In biomedical applications the quantities of interest to get some insight into a phenomenon cannot be measured directly. Instead, they have to be inferred from available measurements of the system under investigation. In several contexts biomarkers are introduced, which are quantities extracted from the measurements, easily interpretable, that convey some information about the quantities of interest. They are introduced inside a scientific community based on experimental knowledge or physical intuition, and they are correlated with the quantity of interest they are meant to reveal. In the case in which the quantity of interest is a hidden parameter of a system, it happens that the associated biomarker is not perfectly correlated with it, or it is also correlated to other unknown parameters of the systems. Thus, by looking at the biomarkers, it is difficult, in certain configurations, to infer the parameters or the quantities of interest, because of “compensation effects”.

To overcome these difficulties, a numerical method is proposed in order to provide a correction to existing biomarkers. The goal is to design a composite biomarker in such a way that it is as much as possible correlated with the parameter it wants to reveal and minimally correlated to all the others.

The method exploits an offline phase of simulation, which is used to generate a database of observables in meaningful scenarios. Then, an optimisation problem is solved in order to construct the correction terms. Several test cases are presented, in synthetic and realistic configurations in cardiac electrophysiology and haemodynamics.

Joint work with Jean-Frédéric Gerbeau and Eliott Tixier.