I'd adjust your definitions somewhat.
Broadly speaking, you have the Northeast Corridor, which is more or less a continuous conurbation from DC to Boston.
Outside of that, the Eastern US generally follows European models of density, with clear densely-populated urban regions (Chicago being the largest city, but more minor cities like Indianapolis or Dayton correspond well to minor urban centers in European countries, population wise), in a field of rural areas where there's basically a quantum of civilization anywhere the land is flat enough to actually support it. There's kind of omnipresent human presence in the rural areas of, say, Ohio (not unlike rural Netherlands, say), while the mountainous regions like West Virginia sees strips of small towns nestled in every river valley while the ridgelines are largely empty (like a lot of the Alps).
The boundary between rural-but-populated and rural-but-unpopulated in the US is not so much the Mississippi River, but the 100°W longitude line, the High Plains (or roughly a line running from Oklahoma City through Wichita and Omaha up to Winnipeg along I-29 and I-35). From here, there's basically nothing until you hit the Front Range and the beginning of the mountains.
Once you hit the Front Range and you look west, you're in a kind of combination of the previous two zones. There's again large urban centers. In some of the big valleys--Columbia, Snake, Central, and Willamette--you see basically a small slice of European-style omnipresent human presence in rural areas. But outside of these areas, the area is largely thoroughly unpopulated, more so than even the High Plains, due to either being a desert, mountainous, or both.