Apparently, it takes only about an hour for barium-based oral contrast agents to coat the intestines.
I find this kind of surprising because it generally takes the body about 24 hours to digest a meal, and in fact, according to one informational page on the Mayo Clinic web site, it takes about 36 hours for food to completely move through the digestive system.
So, how is it that contrast agent can move so much more quickly? Is that true in general for liquids? In other words do liquids move quickly though the digestive tract in only an hour, but it is just solids that take a long time, or do contrast agents have some quality that makes them move faster?
Also, if liquids can move so quickly through the digestive tract, but not solids, how is it that the body is able to move liquids along, but restrain the solids?
First we need to make a distinction between the separate types of oral contrast agents.
We frequently utilize water-insoluble (like barium), or water-soluble (diatrazole). Another distinction is to consider water-soluble as ionic.
Contrast media does not necessarily "absorb" into or through the GI tract (through the intestinal mucosa), in the high-speed you may be referring to. The absorption process is what takes time. Contrast media, however may disperse through-out the GI tract (esophagus, stomach, small intestine, large intestine, sigmoid) in a short duration. Once it has 'arrived', we usually take the image. The arrival (or lack of), is usually the point of interest for a provider ordering the image, and less likely about the absorption.
The speed of the contrast formulation is mainly influenced by its ionic properties/water-solubility, osmolarity relative to what is already present within the intestine, and the viscosity of the formulation. Usually contrast agents are ~5x more hypertonic (thicker with solutes) than that of human serum. This draws water in, which enhances the motility. Additionally, the ionic properties of water soluble contrast agents act independently as a GI stimulant.
So to sum up my answer, the time it takes to arrive to a certain portion of the intestine (even the furthest portion) may be actually pretty quick, but the time for absorption as well as the threshold for stimulating a bowel movement (by accumulation) is what takes longer. We snap the picture when it arrives, because that is usually the most pertinent piece of information for general diagnosis of a functional problem within the GI tract.
This is a really interesting question and Jrapa86 has given a a good answer, I thought of one small extra point though.
When you think about what actually makes the movement of a bolus of food through the GI tract so slow there's two things I think that are worth considering, the first is peristalsis and the second is valves.
Peristalsis is what moves solid-ish material through the GI tract, but it is not necessary for the rapid flow and diffusion of a liquid solution so we can perhaps set it aside.
So the main factor in what impedes the flow of a liquid through the tract are choke points where there are sphincters specifically to control the passage of material, i.e. the pyloric sphicter and the ileocaecal valve.
Food typically only spends 2-6 hours in the small intestine and stomach. The speed of this is determined by the protein and fat content of the meal as well so gastric emptying and transit time can be lower by having the "meal" contain neither of these.
A barium meal will quickly pass from the mouth to the stomach, spend a little while waiting for the pyloric sphincter to open, quickly flow through the small intestine, wait a while at the ileocaecal valve.
Once food passes through the ileocaecal valve it typically can spend 20-30 hours sitting in the colon. By this point a normal bolus will be mostly solid, dehydrated matter. This does not apply to the contrast meal which will flow quickly through the colon which has no valves to impede it. So it can rapidly reach the rectum in a manner food would not.
There is an interesting review article here where they discuss barium and also capsule transit times, which, as you would expect are closer to food transit time.
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