I don't know the piece sorry - but a few ideas - is this for oboe or bassoon?
The solid lines between pitches often indicate glissandi - can be achieved partly by sliding fingers off holes progressively - if however there are keys involved you may have to settle for a chromatic run or a combination of the two. To achieve a note below the normal range may be achieved by choking the note downwards by playing on the very tip of the reed till the vibrations are affected by the actual lip interference. Otherwise inserting a long piece of hose of appropriate diameter may produce the note you require. On a bassoon a 1.2 m vacuum cleaner pipe will get you down to about low G. Whereas a toilet paper inner cardboard roll will only play low A.
As for the arrow - which way does it point? Could it mean octave up or down, or accelerate or decelerate? I am surprised no "key" is given by the composer / publisher.
There is a book of avant garde techniques for woodwind which composers often refer to, which has fingerings for multiphonics and microtones, chords etc - it may offer some ideas - again someone else (Yoshi?) may be able to provide the details.
Christchurch New Zealand
Bassoonist / Teacher / Conductor