Displacement modifier as a wave? To see if it's possible, I'm trying to make pulsating veins on a heart in blender render. This step isn't too difficult, you can use a simple normal geometry of a veroni crackle texture and change the normals over time, or bake that texture into an image and use a displacement modifier and keyframe the strength over time. 

But, the next step is to make this pulsating effect move like a wave through something like an actual heartbeat would, wherein one part on one end of the vein network starts the deformation, then the wave travels through gradually deforming only the vein texture onto the mesh over time. 

Can this be done? 

There is the wave modifier but this is a very outdated modifier that lacks a lot of precision in its control, it's pretty much only useful for large oceans. 

I guess you can think something along the lines of this 
https://www.youtube.com/watch?v=9tcR81BfiVY
Another 'In Principle' option...

Animate a 'pulse' mesh along a curve derived from, or used to construct, your blood vessel, using a Curve deform modifier, keying the location of the pulse mesh along its deformation axis:



Give the blood vessel a  Vertex Group for displacement, set to 0. (Vertices outside the group altogether will not be affected) Assign a Vertex Weight Proximity modifier, using the vertex group, targeted on the pulse mesh:



Assign a Displace modifier to the blood vessel, aimed at the vertex group.



'In principle', because, to say the least, you probably want the shape of your deformer, weight influence, timing, everything to be tweaked differently. :D But all the adjustments are available.

The pulse mesh could itself be shape-keyed on its journey, to modulate the expansion.