title: Statistical analysis of dose heterogeneity in circulating blood: implications for sequential methods of total body irradiation.
abstract: OBJECTIVE
  Improvements in delivery techniques for total body irradiation (TBI) using Tomotherapy and intensity modulated radiation therapy have been proven feasible. Despite the promise of improved dose conformality, the application of these "sequential" techniques has been hampered by concerns over dose heterogeneity to circulating blood. The present study was conducted to provide quantitative evidence regarding the potential clinical impact of this heterogeneity.
  
  
  METHODS
  Blood perfusion was modeled analytically as possessing linear, sinusoidal motion in the craniocaudal dimension. The average perfusion period for human circulation was estimated to be approximately 78 s. Sequential treatment delivery was modeled as a Gaussian-shaped dose cloud with a 10 cm length that traversed a 183 cm patient length at a uniform speed. Total dose to circulating blood voxels was calculated via numerical integration and normalized to 2 Gy per fraction. Dose statistics and equivalent uniform dose (EUD) were calculated for relevant treatment times, radiobiological parameters, blood perfusion rates, and fractionation schemes. The model was then refined to account for random dispersion superimposed onto the underlying periodic blood flow. Finally, a fully stochastic model was developed using binomial and trinomial probability distributions. These models allowed for the analysis of nonlinear sequential treatment modalities and treatment designs that incorporate deliberate organ sparing.
  
  
  RESULTS
  The dose received by individual blood voxels exhibited asymmetric behavior that depended on the coherence among the blood velocity, circulation phase, and the spatiotemporal characteristics of the irradiation beam. Heterogeneity increased with the perfusion period and decreased with the treatment time. Notwithstanding, heterogeneity was less than +/- 10% for perfusion periods less than 150 s. The EUD was compromised for radiosensitive cells, long perfusion periods, and short treatment times. However, the EUD was unaffected (within 10%) for perfusion periods of less than 150 s or treatment times of 20 min or greater. Treatment over six fractions improved the EUD per fraction such that all parametric combinations resulted in unaffected EUD. The stochastic models confirmed these results.
  
  
  CONCLUSIONS
  Dose heterogeneity in circulating blood cells is clinically acceptable for typical treatment times, perfusion rates, and cell types. Development of conformal, sequential TBI treatment techniques should not be withheld based on concerns over circulating blood dose heterogeneity.
authors.affiliation: Department of Radiation Medicine, University of Kentucky, Markey Cancer Center Rm. CC061, 800 Rose Street, Lexington, Kentucky 40536, USA. jmo222@email.uky.edu
authors.forename: Janelle A
authors.initials: JA
authors.lastname: Molloy
mesh_terms: D000465:Algorithms; D001769:Blood / Q000528:radiation effects*; D019583:Dose Fractionation, Radiation; D004307:Dose-Response Relationship, Radiation; D006801:Humans; D015233:Models, Statistical; D009369:Neoplasms / Q000097:blood / Q000532:radiotherapy*; D016011:Normal Distribution; D010477:Perfusion; D011874:Radiometry / Q000379:methods*; D050397:Radiotherapy, Intensity-Modulated / Q000379:methods*; D013269:Stochastic Processes; D013997:Time Factors; D014916:Whole-Body Irradiation / Q000379:methods*