361 research outputs found
Real-time whole-heart electromechanical simulations using Latent Neural Ordinary Differential Equations
Cardiac digital twins provide a physics and physiology informed framework to
deliver predictive and personalized medicine. However, high-fidelity
multi-scale cardiac models remain a barrier to adoption due to their extensive
computational costs and the high number of model evaluations needed for
patient-specific personalization. Artificial Intelligence-based methods can
make the creation of fast and accurate whole-heart digital twins feasible. In
this work, we use Latent Neural Ordinary Differential Equations (LNODEs) to
learn the temporal pressure-volume dynamics of a heart failure patient. Our
surrogate model based on LNODEs is trained from 400 3D-0D whole-heart
closed-loop electromechanical simulations while accounting for 43 model
parameters, describing single cell through to whole organ and cardiovascular
hemodynamics. The trained LNODEs provides a compact and efficient
representation of the 3D-0D model in a latent space by means of a feedforward
fully-connected Artificial Neural Network that retains 3 hidden layers with 13
neurons per layer and allows for 300x real-time numerical simulations of the
cardiac function on a single processor of a standard laptop. This surrogate
model is employed to perform global sensitivity analysis and robust parameter
estimation with uncertainty quantification in 3 hours of computations, still on
a single processor. We match pressure and volume time traces unseen by the
LNODEs during the training phase and we calibrate 4 to 11 model parameters
while also providing their posterior distribution. This paper introduces the
most advanced surrogate model of cardiac function available in the literature
and opens new important venues for parameter calibration in cardiac digital
twins
On the Incorporation of Obstacles in a Fluid Flow Problem Using a Navier-Stokes-Brinkman Penalization Approach
Simulating the interaction of fluids with immersed moving solids is playing
an important role for gaining a better quantitative understanding of how fluid
dynamics is altered by the presence of obstacles and which forces are exerted
on the solids by the moving fluid. Such problems appear in various contexts,
ranging from numerous technical applications such as turbines to medical
problems such as the regulation of hemodyamics by valves. Typically, the
numerical treatment of such problems is posed within a fluid structure
interaction (FSI) framework. General FSI models are able to capture
bidirectional interactions, but are challenging to solve and computationally
expensive. Simplified methods offer a possible remedy by achieving better
computational efficiency to broaden the scope to demanding application problems
with focus on understanding the effect of solids on altering fluid dynamics. In
this study we report on the development of a novel method for such
applications. In our method rigid moving obstacles are incorporated in a fluid
dynamics context using concepts from porous media theory. Based on the
Navier-Stokes-Brinkman equations which augments the Navier-Stokes equation with
a Darcy drag term our method represents solid obstacles as time-varying regions
containing a porous medium of vanishing permeability. Numerical stabilization
and turbulence modeling is dealt with by using a residual based variational
multiscale formulation. The key advantages of our approach -- computational
efficiency and ease of implementation -- are demonstrated by solving a standard
benchmark problem of a rotating blood pump posed by the Food and Drug
Administration Agency (FDA). Validity is demonstrated by conducting a mesh
convergence study and by comparison against the extensive set of experimental
data provided for this benchmark
Whole-heart electromechanical simulations using Latent Neural Ordinary Differential Equations
Cardiac digital twins provide a physics and physiology informed framework to deliver personalized medicine. However, high-fidelity multi-scale cardiac models remain a barrier to adoption due to their extensive computational costs. Artificial Intelligence-based methods can make the creation of fast and accurate whole-heart digital twins feasible. We use Latent Neural Ordinary Differential Equations (LNODEs) to learn the pressure-volume dynamics of a heart failure patient. Our surrogate model is trained from 400 simulations while accounting for 43 parameters describing cell-to-organ cardiac electromechanics and cardiovascular hemodynamics. LNODEs provide a compact representation of the 3D-0D model in a latent space by means of an Artificial Neural Network that retains only 3 hidden layers with 13 neurons per layer and allows for numerical simulations of cardiac function on a single processor. We employ LNODEs to perform global sensitivity analysis and parameter estimation with uncertainty quantification in 3 hours of computations, still on a single processor
Optimal Thinning of MCMC Output
The use of heuristics to assess the convergence and compress the output of
Markov chain Monte Carlo can be sub-optimal in terms of the empirical
approximations that are produced. Typically a number of the initial states are
attributed to "burn in" and removed, whilst the remainder of the chain is
"thinned" if compression is also required. In this paper we consider the
problem of retrospectively selecting a subset of states, of fixed cardinality,
from the sample path such that the approximation provided by their empirical
distribution is close to optimal. A novel method is proposed, based on greedy
minimisation of a kernel Stein discrepancy, that is suitable for problems where
heavy compression is required. Theoretical results guarantee consistency of the
method and its effectiveness is demonstrated in the challenging context of
parameter inference for ordinary differential equations. Software is available
in the Stein Thinning package in Python, R and MATLAB.Comment: To appear in the Journal of the Royal Statistical Society, Series B,
2021
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