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| Hauptseite > Publikationsdatenbank > Numerical investigation of data-driven dynamical brain models with application to inter-individual variability |
| Hauptseite > Publikationsdatenbank > Numerical investigation of data-driven dynamical brain models with application to inter-individual variability |
| Dissertation / PhD Thesis | FZJ-2026-04494 |
2026
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Please use a persistent id in citations: doi:10.34734/FZJ-2026-04494
Abstract: Mathematical optimization problems play a decisive role in various domains of theeconomy, health, and research. Examples include business modeling for profitmaximization or minimization problems in engineering and design. The health sectorconsiders mathematical simulations for optimizing the effects of personalized therapies.In particular, human brain research utilizes mathematical models to replicate measureddata of brain activity as closely as possible. Such an investigation of brain dynamics hasreceived new perspectives following the shift of neuroimaging research towards the so-called resting-state activity. It describes the constantly ongoing mental processes in theabsence of any behavioral task. In the most common approach, the temporal fluctuationsof blood oxygenation level-dependent (BOLD) signals of the brain at rest are measured byfunctional magnetic resonance imaging (fMRI). This process allows for the computationof functional connectivity (FC). It is reflected by a matrix containing the cross-correlationsbetween the corresponding BOLD signals. Resting-state FC is deemed to represent theintrinsic functional organization of the brain. However, the mechanisms underlying theemergence of specific functional patterns in the brain remain vague. The approachdescribed in this thesis builds personalized models of brain activity in terms of FC uponempirical structural data of the brain. To this end, the brain is subdivided into a set ofdistinct regions according to a given brain atlas. While the regions serve as nodes of themodel network, the edges are defined by the empirical structural connectivity (SC) whichrepresents anatomical connections between brain regions extracted from diffusion-weighted MRI (dwMRI). The network nodes are equipped with coupled stochasticdifferential equations (SDEs) whose solutions provide a simulation of the correspondingbrain regions’ mean BOLD signals.In my PhD project, I addressed the optimization problem of approximating those modelparameters that maximize the correlation between empirically measured and model-simulated FC for individual subjects. This is termed model fitting or model validation. Thenon-convexity and non-differentiability of the multimodal objective functions preventsthe application of gradient and quasi-Newton methods. I therefore tested four direct, i.e.,derivative-free search algorithms and compared their performance across subjects withone another and with the results of a dense grid search (GS) in two- and three-dimensional model parameter spaces (study 1). Having identified two most efficientmethods, I proceeded to optimization problems with up to 103 free parameters, where Istudied the reliability of the results and their potential utility in a classification task (study2). I eventually participated in the development of a workflow leading from raw MRI datatowards model-based predictions of human behavior and phenotypes (study 3).The considered derivative-free search schemes were the Nelder-Mead Algorithm (NMA),Particle Swarm Optimization (PSO), the Covariance Matrix Adaptation Evolution Strategy(CMAES) and Bayesian Optimization (BO). Study 1 revealed that CMAES and BO providethe most favorable tradeoff between the required computational resources and therobustness against local optima in low-dimensional parameter spaces. The results ofstudy 2 showed advantages of high-dimensional model fitting for a classification task, butalso highlighted the need for adequate solution selection strategies in cases of severalnear-optimal parameter values. Study 3 demonstrated how the incorporation of modelsimulation results can enhance the prediction quality of behavioral traits andphenotypical characteristics in comparison to empirical data alone. In summary, thepresented studies showed the indispensability of well-conceived parameter optimizationstrategies for simulations of human brain activity and subsequent investigations of inter-individual variability.
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