Mathematical modeling: a valuable training aid for new medical devices

[EN] The paper deals with biomedical modeling in general and in particular how modeling techniques can be used to improve the training of clinical practitioners in the use of new medical devices. The Bioheat Equation is given as an example to show how, even though mathematical models are based on complex equations, the terms of the equations represent phenomena which can be intuitively understood. The paper also describes examples in which mathematical modeling was used to study the performance of medical devices, especially those related with radiofrequency ablation.[ES] Este artículo trata sobre la modelización biomédica en general y cómo las técnicas de modelización pueden ayudar para mejorar la práctica clínica en el uso de nuevos dispositivos médicos en particular. La ecuación “Bioheat” o de difusión del calor en tejido biológico se utiliza como ejemplo para mostrar como, incluso en el caso en que los modelos matemáticos estén basados en ecuaciones complejas, los términos de dichas ecuaciones representan fenómenos que pueden ser entendidos de forma intuitiva. El artículo también presenta ejemplos en los cuales el modelado matemático se usa para estudiar la adecuación de los dispositivos médicos, especialmente aquellos relacionados con la ablación por radiofrecuencia.Berjano, E. (2010). Mathematical modeling: a valuable training aid for new medical devices. Modelling in Science Education and Learning. 3:55-65. doi:10.4995/msel.2010.3112SWORD5565

A cooled intraesophageal balloon to prevent thermal injury during endocardial surgical radiofrequency ablation of the left atrium: a finite element study

[EN] Recent clinical studies on intraoperative monopolar radiofrequency ablation of atrial fibrillation have reported some cases of injury to the esophagus. The aim of this study was to perform computer simulations using three-dimensional finite element models in order to investigate the feasibility of a cooled intraesophageal balloon appropriately placed to prevent injury. The models included atrial tissue and a fragment of esophagus and lung linked by connective tissue. The lesion depth in the esophagus was assessed using a 50 degrees C isotherm and expressed as a percentage of thickness of the esophageal wall. The results are as follows: (1) chilling the esophagus by means of a cooled balloon placed in the lumen minimizes the lesion in the esophageal wall compared to the cases in which no balloon is used (a collapsed esophagus) and with a non-cooled balloon; (2) the temperature of the cooling fluid has a more significant effect on the minimization of the lesion than the rate of cooling (the thermal transfer coefficient for forced convection); and (3) pre-cooling periods previous to RF ablation do not represent a significant improvement. Finally, the results also suggest that the use of a cooled balloon could affect the transmurality of the atrial lesion, especially in the cases where the atrium is of considerable thickness.The authors wish to thank Mr Trevor Lepp for the manuscript corrections, and the reviewers for their comments. This work was partially supported by a grant from the Spanish Ministry of Education and Science (Project CAMAEC-III) and by Programa de Incentivo a la Investigación (Universidad Politécnica de Valencia, Spain).Berjano, E.; Hornero, F. (2015). A cooled intraesophageal balloon to prevent thermal injury during endocardial surgical radiofrequency ablation of the left atrium: a finite element study. Physics in Medicine and Biology. 50(20):269-279. https://doi.org/10.1088/0031-9155/50/20/N03S2692795020Al-Zaben, A., & Chandrasekar, V. (2005). Effect of esophagus status and catheter configuration on multiple intraluminal impedance measurements. Physiological Measurement, 26(3), 229-238. doi:10.1088/0967-3334/26/3/008Bhattacharya, A., & Mahajan, R. L. (2003). Temperature dependence of thermal conductivity of biological tissues. Physiological Measurement, 24(3), 769-783. doi:10.1088/0967-3334/24/3/312Benussi, S., Nascimbene, S., Agricola, E., Calori, G., Calvi, S., Caldarola, A., … Alfieri, O. (2002). Surgical ablation of atrial fibrillation using the epicardial radiofrequency approach: mid-term results and risk analysis. The Annals of Thoracic Surgery, 74(4), 1050-1057. doi:10.1016/s0003-4975(02)03850-xBerjano, E. J., & Hornero, F. (2004). Thermal-Electrical Modeling for Epicardial Atrial Radiofrequency Ablation. IEEE Transactions on Biomedical Engineering, 51(8), 1348-1357. doi:10.1109/tbme.2004.827545Berjano, E. J., & Hornero, F. (2005). What affects esophageal injury during radiofrequency ablation of the left atrium? An engineering study based on finite-element analysis. Physiological Measurement, 26(5), 837-848. doi:10.1088/0967-3334/26/5/020Chang, I. A., & Nguyen, U. D. (2004). Thermal modeling of lesion growth with radiofrequency ablation devices. BioMedical Engineering OnLine, 3(1). doi:10.1186/1475-925x-3-27Chiappini, B., Martìn-Suàrez, S., LoForte, A., Di Bartolomeo, R., & Marinelli, G. (2003). Surgery for atrial fibrillation using radiofrequency catheter ablation. The Journal of Thoracic and Cardiovascular Surgery, 126(6), 1788-1791. doi:10.1016/s0022-5223(03)01045-6Doll, N., Borger, M. A., Fabricius, A., Stephan, S., Gummert, J., Mohr, F. W., … Hindricks, G. (2003). Esophageal perforation during left atrial radiofrequency ablation: Is the risk too high? The Journal of Thoracic and Cardiovascular Surgery, 125(4), 836-842. doi:10.1067/mtc.2003.165Gabriel, C., Gabriel, S., & Corthout, E. (1996). The dielectric properties of biological tissues: I. Literature survey. Physics in Medicine and Biology, 41(11), 2231-2249. doi:10.1088/0031-9155/41/11/001Gaynor, S. L., Diodato, M. D., Prasad, S. M., Ishii, Y., Schuessler, R. B., Bailey, M. S., … Damiano, R. J. (2004). A prospective, single-center clinical trial of a modified Cox maze procedure with bipolar radiofrequency ablation. The Journal of Thoracic and Cardiovascular Surgery, 128(4), 535-542. doi:10.1016/j.jtcvs.2004.02.044Gillinov, A. M., Pettersson, G., & Rice, T. W. (2001). Esophageal injury during radiofrequency ablation for atrial fibrillation. The Journal of Thoracic and Cardiovascular Surgery, 122(6), 1239-1240. doi:10.1067/mtc.2001.118041Haemmerich, D., Webster, J. G., & Mahvi, D. M. (s. f.). Thermal dose versus isotherm as lesion boundary estimator for cardiac and hepatic radio-frequency ablation. Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No.03CH37439). doi:10.1109/iembs.2003.1279532YEN HO, S., SANCHEZ-QUINTANA, D., CABRERA, J. A., & ANDERSON, R. H. (1999). Anatomy of the Left Atrium:. Journal of Cardiovascular Electrophysiology, 10(11), 1525-1533. doi:10.1111/j.1540-8167.1999.tb00211.xHornero, F., Rodriguez, I., Bueno, M., Buendia, J., Dalmau, M. J., Canovas, S., … Montero, J. A. (2004). Surgical Ablation of Permanent Atrial Fibrillation by Means of Maze Radiofrequency:. Mid-Term Results. Journal of Cardiac Surgery, 19(5), 383-388. doi:10.1111/j.0886-0440.2004.04077.xJain, M. K., & Wolf, P. D. (1999). Temperature-controlled and constant-power radio-frequency ablation: what affects lesion growth? IEEE Transactions on Biomedical Engineering, 46(12), 1405-1412. doi:10.1109/10.804568Lemola, K., Sneider, M., Desjardins, B., Case, I., Han, J., Good, E., … Oral, H. (2004). Computed Tomographic Analysis of the Anatomy of the Left Atrium and the Esophagus. Circulation, 110(24), 3655-3660. doi:10.1161/01.cir.0000149714.31471.fdNath, S., Lynch, C., Whayne, J. G., & Haines, D. E. (1993). Cellular electrophysiological effects of hyperthermia on isolated guinea pig papillary muscle. Implications for catheter ablation. Circulation, 88(4), 1826-1831. doi:10.1161/01.cir.88.4.1826Pappone, C., Oral, H., Santinelli, V., Vicedomini, G., Lang, C. C., Manguso, F., … Morady, F. (2004). Atrio-Esophageal Fistula as a Complication of Percutaneous Transcatheter Ablation of Atrial Fibrillation. Circulation, 109(22), 2724-2726. doi:10.1161/01.cir.0000131866.44650.46Sonmez, B., Demirsoy, E., Yagan, N., Unal, M., Arbatli, H., Sener, D., … Ilkova, F. (2003). A fatal complication due to radiofrequency ablation for atrial fibrillation: atrio-esophageal fistula. The Annals of Thoracic Surgery, 76(1), 281-283. doi:10.1016/s0003-4975(03)00006-

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

Purpose: Although theoretical modelling is widely used to study different aspects of radiofrequency ablation (RFA), its utility is directly related to its realism. An important factor in this realism is the use of mathematical functions to model the temperature dependence of thermal (k) and electrical (sigma) conductivities of tissue. Our aim was to review the piecewise mathematical functions most commonly used for modelling the temperature dependence of k and sigma in RFA computational modelling. Materials and methods: We built a hepatic RFA theoretical model of a cooled electrode and compared lesion dimensions and impedance evolution with combinations of mathematical functions proposed in previous studies. We employed the thermal damage contour D63 to compute the lesion dimension contour, which corresponds to Omega = 1, Omega being local thermal damage assessed by the Arrhenius damage model. Results: The results were very similar in all cases in terms of impedance evolution and lesion size after 6 min of ablation. Although the relative differences between cases in terms of time to first roll-off (abrupt increase in impedance) were as much as 12%, the maximum relative differences in terms of the short lesion (transverse) diameter were below 3.5%. Conclusions: The findings suggest that the different methods of modelling temperature dependence of k and sigma reported in the literature do not significantly affect the computed lesion diameter.This work received financial support from the Spanish Plan Nacional de I þ D þ I del Ministerio de Ciencia e Innovacio´n, grant no. TEC2011-27133-C02-01, and from the PAID-06-11 UPV, grant ref. 1988. The authors alone are responsible for the content and writing of the paper.Trujillo Guillen, M.; Berjano, E. (2013). Review of the mathematical functions used to model the temperature dependence of electrical and thermal conductivities of biological tissue in radiofrequency ablation. International Journal of Hyperthermia. 29(6):590-597. https://doi.org/10.3109/02656736.2013.807438S590597296Radiofrequency ablation in liver tumours. (2004). Annals of Oncology, 15(suppl_4), iv313-iv317. doi:10.1093/annonc/mdh945McAchran, S. E., Lesani, O. A., & Resnick, M. I. (2005). Radiofrequency ablation of renal tumors: Past, present, and future. Urology, 66(5), 15-22. doi:10.1016/j.urology.2005.06.127Di Staso, M., Zugaro, L., Gravina, G. L., Bonfili, P., Marampon, F., Di Nicola, L., … Tombolini, V. (2011). A feasibility study of percutaneous radiofrequency ablation followed by radiotherapy in the management of painful osteolytic bone metastases. European Radiology, 21(9), 2004-2010. doi:10.1007/s00330-011-2133-3Sharma, R., Wagner, J. L., & Hwang, R. F. (2011). Ablative Therapies of the Breast. Surgical Oncology Clinics of North America, 20(2), 317-339. doi:10.1016/j.soc.2010.11.003Savoie, P.-H., Lopez, L., Simonin, O., Loubat, M., Bladou, F., Serment, G., & Karsenty, G. (2009). Résultat à deux ans de la thermothérapie prostatique par radiofréquence pour troubles mictionnels liés à l’HBP. Progrès en Urologie, 19(7), 501-506. doi:10.1016/j.purol.2009.03.004Akeboshi, M., Yamakado, K., Nakatsuka, A., Hataji, O., Taguchi, O., Takao, M., & Takeda, K. (2004). Percutaneous Radiofrequency Ablation of Lung Neoplasms: Initial Therapeutic Response. Journal of Vascular and Interventional Radiology, 15(5), 463-470. doi:10.1097/01.rvi.0000126812.12853.77Berjano, E. J. (2006). BioMedical Engineering OnLine, 5(1), 24. doi:10.1186/1475-925x-5-24Tungjitkusolmun, S., Woo, E. J., Cao, H., Tsai, J. Z., Vorperian, V. R., & Webster, J. G. (2000). Thermal—electrical finite element modelling for radio frequency cardiac ablation: Effects of changes in myocardial properties. Medical & Biological Engineering & Computing, 38(5), 562-568. doi:10.1007/bf02345754Shahidi, A. V., & Savard, P. (1994). A finite element model for radiofrequency ablation of the myocardium. IEEE Transactions on Biomedical Engineering, 41(10), 963-968. doi:10.1109/10.324528Solazzo, S. A., Liu, Z., Lobo, S. M., Ahmed, M., Hines-Peralta, A. U., Lenkinski, R. E., & Goldberg, S. N. (2005). Radiofrequency Ablation: Importance of Background Tissue Electrical Conductivity—An Agar Phantom and Computer Modeling Study. Radiology, 236(2), 495-502. doi:10.1148/radiol.2362040965Gabriel, C., Gabriel, S., & Corthout, E. (1996). The dielectric properties of biological tissues: I. Literature survey. Physics in Medicine and Biology, 41(11), 2231-2249. doi:10.1088/0031-9155/41/11/001Jo, B., & Aksan, A. (2010). Prediction of the extent of thermal damage in the cornea during conductive keratoplasty. Journal of Thermal Biology, 35(4), 167-174. doi:10.1016/j.jtherbio.2010.02.004Haemmerich, D., Chachati, L., Wright, A. S., Mahvi, D. M., Lee, F. T., & Webster, J. G. (2003). Hepatic radiofrequency ablation with internally cooled probes: effect of coolant temperature on lesion size. IEEE Transactions on Biomedical Engineering, 50(4), 493-500. doi:10.1109/tbme.2003.809488Jarrard, J., Wizeman, B., Brown, R. H., & Mitzner, W. (2010). A theoretical model of the application of RF energy to the airway wall and its experimental validation. BioMedical Engineering OnLine, 9(1), 81. doi:10.1186/1475-925x-9-81Dodde, R. E., Miller, S. F., Geiger, J. D., & Shih, A. J. (2008). Thermal-Electric Finite Element Analysis and Experimental Validation of Bipolar Electrosurgical Cautery. Journal of Manufacturing Science and Engineering, 130(2). doi:10.1115/1.2902858LAU, M., HU, B., WERNETH, R., SHERMAN, M., ORAL, H., MORADY, F., & KRYSL, P. (2010). A Theoretical and Experimental Analysis of Radiofrequency Ablation with a Multielectrode, Phased, Duty-Cycled System. Pacing and Clinical Electrophysiology, 33(9), 1089-1100. doi:10.1111/j.1540-8159.2010.02801.xBerjano, E. J., Alió, J. L., & Saiz, J. (2005). Modeling for radio-frequency conductive keratoplasty: implications for the maximum temperature reached in the cornea. Physiological Measurement, 26(3), 157-172. doi:10.1088/0967-3334/26/3/002Pätz, T., Kröger, T., & Preusser, T. (2009). Simulation of Radiofrequency Ablation Including Water Evaporation. World Congress on Medical Physics and Biomedical Engineering, September 7 - 12, 2009, Munich, Germany, 1287-1290. doi:10.1007/978-3-642-03882-2_341Jain, M. K., & Wolf, P. D. (2000). A Three-Dimensional Finite Element Model of Radiofrequency Ablation with Blood Flow and its Experimental Validation. Annals of Biomedical Engineering, 28(9), 1075-1084. doi:10.1114/1.1310219Chang, I. A., & Nguyen, U. D. (2004). BioMedical Engineering OnLine, 3(1), 27. doi:10.1186/1475-925x-3-27Yang, D., Converse, M. C., Mahvi, D. M., & Webster, J. G. (2007). Expanding the Bioheat Equation to Include Tissue Internal Water Evaporation During Heating. IEEE Transactions on Biomedical Engineering, 54(8), 1382-1388. doi:10.1109/tbme.2007.890740Bhavaraju, N. C., & Valvano, J. W. (1999). International Journal of Thermophysics, 20(2), 665-676. doi:10.1023/a:1022673524963Baldwin, S. A., Pelman, A., & Bert, J. L. (2001). A Heat Transfer Model of Thermal Balloon Endometrial Ablation. Annals of Biomedical Engineering, 29(11), 1009-1018. doi:10.1114/1.1415521Abraham, J. P., & Sparrow, E. M. (2007). A thermal-ablation bioheat model including liquid-to-vapor phase change, pressure- and necrosis-dependent perfusion, and moisture-dependent properties. International Journal of Heat and Mass Transfer, 50(13-14), 2537-2544. doi:10.1016/j.ijheatmasstransfer.2006.11.045Pennes, H. H. (1998). Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm. Journal of Applied Physiology, 85(1), 5-34. doi:10.1152/jappl.1998.85.1.5Pearce, J., Panescu, D., & Thomsen, S. (2005). Simulation of diopter changes in radio frequency conductive keratoplasty in the cornea. Modelling in Medicine and Biology VI. doi:10.2495/bio050451Zhao, G., Zhang, H.-F., Guo, X.-J., Luo, D.-W., & Gao, D.-Y. (2007). Effect of blood flow and metabolism on multidimensional heat transfer during cryosurgery. Medical Engineering & Physics, 29(2), 205-215. doi:10.1016/j.medengphy.2006.03.005Berjano, E. J., Burdío, F., Navarro, A. C., Burdío, J. M., Güemes, A., Aldana, O., … Gregorio, M. A. de. (2006). Improved perfusion system for bipolar radiofrequency ablation of liver: preliminary findings from a computer modeling study. Physiological Measurement, 27(10), N55-N66. doi:10.1088/0967-3334/27/10/n03Trujillo, M., Alba, J., & Berjano, E. (2012). Relationship between roll-off occurrence and spatial distribution of dehydrated tissue during RF ablation with cooled electrodes. International Journal of Hyperthermia, 28(1), 62-68. doi:10.3109/02656736.2011.631076Doss, J. D. (1982). Calculation of electric fields in conductive media. Medical Physics, 9(4), 566-573. doi:10.1118/1.595107Chang, S.-J., Yu, W.-J., Chang, C.-C., & Chen, Y.-H. (2010). 7 PROTEOMICS ANALYSIS OF MALE REPRODUCTIVE PHYSIOLOGY BY TOONA SINENSIS ROEM. Reproductive BioMedicine Online, 20, S3-S4. doi:10.1016/s1472-6483(10)62425-xBeop-Min Kim, Jacques, S. L., Rastegar, S., Thomsen, S., & Motamedi, M. (1996). Nonlinear finite-element analysis of the role of dynamic changes in blood perfusion and optical properties in laser coagulation of tissue. IEEE Journal of Selected Topics in Quantum Electronics, 2(4), 922-933. doi:10.1109/2944.577317Berjano, E. J., Saiz, J., & Ferrero, J. M. (2002). Radio-frequency heating of the cornea: theoretical model and in vitro experiments. IEEE Transactions on Biomedical Engineering, 49(3), 196-205. doi:10.1109/10.983453Barauskas, R., Gulbinas, A., & Barauskas, G. (2007). Investigation of radiofrequency ablation process in liver tissue by finite element modeling and experiment. Medicina, 43(4), 310. doi:10.3390/medicina43040039Ji, Z., & Brace, C. L. (2011). Expanded modeling of temperature-dependent dielectric properties for microwave thermal ablation. Physics in Medicine and Biology, 56(16), 5249-5264. doi:10.1088/0031-9155/56/16/011Labonte, S. (1994). Numerical model for radio-frequency ablation of the endocardium and its experimental validation. IEEE Transactions on Biomedical Engineering, 41(2), 108-115. doi:10.1109/10.28492

Current Trends in Mathematical Modeling of High-Temperature Thermal Therapies

Haemmerich, D.; Berjano, E. (2010). Current trends in mathematical modeling of high-temperature thermal therapies. The Open Biomedical Engineering Journal. 4(4):1-2. https://doi.org/10.2174/1874120701004010001S124

Lumped Element Electrical Model based on Three Resistors for Electrical Impedance in Radiofrequency Cardiac Ablation: Estimations from Analytical Calculations and Clinical Data

[EN] The electrical impedance measured during radiofrequency cardiac ablation (RFCA) is widely used in clinical studies to predict the heating evolution and hence the success of the procedure. We hypothesized that a model based on three resistors in series can mimic the total electrical impedance measured during RFCA. The three resistors or impedances are given by: impedance associated with the tissue around the active electrode (myocardium and circulating blood) (Z-A), that associated with the tissue around the dispersive electrode (Z-DE) and that associated with the rest of the body (Z-B). Our objective was to quantify the values associated with these three impedance types by an analytical method, after which the values obtained would be compared to those estimated from clinical data from previous studies. The results suggest that an RFCA using a 7 Fr 4-mm electrode would give a Z-A of around 75 ohms, a Z-DE around 20 ohms, and Z-B would be 15±10 ohms (for body surface area variations between 1.5 and 2.5 m^2). Finally, adaptations of the proposed model were used to explain the results of previous clinical studies using a different electrode arrangement, such as in bipolar ablation of the ventricular septum.This work received financial support from the Spanish “Plan Nacional de I+D+I del Ministerio de Ciencia e Innovación” Grant No. TEC2011-27133-C02-01.Berjano, E.; D Avila, A. (2013). Lumped Element Electrical Model based on Three Resistors for Electrical Impedance in Radiofrequency Cardiac Ablation: Estimations from Analytical Calculations and Clinical Data. The Open Biomedical Engineering Journal. 7:62-70. https://doi.org/10.2174/1874120720130603001S62707Nath S, Haines D E. “Biophysics and pathology of catheter energy delivery systems” Prog Cardiovasc Dis 1995 January-February; 37 : 185-204.Berjano E J. “Theoretical modeling for radiofrequency ablation: state-of-the-art and challenges for the future” Biomed Eng Online 2006 April; 5 : 2.Wittkampf F H, and Nakagawa H. “RF catheter ablation: Lessons on lesions” Pacing Clin Electrophysiol 2006 November; 29 : 1285-97.Neufeld G R GR. “Principles and hazards of electrosurgery including laparoscopy” Surg Gynecol Obstet 1978 November; 147 : 705-10.Ragheb T, Riegle S, Geddes L A, and Amin V. “The impedance of a spherical monopolar electrode” Ann Biomed Eng 1992; 20 : 617-27.Panescu D, Whayne J G, Fleischman S D, Mirotznik M S, Swanson D K, and Webster J G. “Three-dimensional finite element analysis of current density and temperature distributions during radio- frequency ablation” IEEE Trans Biomed Eng 1995 September; 42 : 879-90.Foster K R, Schwan H P. “Dielectric properties of tissues and biological materials: a critical review” Crit Rev Biomed Eng 1989; 17 : 25-104.Pearce J A. Electrosurgery. London: Chapman and Hall 1986.Yamamoto T, and Yamamoto Y. “Electrical properties of the epidermal stratum corneum” Med Biol Eng 1976 March; 14 : 151-8.Miklavcic D, Pavselj N, Hart F X. “Electric Properties of Tissues” In: Akay M, Ed. Wiley Encyclopedia of Biomedical Engineering. Hoboken: Wiley 2006; pp. 1-14.Saito M, Nakayama K, Hori M, Fujimori Y. “A fundamental study on the electrodes for cardiac pacemakers” Jpn J Med Electron Biol Eng 1967; 5 : 192-8.Nsah E, Berger R, Rosenthal L, et al. “Relation between impedance and electrode temperature during radiofrequency catheter ablation of accessory pathways and atrioventricular nodal reentrant tachycardia” Am Heart J 1998 November; 136 : 844-51.Wen Z C, Chen S A, Chiang C E, et al. “Temperature and impedance monitoring during radiofrequency catheter ablation of slow AV node pathway in patients with atrioventricular node reentrant tachycardia” Int J Cardiol 1996 December; 57 : 257-63.Strickberger S A, Hummel J, Gallagher M, et al. “Effect of accessory pathway location on the efficiency of heating during radiofrequency catheter ablation” Am Heart J 1995 January; 129 : 54-8.Strickberger S A, Vorperian V R, Man K C, et al. “Relation between impedance and endocardial contact during radiofrequency catheter ablation” Am Heart J 1994 August; 128 : 226-9.Cao H, Tungjitkusolmun S, Choy Y B, Tsai J Z, Vorperian V R, and Webster J G. “Using electrical impedance to predict catheter-endocardial contact during RF cardiac ablation” IEEE Trans Biomed Eng 2002 March; 49 : 247-3.Rodriguez L M, Nabar A, Timmermans C, and Wellens H J. “Comparison of results of an 8-mm split-tip versus a 4-mm tip ablation catheter to perform radiofrequency ablation of type I atrial flutter” Am J Cardiol 2000 January; 85 : 109-12.Sacher F F, O'Neill M D, Jais P, et al. “Prospective randomized comparison of 8-mm gold-tip, externally irrigated-tip and 8-mm platinum- iridium tip catheters for cavotricuspid isthmus ablation” J Cardiovasc Electrophysiol 2007 July; 18 : 709-13.Jackman W M, Wang X Z, Friday K J, et al. “Catheter ablation of atrioventricular junction using radiofrequency current in 17 patients. Comparison of standard and large-tip catheter electrodes” Circulation 1991 May; 83 : 1562-76.Nath S, DiMarco J P, Gallop R G, McRury I D, and Haines D E. “Effects of dispersive electrode position and surface area on electrical parameters and temperature during radiofrequency catheter ablation” Am J Cardiol 1996 April; 77 : 765-7.Santoro I, Xunzhang W, McClelland J, et al. “Effect of skin-patch location and surface area on impedance during radiofrequency catheter ablation” Pacing Clin Electrophysiol 1992; 15 : 580.Borganelli M, el-Atassi R, Leon A, et al. “Determinants of impedance during radiofrequency catheter ablation in humans” Am J Cardiol 1992 April; 69 : 1095-7.Park J K, Halperin B D, Kron J, Holcomb S R, and Silka M J. “Analysis of body surface area as a determinant of impedance during radiofrequency catheter ablation in adults and children” J Electrocardiol 1994 October; 27 : 329-32.Wang D, Hulse J E, Walsh E P, and Saul J P. “Factors influencing impedance during radiofrequency ablation in humans” Chin Med J (Engl) 1995 June; 108 : 450-5.Koruth J S, Dukkipati S, Miller M A, Neuzil P, d'Avila A, and Reddy V Y. “Bipolar irrigated radiofrequency ablation: a therapeutic option for refractory intramural atrial and ventricular tachycardia circuits” Heart Rhythm 2012 December; 9 : 1932-41

Transferencia de Resultados de Investigación desde el Ámbito Académico en Ingeniería Biomédica: Deseos, Realidades y Desatinos

Berjano, E. (2014). Transferencia de Resultados de Investigación desde el Ámbito Académico en Ingeniería Biomédica: Deseos, Realidades y Desatinos. Revista Mexicana de Ingeniería Biomédica. 35(1):7-12. http://hdl.handle.net/10251/113826S71235

An Analytical Solution for Radiofrequency Ablation with a Cooled Cylindrical Electrode

[EN] We present an analytical solution to the electrothermal mathematical model of radiofrequency ablation of biological tissue using a cooled cylindrical electrode. The solution presented here makes use of the method of separation of variables to solve the problem. Green's functions are used for the handling of nonhomogeneous terms, such as effect of electrical currents circulation and the nonhomogeneous boundary condition due to cooling at the electrode surface. The transcendental equation for determination of eigenvalues of this problem is solved using Newton's method, and the integrals that appear in the solution of the problem are obtained by Simpson's rule. The solution obtained here has the possibility of handling different functional dependencies of the source term and nonhomogeneous boundary condition. The solution provides a tool to understand the physics of the problem, as it shows how the solution depends on different parameters, to provide mathematical tools for the design of surgical procedures and to validate other modeling techniques, such as the numerical methods that are frequently used to solve the problem.This work was supported by the Universidad Autonoma de San Luis Potosi (Mexico), which granted Ricardo Romero-Mendez a sabbatical leave to do research in the field of biomedical engineering, and the Government of Spain through the "Plan Estatal de Investigacion, Desarrollo e Innovacion Orientada a los Retos de la Sociedad" (Grants TEC 2014-52383-C3-R and TEC 2014-52383-C3-1-R).Romero-Méndez, R.; Berjano, E. (2017). An Analytical Solution for Radiofrequency Ablation with a Cooled Cylindrical Electrode. Mathematical Problems in Engineering. (9021616):1-12. doi:10.1155/2017/9021616S112902161

Effect of intracardiac blood flow pulsatility during radiofrequency cardiac ablation: computer modeling study

[EN] Purpose To assess the effect of intracardiac blood flow pulsatility on tissue and blood distributions during radiofrequency (RF) cardiac ablation (RFCA). Methods A three-dimensional computer model was used to simulate constant power ablations with an irrigated-tip electrode and three possible catheter orientations (perpendicular, parallel and 45 degrees). Continuous flow and three different pulsatile flow profiles were considered, with four average blood velocity values: 3, 5.5, 8.5 and 24.4 cm/s. The 50 degrees C contour was used to assess thermal lesion size. Results The differences in lesion size between continuous flow and the different pulsatile flow profiles were always less than 1 mm. As regards maximum tissue temperature, the differences between continuous and pulsatile flow were always less than 1 degrees C, with slightly higher differences in maximum blood temperature, but never over 6 degrees C. While the progress of maximum tissue temperature was identical for continuous and pulsatile flow, maximum blood temperature with the pulsatile profile showed small amplitude oscillations associated with blood flow pulsatility. Conclusions The findings show that intracardiac blood pulsatility has a negligible effect on lesion size and a very limited impact on maximum tissue and blood temperatures, which suggests that future experimental studies based on ex vivo or in silico models can ignore pulsatility in intracardiac blood flow.This work was supported by the Spanish Ministerio de Ciencia, Innovacion y Universidades under 'Programa Estatal de IthornDthorni Orientada a los Retos de la Sociedad', Grant No. 'RTI2018-094357-B-C21'.Parés, C.; Berjano, E.; González-Suárez, A. (2021). Effect of intracardiac blood flow pulsatility during radiofrequency cardiac ablation: computer modeling study. International Journal of Hyperthermia. 38(1):316-325. https://doi.org/10.1080/02656736.2021.1890240S31632538

Impedance measurement to assess epicardial fat prior to RF intraoperative cardiac ablation: a feasibility study using a computer model

[EN] Radiofrequency (RF) cardiac ablation is used to treat certain types of arrhythmias. In the epicardial approach, efficacy of RF ablation is uncertain due to the presence of epicardial adipose tissue interposed between the ablation electrode and the atrial wall. We planned a feasibility study based on a theoretical model in order to assess a new technique to estimate the quantity of fat by conducting bioimpedance measurements using a multi-electrode probe. The finite element method was used to solve the electrical problem. The results showed that the measured impedance profile coincided approximately with the epicardial fat profile measured under the probe electrodes and also that the thicker the epicardial fat, the higher the impedance values. When the lateral fat width was less than 4.5 mm, the impedance values altered, suggesting that measurements should always be conducted over a sizeable fat layer. We concluded that impedance measurement could be a practical method of assessing epicardial fat prior to RF intraoperative cardiac ablation, i.e. 'to map' the amount of adipose tissue under the probe.This work was supported by a research grant from the Spanish Government in the 'Plan Nacional de I+D+I del Ministerio de Ciencia e Innovacion' (TEC2008-01369/TEC). The English revision and correction of this note was funded by the Universidad Politecnica de Valencia, Spain.González-Suárez, A.; Hornero, F.; Berjano, E. (2010). Impedance measurement to assess epicardial fat prior to RF intraoperative cardiac ablation: a feasibility study using a computer model. Physiological Measurement. 31(11):95-104. https://doi.org/10.1088/0967-3334/31/11/N03S951043111Ba, M., Fornés, P., Nutu, O., Latrémouille, C., Carpentier, A., & Chachques, J. C. (2008). Treatment of atrial fibrillation by surgical epicardial ablation: Bipolar radiofrequency versus cryoablation. Archives of Cardiovascular Diseases, 101(11-12), 763-768. doi:10.1016/j.acvd.2008.07.004Benjamin, E. J. (1994). Independent risk factors for atrial fibrillation in a population-based cohort. The Framingham Heart Study. JAMA: The Journal of the American Medical Association, 271(11), 840-844. doi:10.1001/jama.271.11.840Berjano, E. J., & Hornero, F. (2004). Thermal-Electrical Modeling for Epicardial Atrial Radiofrequency Ablation. IEEE Transactions on Biomedical Engineering, 51(8), 1348-1357. doi:10.1109/tbme.2004.827545Berjano, E. J., & Hornero, F. (2005). A cooled intraesophageal balloon to prevent thermal injury during endocardial surgical radiofrequency ablation of the left atrium: a finite element study. Physics in Medicine and Biology, 50(20), N269-N279. doi:10.1088/0031-9155/50/20/n03HORNERO, F., & BERJANO, E. J. (2006). Esophageal Temperature During Radiofrequency-Catheter Ablation of Left Atrium: A Three-Dimensional Computer Modeling Study. Journal of Cardiovascular Electrophysiology, 17(4), 405-410. doi:10.1111/j.1540-8167.2006.00404.xCox, J. L., Schuessler, R. B., Lappas, D. G., & Boineau, J. P. (1996). An 8½-Year Clinical Experience with Surgery for Atrial Fibrillation. Annals of Surgery, 224(3), 267-275. doi:10.1097/00000658-199609000-00003Deneke, T., Khargi, K., Müller, K.-M., Lemke, B., Mügge, A., Laczkovics, A., … Grewe, P. H. (2005). Histopathology of intraoperatively induced linear radiofrequency ablation lesions in patients with chronic atrial fibrillation. European Heart Journal, 26(17), 1797-1803. doi:10.1093/eurheartj/ehi255Doss, J. D. (1982). Calculation of electric fields in conductive media. Medical Physics, 9(4), 566-573. doi:10.1118/1.595107Dumas III, J. H., Himel IV, H. D., Kiser, A. C., Quint, S. R., & Knisley, S. B. (2008). Myocardial electrical impedance as a predictor of the quality of RF-induced linear lesions. Physiological Measurement, 29(10), 1195-1207. doi:10.1088/0967-3334/29/10/004Gabriel, S., Lau, R. W., & Gabriel, C. (1996). The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. Physics in Medicine and Biology, 41(11), 2271-2293. doi:10.1088/0031-9155/41/11/003Suárez, A. G., Hornero, F., & Berjano, E. J. (2010). Mathematical Modeling of Epicardial RF Ablation of Atrial Tissue with Overlying Epicardial Fat. The Open Biomedical Engineering Journal, 4(1), 47-55. doi:10.2174/1874120701004020047Hong, K. N., Russo, M. J., Liberman, E. A., Trzebucki, A., Oz, M. C., Argenziano, M., & Williams, M. R. (2007). Effect of Epicardial Fat on Ablation Performance: A Three-Energy Source Comparison. Journal of Cardiac Surgery, 22(6), 521-524. doi:10.1111/j.1540-8191.2007.00454.xKannel, W. ., Wolf, P. ., Benjamin, E. ., & Levy, D. (1998). Prevalence, incidence, prognosis, and predisposing conditions for atrial fibrillation: population-based estimates 11Reprints are not available. The American Journal of Cardiology, 82(7), 2N-9N. doi:10.1016/s0002-9149(98)00583-9Khargi, K., Hutten, B. A., Lemke, B., & Deneke, T. (2005). Surgical treatment of atrial fibrillation; a systematic review☆. European Journal of Cardio-Thoracic Surgery, 27(2), 258-265. doi:10.1016/j.ejcts.2004.11.003Mitnovetski, S., Almeida, A. A., Goldstein, J., Pick, A. W., & Smith, J. A. (2009). Epicardial High-intensity Focused Ultrasound Cardiac Ablation for Surgical Treatment of Atrial Fibrillation. Heart, Lung and Circulation, 18(1), 28-31. doi:10.1016/j.hlc.2008.08.003Miyagi, Y., Ishii, Y., Nitta, T., Ochi, M., & Shimizu, K. (2009). Electrophysiological and Histological Assessment of Transmurality after Epicardial Ablation Using Unipolar Radiofrequency Energy. Journal of Cardiac Surgery, 24(1), 34-40. doi:10.1111/j.1540-8191.2008.00747.xPruitt, J. C., Lazzara, R. R., & Ebra, G. (2007). Minimally invasive surgical ablation of atrial fibrillation: The thoracoscopic box lesion approach. Journal of Interventional Cardiac Electrophysiology, 20(3), 83-87. doi:10.1007/s10840-007-9172-3Santiago, T., Melo, J., Gouveia, R. H., Neves, J., Abecasis, M., Adragão, P., & Martins, A. P. (2003). Epicardial radiofrequency applications: in vitro and in vivo studies on human atrial myocardium☆. European Journal of Cardio-Thoracic Surgery, 24(4), 481-486. doi:10.1016/s1010-7940(03)00344-0Santiago, T., Melo, J. oã. Q., Gouveia, R. H., & Martins, A. P. (2003). Intra-atrial temperatures in radiofrequency endocardial ablation: histologic evaluation of lesions. The Annals of Thoracic Surgery, 75(5), 1495-1501. doi:10.1016/s0003-4975(02)04990-1Wolf, P. A., Abbott, R. D., & Kannel, W. B. (1991). Atrial fibrillation as an independent risk factor for stroke: the Framingham Study. Stroke, 22(8), 983-988. doi:10.1161/01.str.22.8.98

In-silico modeling to compare radiofrequency-induced thermal lesions created on myocardium and thigh muscle

[EN] Beating heart (BH) and thigh muscle (TM) are two pre-clinical models aimed at studying the lesion sizes created by radiofrequency (RF) catheters in cardiac ablation. Previous experimental results have shown that thermal lesions created in the TM are slightly bigger than in the BH. Our objective was to use in-silico modeling to elucidate some of the causes of this difference. In-silico RF ablation models were created using the Arrhenius function to estimate lesion size under different energy settings (25 W/20 s, 50 W/6 s and 90 W/4 s) and parallel, 45 degrees and perpendicular catheter positions. The models consisted of homogeneous tissue: myocardium in the BH model and striated muscle in the TM model. The computer results showed that the lesion sizes were generally bigger in the TM model and the differences depended on the energy setting, with hardly any differences at 90 W/4 s but with differences of 1 mm in depth and 1.5 m in width at 25 W/20 s. The higher electrical conductivity of striated muscle (0.446 S/m) than that of the myocardium (0.281 S/m) is possibly one of the causes of the higher percentage of RF energy delivered to the tissue in the TM model, with differences between models of 2-5% at 90 W/4 s, similar to 9% at 50 W/6 s and similar to 10% at 25 W/20 s. Proximity to the air-blood interface (just 2 cm from the tissue surface) artificially created in the TM model to emulate the cardiac cavity had little effect on lesion size. In conclusion, the TM-based experimental model creates fairly similar-sized lesions to the BH model, especially in high-power short-duration ablations (50 W/6 s and 90 W/4 s). Our computer results suggest that the higher electrical conductivity of striated muscle could be one of the causes of the slightly larger lesions in the TM model.This research was funded by the Spanish Ministerio de Ciencia, Innovacion y Universidades/Agencia Estatal de Investigacion MCIN/AEI/10.13039/501100011033 (Grant number: RTI2018-094357-B-C21)Pérez, JJ.; Berjano, E.; González-Suárez, A. (2022). In-silico modeling to compare radiofrequency-induced thermal lesions created on myocardium and thigh muscle. Bioengineering. 9(7):1-13. https://doi.org/10.3390/bioengineering9070329S1139