Data Assimilation in Brain Tumor Models - Mathematical Methods and Models in Biomedicine - page 251

Fig. 9 Final cell density plots for the first experiment repeated where the time period between
observations is varied. See text for details
uncorrelated errors that have a Gaussian distribution. In reality it is difficult to model
the relationship between cell density and pixel intensity due to the complex means
by which tumors evolve. Additionally there are many factors previously discussed
that lead to uncertainty in a patient tumor MR image. Also any assumed observation
operator will likely have non-Gaussian distributed error with covariance matrix that
is difficult to estimate.
Future work will focus on refinement of the forecast model and validation of
this approach with real clinical imaging data. Our ultimate goal is to apply data
assimilation methods as a treatment aid to help improve management of patient
GMB tumors and positively affect their quality of life.
Acknowledgments Portions of this work were funded by the Barrow Neurological Institute
Women's Foundation and by funds from the Newsome Family Endowed Chair of Neurosurgery
Research held by Dr. Preul. J.M. was supported in part by an Achievement Reward for College
Scientists Scholarship. Y.K. was supported by NSF grants DMS-0436341 and DMS-0920744.