Effects of Sequence Timing on the Spatio-Temporal Properties of 3D BOLD fMRI: A Formal Framework and Analysis
3D sequences provide an alternative to 2D or multiband sequences for BOLD fMRI. The impact of acquisition time differences between slices is well understood for 2D or multiband sequences. For 3D sequences, k-space is partitioned into multiple segments and the final image depends on samples taken over an extended period of time. Any precise timing information is lost during reconstruction. A theoretical description of how sequence timing impacts 3D BOLD fMRI data properties is lacking in the literature. We present a formal framework that models sequence timing effects and draw connections to existing literature. The framework rests on the statistical description of a spin system that allows incorporation of BOLD signal changes and is completed by a general description of spatial encoding and image reconstruction. Using this formulation, we define three key images: the actual image reconstructed from a segmented 3D acquisition, an optimal reference image unaffected by sequence timing, and an error image representing their difference. Two sets of operators are defined that describe the generation of these images and allow us to analyse the effects of sequence timing independent of the object. All operators take the form of spatio-temporal filters. They mix signal content spatially and based on its temporal waveform. High-frequency BOLD signal content is affected more strongly compared to low-frequency content. Simulations demonstrate that while the total variance of 3D image time series can be reduced, spatio-temporal fidelity is increasingly lost. Furthermore, we hypothesize that the heightened sensitivity of 3D sequences to physiological noise (compared to 2D) is caused by sequence timing damping thermal noise more strongly than physiological fluctuations. The impact of motion and system instabilities on image time series needs to be studied further.