Recent advances in high-resolution 3D X-ray computed tomography (CT) allow detailed, non-destructive 3D structural mapping of a complete lithium-ion battery. By repeated 3D image acquisition (time lapse CT imaging) these investigations of material microstructure are extended into the fourth dimension (time) to study structural changes of the device in operando. By digital volume correlation (DVC) of successive 3D images the dimensional changes taking place during charge cycling are quantified at the electrode level and at the Mn2O4 particle scale. After battery discharging, the extent of lithiation of the manganese (III/IV) oxide grains in the electrode is found to be a function of the distance from the battery terminal with grains closest to the electrode/current collector interface having the greatest expansion (≈30%) and grains furthest from the current collector and closest to the counter electrode showing negligible dilation. This implies that the discharge is limited by electrical conductivity. This new CT+DVC technique is widely applicable to the 3D exploration of the microstructural degradation processes for a range of energy materials including fuel cells, capacitors, catalysts, and ceramics.