A Distributed Lumped Parameter Model of Blood Flow

Mirramezani, Mehran; Shadden, Shawn C.

doi:10.1007/s10439-020-02545-6

Cited by 49 publications

(33 citation statements)

References 53 publications

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“…We point out that it is important to define these vessel properties in terms of a time-varying cross-sectional area A, in order to account also for possible deviations from the baseline state, such as hypertension, vessel collapse or postural changes. We also remark that if in definition (24) the time-dependent area A(t) is replaced by the reference value A 0 , then these parameters become constant and coincide with the constant parameters found in standard 0D models, namely…”

Section: Governing Ode Systemsupporting

confidence: 67%

“…The state variables of the above system are the volume V (t) of the vessel compartment and the mean flow rate Q(t) over the vascular segment; the parameters characterizing the 0D model, defined in (24), are R( A), which represents the resistance induced to the flow by the blood viscosity and depends on the chosen velocity profile, and L( A), which represents the inertial term in the momentum equation and is called inductance of the flow. These parameters are said to be nonlinear in the sense that they do no longer depend on a constant reference cross-sectional area A 0 , but on the time-dependent average cross-section A(t), which in turn, as we will see in Section 2.2, will depend on the mean pressure P (t) acting on the vessel in a nonlinear way.…”

Section: Governing Ode Systemmentioning

confidence: 99%

“…In this work, the topology of the original 1D network was fully preserved and the model included arterial vessels with geometric and anatomical data based on the ADAN model [5]. Furthermore in [24], a distributed lumped-parameter (DLP) modelling framework was proposed to efficiently compute blood flow and pressure in vascular domains at a computational cost that is orders of magnitude lower than that of computational fluid dynamics (CFD) simulations. By developing an expression of the generalized resistance R, various sources of energy dissipation, including viscous dissipation, unsteadiness, flow separation, vessel curvature and bifurcations, were taken into account.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear lumped-parameter models for blood flow simulations in networks of vessels

Ghitti¹,

Toro²,

Müller³

2022

Preprint

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To address the issue of computational efficiency related to the modelling of blood flow in complex networks, we derive a family of nonlinear lumped-parameter models for blood flow in compliant vessels departing from a well-established one-dimensional model. These 0D models must preserve important nonlinear properties of the original 1D model: the nonlinearity of the pressure-area relation and the pressure-dependent parameters characterizing the 0D models, the resistance R and the inductance L, defined in terms of a time-dependent cross-sectional area subject to pressure changes. We introduce suitable coupling conditions to join 0D vessels through 0D junctions and construct 0D networks preserving the original 1D network topology. The newly derived nonlinear 0D models are then applied to several arterial networks and the predicted results are compared against (i) the reference 1D results, to validate the models and assess their ability to reproduce good approximations of pressure and flow waveforms in all vessels at a much lower computational cost, measured in terms of CPU time, and (ii) the linear 0D results, to evaluate the improvement gained by including certain nonlinearities in the 0D models, in terms of agreement with the 1D results.

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Section: Governing Ode Systemsupporting

confidence: 67%

Section: Governing Ode Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear lumped-parameter models for blood flow simulations in networks of vessels

Ghitti¹,

Toro²,

Müller³

2022

Preprint

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“…This is prohibitively expensive using 3D CFD. However, the reducedorder modeling method employed here significantly reduces the cost of computation and enables this information in a more efficient and timely manner [12].…”

Section: Discussionmentioning

confidence: 99%

“…SimVascular was used to construct an image-based computer model of the peripheral arteries by creating paths along each vascular segment and segmenting the lumen along each path (Figure 1, panel 2) resulting in 3D computer model (Figure 1, panel 3) [11]. Steady state blood flow and pressure were modeled according to the reduced order modeling procedure described in [12], which considers various sources of pressure losses in vascular domains including turbulence in stenotic lesions. This procedure required specification of a constant flow rate at the model inlet and resistance boundary conditions at the model outlets.…”

Section: Methodsmentioning

confidence: 99%

Untitled

2021

AVS

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Automated generation of 0D and 1D reduced‐order models of patient‐specific blood flow

Pfaller

Pham

Verma

et al. 2022

Numer Methods Biomed Eng

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Three-dimensional (3D) cardiovascular fluid dynamics simulations typically require hours to days of computing time on a high-performance computing cluster.One-dimensional (1D) and lumped-parameter zero-dimensional (0D) models show great promise for accurately predicting blood bulk flow and pressure waveforms with only a fraction of the cost. They can also accelerate uncertainty quantification, optimization, and design parameterization studies. Despite several prior studies generating 1D and 0D models and comparing them to 3D solutions, these were typically limited to either 1D or 0D and a singular category of vascular anatomies. This work proposes a fully automated and openly available framework to generate and simulate 1D and 0D models from 3D patient-specific geometries, automatically detecting vessel junctions and stenosis segments. Our only input is the 3D geometry; we do not use any prior knowledge from 3D simulations. All computational tools presented in this work are implemented in the opensource software platform SimVascular. We demonstrate the reduced-order approximation quality against rigid-wall 3D solutions in a comprehensive comparison with N = 72 publicly available models from various anatomies, vessel types, and disease conditions. Relative average approximation errors of flows and pressures typically ranged from 1% to 10% for both 1D and 0D models, measured at the outlets of terminal vessel branches. In general, 0D model errors were only slightly higher than 1D model errors despite requiring only a third of the 1D runtime. Automatically generated ROMs can significantly speed up model development and shift the computational load from high-performance machines to personal computers.

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A Distributed Lumped Parameter Model of Blood Flow

Cited by 49 publications

References 53 publications

Nonlinear lumped-parameter models for blood flow simulations in networks of vessels

Nonlinear lumped-parameter models for blood flow simulations in networks of vessels

Untitled

Automated generation of 0D and 1D reduced‐order models of patient‐specific blood flow

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