According to Consumer Bulletin, October 1962, p.3:

The proper type of chair is important for those who suffer backaches and other back ailments. Dr. J. J. Keegan of Lawrence, Massachusetts, in an evaluation of 29 chair seats in common use, described the correct seat as having an angle of at least 105 degrees between shoulders and thighs, soft rounded support in the lower lumbar region, and seat length and height not over 16 inches. It was his view that the secretary's chair represents the nearest approach to a correct seat. Automobile seats received the lowest rating. Dr. Keegan suggested that the low back pain sometimes caused by auto seats can be prevented by placement of a properly shaped, soft foam rubber cushion back of the lumbar region.

Vanderbilt developed her inflatable back support in response to work showing that automobile seats were uncomfortable and caused back pain.

Below you can see some of the work she put into the design with two patent drawings (top left and bottom) and an original drawing for the inflatable back support.

Vanderbilt talks about this back support in her oral history.