title: Generalised polynomial chaos-based uncertainty quantification for planning MRgLITT procedures.
abstract: OBJECTIVE
  A generalised polynomial chaos (gPC) method is used to incorporate constitutive parameter uncertainties within the Pennes representation of bioheat transfer phenomena. The stochastic temperature predictions of the mathematical model are critically evaluated against MR thermometry data for planning MR-guided laser-induced thermal therapies (MRgLITT).
  
  
  METHODS
  The Pennes bioheat transfer model coupled with a diffusion theory approximation of laser tissue interaction was implemented as the underlying deterministic kernel. A probabilistic sensitivity study was used to identify parameters that provide the most variance in temperature output. Confidence intervals of the temperature predictions are compared to MR temperature imaging (MRTI) obtained during phantom and in vivo canine (n = 4) MRgLITT experiments. The gPC predictions were quantitatively compared to MRTI data using probabilistic linear and temporal profiles as well as 2-D 60 °C isotherms.
  
  
  RESULTS
  Optical parameters provided the highest variance in the model output (peak standard deviation: anisotropy 3.51 °C, absorption 2.94 °C, scattering 1.84 °C, conductivity 1.43 °C, and perfusion 0.94 °C). Further, within the statistical sense considered, a non-linear model of the temperature and damage-dependent perfusion, absorption, and scattering is captured within the confidence intervals of the linear gPC method. Multivariate stochastic model predictions using parameters with the dominant sensitivities show good agreement with experimental MRTI data.
  
  
  CONCLUSIONS
  Given parameter uncertainties and mathematical modelling approximations of the Pennes bioheat model, the statistical framework demonstrates conservative estimates of the therapeutic heating and has potential for use as a computational prediction tool for thermal therapy planning.
authors.affiliation: Department of Imaging Physics, The University of Texas M.D. Anderson Cancer Center, Houston, TX 77054, USA.
authors.forename: Samuel J
authors.initials: SJ
authors.lastname: Fahrenholtz
authors.forename: R Jason
authors.initials: RJ
authors.lastname: Stafford
authors.forename: Florian
authors.initials: F
authors.lastname: Maier
authors.forename: John D
authors.initials: JD
authors.lastname: Hazle
authors.forename: David
authors.initials: D
authors.lastname: Fuentes
mesh_terms: D000818:Animals; D001921:Brain; D004285:Dogs; D006979:Hyperthermia, Induced / Q000379:methods*; D007834:Lasers; D008279:Magnetic Resonance Imaging; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D013696:Temperature; D035501:Uncertainty