At the earlier stage of crack deceleration, dot(KID) is positive and linear relation with crack tip velocity (Nishioka, 2001)

I am reading the paper of Prof. Nishioka (2001) (Int. Jour. of Solid and Fracture, Vol. 38, 5273-5301). He said that "At the earlier stage of crack deceleration, dot(KID) is positive and linear relation with crack tip velocity". I do not understood that meaning. This is from mathematical, right? If after the earlier stage of crack deceleration, which relation between dot(KID) and crack tip velocity?