title: [Mathematical protocol for radiofrequency ablation of liver tumors and its clinical application].
abstract: OBJECTIVE
  To develop a preoperative protocol for ultrasonography-guided percutaneous radiofrequency ablation (RFA) on liver tumors larger than 3.5 cm in diameter based on mathematical models and clinical experience, and to evaluate its ablated effect compared to the previous non-math method.
  
  
  METHODS
  One hundred and twenty-five patients with 80 primary and 55 secondary liver tumors (4.7 +/- 0.9 cm in diameter, ranged from 3.6 - 7.0 cm) were enrolled in this study, of which the first 22 patients (23 tumors) had been treated empirically before the mathematical model was set up and were referred as the non-math group. The rest 103 patients (112 tumors) were treated based on the mathematical model and referred as the math group. Based on principle of overlapping spheres, a mathematical analysis was performed to investigate how multiple ablation spheres could overlap and cover larger tumors most efficiently. Some mathematical models such as regular prism and regular polyhedron model were chosen to estimate the mathematical protocol which included least ablation (sphere) number and optimal overlapping mode required to adequately ablate a large and spherical target lesion. The target volume consisted of the tumor plus a 0.5 - 1 cm tumor-free margin. The operation method for electrode placement was also described.
  
  
  RESULTS
  The procedure success rate for the math group was 88.4% (99/112), local recurrence rate and estimated mean time until local recurrence were 25.9% (29/112) and 17.5 months, respectively. While for the non-math group the results were 52.2% (12/23) (P < 0.01), 56.5% (13/23) (P < 0.05) and 11.9 months (P < 0.05), respectively. The therapy results in the math group were much better than in the non-math group.
  
  
  CONCLUSIONS
  This study provides theoretic basis and clinical guidance for RFA therapy for liver tumors larger than 3.5 cm. These results could be used to reduce local recurrence rate and improve treatment response.
authors.affiliation: Department of Ultrasound, Clinical Oncology Institute, Peking University, Beijing 100036, China.
authors.forename: Min-hua
authors.initials: MH
authors.lastname: Chen
authors.forename: Wei
authors.initials: W
authors.lastname: Yang
authors.forename: Kun
authors.initials: K
authors.lastname: Yan
authors.forename: Ming-wu
authors.initials: MW
authors.lastname: Zou
authors.forename: Ying
authors.initials: Y
authors.lastname: Dai
authors.forename: Wen
authors.initials: W
authors.lastname: Gao
authors.forename: Xiao-peng
authors.initials: XP
authors.lastname: Zhang
authors.forename: Xin-fu
authors.initials: XF
authors.lastname: Huang
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D017115:Catheter Ablation; D005260:Female; D006801:Humans; D008113:Liver Neoplasms / Q000601:surgery*; D008297:Male; D008433:Mathematics; D008875:Middle Aged; D009364:Neoplasm Recurrence, Local / Q000517:prevention & control; D014057:Tomography, X-Ray Computed; D018084:Ultrasonography, Interventional