scholarly journals Inverse problems in Cardiovascular Mathematics: toward patient-specific data assimilation and optimization

2013 ◽  
Vol 29 (7) ◽  
pp. 723-725 ◽  
Author(s):  
Alessandro Veneziani ◽  
Christian Vergara
Keyword(s):  
Data Assimilation ◽  
Inverse Problems ◽  
Patient Specific ◽  
Specific Data

scholarly journals Inverse problems in reduced order models of cardiovascular haemodynamics: aspects of data assimilation and heart rate variability

2017 ◽  
Vol 14 (126) ◽  
pp. 20160513 ◽  
Author(s):  
Sanjay Pant ◽  
Chiara Corsini ◽  
Catriona Baker ◽  
Tain-Yen Hsia ◽  
Giancarlo Pennati ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Inverse Problems ◽  
Unscented Kalman Filter ◽  
Clinical Situation ◽  
Specific Model ◽  
Patient Specific ◽  
Model Parameters ◽  
Heart Rates ◽  
Model Predictions ◽  
Patient State

Inverse problems in cardiovascular modelling have become increasingly important to assess each patient individually. These problems entail estimation of patient-specific model parameters from uncertain measurements acquired in the clinic. In recent years, the method of data assimilation, especially the unscented Kalman filter, has gained popularity to address computational efficiency and uncertainty consideration in such problems. This work highlights and presents solutions to several challenges of this method pertinent to models of cardiovascular haemodynamics. These include methods to (i) avoid ill-conditioning of the covariance matrix, (ii) handle a variety of measurement types, (iii) include a variety of prior knowledge in the method, and (iv) incorporate measurements acquired at different heart rates, a common situation in the clinic where the patient state differs according to the clinical situation. Results are presented for two patient-specific cases of congenital heart disease. To illustrate and validate data assimilation with measurements at different heart rates, the results are presented on a synthetic dataset and on a patient-specific case with heart valve regurgitation. It is shown that the new method significantly improves the agreement between model predictions and measurements. The developed methods can be readily applied to other pathophysiologies and extended to dynamical systems which exhibit different responses under different sets of known parameters or different sets of inputs (such as forcing/excitation frequencies).

Evaluation of a computerized cardiovascular simulation system using patient-specific data

2013 ◽  
Vol 61 (S 01) ◽  
Author(s):  
M Kaur ◽  
N Sprunk ◽  
U Schreiber ◽  
R Lange ◽  
J Weipert ◽  
...  
Keyword(s):  
Simulation System ◽  
Patient Specific ◽  
Specific Data ◽  
Cardiovascular Simulation

Jointly learning variational data assimilation models and solvers for geophysical dynamics

2021 ◽  
Author(s):  
Ronan Fablet ◽  
Bertrand Chapron ◽  
Lucas Drumetz ◽  
Etienne Memin ◽  
Olivier Pannekoucke ◽  
...  
Keyword(s):  
Neural Networks ◽  
Data Assimilation ◽  
Inverse Problems ◽  
Automatic Differentiation ◽  
Variational Data Assimilation ◽  
Point Of View ◽  
Variational Model ◽  
Short Term ◽  
End To End ◽  
Short Term Forecasting

<p>This paper addresses representation learning for the resolution of inverse problems  with geophysical dynamics. Among others, examples of inverse problems of interest include space-time interpolation, short-term forecasting, conditional simulation w.r.t. available observations, downscaling problems… From a methodological point of view, we rely on a variational data assimilation framework. Data assimilation (DA) aims to reconstruct the time evolution of some state given a series of  observations, possibly noisy and irregularly-sampled. Here, we investigate DA from a machine learning point of view backed by an underlying variational representation.  Using automatic differentiation tools embedded in deep learning frameworks, we introduce end-to-end neural network architectures for variational data assimilation. It comprises two key components: a variational model and a gradient-based solver both implemented as neural networks. A key feature of the proposed end-to-end learning architecture is that we may train the neural networks models using both supervised and unsupervised strategies. We first illustrate applications to the reconstruction of Lorenz-63 and Lorenz-96 systems from partial and noisy observations. Whereas the gain issued from the supervised learning setting emphasizes the relevance of groundtruthed observation dataset for real-world case-studies, these results also suggest new means to design data assimilation models from data. Especially, they suggest that learning task-oriented representations of the underlying dynamics may be beneficial. We further discuss applications to short-term forecasting and sampling design along with preliminary results for the reconstruction of sea surface currents from satellite altimetry data. </p><p>This abstract is supported by a preprint available online: https://arxiv.org/abs/2007.12941</p>

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