The effect of red blood cell orientation on the electrical impedance of pulsatile blood with implications for impedance cardiography

Impedance cardiography is an application of bioimpedance analysis primarily used in a research setting to determine cardiac output. It is a non invasive technique that measures the change in the impedance of the thorax which is attributed to the ejection of a volume of blood from the heart. The cardiac output is calculated from the measured impedance using the parallel conductor theory and a constant value for the resistivity of blood. However, the resistivity of blood has been shown to be velocity dependent due to changes in the orientation of red blood cells induced by changing shear forces during flow. The overall goal of this thesis was to study the effect that flow deviations have on the electrical impedance of blood, both experimentally and theoretically, and to apply the results to a clinical setting. The resistivity of stationary blood is isotropic as the red blood cells are randomly orientated due to Brownian motion. In the case of blood flowing through rigid tubes, the resistivity is anisotropic due to the biconcave discoidal shape and orientation of the cells. The generation of shear forces across the width of the tube during flow causes the cells to align with the minimal cross sectional area facing the direction of flow. This is in order to minimise the shear stress experienced by the cells. This in turn results in a larger cross sectional area of plasma and a reduction in the resistivity of the blood as the flow increases. Understanding the contribution of this effect on the thoracic impedance change is a vital step in achieving clinical acceptance of impedance cardiography. Published literature investigates the resistivity variations for constant blood flow. In this case, the shear forces are constant and the impedance remains constant during flow at a magnitude which is less than that for stationary blood. The research presented in this thesis, however, investigates the variations in resistivity of blood during pulsataile flow through rigid tubes and the relationship between impedance, velocity and acceleration. Using rigid tubes isolates the impedance change to variations associated with changes in cell orientation only. The implications of red blood cell orientation changes for clinical impedance cardiography were also explored. This was achieved through measurement and analysis of the experimental impedance of pulsatile blood flowing through rigid tubes in a mock circulatory system. A novel theoretical model including cell orientation dynamics was developed for the impedance of pulsatile blood through rigid tubes. The impedance of flowing blood was theoretically calculated using analytical methods for flow through straight tubes and the numerical Lattice Boltzmann method for flow through complex geometries such as aortic valve stenosis. The result of the analytical theoretical model was compared to the experimental impedance measurements through rigid tubes. The impedance calculated for flow through a stenosis using the Lattice Boltzmann method provides results for comparison with impedance cardiography measurements collected as part of a pilot clinical trial to assess the suitability of using bioimpedance techniques to assess the presence of aortic stenosis. The experimental and theoretical impedance of blood was shown to inversely follow the blood velocity during pulsatile flow with a correlation of -0.72 and -0.74 respectively. The results for both the experimental and theoretical investigations demonstrate that the acceleration of the blood is an important factor in determining the impedance, in addition to the velocity. During acceleration, the relationship between impedance and velocity is linear (r2 = 0.98, experimental and r2 = 0.94, theoretical). The relationship between the impedance and velocity during the deceleration phase is characterised by a time decay constant, ô , ranging from 10 to 50 s. The high level of agreement between the experimental and theoretically modelled impedance demonstrates the accuracy of the model developed here. An increase in the haematocrit of the blood resulted in an increase in the magnitude of the impedance change due to changes in the orientation of red blood cells. The time decay constant was shown to decrease linearly with the haematocrit for both experimental and theoretical results, although the slope of this decrease was larger in the experimental case. The radius of the tube influences the experimental and theoretical impedance given the same velocity of flow. However, when the velocity was divided by the radius of the tube (labelled the reduced average velocity) the impedance response was the same for two experimental tubes with equivalent reduced average velocity but with different radii. The temperature of the blood was also shown to affect the impedance with the impedance decreasing as the temperature increased. These results are the first published for the impedance of pulsatile blood. The experimental impedance change measured orthogonal to the direction of flow is in the opposite direction to that measured in the direction of flow. These results indicate that the impedance of blood flowing through rigid cylindrical tubes is axisymmetric along the radius. This has not previously been verified experimentally. Time frequency analysis of the experimental results demonstrated that the measured impedance contains the same frequency components occuring at the same time point in the cycle as the velocity signal contains. This suggests that the impedance contains many of the fluctuations of the velocity signal. Application of a theoretical steady flow model to pulsatile flow presented here has verified that the steady flow model is not adequate in calculating the impedance of pulsatile blood flow. The success of the new theoretical model over the steady flow model demonstrates that the velocity profile is important in determining the impedance of pulsatile blood. The clinical application of the impedance of blood flow through a stenosis was theoretically modelled using the Lattice Boltzman method (LBM) for fluid flow through complex geometeries. The impedance of blood exiting a narrow orifice was calculated for varying degrees of stenosis. Clincial impedance cardiography measurements were also recorded for both aortic valvular stenosis patients (n = 4) and control subjects (n = 4) with structurally normal hearts. This pilot trial was used to corroborate the results of the LBM. Results from both investigations showed that the decay time constant for impedance has potential in the assessment of aortic valve stenosis. In the theoretically modelled case (LBM results), the decay time constant increased with an increase in the degree of stenosis. The clinical results also showed a statistically significant difference in time decay constant between control and test subjects (P = 0.03). The time decay constant calculated for test subjects (ô = 180 - 250 s) is consistently larger than that determined for control subjects (ô = 50 - 130 s). This difference is thought to be due to difference in the orientation response of the cells as blood flows through the stenosis. Such a non-invasive technique using the time decay constant for screening of aortic stenosis provides additional information to that currently given by impedance cardiography techniques and improves the value of the device to practitioners. However, the results still need to be verified in a larger study. While impedance cardiography has not been widely adopted clinically, it is research such as this that will enable future acceptance of the method.

Effect of Reynolds numbers on flow past four square cylinders in an in-line square configuration for different gap spacings

In this paper two-dimensional (2-D) numerical investigation of flow past four square cylinders in an in-line square configuration are performed using the lattice Boltzmann method. The gap spacing g=s/d is set at 1, 3 and 6 and Reynolds number ranging from Re=60 to 175. We observed four distinct wake patterns: (i) a steady wake pattern (Re=60 and g=1) (ii) a stable shielding wake pattern (80≤Re≤175 and g=1) (iii) a wiggling shielding wake pattern (60≤Re≤175 and g=3) (iv) a vortex shedding wake pattern (60≤Re≤175 and g=6) At g=1, the Reynolds number is observed to have a strong effect on the wake patterns. It is also found that at g=1, the secondary cylinder interaction frequency significantly contributes for drag and lift coefficients signal. It is found that the primary vortex shedding frequency dominates the flow and the role of secondary cylinder interaction frequency almost vanish at g=6. It is observed that the jet between the gaps strongly influenced the wake interaction for different gap spacing and Reynolds number combination. To fully understand the wake transformations the details vorticity contour visualization, power spectra of lift coefficient signal and time signal analysis of drag and lift coefficients also presented in this paper.

Numerical study of lid-driven square cavity with heat generation using LBM

In this study, the mixed convection heat transfer and fluid flow behaviors in a lid-driven square cavity filled with high Prandtl number fluid (Pr = 5400, ν = 1.2×10-4 m2/s) at low Reynolds number is studied using thermal Lattice Boltzmann method (TLBM) where ν is the viscosity of the fluid. The LBM has built up on the D2Q9 model and the single relaxation time method called the Lattice-BGK (Bhatnagar-Gross-Krook) model. The effects of the variations of non dimensional mixed convection parameter called Richardson number(Ri) with and without heat generating source on the thermal and flow behavior of the fluid inside the cavity are investigated. The results are presented as velocity and temperature profiles as well as stream function and temperature contours for Ri ranging from 0.1 to 5.0 with other controlling parameters that present in this study. It is found that LBM has good potential to simulate mixed convection heat transfer and fluid flow problem. Finally the simulation results have been compared with the previous numerical and experimental results and it is found to be in good agreement.

Spatially averaged model of complex-plasma discharge with self-consistent electron energy distribution

A global, or averaged, model for complex low-pressure argon discharge plasmas containing dust grains is presented. The model consists of particle and power balance equations taking into account power loss on the dust grains and the discharge wall. The electron energy distribution is determined by a Boltzmann equation. The effects of the dust and the external conditions, such as the input power and neutral gas pressure, on the electron energy distribution, the electron temperature, the electron and ion number densities, and the dust charge are investigated. It is found that the dust subsystem can strongly affect the stationary state of the discharge by dynamically modifying the electron energy distribution, the electron temperature, the creation and loss of the plasma particles, as well as the power deposition. In particular, the power loss to the dust grains can take up a significant portion of the input power, often even exceeding the loss to the wall.

A kinetic model for an argon plasma containing dust grains

A complex low-pressure argon discharge plasma containing dust grains is studied using a Boltzmann equation for the electrons and fluid equations for the ions. Local effects, such as the spatial distribution of the dust density and external electric field, are included, and their effect on the electron energy distribution, the electron and ion number densities, the electron temperature, and the dust charge are investigated. It is found that dust particles can strongly affect the plasma parameters by modifying the electron energy distribution, the electron temperature, the creation and loss of plasma particles, as well as the spatial distributions of the electrons and ions. In particular, for sufficiently high grain density and/or size, in a low-pressure argon glow discharge, the Druyvesteyn-like electron distribution in pristine plasmas can become nearly Maxwellian. Electron collection by the dust grains is the main cause for the change in the electron distribution function.

On the effect of Reynolds number for flow past three side-by-side square cylinders for unequal gap spacings

Flow patterns and aerodynamic characteristics behind three side-by-side square cylinders has been found depending upon the unequal gap spacing (g1 = s1/d and g2 = s2/d) between the three cylinders and the Reynolds number (Re) using the Lattice Boltzmann method. The effect of Reynolds numbers on the flow behind three cylinders are numerically studied for 75 ≤ Re ≤ 175 and chosen unequal gap spacings such as (g1, g2) = (1.5, 1), (3, 4) and (7, 6). We also investigate the effect of g2 while keeping g1 fixed for Re = 150. It is found that a Reynolds number have a strong effect on the flow at small unequal gap spacing (g1, g2) = (1.5, 1.0). It is also found that the secondary cylinder interaction frequency significantly contributes for unequal gap spacing for all chosen Reynolds numbers. It is observed that at intermediate unequal gap spacing (g1, g2) = (3, 4) the primary vortex shedding frequency plays a major role and the effect of secondary cylinder interaction frequencies almost disappear. Some vortices merge near the exit and as a result small modulation found in drag and lift coefficients. This means that with the increase in the Reynolds numbers and unequal gap spacing shows weakens wakes interaction between the cylinders. At large unequal gap spacing (g1, g2) = (7, 6) the flow is fully periodic and no small modulation found in drag and lift coefficients signals. It is found that the jet flows for unequal gap spacing strongly influenced the wake interaction by varying the Reynolds number. These unequal gap spacing separate wake patterns for different Reynolds numbers: flip-flopping, in-phase and anti-phase modulation synchronized, in-phase and anti-phase synchronized. It is also observed that in case of equal gap spacing between the cylinders the effect of gap spacing is stronger than the Reynolds number. On the other hand, in case of unequal gap spacing between the cylinders the wake patterns strongly depends on both unequal gap spacing and Reynolds number. The vorticity contour visualization, time history analysis of drag and lift coefficients, power spectrum analysis of lift coefficient and force statistics are systematically discussed for all chosen unequal gap spacings and Reynolds numbers to fully understand this valuable and practical problem.

Calculations of the free energy of interaction of the c-Fos−c-Jun coiled coil: Effects of the solvation model and the inclusion of polarization effects

The leucine zipper region of activator protein-1 (AP-1) comprises the c-Jun and c-Fos proteins and constitutes a well-known coiled coil protein−protein interaction motif. We have used molecular dynamics (MD) simulations in conjunction with the molecular mechanics/Poisson−Boltzmann generalized-Born surface area [MM/PB(GB)SA] methods to predict the free energy of interaction of these proteins. In particular, the influence of the choice of solvation model, protein force field, and water potential on the stability and dynamic properties of the c-Fos−c-Jun complex were investigated. Use of the AMBER polarizable force field ff02 in combination with the polarizable POL3 water potential was found to result in increased stability of the c-Fos−c-Jun complex. MM/PB(GB)SA calculations revealed that MD simulations using the POL3 water potential give the lowest predicted free energies of interaction compared to other nonpolarizable water potentials. In addition, the calculated absolute free energy of binding was predicted to be closest to the experimental value using the MM/GBSA method with independent MD simulation trajectories using the POL3 water potential and the polarizable ff02 force field, while all other binding affinities were overestimated.