3.1.

Calibration Experiments

Calibration experiments were conducted to quantify the ability of the system to measure velocities at high frame rates using the capturing method described earlier. Two separate experiments were run: one to assess the sensitivity and accuracy of the velocity measurements, and another to determine the system’s ability to estimate the velocity and radial position of particles moving through a tube of similar diameter to the microlymphatics. For the first set of experiments, a wheel was used that rotated at various revolutions per minute and was positioned under the microscope for imaging. The wheel consisted of a motor-driven rotating disk with markings on it at a fixed radial distance. Image sequences were recorded with the high-speed video camera [Dalstar64K1M, 1M fps $245\times 245$ , charge-coupled device (CCD) camera] at a fixed radial distance $\left(28.5\mathrm{mm}\right)$ on the wheel while varying the angular velocity, so that a range of velocities could be measured that would be similar to those that were expected to occur physiologically (up to $15\mathrm{mm}∕\sec$ ). Multiple measurements were taken while maintaining a constant speed to quantify the sensitivity of such measurements.

For the second set of experiments, we designed a physical model that simulated the sizes and arrangements of lymphocytes flowing through a microlymphatic vessel using a suspension of microspheres that was passed through a glass capillary tube. A solution of sodium chloride was prepared that matched the specific gravity of the microspheres used to simulate the white blood cells. The saline solution also served to dilute the $7.12\text{-}\mu \mathrm{m}$ -diam microspheres to a concentration of about $5\bullet {10}^5\text{microspheres}∕\mathrm{mL}$ , approximating the size and count of lymphocytes. A glass capillary tube was heated and pulled out to a diameter of $140\mu \mathrm{m}$ , equivalent to the diastolic diameters of the lymphatic vessels we are studying. These values were chosen to mimic the dimensions that occur in the microlymphatics being measured in situ as closely as possible. The fluid was passed through the tubing by applying a constant pressure with a level pressure head that could be moved up and down to control pressure. The outflow resistance was set to yield velocities that are similar to those measured in situ. The tubing was magnified using the same microscope optics used to record the lymphatic vessels. The images were recorded at a frame rate of $500\text{frames}∕\sec$ . Velocity measurements were made at fixed moments in time $\left(25\mathrm{ms}\right)$ for a range of flow rates $(15\text{to}250\mu \mathrm{L}∕\mathrm{hr})$ . The actual flow rate was measured by using a bubble tracking technique, and compared to the flow rates calculated from the images.

3.2.

In Situ Lymph Velocity Measurements

Three male Sprague-Dawley rats weighing $180\text{to}220\mathrm{g}$ were used for these experiments. The rats were housed in an environmentally controlled, American Association for Accreditation of Laboratory Animal Care approved vivarium. Each animal was fasted for $12\text{to}15\mathrm{h}$ before the experiments, while water was available ad libitum. Each rat was anesthetized with an intramuscular injection of Fentanyl-Droperidol $(0.3\mathrm{mL}∕\mathrm{kg})$ and Diazepam $(2.5\mathrm{mg}∕\mathrm{kg})$ . Supplemental doses of the anesthetic were given as needed. An abdominal incision was made to gain access to the mesenteric lymphatic vessels. A loop of the small intestine was exteriorized through the incision and gently positioned over a semicircular viewing pedestal on a Plexiglas preparation board. A lymphatic vessel was centered over an optical window in the preparation board. The exteriorized tissue was perfused with a phosphate buffered solution supplemented with HEPES $\left(10\mathrm{mM}\right)$ and 1% bovine serum albumin. The solution was prewarmed to $38°\mathrm{C}$ , and the pH adjusted to 7.4. The temperature of the exteriorized tissue and the animal’s core were maintained at $36\text{to}38°\mathrm{C}$ . The preparation board was placed on the stage of an intravital microscope (Zeiss), and the lymphatic vessel was observed at a magnification of 100 to $200\times$ using an $80\text{-}\mathrm{mm}$ projective lens, a $10\times$ water immersion objective, and a variable magnification intermediate lens. The depth of field for this optic setup was approximately $14\mu \mathrm{m}$ . All the experiments were digitized with the high-speed video camera (Dalstar64K1M, 1M fps $245\times 245$ , CCD camera) using the capturing technique described previously. After imaging and recording the specimen, the image sequences were loaded for analysis in Epix, an image analysis software package using the three point measuring method described in Sec. 2. To record the wall measurements, a sequence of images was loaded through a program written in Matlab, and three coordinates were selected with a cursor along the wall, as shown in Fig. 1. This was done for sets of 51 images for the entire sequence of 6258 images. This ensured that the luminal diameter was being measured at the same location for the entire recording sequence. These coordinates were then imported into a program to make all of the necessary calculations. Lymphocytes were tracked manually by recording the location of the coordinates of the lymphocyte. An arbitrary lymphocyte within the field of view and depth of focus was chosen, and that particle was tracked for $24\mathrm{ms}$ . Software was developed to import these coordinates and calculate the lymphocyte velocity, the distance of the particle from the centerline, and the volume flow rate.

4.1.

Calibration Experiments

Calibration experiments were conducted to ensure the accuracy of the camera timing and our velocity estimation procedure. The calibration wheel was imaged at ten different velocities three times each, and the velocities were calculated from the images and compared with the actual velocity of the wheel to test for system accuracy and sensitivity. Figure 2 shows the actual versus measured velocities for all measurements $(R^2=0.999)$ . The system showed accuracy with less than 2% error when compared to actual velocities, and a sensitivity that yielded an average standard deviation of $\sim 0.17\mathrm{mm}∕\sec$ for multiple measurements at a given velocity.

Fig. 2

Actual versus measured velocities of in vitro calibration wheel with error bars.

For the second set of calibration experiments, images were recorded while flowing fluid and microspheres through a synthetic vessel. Velocities and the distance of the particles from the centerline were measured five different times throughout the sequence of flow for eight different flow rates. Figure 3 shows the actual versus average predicted flow rates for each of the eight measurements along with error bars $(R^2=0.999)$ . Since the Reynolds number is very small $(<5)$ , the volume flow rate could be calculated from the particle’s velocity and position given by Eq. 5, which is derived from Navier-Stokes for laminar flow through a tube ( $Q=\text{volume}$ flow rate, $V_{\overline{r}}=\text{velocity}$ of particle measured at some distance $\overline{r}$ from the center, $r=\text{vessel}$ radius).

Fig. 3

Actual versus measured volume flow rates of microspheres flowing through $140\text{-}\mu \mathrm{m}$ glass tube.

4.2.

In Situ Experiments

Preliminary results for several contractions for three different rats have shown the viability of this system to measure the velocity in the microlymphatic vessel of the rat while simultaneously recording the diameter of the vessel [Figs. 4(a), 4(b), 4(c) ]. Lymphocytes velocities ranged from $-1\text{to}7\mathrm{mm}∕\sec$ . As can be seen by the three figures, the pattern and dynamic range of the diameters and the contraction frequencies varied from rat to rat. Quantitative measurements of fluid velocities in the microlymphatics were recorded through the entire contraction cycle and fast video microscopy was used to measure velocities greater than $1\mathrm{mm}∕\sec$ for the first time. As expected, the velocity of the lymph fluid fluctuates in a cyclical pattern at the same frequency as the wall contractions with a slight phase difference. The range of values measured for the lymphocyte velocities is much larger than previous systems were capable of measuring using standard video microscopy. For example, the typical field of view when applying the necessary magnification to these vessels is $250\times 250\mu \mathrm{m}$ . To track a particle, one must measure that particle’s location at two different times. This means that the particle can travel no further than $125\mu \mathrm{m}$ to ensure thatthe particle is captured twice before it leavesthe field of view. Therefore, the maximum velocity a $30\text{frame}∕\sec$ camera could theoretically measure is $3.75\mathrm{mm}∕\sec$ $(\text{velocity}=\text{distance}∕\text{time}=125\mu \mathrm{m}∕0.033\mathrm{s})$ . This is under an ideal scenario in which one could resolve the $125\mu \mathrm{m}$ “streak” that would occur as a result of the moving particle when imaging at $30\mathrm{fps}$ (assuming that you are not electronically shuttering). This is illustrated by the images shown in Figs. 5(a), 5(b), 5(c) . These images were taken during the peak velocity measurement at time $t=6.08\sec$ from Fig. 4(a), which is during a peak velocity measurement of $5.8\mathrm{mm}∕\sec$ (larger than the $3.75\text{-}\mathrm{mm}∕\sec$ limit). As seen by comparing Figs. 5(a) and 5(b), which occur $2\mathrm{ms}$ apart, both particles appear in the field of view. However, in Fig. 5(c), taken $33\mathrm{ms}$ after Fig. 5(a), neither lymphocyte is in the field of view. It should be noted that each image has been subtracted from the image immediately following it to remove the background and enhance objects in motion. Coordinates of the lymphocyte are also shown to illustrate the displacement of the lymphocyte from Figs. 5(a) and 5(b). In conclusion, a conventional $30\text{-}\mathrm{fps}$ imaging system is too slow, given the velocities that we have measured in situ.

Fig. 5

(a) In situ image taken during $5.8\mathrm{mm}∕\sec$ fluid flow at time $t=0$ . The coordinates correspond to the lower lymphocyte. (b) In situ image taken at time $t=2\mathrm{ms}$ . The lymphocyte has moved $12\text{pixels}$ . (c) In situ image taken at time $t=33\mathrm{ms}$ . Neither lymphocyte is present in the image; however, new ones have appeared.

Fig. 4

(a), (b), and (c) Vessel lumen diameter (mm) and lymphocyte velocity (mm/sec) for $10\text{-}\sec$ intervals for three rats.

The maximum contractions observed in the microlymphatics of rats can be 60%, with average contractions being approximately 40 to 50% of the vessel diameter.⁵ In this particular set of rats, the contractions were about 40% of the maximum diameter. This would lead one to believe that in vessels with even larger contractions, the maximum velocities observed would be even greater than the $7\mathrm{mm}∕\sec$ observed in this case, further emphasizing the need for a fast imaging system. Figure 6 shows the estimated volume flow rate from the datasets shown in Fig. 4(a). Similar plots can be generated from our measurements shown in Figs. 4(b) and 4(c).

Fig. 6

Estimation of volume flow rates $(\mu \mathrm{L}∕\mathrm{hr})$ from velocity data in Fig. 4(a).

There have been several other techniques that have been developed over the years to quantify flow and map outthe structure of both blood and lymphatic flow.^{3, 8, 9, 10, 11, 12, 13, 14, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36} The most common approaches include fluorescence techniques,^{9, 11, 14, 23, 24, 37, 38} Doppler Flowmetry,^{27, 28, 29, 30, 31, 32, 33, 34, 35, 36} and video microscopy.^{5, 10, 16, 18, 20, 21, 22, 39, 40, 41} While fluorescent techniques are useful in obtaining bulk flow information, one big disadvantage is that injection is often difficult in smaller vessels, and the introduction of foreign fluorescent particles into the system is likely to alter the contraction cycle that normally occurs physiologically.

While Doppler methods have been used with microscopy to measure flow for over $30\text{years}$ ,²⁷ flow through lymph vessels has proved to be more difficult, as the method is dependent on the presence of numerous scatterers flowing through the system. In most lymphatic vessels, the presence of particles, particularly white blood cells, is much scarcer than red blood cells in the blood. The velocity patterns in lymphatic capillaries are also much more complicated due to the presence of backflow and multiple valves, as discussed previously. These complications make a Doppler approach much more difficult for the lymphatic system than for blood flow measurements. However, one group has successfully used a Doppler-based approach to acquire direct measurements of lymph flow in the posterior lymph heart of toads.³⁶ In this specific case, many of the disadvantages discussed before do not occur, as the lymphatic systems of most amphibians behave more like the circulatory system with a pumping organ pushing flow through the vessels.

Video microscopy analysis has long been the gold standard for imaging flow through vessels and measuring vessel diameter.^{5, 10, 14, 21, 22, 39, 40, 41} The technology itself has existed for many decades; however, recent developments in computing speed have allowed for more exhaustive image analysis algorithms to be developed. Almost all applications of such systems for lymph flow have been captured with a standard video camera at a rate of $30\text{frames}∕\sec$ . This has proved acceptable for measurements in contraction speed and average lymph flow, as the velocities that occur in such cases are not beyond the speed of the camera (less than $1\mathrm{mm}∕\sec$ for microlymphatic flow, given a magnification of around 100 to $200\times$ ). However, our group observed in initial experiments highly blurred particles during contractions that indicated that velocities of local flow during the phasic contractions are much higher than those that current video systems are capable of measuring. For example, a particle moving at $7\mathrm{mm}∕\sec$ , if imaged with a conventional video microscopy system, would in theory be a blurred streak of about $250\mu \mathrm{m}$ in length. The problem is that the contrast between white blood cells and the lymph media is so poor given the complex in situ image that the length of this streak cannot be measured, or even seen in some cases, and the velocity cannot be deduced. Therefore, we pursued the use of a high-speed camera, using capture rates of up to $500\text{frames}∕\sec$ , to measure these higher-end velocities. The advantage of this system is the ability for excellent resolution, both temporally and spatially.