Mathematical and Ex Vivo Thermal Modeling for Renal Tumor Radiofrequency Ablation with Pyeloperfusion

Abstract

Background and Purpose:

Radiofrequency ablation (RFA) is an effective technique for the treatment of patients with small renal tumors, although it is often limited to tumors at least 2 cm from the renal pelvis or ureter. Retrograde pyeloperfusion (PPF) of the pelvis with cold saline during RFA may protect the pelvis and ureter. We designed a mathematical and ex vivo model of RFA to investigate the effects of PPF.

Methods:

Our theoretical model uses heat transfer principles simplifying the RFA probe to a heat-emitting cylinder within a material. In the ex vivo model, an RFA probe was placed 18 mm from the pelvis in porcine kidneys and with temperature probes on either side of the RFA probe. Control trials with no PPF were compared with either cold saline (2°C), warm saline (38°C), or antifreeze (−20°C) pumped into the renal calix at a rate of 60 mL/min. Ablated volumes were measured and confirmed histologically.

Results:

The average steady state temperatures at each probe were highest with no PPF, followed by warm saline, cold saline, then antifreeze. Compared with no PPF, temperatures were significantly (P<0.05) colder with warm saline (−8.4°C), cold saline (−18°C), and significantly colder at the calix (warm −14°C, cold −27°C). While RFA output a constant voltage, significantly lower resistances in warm (171Ω) and cold (124Ω) PPF vs no PPF (363Ω) translated to significantly greater power outputs in warm (40 W) and cold (42 W) vs no PPF (14 W). The ablated volumes were significantly higher in warm saline (2.3 cm³) vs cold saline (0.84 cm³) and no PPF (1.1 cm³). Mathematical modeling produced a predictive temperature curve with R2=0.44.

Conclusion:

PPF lowers temperatures throughout the entire kidney during RFA, most notably near the collecting system and is dependent on the temperature of the liquid used. In addition, PPF may cause less charring of the tissue around the probe resulting in lower resistance and higher power outputs.

Introduction

More than 65,000 new cases of renal-cell carcinoma (RCC) are diagnosed annually resulting in 13,680 deaths in the United States in 2013.¹ The increased use of diagnostic imaging has led to subsequent increases in incidentally found renal tumors and in the number of comorbidities in patients with renal tumors.² The current gold standard of treatment for patients with small renal masses (SRM)—defined as those <4 cm—has been partial nephrectomy for T_1a although energy-ablative therapies such as cryoablation and radiofrequency ablation (RFA) have become increasingly prevalent.³

RFA is a well-established technique for the minimally invasive treatment of patients with small renal tumors. A probe is inserted into a renal mass; heat is generated within the surrounding tissue as a result of the high current density at the exposed electrode of the probe during radiofrequency current emission, eventually resulting in coagulation and cell death. High frequency (350–500 kHz) alternating current is used to avoid stimulating nerves or muscle. The minimally invasive nature of this nephron-sparing technique makes it ideal for patients with multiple comorbidities, marginal renal function, a solitary kidney, or multiple renal tumors.⁴

The modality is often limited by a tumor's distance (<1.5 cm) from the renal pelvis. Excessive heat to the pelvis and proximal ureter has been associated with urinoma, ureteral obstruction, and chronic stricture.⁵ Several groups have reported performing retrograde pyeloperfusion (PPF) of the pelvis during RFA to keep renal pelvis temperatures low.^6
–8 The retrograde PPF of cool liquid up the ureter and to the renal pelvis during RFA is thought to transfer heat away from the pelvis by convection and protect it from potentially damaging temperatures. Cantwell and associates⁶ used PPF of cooled D5W during 19 ablations of renal tumors less than 1.5 cm from the ureter with no heat-related complications and three (16%) recurrences.

According to our literature search, there is a paucity of basic science research published to support the use of PPF during RFA. The purpose of this investigation is to determine the efficacy and limitations of using PPF of varying substances and temperatures to possibly expand the range of tumors amenable to RFA management. Our group created a theoretical mathematical model using heat transfer principles that can predict the temperatures throughout the kidney during RFA with PPF of varying substances and temperatures. We then tested our model RFA in ex-vivo porcine kidneys to investigate the effects of PPF.

Methods

Theoretical model

Creating a mathematical model of RFA with PPF first involved simplifying the structures. The RFA probe is represented by a cylinder of radius (r) and length (l) inside a solid mass with output power Q inside the renal cortex. The probe is assumed to be some distance (d) away from a flat surface of cross-sectional area (A) with fluid on the other side (Fig. 1). At steady state, it is assumed all of the heat (Q) from the probe should conduct through the tissue with thermal conductivity constant k and into the convecting liquid with convection constant h and temperature T_L. From this we can first calculate: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \rm Equation \ ( 1 ) \, :} \ \dot{{ \rm Q}} = { \rm kS} \ ( { \rm T}_{ \rm P} - { \rm T}_{ \rm CS} ) \ { \rm with \ S} \\ ( {\rm shape \ factor}) = \frac {2 \pi l} {{ \rm ln} [\frac {d} {r}]} \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ { \rm Equation \ ( 2 ) \, :} \ \dot{{ \rm Q}} = { \rm hA} \ ( { \rm T}_{ \rm CS} - { \rm T}_{ \rm L} )}\end{align*} \end{document}

FIG. 1.

A theoretical model of heat (Q) moving out of a cylindrical radiofrequency ablation (RFA) probe of radius (r) at temperature (T_P) through tissue and into the edge of the collecting system at temperature (T_cs) that is being cooled by a circulating liquid at temperature (T_L).

where T_P, is the probe temperature, T_CS is the temperature at the surface where the collecting system would meet the convecting fluid, and S is the shape factor for a long cylinder (l >>r) against a parallel planar surface with a distance (d) from the surface that is much greater than the radius (r).⁹ The shape factor accounts for the geometric effects.

Equation 1 states that the heat moving out of the probe per second ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\dot{{ \rm Q}}$$ \end{document} ) is equal to the heat conducting through the tissue: kS(T_P – T_CS). Equation 2 states that the heat output by the probe is also equal to that which is being transferred into the fluid by its the mass flow via convection: hA(T_CS – T_L).

With two variables and two equations, we can substitute and solve for each. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} { \rm Equation \ ( 3 ) \, : } \ { \rm T } _ { \rm CS } = \frac { Q } { h*A } + { \rm T } _ { \rm L } \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} { \rm Equation \ ( 4 ) \, : } \ { \rm T } _ { \rm P } = \frac { Q } { k * S } + { \rm T } _ { \rm CS } \end{align*} \end{document}

Once the temperatures of tissue at both the probe and the collecting system are calculated, a logarithmic relationship was assumed to describe the temperatures between those two points. From this, a Microsoft Excel sheet was created where the necessary constants could be entered and a temperature profile produced. A literature search revealed possible values for the constants of conduction (k=0.50 W/mK)¹⁰ and convection (h=50 – 500 W/m²K)¹⁰ in the mathematical model. Using these constants, an appropriate predictive temperature profile could be estimated for our experiment.

Ex vivo porcine experiments

Kidneys were harvested at the University of Miami Division of Veterinary Resources. Twenty-four RFA trials were performed on ex vivo porcine kidneys with a ValleyLab CoolTip RFA system (Covidien, Boulder, CO); ablations were performed under an approved Institutional Animal Care and Use Committee protocol. A 20-mm RFA probe (Covidien, Boulder, CO) was place 18 mm from the pelvis using ultrasound guidance (SSD-4000 ultrasound system, Hitachi Aloka, Wallingford, CT). Fiberoptic thermal sensors (Focal Point, Lumasense, Santa Clara, CA) were placed on either side of the RFA probe along the plane perpendicular to the probe axis plus at the location of the probe (Fig. 2). The experiment was conducted in a heat chamber set at 38°C to warm up the kidney before the ablation (Fig. 3a). Ablations were performed with either cold saline (2°C), warm saline (38°C), polyethylene (PEG) glycol (−20°C), or no fluid PPF through the renal cortex using a peristaltic pump (FH100 peristaltic pump, ThermoFisher Scientific, Waltham, MA), (Fig. 3b).

FIG. 2.

The experimental setup for measuring the temperatures throughout the renal parenchyma during radiofrequency ablation (RFA) with fluid circulating through the collecting system by retrograde pyeloperfusion.

FIG. 3.

(a) Heat chamber with fiberoptic thermal sensors and (b) the radiofrequency ablation (RFA) system with the pyeloperfusion pump. This heat chamber would heat the kidney to approximately the body temperature before RFA.

Six ablations were performed per PPF type. PEG was used to compare its different conductive and convective fluid properties to the other perfusates. Fluids were pumped at a rate of 60 mL/min for 3 minutes before starting RFA. RFA was performed for 12 minutes. Temperatures were measured both during RFA and for 5 minutes cool-down after the completion of RFA as per the protocol described by Rouvière.⁷ The RFA system was set on manual mode at three-fourths the maximum output. The temperatures throughout the kidney were recorded by a data acquisition program written in Labview (National Instruments, Austin, TX). The RFA probe power output, voltage, current, and impedance were recorded via a program designed by the RFA system manufacturer. After ablation, the kidneys were dissected coronally, and ablation zone dimensions were measured using calipers along its length (upper to lower pole), width (medial to lateral), and depth (anterior to posterior). A coronal plane comprised of parenchyma and collecting system was sent for histologic analysis. Viability stains were not used because these were extirpated kidneys.

As the tissue surrounding the RFA probe desiccates, its impedance will rise dramatically. The power from the RFA system will, therefore, fluctuate on and off according to its impedance algorithm when using the impedance mode. In this investigation, we used the manual mode. Nonetheless, the temperatures measured from each ablation appeared to fluctuate above and below a steady state temperature within the final 2 minutes of the ablation. The average steady state temperatures were calculated using the mean of the last 2 minutes of RFA and analyzed using SPSS software. Steady state temperatures for each thermal sensor were compared with their conjugate on the other side of the RFA probe, within other PPF types, and to our theoretical model using a two-tailed t test.

Combining ex vivo and theoretical models

The experimentally found temperatures at both the probe and the collecting system allowed for calculated constants of conduction (k) and convection (h) using the above described theoretical model. Three trials for warm saline had to be removed from these theoretical model calculations because they had measured tissue temperatures at the collecting system lower than that of the perfusing fluid that cannot be accounted for mathematically. The predictive model was used to calculate temperatures at the core and at the collecting system based on the calculated thermal constants. To do this, all power outputs were decreased by 25% (number determined through estimation) to account for heat loss in directions other than that of the convecting fluid.

Results

Theoretical model

Using the thermal constants mentioned in the literature, an RFA with an output power of 42 W would produce maximum tissue temperatures of 6°C and temperatures at the collecting system of 44°C when implementing a 2°C cold saline PPF (Fig. 4). The same temperature profiles were created for warm saline (T_L=38°C), no PPF (h=50), and for PEG (T_L=−20°C). The predicted temperatures at the probe and the collecting system are given in Table 1. As expected, the temperatures at the probe and the collecting system were predicted to be warmer with the warm saline and no PPF than those with the cold saline and the PEG.

FIG. 4.

With these given constants, which can be manipulated based on changing experimental factors, theoretical curves can be generated for the temperatures throughout the kidney during radiofrequency ablation (RFA) with pyeloperfusion.

Table 1.

Predicted Temperatures of the Probe and the Collecting System at Steady State

Condition	T_Probe (°C)	T_CS (°C)
Cold saline	63.7	42
Warm saline (T_L=38°C)	99.7	80
No pyeloperfusion (h=50)	189.7	170
PEG (T_L=−20°C)	41.7	22

PEG=polyethylene glycol.

Ex vivo model

The average steady state temperatures from all distances from the RFA probe were highest for no PPF, followed by warm saline, cold saline, and PEG (Table 2) Compared with no PPF, (70.6°C) average temperatures were significantly (P<0.05) colder with warm saline PPF (62.2°C) and cold saline PPF (52.9°C). When considering all the distances from the probe, the difference in average steady state temperatures were greater between cold saline and no PPF (13.1%–47.6%) than between warm saline and no PPF (1.0%–18.5%). In addition, cold saline PPF was shown to have significantly colder temperatures than warm saline PPF (P=0.046).

Table 2.

Average Steady State Temperatures of All Distances from RFA Probe and Temperatures at the Collecting System

Condition	Average overall SS temperature (^oC)	P value against no PPF	Average temperature at T_CS (^oC)	P value against no PPF
Cold	52.9	<0.001	29.5	0.005
Warm	62.2	0.020	42.7	0.022
No PPF	70.6	N/A	56.4	N/A
PEG	42.7	<0.001	27.5	0.052

SS=steady state; PPF=pyeloperfusion; PEG=polyethylene glycol; RFA=radiofrequency ablation.

On analyzing each specific distance from the RFA probe, we notice that PPF effects were seen most prominently at the collecting system (T_CS) where the average temperature of warm saline (42.7°C) and cold saline (29.5°C) were significantly lower than no PPF (56.4°C) (Table 2). Cold saline PPF showed significantly cooler temperatures than warm PPF or no PPF for the other distances. PEG PPF appears to cool similarly to cold saline PPF toward the collecting system but behaves more akin to warm PPF or no PPF at distances greater than 1 cm from the collecting system (Fig. 5).

FIG. 5.

The average steady state temperatures of the renal parenchyma at different distances from the radiofrequency ablation (RFA) probe during different conditions of pyeloperfusion. Cold saline appears to cool down the renal parenchyma the most.

The RFA probe output: A constant voltage (75V) based on its setting in manual mode. Significantly lower resistances, however, in warm (171 Ω) and cold (124 Ω) PPF compared with no PPF (363 Ω) translated to significantly greater power outputs in warm (40 W) and cold PPF (42 W) when compared with no PPF (14.1 W) (Table 3). The ablated volumes were significantly higher in warm saline (2.3 cm³) when compared with cold saline (0.81 cm³) and no PPF (1.1 cm³) (Table 3). No ablated volumes were visible after antifreeze PPF.

Table 3.

Comparing Power Emissions and Ablative Volumes in Ex Vivo Experiments

Condition	Average power emitted (W)	P value against no PPF	Average ablative volume (cm³)	P value against warm PPF
Cold	42	0.032	0.81	0.047
Warm	40	0.010	2.26	N/A
No pyeloperfusion	14	N/A	1.09	0.036

According to histologic analysis, thermal ablation of the tissue architecture was located in areas having temperatures greater than 60°C. Perfusing cold saline was able to preserve the architecture at the collecting system (Fig. 6a). Thermal ablation at the renal calix was observed for RFA with warm saline PPF (Fig. 6b) and no PPF (Fig. 6c). Pyeloperfusing antifreeze (Fig. 6d) at −20°C showed the greatest degree of cellular destruction despite the relatively low temperatures. Histologic analysis was complicated by generalized tissue changes most likely attributed to freezing the tissue during storage.

FIG. 6.

Slides A–D (top left to right, to bottom left to right): (a) Cold saline pyeloperfusion (PPF) showing preservation of the collecting system. (b) Warm saline PPF. (c) No PPF. (d) Polyethylene glycol PPF with heavily disrupted cellular architecture. All oriented with probe toward the top left corner and the collecting system toward the bottom right.

Comparing theoretical and ex vivo models

As mentioned above, the thermal conductivity (k) of the renal tissue and the convection constant of the PPF fluid (h) were calculated based on matching the predicted values of our algorithm with the values measured from the experiments. The thermal conductivity and convection values measured for each PPF scenario are given in Table 4. The values for the thermal conductivity (k) and thermal convection constant ranged from 0.09 (no PPF) to 0.18 (warm saline PPF) W/mK and from 125 (PEG PPF) to 528 (warm saline PPF) W/m²K, respectively. When implementing the thermal properties for each respective PPF solution, the experimental temperature values at the probe and collecting system were similar to the predicted values for both warm and cold saline PPF (Fig. 7). There were no similarities, however, between the experimental and predicted values for both the no PPF and the PEG PPF, which may be attributed to their low, calculated thermal properties. This was then plotted to compare the predicted temperatures with the actual temperatures (Fig. 7). A linear regression of this plot found an R² value of 0.44. This shows some predictability of the mathematical model but below a standard that would be effective intraoperatively.

FIG. 7.

The accuracy of the theoretical model in determining the temperatures found experimentally showing the most accuracy during cold pyeloperfusion. PEG=polyethylene glycol.

Table 4.

Calculated Constants Based on Ex Vivo Trials

Condition	Calculated k (W/mK)	Calculated h (W/m²K)
Cold	0.16	231
Warm^a	0.18	528
No pyeloperfusion	0.09	154
PEG	0.15	125

Calculated based on three trials.

Discussion

RFA is an effective treatment for patients with SRMs, although treatment is often hindered by the proximity to the renal collecting system. We created a mathematical and ex vivo model to elucidate the effectiveness of PPF to protect the collecting system during RFA.

Theoretical model

The mathematical model was able to demonstrate theoretical effectiveness of PPF that would be affected by the temperature of the PPF liquid. Using constants obtained from previous experiments, the model predicted cold saline PPF steady state temperatures that ranged from >70°C at the probe to <35°C at the collecting system. This temperature range is consistent with tissue ablation at the probe while conferring a degree of protection at the collecting system.¹¹ The model then predicted an inability to protect the tissue at the collecting system for both warm saline PPF and no PPF, which matches ex vivo temperature profiles and histologic analysis.

The model tended to break down at conditions with low amounts of convection. This affected primarily the no PPF and the PEG PPF predicted temperatures. Because the fluid has lower amounts of convection, a greater proportion of the heat from the probe may escape through other sources.

When using constants obtained from the ex vivo experiment, the model tended to overestimate the temperatures. This is likely the result of heat loss from the probe to places other than the perfusing liquid and is largely corrected when it is assumed that only 75% of the total power output will enter the perfusing liquid. This ultimately allowed for a predictive temperature model with an R² value at 0.44.

While these experiments focused on the final steady state temperatures achieved, it should be noted that the rate at which the temperature rises in renal tissue has been largely associated with the degree of destruction independent of the final temperature.¹¹ Future models could try to incorporate this information.

The true goal of any ablative therapy is achieving high energy density in the zone of ablation with a steep drop-off at the target boundaries to protect the surrounding tissue. By acting as a heat sink, the mathematical model shows the effectiveness of PPF.

Ex vivo model

The ex vivo model confirmed the effectiveness of PPF. The tissue temperatures during cold saline PPF were significantly decreased throughout all of the tissue. The effect was exaggerated at the collecting system, which was cooled from unsafe temperatures >60°C without PPF to safe temperatures <30°C with PPF. The effect does appear to be somewhat dependent on the temperature of the perfusing fluid; however warm saline was still able to convect a large amount of heat away from the tissues and allow a temperature rise at the collecting system that may not affect the collecting system within the RFA treatment cycle used in this investigation. It is likely that the pyeloperfusing fluid would draw heat from the surrounding tissues and increase in temperature in an in vivo kidney, even though this would most likely not negate the effect of PPF in protecting the renal calix. Future studies in in vivo kidneys are nonetheless encouraged.

The voltage output was the variable setting on the ValleyLab CoolTip RFA system in manual mode. The voltage output was 75 V for all of our experiments. Because tissue would often char around the probe, however, the impedance would quickly increase because of tissue charring surrounding the probe. This impedance rise would drive the current and power output down. This occasionally made the RFA output low powers (<10 W) and resulted in no ablation zone. This may add some level of unpredictability to the method. Ultimately, much larger power outputs were observed during PPF as a result of less charring of the surrounding tissue. Despite these increased power outputs, temperatures still remained lower during PPF.

Cold saline PPF may sacrifice some size of the visible ablation zone, which was smaller than that of no PPF. Interestingly, warm saline PPF had the opposite effect, significantly increasing the size of the ablation zone. This implies that it may have had the steepest drop in energy density as it ablated a large volume but appeared to keep temperatures at the calix relatively low. We suspect that this may be because of the decreased charring and therefore higher power outputs in comparison with the temperatures of the perfusing fluid.

Meireles and coworkers¹² saw no alteration to the integrity of the excretory system when applying RFA with the RITA RFA system, but also observed no change in the ablation size between saline-cooled and nonpyeloperfused porcine kidneys in vivo. This study, however, used a perfusion rate of 30 mL/min, while our investigation used a rate of 60 mL/min. Their study also perfused for 2 minutes before RFA, while our investigation perfused for 3 minutes before RFA. These differences in needle type and treatment parameters may be the reason for our investigation witnessing a change in ablation sizes for different PPF situations. Changes in PPF rate and time before RFA may also influence the amount of heat that can be applied.

Histology confirmed that cold saline PPF was able to adequately and consistently protect the collecting system from heat damage. Oddly, while no visible ablation zone was present with −20°C antifreeze PPF, histology confirmed complete destruction of the surrounding tissues. The damage may be secondary to the extreme differences in temperature between the RFA probe and the PPF liquid.

By changing the temperature or the thermal properties of the perfusate, our preliminary study elucidates new variables that could allow for more precise discrimination of tissue ablation. Future in vivo experimentation is the logical next step along with advancement of our theoretical model, which could potentially determine an appropriate perfusate for a desired ablation zone.

Conclusion

PPF lowers temperatures throughout the entire kidney during RFA, most notably near the collecting system, and is dependent on the temperature of the liquid used. PEG PPF appears to cool similarly to cold saline. In addition, PPF may cause less charring of the tissue around the probe resulting in lower resistance and higher power outputs. Further studies should be performed to investigate the effect of RFA probe position, PPF rate, PPF start time before RFA, and the possible effect of blood flow.

Acknowledgments

The Endourological Society 2013 Summer Student Scholarship for providing support to the lead author, Covidien, Inc. for providing the RFA probes, and to Dr. Julia Zaias at the Department of Veterinary Resources, University of Miami Miller School of Medicine, for providing assistance in the histologic analysis.

Disclosure Statement

Dr. Leveille is a consultant for Covidien, Inc. No competing financial interests exist for the remaining authors.

Footnotes

Abbreviations Used

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