If making again, will make the sideways valve smaller, so it’s stiffer, and the split valves larger, so they look okay lined.

Stuffed it with a mixture of polyfill and plastic beads (in a nylon) so that it can work as a stress ball.
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Modified a bit. For the first valve, added short rows and doubled it so that it could be lined.

From the cast-on, after binding off half the stitches:
Working in stockinette the whole time, and do short rows however you like.
Cast on 16 stitches. Work 18 towards the body, turn. Work to end.
Work back 16, turn, work to end.
Work 14, turn, work to end.
Work 26 stitches, picking up wraps or doing your favourite gap-closing trick.

Cast on 16 stitches. Repeat short rows as for first half.

Work about 2” of stitches, with middle short rows at least twice (I only did once, wish I’d done one or two more of these). That is, work to 10 stitches from the end, turn, work to 10 stitches from the other end, turn. This is to make the centre ever so slightly larger, so that turning the ends in is easier.

Once you’re nearly happy with the circumference of this valve, stop. Work short rows as when you cast on, so that the short-rowed ends will meet up around the valve stem. It gives it just enough roundness to keep the valve stem from flattening.

Do not bind off. Because I’m crazy, I kitchenered it. Because I’m really crazy, I seamed the two edges first, then kitchenered the tube. I really should have taken a picture. Don’t forget to stuff the stem of the valve before it gets completely enclosed.

But the point is to get your final row stitched down seamlessly to the cast-on of this branch and the bind-off of the stem, so it’s all nice and neat. And then the ends, which will be somewhat smaller because of the inner short rows, can be folded in to add some structure so you don’t have to stuff that valve. And if you’re really crazy, as I am, you can seam the two ends of the tube together, so they stay put inside the tube.

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For the second valve (aorta) did not need 8”, undid a bunch. Increased the row before splitting. Would increase another time or two after splitting if doing it again.

Knit as required, but instead of binding off, decreased a couple of times and knit another 7 rounds, then decreased to 3 and cinched closed. This meant I could flip it inside out and stuff the valve but still have it open. It ends up a lot smaller, though.