Numerical simulation of cardiovascular dynamics with healthy and diseased heart valves

Korakianitis, Theodosios; Shi, Yubing

doi:10.1016/j.jbiomech.2005.06.016

Cited by 135 publications

(163 citation statements)

References 29 publications

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“…This model estimated a cardiac output at rest of 8171.15 ml/min, averagely for all subjects, can be compared to predictions 7500 ml/min (Korakianitis & Shi, 2006;Kim et al, 2009). Such assessments have applied a finite element technique coupled a lumped parameter method, a Wind-Kassel approach (Korakianitis & Shi, 2006), as well as an electrical integration circuit (Podnar et al, 2002). Data derived from Christie et al (1987) agrees with our results.…”

Section: Comparison To Literaturesupporting

confidence: 73%

“…Nevertheless, this study compares in a good manner to other numerical approaches used to evaluate cardiac function at rest. This model estimated a cardiac output at rest of 8171.15 ml/min, averagely for all subjects, can be compared to predictions 7500 ml/min (Korakianitis & Shi, 2006;Kim et al, 2009). Such assessments have applied a finite element technique coupled a lumped parameter method, a Wind-Kassel approach (Korakianitis & Shi, 2006), as well as an electrical integration circuit (Podnar et al, 2002).…”

Section: Comparison To Literaturementioning

confidence: 99%

See 1 more Smart Citation

Numerical method to measure velocity integration, stroke volume and cardiac output while rest: using 2D fluid-solid interaction model

Khosravi¹,

Bahraseman²,

Hassani³

et al. 2014

10.5267/j.esm

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Development of knowledge of cardiovascular diseases and treatments strongly depends on understanding of hemodynamic measurements. Hemodynamic parameters, therefore, have been investigated using simulation-based methods. A two-dimensional model was applied for seven healthy subjects with echo-Doppler at rest. Echocardiography imaging was also utilized to gain the geometry of the aortic valve. Fluid-Structure Interaction (FSI) model was carried out, coupling an Arbitrary Lagrangian-Eulerian mesh. Pressure loads were used as boundary conditions on the valve's ventricular and aortic sides. Pressure loads used were the calculated brachial pressures plus differences between brachial, central and left ventricular pressures. The FSI model predicted the velocity integration, stroke volume and cardiac output over a range of heart rates while rest. Numerical results generally had a difference of 5.4 to 15.87% with Doppler results. Linear correlations between numerical and clinical approaches have been applied. This makes possible predictions achieved from the FSI model to be gained which are highly accurate (e.g. correlation factor r = 0.995, 0.990 and 0.990 for velocity integration, stroke volume and cardiac output, respectively). The obtained numerical results showed that numerical methods can be combined with clinical measurements to provide good estimates of patient specific hemodynamics for different subjects.

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Section: Comparison To Literaturesupporting

confidence: 73%

Section: Comparison To Literaturementioning

confidence: 99%

Numerical method to measure velocity integration, stroke volume and cardiac output while rest: using 2D fluid-solid interaction model

Khosravi¹,

Bahraseman²,

Hassani³

et al. 2014

10.5267/j.esm

View full text Add to dashboard Cite

show abstract

“…Namely, it was assumed that r R ¼ 0.7, r C ¼ 0.3 and t ¼ 0.00625 s for both lungs, on the basis of values adopted in previous LPM models of pulmonary vasculature [11][12][13] and clinical measurements [14].…”

Section: Multi-scale Modelsmentioning

confidence: 99%

Boundary conditions of patient-specific fluid dynamics modelling of cavopulmonary connections: possible adaptation of pulmonary resistances results in a critical issue for a virtual surgical planning

et al. 2011

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Cavopulmonary connections are surgical procedures used to treat a variety of complex congenital cardiac defects. Virtual pre-operative planning based on in silico patient-specific modelling might become a powerful tool in the surgical decision-making process. For this purpose, three-dimensional models can be easily developed from medical imaging data to investigate individual haemodynamics. However, the definition of patient-specific boundary conditions is still a crucial issue. The present study describes an approach to evaluate the vascular impedance of the right and left lungs on the basis of pre-operative clinical data and numerical simulations. Computational fluid dynamics techniques are applied to a patient with a bidirectional cavopulmonary anastomosis, who later underwent a total cavopulmonary connection (TCPC). Multi-scale models describing the surgical region and the lungs are adopted, while the flow rates measured in the venae cavae are used at the model inlets. Pre-operative and post-operative conditions are investigated; namely, TCPC haemodynamics, which are predicted using patient-specific pre-operative boundary conditions, indicates that the pre-operative balanced lung resistances are not compatible with the TCPC measured flows, suggesting that the pulmonary vascular impedances changed individually after the surgery. These modifications might be the consequence of adaptation to the altered pulmonary blood flows.

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“…The KS heart valve model [3] that describes the dynamics of the heart valve is shown in equation (1) below:…”

Section: The Ks Heart Valve Modelmentioning

confidence: 99%

“…An equation is said to be stiff if certain numerical schemes that are not absolutely stable cannot be used to seek an approximate solution to the problem [2]. Consequently, the conventional fourth order explicit Runge-Kutta method used to find a solution to the KS heart valve model in previous studies [1,[3][4] may not give accurate results for large step size, while smaller steps size may increase the round-off errors and increase computation time.On cannot exhaust the list of numerical techniques and their suitability for solving ODE as older ones are being modified and newer ones are developed. Butcher [5] reported a good number of these solvers developed over the 20 th century.…”

mentioning

confidence: 99%

Comparative Study of Matlab ODE Solvers for the Korakianitis and Shi Model

Emagbetere

Oluwole

Salau

2017

BMSA

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Abstract. Changing parameters of the Korakianitis and Shi heart valve model over a cardiac cycle has led to the investigation of appropriate numerical technique(s) for good speed and accuracy. Two sets of parameters were selected for the numerical test. For the seven MATLAB ODE solvers, the computed results, computational cost and execution time were observed for varied error tolerance and initial time steps. The results were evaluated with descriptive statistics; the Pearson correlation and ANOVA at 0.05 . The dependence of the computed result, accuracy of the method, computational cost and execution time of all the solvers, on relative tolerance and initial time steps were ascertained. Our findings provide important information that can be useful for selecting a MATLAB ODE solver suitable for differential equation with time varying parameters and changing stiffness properties. IntroductionThe Korakianitis and Shi (KS) heart valve model is a zero-dimensional, second order, nonlinear, Ordinary Differential Equation (ODE) that describes the dynamics of the human heart valve. The equation is embedded in the overall model of other parts of the entire cardiovascular system [1]. The equation may change from being non-stiff to stiff and vice versa, as its parameter changes within a heart cycle. An equation is said to be stiff if certain numerical schemes that are not absolutely stable cannot be used to seek an approximate solution to the problem [2]. Consequently, the conventional fourth order explicit Runge-Kutta method used to find a solution to the KS heart valve model in previous studies [1,[3][4] may not give accurate results for large step size, while smaller steps size may increase the round-off errors and increase computation time.On cannot exhaust the list of numerical techniques and their suitability for solving ODE as older ones are being modified and newer ones are developed. Butcher [5] reported a good number of these solvers developed over the 20 th century. Evaluations of ODE solvers have a long history [6-9] and earlier intentions were either to ascertain their effectiveness [6][7] or to categorize them as either stiff or non-stiff solvers [10][11][12][13]. Some researchers, however, reported the performance of the solving environment for some of these ODE solvers [14][15][16]. Very recently, focus has been to investigate ODE solvers for specific problem sets [17][18][19][20].The MATLAB software is widely used in engineering studies. Its ODE suite has seven powerful solvers, three of which are explicit schemes while the other four are implicit schemes. The ode45, ode23 and ode113 are the three explicit schemes while ode23t, ode23s, ode15s and ode23tb are the four implicit solvers. Interested readers are referred to the literatures [21-23] for mathematical details of the different solvers in the MATLAB ODE suite.Runge-Kutta methods are widely discussed in the literature [24][25][26][27]. The ode23 and ode45 solvers implement "Runge-Kutta formula of order 2 and 3" [21] and the "Dormand-Prince (4,5) pair"...

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Numerical simulation of cardiovascular dynamics with healthy and diseased heart valves

Cited by 135 publications

References 29 publications

Numerical method to measure velocity integration, stroke volume and cardiac output while rest: using 2D fluid-solid interaction model

Numerical method to measure velocity integration, stroke volume and cardiac output while rest: using 2D fluid-solid interaction model

Boundary conditions of patient-specific fluid dynamics modelling of cavopulmonary connections: possible adaptation of pulmonary resistances results in a critical issue for a virtual surgical planning

Comparative Study of Matlab ODE Solvers for the Korakianitis and Shi Model

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