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When we think about living donor transplant, what we're banking on is the ability of the liver to regenerate itself. Now, it's not the same sort of regeneration we think about with the starfish where we cut off the arm and it grows a new arm. With the liver, what happens is the remaining liver gets bigger, and your body knows the size of the liver that it needs, and when it recognizes that there is not enough liver, it sends nutrients and signals to the liver and says "get bigger."

Source: www.ucsfbenioffchildrens.org
When we think about living donor transplant, what we're banking on is the ability of the liver to regenerate itself. Now, it's not the same sort of regeneration we think about with the starfish where we cut off the arm