Deterioration in vs deterioration of

Solution 1:

If you use the first ‘the injury caused a deterioration in his physical function’ then you speak of how he as a being is less able to function. For example, he might no longer be able to pick up an egg-cup, unaided. We speak here of ‘what he can do’.

If you use the second one ‘the injury caused a deterioration of his physical functioning’, it speaks of the quality of the functioning going on within him, i.e. how his body functions. For example, the motor neurons in his hand no longer send impulses that allow him to close his fingers. ‘Body’ is implied here; i.e. ‘the injury caused a deterioration of his physical (body) functioning’.