Estimating Biophysical Parameters from BOLD Signals through Evolutionary-Based Optimization

  • Pablo MesejoEmail author
  • Sandrine Saillet
  • Olivier David
  • Christian Bénar
  • Jan M. Warnking
  • Florence Forbes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9350)


Physiological and biophysical models have been proposed to link neural activity to the Blood Oxygen Level-Dependent (BOLD) signal in functional MRI (fMRI). They rely on a set of parameter values that cannot always be extracted from the literature. Their estimation is challenging because there are more than 10 potentially interesting parameters involved in non-linear equations and whose interactions may result in identifiability issues. However, the availability of statistical prior knowledge on these parameters can greatly simplify the estimation task. In this work we focus on the extended Balloon model and propose the estimation of 15 parameters using an Evolutionary Computation (EC) global search method. To combine both the ability to escape local optima and to incorporate prior knowledge, we derive the EC objective function from Bayesian modeling. This novel method provides promising results on a challenging real fMRI data set involving rats with epileptic activity and compares favorably with the conventional Expectation Maximization Gauss-Newton approach.


Functional MRI BOLD signal Biophysical parameters Evolutionary Computation Differential Evolution Expectation Maximization 


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  1. 1.
    Buxton, R.B., Uludağ, K., Dubowitz, D.J., Liu, T.T.: Modeling the hemodynamic response to brain activation. Neuroimage 23, S220–S233 (2004)Google Scholar
  2. 2.
    Buxton, R.B., Wong, E.C., Frank, L.R.: Dynamics of blood flow and oxygenation changes during Brain activation: the balloon model. Magn. Reson. Med. 39, 855–864 (1998)CrossRefGoogle Scholar
  3. 3.
    Chumbley, J.R., Friston, K.J., Fearn, T., Kiebel, S.J.: A Metropolis-Hastings algorithm for dynamic causal models. Neuroimage 38(3), 478–487 (2007)CrossRefGoogle Scholar
  4. 4.
    Coquery, N., Francois, O., Lemasson, B., Debacker, C., Farion, R., Rémy, C., Barbier, E.L.: Microvascular MRI and unsupervised clustering yields histology-resembling images in two rat models of glioma. J. Cereb. Blood Flow Metab. 34(8), 1354–1362 (2014)CrossRefGoogle Scholar
  5. 5.
    Das, S., Suganthan, P.: Differential Evolution: A Survey of the State-of-the-Art. IEEE T. Evolut. Comput. 15, 4–31 (2011)CrossRefGoogle Scholar
  6. 6.
    David, O., Guillemain, I., Saillet, S., Reyt, S., Deransart, C., Segebarth, C., Depaulis, A.: Identifying neural drivers with functional MRI: an electrophysiological validation. PLoS Biol. 6(12), 2683–2697 (2008)CrossRefGoogle Scholar
  7. 7.
    Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer (2003)Google Scholar
  8. 8.
    Frau-Pascual, A., Ciuciu, P., Forbes, F.: Physiological models comparison for the analysis of ASL fMRI data. In: EEE International Symposium on Biomedical Imaging (ISBI) (2015)Google Scholar
  9. 9.
    Friston, K.J.: Bayesian estimation of dynamical systems: an application to fMRI. Neuroimage 16, 513–530 (2002)CrossRefGoogle Scholar
  10. 10.
    Friston, K.J., Mechelli, A., Turner, R., Price, C.J.: Nonlinear responses in fMRI: the balloon model, Volterra kernels, and other hemodynamics. Neuroimage 12, 466–477 (2000)CrossRefGoogle Scholar
  11. 11.
    Khalidov, I., Fadili, J., Lazeyras, F., Van De Ville, D., Unser, M.: Activelets: Wavelets for sparse representation of hemodynamic responses. Signal Process 91(12), 2810–2821 (2011)CrossRefGoogle Scholar
  12. 12.
    Marreiros, A., Kiebel, S., Friston, K.: Dynamic causal modelling for fMRI: A two-state model. NeuroImage 39, 269–278 (2008)CrossRefGoogle Scholar
  13. 13.
    Silvennoinen, M., Clingman, C., Golay, X., Kauppinen, R., van Zijl, P.: Comparison of the dependence of blood R2 and R* on oxygen saturation at 1.5 and 4.7 Tesla. Magn. Reson. Med. 49(1), 47–60 (2003)CrossRefGoogle Scholar
  14. 14.
    Stephan, K.E., Weiskopf, N., Drysdale, P.M., Robinson, P.A., Friston, K.J.: Comparing hemodynamic models with DCM. Neuroimage 38(3), 387–401 (2007)CrossRefGoogle Scholar
  15. 15.
    Stephan, K., Kasper, L., Harrison, L., Daunizeau, J., den Ouden, H., Breakspear, M., Friston, K.: Nonlinear dynamic causal models for fMRI. NeuroImage 42(2), 649–662 (2008)CrossRefGoogle Scholar
  16. 16.
    Vakorin, V.A., Krakovska, O.O., Borowsky, R., Sarty, G.E.: Inferring neural activity from BOLD signals through nonlinear optimization. Neuroimage 38(2), 248–260 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Pablo Mesejo
    • 1
    Email author
  • Sandrine Saillet
    • 2
    • 5
  • Olivier David
    • 2
    • 5
  • Christian Bénar
    • 3
    • 4
  • Jan M. Warnking
    • 2
    • 5
  • Florence Forbes
    • 1
  1. 1.INRIAUniv. Grenoble Alpes, LJKGrenobleFrance
  2. 2.INSERM, U836GrenobleFrance
  3. 3.INSERM, UMR1106MarseilleFrance
  4. 4.Institut de Neurosciences des SystèmesAix-Marseille UniversitéMarseilleFrance
  5. 5.Univ. Grenoble Alpes, GINGrenobleFrance

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