The heart and blood vessels develop from vasculogenesis and angiogenesis. Vasculogenesis is process were vessels are formation is by locally formed endothelial vesicles such as in the case of the great vessels while angiogenesis is by outgrowth or branching out of preformed vessels such as in the formation of peripheral body vessels.
This figure below is a schematic of the stages of vascularization, were angioblastic or hematopiotic cells from the yolk sac (intially epigastric cells) migrates into the body cavity (coalesce) between the lateral mesoderm and aggregaties to form cell clusters called the blood island. The outermost layer of cells becomes the endothelial cells while innermost become the blood cells (haematopoiesis). Incorperation of the adjacents capillaries give rise to long large vessel.
stages of vascularization from angioblastic cells to blood island which gradually forms thinny vessels which enlongated to form larger vessels
A total for 2 paired vessels are formed by the end of the 4th week, blood vessels run along the long axis of the germ disk: left and right dorsal aorta with another pair runing within the lateral edge of the embryo (one on each edge).