Atlatlista, I think your backing has a lot to do with whether or not you leave sapwwod on the bow.  A friend who made lots of hickory backed cedar bows used mostly the heart wood, the heartwood for compression, the hickory for tension.  If he made a bamboo backed cedar bow, he always left some sapwood but not much, he said too much made the bow loggy and slow.  The bamboo was there to keep the bow from breaking, I would guess the same would hold for something like silk or rawhide, don't have a clue about sinew except you probably won't need any sapwood as the sinew would be suppling the tension.  Does that help?