[Paper Review] Toric degenerations of Bott-Samelson varieties

Philip Foth, Sangjib Kim|arXiv (Cornell University)|May 9, 2009

Commutative Algebra and Its Applications10 references4 citations

TL;DR

This study proposes a novel method to model dynamic affective processing in resting-state fMRI by mapping brain activity to a low-dimensional valence-arousal space, enabling neural decoding of temporal derivatives that form neurally constrained ODEs. The approach yields significantly more accurate simulations of affective dynamics than random sampling, with significant closed-loop predictions for up to four time steps (Δt = 2.0 s), and reveals neural representations in affect-related brain regions.

ABSTRACT

There exists growing interest in understanding the dynamics of resting state functional magnetic resonance imaging (rs-fMRI) to establish mechanistic links between individual patterns of spontaneous neural activation and corresponding behavioral measures in both normative and clinical populations. Here we propose and validate a novel approach in which whole-brain rs-fMRI data are mapped to a specific low-dimensional representation-affective valence and arousal processing-prior to dynamic analysis. This mapping process constrains the state space such that both independent validation and visualization of the system's dynamics become tractable. To test this approach, we constructed neural decoding models of affective valence and arousal processing from brain states induced by International Affective Picture Set image stimuli during task-related fMRI in (<i>n</i> = 97) healthy control subjects. We applied these models to decode moment-to-moment affect processing in out-of-sample subjects' rs-fMRI data and computed first and second temporal derivatives of the resultant valence and arousal time-series. Finally, we fit a second set of neural decoding models to these derivatives, which function as neurally constrained ordinary differential equations (ODE) underlying affect processing dynamics. To validate these decodings, we simulated affect processing by numerical integration of the true temporal sequence of neurally decoded derivatives for each subject and demonstrated that these decodings generate significantly less (<i>p</i> < 0.05) group-level simulation error than integration based upon decoded derivatives sampled uniformly randomly from the true temporal sequence. Indeed, simulations of valence and arousal processing were significant for up to four steps of closed-loop simulation (Δt = 2.0 s) for both valence and arousal, respectively. Moreover, neural encoding representations of the ODE decodings include significant clusters of activation within brain regions associated with affective reactivity and regulation. Our work has methodological implications for efforts to identify unique and actionable biomarkers of possible future or current psychopathology, particularly those related to mood and emotional instability.

Motivation & Objective

• To develop a tractable framework for analyzing dynamic neural processes in resting-state fMRI by constraining the state space to affective valence and arousal.
• To validate neural decoding models of valence and arousal derived from task-related fMRI data for use in out-of-sample resting-state data.
• To model the underlying dynamics of affective processing using first and second temporal derivatives of decoded valence and arousal time-series.
• To test whether neurally decoded derivatives can generate more accurate simulations of affective dynamics than random sampling.
• To identify neural representations of the derived ODEs in brain regions associated with affective reactivity and regulation.

Proposed method

• Neural decoding models of affective valence and arousal were trained on fMRI data from 97 healthy subjects during task-based stimulation with the International Affective Picture Set.
• These models were applied to decode moment-to-moment valence and arousal from out-of-sample resting-state fMRI data.
• First and second temporal derivatives of the decoded valence and arousal time-series were computed to represent dynamic change rates.
• A second set of neural decoding models was trained on these derivatives to generate neurally constrained ordinary differential equations (ODEs) of affective dynamics.
• Simulations of affective processing were performed via numerical integration of the decoded ODEs, with performance compared to simulations based on randomly sampled derivatives.
• Neural encoding representations of the ODE decodings were analyzed to identify brain regions supporting the derived dynamics.

Experimental results

Research questions

• RQ1 Can affective valence and arousal be reliably decoded from resting-state fMRI data using models trained on task-related fMRI data?
• RQ2 Do the temporal derivatives of decoded valence and arousal time-series reflect biologically plausible dynamics of affective processing?
• RQ3 Can neurally constrained ODEs derived from these derivatives produce more accurate simulations of affective dynamics than random derivative sampling?
• RQ4 How do the neural representations of the derived ODEs compare to known brain networks involved in affect regulation?
• RQ5 To what extent can the simulated dynamics predict future affective states in a closed-loop manner?

Key findings

• Neural decoding of valence and arousal from resting-state fMRI data was successfully achieved using models trained on task-related fMRI data.
• Simulations based on neurally decoded derivatives of valence and arousal produced significantly lower group-level simulation error than simulations based on randomly sampled derivatives (p < 0.05).
• Significant closed-loop simulation accuracy was maintained for up to four time steps (Δt = 2.0 s) in both valence and arousal dynamics.
• The neural encoding representations of the ODE decodings included significant clusters of activation in brain regions associated with affective reactivity and regulation.
• The approach demonstrates potential for identifying unique, actionable biomarkers of mood and emotional instability in clinical populations.