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Measurement of wall shear stress distal to a tri-leaflet valve in a rigid model of the aortic arch with branch flows.

Flush mounted hot film anemometer probes were used to measure wall shear stress magnitudes on the inside and outside walls of a rigid model of the human aortic arch. The effects of the presence of an Ionescu-Shiley tri-leaflet bioprosthetic heart valve at the entrance of the aortic arch and the side flows through arteries located in the mid-arch region on wall shear stress magnitudes were determined. It was found that the presence of the tri-leaflet valve leads to an elevation of wall shear stress (relative to the same flow without a valve) over the entire aortic arch region by as much as 50 percent. The valve influence extended to about 180 deg from the entrance to the aorta on the inside wall and even further on the outside wall based on extrapolation of available data. Peak wall shear stress magnitudes measured on the outside wall were in the range of 1.5-4.0 N/m2 (15-40 dynes/cm2) over the length of the aortic arch and took on their highest values in the mid-arch region. Inside wall values were of comparable magnitude. It was observed that the presence of the aortic valve and side flow from the top of the aortic arch reduced wall shear stress reversal in the arch region.

Aorta, Thoracic↗

Velocity profiles in stenosed tube models using magnetic resonance imaging.

A time-of-flight MRI velocity measurement technique is evaluated against corresponding LDV measurements in a constriction tube model over a range of physiologic flow conditions. Results from this study show that MR displacement images can: 1) be obtained within both laminar and turbulent jets (maximum stenotic Re approximately equal to 4,200), 2) measure mean jet velocities up to 172 cm/s, and, 3) detect low forward and reverse stenosis (0 less than or equal to L/D less than or equal to 2). Regions between the jet termination point and re-establishment of laminar flow (Re greater than or equal to 1500, greater than or equal to 1000, and greater than or equal to 110 downstream of 40, 60, and 80 percent stenosis, respectively) cannot presently be detected by this technique.

Blood Flow Velocity↗

Flow measurements in a human femoral artery model with reverse lumen curvature.

Flow visualization and wall pressure measurements were made in a smooth reverse curvature model that conformed to the gentle "s" shape of a left femoral artery angiogram of a patient in a clinical trial. Observed lesion localization at the inner (lesser) curvatures appeared to be associated with secondary flows in the wall vicinity directed toward the inner curvatures that tended to reverse direction in the flow entering the reverse curvature region. Moderate flow resistance increases of about 20 percent above the Poiseuille flow relation were found at the higher physiological Reynolds numbers Re above about 600-700 and thus Dean numbers for steady flow. For pulsatile flow simulation, flow resistances did not increase up to the largest Re of 470 tested. Apparently, the large variations in velocity during the cardiac cycle disrupted the stronger secondary flow patterns observed at the higher Reynolds numbers for steady flow.

Arteriosclerosis↗

Flow measurements in an atherosclerotic curved, tapered femoral artery model of man.

Flow visualization and pressure measurements were made for physiological conditions in a model derived from a femoral angiogram of a patient with lesion localization on the inner curvature wall and with vessel taper. Effects of curvature and taper were evaluated separately in other curved, tapered, smooth and straight, tapered, smooth models. Double helical secondary flow patterns were modified by plaque on the inner wall, and flow separations were observed between plaques at higher flow rates and Reynolds numbers. Pressure drop data for the plaque simulation model were similar in trend with Reynolds number as for the smooth model, but flow resistances were 25 to 40 percent higher. Significant pressure drops were measured due to the mild taper which could be estimated from momentum considerations, and smaller increased pressure drops were found due to curvature effects at the higher Dean numbers. Flow resistances for in vivo pulsatile flow simulation were about 10 percent higher than for steady flow for the plaque model, whereas no differences were observed for the smooth model.

Arteriosclerosis↗

Shear-layer detection in poststenotic flow by spectrum analysis of Doppler signals.

Spectrum analysis of the Doppler signals was performed 0.5 tube diameters downstream from an axisymmetric constriction with an area reduction of 80 percent in steady flow at a jet Reynolds number of 2840. Both pulsed and continuous wave (CW) Doppler spectra showed significant reverse flow components in the separated flow. The pulsed Doppler spectra exhibited sudden changes when the sample volume crossed the shear layer between the center jet and the separated flow. A power spectrum equation was theoretically derived from continuity of flow to define the Doppler shift frequency for the shear layer velocity. The CW Doppler spectrum showed a minimum spectrum density at a frequency which equalled the shear layer Doppler shift frequency derived from the equation. The pulsed spectra exhibited the sudden changes at the same frequency as well.

Blood Flow Velocity↗

Model studies at mechanical aortic heart valve prostheses--Part I: Steady-state flow fields and pressure loss coefficients.

In a 3:1 scaled model of the human aorta models of the Omniscience, Björk-Shiley Convexo-Concave, Björk-Shiley Monostrut, Medtronic-Hall, Duromedics (Hemex) and the Saint Jude Medical heart valve prostheses are studied in steady flow representing the systolic peak flow phase. Detailed flow visualization experiments show flow separations at all inner ring surfaces as well as at most of the occluders. The resulting stagnation areas increase the risk of thrombus accumulation. Flow separations also stimulate vortex formation and turbulent mixing at the downstream jet boundaries and thus may intensify blood damage by turbulent shear stresses. The different influences of struts and occluder guides on the flow around the occluders are discussed. The effects of the individual valve components on the flow fields are analyzed and correlated with the resulting pressure losses.

Aortic Valve↗

A finite-element simulation of pulsatile flow in flexible obstructed tubes.

A finite-element model for pulsatile flow in a straight flexible partially obstructed tube is developed. In the unobstructed sections of the tube the model considers the continuity equation, the one-dimensional momentum equation, and an equation of state relating tube cross-sectional area to pressure. For the obstructed region, a nonlinear relationship between the flow and the pressure drop across the stenosis is considered. The applicability of a model is checked by comparing predicted flow and pressure waveforms with corresponding in-vitro experimental measurements obtained on a mechanical system. These comparisons indicated that the model satisfactorily predicts pressures and flows under variety of frequencies of oscillation and stenosis severities.

Arterial Occlusive Diseases↗

Bioengineering studies of periodic external compression as prophylaxis against deep vein thrombosis-part II: experimental studies on a stimulated leg.

In this companion paper to "Part I: Numerical Simulations, " we report in vitro experimental studies performed on a simple model leg consisting of a "vein" of thin-walled latex tubing surrounded by "tissue" of open-pore foam rubber. Three modes of periodic external compression, were investigated: i) uniform compression; (ii) graded compression, decreasing from ankle to knee; and (iii) sequential compression, progressing from ankle to knee. The modes are compared on the basis of three hemodynamic criteria: degree of vessel collapse, level of fluid velocity, and level of shear stress. In uniform compression these measures of merit are distributed very nonuniformly along the length of the leg: they are high near the proximal end of the cuff but low elsewhere, a result due to the formation proximally of a partially occlusive throat. The latter does not form in either graded or sequential compression, with the consequence that favorable values of the three measures of merit occur more uniformly along the length of the pressurized region. It is concluded that either the graded or sequential mode of compression, or perhaps a combination of the two, would be more effective than uniform compression as a prophylaxis against deep vein thrombosis.

Gravity Suits↗

An application of optimization methods to evaluate conditioning intervals.

A decision rule is obtained to determine when exercise is beneficial. The term beneficial used in this context refers to the extension of lifetime based on studies of cardiovascular conditioning. Models are used to characterize changes in heart rate with intense exercise. In addition, it is necessary to consider a model involving a heartbeat bank to help determine the conditioning interval. Optimization procedures are used to develop the decision rule, to examine the assumptions in the problem, and to point out when a unique solution exists. This procedure is applied to empirical data for one individual (inter-subject study) and a unique conditioning interval is obtained.

Animals↗

Oscillometric determination of diastolic, mean and systolic blood pressure--a numerical model.

A theoretical model of oscillometric blood pressure measurement is presented. Particular emphasis is paid to the collapse behavior of the artery, and an exponential volume-pressure curve is used. The results of this study suggest that mean blood pressure can be accurately predicted from the peak of the oscillometric curve if corrections related to the cuff pressure waveform are applied. It is also shown, however, that systolic and diastolic pressure may not in general be accurately determined from fixed amplitude ratios based on the oscillometric peak due to the sensitivity of the method to variations in blood pressure waveform, pulse pressure, and arterial compliance. No simple procedures are found to correct for these effects.

Biomechanical Phenomena↗

A constitutive description of contracting papillary muscle and its implications to the dynamics of the intact heart.

A simple mathematical model capable of simulating the major biomechanical attributes of contracting cardiac muscle is presented. This model is based on the phenomenological observations on heart muscle. The form of the equation can be readily extended to describe the pressure-volume-time-velocity of the intact heart as well, thus allowing a direct bridge between the dynamics of papillary muscle and the dynamics of intact heart. Parameters that are sensitive to inotropic state of the muscle can be obtained directly from the isometric tension-time record of the muscle or the isovolumic pressure-time record of the ventricle. These parameters have the potential to serve as quantitative measures of cardiac health.

Animals↗

A comparative analysis of thermal blood perfusion measurement techniques.

The object of this study was to devise a unified method for comparing different thermal techniques for the estimation of blood perfusion rates and to perform a comparison for several common techniques. The approach used was to develop analytical models for the temperature response for all combinations of five power deposition geometries (spherical, one- and two-dimensional cylindrical, and one- and two-dimensional Gaussian) and three transient heating techniques (temperature pulse-decay, temperature step function, and constant-power heat-up) plus one steady-state heating technique. The transient models were used to determine the range of times (the time window) when a significant portion of the transient temperature response was due to blood perfusion. This time window was defined to begin when the difference between the conduction-only and the conduction-plus-blood flow transient temperature (or power) responses exceeded a specified value, and to end when the conduction-plus-blood flow transient temperature (or power) reached a specified fraction of its steady-state value. The results are summarized in dimensionless plots showing the size of the time windows for each of the transient perfusion estimation techniques. Several conclusions were drawn, in particular: (a) low perfusions are difficult to estimate because of the dominance of conduction, (b) large heated regions are better suited for estimation of low perfusions, (c) noninvasive heating techniques are superior because they have the potential to minimize conduction effects, and (d) none of the transient techniques appears to be clearly superior to the others.

Biophysical Phenomena↗

A theoretical model for water flux through the artery wall.

A two layer model for water flux through the artery is studied using a mathematical model based on the theory for the consolidation of water saturated soils. The matrix is considered to be constituted by two layers with different permeabilities and different elastic constants and the two systems of equations are coupled with the condition of continuity of pressure, total stress, solid displacement and fluid seepage velocity at the interface. The luminal pressure is considered to be harmonic in time. Exact solutions are obtained for displacements and pressures in both the layers. For large consolidation times, large pressure gradients are found to exist near the boundaries and at the interface. The heterogeneous model may not only be useful to understand the mechanics of transport in the physiological system but it will also help the bioengineers to choose proper implant materials to design artificial vascular organs for the purpose of prosthesis.

Arteries↗

Persistence of asymmetry in nonaxisymmetric entry flow in a circular cylindrical tube and its relevance to arterial pulse wave diagnosis.

In an experiment motivated by the study of arterial blood flow along the lines suggested by the traditional Chinese medicine, the flow in a pipe whose lumen was blocked by a semi-circular plug two tube-diameters long was visualized by suspended particles, recorded by cinematography, and analyzed digitally. The Reynolds number was in the range of 100 to 450 based on the pipe diameter, similar to that of blood flow in the radial artery in the arms of man. The blockage was found to have a profound effect on the velocity profile of the flow in the wake, but it had little influence on the symmetry of the velocity profile upstream of the block, except in its immediate neighborhood. When the end conditions far away from the block were steady, the flow in the wake was steady. The asymmetry of the flow in the wake can be judged by the deviation of the location of the maximum axial velocity from the center line of the pipe as seen in the plane of symmetry of the blockage. Our results show that the deviation can be described as the sum of two components. The first is a strong one which decays exponentially in an entry length which is about twice as long as the classical Boussinesq entry length of axisymmetric flow. The second is a weaker component which is wavy spatially and persists far downstream (many times the entry length). The separated flow and vortex system behind the blockage are sensitive to the flow rate.(ABSTRACT TRUNCATED AT 250 WORDS)

Blood Flow Velocity↗

Monte carlo parametric study of stent impact on dose for catheter-based intravascular brachytherapy with 90Sr/90Y.

The radiation treatment of catheter-based beta-emitter sources is being used to prevent restenosis following interventional coronary procedures. We present the results of a Monte Carlo calculation study to assess the dosimetric impact in the vessel tissue due to the presence of the stent. A catheter-based beta-emitter system is modeled using the Monte-Carlo code MCNP4B. Dose distributions are calculated in annular voxels (0.050 x 0.025 mm2 section) along the axis of a 40 mm. 90Sr/90Y source with and without the stent (at a distance of 1.5-3.0 mm from the longitudinal axis of the source). The main results include: (a) a clear difference between the local perturbation just behind the strut and a more general perturbation seen deeper into the vessel tissue; (b) the local perturbations disappears at a depth of 300-400 microm while the more general perturbation affects the tissue in its full thickness including the prescription point; (c) in the local perturbation the maximum impact is determined mainly by the material and the thickness of the strut while the spatial attenuation of this impact is defined mainly by the strut width; (d) in the general perturbation, the most important magnitude is the free-area ratio for the path of the electrons, being the material characteristics and strut thickness of secondary importance; (e) analytical expressions are presented to estimate the magnitude of this perturbation according to the complete characteristics of the expanded strut, i.e., thickness, free-area ratio, and material; and (f) a simple algorithm is presented for estimating the free-area ratio when this information is not available.

Algorithms↗

Numerical simulations of phase contrast velocity mapping of complex flows in an anatomically realistic bypass graft geometry.

Combined in vitro experiments and numerical simulations were performed to study flow artifacts in phase contrast (PC) velocity mapping of steady flow through an anatomically realistic aortocoronary bypass graft model. The geometry was obtained through imaging and computational reconstruction of a left anterior descending (LAD) coronary artery of a porcine heart. Simulated images of through-plane velocity were obtained at selected slices of the geometry. These were then compared and contrasted with velocity images of corresponding sites that were obtained from in vitro experiments. The shift and distortion of the measured velocity profile was well predicted by the simulation, while trajectories obtained from particle tracking were shown to be useful in understanding the origins of the flow artifacts that were observed.

Algorithms↗