title: A Mathematical Method to Calculate Tumor Contact Surface Area: An Effective Parameter to Predict Renal Function after Partial Nephrectomy.
abstract: We proposed a mathematical formula to calculate contact surface area between a tumor and renal parenchyma. We examined the applicability of using contact surface area to predict renal function after partial nephrectomy.
  
  
  
  We performed this retrospective study in patients who underwent partial nephrectomy between January 2012 and December 2014. Based on abdominopelvic computerized tomography or magnetic resonance imaging, we calculated the contact surface area using the formula (2*π*radius*depth) developed by integral calculus. We then evaluated the correlation between contact surface area and perioperative parameters, and compared contact surface area and R.E.N.A.L. (Radius/Exophytic/endophytic/Nearness to collecting system/Anterior/Location) score in predicting a reduction in renal function.
  
  
  
  Overall 35, 26 and 45 patients underwent partial nephrectomy with open, laparoscopic and robotic approaches, respectively. Mean ± SD contact surface area was 30.7±26.1 cm(2) and median (IQR) R.E.N.A.L. score was 7 (2.25). Spearman correlation analysis showed that contact surface area was significantly associated with estimated blood loss (p=0.04), operative time (p=0.04) and percent change in estimated glomerular filtration rate (p <0.001). On multivariate analysis contact surface area and R.E.N.A.L. score independently affected percent change in estimated glomerular filtration rate (p <0.001 and p=0.03, respectively). On ROC curve analysis contact surface area was a better independent predictor of a greater than 10% change in estimated glomerular filtration rate compared to R.E.N.A.L. score (AUC 0.86 vs 0.69).
  
  
  
  Using this simple mathematical method, contact surface area was associated with surgical outcomes. Compared to R.E.N.A.L. score, contact surface area was a better predictor of functional change after partial nephrectomy.
authors.affiliation: Department of Urology, China Medical University Hospital, Taichung, Taiwan.
authors.forename: Po-Fan
authors.initials: PF
authors.lastname: Hsieh
authors.affiliation: Department of Urology, China Medical University Hospital, Taichung, Taiwan.
authors.forename: Yu-De
authors.initials: YD
authors.lastname: Wang
authors.affiliation: Department of Urology, China Medical University Hospital, Taichung, Taiwan.
authors.forename: Chi-Ping
authors.initials: CP
authors.lastname: Huang
authors.affiliation: School of Medicine, China Medical University, Taichung, Taiwan; Department of Urology, An-Nan Hospital, Tainan, Taiwan.
authors.forename: Hsi-Chin
authors.initials: HC
authors.lastname: Wu
authors.affiliation: Department of Urology, China Medical University Hospital, Taichung, Taiwan.
authors.forename: Che-Rei
authors.initials: CR
authors.lastname: Yang
authors.affiliation: Department of Urology, China Medical University Hospital, Taichung, Taiwan.
authors.forename: Guang-Heng
authors.initials: GH
authors.lastname: Chen
authors.affiliation: Department of Urology, China Medical University Hospital, Taichung, Taiwan; School of Medicine, China Medical University, Taichung, Taiwan. Electronic address: D8395@mail.cmuh.org.tw.
authors.forename: Chao-Hsiang
authors.initials: CH
authors.lastname: Chang
mesh_terms: D000328:Adult; D000368:Aged; D002292:Carcinoma, Renal Cell / Q000473:pathology* / Q000601:surgery; D005260:Female; D006801:Humans; D007677:Kidney Function Tests; D007680:Kidney Neoplasms / Q000473:pathology* / Q000601:surgery; D008297:Male; D008875:Middle Aged; D009392:Nephrectomy; D011183:Postoperative Complications / Q000175:diagnosis / Q000209:etiology*; D011379:Prognosis; D051437:Renal Insufficiency / Q000175:diagnosis / Q000209:etiology*; D012189:Retrospective Studies; D047368:Tumor Burden
keywords: kidney function tests; nephrectomy; prognosis; treatment outcome