"Chemical Shift Imaging (CSI) or Chemical Shift Encoded Magnetic Resonance Imaging (CSE-MRI) enables the quantification of different chemical species in the human body, and it is one of the most widely used imaging modalities used to quantify fat in the human body. Although there have been substantial improvements in the design of signal acquisition protocols and the development of a variety of methods for the recovery of parameters of interest from the measured signal, it is still challenging to obtain a consistent and reliable quantification over the entire field of view. In fact, there are still discrepancies in the quantities recovered by different methods, and each exhibits a different degree of sensitivity to acquisition parameters such as the choice of echo times. Some of these challenges have their origin in the signal model itself. In particular, it is non-linear, and there may be different sets of parameters of interest compatible with the measured signal. For this reason, a thorough analysis of this model may help mitigate some of the remaining challenges, and yield insight into novel acquisition protocols. In this work, we perform an analysis of the signal model underlying CSI, focusing on finding suitable conditions under which recovery of the parameters of interest is possible. We determine the sources of non-identifiability of the parameters, and we propose a reconstruction method based on smooth non-convex optimization under convex constraints that achieves exact local recovery under suitable conditions. A surprising result is that the concentrations of the chemical species in the sample may be identifiable even when other parameters are not. We present numerical results illustrating how our theoretical results may help develop novel acquisition techniques, and showing how our proposed recovery method yields results comparable to the state-of-the-art. "

Estimation of cardiovascular model parameters from electronic health records (EHRs) poses a significant challenge primarily due to lack of identifiability. Structural non-identifiability arises when a manifold in the space of parameters is mapped to a common output, while practical non-identifiability can result due to limited data, model misspecification or noise corruption. To address the resulting ill-posed inverse problem, optimization-based or Bayesian inference approaches typically use regularization, thereby limiting the possibility of discovering multiple solutions. In this study, we use inVAErt networks, a neural network-based, data-driven framework for enhanced digital twin analysis of stiff dynamical systems. We demonstrate the flexibility and effectiveness of inVAErt networks in the context of physiological inversion of a six-compartment lumped‐parameter haemodynamic model from synthetic data to real data with missing components. This article is part of the theme issue ‘Uncertainty quantification for healthcare and biological systems (Part 2)’.

Publisher:  Computer Methods in Applied Mechanics and Engineering  Link>

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