What is the best way to explain the change of my research interest in my Statement of Purpose for a PhD application?
How about explaining just along the same lines within your statement of purpose, as you do in your question, in a more developed way?

If you have a strong line of argument to underpin your change of research interests, and you can demonstrate you are committed to go further with this line of enquiry, and how your previous research can help with what is to come, and/or demonstrate how the knowledge and skills you've acquired and developed so far will support your future research efforts, that would be a good way to address this change in your application.