Blood Flow, Hemodynamics

Analytical expressions correlating the volumetric flow rate to the inlet and outlet pressures are derived for the time-independent flow of Newtonian fluids in cylindrically-shaped elastic tubes using a one-dimensional Navier-Stokes flow model with two pressure-area constitutive relations. These expressions for elastic tubes are the equivalent of Poiseuille and Poiseuille-type expressions for rigid tubes which were previously derived for the flow of Newtonian and non-Newtonian fluids under various flow conditions. Formulae and procedures for identifying the pressure field and tube geometric profile are also presented. The results are validated by a finite element method implementation. Sensible trends in the analytical and numerical results are observed and documented.

We present a numerical investigation of tapered arteries that addresses the transient simulation of non-Newtonian bio-magnetic fluid dynamics (BFD) of blood through a stenosis artery in the presence of a transverse magnetic field. The current model is consistent with ferro-hydrodynamic (FHD) and magneto-hydrodynamic (MHD) principles. In the present work, blood in small arteries is analyzed using the Carreau-Yasuda model. The arterial wall is assumed to be fixed with cosine geometry for the stenosis. A parametric study was conducted to reveal the effects of the stenosis intensity and the Hartman number on a wide range of flow parameters, such as the flow velocity, temperature, and wall shear stress. Current findings are in a good agreement with recent findings in previous research studies. The results show that wall temperature control can keep the blood in its ideal blood temperature range (below 40˚C) and that a severe pressure drop occurs for blockages of more than 60 percent. Additionally, with an increase in the Ha number, a velocity drop in the blood vessel is experienced.

Muscle oxygen uptake (V O2 ,mus ) dynamics at the onset of exercise can be affected by prior heavy exercise. We tested the hypothesis that elevated forearm blood flow (FBF) following prior circulatory occlusion would also be associated with accelerated VO2 ,mus dynamics during sub-sequent heavy hand-grip exercise. Ten trained young men performed 5 min of heavy hand-grip exercise at 30% MVC as a control (CON), and four additional heavy bouts after brief recovery from: (1) prior heavy exercise (Heavy A), (2) heavy exercise followed by 2 min occlusion (Heavy B), (3) 15 min occlusion (Heavy C), and (4) 5 min occlusion with1 min of moderate exercise during occlusion (Heavy D). FBF was measured by ultrasound and arterial venous oxygen content difference was calculated from venous blood samples to estimate VO2 ,mus . FBF and VO2 ,mus dynamics were quantified from the rise time. All priming conditions elevated FBF immediately before the start of subsequent heavy bout (Heavy A: 207.4 ± 92.8, B: 207.8 ± 75.8, C: 135.8 ± 59.2, D: 199.5 ± 59.0 vs. CON: 57.4 ± 16.6 ml min−1 , P < 0.01). Unexpectedly, prior occlusion reduced FBF and O2 extraction at the onset of subsequent heavy exercise and consequently slowed VO2 ,mus dynamics (Heavy C: rise time = 95.9 ± 28.9 vs. CON: 58.6 ± 14.3 s, P < 0.01). FBF and VO2 ,mus dynamics were faster in Heavy A, B and D compared to CON (P < 0.05). Overall, there was a positive correlation between the rise times for VO2 ,mus and FBF (r 2 = 0.75) indicating that VO2 ,mus dynamics during heavy forearm exercise are linked to O2 delivery in trained young men. To investigate a possible mechanism for slower adaptation of VO2 ,mus following ischaemia, the prior occlusion condition was repeated after ingesting a high dose of ibuprofen. This resulted in restoration of the FBF and VO2 ,mus to control levels suggesting that a prostaglandin-mediated mechanism after occlusion retarded the adaptation of blood flow and oxygen consumption at the onset of subsequent heavy exercise.

In today's world, research on cardiovascular diseases has increased due to the social losses. Diagnosis and treatment of cardiovascular disorders are necessary to understand the biological and mechanical causes of the diseases. In vitro and in vivo experiments are performed to understand the mechanism of the disease. In in vitro experiments physiological blood flow signals are used to simulate the blood flow inside human body. In this study novel closed-loop flow control system has been developed with control technique and flow control devices to simulate the physiological waveform, unlike studies conducted to date. In vitro experimental system consists of centrifugal pump, pump driver card, solenoid valve, valve driver card, data acquisition card (DAQ), flow meters, in vitro model and sample fluid piping system. The control algorithm is written and run using Matlab/ Simulink AC pump and solenoid valves were used to simulate the pulsatile flow in femoral and coronary arteries that they have the high and low flow rates of 25 and 3 ml/s, respectively. In the human body blood flow velocity and geometry of the measurement location can be recorded and visualized by MR imaging techniques. Images of blood flow signal can be transferred to experimental system by providing equivalence of dynamic simulation. For realization of blood flow, Fourier coefficients were obtained from MR blood flow image using image processing techniques and they were used to create flow velocity profile. Using Fourier coefficients femoral and coronary artery blood flow have been realized on the experimental system. Error performance (EP) criterion was developed during the studies to compare human blood flow signal to in vitro experimental blood flow signal. This study is a pioneer in terms of using close-loop control, two flow control devices and EP criteria in in vitro experimental systems. The algorithm developed in this research will be applied to different regions of cardiovascular system for future studies to better understand the cardiovascular diseases and related treatment. Over the years, spine surgeons have been obliged to revise pedicle screws due to the increasing number of the pedicle screw instru-mentation in elderly osteoporotic population. There are many ways to salvage pedicle screws such as using larger and/or longer size pedicle screws, augmentation or inserting screws in a different trajectory. Lumbar vertebrae were harvested from 4 calves and the bone mineral density (BMD) value was measured. Each vertebra was then placed into a beher-glass filled with hydrochloric acid decalcifier solution for 24 h to obtain osteoporotic specimens. Stage 1: Primary polyaxial pedicle screws were randomly inserted to left or right pedicle. The screws were pulled out in a random order at 10 mm/min with Instron Material Testing Machine. The pull-out strength (POS) results of all specimens were recorded. Stage 2: Revision pedicle screws were randomly assigned to be replaced in the same pedicles by either pedicle hole PMMA augmentation (Group 1) or kyphoplasty (Xvoid TM) augmented pedicle screws (Group 2). The pull-out tests of the specimens were repeated. The mean BMD result of the specimens before the decalcification was 1.6867227.9 and 1.4327157.1 g/cm 2 after decalcification. There was a statistically significant difference between BMD results before and after the decalcification (po0.001). Group 1: The mean POS of primary screws was 344371086 N/m 2. After pedicle hole augmentation, the mean POS was 20887 924 N/m 2. The statistical difference was found between the primary and revision screws POS in group 1 (p¼0.006). Group 2: The mean POS of primary screws was 370271063 N/m 2 and after kyphoplasty augmentation, the mean POS was decreased to 366471057 N/m 2. There was no statistical significant difference between the primary and kyphoplasty augmented screws in group 2 (p¼0.934). There was also significant difference between the pedicle hole versus kyphoplasty augmented revision screw's POS (p¼0.002). There was a strong correlation between POS and BMD for the primary screw (po0.001). However, no statistical significance was obtained between BMD score and both the revision techniques POS (p¼0.808). Even thought pedicle hole PMMA augmentation has been known to be the gold standard for the failed screw in an osteoporotic bone, kyhoplasty augmented pedicle screw seems to be the most powerful salvage technique for a failed pedicle screw. Mathematically, bipedal walking can be modeled as a combination of two serial manipulators, namely stance leg and swing leg, having two revolute type joints (two R–R type serial manipulators). During motion, each leg changes its state from stance leg to swing leg periodically and it is assumed that the legs can only be in the same phase (stance leg phase) at the beginning and at the end of the motion. In walking phenomenon, trajectories of hip and knee articula-tions have great importance for the reason that they guarantee the synchronized movement of the joints thereby yielding a stable walking characteristic.

In this paper, analytical expressions correlating the volumetric flow rate to the pressure drop are derived for the flow of Carreau and Cross fluids through straight rigid circular uniform pipes and long thin slits. The derivation is based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to obtain flow solutions for generalized Newtonian fluids through pipes and our adaptation of this method to the flow through slits. The derived expressions are validated by comparing their solutions to the solutions obtained from direct numerical integration. They are also validated by comparison to the solutions obtained from the variational method which we proposed previously. In all the investigated cases, the three methods agree very well. The agreement with the variational method also lends more support to this method and to the variational principle which the method is based upon.

"In this research, we numerically investigate the physics of a pulsatile non-Newtonian flow confined within a three-dimensional (3D) channel with an idealised stenosis formed eccentrically on the upper wall using the method of large-eddy simulation (LES). A new consistent modelling approach is proposed to perform LES of non-Newtonian flow by implementing the advanced subgrid-scale (SGS) stress model of Wang and Bergstrom (2005) in the current numerical procedure. The proposed modelling approach for LES resolves the previous conceptual inconsistency in modelling the molecular and SGS viscosities, as it warrants that both the molecular and SGS viscosities are non-linear functions of the resolved strain rate tensor. The Womersley number tested in the simulation is fixed at 10.5 and the Reynolds number tested is set
to 1200, which are characteristics of human blood flows in large arteries. An in-house 3D LES code has been modified to conduct our unsteady numerical simulations, and the results obtained
have been validated using two different grid arrangements and reported experimental data."

During diastole, coronary perfusion depends on the pressure gradient between the myocardial tissue and the coronary origin located at the aortic root. This pressure gradient is influenced by the flow field near the closing valve leaflets. Clinical evidence is conclusive that patients with severe aortic stenosis (AS) suffer from diastolic dysfunction during hyperemia, but show increased coronary blood flow during rest. Physiological or pathological factors do not provide an explanation of this effect. Transcatheter aortic valve implantation (TAVI) was shown to decrease the coronary flow along with its main purpose of improving the aortic flow and reducing the risk of heart failure. There is no clear physiological or pathological explanation for the increase of coronary flow due to AS and its decrease immediately after TAVI.
In this manuscript, we present a numerical study that examines the impact of AS and valve replacement on the coronary perfusion during rest conditions. The study compares the hemodynamics of five different 2D numerical models: a baseline “healthy valve” case, two AS cases and two TAVI cases. The analysis used time-dependent computational fluid-structure interaction (FSI) simulations of the blood flow in the aortic root including the dynamics of the flexible passive valve leaflets and the varying resistance of the coronary arteries.
Despite its simplifications, our 2D model succeeded to capture the major effects that dominant the blood hemodynamics in the aortic root, and to explain the hemodynamic effect that leads to the changes in coronary flow found in other in-vitro and clinical studies. It provides an important insight and emphasizes the need for more comprehensive studies on coronary's hemodynamics after valve replacement. There are numerous variations of TAVI designs and it is very difficult and time consuming to cover all the possible models using complex 3D models. The use of a simple 2D model with FSI and varying coronary resistance can be of great help to demonstrate the main features of the design.

The hemodynamic simulation studies have been frequently used to gain a better understanding of functional, diagnostic and therapeutic aspects of blood flow. Many fundamental issues of blood flow, like effects associated with pressure and viscous force field are not fully understood or entirely explained through mathematical formulation and characterization of blood flow is still a challenging task. The study of behaviour of blood flow in the blood vessels also provides understanding of relation of blood flow and development of associated
diseases to the cardiovascular experts. The understanding of the flow dynamics past prosthetic devices such as heart valves, vascular grafts and artificial heart will improve the design of implant and exhibit the better scenario for remedial option of cardiac surgery i.e. open heart surgery, bypass surgery etc.
In this paper the Newtonian effect of blood flow in the portal vein has been simulated for normal flow condition and considering portal hypertension case (with the formation of Thrombosis) and compared and validated with the results (with non-Newtonian effect) of C.C. Botar et al (2010). The 3-D geometry is prepared using 3D CAD software Pro-E and simulation has been carried out using commercial CFD code Ansys FLUENT. It has been observed that considering blood as Newtonian or non-Newtonian has no significant effect on the results for measurement of wall shear stress as the primary
consideration.

N. Herbots, ASU / SiO2 NanoTech, R.J. Culbertson, Q.Xing, D.A. Sell, A.M. Murphy, R.B. Bennett-Kennett*, S.D. Whaley, ASU, Drs. C.H. Sell, MD & H.M. Kwong, Arizona Vitro-Retinal Consultants , T. Kutz, A.S. Benitez, B.J. Wilkens, ASU.

Silicone inter-occular lenses and laparoscopic lenses can fog during surgery. This work solves the problem by modifying water affinity of silicone and acrylic, as well as silica lenses via a bio-identical visco-elastic colloidal emulsion, VitreOx™ [1-5] with a 100% success rate in the lab. Ten surgical trials yielded success rate of 80% with failure inferred to be due to blood proteins.
The protein that prevents coagulation, heparin, during surgery, is investigated. Heparin behaves identically to H2O on hydrophobic surfaces. It does not prevent fogging nor interfere with our anti-fogging emulsion.
Fibrinogen is also investigated because it causes coagulation. Fibrinogen applied to IOL's in various dilutions does prevent fogging. Our research shows that the blood proteins studied as well as whole do not modify the hydro-affinity of the surfaces we treated nor their condensation behavior.
We presently combine the bio-identical visco-elastic colloidal emulsion we have developed with blood proteins to modify tissue growth and cell accumulation on implant surfaces.

[1] U. S. Patent Pending, Filed 11/9/10
[2] PhD Dissertation, Q. Xing, ASU (2011).
[3] N. Herbots, Q. Xing, et al. Nucl. Instr. & Meth. B, IBMM 17 (2010), www.sciencedirect.com/science/article/pii/S0168583X11001170

* Presenter at the AVS

Nowadays, a Ventricular Assist Device (VAD) is a hope of clinic solution to patients with heart failure. This study presents the design of the “trumpet mouth” ventricular cannula (TMVC) connected to a pediatric VAD, optimized to reduce the conditions that generate blood damage. The flow through the TMVC is analysed using Computational Fluid Dynamics (CFD) techniques. The optimization of the TMVC considered the turbulent and byphasic nature of the flow at the systolic and diastolic phases of the cardiac cycle. To assess the hemodynamic performance of the cannula, three geometric parameters were chosen as input or independent
variables in the optimization: the cannula tip curvature angle (θ) and the inner and outer curvature radii (R1 and R2). The output parameters or objective functions were the Modified Index of Hemolysis (MIH), the Modified Index of Platelet Lysis (MILpl) and the fluid pressure drop (ΔP). The mathematical optimization
passed through an enhanced sampling process of combined scenarios of input parameters and thereafter, the response surface was generated using the Kriging algorithm. The selection of the geometric parameters that minimized MIH, MILpl and ΔP were obtained after the application of a Multi-Objective Genetic Algorithm (MOGA) and the generation of Pareto fronts to obtain the points that met the established conditions of reduction of blood damage. The optimal geometric parameters for the ventricular cannula obtained through the optimization process are: θ (27.29 degrees), R1 (0.83 mm) and R2 (0.20 mm). The final results showed a
reduction in MIH for both cardiac phase configurations in the zone of the cannula tip and an overall reduction of 25% and 60% in the MIH and MILpl, respectively, compared to the damage for the cannula with nominal input parameters.

The pulsatile blood flow in an eccentric catheterized artery is studied numerically by making use of an extended version of the fast algorithm of Borges and Daripa [J. Comp. Phys., 2001]. The mathematical model involves the usual assumptions that the arterial segment is straight, the arterial wall is rigid and impermeable, blood is an incompressible Newtonian fluid, and the flow is fully developed. The flow rate (flux) is considered as a periodic function of time (prescribed). The axial pressure gradient and velocity distribution in the eccentric catheterized artery are obtained as solutions of the problem. Through the computed results on axial pressure gradient, the increases in mean pressure gradient and frictional resistance in the artery due to catheterization are estimated. These estimates can be used to correct the error involved in the measured pressure gradients using catheters.

The reaction of the lower limb regional blood flow to the step ergometer
load varies in athletes depending on the nature of the training process (Figure 1). For those engaged
in sport games an increase of blood filling of the vessels of the thigh is characteristic as
well as an increase of the tone of the large caliber arteries at the constant level of venous outflow,
and an increase of peripheral vascular resistance at the pre- and post-capillary levels. This
group was characterized by a high level of venous outflow in the state of relative rest. Athletes
involved in martial arts demonstrated a reaction of the regional blood flow that was in many
ways the opposite: blood filling of the peripheral vessels did not change significantly in response
to the load (a high level of blood filling in the state of relative rest was registered in this group), the tone of large caliber arteries remained unchanged. The decreased pre- and post-capillary peripheral
resistance was registered after the load (by the increased tone of pre-capillaries and its
decrease at the post-capillary level), that leading to increased venous outflow.
Sport games and martial arts are situational sports requiring a complex manifestation of physical
qualities and motor skills in variable modes of motor activity, continuous changes of situations
and forms of action. However, the ratio of static and dynamic loads in the training process of athletes
is different. Apparently, the prevalence of dynamic loads in the training structure of athletes
involved in sport games predetermines high «readiness» of blood filling of lower limb regional
vessels for a rapid response to a load and a high level venous outflow even in the state of rest. In
the group of athletes involved in martial arts, the amount of static loads (especially for the lower
limb muscles) is higher, which leads to high blood filling in the state of relative rest and the venous
outflow enhancement in response to the load through the tone redistribution between the
pre-and post-capillary sphincters.

The flow of fluids at branching junctions plays important kinematic and dynamic roles in most biological and industrial flow systems. The present paper highlights some key issues related to the flow of fluids at these junctions with special emphasis on the biological flow networks particularly blood transportation vasculature.

Blood is a complex suspension that demonstrates several non-Newtonian rheological characteristics such as deformation-rate dependency, viscoelasticity and yield stress. In this paper we outline some issues related to the non-Newtonian effects in blood circulation system and present modeling approaches based mostly on the past work in this field.