A Two-Layered Diffusion Model Traces the Dynamics of Information Processing in the Valuation-and-Choice Circuit of Decision Making

Figure 1

Drift diffusion model. The randomness of the path taken under the influence of noisy stimuli characterizes the diffusion models. A stimulus is represented in a diffusion equation by its influence on the drift rate of a random variable. This random variable, say the difference of evidence corresponding to the alternatives, accumulates the effects of the inputs over time until one of the boundaries is reached. The decision process ends when evidence reaches the threshold, and the time at which it occurs is called response time (RT). Response time (RT) depends on (a) the distance between the boundaries and the starting point, (b) the drift, that is, the rate at which the average (trend) of the random variable changes, and (c) the diffusion, that is, the variability of the path from the trend. These elements characterize the so-called drift diffusion model (DDM). The accumulation of evidence is then driven both by a deterministic component (drift) that is proportional to the stimulus intensity and by a stochastic component of noise (diffusion) that makes the evidence deviate from its own trend. The rationale of DDM is that, since the transmission and codification of the stimuli are inherently noisy, the quality of the feature extraction from such inputs may call for accumulation of a sufficient large sequence of the stimuli to get information [34]. Knowing the threshold level and the RT enables one to take a sight into the mechanism underlying the decision process [12, 88]. We can draw an analogy with a physical system and imagine the decisional process as the state of a “particle” moving within a potential well. Under this point of view, the persistence for relatively long periods of the state variable in the subthreshold area implies that the particle still entangled in the potential well enters an excited state where it remains for an exponentially distributed time interval with a certain decay time . If the combination of input and noise is sufficiently strong, then the particle is able to jump the barrier, that is, the threshold, and the system returns to an equilibrium state. The dynamics of the particle thus may resolve in a relaxation process [38] characterized by the oscillations between periods of subthreshold “disorder” inside the potential well and short impulses that trigger the system beyond the threshold in the rest state. This physical analogy allows better perception of how the DDM may fit the evolution of the input-output map underlying the neuronal model of the decision making process.