On deriving lumped models for blood flow and pressure in the systemic arteries

OLUFSEN, M; NADIM, A

doi:10.1016/b978-008044046-0/50436-x

Cited by 22 publications

(36 citation statements)

References 20 publications

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“…Considering conservation of linear momentum in each compartment depicted in Figure , the 0D reduced pressure‐flow relation reads

L \frac{normald q}{normald t} + R q = p,

with the individual compartment's inertance L and its resistance R . Note that these relations can be derived from considering axisymmetric flow of incompressible Newtonian fluid of density ϱ and dynamic viscosity η through a rigid vessel with length l 0 and radius r 0 …”

Section: Methodsmentioning

confidence: 99%

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A monolithic 3D‐0D coupled closed‐loop model of the heart and the vascular system: Experiment‐based parameter estimation for patient‐specific cardiac mechanics

Hirschvogel

Bassilious

Jagschies

et al. 2017

Numer Methods Biomed Eng

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A model for patient-specific cardiac mechanics simulation is introduced, incorporating a 3-dimensional finite element model of the ventricular part of the heart, which is coupled to a reduced-order 0-dimensional closed-loop vascular system, heart valve, and atrial chamber model. The ventricles are modeled by a nonlinear orthotropic passive material law. The electrical activation is mimicked by a prescribed parameterized active stress acting along a generic muscle fiber orientation. Our activation function is constructed such that the start of ventricular contraction and relaxation as well as the active stress curve's slope are parameterized. The imaging-based patient-specific ventricular model is prestressed to low end-diastolic pressure to account for the imaged, stressed configuration. Visco-elastic Robin boundary conditions are applied to the heart base and the epicardium to account for the embedding surrounding. We treat the 3D solid-0D fluid interaction as a strongly coupled monolithic problem, which is consistently linearized with respect to 3D solid and 0D fluid model variables to allow for a Newton-type solution procedure. The resulting coupled linear system of equations is solved iteratively in every Newton step using 2 × 2 physics-based block preconditioning. Furthermore, we present novel efficient strategies for calibrating active contractile and vascular resistance parameters to experimental left ventricular pressure and stroke volume data gained in porcine experiments. Two exemplary states of cardiovascular condition are considered, namely, after application of vasodilatory beta blockers (BETA) and after injection of vasoconstrictive phenylephrine (PHEN). The parameter calibration to the specific individual and cardiovascular state at hand is performed using a 2-stage nonlinear multilevel method that uses a low-fidelity heart model to compute a parameter correction for the high-fidelity model optimization problem. We discuss 2 different low-fidelity model choices with respect to their ability to augment the parameter optimization. Because the periodic state conditions on the model (active stress, vascular pressures, and fluxes) are a priori unknown and also dependent on the parameters to be calibrated (and vice versa), we perform parameter calibration and periodic state condition estimation simultaneously. After a couple of heart beats, the calibration algorithm converges to a settled, periodic state because of conservation of blood volume within the closed-loop circulatory system. The proposed model and multilevel calibration method are cost-efficient and allow for an efficient determination of a patient-specific in silico heart model that reproduces physiological observations very well. Such an individual and state accurate model is an important predictive tool in intervention planning, assist device engineering and other medical applications.

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“…Considering conservation of linear momentum in each compartment depicted in Figure , the 0D reduced pressure‐flow relation reads

L \frac{normald q}{normald t} + R q = p,

Section: Methodsmentioning

confidence: 99%

“…Therein,

λ_{q} = 1 false/ β_{1}^{2}

, with β 1 being the first root of the zeroth‐order Bessel function of the first kind. Further details of fluid mechanics derivations of 0‐dimensional flow models can be found in the work of Olufsen et al…”

Section: Methodsmentioning

confidence: 99%

A monolithic 3D‐0D coupled closed‐loop model of the heart and the vascular system: Experiment‐based parameter estimation for patient‐specific cardiac mechanics

Hirschvogel

Bassilious

Jagschies

et al. 2017

Numer Methods Biomed Eng

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“…In contrast, the present preliminary study proposes a new concept of a mechanical extracorporeal device, which is capable to mobilize at least four In general, the clinical applications of ESS with cardiac-assist devices (CAD) are controlled by several diversities between the cardiovascular system and lumped models (45,46). As shown in (Fig.…”

Section: Discussionmentioning

confidence: 99%

Circulatory Flow Restoration Versus Cardiopulmonary Resuscitation: New Therapeutic Approach in Sudden Cardiac Arrest

2017

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Sudden cardiac arrest (SCA) remains a major problem for health authorities worldwide. Insufficiencies of current cardiopulmonary resuscitation (CPR) are most probably related to an inappropriate concept and applied methods that still concentrate on heartbeat as priority, instead of blood circulation to maintain organs' perfusions. The aim of this works is to propose a new therapeutic approach for SCA in a more effective and secure manner compared with current CPR methods. It correlates to a non-invasive circulatory flow restoration (CFR) device composed of a multilayered thoracic and infradiaphragmatic compartments that will be pulsated alternatively and in fixed frequencies using a low-pressure pneumatic generator. Proof-of-concept studies with different prototypes and methods of SCA, showed restoration of hemodynamics (BP ≥ 100 mm Hg) and increased urine output after 20 min of cardiac arrest in pediatric dogs and piglets. In summary, a CFR device can induce shear stress-mediated endothelial function to restore microcirculation and cellular metabolism. This represents a cost-effective method, predisposes to return of spontaneous circulation in case of SCA, adaptable for all age groups, in public and hospital environments.

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“…Considering that an artery is cylindrical, we can study the Poiseuille flow in the artery . Because of the cylindrical symmetry of the artery and assuming that the blood flow is axisymmetric in one dimension through a rigid artery that means the pressure inside the artery will be assumed to be independent of the radial coordinate, then the Navier–Stokes equation becomes

ρ \partial_{t} υ_{x} (r MathClass-punc, t) MathClass-bin- η ([], \partial_{r}^{2} MathClass-bin+ \frac{1}{r} \partial_{r}) υ_{x} (r MathClass-punc, t) MathClass-rel= MathClass-bin- \partial_{r} p (r MathClass-punc, t)

The boundary and initial conditions for υ χ (r,t) are

υ_{x} (a MathClass-punc, t) MathClass-rel= 0 MathClass-punc, \partial_{x} υ_{x} (0 MathClass-punc, t) MathClass-rel= 0 MathClass-punc, υ_{x} (r MathClass-punc, 0) MathClass-rel= \frac{Δp}{4 ηℓ} ((), a^{2} MathClass-bin- r^{2}) MathClass-punc, υ_{x} (r MathClass-punc, MathClass-rel\infty) MathClass-rel= 0

where Δ p is the change in pressure between the inlet and the outlet of the artery, and ℓ is the length of the artery taking into account that the blood stops flowing in the end (Figure ).…”

Section: Methodsmentioning

confidence: 99%

Mathematical and physical modelling of the dynamic fluidic impedance of arteries using electrical impedance equivalents

Giannoukos

Min

2013

Math. Meth. Appl. Sci.

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On deriving lumped models for blood flow and pressure in the systemic arteries

Cited by 22 publications

References 20 publications

A monolithic 3D‐0D coupled closed‐loop model of the heart and the vascular system: Experiment‐based parameter estimation for patient‐specific cardiac mechanics

A monolithic 3D‐0D coupled closed‐loop model of the heart and the vascular system: Experiment‐based parameter estimation for patient‐specific cardiac mechanics

Circulatory Flow Restoration Versus Cardiopulmonary Resuscitation: New Therapeutic Approach in Sudden Cardiac Arrest

Mathematical and physical modelling of the dynamic fluidic impedance of arteries using electrical impedance equivalents

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