Growth of brain stimulation reward as a function of duration and stimulation strength.

The strength of a train of rewarding brain stimulation required to support a criterion level of operant performance declines hyperbolically as the duration is increased. This finding has been attributed to a process of leaky integration. However, the rate at which integration approaches asymptote has been shown to depend on stimulation strength, a finding that differs from the behavior of a simple leaky integrator. The authors replicate both findings and show that they are both well described by a new model that incorporates a hyperbolic strength-duration function, a logistic function mapping stimulation frequency onto reward intensity, and another logistic function mapping reward intensity onto performance.

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