Hypothalamic effective connectivity at rest is associated with body weight and energy homeostasis

Abstract Hunger and satiety drive eating behaviours via changes in brain function. The hypothalamus is a central component of the brain networks that regulate food intake. Animal research parsed the roles of the lateral hypothalamus (LH) and medial hypothalamus (MH) in hunger and satiety, respectively. Here, we examined how hunger and satiety change information flow between human LH and MH brain networks, and how these interactions are influenced by body mass index (BMI). Forty participants (16 overweight/obese) underwent two resting-state functional MRI scans while being fasted and sated. The excitatory/inhibitory influence of information flow between the MH and LH was modelled using spectral dynamic causal modelling. Our results revealed two core networks interacting across homeostatic state and weight: subcortical bidirectional connections between the LH, MH and the substantia nigra pars compacta (prSN), and cortical top-down inhibition from fronto-parietal and temporal areas. During fasting, we found higher inhibition between the LH and prSN, whereas the prSN received greater top-down inhibition from across the cortex. Individuals with higher BMI showed that these network dynamics occur irrespective of homeostatic state. Our findings reveal fasting affects brain dynamics over a distributed hypothalamic-midbrain-cortical network. This network is less sensitive to state-related fluctuations among people with obesity.


Spectral Dynamic Causal Modelling
Dynamic causal modelling (DCM) is Bayesian framework that infers the directed (causal) connectivity among the neuronal systemsreferred to as effective connectivity.We recently proposed a new DCM for resting state fMRIbased upon a deterministic model that generates predicted cross spectrareferred to as spectral DCM (Friston et al., 2014).In order to model resting state activityin the absence of external stimuliwe will have to add a stochastic component, i.e. neural fluctuations, to the classical DCM based on ordinary differential equations.Mathematically, we can express the formulation of the stochastic generative model using a set of two equations.First is the neuronal state equation, namely and second is the observation equation, which is a static nonlinear mapping from the hidden physiological states in (1) to the observed BOLD activity and is written as: We used standard Bayesian model inversion to infer the parameters of the model in (1), ( 2) and (3), from the observed signal ().The description of the Bayesian model inversion procedures based on variational Laplace can be found elsewhere for the interested readers (Friston et al., 2007).

Relationship between BMI and Fasting Blood Glucose Levels.
There was a significant positive relationship between BMI and fasting blood glucose levels: with each increase in BMI by 1 kg/m 2 , blood glucose levels increased by 0.

Supplementary Results
Table S1.
S2)where (t) is the rate of change of the neuronal states (),  are unknown parameters (i.e., the effective connectivity) and () (resp.()) is the stochastic processcalled the state noise (resp.the measurement or observation noise)modelling the random neuronal fluctuations that drive the resting state activity.In the observation equations,  are the unknown parameters of the (haemodynamic) observation function and () represents any exogenous (or experimental) inputs that drive the hidden statesthat are usually absent in resting state designs(Friston et al., 2014).Spectral DCM furnishes a constrained inversion of the stochastic model by parameterising the neuronal fluctuations ().Spectral DCM simplifies the generative model by replacing the original timeseries with their second-order statistics (i.e., cross spectra).This means, instead of estimating time varying hidden states, we are estimating their covariance which is time invariant.Then we simply need to estimate the covariance of the random fluctuations; where a scale free (power law) form for the state noise (resp.observation noise) is usedmotivated from previous work on neuronal activity (Beggs & Plenz, 2003)as follows:   (, ) =    −    (, ) =    −  (S3) Here, {, } ⊂  are the parameters controlling the amplitudes and exponents of the spectral density of the neural fluctuations.The parameterisation of endogenous fluctuations means that the states are no longer probabilistic; hence the inversion scheme is significantly simpler, requiring estimation of only the parameters (and hyperparameters) of the model.

Figure S2 .
Figure S2.Relationship between BMI and fasting blood glucose levels for all participants (N

Table S3 .
Hypothalamic network associated with BMI x Homeostatic State interaction