Estimation and Validation of Individualized Dynamic Brain Models with Resting State fMRI

Abstract

20A key challenge for neuroscience is to develop generative, causal models of the human 21 nervous system in an individualized, data-driven manner. Previous initiatives have either 22 33 34 MAIN TEXT 35 36 45 Generative models are then formed by integrating these cellular-level observations with known 46 neuronal biophysics at the spatial scale of individual neurons or small populations (e.g. [1]). 47 48 In contrast, another set of large initiatives has instead focused on modeling individual 49 human brain function using an approach often referred to as "connectomics" (e.g., Human 50 Page 2 of 38 Connectome Project, [2]). This approach relies on descriptive statistics, typically correlation 51 between fluctuating activity signals in brain regions assessed during the resting state (``resting 52 state functional connectivity" or rsFC; [3]). As a result, it is sometimes difficult to make 53 mechanistic inferences based upon functional connectivity correlations ( [4]). Moreover, neural 54 processes are notoriously nonlinear and inherently dynamic, meaning that stationary descriptions, 55 such as correlation/functional connectivity, may be unable to fully capture brain mechanisms. 56 Nevertheless, rsFC remains the dominant framework for describing connectivity patterns in 57 individual human brains. 59Despite the promise of human connectomics, there have been only a few attempts to equip 60 human fMRI studies with the sorts of generative neural population models that have powered 61 insights into non-human nervous systems. Notable advances have occurred in data-driven 62 approaches, with methods being developed to identify directed, causal influences between brain 63 regions (e.g. [5]). Conversely, neural mass modeling approaches have also been extended to study 64 human brain activity in a generative fashion, and these have provided new insights into the 65 computational mechanisms underlying fMRI and MEG/EEG activity dynamics ( [6] [7] [8]). 66 Neural mass modeling approaches have also been applied to individuals by incorporating single 67 subject diffusion data and anatomy ( [6]), but, unlike (linear) data-driven approaches (e.g. 68 Dynamic Causal Modeling; [5]), these models have not been directly fit to the individual brain 69 activity dynamics they seek to capture. However, both of these approaches have important 70 limitations. In particular, the data-driven approaches are subject to potential misinferences due to 71 assumptions of linearity ( [9]) or limitation to a relatively small number of brain regions (e.g. [5]). 72 Likewise, with neural mass modeling approaches, their ability to quantitatively recreate key 73 features of individual-level functional connectivity has also been limited ( [10] [7] [8]). This may 74 be because the most common approach is to parameterize connectivity from estimates of white 75 matter integrity from diffusion imaging, which also can lead to potential misinference, since these 76 connectivity estimates are constrained to be symmetric and positive ( [11]). ...

Scalable surrogate deconvolution for identification of partially-observable systems and brain modeling

“…Instead, most current procedures to deal with fMRI-based systems identification at scale ignore inter-regional variability in h i and instead seek to retrieve x t by fixing HRF parameters (e.g. [31], [30]) to the so-called "canonical HRF" (e.g. α = 6, β = 1).…”

“…The hyperparameter k < n determines the rank of the low-rank component W L and the regularization hyperparameters {λ i } define statistical priors on each of the weight matrix components (Laplace prior for W S ,W 1 ,W 2 and a normal prior for W L := W 1 W T 2 ). This decomposition has been shown useful to estimating large brain networks ( [30]). The nonlinear function ψ is parameterized by the parameter vector γ ∈ R n with ψ γ (x) = γ 2 + (bx t + .5) 2 − γ 2 + (bx t − .5) 2 (34)…”

“…Data were processed according to the recommendations of Siegel and colleagues ( [29]) and divided into 419 brain regions ( [28]). We then fit MINDy models either with or without surrogate deconvolution to this data using the same fitting procedure and hyperparameters ( [30]) as before. Results indicated the the parameters which describe the hemodynamic response function are reliable across scanning days and reliably differ between individuals (Fig.…”

Scalable Surrogate Deconvolution for Identification of Partially-Observable Systems and Brain Modeling

“…MINDy model fitting consists of using NADAM-enhanced gradient updates ( [26]) to minimize the following cost function: . This decomposition has been shown useful to estimating large brain networks ( [30]). The nonlinear function ψ is parameterized by the parameter vector γ ∈ R n with…”

“…The process noise ε t was Gaussian (σ 2 = .625) and independent between channels. The simulation parameters and generic MINDy fitting hyperparameters were generally identical to those in the original 40-network MINDy simulations ( [30]). Ground-truth connectivity parameters (W ) for the simulations were generated by a hyperdistribution characterized by four hyperparameters which scale the reduced-rank magnitude (σ 1 ), sparseness (σ 2 ), degree of asymmetry (σ a ), and degree of population clustering (p).…”