  Causal mediation analysis is increasingly abundant in biology, psychology,
and epidemiology studies, etc. In particular, with the advent of the big data
era, the issue of high-dimensional mediators is becoming more prevalent. In
neuroscience, with the widespread application of magnetic resonance technology
in the field of brain imaging, studies on image being a mediator emerged. In
this study, a novel causal mediation analysis method with a three-dimensional
image mediator is proposed. We define the average casual effects under the
potential outcome framework, explore several sufficient conditions for the
valid identification, and develop techniques for estimation and inference. To
verify the effectiveness of the proposed method, a series of simulations under
various scenarios is performed. Finally, the proposed method is applied to a
study on the causal effect of mother$^{\prime}$s delivery mode on
child$^{\prime}$s IQ development. It is found that the white matter in certain
regions of the frontal-temporal areas has mediating effects.
