Mechanistic inference of the metabolic rates underlying ¹³ C breath test curves

Abstract: Carbon stable isotope breath tests offer new opportunities to better understand gastrointestinal function in health and disease. However, it is often not clear how to isolate information about a gastrointestinal or metabolic process of interest from a breath test curve, and it is generally unknown how well summary statistics from empirical curve fitting correlate with underlying biological rates. We developed a framework that can be used to make mechanistic inference about the metabolic rates underlying a ¹³C breath test curve, and we applied it to a pilot study of ¹³C-sucrose breath test in 20 healthy adults. Starting from a standard conceptual model of sucrose metabolism, we determined the structural and practical identifiability of the model, using algebra and profile likelihoods, respectively, and we used these results to develop a reduced, identifiable model as a function of a gamma-distributed process; a slower, rate-limiting process; and a scaling term related to the fraction of the substrate that is exhaled as opposed to sequestered or excreted through urine. We demonstrated how the identifiable model parameters impacted curve dynamics and how these parameters correlated with commonly used breath test summary measures. Our work develops a better understanding of how the underlying biological processes impact different aspect of ¹³C breath test curves, enhancing the clinical and research potential of these ¹³C breath tests.