The use of mathematical models in biomedical research largely developed in the second half of the 20th century. However, their translation to clinically useful tools has proved challenging. Reasoning with deep biomedical models is computationally demanding as parameters are typically subject to nonlinear relations, dynamic behavior, and uncertainty. This paper proposes a new approach for assessing the reliability of the conclusions drawn from these models given the underlying uncertainty. It relies on probabilistic constraint programming for a sound propagation of uncertainty from model parameters to results. The advantages of the approach are illustrated on an important problem in the obesity research field, namely the estimation of free-living energy intake in humans. Based on a well known energy intake model, our approach is able to correctly characterize the provided estimates given the uncertainty inherent to the model parameters.