I sort of took "the heart" of what you were talking about and simplified it (I think) and added the slogan, "your good health, we're at the heart of it all." Heart meaning center of, but also dental affects heart health, etc.--yet i think this gives the idea in a way it can be grasped quickly, which in a logo is basically the only way since you only have a moment to make that impression with a logo
If you have variations you'd like me to try (colors, fonts, subtractions, additions), let me know. Thanks. C