Adjoint-based inverse analysis of windkessel parameters for patient-specific vascular models

Ismail, Mahmoud; Wall, Wolfgang A.; Gee, Michael W.

doi:10.1016/j.jcp.2012.10.028

Cited by 48 publications

(48 citation statements)

References 36 publications

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“…Note that the methodology used for parameter estimation can be improved with the objective of avoiding the oscillatory behavior of the pressure in the descending aorta. Some authors [23][24] use the three-element Windkessel model for improving the fitting of the lumped model. The approach used in this work is however much simpler in the mathematical treatment, while still being able to match the systolic, diastolic and mean pressure values.…”

Section: Resultsmentioning

confidence: 99%

A reduced-order model based on the coupled 1D-3D finite element simulations for an efficient analysis of hemodynamics problems

et al. 2014

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A reduced-order model for an efficient analysis of cardiovascular hemodynamics problems using multiscale approach is presented in this work. Starting from a patient-specific computational mesh obtained by medical imaging techniques, an analysis methodology based on a two-step automatic procedure is proposed. First a coupled 1D-3D Finite Element Simulation is performed and the results are used to adjust a reduced-order model of the 3D patient-specific area of interest. Then, this reduced-order model is coupled with the 1D model. In this way, threedimensional effects are accounted for in the 1D model in a cost effective manner, allowing fast computation under different scenarios. The methodology proposed is validated using a patient-specific aortic coarctation model under rest and non-rest conditions

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Section: Resultsmentioning

confidence: 99%

A reduced-order model based on the coupled 1D-3D finite element simulations for an efficient analysis of hemodynamics problems

et al. 2014

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“…The characteristic values of the residuals for pressure, flow rate split and flow rate objectives were set to 1.0 mmHg, 0.005 and 3 ml respectively, and the tolerance limits for evaluating convergence to 0.1 mmHg, 0.0005, and 0.3 ml respectively. The nonlinear system in (20) was solved in two different configurations: -the configuration in Figure 2, whereas structured trees are used as outlet boundary conditions and the hierarchical parameter estimation framework in Figure 1 is applied; -a configuration wherein three-element windkessel models are used as outlet boundary conditions and only the first stage of the parameter estimation framework in Figure 1 is applied (step 9 is removed). The proximal resistance of each windkessel model is set equal to the characteristic resistance of the vessel and is maintained constant throughout the parameter estimation procedure:…”

Section: Reduced-order Patient-specific Flow Computation For Aortic Cmentioning

confidence: 99%

“…Since for the supra-aortic branches only the total compliance C SupraAo is used as parameter in (20), in both configurations it is distributed to the outlet boundary condition models of the three branches, based on a power law relationship:…”

Section: Reduced-order Patient-specific Flow Computation For Aortic Cmentioning

confidence: 99%

“…(26) Next, we present the calibration results obtained by applying the hierarchical parameter estimation framework for the configuration which uses structured tree boundary conditions. The objective and parameter values obtained by running steps 6-9 of the parameter estimation framework for the nonlinear system of equations in (20) are displayed in Figure 3. We have marked with a dotted red line the iteration at which the value of each objective enters the tolerance window around the target value (and does not leave it at subsequent iterations).…”

Section: Reduced-order Patient-specific Flow Computation For Aortic Cmentioning

confidence: 99%

“…A more efficient optimization method was proposed in [19], which resulted in faster convergence and was shown to be robust against the choice of initial guess. An adjoint based method for calibrating the windkessel parameters was also proposed , where the Jacobian was computed without the use of finite-differences [20]. Furthermore, a reduced-order model with resistance outlet boundary conditions was introduced [21], under which the terminal resistance values of the arterial model of the arm were adapted to obtain desired flow rate distributions between vascular territories.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Personalized blood flow computations: A hierarchical parameter estimation framework for tuning boundary conditions

Itu

Sharma

Suciu

et al. 2016

Numer Methods Biomed Eng

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We propose a hierarchical parameter estimation framework for performing patient-specific hemodynamic computations in arterial models, which use structured tree boundary conditions. A calibration problem is formulated at each stage of the hierarchical framework, which seeks the fixed point solution of a nonlinear system of equations. Common hemodynamic properties, like resistance and compliance, are estimated at the first stage in order to match the objectives given by clinical measurements of pressure and/or flow rate. The second stage estimates the parameters of the structured trees so as to match the values of the hemodynamic properties determined at the first stage. A key feature of the proposed method is that to ensure a large range of variation, two different structured tree parameters are personalized for each hemodynamic property. First, the second stage of the parameter estimation framework is evaluated based on the properties of the outlet boundary conditions in a full body arterial model: the calibration method converges for all structured trees in less than 10 iterations. Next, the proposed framework is successfully evaluated on a patient-specific aortic model with coarctation: only six iterations are required for the computational model to be in close agreement with the clinical measurements used as objectives, and overall, there is a good agreement between the measured and computed quantities. Copyright © 2016 John Wiley & Sons, Ltd.

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Patient‐specific assessment of cardiovascular function by combination of clinical data and computational model with applications to patients undergoing Fontan operation

Liang

Sughimoto

Matsuo

et al. 2014

Numer Methods Biomed Eng

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The assessment of cardiovascular function is becoming increasingly important for the care of patients with single-ventricle defects. However, most measurement methods available in the clinical setting cannot provide a separate measure of cardiac function and loading conditions. In the present study, a numerical method has been proposed to compensate for the limitations of clinical measurements. The main idea was to estimate the parameters of a cardiovascular model by fitting model simulations to patient-specific clinical data via parameter optimization. Several strategies have been taken to establish a well-posed parameter optimization problem, including clinical data-matched model development, parameter selection based on an extensive sensitivity analysis, and proper choice of parameter optimization algorithm. The numerical experiments confirmed the ability of the proposed parameter optimization method to uniquely determine the model parameters given an arbitrary set of clinical data. The method was further tested in four patients undergoing the Fontan operation. Obtained results revealed a prevalence of ventricular abnormalities in the patient cohort and at the same time demonstrated the presence of marked inter-patient differences and preoperative to postoperative changes in cardiovascular function. Because the method allows a quick assessment and makes use of clinical data available in clinical practice, its clinical application is promising.

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Adjoint-based inverse analysis of windkessel parameters for patient-specific vascular models

Cited by 48 publications

References 36 publications

A reduced-order model based on the coupled 1D-3D finite element simulations for an efficient analysis of hemodynamics problems

A reduced-order model based on the coupled 1D-3D finite element simulations for an efficient analysis of hemodynamics problems

Personalized blood flow computations: A hierarchical parameter estimation framework for tuning boundary conditions

Patient‐specific assessment of cardiovascular function by combination of clinical data and computational model with applications to patients undergoing Fontan operation

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