A separation model for breath test analysis.

*(English)*Zbl 0836.92012
Dillen, Franki (ed.) et al., Geometry and topology of submanifolds, VI. Proceedings of the international meetings on ‘Pure and applied differential geometry’ and on ‘Theory of submanifolds’ which were held in combination on July 10, 11, 14, 1993 at Leuven and on July 12, 13, 1993 at Brussel, Belgium. Singapore: World Scientific. 258-271 (1994).

The stomach is an important organ in the process of the nutrient assimilation. The gastric emptying rate determines the rate at which the food can be absorbed in the small intestine. For this reason, many researchers have devoted a lot of time in the development and validation of secure and simple tests to measure gastric emptying. Now, a scintigraphical screening of the stomach is worldwide accepted as the standard test. It is a direct test to measure the stomach evacuation. As any test, it is not perfect.

On the other hand, other researchers have been searching for alternative tests. Tests which have the same qualities as the standard test and have some advantages over it. During the last years, at the lab ‘Digestion and Absorption’, a new test for analysis of stomach evacuation has been developed. The test has some advantages over the scintigraphical test. However, it is not validated to the same extent as the former test. At the laboratory, people are working to validate the test in all possible circumstances.

We will develop a mathematical theory, which will enable us to demonstrate that some of the drawbacks of the new test can be eliminated by a good mathematical analysis. The article will only consider the purely mathematical concepts. In future articles, we will describe the technical and physiological aspects related to this test. Before starting with the mathematical theory, the breath test will be described, after which we will introduce the separation model, together with some of the basic properties.

For the entire collection see [Zbl 0832.00044].

On the other hand, other researchers have been searching for alternative tests. Tests which have the same qualities as the standard test and have some advantages over it. During the last years, at the lab ‘Digestion and Absorption’, a new test for analysis of stomach evacuation has been developed. The test has some advantages over the scintigraphical test. However, it is not validated to the same extent as the former test. At the laboratory, people are working to validate the test in all possible circumstances.

We will develop a mathematical theory, which will enable us to demonstrate that some of the drawbacks of the new test can be eliminated by a good mathematical analysis. The article will only consider the purely mathematical concepts. In future articles, we will describe the technical and physiological aspects related to this test. Before starting with the mathematical theory, the breath test will be described, after which we will introduce the separation model, together with some of the basic properties.

For the entire collection see [Zbl 0832.00044].

##### MSC:

92C50 | Medical applications (general) |

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\textit{G. Mys} et al., in: Geometry and topology of submanifolds, VI. Proceedings of the international meetings on `Pure and applied differential geometry' and on `Theory of submanifolds' which were held in combination on July 10, 11, 14 at Leuven and on July 12, 13 at Brussel, Belgium. Singapore: World Scientific. 258--271 (1994; Zbl 0836.92012)