Processes of evidence accumulation can make driver models more realistic, by explaining how drivers adjust their actions based on perceptual inputs and decision boundaries. The absence of a standard modelling approach limits their adoption; existing methods are hand-crafted, hard to adapt, and computationally inefficient. This paper presents Akkumula, an evidence accumulation modelling framework that uses Spiking Neural Networks and other deep learning techniques. Tested on data from a test-track experiment, the model can reproduce the time course of braking, accelerating, and steering. Akkumula integrates with existing machine learning architectures, scales to large datasets, adapts to different driving scenarios, and keeps its internal logic relatively transparent.