Optimization of radiation dosing schedules for proneural glioblastoma

H. Badri, K. Pitter, E. C. Holland, F. Michor, K. Leder

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Glioblastomas are the most aggressive primary brain tumor. Despite treatment with surgery, radiation and chemotherapy, these tumors remain uncurable and few significant increases in survival have been observed over the last half-century. We recently employed a combined theoretical and experimental approach to predict the effectiveness of radiation administration schedules, identifying two schedules that led to superior survival in a mouse model of the disease (Leder et al., Cell 156(3):603–616, 2014). Here we extended this approach to consider fractionated schedules to best minimize toxicity arising in early- and late-responding tissues. To this end, we decomposed the problem into two separate solvable optimization tasks: (i) optimization of the amount of radiation per dose, and (ii) optimization of the amount of time that passes between radiation doses. To ensure clinical applicability, we then considered the impact of clinical operating hours by incorporating time constraints consistent with operational schedules of the radiology clinic. We found that there was no significant loss incurred by restricting dosage to an 8:00 a.m. to 5:00 p.m. window. Our flexible approach is also applicable to other tumor types treated with radiotherapy.

Original languageEnglish (US)
Pages (from-to)1301-1336
Number of pages36
JournalJournal of Mathematical Biology
Issue number5
StatePublished - Apr 1 2016


  • Brain tumors
  • Linear-quadratic model
  • Nonlinear programming
  • Radiotherapy

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