A Novel Device for the Quantification of Synovial Fluid Viscosity Via Magnetic Deflection

Abstract

Changes in synovial fluid viscosity may be used to detect joint disease; however, methods to evaluate these changes at the point-of-care are currently rudimentary. Previously, we demonstrated that magnetic particle translation through static synovial fluid could serve as a surrogate marker of synovial fluid mechanics. In this work, we examine the magnetic deflection of a stream of particles flowing through a stream of synovial fluid and relate this deflection to changes in fluid mechanics. First, a flow device was designed, where a stream of magnetic particles flows along with synovial fluid. As the particle stream approaches and passes a fixed permanent magnet, the particle stream deflects. Conceptually, as the synovial fluid viscosity decreases, the deflection of the particle stream should increase due to a decreased drag force opposing the force magnetization. To assess this concept, particle deflection was first measured in Newtonian glycerol solutions of known varying viscosity under different flow conditions. Next, the device was used to test bovine synovial fluid viscosity, which had been progressively degraded using ultrasonication. A strong correlation was observed between the deflection of the magnetic particles and the viscosity of the glycerol solutions (R² = 0.987) and the amount of ultrasonic degradation of synovial fluid (R² = 0.7045). In the future, the principle of particle deflection may be used to design point-of-care quantification of synovial fluid mechanics, as the assessment does not require particles to be separated from the fluid for quantification and could be conducted under simple flow conditions.

1 Introduction

Degradation of synovial fluid can occur in multiple joint diseases, including osteoarthritis, rheumatoid arthritis, gout, inflammatory arthritis, and septic arthritis [1–4]. With this degradation, synovial fluid viscosity is reduced with the associated breakdown of hyaluronic acid chains [3,5,6]. Historically, measurements of synovial fluid viscosity were conducted in a laboratory using capillary flow rheometers. However, these techniques require bulky equipment, large sample volumes, and cannot account for the non-Newtonian properties of synovial fluid [4]. Clinically, synovial fluid is often aspirated for pathological evaluations of cells and inflammatory activity; during this removal, fluid viscosity is often estimated with a very rudimentary “stringiness” test, where a drop of fluid is pulled between two fingers and qualitatively assessed for its ability to form a long string [7]. More recently, synovial fluid viscosity has been assessed using extension rheometers and cone and plate rheometers [8,9]. Unlike capillary flow rheometers, these methods can account for complex properties but still require laboratory-based equipment and large sample volumes.

Due to the above limitations, microrheometry has been investigated to evaluate non-Newtonian fluids using small sample volumes [6,10], including active and passive microrheology. In passive microrheology, the thermally driven motion of monodisperse spheres in a colloid suspension is measured, with the mean square displacement quantified as a surrogate measure of fluid viscoelasticity [11]. Alternatively, active microrheology subjects suspended particles to an external force such as magnetism, measuring the resultant motion of the particles as a surrogate measure for fluid mechanics [10,12,13]. However, in both passive and active microrheologic techniques, the fluid being tested is static. Moreover, the assays rely on techniques and analytical modeling that are not easily accomplished at the point-of-care. As a result, microrheometers have not translated from the basic science laboratory into diagnostics, despite advantages in sample size and ability to measure non-Newtonian fluid behaviors.

Microfluidic rheometers have also been developed to assay small volumes of non-Newtonian fluids [14]. For example, Solomon et al. developed and validated a fixed-pressure, rate-sensing microfluidic rheometer that used a cellphone camera for measurement [15]. Surface tension-based devices have also been developed using video measurement in a disposable device [16]. However, despite these advantages, microfluidic rheometers have not yet translated to clinical practice. Instead, the most common measure of synovial fluid viscosity conducted by clinicians continues to be the stringiness test [7]. Here, there is no control of sample volume or the rate at which the fluid is stretched. While a more objective form of this technique was developed using a white blood cell pipette as a capillary rheometer [11], this version of the stringiness test has also not been widely adopted in veterinary or clinical practice.

Our group's goal is to move toward a point-of-care assessment of synovial fluid mechanics that is both rapid and quantitative. Our previous efforts demonstrated that the simple collection of magnetic particles from a small volume of synovial fluid correlated to the synovial fluid viscosity [13] and could be modeled and predicted [17]. While this approach only requires inexpensive magnetic beads and common lab supplies, it requires several minutes to collect beads from static synovial fluid and relies on spectrophotometry equipment that is typically not available at point-of-care. Here, instead of collecting a dispersion of particles from static synovial fluid, we investigate measuring the deflection of a stream of magnetic particles flowing through a laminar flow of synovial fluid. As the particle stream approaches a permanent magnet, the magnetization force on the particles deflects the stream toward the magnet, while a drag force related to the viscosity of the synovial fluid resists this deflection. As the viscosity of the fluid reduces, the deflection of the particle stream should increase. While this approach is conceptually more complex than particle collection from static fluid, the viscosity of the fluid could be assessed with a simple picture of the particle stream, allowing for a rapid and quantitative point-of-care measure of synovial fluid viscosity. In this paper, a proof-of-principle is demonstrated for this concept. The accuracy of this measure is demonstrated in both a Newtonian glycerol solution and in various levels of degraded non-Newtonian synovial fluid. While this work focuses on proof-of-principle, future work will aim to generate a small volume and point-of-care devices using similar principles.

2 Methods

2.1 Magnetic Deflection Concept.

Magnetic deflection relies on the balance between a force generated from a magnetic dipole–dipole interaction and an opposing Stokes drag force proportional to the sample fluid's viscosity. The magnetic force is represented by Eq. (1) [18], where $\mathbf{m}$ represents the dipole moment of the particle and $\mathbf{B}$ represents the magnetic field of the fixed, deflecting magnet, which will be heretofore referred to as the magnet.

$${\mathbf{F}}_m=\hspace{0.17em}\left(\mathbf{m}\hspace{0.17em}\cdot \hspace{0.17em}\mathbf{\nabla }\right)\hspace{0.17em}\mathbf{B}$$ (1)

The Stokes drag force is given by Eq. (2), where $\eta \hspace{0.17em}$represents the viscosity of the sample fluid, $r_{\mathrm{mp}}$ represents the particle's hydrodynamic radius, and $\mathbf{v}$ represents the particle's velocity relative to the fluid [17].

$${\mathbf{F}}_d=-6\pi \eta r_{\mathrm{mp}}\mathbf{v}$$ (2)

The balance of these forces determines the acceleration of the particle, as shown in Eq. (3), where $m_p$ represents the particle's mass and $\mathbf{a}$ represents the particle's resultant acceleration vector.

$${\mathbf{F}}_m+{\mathbf{F}}_d=m_p\mathbf{a}$$ (3)

Ultimately, this acceleration will determine the deflection of a particle stream, where the magnetic particle's acceleration will depend upon the particle's velocity through a static magnetic gradient produced by a fixed magnet and the drag force produced by the surrounding fluid.

To demonstrate magnetic deflection experimentally, our group designed a device shown in Fig. 1. Figure 1(a) shows the device components, Fig. 1(b) provides the relevant measurements, and Fig. 1(c) demonstrates the principles discussed above. A sample solution, shown as blue, flows upward at a fixed laminar rate while a laminar stream of magnetic particles is injected into the center of the device. This particle stream also flows upwards toward the magnet. As the particle stream approaches the magnet, the superparamagnetic particles become magnetized (F_m > 0) and thus begin to experience a transient attractive force which accelerates the particles toward the magnet (Eq. (1)). As a particle moves through this magnetic field, the force on the particle changes in relation to its relative position in the magnetic field. In addition, the particle's motion induces a drag force, which is theoretically proportional to the sample fluid's viscosity (Eq. (2)). As long as the particle's velocity is sufficiently high, the particle passes through the magnetic field collection, but the magnet deviates the particle's trajectory away from the center of the flow, with this deviation relating to the surrounding fluid's viscosity.

Fig. 1.

A device was designed to evaluate the magnetic particle deflection approach. (a) A photo of the device with labeled components. (b) Relevant dimensions of the device. (c) An illustration of the concept of magnetic particle deflection; at position 0, the particle enters the chamber far from the magnet and flows upward at a steady-state velocity $\mathbf{v}$. At position 1, the particle approaches the magnet and experiences a magnetic force ${\mathbf{F}}_{m1}$ which accelerates the particle toward the magnet. This motion induces an opposing drag force ${\mathbf{F}}_{d1}$ which results in velocity ${\mathbf{v}}_1$. At position 2, the particle experiences a stronger magnetic field which results in greater magnetic $\left({\mathbf{F}}_{m2}\right)$ and drag $\left({\mathbf{F}}_{d2}\right)$ forces. At position 3, the particle is again far from the magnet and returns to velocity $\mathbf{v}$, related to the flow field in the chamber. The displacement of the stream (d) is measured using a reference point.

2.2 Magnetic Particles.

All studies described herein use commercially available particles. These particles are 1 μm diameter, polystyrene microparticles embedded with superparamagnetic iron oxide nanoparticles. For all experiments, a particle concentration of 2.5 μg particles/μl in phosphate-buffered saline was used.

2.3 Experimental Designs and Device Settings.

Early testing showed that at certain flow rates and magnet positions, particles would collect on the device wall; here, the particles are being captured by the magnet rather than escaping the magnetic gradient and producing a measurable deflection. To isolate the effect of sample viscosity on the particle stream deflection, we established standard settings for our experiments, whereby fluid flow rate, particle flow rate, and magnetic position were held constant. While the range of viscosity that could be assessed was limited to a fixed range based on the flow rates and magnet positions, the device and experiments did allow us to test the dependence of a magnetic deflection measurement on the sample viscosity in our proof-of-concept experiments. These experimental design parameters are described below.

2.3.1 Experimental Design Describing the Effects of Flow Rates on Magnetic Deflection.

Glycerol solutions (10%, 45%, and 65%) were made with their viscosities calculated from an empirical formula, described in Ref. [19]. Prior to each trial, particle solutions were resuspended in a sonication bath to reduce aggregation, and glycerol aliquots were mixed for 30 s by vortex. The settings described in Table 1 were used to flow the glycerol solutions through the device. Here, the glycerol flow rate was varied, and the flow rate of the particle solution was held in proportion using a fixed ratio of volumetric flow (192.3 = sample fluid/particle stream). The magnet position for a given glycerol solution was held constant.

Table 1.

Experimental parameters used to evaluate magnetic deflection in glycerol solution under varying flow rates

Glycerol/water mixture (%v/v)	Sample flow rate (ml/min)	Particle flow rate (μl/min)	Magnet position (mm)
65.00	1.25	6.45	2
65.00	1.88	9.68	2
65.00	2.5	12.90	2
65.00	3.75	19.35	2
65.00	5	25.81	2
45.00	2.25	11.61	4
45.00	3.38	17.42	4
45.00	4.5	23.23	4
45.00	6.75	34.84	4
45.00	9	46.45	4
10.00	9	46.45	7.5
10.00	10.75	55.48	7.5
10.00	12.5	64.52	7.5
10.00	14.25	73.55	7.5
10.00	16	82.58	7.5

2.3.2 Experimental Design Describing the Effects of Sample Viscosity on Magnetic Deflection in a Newtonian Solution.

Again, a range of glycerol solutions was prepared to assess the effect of sample fluid viscosity on magnetic deflection; here, the physiological range of synovial fluid viscosity was simulated using 0–55% glycerol [20]. As above, aqueous glycerol aliquots were vortexed for 30 s, magnetic particles were briefly sonicated before each trial, and the volumetric flow of the particle solution was held in constant proportion to the sample flow rate (192.3 = sample fluid/particle stream). Only the glycerol solution was varied (Table 2).

Table 2.

Experimental parameters used to evaluate magnetic deflection in glycerol solution under varying viscosities

Glycerol/water mixture (%v/v)	Sample flow rate (ml/min)	Particle flow rate (μl/min)	Magnet position (mm)
55.00	2.65	13.68	2
61.25	2.65	13.68	2
67.50	2.65	13.68	2
73.75	2.65	13.68	2
80.00	2.65	13.68	2
30.00	6.5	33.55	4
37.50	6.5	33.55	4
45.00	6.5	33.55	4
52.50	6.5	33.55	4
60.00	6.5	33.55	4
0.00	7.75	40.00	8
8.75	7.75	40.00	8
17.50	7.75	40.00	8
26.25	7.75	40.00	8
35.00	7.75	40.00	8

2.3.3 Experimental Design Describing the Effects of Sample Viscosity on Magnetic Deflection in Non-Newtonian Synovial Fluid.

Bovine synovial fluid was obtained commercially and then mechanically degraded using ultrasonication as previously described [13,21]. Briefly, 300 ml of synovial fluid was placed on ice and repeatedly exposed to ultrasonication at 38% intensity in 10 s pulses. After every 20 s interval of sonication, a 30 ml aliquot was withdrawn until eight total aliquots were prepared. These 30 ml samples were then divided into 10 ml aliquots, testing the experimental error of the device in triplicate. As in Sec. 2.3.1, sample flow and particle flow were held in proportion; only the amount of synovial fluid ultrasonication was varied (Table 3).

Table 3.

Experimental parameters used to evaluate magnetic deflection in degraded bovine synovial fluid

Sonication time (s)	Sample flow rate (ml/min)	Particle flow rate (μl/min)	Magnet position (mm)
0	2.65	13.68	2
20	2.65	13.68	2
40	2.65	13.68	2
60	2.65	13.68	2
80	2.65	13.68	2
100	2.65	13.68	2
120	2.65	13.68	2
140	2.65	13.68	2

2.4 Measurement and Analysis.

During the flow experiments, a video camera is placed 30 cm from the device, recording the entire 2 min of the particle stream flow. For analysis, video frames that visually represented 10 s of steady-state particle stream deflection were clipped; then, software was used to measure stream deflection in three random frames from the 10 s clip [22]. In each analyzed frame, two critical distances were measured: (1) the distance from the far edge of the device (reference point in Fig. 1) to the far edge of the particle stream, and (2) the distance from the reference point to the center of the channel. Deflection is then the difference between these distances. Distances measured within a trial are then averaged, such that one measurement is calculated for each sample aliquot.

3 Results

3.1 Effect of Flow Rate on Magnetic Deflection.

As expected, the deflection of the particle stream depends on the velocity of the particle stream as it flows through the magnetic field (Fig. 2). As the viscosity of the glycerol solution increased, the magnitude of the slope decreased, indicating relatively less stream deflection with higher fluid viscosity and a decrease in the sensitivity to viscosity shifts with higher flow velocities. For all viscosities, the relationship between stream deflection and flow velocity appeared to be reasonably linear, despite the complex forces associated with the magnetization of the particles.

Fig. 2.

Glycerol solutions (10%, 45%, and 65%) were tested at varying flow rates and a fixed magnet position (8 mm, 4 mm, and 2 mm, respectively). Magnetic particle deflection had an approximately linear correlation with the sample flow rate. Data are presented as a data point for each aliquot tested, with each data point being the average of three frames from that aliquot's run through the device.

3.2 Effect of Sample Viscosity on Magnetic Deflection in Newtonian Glycerol.

When flow rate and magnet position are held constant, magnetic deflection in glycerol solutions is related to sample viscosity (Fig. 3), with the relationship being nonlinear. For low viscosity samples (1.79–8.36 mPa·s), a flow rate of 7.75 ml/min and a magnet position of 8 mm resulted in magnetic deflections ranging from approximately 2 mm to 0.5 mm. For midviscosity samples (6.35–49.89 mPa·s), a flow rate of 6.50 ml/min and a magnet position of 4 mm created a similar magnetic deflection range; and for high viscosity samples (32.71–431.75 mPa·s), a flow rate of 2.65 ml/min and a magnet position of 2 mm created a similar magnetic deflection range. Using these ranges, several fold differences in fluid viscosity could be detected.

Fig. 3.

Using a proportional sample and particle flow rate with a fixed magnet position, the magnetic deflection of a particle stream could be related to the sample viscosity. As viscosity increased, the distance the particle stream deflected decreased. With higher viscosity solutions, slower flow rates and closer magnet positions were needed to deflect the particle stream between 0.25 and 2.5 mm. Data are presented as a data point for each aliquot tested, with each data point being the average of three frames from that aliquot's run through the device.

3.3 Effect of Sample Viscosity on Magnetic Deflection in Non-Newtonian Synovial Fluid.

As sonication time of the synovial fluid sample increased, the distance the particle stream deflected also increased (Fig. 4). Despite non-Newtonian behavior, magnetic deflection in synovial fluid followed a near-linear trend between the various levels of synovial fluid degradation (R² = 0.7045). However, relative to glycerol solutions, variation within synovial fluid samples increased. As a reference, using an analogous ultrasonication technique, the low-shear viscosity (shear rate = 10 s⁻¹) of healthy synovial fluid is near 45 mPa·s, reducing to near 15 mPa·s with 160 s of sonication [13]. The high-shear viscosity (shear rate = 1000 s⁻¹) is near 5 mPa·s for both 0 and 160 s of sonication; thus, these data indicate that particle stream deflection relates to some measurable range of viscosity differences between samples that likely is most likely related to a low-shear condition. Using the measured magnetic particle stream displacements of 0.40–1.20 mm in Fig. 4 and using the glycerol solutions measured under identical flow and magnet positions in Fig. 3, one would approximate the deflections of 0.40–1.20 mm to relate to viscosities of 80–220 mPa·s, respectively.

Fig. 4.

As the bovine synovial fluid was progressively degraded, the distance the particle stream deflected increased. Data are presented as a data point for each aliquot tested, with each data point being the average of three frames from that aliquot's run through the device.

4 Discussion

In this paper, a proof-of-principle was demonstrated for using the deflection of a magnetic particle stream as a surrogate measure of sample viscosity. The principle was first demonstrated in simple, Newtonian glycerol solutions with known viscosities. Figure 3 shows the strong correlations between the magnitude of deflection and sample viscosity; Fig. 4 further demonstrates that magnetic deflection can be extended to viscosity changes in non-Newtonian synovial fluid viscosity, despite its complex behavior. The variability within synovial fluid groups did increase relative to glycerol solutions; this is likely due to an increase in the complexity of the fluid being tested. However, the principle that magnetic deflection increases in less viscous samples remained. The direct relationship between the particle deflection and the fluid's complex viscosities is not yet known, but our data imply that the deflection of our relatively large 1 μm diameter magnetic beads most likely corresponds with the low-shear viscosity of synovial fluid. Combined, these data demonstrate that the magnetic deflection of a particle stream could potentially be used as a surrogate measure for synovial fluid viscosity.

While this study is a proof-of-principle, a limitation of our current approach is the relatively short range of viscosities that can be handled within a given set of flow conditions; this necessitated three separate configurations to span the possible range of samples seen in synovial fluid or other biological fluids. However, future iterations of the magnetic deflection device can overcome this limitation by substituting the single, adjustable magnet with a sequential array of magnets positioned along the flow chamber. For example, in a hypothetical configuration of ten magnets, each magnet would move the particle stream incrementally closer to the chamber wall, eventually capturing particles on the wall. The time to capture would relate to the degree of deflection across the flow, and thus, the magnet array could be calibrated at a single flow rate. Here, rather than measuring deflection, one would assess which magnet in the array captured the particles. Moreover, the device could be designed such that capture by the first magnet would reflect a particle deflection similar to water, and capture by the last magnet could reflect healthy synovial fluid. With the device calibrated, the collection location would relate to a sample fluid's approximate viscosity, allowing for discrete measurements to be performed visually at the point-of-care without any additional equipment.

Another clear limitation of our experiments is that this proof-of-principle is demonstrated via the build of a macroscale device; however, to reasonably serve as a point-of-care test, this principle will need to be scaled down and use far smaller sample volumes. There are technical limitations with this scaling, both related to the device and the particles. In particular, when scaling down to a microfluidic level, the monodispersity of the particles will become more important because small variations in size and magnetic content will have greater effects at smaller length scales. Most commercially available particles are unlikely to consistently meet these design criteria; thus, specialized particle synthesis may also be required.

5 Conclusion

In this study, a proof-of-principle is demonstrated for measuring synovial fluid viscosity using the magnetic deflection of a stream of magnetic microparticles in a flow chamber. The method was first tested using glycerol solutions of known varying viscosities and under different flow conditions. Then, these results and conditions were extended to bovine synovial fluid, where deflection increased with the degradation of the fluid. Since this principle can be evaluated in a self-contained device, it may allow for easy quantifiable measurements at the point-of-care, but future challenges related to scale and calibration need to be further addressed.

Funding Data

• Research reported in this publication was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases of the National Institutes of Health (Award No. R01AR068424; Funder ID: 10.13039/100000069).

Conflict of Interest

The authors have no conflicts of interest to report.