In the recent years, the organic electrochemical transistors (OECT) have attracted considerable attention for biosensing applications due to the biocompatibility of their materials and their low operating voltages. Upon exposure to an electrolyte, the drain current becomes ion-dependent. This can be exploited for sensing ion applications. To facilitate the process of designing such powerful ion sensing devices one needs the ability to simulate the transient dynamical behavior of many OECT elements connected in a network. We have developed a generic theoretical model of the OECT element that can be used for such purposes. Our OECT element resembles a typical FET three-port element with the response function parameterized with an additional time-dependent variable, T, which describes how far the element operates from the stationary state. We have constructed a dynamical equation that describes how T changes in time when the element is exposed to arbitrary external voltages. This makes the element model highly interoperable with generic electrical circuit simulators. We provide an example of possible numerical implementation using the modified nodal analysis. We tested the underlying theoretical assumptions by comparing model predictions with experimental data and found a reasonable agreement. Our model describes the typical current spikes observed in the literature.