ESB Keynote Lecture—Dublin 2000An introduction to biofluid mechanics—basic models and applications
Introduction
Biofluid mechanics describe the kinematics and dynamics of body fluids in humans, animals and plants. We distinguish between external flow around bodies as in bird flight or the airflow around bodies in air conditioning situation, and internal flow through bodies such as blood flow through blood vessels.
Hemodynamics deals with body fluids in humans. Classical hemodynamics deals with in vivo and in vitro measurements of pressure, flow and resistance. Modern biofluid mechanics measures and analyzes local time-dependent velocities and flow in blood vessels, the respiratory system, the lymphatic system and the microcirculation (Hosoda et al., 1994; Mosoro et al., 1989; Kerber and Liepsch, 1994; Stein, 1981).
Biofluid mechanic factors must be taken into consideration in clinical areas such as end-to-end and end-to-side anastomoses; artificial heart, organ and vessel development; urological measurements and artificial urethra; shock wave treatment of kidney stones; blood rheology; mass and material transport through membranes, wave spreading, diffusion processes, and the influence of airflow around bodies. To investigate all these processes, it is important to do model experiments. Models have many advantages compared to in vivo and in vitro experiments; most importantly, the experiments are reproducible. Individual flow parameters, such as geometry, non-Newtonian flow characteristics, wall elasticity, steady and pulsatile flow can be studied individually. Practical applications include testing of catheter techniques and stents, and training for stent implantation.
The most important application of biofluid mechanics is in research into atherosclerosis and aging (Caro, 1981; Chien, 1988; Liepsch et al., 1981; Liepsch, 1990; Naumann and Schmid-Schönbein, 1984; Niimi, 1979; Stehbens, 1993; Texon, 1980; Yamaguchi and Hanai, 1990; Yoshida et al., 1988). Fundamental studies analyze the flow parameters mentioned above. Hemodynamics, the consistency and rheology of blood and, finally, the geometry of the blood vessels all contribute to atherogenesis.
The entire flow field in bends and bifurcations must be measured to obtain exact velocity vectors. At present, MRI in vivo velocity measurements take far too long, requiring patients to remain motionless for extended periods. Color Doppler ultrasound techniques look promising but the local resolution is still not high enough. So, model experiments with high spatial and temporal resolution techniques such as laser-Doppler-anemometry are necessary. We have studied the flow in various silicon rubber models of the aortic arch with abdominal aorta and kidney arteries; femoral arteries, coronary arteries, and carotid artery. From these detailed macroscopic measurements it is possible to calculate shear stresses very precisely. Shear stresses act not only on endothelial cells, but also affect the intermedia. Particles and blood cells in re-circulation zones must be investigated more closely. Normally, they do not remain inside flow separation areas for long periods, however, a few particles or an agglomeration of particles, occasionally rotate over several periods in these zones, as visualized with our photoelasticity apparatus with a birefringent solution.
Section snippets
Flow parameters and experimental methods
Many scientists have studied the flow behavior in bends and bifurcations; however, most studies have been done in rigid or simplified models (Karino and Goldsmith (1977), Karino and Goldsmith (1979); Ku and Giddens, 1983; Palmen, 1994). An overview is given in Zheng et al. (1992).
We used true-to-scale, 1:1 models, so that the geometry of both pathological and healthy blood vessels was correct (Liepsch et al., 1992). The following flow parameters were studied: geometry, steady/unsteady flow,
Model fluids
To simulate the flow characteristics of blood, a blood analog was developed which has a refraction index identical to that of the model wall. The fluid consists of 51% by weight aqueous Dimethylsulfoxide into which various polyacrylamides are added (0.0035% Separan AP-302 and 0.0025% AP-45, Dow Chemical). The rheological behavior of this fluid is nearly identical to that of blood with a hematocrit of 46%. Fig. 2 (top) compares the viscosity over the shear rate of the model fluid at 21°C with
Carotid artery models
The geometry and influence of the bifurcation angle (27–49°) between the internal and external carotid arteries has been studied extensively (Liepsch et al., 1998). It is important to remember that these two branches do not normally lie in one plane. The spatial situation is important and must be considered. The bifurcation angle influences flow separation. With larger bifurcation angles, the flow separation regions extend slightly. However, these differences in the flow behavior are small
Patches in carotid arteries
Plastic patches are used in vessel surgery to restore an area from which a stenosis has been removed. The sizes of these patches vary. Three different types, similar in length, but different in width or positioning were studied. The patches were stitched into a vessel removed at autopsy. A 1:1 true-to-scale silicon rubber model was prepared from this vessel. The procedure has been described several times (Liepsch et al., 1992). Flow visualization studies with dyes demonstrated that in the
End-to-end, end-to-side anastomoses
The amount and nature of flow disturbance created by an anastomosis depends largely on the vessel in which the anastomosis is done. Additional flow disturbances are created by end-to-end anastomoses (Maurer et al., 1979). Flow studies in stenosed models and in models with patches of the arteria profunda femoralis showed that the highly disturbed flow in the stenosed areas could be restored with a profunda plastic. If a total femoralis–superficialis blockage exists, the dead-end branch should be
Arteriovenous fistulas
Several arteriovenous fistula models with lengths of 0.5, 1.0 and 2.0 cm were prepared for distal bypass operation. The elastic silicon rubber models were prepared from original polytetrafluorethylene (PTFE) grafts of 6 mm diameter. High velocity fluctuations and vortices were found in small fistula models. The 2 cm common ostium fistula resulted in a smooth flow pattern (Maurer et al., 1992, Veith, 1992). Laser vibrometer studies in the arteriovenous fistulas of the carotid artery in rabbits
Aneurysms, stents and veins
Many flow studies have been done in rigid and elastic models with aneurysms (Kerber et al., 1996; Liepsch et al., 1987; Steiger et al., 1989; Ujiie et al., 1994). While the wall structure must be considered in any study of the genesis of aneurysm, the flow probably has the greatest influence. Current considerations include how to determine which aneurysms will grow and rupture and which will not. These questions play an important role in determining a course of therapy or surgery. The forces
Ultrasound catheters
Tests have been conducted in stenosed models to determine whether the insertion of an ultrasound catheter may provide the physicians with false information or with information that may be incorrectly interpreted. Ultrasound catheters are used to measure the blood velocity in vivo in the coronary or femoral artery. Previous experiments with older catheter designs showed differences of >50% of the velocity (Liepsch et al., 1995). Newer catheters are smaller in diameter (0.34 mm). A smaller design
Numerical studies
It is also possible to use the fundamental equations for computational fluid dynamics. Numerical results come very close to physiological flow conditions if the boundary conditions are known. Scientists (Perktold and Liepsch, 1994; Perktold and Rappitsch, 1995; Yamaguchi and Hanai, 1990) now use numerical programs to simulate flow behavior. This is done, for example, with finite element methods. In such studies, it is important that the geometry is precisely reproduced. With modern laser and
Conclusions
Velocity distribution and the hemodynamic forces acting on the vessel wall and blood cells are very important. Normally under physiological flow conditions, the flow is neither fully developed laminar flow nor turbulent flow. It can be described as laminar flow with periodically returning vortices. These vortices are created at the beginning of the diastolic phase. Flow separation regions form only in specific areas of the circulatory systems i.e. at bends and bifurcations especially in the
Acknowledgments
Some of the studies were made possible by the support of the Deutsche Forschungsgemeinschaft under contract Li 256/1-42. Thanks are due to the many doctoral candidates who helped with the experiments. Thanks also to Joyce McLean for discussions and editorial support.
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