A State Space Transformation Can Yield Identifiable Models for Tracer Kinetic Studies with Enrichment Data |
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Authors: | Rajasekhar Ramakrishnan Janak D Ramakrishnan |
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Institution: | (1) Departments of Chemistry and Earth Sciences, Dartmouth College, Hanover, NH 03755, USA |
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Abstract: | Tracer studies are analyzed almost universally by multicompartmental models where the state variables are tracer amounts or
activities in the different pools. The model parameters are rate constants, defined naturally by expressing fluxes as fractions
of the source pools. We consider an alternative state space with tracer enrichments or specific activities as the state variables,
with the rate constants redefined by expressing fluxes as fractions of the destination pools. Although the redefinition may
seem unphysiological, the commonly computed fractional synthetic rate actually expresses synthetic flux as a fraction of the
product mass (destination pool). We show that, for a variety of structures, provided the structure is linear and stationary,
the model in the enrichment state space has fewer parameters than that in the activities state space, and is hence better
both to study identifiability and to estimate parameters. The superiority of enrichment modeling is shown for structures where
activity model unidentifiability is caused by multiple exit pathways; on the other hand, with a single exit pathway but with
multiple untraced entry pathways, activity modeling is shown to be superior. With the present-day emphasis on mass isotopes,
the tracer in human studies is often of a precursor, labeling most or all entry pathways. It is shown that for these tracer
studies, models in the activities state space are always unidentifiable when there are multiple exit pathways, even if the
enrichment in every pool is observed; on the other hand, the corresponding models in the enrichment state space have fewer
parameters and are more often identifiable. Our results suggest that studies with labeled precursors are modeled best with
enrichments. |
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