Situating edge time series within the generalized linear model framework
Poster No:
1487
Submission Type:
Abstract Submission
Authors:
Richard Betzel1, Haily Merritt1, Amanda Mejia1
Institutions:
1Indiana University, Bloomington, IN
First Author:
Co-Author(s):
Introduction:
Functional connectivity (FC) is typically modeled as a linear correlation between time courses recorded at distinct locations in the brain. Recent work has shown that static FC can be transformed into "edge time series" (eTS; Figure 1a), revealing framewise fluctuations in connections' weights (Zamani Esfahlani et al 2020; Figure 1b).
To date, eTS have largely been interpreted in terms of time-varying FC. Here, however, we show that eTS can also be interpreted through a statistical lens. Namely, the derivation of the eTS between regions i and j is identical to the interaction term in a standard linear model (Figure 1c). Here, we exploit this link to build linear models in which we explain time-varying behavior using both activations and edge time series (their interaction). For this abstract, we focus on calcium imaging recordings made in larval zebrafish (Chen et al 2018).
To date, eTS have largely been interpreted in terms of time-varying FC. Here, however, we show that eTS can also be interpreted through a statistical lens. Namely, the derivation of the eTS between regions i and j is identical to the interaction term in a standard linear model (Figure 1c). Here, we exploit this link to build linear models in which we explain time-varying behavior using both activations and edge time series (their interaction). For this abstract, we focus on calcium imaging recordings made in larval zebrafish (Chen et al 2018).
Methods:
Consider the z-scored activity time series from region i, zi. We can calculate the edge time series between regions i and j as rij = zi*zj, where * denotes element-wise multiplication. The element rij(t)=zi(t)zj(t) corresponds to the instantaneous co-fluctuation between regions i and j at time t.
In statistics, it is common to explain a variable y as a linear combination of predictors x1, x2, x3, and so on. It is also common to include interactions between predictors as x1*x2. Note that if x1 and x2 are z-scored, then the interaction between predictors 1 and 2 is calculated identically to their eTS.
Here, we models of the following form to explain some time-varying behavior, y:
y = βizi + βjzj + βijzi*zj + β0 + ε.
We fit models of this type for every pair of regions, ij, and calculate t-statistics for each regression coefficient, including βij. If we find that βij is statistically significant, i.e. that there is a significant interaction between i and j, then we can also conclude that the time-varying edge between i and j--the edge time series--carries unique explanatory power not carried by the activities of regions i and j alone.
We applied this framework to calcium imaging recordings of N=18 larval zebrafish. Neurons were assigned to one of 164± 39 parcels (defined at the single-subject level and were functionally homogeneous and spatially co-localized) and mean time courses derived for each parcel. Though unable to move freely, the animals engaged in fictive spontaneous behavior, including swimming (left/turns turns and forward movements decoded from motor neuron outputs) and eye movements.
In statistics, it is common to explain a variable y as a linear combination of predictors x1, x2, x3, and so on. It is also common to include interactions between predictors as x1*x2. Note that if x1 and x2 are z-scored, then the interaction between predictors 1 and 2 is calculated identically to their eTS.
Here, we models of the following form to explain some time-varying behavior, y:
y = βizi + βjzj + βijzi*zj + β0 + ε.
We fit models of this type for every pair of regions, ij, and calculate t-statistics for each regression coefficient, including βij. If we find that βij is statistically significant, i.e. that there is a significant interaction between i and j, then we can also conclude that the time-varying edge between i and j--the edge time series--carries unique explanatory power not carried by the activities of regions i and j alone.
We applied this framework to calcium imaging recordings of N=18 larval zebrafish. Neurons were assigned to one of 164± 39 parcels (defined at the single-subject level and were functionally homogeneous and spatially co-localized) and mean time courses derived for each parcel. Though unable to move freely, the animals engaged in fictive spontaneous behavior, including swimming (left/turns turns and forward movements decoded from motor neuron outputs) and eye movements.
Results:
Across animals, we found robust evidence that eTS explained time-varying behavior at a level above and beyond that of activations alone (see Figure 2 for results from a representative animal). We found that, across behavioral measures, 24.4%±21.3% of edges exhibited statistically significant effects (FDR corrected at q=0.01; mean adjusted p-value of 0.0025). We found evidence supporting the hypothesis that the same or similar sets of edges are significantly associated with multiple distinct behavioral measures and that significant edges share a common neuroanatomical substrate, favoring the rhombencephalon.
Conclusions:
In summary, our findings suggest that edges, above and beyond activations alone, carry meaningful information about time-varying behavioral measures. These findings suggest that dynamic coupling between groups of neurons--rather than reflecting stochastic fluctuations--may be neurobiologically meaningful and challenge the view that FC is purely time-invariant.
Modeling and Analysis Methods:
Connectivity (eg. functional, effective, structural) 1
Multivariate Approaches 2
Novel Imaging Acquisition Methods:
Imaging Methods Other
Keywords:
Other - Network; edge-centric; time-varying connectivity
1|2Indicates the priority used for review
·Figure 1
·Figure 2
Provide references using author date format
Chen, X., Mu, Y., Hu, Y., Kuan, A. T., Nikitchenko, M., Randlett, O., ... & Ahrens, M. B. (2018). Brain-wide organization of neuronal activity and convergent sensorimotor transformations in larval zebrafish. Neuron, 100(4), 876-890.