title: Optimal MRI interval for detection of asymptomatic recurrence in surgically treated early cervical cancer by use of a mathematical model.
abstract: BACKGROUND
  Applications of mathematical modeling may provide an insight into the timing of surveillance modalities. We aimed to determine the optimal magnetic resonance imaging (MRI) interval for the detection of surgically treated early cervical cancer asymptomatic recurrence by using a mathematical model for volumetric tumor growth time.
  
  
  METHODS
  We assumed that tumor volume increases by a factor equal to the basis of natural logarithms (e~2.718) at constant time intervals. Using a mathematical formula, the tumor volume (V) was converted to diameter (D), which could be expressed as a function of time (t), given an initial diameter Di (corresponding to initial volume Vi) and a constant DT, where DT is the time required for volumetric tumor growth by a factor (e). Three different DTs were used for demonstration of the model, i.e. 20, 100 and 400 days.
  
  
  RESULTS
  Assuming complete surgical clearance, a worst-case scenario for a 20-day DT indicated that a 20 μm cervical tumor would need at least 12 months to reach 10 mm in diameter, which would be detected with an annual surveillance interval MRI. Over a 5-year (60 months) follow-up, nearly five surveillance MRIs would be required if the threshold of 10 mm was desired. For a 100-day DT over a 5-year (60 months) follow-up, a single only MRI would be required, if the threshold of 10 mm was desired. In the case of an indolent tumor (DT is 400 days), the model would not recommend a surveillance MRI to detect asymptomatic recurrence. A positive linear association between optimal MRI intervals and volumetric tumor DTs was demonstrated.
  
  
  CONCLUSIONS
  In the absence of evidence, we postulate annual MRI scanning is probably the shortest interval, which can be clinically useful for optimization of routine surveillance follow-up protocols in surgically treated early cervical cancer. This mathematical model requires proper verification in prospective clinical studies. Hippokratia 2016, 20(1): 4-8.
authors.affiliation: Gynecologic Oncology Firm, Churchill Hospital, Oxford University Hospitals NHS Trust, Oxford, UK.
authors.forename: A
authors.initials: A
authors.lastname: Laios
authors.affiliation: Gynecologic Oncology Firm, Churchill Hospital, Oxford University Hospitals NHS Trust, Oxford, UK.
authors.forename: K
authors.initials: K
authors.lastname: Gubbala
authors.affiliation: Department of Obstetrics and Gynecology, University of Debrecen, Hungary.
authors.forename: R
authors.initials: R
authors.lastname: Lampe
authors.affiliation: School of Mechanical Engineering, Sector of Industrial Management and Operational Research, National Technical University of Athens, Athens, Greece.
authors.forename: A
authors.initials: A
authors.lastname: Tolis
keywords: Cervical cancer; mathematical model; optimal MRI interval; tumor growth