I am skeptical of the "glycerin in veins" theory. Glycerin is a liquid at room temperature. If this theory is correct, then glycerin "rivers" in the soap would be runny, wet channels, not clear trails of firm soap.
The old soap makers (1800s to early 1900s) made mottled soaps that were popular with the customers of the day. They would add a coloring agent to a finished soap, pour the soap into "frames" (large molds), and carefully control the rate of cooling. The soap molecules formed from short-chain fatty acids (palmitic, lauric, myristic, and stearic) would solidify into pale-colored "islands" first, essentially concentrating the color into the remaining fluid oleic and linoleic soaps. When the oleic and linoleic soaps solidified at a cooler temperature, they formed "rivers" of darker color around the "islands". The size and appearance of the mottles were controlled by the oils in the recipe, the way the finished soap was handled, and the rate of cooling of the soap in the frames.
The old makers used dyes to make the "rivers" dark colored and the "islands" lighter. Titanium dioxide is a ground pigment, not a dye, so it will concentrate differently if used in a soap -- it obviously is trapped within the "islands" not the "rivers".
"...When [soap] is permitted to cool rapidly the colouring matter remains uniformly disseminated throughout the mass; but when means are taken to cause the soap to cool and solidify slowly a segregation takes place: the stearate and palmitate form a semicrystalline solid, while the oleate, solidifying more slowly, comes by itself into translucent veins, in which the greater part of the coloured matter is drawn. In this way curd, mottled or marbled soap is formed..." Source:
http://www.1911encyclopedia.org/Soap
Related thread:
http://www.soapmakingforum.com/showthread.php?t=35815