Measurement of internal diameters of capillaries and glass syringes using gravimetric and optical methods for microflow applications

Introduction

In the last decade, new flow sensing methods for the calibration of microflow devices have been developed [1], [2], [3]. These methods rely on optical technology and a key element of the setup is the knowledge of the inner diameter of the liquid displacement tube. The measurement of the inner diameters below 1 mm is only achieved by very few NMIs all over the world. Some of the used techniques are 3D Coordinate Measuring Machine, 1-D comparator and focusing microscope and 1-D comparator with mechanical probe and laser interferometry. This subject is also of interest for some researchers, for example F. Wolf [4] has used the stereo microscope software that employs a high-resolution camera and image analysis to measure capillaries of 0.5 mm diameter with 0.4% expanded uncertainty and S. Kwon et al. [5] has employed the X-ray image technique to a capillary of 0.1 mm diameter with 1.2% expanded uncertainty. All these techniques use very expensive instrumentation, and their handling needs experts and personnel with very specific training.

This work has the objective of presenting two new techniques for inner diameter measurements of both glass capillaries and precision glass syringes used in displacement pumps, the gravimetric method [6, 7] and the optical method [2], performed in the frame of EMPIR – project MeDDII – Metrology for Drug Delivery [8], is a cooperation between IPQ – Portuguese Institute for Quality, UNIDEMI- Department of Mechanical and Industrial Engineering of the NOVA School of Science and Technology, CETIAT – Centre Technique des Industries Aérauliques et Thermiques and CMI – Czech Metrology Institute.

The gravimetric method is the most common method for volume determination with very low uncertainties, typically 0.01% (k=2) [9]. If the liquid volume inside a specific tube length is known, it is possible to determine its average inner diameter. This can be achieved by volume determination at reference lines in specific positions, in order to cover the majority of the length of the instruments.

The optical method [2] used is based on the front track principle that uses a high-resolution camera and ImageJ software, to determine the diameter at both ends of each capillary, since it’s assumed that the inner diameter can varies its linearity from end to another.

To validate the developed methods, a comparison was made between IPQ, CETIAT and CMI. The experiments done by each partner are explained in the following Table 1.

Experimental setup gravimetric method

The gravimetric method [6, 7] used by IPQ consists of measuring the liquid volume of a specific length of the glass tube. Knowing these two quantities it is possible to determine the average inner diameter of a capillary or syringe. The experimental setup involved the use of the following components: a Mettler Toledo AX 26 balance, with an evaporation trap, that has 20 g maximum capacity and 1 µg resolution, a glass syringe or capillary, a temperature sensor PT100 of 0.001 °C resolution, a calibrated caliper with 0.05 mm resolution and ultra-pure water (Figures 1 and 2).

Figure 1:

Gravimetric experimental setup for the syringe.

Figure 2:

Gravimetric experimental setup for the capillary.

The procedure for the syringe internal diameter calibration consists of the following steps:

1. Choose 3 different reference positions/lines along the length of the syringe which according to ISO 8655 [6, 7];

2. Measure the ambient temperature (with a thermometer of resolution 0.01 °C) and humidity (with a hygrometer of resolution 0.01%), and atmospheric pressure (with a barometer of resolution 0.01 hPa) to determine the air density [10];

3. Measure the water temperature in the water vessel before filling the syringe;

4. Fill the syringe completely taking care that there are no bubbles inside;

5. Manually align the piston with the 1st reference position (nominal volume);

6. Remove any water outside the tip of the syringe so it is not transferred to the weighing vessel upon delivery;

7. Register the mass value read in the balance before delivering the liquid;

8. Deliver the liquid of the syringe to the weighing vessel by touching the wall of the vessel, just above the water level, without touching the water inside the weighing vessel. Also, any splashing must be avoided;

9. Register the mass value read in the balance after delivering the liquid;

10. Measure the displacement of the piston inside the syringe, manually, using a caliper, from the initial scale position to the chosen reference line;

11. Repeat steps 2–9, ten times for the other two reference lines (50% and 10%).

The procedure for the capillary internal diameter calibration consists of the following steps:

1. Mark three reference lines in the capillary vertically with a pen, distributed equally within the length of the capillary preferably at 90, 50 and 10% of the total length of the capillary;

2. Measure the water temperature, ambient temperature and humidity, and atmospheric pressure;

3. Connect the capillary tube to a filling/discharging device (e.g. syringe), assuring that the connection is airtight and there are no bubbles inside the syringe;

4. Fill the syringe with a small volume of water, then aspire air in order to create a volume of air inside the capillary (Figure 3);

5. Fill the capillary to the first reference line, manually aligning the meniscus with the top side of the line;

6. Remove any water outside the capillary;

7. Register the mass value read in the balance before delivering the liquid;

8. Deliver the liquid inside the capillary to the weighing vessel by touching the wall of the vessel until the air volume is reached, just above the water level, without touching the water inside the weighing vessel. Also, any splashing must be avoided;

9. Register the mass value read in the balance after delivering the liquid;

10. Measure the displacement of the meniscus inside the capillary, manually, using a caliper, from the tip of the capillary to the top side of the line;

11. Repeat steps 2–10, ten times for each reference line.

Figure 3:

Water and air interface, meniscus alignment.

The diameter of the capillaries and the syringes are determined in 3 different positions to determine uniformity of the volume-per-length between chosen segments of the lumen.

Theoretical model and calculation of uncertainty

The volume [6] is calculated by the following equation (1):

Where: V 20 – Volume at 20 °C, µL, M – Mass, mg, ρ w – Water density, mg/µL, ρ A – Air density, mg/µL, ρ B – Density of weighs, mg/µL, γ – Capillary/syringe material coefficient of expansion, °C⁻¹, T – Water temperature, °C

Then, the internal diameter value of the syringe or the capillary is determined by the equation (2):

Where: D – Diameter, mm, V – Volume, µL, d – Meniscus or syringe piston displacement, mm.

The average diameter is determined based on the 3 chosen positions.

The measurement uncertainty is normally estimated according to the Guide to the expression of Uncertainty in Measurement [11].

The main sources of uncertainty considered were the following:

1. Distance, u _d : distance between the meniscus reference line and the end of the volume delivery position;

2. Volume, u _V : volume within the distance length;

3. Reproducibility, u_repr: variation within the difference reference positions.

The standard uncertainty of each component is described and presented in Table 2.

The sensitivity coefficients, c _i , of each component can be calculated by the following equations:

For the reproducibility, the sensitivity coefficient is equal to 1.

The combined uncertainty of the diameter is given by equation (5).

And the expanded uncertainty, U (D), is calculated using equation (6).

Where k is the coverage factor with a probability of 95% and is evaluated by the effective degrees of freedom (ν _eff ) by the Welch-Satterwhite formula [9], as follows:

Measurement results gravimetric method

Seven glass syringes of ILC gas tight were calibrated 2 times each in 3 reference points by IPQ. 3 Glass capillaries of different internal diameter were calibrated three times each in 3 reference points. The results of the calibration of the seven syringes are presented in Table 3 and Figure 4.

Figure 4:

Syringes uncertainty.

In Figure 4 is presented a chart that relates the syringes volumes with the uncertainty obtained in each syringe calibration. This relation can be approximated by a linear equation, that can be used to estimate the uncertainty for different syringes volumes.

The results of the calibration of the three capillaries are presented in the Table 4. A sample of 3 capillaries of the same nominal diameter was used. The capillaries were calibrated at 3 reference points.

Two examples are presented in the following tables concerning uncertainty determination for the gravimetric method. These examples are related to the maximum volume and distance determined for each instrument.

Table 5 presents the results obtained for the diameter calibration of the 1 mL syringe in one reference point.

Table 6 presents the results obtained for the diameter calibration of the 1.61 mm capillary in one reference point.

Experimental setup optical method

The optical method used by CETIAT is based on the front track principle that uses a high-resolution camera and ImageJ software, to determine the diameter at both ends of each capillary.

The capillary tubes were held vertically and slightly tilted towards the camera in a way that its projection on the (x, y) plane is perfectly parallel to the camera’s axis. The tube’s end appears like an ellipse and the diameter in this case is the undistorted major axis of the ellipse. The following drawing illustrates the alignment (Figure 5).

Figure 5:

Illustration of the capillary alignment.

The images of the capillaries’ ends have been acquired using a 12 Mega Pixels resolution JAI SP-12000M-CXP4-F camera, a Qioptiq Optem FUSION telecentric Lens System with a motorized zoom, and a Schott KL 2500 LED cold light source (Figure 6). The telecentric tube lens makes negligible the lens distortion, which has been measured at 0.75 µm for the zoom factor used in this article.

Figure 6:

Optical experimental setup for the capillary.

The measurements have been carried following the steps below:

1. A Gaussian blur filter was applied on each image to reduce the noise;

2. The edges of the capillary’s end were detected using the Canny Edge detection filter in Python/OpenCV;

3. The intensity profile along the major axis of the ellipse was extracted and finally;

4. The diameter in pixels was determined from the obtained intensity profile.

The pixel sizes used to convert the diameters from number of pixels to micrometers were obtained from the calibration of the camera using a calibrated objective micrometer as explained in [2], in order to assure the traceability to the International System of Units (SI).

Uncertainties were calculated by considering the camera resolution and calibration, and the extracted intensity profiles, including the edges detection method and thickness as uncertainty source. A complete uncertainty budget description and quantification is available in [3].

Measurement results optical method

CETIAT determined the diameter of glass capillaries. The obtained results using the optical method for a set of 9 capillary of 500 µm nominal diameter are shown in Table 7. The fabrication tolerance given by the manufacturer is 10% of the given nominal diameter.

The obtained average results for all capillaries are shown in Table 8. The diameters values obtained at the different ends of the capillaries are different because of inner diameter inhomogeneity, given the uncertainty showed in Table 8.

Experimental setup coordinate measuring machine

At CMI the calibration of the inner diameter of the syringe is done using a coordinate measuring machine (Figure 7), this is performed by scanning the measuring points on the surface of the object to be measured. This scanning is executed by a contact scanning system. The XYZ coordinates of the measured points are transferred to a computer software, which further processes them. The processing is done by comparing the points with geometric primitives.

Figure 7:

Experimental setup coordinate measuring machine.

This procedure is already implemented by CMI and accredited by Czech Institute of Accreditation. The CMCs are available for consultation.

Measurement results with a coordinate measuring machine

CMI used a coordinate measuring machine to determine the inner diameter of the ILC 1 mL syringe in 5 different positions, as described in Table 9. CMI obtained an average value of 4.605 mm with an expanded uncertainty of 0.001 mm.

Validation results

To validate the developed methods for diameter determination, a bilateral comparison between IPQ and CETIAT was performed using the average value of a set of capillaries of 0.5 mm nominal diameter.

The average results of the capillaries determined by IPQ and CETIAT are compared in Figure 8.

Figure 8:

Comparison capillary 0.5 mm.

The results obtained are very similar between both laboratories, with IPQ having larger uncertainty values. Also, a bilateral comparison between IPQ and CMI was performed using the 1 mL syringe.

The average results of the of the 1 mL syringe diameter determined by IPQ and CMI are compared in Figure 9.

Figure 9:

Comparison syringe 1 mL.

The results obtained are very similar between both laboratories, with IPQ having larger uncertainty values.

In order to determine the consistency of the results between the laboratories (IPQ, CETIAT and CMI) the E_n number statistics [12] was applied, according to equation (8) to the results described in Figures 7 and 8.

The results are considered consistent with the reference value if |E_n| <1.

The obtained E_n results for the 0.5 mm capillary are presented in Table 10.

It can be seen from Table 10 that the results obtained by IPQ and CETIAT for the 0.5 mm capillary are consistent with the |E_n|<1. A validation of CETIAT’s internal diameters measurements method, by comparison with a traceable confocal microscope, is currently undergoing and will be published in 2022 in order to validate CETIAT’s method for the whole range of diameters.

The obtained E_n results for the 1 mL syringe obtained by IPQ and CMI are presented in Table 11.

It can be seen from Table 10 that the results between IPQ and CMI are consistent with |E_n| <1.

Calibration of a Nexus pump

To understand the influence of the diameter calibration in volume flow rate determination, a Nexus 3,000 syringe pump was calibrated using the interferometry method [1] at four different flow rates using a 1 mL glass syringe.

The calculation was performed using the syringe diameter determined by the caliper and by the gravimetric method.

Table 12 shows the flow results obtained when using a 4.60 mm diameter with an uncertainty of 0.03 mm determined by the caliper [1].

Table 13 shows the flow results obtained using the 4.607 mm diameter with an uncertainty of 0.0071 mm determined by the gravimetric method.

It can be seen from the above tables that the results are within the mutual uncertainty and therefore consistent. Also, the obtained flow results when using the values of the gravimetric diameter calibration have significantly lower uncertainty when compared with the ones obtained using the caliper method, with a major impact in the low flow rates. This expanded uncertainty values of the 1 mL syringe diameter have been reduced from 0.74% using a caliper, to 0.16% using the new gravimetric method.

Conclusions

Accurate diameter measurements are essential when using the new calibration methods based on optical technology developed under MeDDII project that can be applied in microflow measuring devices.

Glass syringes and capillaries with different internal diameters were calibrated with the gravimetric method and with optical methods. To validate the new methods developed for inner diameter determination, the gravimetric method and the optical method, two bilateral comparisons were performed, one between IPQ and CETIAT for the capillaries and other between IPQ and CMI for the 1 mL syringe. It was observed that the obtained results using different methods by different laboratories were consistent for both type of instruments tested.

The diameter values obtained by gravimetric diameter measurement method were applied in the flow calibration of a NEXUS pump using an interferometric method. The obtained flow results presented lower uncertainty values, when compared with the ones obtained using the previous caliper diameter measurement method.

With these two new developed methods, the flow laboratories specially using optical technology for microflow measurements, can now determine by themselves the inner diameter of tubes with reasonable uncertainty values.