Blood flow subject to a single cycle of body acceleration

The present study deals with the effect of a single cycle of body accelerations on blood flow in arteries. Such body accelerations are usually caused unintentionally, for example during travel in road vehicles, aircraft or spacecraft. A mathematical model of flow in single arteries subject to a pulsating pressure gradient due to the normal heart action as well as body acceleration expressible in terms of unit functions is presented. The body acceleration is such that it builds up from zero to a maximum value at a uniform rate, remains constant at the maximum value for some time, and thereafter reduces to zero at a uniform rate. The resulting equations are solved by using the technique of Laplace transforms. Computational results are presented for the effects of body accelerations on flow variables namely flow rate, velocity of flow, acceleration and shear stress corresponding to blood flow in the human aorta.     

Pulsatile flow of blood through a stenosed tube: effect of periodic body acceleration and a magnetic field

A proper understanding of the interactions of body acceleration and a magnetic field with blood flow could be useful in the diagnosis and treatment of some health problems. In the work reported in this paper we studied the pulsatile flow of blood through stenosed arteries, including the effects of body acceleration and a magnetic field. Blood is regarded as an electrically conducting, incompressible, couple-stress fluid in the presence of a magnetic field along the radius of the tube. The effects of the body acceleration and the magnetic field on the axial velocity, flow rate, and fluid acceleration were obtained analytically by use of the Hankel transform and the Laplace transform. Velocity variations under different conditions are shown graphically. The results have been compared with those from other theoretical models, and are in good agreement. Finally, our mathematical model gives a simple velocity expression for blood flow so it will help not only in the field of physiological fluid dynamics but will also help medical practitioners with elementary knowledge of mathematics.     

Arterial flow under periodic body acceleration

The present study deals with the effect of externally-imposed body accelerations on blood flow in arteries. Body accelerations may be caused deliberately, for example making the subjecs lie down on vibrating tables: or unintentionally during travel in road vehicles, aircraft or spacecraft. A mathematical model of flow in single arteries subject to a pulsating pressure gradient as well as body acceleration is presented. The resulting equations are solved by using the technique of Laplace transforms. Computational results are presented for the effects of body accelerations on flow variables namely flow rate, velocity of flow, acceleration and shear stress corresponding to typical arteries of human subjects.     

Modeling of particle dynamics in a thruster

Numerical solutions to the equations describing the process of ion acceleration in a Hall current plasma accelerator (thruster) are studied. The system itself represents a three-component plasma: neutral atoms, free electrons, and singly-ionized atoms. The ions in the acceleration tract move without collisions, i.e., the length of the free path of ions is larger than that of the acceleration tract, while electrons move in a diffusion mode across the magnetic field. It is shown that in case the Poisson equation for an electric field is used the set of dynamic equations does not have an acoustic peculiarity that appears when solving a quasineutral set when the velocity of the ion flow and the ion-acoustic velocity coincide.     

RV instantaneous intraventricular diastolic pressure and velocity distributions in normal and volume overload awake dog disease models

Intraventricular diastolic right ventricular (RV) flow field dynamics were studied by functional imaging using three-dimensional (3D) real-time echocardiography with sonomicrometry and computational fluid dynamics in seven awake dogs at control with normal wall motion (NWM) and RV volume overload with diastolic paradoxical septal motion. Burgeoning flow cross section between inflow anulus and chamber walls induces a convective pressure rise, which represents a "convective deceleration load" (CDL). High spatiotemporal resolution dynamic pressure and velocity distributions of the intraventricular RV flow field revealed time-dependent, subtle interactions between intraventricular local acceleration and convective pressure gradients. During the E-wave upstroke, the total pressure gradient along intraventricular flow is the algebraic sum of a pressure decrease contributed by local acceleration and a pressure rise contributed by a convective deceleration that partially counterbalances the local acceleration gradient. This underlies the smallness of early diastolic intraventricular gradients. At peak volumetric inflow, local acceleration vanishes and the total adverse intraventricular gradient is convective. During the E-wave downstroke, the strongly adverse gradient embodies the streamwise pressure augmentations from both local and convective decelerations. It induces flow separation and large-scale vortical motions, stronger in NWM. Their dynamic corollaries on intraventricular pressure and velocity distributions were ascertained. In the NWM pattern, the strong ring-like vortex surrounding the central core encroaches on the area available for flow toward the apex. This results in higher linear velocities later in the downstroke of the E wave than at peak inflow rate. The augmentation of CDL by ventriculoannular disproportion may contribute to E wave and E-to-A ratio depression with chamber dilatation.     

Use of microspheres in measurement of regional blood flows during +GZ stress

The use of the radiolabeled microsphere technique for the study of the effects of +GZ acceleration on regional blood flow is examined. A theoretical analysis of the limits of this technique in a high acceleration environment is presented. Chronically implanted, electromagnetic, aortic flow probes were used to determine the relationship between aortic blood flow velocity and +GZ acceleration in conscious adult miniature swine. It was found that conscious straining adult miniature swine, with the assistance of an inflated anti-G suit, are able to compensate quite well to acceleration levels less than or equal to +7 GZ. Exposure to +9 GZ often resulted in unstable cardiovascular states involving relative bradycardia, often progressing to asystole, declining aortic blood pressure, and markedly diminished cardiac outputs approaching zero. It was found that, if aortic pressure and heart rate attain a relatively steady state during acceleration, and if heart level mean aortic pressure is greater than or equal to 100 Torr, the application of the microsphere technique during +GZ acceleration is theoretically valid. This hypothesis was tested using the microsphere technique (9.0 +/- 0.8 microns diam) in conscious miniature swine during exposure to +GZ acceleration. It is concluded that within the defined limits the radiolabeled microsphere technique is as accurate for use during acceleration studies as it is for use in routine laboratory studies.     

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

3D-PTV is a quantitative flow measurement technique that aims to track the Lagrangian paths of a set of particles in three dimensions using stereoscopic recording of image sequences. The basic components, features, constraints and optimization tips of a 3D-PTV topology consisting of a high-speed camera with a four-view splitter are described and discussed in this article. The technique is applied to the intermediate flow field (5 <x/d <25) of a circular jet at Re ≈ 7,000. Lagrangian flow features and turbulence quantities in an Eulerian frame are estimated around ten diameters downstream of the jet origin and at various radial distances from the jet core. Lagrangian properties include trajectory, velocity and acceleration of selected particles as well as curvature of the flow path, which are obtained from the Frenet-Serret equation. Estimation of the 3D velocity and turbulence fields around the jet core axis at a cross-plane located at ten diameters downstream of the jet is compared with literature, and the power spectrum of the large-scale streamwise velocity motions is obtained at various radial distances from the jet core.     

Inflation waves induced by axial acceleration of the aorta

The phenomenon of high-amplitude inflation waves resulting from a sharp axial acceleration of the aorta, as may occur in road accidents, is investigated theoretically. The aorta is modeled as an axisymmetric tapered membranic shell (tube) made of an incompressible, nonlinear viscoelastic material with cylindrical orthotropy. It is filled with an inviscid, incompressible fluid whose flow is considered as quasi-one dimensional along the tube axis. The equations of motion of the tube and of the fluid are solved numerically, by using a two-step explicit scheme, for several axial acceleration profiles. The solutions shows that an inflation wave is generated and it propagates in opposite direction to that of the acceleration. The wall stresses, deformations and their time derivatives as well as fluid velocity and pressure are determined along the tube at different time intervals. Peak axial and circumferential stresses are high, with the latter far exceeding the former. These stresses may cause rupture of the aorta.     

Casson fluid model for pulsatile flow of blood under periodic body acceleration

Pulsatile flow of a Casson fluid under the influence of a periodic body acceleration has been studied in this paper. An implicit finite difference numerical procedure has been used to analyze the flow. Applicability of this method has been checked by comparing the obtained results with the analytical solution for Newtonian flow and explicit scheme solution. The agreement between the implicit and explicit scheme solutions and the analytical solution is good (error less than 1%). Flow variables have been computed at three locations in cardiovascular system (wide (femoral) and narrow (arteriole and coronary) tubes). Effects of yield stress, tube radius and pressure gradient combined, body acceleration amplitude and frequency etc., on flow have been studied. The following observations have been made: (i) Initial transient time It changes with yield stress in narrow tubes are insignificant, whereas in wide tubes It decreases with yield stress; (ii) The axial velocity and fluid acceleration variations with yield stress are uniform (changes only quantitatively, profiles shape remain same) in narrow tubes, whereas in wide tubes these variations are non-uniform (profiles change qualitatively as well as quantitatively); (iii) Yield stress effects on wall shear amplitude are insignificant in narrow tubes (congruent to 0.3% in arteriole and congruent to 6% in femoral); and (iv) For Newtonian fluid, mean flow rate does not change with body acceleration amplitude a0 and frequency fb but it increases (decreases) with a0(fb) for Casson fluid.     

Bidirectional flow of endoplasm inPhysarum plasmodium under centrifugal acceleration

Summary The behavior of cytoplasmic streaming in plasmodial strand ofPhysarum polycephalum was studied under centrifugal acceleration using a centrifuge microscope of the stroboscopic type. Cytoplasmic streaming in the plasmodium was greatly affected by changes in the acceleration. The endoplasmic flow in the centrifugal direction was accelerated, while that in the centripetal was retarded, by centrifugal acceleration. The centrifugal acceleration required to stop the endoplasmic flow in the centripetal direction did not cause total cessation of streaming but always induced a bidirectional flow of endoplasm in one and the same strand. Each profile of velocity distribution of the bidirectional flow was both parabola with flattened apex. One possible cause of the bidirectional flow is discussed.Dedicated to Emeritus Professor Noburo Kamiya on the occasion of his 80th birthday     

Cerebral blood flow velocity and cranial fluid volume decrease during +Gz acceleration

Cerebral blood flow (CBF) velocity and cranial fluid volume, which is defined as the total volume of intra- and extracranial fluid, were measured using transcranial Doppler ultrasonography and rheoencephalography, respectively, in humans during graded increase of +Gz acceleration (onset rate: 0.1 G/s) without straining maneuvers. Gz acceleration was terminated when subjects' vision decreased to an angle of less than or equal to 60 degrees, which was defined as the physiological end point. In five subjects, mean CBF velocity decreased 48% from a baseline value of 59.4 +/- 11.2 cm/s to 31.0 +/- 5.6 cm/s (p<0.01) with initial loss of peripheral vision at 5.7 +/- 0.9 Gz. On the other hand, systolic CBF velocity did not change significantly during increasing +Gz acceleration. Cranial impedance, which is proportional to loss of cranial fluid volume, increased by 2.0 +/- 0.8% above the baseline value at the physiological end point (p<0.05). Both the decrease of CBF velocity and the increase of cranial impedance correlated significantly with Gz. These results suggest that +Gz acceleration without straining maneuvers decreases CBF velocity to half normal and probably causes a caudal fluid shift from both intra- and extracranial tissues.     

Hemodynamics for medical students

The flow of blood through the cardiovascular system depends on basic principles of liquid flow in tubes elucidated by Bernoulli and Poiseuille. The elementary equations are described involving pressures related to velocity, acceleration/deceleration, gravity, and viscous resistance to flow (Bernoulli-Poiseuille equation). The roles of vascular diameter and number of branches are emphasized. In the closed vascular system, the importance of gravity is deemphasized, and the occurrence of turbulence in large vessels is pointed out.     

Flow pattern and shear stress distribution of distal end-to-side anastomoses. A comparison of the instantaneous velocity fields obtained by particle image velocimetry

OBJECTIVE: To describe the local hemodynamics and pressure losses of crural bypass anastomoses using instantaneous velocity fields acquired by particle image velocimetry (PIV). METHODS: Silastic models of a Taylor patch, a Miller cuff and a femoro-crural patch prosthesis (FCPP) were attached to a circuit driven by a Berlin Heart, providing a pulsatile flow with an amplitude of 450 to 25 ml/min (mean 200 ml/min). An outflow resistance of 0.5 mmHg/ml/min (peripheral resistance units, PRU) was modeled using small silastic tubes providing a phase shift of -12 degrees between flow and pressure curves. The working fluid consisted of a glycerine/water mixture with a viscosity of 4 mPas. Hollow glass spheres with a mean size of 9-13 microm were used as tracer particles. Instantaneous velocity fields were obtained by means of PIV and shear rates as well as shear stresses were calculated. Triggered by the flowmeter signal, 10 measurements at 100 ms intervals per cardiac cycle were obtained. The pressures were measured on the inflow and at both distal outflows. The resulting mean pressure losses due to flow separation and distal fluid acceleration were calculated. RESULTS: Inside the Taylor patch anastomosis a large flow separation at the hood containing a clockwise rotating vortex was found. Additionally a smaller flow separation at the heel and a flow stagnation zone on the floor of the recipient artery were observed. Conversely, inside the Miller cuff a counterclockwise rotating vortex was seen inside a large heel flow separation. The FCPP also showed typical separation areas at the hood and heel of the anastomosis, although these were smaller compared to the other anastomoses. Inside the FCPP anastomosis no vortex creation was observed throughout the cardiac cycle. The mainstream velocities at the inlet levels were comparable for the three anastomoses. A significant fluid acceleration was present at the antegrade as well as the retrograde outlets of the Taylor and Miller cuff, while the fluid acceleration at the antegrade outflow of the FCPP was small, which was attributed to the end-to-end configuration of the antegrade FCPP leg. The calculated normalized antegrade and retrograde pressure losses for the Taylor form were 0.90 and 0.88, for the Miller cuff 0.89 and 0.86 and for the FCPP 0.94 and 0.86, respectively. The shear stresses inside the flow separations of the three anastomoses were significantly lower than normal wall shear stresses. High shear stress levels were found inside the transition zones between flow separation and high velocity mainstream. CONCLUSIONS: The flow pattern inside cuffed or funnel shaped anastomoses consists of large flow separation zones, which are thought to be associated with intimal hyperplasia development. In addition, fluid accelerations at the distal outlets result in pressure losses, which may contribute to impaired crural perfusion.     

Acceleration of electron bunches injected into a wake wave

The process of trapping and acceleration of nonmonoenergetic electron bunches by a wake wave excited by a laser pulse in a plasma channel is investigated. The electrons are injected into the vicinity of the maximum of the wakefield potential with a velocity lower than the wave phase velocity. The study is aimed at utilizing specific features of a wakefield with substantially overlapped focusing and accelerating phases for achieving monoenergetic electron acceleration. Conditions are found under which electrons in a finite-length nonmonoenergetic bunch are accelerated to high energies, while the energy spread between them is minimal. The effect of energy grouping of electrons makes it possible to obtain compact high-energy electron bunches with a small energy spread during laser plasma acceleration.     

Forward and backward running waves in the arteries: analysis using the method of characteristics

The one-dimensional equations of flow in the elastic arteries are hyperbolic and admit nonlinear, wavelike solutions for the mean velocity, U, and the pressure, P. Neglecting dissipation, the solutions can be written in terms of wavelets defined as differences of the Riemann invariants across characteristics. This analysis shows that the product, dUdP, is positive definite for forward running wavelets and negative definite for backward running wavelets allowing the determination of the net magnitude and direction of propagating wavelets from pressure and velocity measured at a point in the artery. With the linearizing assumption that intersecting wavelets are additive, the forward and backward running wavelets can be separately calculated. This analysis, applied to measurements made in the ascending aorta of man, shows that forward running wavelets dominate during both the acceleration and deceleration phases of blood flow in the aorta. The forward and backward running waves calculated using the linearized analysis are similar to the results of an impedance analysis of the data. Unlike the impedance analysis, however, this is a time domain analysis which can be applied to nonperiodic or transient flow.     

Kinematic and Dynamic Characteristics of Pulsating Flow in 180^o Tube

Kinematic and dynamic characteristics of pulsating flow in a model of human aortic arch are obtained by a computational analysis. Three-dimensional flow processes are summarized by pressure distributions on the symmetric plane together with velocity and pressure contours on a few cross sections for systolic acceleration and deceleration. Without considering the effects of aortic tapering and the carotid arteries, the development of tubular boundary layer with centrifugal forces and pulsation are also analyzed for flow separation and backflow during systolic deceleration.     

Influence of pulsatility on the development of intracardiac jets: an in vitro laser Doppler study.

So far, it has been hypothesized that numerical data obtained in steady flow conditions apply to pulsatile flows. In order to study the modifications of the velocity fields due to pulsatility, jets were produced by 8 orifices (with a diameter "D" of 4.4 to 11.3 mm) included in a chamber of 50 mm. The velocity was measured using laser Doppler anemometry with a pulsatile flow ("pf") and compared to the values obtained in steady ("sf"): at maximum velocity, the longitudinal velocity profile is qualitatively similar to this observed in steady flow: it is made of a plateau followed by an hyperbolic velocity decay in the turbulent area. The length of the core ("Lpf") is strongly related to "D" (Lpf = 3.72 D + 5.49, r = .99) and the velocity decay depends on the ratio between the distance "x" from the orifice and "D" (V/Vo = 2.83D/x + 3.46, r = .85, where V is the velocity at "x" and Vo the initial velocity). During the acceleration and the deceleration, the laminar core is disturbed by turbulences. The comparison of "pf" data with "sf" data demonstrated similar diameters at the origin of the jets (Dpf = 0.96 Dsf + .12, r = .99), but significant (p less than .0001) differences both for "L" and "V/Vo": Lpf = .91Lsf + 6.58, r = .97, V/Vopf = .63 V/Vosf + .34, r = .76. Thus, pulsatility modifies velocity fields and the results obtained in steady flow conditions do not apply to pulsatile jets.     

Temporal-spatial reach parameters derived from inertial sensors correlate to neurodevelopment in toddlers born preterm

Temporal-spatial reach parameters are revealing of upper-limb function in children with motor impairments, but have not been quantified in a toddler population. This work quantitatively characterizes temporal-spatial reach in typically-developing (TD) and very-low-birth-weight (VLBW) preterm toddlers, who are at increased risk of motor impairment. 47 children born VLBW (<1500 g birth-weight; ≤32 weeks gestation) and 22 TD children completed a reaching assessment at 18–22 months of age, adjusted for prematurity. Inertial sensors containing accelerometers, gyroscopes and magnetometers were fixed to toddlers’ wrists while they reached for a cube. Reach time, path length, velocity at contact, peak velocity magnitude and timing, acceleration at contact, and peak acceleration were derived from inertial-sensor and high-speed video data. Preterm children also received the Bayley Scales of Infant Development—3rd Edition (BSID-III). Compared to TD toddlers, preterm toddlers had significantly different reach path length, velocity at contact, peak velocity magnitude and timing, acceleration at contact, and peak acceleration. Among preterm toddlers, decreased reach time (rho = −.346, p = .018), decreased time to peak velocity (r = −.390, p = .007), and increased peak acceleration (r = .298, p = .044) correlated to higher BSID-III fine motor scores. Toddlers with below-average fine motor scores had significantly higher peak and contact velocity. Preterm toddlers demonstrated substantial differences in temporal-spatial reach parameters compared to TD toddlers, and evidence indicated several reach parameters were revealing of function and may be useful as a clinical assessment.