The handle to the dropdown menu must be available in the same workspace that updates the cell array. If that's done in AppDesigner, the handle should be in the app class variable. If the cell array is updated outside of app designer, you'll need to pass the dropdown menu handle (or entire app handle) to that function.
Every time the cell is updated, update the Items propery of the uidropdown menu.
An alternative and less efficient method would be to define the cell array as an app property and use a timer object to iteratively check if the cell array has changed and to update the Items list.
