Data assimilation for identification of cardiovascular network characteristics

Lal, Rajnesh; Mohammadi, Bijan; Nicoud, Franck

doi:10.1002/cnm.2824

Cited by 17 publications

(35 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Blum, Le Dimet and Navon (2009), Voss, Timmer and Kurths (2004) and Le Dimet and Talagrand (1986) for a detailed discussion. In the past decade several works dealing with cardiovascular applications have focused on data assimilation (Sermesant et al 2006, Bertagna, D'Elia, Perego and Veneziani 2014, Lal, Mohammadi and Nicoud 2016, which has been considered, in many cases, as synonymous with parameter estimation.…”

Section: Parameter Estimation From Clinical Datamentioning

confidence: 99%

The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications

Quarteroni

Manzoni

Vergara³

2017

Acta Numerica

194

125

View full text Add to dashboard Cite

Mathematical and numerical modelling of the cardiovascular system is a research topic that has attracted remarkable interest from the mathematical community because of its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. In this review article we will address the two principal components of the cardiovascular system: arterial circulation and heart function. We will systematically describe all aspects of the problem, ranging from data imaging acquisition, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, proposing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiocirculatory system, the multiscale nature of the physiological processes involved, and the need to devise computational methods that are stable, reliable and efficient. Critical issues involve filtering the data, identifying the parameters of mathematical models, devising optimal treatments and accounting for uncertainties. For this reason, we will devote the last part of the paper to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are of paramount importance when solving problems with high complexity, which would otherwise be out of reach.

show abstract

Section: Parameter Estimation From Clinical Datamentioning

confidence: 99%

The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications

Quarteroni

Manzoni

Vergara³

2017

Acta Numerica

194

125

View full text Add to dashboard Cite

show abstract

“…With time‐series observations y o b s ( t ), different functional J can be considered. Following Lal and colleagues, this work aims at minimizing a time‐dependent functional based on instantaneous incoming information:

J (t, y (x, z, t), {boldy}_{boldobs} (t)) = {‖ y (x, z, t) - {boldy}_{boldobs} (t) ‖}_{*} = \frac{1}{2} ‖ y (x, z, t) - {boldy}_{boldobs} (t) {false‖}^{2} .

…”

Section: Modeling and Problem Specificationmentioning

confidence: 99%

“…The inverse hemodynamic problem aims at identifying unknown parameters (the arterial stiffness and the WK3 model boundary parameters) for the network as shown in Figure D and as described in Lal and colleagues . In the parameter estimation problem, both available patient‐specific flow rate waveforms for the right internal carotid (R‐ICA; #21 in Table ) and the left internal carotid (L‐ICA; #23 in Table ) were used as observations during EnKF assimilation steps.…”

Section: Patient‐specific Clinical Datamentioning

confidence: 99%

“…With time-series observations y obs (t), different functional J can be considered. Following Lal and colleagues, 25,26 this work aims at minimizing a time-dependent functional based on instantaneous incoming information:…”

Section: Problem Specificationmentioning

confidence: 99%

“…The inverse hemodynamic problem aims at identifying unknown parameters (the arterial stiffness and the WK3 model boundary parameters) for the network as shown in Figure 3D and as described in Lal and colleagues. 25,26 In the parameter estimation problem, both available patient-specific flow rate waveforms for the right internal carotid (R-ICA; #21 in Table 1) and the left internal carotid (L-ICA; #23 in Table 1) were used as observations during EnKF assimilation steps. Blood rheological parameters and were set at 0.004 Pa s and 1050 kg m −3 , and at the inlet (ascending aorta, compartment #1 in Figure 3D), specific values of flow rates, q in , measured by PC-MRI (see Figure 2A,B) were imposed.…”

Section: Patient-specific Clinical Datamentioning

confidence: 99%

See 2 more Smart Citations

Backward sensitivity analysis and reduced‐order covariance estimation in noninvasive parameter identification for cerebral arteries

Rapadamnaba

Nicoud

Mohammadi

2018

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

Using a previously developed inversion platform for functional cerebral medical imaging with ensemble Kalman filters, this work analyzes the sensitivity of the results with respect to different parameters entering the physical model and inversion procedure, such as the inlet flow rate from the heart, the choice of the boundary conditions, and the nonsymmetry in the network terminations. It also proposes an alternative low complexity construction for the covariance matrix of the hemodynamic parameters of a network of arteries including the circle of Willis. The platform takes as input patient‐specific blood flow rates extracted from magnetic resonance angiography and magnetic resonance imaging (dicom files) and is applied to several available patients data. The paper presents full analysis of the results for one of these patients, including a sensitivity study with respect to the proximal and distal boundary conditions. The results notably show that the uncertainties on the inlet flow rate led to uncertainties of the same order of magnitude in the estimated parameters (blood pressure and elastic parameters) and that three‐lumped parameters boundary conditions are necessary for a correct retrieval of the target signals.

show abstract

Assessment of reduced‐order unscented Kalman filter for parameter identification in 1‐dimensional blood flow models using experimental data

Caiazzo

Caforio

Montecinos

et al. 2017

Numer Methods Biomed Eng

View full text Add to dashboard Cite

This work presents a detailed investigation of a parameter estimation approach on the basis of the reduced-order unscented Kalman filter (ROUKF) in the context of 1-dimensional blood flow models. In particular, the main aims of this study are (1) to investigate the effects of using real measurements versus synthetic data for the estimation procedure (i.e., numerical results of the same in silico model, perturbed with noise) and (2) to identify potential difficulties and limitations of the approach in clinically realistic applications to assess the applicability of the filter to such setups. For these purposes, the present numerical study is based on a recently published in vitro model of the arterial network, for which experimental flow and pressure measurements are available at few selected locations. To mimic clinically relevant situations, we focus on the estimation of terminal resistances and arterial wall parameters related to vessel mechanics (Young's modulus and wall thickness) using few experimental observations (at most a single pressure or flow measurement per vessel). In all cases, we first perform a theoretical identifiability analysis on the basis of the generalized sensitivity function, comparing then the results owith the ROUKF, using either synthetic or experimental data, to results obtained using reference parameters and to available measurements.

show abstract

Data assimilation for identification of cardiovascular network characteristics

Cited by 17 publications

References 57 publications

The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications

The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications

Backward sensitivity analysis and reduced‐order covariance estimation in noninvasive parameter identification for cerebral arteries

Assessment of reduced‐order unscented Kalman filter for parameter identification in 1‐dimensional blood flow models using experimental data

Contact Info

Product

Resources

About