Based on this concept, Velcro was invented by Mestral.
Based on this concept, Velcro is the invention of Mestral.
Mestral based their invention of Velcro on this concept.
Mestral invented Velcro, [which is] based on this concept
In the first two, Velcro is the subject; so you can use the Based on structure (that is, beginning the sentence with those words). In the second two, it is the object, so you have to paraphrase.
(Of course, people widely use the mis-related version. When there's no ambiguity, I have no serious problem with it. But if you want to pass any EFL exams, avoid it.)