume on temperature generation.
Modeling of Phantom Heating
To model the three-dimensional response surface of temperature, NaCl pretreatment volume, and NaCl pretreatment concentration, the effect of one variable (either concentration or volume) on temperature was examined with the other variable held constant. Step-wise systematic increases in either the volume or the concentration of NaCl allowed for the effect of one variable on temperature to be studied without being influenced by the other variable. This univariate analysis was expanded to counter interactions between volume and concentration as we attempted to define a response surface between temperature, volume of NaCl, and concentration of NaCl. Response-surface methodology involving the use of linear and higher order polynomial models and empirical functions that established the goodness of fit between the experimentally determined temperature, the NaCl volume, and the NaCl concentration were compared. Nonlinear regression analysis involving the use of software that employed the Levenberg-Marquardt algorithm was used to refine an empirical three-dimensional function with the best goodness of fit (27). The large number of data points enabled good estimation of the initial values in the algorithm (28). This empirical function was tested and again compared with various higher order polynomial functions by using modeling and statistical analysis software (DataFit, version 7.1.44, Oakdale Engineering, Oakdale, Pa; Design-Expert, version 6, Stat-Ease, Minneapolis, Minn; and IDL, version 5.4, Research Systems, Boulder, Colo).
Modeling of Animal Data
In an attempt to determine the validity of the empirical function modeled from our phantom apparatus to in vivo systems, data from a previously published animal study (22) also were used to model a response surface. In this referenced study, 11 combinations of NaCl volumes and concentrations were injected into in vivo porcine livers, which were subjected to RF energy deposition. NaCl volume, NaCl concentration, and temperature (measured 20 mm from the RF source, as in our phantom model) data were fitted to the empirical phantom model previously described. Nonlinear regression analysis was applied to the model to determine the goodness of fit.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONREFERENCES |
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Effect of Concentration
Compared with the temperatures reached with an NaCl concentration of 0%, the temperatures generated at 20 mm from the electrode with increasing NaCl concentrations and volumes greater than 1 mL were significantly higher (P < .007). However, this phenomenon was not linear because with increasing NaCl concentrations and a fixed volume of NaCl (v = constant), the temperature increased to a maximum (Tm,v=constant), after which further increases in NaCl concentration resulted in decreasing temperatures (Fig 2). This maximum temperature, with a fixed volume of NaCl gel, was limited either electrically by the RF generator output (ie, reaching the current limit of 2,000 mA) or thermally by the NaCl gel beginning to boil and overflow from the well. With large NaCl volumes (greater than 12 mL), the temperature maximums, or Tm,v=constant values, were reached at 0.9% NaCl. Further increases in NaCl gel concentration resulted in lower temperatures due to the RF current or the thermal limitations just described (Table 1).
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Relationship between Concentration and Volume at Temperature Maximums
On the basis of observations regarding the generator energy–dependent and generator current–limited regions just described, local temperature maximums were used to demarcate the temperature response surface into two regions to fit models that adequately described each region. The loci of the experimentally observed temperature maximums—that is, the Tm,c,v values—were related by the equation
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This equation, together with the observation that NaCl volumes greater than 12 mL resulted in decreasing temperatures with increasing NaCl concentration, was used to separate a three-dimensional space of temperature, NaCl volume, and NaCl concentration into two regions: a generator energy–dependent region for volumes less than or equal to 12 mL and concentrations less than or equal to 35.1 · V -1.05 and a generator current–limited region for all other volumes and concentrations.
Modeling of Generator Energy–dependent Region
Regression modeling with interactions demonstrated that temperature was significantly (P < .02) influenced by both the volume and the concentration of NaCl in the generator-dependent region. Initial steps toward modeling this region by using univariate regression analysis (at fixed NaCl volumes) revealed strong correlations between temperature and NaCl concentration for temperature as a logarithmic function, parabolic function, or power function of NaCl concentration (r2 = 0.95–0.97). Results of univariate regression analysis with fixed concentrations for similar functions again showed a strong correlation (r2 = 0.85–0.97).
To generate the three-dimensional response surface of the generator energy–dependent region, combinations of the previous functions were tested with multivariate regression analysis. However, simple additive combinations failed to generate a response surface that adequately described the experimental data (r2 = 0.81–0.89), with coefficients in the model having poor statistical significance (P <.1 to P = .4). Multiplicative combinations of second-order polynomials and second-order polynomial–power function combinations yielded stronger correlations with the data (r2 = 0.95–0.97), but the response surface had discontinuities, as well as multiple steep valleys between closely spaced experimental data. Furthermore, in some cases, the coefficients of these multiplicative models were not significant (P < .7 to P = .95). However, an empirical modified gamma-variate function was shown to fit the generator energy–dependent region of the temperature surface with the best goodness of fit (r2 = 0.94) and with coefficients of the function bearing significance (P < .05).
Modeling of Generator Current–limited Region
Attempts to model the generator current–limited portion of the response surface with power, parabolic, and logarithmic functions were unsuccessful due to either poor correlation or poor statistical significance for the coefficients of these models. However, an additive exponential function fit the experimental data well (r2 = 0.90), with significant coefficients (P < .05).
Combined Model Encompassing Both Generator Energy–dependent and Current-limited Regions
On the basis of the considerations just discussed, the best fit equations modeled for these data are expressed as follows:
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Modeling of Animal Data
Data from a previously published animal study (22) were obtained by using 11 combinations of NaCl volumes and concentrations that were injected into in vivo porcine livers, which were subjected to RF energy deposition. Although the use of a Simplex strategy in that study enabled the identification of the temperature maximum, the effects of the concentration and volume of NaCl could not be systematically studied for the purposes of modeling. To overcome this limitation, all possible combinations (n = 211) of the animal data (in terms of their location in either the generator energy–dependent or generator current–limited region) were modeled by using the empirical model established for the phantom data. The combinations were then ranked by correlation coefficients for goodness of fit. One particular combination yielded good agreement between the model and the experimental animal data (r2 = 0.86), with the generator-dependent region limited to NaCl volumes of less than 7 mL.
The best fit equation modeled for these data is expressed by the following equations:
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONREFERENCES |
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Recent strategies have focused on the other variables of the bio-heat equation—namely, to increase local tissue interactions such as electrical conductivity or to decrease heat loss by means of alteration of blood flow with the use of adjuvants (34,35). Three mechanisms to account for the increased RF-induced heating achieved with adjuvant NaCl have been proposed: (a) Electrical properties such as conductivity are altered in the vicinity of the NaCl, allowing increased RF energy deposition. (b) NaCl, when injected at the time of RF application, improves thermal flux within the surrounding medium by means of convection. (c) The injected adjuvant NaCl raises the boiling point of the surrounding medium, leading to increased electrical and thermal stability and permitting greater energy deposition with less tissue boiling. The net effect of the adjuvant NaCl solution with RF ablation is a flattening of the heat distribution curve, allowing greater energy deposition with less tissue boiling.
It has previously been shown that an adjuvant injection of a fixed volume of NaCl solution administered as either a pretreatment (21) or a continuous infusion (17,18) substantially increases RF-induced heating compared with RF alone. For example, Miao et al (19) infused 5% hypertonic saline solution into ex vivo livers with a cooled wet electrode and achieved coagulation of an area 6 cm in diameter. Goldberg et al (21) investigated the relationship between NaCl injection and RF energy deposition in both phantom agar models and in vivo porcine livers, establishing the relationship between increased coagulation and altered tissue conductivity. However, the precise relationship between NaCl volume and concentration and either tissue heating or coagulation volume was not established. The same group later established that increasing the NaCl concentration at a fixed volume led to increased RF-induced heating and coagulation in a canine tumor model (22).
In our study, we confirmed that adjuvant NaCl injection leads to substantial increases in RF-induced heating compared with RF alone. By using a given RF power generator source (of fixed maximum power and current capacity) and electrode, we demonstrated that an up to 83°C temperature increase (from a baseline temperature of 8°–91°C) can be achieved in a predictable and reproducible manner, with the ability to reproducibly achieve a particular temperature 20 mm from a specified RF electrode by using a defined volume and concentration of NaCl gel.
The present study results differ from previously published results in one key aspect—namely, that with our approach, extraneous variables were eliminated in a clinically relevant model. Prior phantom-based experiments involved varying the conductivity of the entire phantom, whereas in actual animal models, the distribution of injected NaCl solution around the RF electrode is poorly controlled and reliant on passive diffusion (21). Furthermore, the results of prior animal studies have shown that there are problems with injecting large volumes of NaCl solution into tissue, including irregular distribution of larger volumes (ie, >10 mL) resulting in irregular RF zones of necrosis (22). Difficulties injecting large volumes of NaCl solution to overcome the surrounding interstitial pressure have been encountered in other studies (36). To overcome these difficulties, in our phantom experiments, we systematically studied the effect of varying the local conductivity in the region of the RF electrode by using NaCl gel–filled wells with volumes of NaCl solution similar to those used in prior animal studies. This model offers the investigator a tool to maximize temperature generation by allowing the optimal NaCl concentration to be selected while the volume is constrained.
In the present study, the maximum temperature was achieved with a small volume of NaCl gel, which may be beneficial for clinical practice, where it is difficult to uniformly inject large volumes into a tumor. This finding confirms a previously demonstrated result (21,22): that increasing tissue electrical conductivity at very high saline concentrations decreases the extent of heating. Increased electrical conductivity has competing effects on RF ablation: It enables increased energy deposition and greater heating, but it also increases the energy required to heat a given volume of tissue. If this amount of energy cannot be delivered—that is, it is beyond the maximum generator output—then less actual heating, and thus less coagulation, results.
The described model, although empirical, has a physical basis. The generator energy–dependent region is limited by the thermal stability of the medium but is proportional to the overall energy deposition. The resultant complex mathematical relationship of the upslope can be expected, given the complicated method of pulsed heat generation that is matched to thermal impedance and stability. In the generator current– limited region, the medium acts as a thermal sink and an exponential decay of the temperature results.
Our work further highlights a clinically relevant RF phenomenon—namely, that alteration of conductivity has different effects, depending on generator capabilities. Knowledge of the maximum generator output and the resultant generator current–limited zone of operation is important because increasing conductivity is detrimental in this case. However, judicious alteration of conductivity is clearly beneficial because in many cases, it enables greater energy deposition.
The model generated in this study shows that reproducible temperatures can be reliably predicted on the basis of the volume and concentration of NaCl, at least for agar phantoms. The extension of this mathematical model to previously published in vivo porcine data with good correlation suggests that the effects of altering tissue electrical conductivity hold true, despite greater potential physiologic in vivo variability. Nevertheless, blood flow and NaCl diffusion in living tissue appear to at least modify the coefficients of the mathematical relationship.
Higher concentrations and volumes of NaCl are needed in in vivo systems to achieve equivalent generator-dependent conditions because blood flow decreases tissue temperature and diffusion limits the actual concentration. Additional data from in vivo animal models to further confirm this empirical mathematical form would be encouraging. The near-term application of this model could represent an efficient approach to minimizing the number of animals used in future RF ablation experiments that involve adjuvant NaCl solution injection. When sufficiently corroborated, the model has the potential to satisfy the definite need to create reliable zones of coagulation and thus match the treatment to the tumor volume.
Several limitations of this study must be addressed. First, the described model predicts temperature as a function of volume and concentration of NaCl gel in the controlled setting of agar phantoms. Further verification in other in vivo tissues and/or tumor models is needed because the thermal and electrical conductivities of different tissues and the effects of perfusion-mediated tissue cooling (35,36) influence the shape and characteristics of the temperature response. Additionally, the use of a gel, which was useful for our experimental design because it limited both the boiling and the diffusion of the well contents, even at low viscosity, that result from higher temperatures, may produce a somewhat altered response, as compared with the use of aqueous saline in tissue.
The present study was also limited to the use of a 2-cm internally cooled RF electrode and a 2,000-mA generator; further experiments with different-sized electrodes will be necessary to determine how the model will scale appropriately to other RF systems. Additionally, because we were unable to measure temperature in all three dimensions, there was uncertainty with respect to the ultimate volume of coagulation that will be created in tissues. Because we were unable to measure the exact location of the 50°–55°C isotherm (37), the true potential maximum increase in coagulation is unknown. Although the model predicts temperature reliably, it remains to be seen whether the volume of the wells or the diameter of the wells (in the present study, all wells had the same depth) has the greatest influence on temperature. Finally, it is conceivable that if additional points were tested, a better representation of the response surface would emerge.
Our study results show that temperature induced by RF heating with given volumes and concentrations of NaCl gel can be reliably predicted in an agar phantom model. Our work points to the need for further modeling and predictive capabilities from our expanded knowledge base of RF-induced heat generation and distribution. Ideally, Pennes’ (16) complex partial differential bio-heat equation will need to be solved with appropriate boundary conditions for a range of tissue electrical and thermal conductivities. This will enable a better understanding of RF and system parameters that transform an agar phantom model into an in vivo system. Such analysis could potentially reveal avenues to further modulate RF ablation for improved clinical effects.
Practical applications. In the present study, we confirmed the nonlinear surface response of RF-induced heating by varying NaCl volume and concentration in the vicinity of the RF electrode. The response surface of RF-induced heating can be quantified and mathematically modeled. The definition of this relationship for given clinical RF electrode systems may permit greater reliability and reproducibility of induced thermal coagulation when adjuvant NaCl solutions are used with RF ablation in clinical practice. It is our hope that this improved understanding of RF ablation will translate into improvements in the field of clinical RF tumor ablation therapy.
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FOOTNOTES |
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Abbreviation: RF = radiofrequency
Author contributions: Guarantors of integrity of entire study, S.M.L., S.N.G.; study concepts, S.M.L., R.E.L., S.N.G.; study design, S.M.L., J.B.K., R.E.L., S.N.G.; literature research, S.M.L., M.A., S.N.G.; experimental studies, S.M.L., K.S.A., M.A., S.N.G.; data acquisition, S.M.L., K.S.A., M.A.; data analysis/interpretation, S.M.L., R.E.L., S.N.G.; statistical analysis, S.M.L., R.E.L., S.N.G.; manuscript preparation, S.M.L., S.N.G.; manuscript definition of intellectual content, S.M.L., R.E.L., S.N.G.; manuscript editing, S.M.L., M.A., J.B.K., R.E.L., S.N.G.; manuscript revision/review and final version approval, all authors
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONREFERENCES |
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