Advice on Constants - Notice: Undefined Constant

I'm currently developing a web site that stores two security levels of the client logged in. These security levels and including a few other variables are returning a PHP notice statement, "Notice: Undefined constant...". Now these variables are set at initial login into the web site and are stored into a the session file to reduce security checking routines and with the concept of why do a check again when we already know the value. To resolve this PHP notice issue I figured no big deal I will just declare the variable as a constant using define(). But by doing this correct me if I'm wrong you now no longer refer to the variable with a dollar sign and the variable name. Which is fine but can I store the constant into the session file? My concern and question is what the best direction to resolve this? At present if I just define the variables as a constant I get another PHP message "Notice: Undefined offset..." throughout my code when referencing my session variable (_SESSION[name]). Any advice would be greatly appreciated.