  We propose a new, modular, open-source, Python-based 3D+time fMRI data
simulation software, \emph{SNAKE-fMRI}, which stands for \emph{S}imulator from
\emph{N}eurovascular coupling to \emph{A}cquisition of \emph{K}-space data for
\emph{E}xploration of fMRI acquisition techniques.Unlike existing tools, the
goal here is to simulate the complete chain of fMRI data acquisition, from the
spatio-temporal design of evoked brain responses to various multi-coil k-space
data 3D sampling strategies, with the possibility of extending the forward
acquisition model to various noise and artifact sources while remaining
memory-efficient.By using this \emph{in silico} setup, we are thus able to
provide realistic and reproducible ground truth for fMRI reconstruction methods
in 3D accelerated acquisition settings and explore the influence of critical
parameters, such as the acceleration factor and signal-to-noise ratio~(SNR), on
downstream tasks of image reconstruction and statistical analysis of evoked
brain activity.We present three scenarios of increasing complexity to showcase
the flexibility, versatility, and fidelity of \emph{SNAKE-fMRI}: From a
temporally-fixed full 3D Cartesian to various 3D non-Cartesian sampling
patterns, we can compare -- with reproducibility guarantees -- how experimental
paradigms, acquisition strategies and reconstruction methods contribute and
interact together, affecting the downstream statistical analysis.
