title: Review of the mathematical functions used to model the temperature dependence of electrical and thermal conductivities of biological tissue in radiofrequency ablation.
abstract: OBJECTIVE
  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 (σ) conductivities of tissue. Our aim was to review the piecewise mathematical functions most commonly used for modelling the temperature dependence of k and σ in RFA computational modelling.
  
  
  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 Ω = 1, Ω 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 σ reported in the literature do not significantly affect the computed lesion diameter.
authors.affiliation: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Spain. matrugui@mat.upv.es
authors.forename: Macarena
authors.initials: M
authors.lastname: Trujillo
authors.forename: Enrique
authors.initials: E
authors.lastname: Berjano
mesh_terms: D017115:Catheter Ablation; D004553:Electric Conductivity; D008962:Models, Theoretical; D013696:Temperature; D013814:Thermal Conductivity