6.2.1 Introduction
Experiments testing blood flow in tubes with diameters under 300 μm show that the hematocrit is lower in the tube than at the exit point because hematocrit at the exit is weighted by the local velocity. This phenomenon is known as the Fahraeus effect and it arises due to the two-phase nature of blood flow [159]. As a result of red cell aggregation in the center of blood vessels due to the Fahraeus effect, white blood cells are marginated to the vessel walls, where they are better able to roll along the endothelium and come into contact with various ligands [160]. We aimed to take advantage of this behavior by immobilizing IL-8 on the inner lumen of fibers that would act as the artificial microcirculation in our cell programming device.
To facilitate immobilization on and testing of the inner fiber lumens, we potted the fibers in modules resembling scaled down dialyzers, approximately 1/400th of a standard dialyzer containing 10,000 fibers. The completed fiber module can be seen in Figure 82. The same process of immobilization and IL-8 quantification was carried out with these modules. The protocols were modified to accommodate the different fiber configuration and chemistry, as described in Section 6.3.
Figure 82. 16 cm long fiber module containing 25 aminated polysulfone fibers.
The modules were tested for leaks and fiber blockage prior to using them for any experiments. To do this, we used the Hagen-Poiseuille equation for laminar flow in a cylindrical tube [86]: 4 1 2 8 d LQ P (9)
Where ∆P is the theoretical pressure drop, μ is the dynamic viscosity, L is the length of the tube,
Q is the volumetric flow rate, and d is the diameter of the tube. Once the modules were
confirmed to be free of any blockages or leaks, they were used for IL-8 immobilization (see Section 6.3).
6.2.2 Methods
The fibers modules were fabricated in the lab from various polycarbonate components. The body of the device was a clear polycarbonate tube, either 7/5 or 15 cm long with a 0.5 cm inner diameter. Two holes were drilled in the body of the tube into which two female luer lock polycarbonate fittings were glued to serve as the shell side ports. For each module, either 25 fibers (15 cm long modules) or 50 fibers (7.5 cm long modules) were bound together and fed through the module. UV-curing glue (Permatex; Solon, OH) was used to pot the fibers in the device before being trimmed to prevent glue from entering the tube side of the fibers. Once the
glue had cured, the potted ends were trimmed and capped with polycarbonate female luer lock fittings.
Pressure drop measurements across the device were taken to ensure the consistency of the fiber modules. The tube side inlet of one module was first connected to a syringe pump (Harvard Apparatus; Holliston, MA) filled with DI water. The tube side outlet was connected to tubing draining into a beaker. The shell side was filled with DI water and both the inlet and outlet ends of the module were connected with a three-way stopcock and water-filled tubing to a pressure transducer. The setup for the pressure versus flow rate experiment can be seen in Figure 83.
Figure 83. Pressure versus flow rate test setup.
The pressure transducer reported voltages which were recorded and then converted to a pressure using the following relationship which was specific to the pressure transducer used:
Pressure (mmHg)= 20.119 * Voltage (V) (10)
Inlet and outlet pressures were measured in duplicate for the following flow rates: 1.0, 0.8, 0.6, 0.4, 0.2, and 0.0 ml/min. The slope of the pressure drop versus flow rate line was compared to
Syringe pump
Pressure
transducer
Voltmeter
Fiber module
the value of R obtained from the following equation, obtained from the Hagen-Poiseuille equation (Eq. 9):
R128L
d4N (11)
Where R is pressure drop over flow rate and N is the total number of fibers. Modules for which the slope of the pressure drop versus flow rate data was not within 15% of the theoretical R value were not used.
6.2.3 Results and Discussion
Scaled-down fiber modules based on full-size clinical dialyzers were fabricated to allow for immobilization of IL-8 on the inner lumen of fibers. Figure 84 shows a representative data set for the pressure drop versus flow rate characterization test. These modules were fabricated using a 15 cm polycarbonate body containing 25 aminated polysulfone fibers (described in Section 6.3), giving a theoretical R value of 15.52 mmHg∙ml/min for each module.
Figure 84. 15 cm long fiber module containing 25 aminated polysulfone fibers.
In the data shown in Figure 84, two of the modules failed because their R values were too far outside the acceptable range of ±15%, corresponding to 13.19-17.85 mmHg∙ml/min. Failures due to blocked fibers are characterized by a slope that is too high, as the blocked fibers effectively decrease the numbers of fibers through which flow occurs. Conversely, leaking within the module due to broken fibers causes a decrease in pressure drop and modules fail the pressure drop versus flow rate test because of an unacceptably low slope. Data for the 7.5 cm, 50-fiber modules are not shown because the value of N∙L for the two types of devices remains the same and therefore their theoretical R value does not change.
y = 24.856x R² = 0.9972 y = 17.878x R² = 0.994 y = 12.108x R² = 0.9985 0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1
pr
ess
ur
e
dr
op
(mmH
g)
flow rate (ml/min)
Fail
(blockage) Pass