How to set custom upload directory per user after moving content directory

I set the content and the wordpress directory of wordpress like described in the codex:

define('WP_SITEURL', 'https://' . $_SERVER['SERVER_NAME'] . '/wordpress');
define('WP_CONTENT_DIR', dirname(__FILE__) . '/content');

Now what I want to do is set an individual upload directory for every user, like this:

wpinstance.org/content/uploads/user-name/here-goes-the-file.jpg

I already tried a lot using

define( 'UPLOADS', dirname(__FILE__) . '/content/uploads'.$current_user->user_name.'/');

as well as many combinations without dirname() and so on. It all turned out to take the files up to wordpress/…something and leaving the user name part empty. So how can I achieve this? Any ideas?