Population‐based priors in cardiac model personalisation for consistent parameter estimation in heterogeneous databases

Abstract

Personalised cardiac models are a virtual representation of the patient heart, with parameter values for which the simulation fits the available clinical measurements. Models usually have a large number of parameters while the available data for a given patient are typically limited to a small set of measurements; thus, the parameters cannot be estimated uniquely. This is a practical obstacle for clinical applications, where accurate parameter values can be important.Here, we explore an original approach based on an algorithm called Iteratively Updated Priors (IUP), in which we perform successive personalisations of a full database through maximum a posteriori (MAP) estimation, where the prior probability at an iteration is set from the distribution of personalised parameters in the database at the previous iteration. At the convergence of the algorithm, estimated parameters of the population lie on a linear subspace of reduced (and possibly sufficient) dimension in which for each case of the database, there is a (possibly unique) parameter value for which the simulation fits the measurements. We first show how this property can help the modeller select a relevant parameter subspace for personalisation. In addition, since the resulting priors in this subspace represent the population statistics in this subspace, they can be used to perform consistent parameter estimation for cases where measurements are possibly different or missing in the database, which we illustrate with the personalisation of a heterogeneous database of 811 cases. KEYWORDScardiac electromechanical modelling, parameter estimation, parameter selection, personalised modelling INTRODUCTIONPersonalised cardiac models are of increasing interest for clinical applications. [1][2][3] To that end, parameter values of a cardiac model are estimated to get a personalised simulation that reproduces the available measurements for a clinical case. Then the personalised simulations can be used for advanced analysis of pathologies. In particular, recent works have been successful in predicting haemodynamic changes in cardiac resynchronization therapy, 4 ventricular tachycardia inducibility and dynamics, 5 and in detecting and localising infarcts 6 using 3D personalised models. Int J Numer Meth Biomed Engng. 2019;35:e3158. wileyonlinelibrary.com/journal/cnm

Non-invasive Pressure Estimation in Patients with Pulmonary Arterial Hypertension: Data-Driven or Model-Based?

“…Secondly, our 0D model is highly reduced, some important measurements like V T I RV OT and T R max which exhibit important hemodynamic characteristics, is not compatible. Whereas, unlike the imperative demand of complete data for regression methods, 0D model personalisation can deal with missing data issue naturally [10].…”

“…Reduced deformation and stress tensors demonstrate good representation of important cardiac characteristics, such as heart contractility (σ 0 ) and stiffness (C 1 ). This 0D model has manifested its modeling potential in solving personalisation problems [10]. Consider a 0D model M , with a set of parameters P M and model states O M .…”

“…We solve this high-dimensional and non-convex problem by applying a nonparametric evolutionary strategy CMA-ES [6]. Iteratively Updated Prior (IUP) method, as defined in [10], is deployed to iteratively update the prior distribution based on former population personalisation results.…”

Large Scale Cardiovascular Model Personalisation for Mechanistic Analysis of Heart and Brain Interactions

“…Since the solution of equation 1 is non-unique, there is an observability difficulty in this personalisation problem. To tackle this issue, we used the iterativeupdate prior (IUP) approach presented in [9] to introduce constraints in the fitting process. In the IUP method a regularization term, R(θ, µ, Σ), is used to reduce the variability in the estimation of the parameters.…”

“…In this paper we aim to study the relationship between cardiovascular indicators and brain volumetric features extracted from the imaging data available in UK Biobank, through the personalisation of a cardiovascular lumped model using the approach presented in [9]. The use of this approach allows us to tackle the ill-posedness nature of the personalisation and identify plausible and coherent solutions across the population.…”