2016, 13(2): 281-301. doi: 10.3934/mbe.2015003

Electrical-thermal analytical modeling of monopolar RF thermal ablation of biological tissues: determining the circumstances under which tissue temperature reaches a steady state

1. 

Applied Mathematics Department, Universitat Politècnica de València, Camino de Vera 46022 Valencia, Spain, Spain

2. 

Biomedical Synergy, Electronic Engineering Department, Universitat Politècnica de València, Camino de Vera 46022 Valencia, Spain

Received  March 2015 Revised  July 2015 Published  November 2015

It has been suggested that during RF thermal ablation of biological tissue the thermal lesion could reach an equilibrium size after 1-2 minutes. Our objective was to determine under which circumstances of electrode geometry (needle-like vs. ball-tip), electrode type (dry vs. cooled) and blood perfusion the temperature will reach a steady state at any point in the tissue. We solved the bioheat equation analytically both in cylindrical and spherical coordinates and the resultant limit temperatures were compared. Our results demonstrate mathematically that tissue temperature reaches a steady value in all cases except for cylindrical coordinates without the blood perfusion term, both for dry and cooled electrodes, where temperature increases infinitely. This result is only true when the boundary condition far from the active electrode is considered to be at infinitum. In contrast, when a finite and sufficiently large domain is considered, temperature reaches always a steady state.
Citation: J. A. López Molina, M. J. Rivera, E. Berjano. Electrical-thermal analytical modeling of monopolar RF thermal ablation of biological tissues: determining the circumstances under which tissue temperature reaches a steady state. Mathematical Biosciences & Engineering, 2016, 13 (2) : 281-301. doi: 10.3934/mbe.2015003
References:
[1]

B. L. Yun, J. M. Lee, J. H. Baek, S. H. Kim, J. Y. Lee, J. K. Han and B. I. Choi, Radiofrequency ablation for treating liver metastases from a non-colorectal origin, Korean Journal Radiology, 12 (2011), 579-587. doi: 10.3348/kjr.2011.12.5.579.

[2]

E. R. Cosman Jr. and E. R. Cosman Sr., Electric and thermal field effects in tissue around radiofrequency electrodes, Pain Medicine, 6 (2005), 405-424.

[3]

A. Thiagalingam, C. R. Campbell, A. C. Boyd, V. E. Eipper, D. L. Ross and P. Kovoor, Cooled intramural needle catheter ablation creates deeper lesions than irrigated tip catheter ablation, Pacing and Clinical Electrophysiology, 27 (2004), 965-970. doi: 10.1111/j.1540-8159.2004.00566.x.

[4]

S. I. Cho, B. Y. Chung, M. G. Cho, J. H. Baek, C. W. Park, C. H. Lee and H. O. Kim, Evaluation of the clinical efficacy of fractional radiofrequency microneedle treatament in acne scars and large facial pores, Dermatologic survey, (2012), 1017-1024.

[5]

T. H. Everett 4th, K. W. Lee, E. E. Wilson, J. M. Guerra, P. D. Varosy and J. E. Olgin, Safety profiles and lesion size of different radiofrequency ablation technologies: A comparison of large tip, open and closed irrigation catheters, Journal of Cardiovascular Electrophysiology, 20 (2009), 325-335.

[6]

Y. Nakasone, O. Ikeda, K. Kawanaka, K. Yokoyama and Y. Yamashita, Radiofrequency ablation in a porcine kidney model: Effect of occlusion of the arterial blood supply on ablation temperature, coagulation diameter, and histology, Acta Radiologica, 53 (2012), 852-856. doi: 10.1258/ar.2012.110530.

[7]

E. J. Berjano, Theoretical modeling for radiofrequency ablation: State-of-the-art and challenges for the future, Biomedical Engineering Online, 18 (2006), p24.

[8]

Y. Jiang, W. Chong, M. C. Diel Rambo, L. A. Bortolaia and A. C. Valdiero, Analytical solution of temperature distributions in radiofrequency ablation due to a point source of electrical current, 60 Brasilean Conference on Dynamics, Control and Their Applications, Dincon'2007, (2007), 21-27.

[9]

M. J. Rivera, M. Trujillo, V. Romero García, J. A. López Molina and E. J. Berjano, Numerical resolution of the hyperbolic heat equation using smooted mathematical functions instead of Heaviside and dirac delta distributions, International Communications in Heat and Mass Transfer, 46 (2013), 7-12.

[10]

J. D. Wiley and J. G. Webster, Analysis and control of the current distribution under circular dispersive electrodes, IEEE Transactions on Biomedical Engineering, 29 (1982), 381-385. doi: 10.1109/TBME.1982.324910.

[11]

K. M. Overmyer, J. A. Pearce and D. P. de Witt, Measurements of temperature distributions at electro-surgical dispersive electrode sites, Transactions of the ASME, Journal of Biomechanical Engineering, 101 (1979), 66-72.

[12]

W. M. Honig, The mechanism of cutting in electrosurgery, IEEE Transactions on Biomedical Engineering, 22 (1975), 58-62. doi: 10.1109/TBME.1975.324541.

[13]

A. Erez and A. Shitzer, Controlled destruction and temperature distributions in biological tissues subjected to monoactive electroagulation, Journal of Biomechanical Engineering, 102 (1980), 42-49.

[14]

D. E. Haines and D. D. Watson, Tissue heating durin radiofrequency catheter ablation: A thermodynamic model and observations in isolated perfused and superfused canine right ventricular free wall, Pacing and Clinical Electrophysiology, 12 (1989), 962-967.

[15]

D. Haemmerich, L. Chachati, A. S. Wright, D. M. Mahvi, F. T. Lee Jr. and J. G. Webster, Hepatic radiofrequency ablation with internally cooled probes: Effect of coolant temperature on lesion size, IEEE Transactions on Biomedical Engineering, 50 (2003), 493-500. doi: 10.1109/TBME.2003.809488.

[16]

J. A. López Molina, M. J. Rivera, M. Trujillo and E. J. Berjano, Effect of the thermal wave in radiofrequency ablation modeling: An analytical study, Physics in Medicine and Biology, 53 (2008), 1447-1462. doi: 10.1088/0031-9155/53/5/018.

[17]

J. A. López Molina, M. J. Rivera and E. J. Berjano, Analytical model based on a cylindrical geometry to study of RF ablation with needle-like internally cooled electrode, Mathematical Problems in Engineering, (2012), Article ID 834807, 16 pages.

[18]

M. J. Rivera, J. A. López Molina, M. Trujillo and E. J. Berjano, Theoretical modeling of RF ablation with internally cooled electrodes: Comparative study of different thermal boundary conditions at the electrode-tissue interface, Mathematical Biosciences and Engineering, 6 (2009), 611-627. doi: 10.3934/mbe.2009.6.611.

[19]

G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995.

[20]

E. J. Berjano, E. Navarro, V. Ribera, J. Gorris and J. L. Alió, Radiofrequency heating of the cornea: An engineering review of electrodes and applicators, Open Biomedical Engineering Journal, 11 (2007), 71-76.

[21]

M. Trujillo, J. Alba and E. J. Berjano, Relationship between roll-off occurrence and spatial distribution of dehydrated tissue during RF ablation with cooled electrodes, International Journal of Hyperthermia, 28 (2012), 62-68. doi: 10.3109/02656736.2011.631076.

[22]

I. A. Chang, Finite elements analysis of hepatic radiofrequency ablation probes using temperature-dependent electrical conductivity, Biomedical Engineering Online, 8 (2003), p12.

[23]

I. A. Chang and U. D. Nguyen, Thermal modeling of lesions growth with radiofrequency ablation devices, Biomedical Engineering Online, 6 (2004), p27.

show all references

References:
[1]

B. L. Yun, J. M. Lee, J. H. Baek, S. H. Kim, J. Y. Lee, J. K. Han and B. I. Choi, Radiofrequency ablation for treating liver metastases from a non-colorectal origin, Korean Journal Radiology, 12 (2011), 579-587. doi: 10.3348/kjr.2011.12.5.579.

[2]

E. R. Cosman Jr. and E. R. Cosman Sr., Electric and thermal field effects in tissue around radiofrequency electrodes, Pain Medicine, 6 (2005), 405-424.

[3]

A. Thiagalingam, C. R. Campbell, A. C. Boyd, V. E. Eipper, D. L. Ross and P. Kovoor, Cooled intramural needle catheter ablation creates deeper lesions than irrigated tip catheter ablation, Pacing and Clinical Electrophysiology, 27 (2004), 965-970. doi: 10.1111/j.1540-8159.2004.00566.x.

[4]

S. I. Cho, B. Y. Chung, M. G. Cho, J. H. Baek, C. W. Park, C. H. Lee and H. O. Kim, Evaluation of the clinical efficacy of fractional radiofrequency microneedle treatament in acne scars and large facial pores, Dermatologic survey, (2012), 1017-1024.

[5]

T. H. Everett 4th, K. W. Lee, E. E. Wilson, J. M. Guerra, P. D. Varosy and J. E. Olgin, Safety profiles and lesion size of different radiofrequency ablation technologies: A comparison of large tip, open and closed irrigation catheters, Journal of Cardiovascular Electrophysiology, 20 (2009), 325-335.

[6]

Y. Nakasone, O. Ikeda, K. Kawanaka, K. Yokoyama and Y. Yamashita, Radiofrequency ablation in a porcine kidney model: Effect of occlusion of the arterial blood supply on ablation temperature, coagulation diameter, and histology, Acta Radiologica, 53 (2012), 852-856. doi: 10.1258/ar.2012.110530.

[7]

E. J. Berjano, Theoretical modeling for radiofrequency ablation: State-of-the-art and challenges for the future, Biomedical Engineering Online, 18 (2006), p24.

[8]

Y. Jiang, W. Chong, M. C. Diel Rambo, L. A. Bortolaia and A. C. Valdiero, Analytical solution of temperature distributions in radiofrequency ablation due to a point source of electrical current, 60 Brasilean Conference on Dynamics, Control and Their Applications, Dincon'2007, (2007), 21-27.

[9]

M. J. Rivera, M. Trujillo, V. Romero García, J. A. López Molina and E. J. Berjano, Numerical resolution of the hyperbolic heat equation using smooted mathematical functions instead of Heaviside and dirac delta distributions, International Communications in Heat and Mass Transfer, 46 (2013), 7-12.

[10]

J. D. Wiley and J. G. Webster, Analysis and control of the current distribution under circular dispersive electrodes, IEEE Transactions on Biomedical Engineering, 29 (1982), 381-385. doi: 10.1109/TBME.1982.324910.

[11]

K. M. Overmyer, J. A. Pearce and D. P. de Witt, Measurements of temperature distributions at electro-surgical dispersive electrode sites, Transactions of the ASME, Journal of Biomechanical Engineering, 101 (1979), 66-72.

[12]

W. M. Honig, The mechanism of cutting in electrosurgery, IEEE Transactions on Biomedical Engineering, 22 (1975), 58-62. doi: 10.1109/TBME.1975.324541.

[13]

A. Erez and A. Shitzer, Controlled destruction and temperature distributions in biological tissues subjected to monoactive electroagulation, Journal of Biomechanical Engineering, 102 (1980), 42-49.

[14]

D. E. Haines and D. D. Watson, Tissue heating durin radiofrequency catheter ablation: A thermodynamic model and observations in isolated perfused and superfused canine right ventricular free wall, Pacing and Clinical Electrophysiology, 12 (1989), 962-967.

[15]

D. Haemmerich, L. Chachati, A. S. Wright, D. M. Mahvi, F. T. Lee Jr. and J. G. Webster, Hepatic radiofrequency ablation with internally cooled probes: Effect of coolant temperature on lesion size, IEEE Transactions on Biomedical Engineering, 50 (2003), 493-500. doi: 10.1109/TBME.2003.809488.

[16]

J. A. López Molina, M. J. Rivera, M. Trujillo and E. J. Berjano, Effect of the thermal wave in radiofrequency ablation modeling: An analytical study, Physics in Medicine and Biology, 53 (2008), 1447-1462. doi: 10.1088/0031-9155/53/5/018.

[17]

J. A. López Molina, M. J. Rivera and E. J. Berjano, Analytical model based on a cylindrical geometry to study of RF ablation with needle-like internally cooled electrode, Mathematical Problems in Engineering, (2012), Article ID 834807, 16 pages.

[18]

M. J. Rivera, J. A. López Molina, M. Trujillo and E. J. Berjano, Theoretical modeling of RF ablation with internally cooled electrodes: Comparative study of different thermal boundary conditions at the electrode-tissue interface, Mathematical Biosciences and Engineering, 6 (2009), 611-627. doi: 10.3934/mbe.2009.6.611.

[19]

G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995.

[20]

E. J. Berjano, E. Navarro, V. Ribera, J. Gorris and J. L. Alió, Radiofrequency heating of the cornea: An engineering review of electrodes and applicators, Open Biomedical Engineering Journal, 11 (2007), 71-76.

[21]

M. Trujillo, J. Alba and E. J. Berjano, Relationship between roll-off occurrence and spatial distribution of dehydrated tissue during RF ablation with cooled electrodes, International Journal of Hyperthermia, 28 (2012), 62-68. doi: 10.3109/02656736.2011.631076.

[22]

I. A. Chang, Finite elements analysis of hepatic radiofrequency ablation probes using temperature-dependent electrical conductivity, Biomedical Engineering Online, 8 (2003), p12.

[23]

I. A. Chang and U. D. Nguyen, Thermal modeling of lesions growth with radiofrequency ablation devices, Biomedical Engineering Online, 6 (2004), p27.

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