Shear-scaling-based approach for irreversible energy loss estimation in stenotic aortic flow – An in vitro study
Introduction
Studies on blood flow have shown that the flow in the circulatory system becomes turbulent in some pathological cases such as stenosis, heart valve malfunctioning, and arterial stiffening. These conditions lead to loss of kinetic energy having a direct influence on the cardiac output and cardiovascular efficiency (Barker et al., 2014, Binter et al., 2013, Dyverfeldt et al., 2006, Garcia et al., 2000, Gülan et al., 2014a, Gülan et al., 2014b, Knobloch et al., 2014). Although the flow in the circulatory system is generally laminar, it may become turbulent in larger arteries, such as the aorta even if they are healthy (Ku, 1997, Gulan et al., 2012). In general, it is considered important to not only measure mean velocities in a spatial domain but also assess velocity fluctuations associated with turbulent flows. The mean kinetic energy in the fluctuating velocity field is referred to as turbulent kinetic energy (TKE), and can serve as a measure for the energy loss associated with turbulence.
Turbulent flow is highly dissipative and there is a continuous energy conversion from kinetic energy to heat due to viscous dissipation of TKE. This energy dissipation is irreversible and plays an important role for the assessment of cardiovascular energy efficiency. However, a direct measurement of the dissipation of TKE is difficult as this requires instantaneous measurements of the full tensor of spatial velocity derivatives. Until recently, the quantification of turbulence and TKE in the cardiovascular system in vivo was limited to experimental methods using hot film anemometry and ultrasound Doppler (Nygaard et al., 1994, Nyboe et al., 2006). Detailed space and time resolved measurements of turbulent flow velocity have been obtained in vitro via optical techniques such as particle image velocimetry (Li et al., 2009) and particle tracking velocimetry (Gulan et al., 2012). In addition, Computational Fluid Dynamics (CFD) has been applied in silico to reconstruct highly resolved blood flow patterns in realistic and fully patient-specific simulations of thoracic aorta hemodynamics (Gallo et al., 2014, Lantz and Karlsson, 2012, Liu et al., 2011, Morbiducci et al., 2013). By means of the introduction of generalized PC-MRI (Dyverfeldt et al., 2006) a noninvasive approach for assessing fluctuating velocities has become available and the potential of the method for quantifying flow fields and TKE in healthy subjects and in patients has been demonstrated (Dyverfeldt et al., 2008, Manka et al., 2014).
Given that direct measurements of viscous dissipation of TKE via PC-MRI remain elusive, an alternative method is explored in this paper. We use experimental three-dimensional velocity measurements in a compliant silicon model of an ascending aorta and propose a ‘shear scaling’ approach that makes use of TKE and the flow’s mean shear for the indirect measurement of the irreversible viscous energy dissipation of kinetic energy.
Section snippets
Energy loss estimation theory
In turbulent flows, energy is transferred from the large to smaller eddies until it is dissipated into heat (Pope, 2000). The total kinetic energy, which includes both mean kinetic energy (MKE) and TKE, is defined aswhere is the instantaneous velocity. The transport equation for the total kinetic energy can be written aswhere the flux is (p is the pressure, is the strain rate tensor, is the kinematic viscosity and
Results
We will first focus on properties of laminar and turbulent losses measured by 3D-PTV, before validating the shear scaling approach on MRI, as well as the numerical data of Casas et al. (2016).
Discussion
In this study, we proposed a novel MRI-applicable approach for the measurement of the irreversible energy loss in aortic flows. The approach is based on the fact that in turbulent shear flow, the large eddy turnover time is expected to be proportional to the mean shear time scale. This appeared to be the case for stenosed aortic flow, where strong shear layers are responsible for turbulence production and define relevant length and time scales of the turbulent eddies. The flow in the
Conclusions
We conclude that measuring the laminar viscous losses does not reflect the total losses of stenotic flows in general since the contribution of the laminar losses becomes smaller than the turbulent losses for more severe stenosis types. We introduced a new MRI-applicable shear scaling approach for the estimation of total energy loss. While the new approach works well for all tested cases from minor to severe stenosis severities, both simplified and modified Bernoulli approaches were found to
Conflict of interest statement
All authors declare that they have no financial and personal relationships with other people or organizations that could have inappropriately influenced (biased) the submitted work.
Acknowledgements
This work was supported by SNSF Research Grant Nr. 144218 and SNSF Research Grant Nr. 159686.
References (28)
- et al.
Magnetic resonance measurement of turbulent kinetic energy for the estimation of irreversible pressure loss in aortic stenosis
JACC Cardiovasc. Imag.
(2013) - et al.
Analysis of thoracic aorta hemodynamics using 3D particle tracking velocimetry and computational fluid dynamics
J. Biomech.
(2014) - et al.
An in vitro investigation of the influence of stenosis severity on the flow in the ascending aorta
Med. Eng. Phys.
(2014) - et al.
Large eddy simulation of LDL surface concentration in a subject specific human aorta
J. Biomech.
(2012) - et al.
Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta
J. Biomech.
(2011) - et al.
Inflow boundary conditions for image-based computational hemodynamics: impact of idealized versus measured velocity profiles in the human aorta
J. Biomech.
(2013) - et al.
Turbulent stresses downstream of three mechanical aortic valve prostheses in human beings
J. Thoracic Cardiovasc. Surg.
(1994) - et al.
Viscous energy loss in the presence of abnormal aortic flow
Magn. Reson. Med.
(2014) - et al.
On the accuracy of viscous and turbulent loss quantification in stenotic aortic flow using phase-contrast MRI
Magn. Reson. Med.
(2015) - et al.
Bayesian multipoint velocity encoding for concurrent flow and turbulence mapping
Magn. Reson. Med.
(2013)
4D Flow MRI-based pressure loss estimation in stenotic flows: Evaluation using numerical simulations
Magn. Reson. Med.
Quantification of intravoxel velocity standard deviation and turbulence intensity by generalizing phase-contrast MRI
Magn. Reson. Med.
Assessment of fluctuating velocities in disturbed cardiovascular blood flow: in vivo feasibility of generalized phase-contrast MRI
J. Magn. Reson. Imag.
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