Parameter Identification Of A Nonlinear Model For The Hemodynamic System In Functional Magnetic Resonance Imaging

Shams, Seyed Mohammad; Hossein-Zadeh, Gholam Ali; Karimi, Mohammad Mehdi

doi:10.22041/ijbme.2007.13484

Parameter Identification Of A Nonlinear Model For The Hemodynamic System In Functional Magnetic Resonance Imaging

Document Type : Full Research Paper

Authors

Seyed Mohammad Shams ¹

Gholam Ali Hossein-Zadeh ¹

Mohammad Mehdi Karimi ²

¹ Control and Intelligent Processing Center of Excellence, Electrical and Computer Engineering Department, School of Engineering, University of Tehran - School of Cognitive Science, Institute For Studie In Theoretical Physics and Mathematics

² School of Cognitive Science, Institute For Studie In Theoretical Physics and Mathematics

10.22041/ijbme.2007.13484

Abstract

In order to analyze the functional Magnetic Resonance Imaging (fMRI) data, the parameters of a nonlinear model for the hemodynamic system, so called Balloon model, were characterized and estimated. Two different approaches were applied to estimate these parameters. In the first step of both approaches, the voxels which show neural activity were identified. Then, the parameters of the balloon model for these active voxels were estimated by both steepest descent algorithm, and through genetic algorithm. Proposed approaches were applied on experimental fMRI data and the parameters of nonlinear Balloon model were estimated for different brain voxels. Accuracy of these characterizations was assessed via comparing the measured time series at each voxel with the modeled time series. Also, it was shown that the results of the parameter-estimation are consistent with the results obtained from system characterization via Volterra Kernels (which were reported in previous studies). It was concluded that the suggested approaches could accomplish a nonlinear system characterization through numerical methods, whereas they avoid theoretical complexities and they have acceptable speed (especially steepest descent algorithm).

Keywords

System identification

Fmri (Functional Mri)

Hemodynamic System

Nonlinear Modeling

Balloon Model

Subjects

[1] حسین‌زاده غلامعلی، تشخیص فعالیت در تصویرنگاری عملکردی تشدید مغناطیسی با استفاده بهینه از اطلاعات مکانی، رساله دکتری، دانشکده فنی دانشگاه تهران، اسفند 1381.

[2] Cohen MS; Parametric analysis of fMRI data using linear systems methods; NeuroImage 1997; 6:93–103.

[3] Bandettini PA, Cox RW; Event-related fMRI contrast when using constant inter stimulus interval: Theory and experiment; Magnetic Resonance in Medicine 2000; 43: 540–548.

[4] Friston KJ, Josephs O, Rees G, Turner R; Nonlinear event-related response in fMRI; Magnetic Resonance in Medicine 1998; 39: 41–52.

[5] Vazquez AL, Noll DC; Nonlinear aspects of the BOLD response in functional MRI; NeuroImage 2001; 13: 1– 12.

[6] Miller KL, Luh W, Liu TT, Martinez A, Obata T, Wong EC, Frank LR, Buxton RB; Nonlinear temporal dynamics of the cerebral blood flow response; Human Brain Mapping 2001; 13: 1–12.

[7] Buxton RB, Wong EC, Frank LR; Dynamics of blood flow and oxygenation changes during brain activation: The Balloon model; Magnetic Resonance in Medicine 1998; 39: 855–864.

[8] Friston KJ, Mechelli A, Turner R, Price CJ; Nonlinear responses in fMRI: The Baloon model, Voltera kernels, and other hemodynamics; NeroImage 2000; 12: 466–477.

[9] Gholam-Ali H-Z, Babak A, and Hamid S; A signal subspace approach for modeling the hemodynamic response in fMRI; Magnetic Resonance Imaging 2003; 21: 835–843.

[10] Buckner RL, Snyder AZ, Sanders AL, Raichle ME, Morris JC; Functional brain imaging of young, nondemented, and demented older adults; Journal of Cognitive Neuroscience 2000; 12(2): 24–34.

[11] fMRI data center at http://www.fmridc.org (Accession #: 2-2000-1118W).

[12] Talairach J, Tournoux P; A Co-planar stereotaxic atlas of a human brain; Thieme, Stuttgart, 1988.

[13] Chen B, Lee F, Peng S; Maximum likelihood parameter estimation of F-ARIMA process using the genetic algorithm in the frequency domain; IEEE Transaction on Signal Processing 2002; 50: 2208– 2220.