Uncertainty in cardiovascular digital twins despite non-normal errors in 4D flow MRI: identifying reliable biomarkers such as ventricular relaxation rate

Abstract

Cardiovascular digital twins and mechanistic models can be used to obtain new biomarkers from patient-specific hemodynamic data. However, such model-derived biomarkers are only clinically relevant if the variation between timepoints/patients is smaller than the uncertainty of the biomarkers. Unfortunately, this uncertainty is challenging to calculate, as the uncertainty of the underlying hemodynamic data is largely unknown and has several sources that are not additive or normally distributed. This violates normality assumptions of current methods; implying that also biomarkers have an unknown uncertainty. To remedy these problems, we herein present a method, with attached code, for uncertainty calculation of model-derived biomarkers using non-normal data. First, we estimated all sources of uncertainty, both normal and non-normal, in hemodynamic data used to personalize an existing model; the errors in 4D flow MRI-derived stroke volumes were 5-20% and the blood pressure errors were 0+-8 mmHg. Second, we estimated the resulting model-derived biomarker uncertainty for 100 simulated datasets, sampled from the data distributions, by: 1) combining data uncertainties 2) parameter estimation, 3) profile-likelihood. The true biomarker values were found within a 95% confidence interval in 98% (median) of the cases. This shows both that our estimated data uncertainty is reasonable, and that we can use profile-likelihood despite the non-normality. Finally, we demonstrated that e.g. ventricular relaxation rate has a smaller uncertainty (~10%) than the variation across a clinical cohort (~40%), meaning that these biomarkers have clinical usefulness. Our results take us one step closer to the usage of model-derived biomarkers for cardiovascular patient characterization.