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@INPROCEEDINGS{Wischnewski:903158,
      author       = {Wischnewski, Kevin and Eickhoff, Simon and Popovych,
                      Oleksandr},
      title        = {{E}fficient validation of dynamical whole-brain models via
                      mathematical optimization algorithms},
      school       = {Heinrich Heine University Düsseldorf},
      reportid     = {FZJ-2021-04881},
      year         = {2021},
      abstract     = {INTRODUCTION: Investigating the resting-state brain
                      dynamics involves its simulation by dynamical whole-brain
                      models that have attracted a great interest over the last
                      years [1]. With a rising number of utilized mathematical
                      models and their complexity, the challenge of adequate model
                      fitting to empirical data has become apparent. An intuitive
                      approach is to optimize model parameters by a grid search.
                      However, an exploration of the entire parameter space on a
                      dense grid becomes computationally expensive for models with
                      many free parameters. In search of alternatives,
                      mathematical optimization algorithms have received increased
                      attention [2]. These methods can outperform the grid search
                      approach regarding computation time and result quality. In
                      this work, we investigate several such optimization schemes
                      for the validation of whole-brain models and compare their
                      outcomes as well as computational costs with each other and
                      the grid search. We suggest two most efficient algorithms
                      for the optimization of the correspondence between simulated
                      and empirical data. METHODS: Neuroimaging data of 105
                      subjects of the Human Connectome Project [3] were used for
                      the extraction of structural and resting-state functional
                      connectivity (SC and FC, respectively). Schaefer’s
                      functional atlas [4] with 100 cortical regions was chosen as
                      a brain parcellation. Additionally, an MRtrix-based
                      probabilistic tractography [5] was applied to compute
                      atlas-based SC. It was used to determine the coupling
                      weights and delays between units of the dynamical model of
                      coupled phase oscillators [6]. The model was deployed to
                      simulate resting-state brain dynamics and eventually
                      generate simulated FC (sFC). This in turn was fitted to
                      empirical FC (eFC) by simultaneously adjusting up to 3 model
                      parameters: global coupling and delay (2Dim parameter space)
                      as well as noise intensity (3Dim parameter space). In
                      addition to the grid search, the following derivative-free
                      methods were tested: Nelder Mead Algorithm (NMA, [7]),
                      Particle Swarm Optimization (PSO, [8]), Covariance Matrix
                      Adaptation Evolution Strategy (CMAES, [9]) and Bayesian
                      Optimization (BO, [10]). NMA is a deterministic local search
                      method, the others represent global stochastic approaches.
                      PSO and CMAES share the feature of being population-based.
                      RESULTS: For all tested algorithms, the detected
                      goodness-of-fit values range from $-5\%$ to $+11\%$ around
                      those found by the grid search. Among the methods, the order
                      PSO > CMAES > BO > NMA in respect of the goodness-of-fit
                      (larger is better) can be observed. The values of the best
                      fit in the 3Dim parameter space are on average around $16\%$
                      higher than those obtained in the 2Dim case, regardless of
                      applied algorithm. We found that the algorithms reliably
                      detect global maxima in the parameter space, where the
                      spread of solutions was tested for multiple random initial
                      conditions. This effect is most pronounced for CMAES, while
                      NMA demonstrates a high susceptibility to local optima.
                      Comparing the computation time required by the investigated
                      methods to the grid search $(100\%)$ yielded relative values
                      from $3500\%$ (PSO) to $87\%$ (NMA) in 2Dim and from $73\%$
                      (PSO) to $2\%$ (BO) in 3Dim. To evaluate methods, we
                      analyzed a cost function that included the goodness-of-fit
                      values, spread of algorithm solutions as well as the
                      required computation time. We identified CMAES and BO as the
                      most efficient approaches that may be used for the
                      validation of dynamical models. CONCLUSIONS: We showed that
                      some available mathematical optimization algorithms can be
                      used as an efficient tool to improve and accelerate the
                      search for the parameters that maximize the similarity
                      between empirical and simulated data. The tested methods
                      perform a continuous search and do not rely on a selected
                      grid granularity in order to detect optimal solutions. Thus,
                      our findings may contribute to a more efficient validation
                      of complex models with high-dimensional parameter spaces and
                      facilitate precise and personalized modeling of brain
                      dynamics. REFERENCES: [1] doi:10.3389/fnsys.2018.00068, [2]
                      doi:10.1007/s12021-018-9369-x, [3]
                      doi:10.1016/j.neuroimage.2013.05.041, [4]
                      doi:10.1093/cercor/bhx179, [5]
                      doi:10.1016/j.neuroimage.2019.116137, [6]
                      doi:10.1016/j.neuroimage.2011.04.010, [7]
                      doi:10.1093/comjnl/7.4.308, [8]
                      doi:10.1007/s11721-007-0002-0, [9]
                      doi:10.1145/2330784.2330919, [10]
                      doi:10.1287/educ.2018.0188},
      month         = {Jun},
      date          = {2021-06-21},
      organization  = {The 27th Annual Meeting of the
                       Organization for Human Brain Mapping,
                       Virtual (Virtual), 21 Jun 2021 - 25 Jun
                       2021},
      subtyp        = {After Call},
      cin          = {INM-7},
      cid          = {I:(DE-Juel1)INM-7-20090406},
      pnm          = {5232 - Computational Principles (POF4-523) / HBP SGA2 -
                      Human Brain Project Specific Grant Agreement 2 (785907) /
                      HBP SGA3 - Human Brain Project Specific Grant Agreement 3
                      (945539) / VirtualBrainCloud - Personalized Recommendations
                      for Neurodegenerative Disease (826421)},
      pid          = {G:(DE-HGF)POF4-5232 / G:(EU-Grant)785907 /
                      G:(EU-Grant)945539 / G:(EU-Grant)826421},
      typ          = {PUB:(DE-HGF)24},
      url          = {https://juser.fz-juelich.de/record/903158},
}