How do I set my Oracle session's globalization to be the same as my current thread in .NET?

For example, it would be great if I could do the following:

private void SetSessionGlobalization(Oracle.DataAccess.Client.OracleConnection aConnection)
{
    System.Globalization.CultureInfo lCultureInfo = System.Threading.Thread.CurrentThread.CurrentCulture;
    aConnection.SetSessionInfo(lCultureInfo);
}

But that does not work because SetSessionInfo takes a OracleGlobalization class as a parameter, not a CultureInfo!

And this does not work either:

private void SetSessionGlobalization(Oracle.DataAccess.Client.OracleConnection aConnection)
{
    Oracle.DataAccess.Client.OracleGlobalization lClientGlobalization = Oracle.DataAccess.Client.OracleGlobalization.GetClientInfo());
    aConnection.SetSessionInfo(lClientGlobalization);
}

Because GetClientInfo gets Oracle's version of the client globalization settings, not Windows.

What am I missing here? How do I set my database connection session to be the same as that used by my thread?