title: A novel approach to calibrate the hemodynamic model using functional Magnetic Resonance Imaging (fMRI) measurements.
abstract: BACKGROUND
  The calibration of the hemodynamic model that describes changes in blood flow and blood oxygenation during brain activation is a crucial step for successfully monitoring and possibly predicting brain activity. This in turn has the potential to provide diagnosis and treatment of brain diseases in early stages.
  
  
  METHODS
  We propose an efficient numerical procedure for calibrating the hemodynamic model using some fMRI measurements. The proposed solution methodology is a regularized iterative method equipped with a Kalman filtering-type procedure. The Newton component of the proposed method addresses the nonlinear aspect of the problem. The regularization feature is used to ensure the stability of the algorithm. The Kalman filter procedure is incorporated here to address the noise in the data.
  
  
  RESULTS
  Numerical results obtained with synthetic data as well as with real fMRI measurements are presented to illustrate the accuracy, robustness to the noise, and the cost-effectiveness of the proposed method.
  
  
  CONCLUSIONS
  We present numerical results that clearly demonstrate that the proposed method outperforms the Cubature Kalman Filter (CKF), one of the most prominent existing numerical methods.
  
  
  CONCLUSIONS
  We have designed an iterative numerical technique, called the TNM-CKF algorithm, for calibrating the mathematical model that describes the single-event related brain response when fMRI measurements are given. The method appears to be highly accurate and effective in reconstructing the BOLD signal even when the measurements are tainted with high noise level (as high as 30%).
authors.affiliation: Department of Mathematics & Interdisciplinary Research Institute for the Sciences, IRIS, California State University Northridge (CSUN), Northridge, USA.. Electronic address: nafiseh.khoram.25@my.csun.edu.
authors.forename: Nafiseh
authors.initials: N
authors.lastname: Khoram
authors.affiliation: Department of Applied Mathematics and Computational Science, King Abdullah University of Science and Technology (KAUST), Saudi Arabia. Electronic address: chadia.zayane@kaust.edu.sa.
authors.forename: Chadia
authors.initials: C
authors.lastname: Zayane
authors.affiliation: Department of Mathematics & Interdisciplinary Research Institute for the Sciences, IRIS, California State University Northridge (CSUN), Northridge, USA.. Electronic address: rabia.djellouli@csun.edu.
authors.forename: Rabia
authors.initials: R
authors.lastname: Djellouli
authors.affiliation: Department of Applied Mathematics and Computational Science, King Abdullah University of Science and Technology (KAUST), Saudi Arabia. Electronic address: taousmeriem.laleg@kaust.edu.sa.
authors.forename: Taous-Meriem
authors.initials: TM
authors.lastname: Laleg-Kirati
mesh_terms: D000465:Algorithms; D001921:Brain / Q000098:blood supply* / Q000000981:diagnostic imaging*; D002138:Calibration; D006439:Hemodynamics; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008279:Magnetic Resonance Imaging; D008959:Models, Neurological; D010100:Oxygen
chemical_list: D010100:Oxygen
keywords: Balloon model; Brain response; Cubature Kalman Filter; Newton method; Nonlinear hemodynamic model; Parameter estimation; Tikhonov regularization; fMRI measurements