Combined Experimental Approach and Finite Element Modeling of Small Molecule Transport Through Joint Synovium to Measure Effective Diffusivity

Abstract

Trans-synovial solute transport plays a critical role in the clearance of intra-articularly (IA) delivered drugs. In this study, we present a computational finite element model (FEM) of solute transport through the synovium validated by experiments on synovial explants. Unsteady diffusion of urea, a small uncharged molecule, was measured through devitalized porcine and human synovium using custom-built diffusion chambers. A multiphasic computational model was constructed and optimized with the experimental data to extract effective diffusivity for urea within the synovium. A monotonic decrease in urea concentration was observed in the donor bath over time, with an effective diffusivity found to be an order of magnitude lower in synovium versus that measured in free solution. Parametric studies incorporating an intimal cell layer with varying thickness and varying effective diffusivities were performed, revealing a dependence of drug clearance kinetics on both parameters. The findings of this study indicate that the synovial matrix impedes urea solute transport out of the joint with little retention of the solute in the matrix.

Introduction

The diarthrodial joint consists of two or more articulating bony elements, enclosed by a synovial membrane that separates the fluid-filled joint space from the surrounding, vascularized tissue. Pathologies of the joint include rheumatoid arthritis, psoriatic arthritis, osteoarthritis, post-traumatic arthritis, and gout, among others [1,2]. Together, these arthritides contribute to a high disease burden of disability and pain annually [3–5]. While systemic delivery of disease-modifying compounds has demonstrated potential in the treatment of inflammatory pathologies such as rheumatoid and psoriatic arthritis [6,7], the risk-benefit ratio, lack of efficacy, and high cost associated with currently available immunomodulatory agents (such as IL-1 receptor antagonist and anti-TNF) precludes their use in the treatment of single-joint pathologies such as gout and osteoarthritis [8,9]. Nonetheless, intra-articular (IA) drug delivery has many advantages over systemic delivery for treating mono- or oligoarticular arthritides including increased bioavailability at the affected joint, reduced systemic exposure resulting in fewer side effects, and lower total drug cost [10,11]. Short residence times of the injected drug at the affected joint limit the potential benefits of IA drug delivery [12]. Compounds delivered via IA injection are rapidly cleared through the surrounding synovial membranes [13–16]. Recently, drug-containing microparticles that potentially extend the residence time of the drug in the joint space have been approved for IA administration in the treatment of knee osteoarthritis [17,18]. Thus, further understanding of trans-synovial drug transport will guide strategies in modulating drug size, charge, and availability in the joint space that may lead to improved IA therapy.

Studies of IA drug transport in animals and humans have been performed using invasive labels (e.g., radioactive or fluorescent labels) or costly sampling methods (e.g., periodic blood draws or animal sacrifice) [16,19,20]. While these studies revealed an empirical relationship between drug size, disease status, and serum residence time, the mechanisms that govern mass transport through the synovium are still unclear. The synovium is a connective tissue of varying thickness, with a superficial intimal layer containing compacted fibroblast-like synoviocytes [15,21]. Underlying the intima is the subintima, a connective tissue comprised largely of collagen, fat and blood and lymphatic vessels [22–24]. Drug transport through the intimal and subintimal layers is driven by a concentration gradient between the joint space and the synovial tissue [25,26] with many compounds draining out of the joint space via underlying capillaries and lymphatic vessels [27–29]. Therapeutic compounds are likely to transport through a number of distinct and complex, yet still uncharacterized mechanisms. To understand transport processes occurring within the porous, connective tissue of the synovium, it is necessary to establish the relative influences of different transport phenomena including passive solute diffusivity through the tissue, pressure-driven convective transport, reversible and irreversible binding of compounds to the extracellular matrix, cell-mediated compound uptake, and lymphatic drainage. Investigating these phenomena requires fundamental knowledge of synovium porosity or solid volume fraction, hydraulic permeability to solvent flow, tissue mechanics, and other transport parameters based on solute-tissue interactions which have not yet been studied in humans or animals.

Several groups have begun to characterize solute transport through the synovium in model systems. Studies of cell monolayers upon membranes and microphysiological models of synovium identified the intima as a size-selective barrier for macromolecules [30–32]. However, these approaches did not take into account a role for the extracellular matrix in the subintima as a secondary regulator of solute transport. To this end synovial explant models provide an attractive system to investigate the role of the subintima in regulating mass transport and provide a means to estimate a solute diffusivity. Sterner and coworkers used customized diffusion chambers to measure passive diffusion of polyethylene glycol polymers (6–200 kDa) across bovine synovium and found a correlation between polymer molecular weight and transport speed. Recently, Stefani and coworkers assessed the permeability of 70 kDa dextran in bovine synovium explants using a Transwell^® system. While the authors identified differential transport behaviors between native synovial tissues and an engineered microphysiological model, intrinsic solute diffusivities within explant tissues are still unknown [31,33].

The similarities in microstructure between the synovium and other connective tissues, including cartilaginous tissues, suggest that synovial tissue is best materially described as a heterogeneous, porous solid, fully saturated with solute-filled solvents, and encapsulated cells [34–37]. Models of solute transport in constructs of cartilage, meniscus, and intervertebral disk allow for explicit representations of tissue porosity, solute diffusivity, permeability, and binding kinetics. In this paper, we report in vitro studies of solute transport through porcine and human synovium explants, for a small uncharged solute (urea). A computational model of synovium as a porous and fluid-saturated, multiphasic mixture was constructed using finite element methodology (FEM, FEBio) in order to facilitate modeling of the experimentally measured one-dimensional transport of urea through the tissue explant. Model predictions were matched to experimental data from one-dimensional transport of urea through tissue explants. We sought to develop an experimental and computational modeling strategy for measuring the transport properties of urea here, toward the goal of studying therapeutic drug diffusion through synovium under healthy and diseased conditions.

Materials and Methods

Sample Collection and Preparation.

Fresh synovial tissue was collected from three regions of porcine knee joints obtained within 4 h of sacrifice. Human samples of synovial tissue were obtained from donor knee joints through an agreement with the Mid-America Transplant Foundation. In all cases, synovium was procured from three distinct regions adjacent to the lateral femoral condyle, the medial femoral condyle, and between the femoral condyles on the posterior side of the femur (Figs. 1(a) and 1(b)). Immediately postcollection, explants were cryoprotected by immersion in 15% sucrose in phosphate buffered saline (PBS) at 4 °C (16–24 h) followed by soaking in 30% sucrose in PBS at 4 °C overnight. To devitalize the tissue, samples were embedded in low-temperature cutting media (Tissue-Plus^TM OCT, Fisher Healthcare, Hampton NH) and snap-frozen in isopentane (Sigma-Aldrich, St. Louis, MO) cooled by liquid nitrogen. Frozen explants were stored at −20 °C for no less than 48 h to ensure loss of viable cells. The frozen blocks were trimmed to less than 1 mm in thickness by a sledge microtome (Leica SM2400, Allendale NJ). Prior to diffusion experiments, samples were thawed at room temperature and soaked in PBS at 4 °C overnight, and the surface area of the samples trimmed to 10 mm × 10 mm.

Fig. 1.

(a) Knee joint showing the regions from which synovium explants were harvested highlighted by dashed red lines. (b) Photomicrograph of knee joint. (c) Schema of an assembled diffusion test apparatus with synovium mounted between two fluid baths of 1 mL in volume each. (d) Plot of urea concentration in the donor bath normalized by starting concentration over time.

Diffusion Experiments.

Unsteady transport of urea (60 Da) was studied in devitalized synovial explants to assess the diffusivity for a small, uncharged solute through the extracellular space within the tissue. A custom-built diffusion test apparatus was machined from acrylic blocks (Fig. 1(c)), which consisted of two chambers, one each for the “donor” and “sink” baths (1 mL volume each, 9.5 mm diameter). The sink bath was fitted with two standard Luer fluid ports connected to 1/16 in. tubing (Tygon, Akron OH) to allow for fluid flow. Additionally, vents atop each bath allowed for aliquots to be collected via pipetting. Tissue-clamping rings 3D-printed from polylactic acid filaments were used to secure explants between the two fluid baths and an O-ring was used to seal the assembled test apparatus.

Porcine or human synovial explants were gently stretched between the two tissue-clamping rings and placed between the fluid baths with the intimal surface facing the donor bath. The donor bath was filled with a solution of urea prepared in PBS at 50 mg/mL (833 mM, Sigma Aldrich) while the downstream sink was filled with pure PBS. The concentration of 833 mM was chosen in order to be within the detection limit of the assay used as described in the following. In order to ensure continuously dilute conditions in the downstream sink, syringe pumps were attached to both fluid ports of the sink bath to continuously replace the PBS at a rate of 2 mL/h. The diffusion chamber was placed atop a 3D nutating shaker (Benchmark Scientific B3D2300, Edison, NJ) for the duration of the experiment to promote efficient mixing within each fluid bath. Aliquots (5 μL) were collected from the donor bath at intervals from 0 to 72 h; urea concentration was measured in each aliquot via a colorimetric assay and compared against a standard curve (BioAssay Systems, Hayward, CA). Values for urea concentration in the donor bath were plotted against time as shown in Fig. 1(d).

Following the end of an experiment, explants were removed from the diffusion test chamber and placed atop a glass slide. At several regions of each specimen, thickness was measured via optical microscopy. These specimen-specific values were used for finite element analysis, as explained in the Computational Model section.

Measurement of Solid Volume Fraction.

Specimens were weighed before and after lyophilization for 48 h to obtain wet weight ($W_{\text{wet}}$) and dry weight ($W_{\text{dry}}$), respectively, for determination of water and solid mass (m_w, m_s) and a water volume fraction (${\varphi }_W$). The intrinsic or true density of the dry lyophilized tissue (${\rho }_s$)_T was assumed to be 1.42 g/mL [38] for purposes of this calculation

$${\varphi }_W=\frac{(m_w-m_s)/{\rho }_W}{(m_w-m_s)/{\rho }_W+m_s/{\left({\rho }_s\right)}_T\hspace{0.17em}}$$ (1)

Computational Model.

The experiment described previously was modeled as unsteady, one-dimensional diffusive transport of a solute through a porous, hydrated tissue layer [39,40]. The finite element code, FEBio, was used to implement a mixture model for the devitalized synovial tissue with geometric and material assumptions as previously described [41,42]. Model geometry consisted of the donor fluid bath (1 mL volume) overlaying an isotropic and porous, fluid-saturated solid layer representing the synovial explant (Fig. 2(a)). A mesh was created from this model using eight-node hexahedral elements that were refined closer to the boundary between the synovium and the bath. The synovium was modeled as a multiphasic material with a homogeneous, neo-Hookean solid phase of uniform hydraulic permeability, modulus and Poisson's ratio, and a value of ${\mathrm{\varphi }}_{\mathrm{s}}=0.19\hspace{0.17em}$ for solid volume fraction (based on measurements from equation [1]). The fluid bath was modeled using the multiphasic material element, but with a porosity of unity (${\mathrm{\varphi }}_{\mathrm{s}}$ of 0). Urea was modeled with a free diffusivity (D _free) of 0.00134 mm²/s [43]; diffusivities in the bath were set to 1000 fold higher to model a well-mixed bath, as has been done previously [44,45]. Moduli values for the synovium were set to 10⁵ Pa according to previously reported measurements with a Poisson's ratio of 0.4 [46]. The hydraulic permeability for synovium is not known and was chosen to generate observed tissue behaviors as described in the following.

Fig. 2.

FEM and experimental data for synovium in the 1D unsteady diffusive transport of urea modeling IA drug delivery. (a) FEM mesh showing boundary conditions of C(x = L) = 833 mM and C(x = 0) = 0 mM. (b) Analytical (solid lines) and FEM (circles) solutions to the canonical 1D transient diffusion problem at three representative time points, with the steady-state solution shown at the longest time point. Good agreement between the two solutions validates the use of FEM as a model of transport between two baths. ((c) and (d)) Experimental data for transient urea concentration values in the donor bath as measured by UV/vis (open circles). FEM model fit (dashed lines) to experimental data is shown for a representative (c) porcine synovium sample (800 μm thick), and (d) human synovium sample (870 μm thick).

In this model, the driving mechanism for solute diffusion is given by the gradient in the electrochemical potential of solvent phases between the donor bath and sink and the synovium explant. Given our study of urea as an uncharged solute, the boundary conditions may be formulated in terms of an effective fluid pressure $\left(\tilde{p}\right)$ that is defined as a mechano-chemical fluid pressure resulting from the hydrostatic fluid pressure $\left(p\right)$ and an osmotic contribution due to the presence of the modeled solute

$$\tilde{p}=p+\mathit{RTC}\varphi$$ (2)

In this expression, R is the ideal gas constant and is equal to 8.314 J/mol K and the absolute temperature is 310 K. Hydrostatic fluid pressure ($p$) was assumed to be 0 at equilibrium with atmosphere; the osmotic coefficient (ϕ) was assumed to be unity in both the fluid baths and the tissue. Formulation of boundary conditions is then provided in terms of $\tilde{p}$, a function of C(x,t) as defined in the following.

Model Verification for Free Diffusion of a Solute Under Steady-State Transport Conditions.

To validate the febio model, computational predictions were compared against those from the analytical solution for one-dimensional transport of a solute through a dilute bath governed by Fick's Law. The analytical solution for solute transport was obtained under conditions where the solute concentration, C ₀, is held constant on one face (x = L) and held to be dilute on the opposite face (x = 0)

$$C\left(x,t\right)={\mathrm{C}}_0\frac{x}{L}+\sum _{n=1}^{\infty }\left(\frac{2C_0}{\pi n}{\left(-1\right)}^n\hspace{0.17em}\text{sin}\left(\frac{\pi n}{L}x\right)\right)e^{-{\left(\frac{\pi n}{L}\right)}^2{D}_{\text{eff}}t}$$ (3)

Here, x is the spatial dimension, t is time, C₀ is the concentration of the donor bath, L is the path length or thickness of the modeled construct, and D _eff is the diffusion coefficient for the solute in the construct. An FE model of a multiphasic tissue layer was setup to simulate this problem (Fig. 2(b)), with the solid matrix stress–strain response modeled as described earlier. To match Fick's law, the solid model was assumed to be of ϕ_s = 0 and an effective diffusivity was taken to be equal to the free diffusivity of urea, as D _eff = 0.00134 mm²/s was chosen in both analytical and computational models.

FE Model Simulation of the Unsteady Transport Problem and Optimization to Determine D _eff.

Unsteady transport of urea through the synovial explant was modeled to simulate the case of IA bolus delivery of a drug. Here, the initial conditions for the donor bath were defined [C(x = L, t = 0) = C ₀] and the concentration for urea at the sink [C(x = 0, t) = 0] was held constant at 0 for all time; this consistently dilute downstream bath was meant to simulate conditions present in a healthy joint where lymphatics drain solutes from the extracellular spaces resulting in rapid clearance of delivered drugs from the joint space.

The effective diffusivity for solute in the model (D _eff) was obtained by numerically matching the concentration measured experimentally in the donor bath against FE model predictions using an optimization subroutine supported by febio. The module seeks to minimize the residual sum of squares (RSS) between predicted and measured urea concentration in the entire donor bath over time, using a modified Levenberg–Marquardt algorithm [47]. Thickness of the synovium in this finite element model (FEM) simulation was chosen to construct a sample-specific model for each experimental condition.

Parametric Studies of D _eff in Synovial Intima.

Here we modeled the synovial explant as a single layer of subintimal connective tissue to readily attain a value for solute diffusivity through the extracellular spaces. It is important to note, however, that there exists a compacted cell layer similar to an intima that will vary in composition and thickness. A numerical model would be required to predict the role of zone-specific diffusivity and morphometry upon solute diffusivity for the complexity of the theoretical model. For that reason, we constructed a multizone model of a synovial explant (Fig. 3(a)) to estimate the effect of a synovial intima with lower effective diffusivity (D _intima or D _i). The intima was modeled as a layer with thickness L _intima (or L _i = 10 μm) and a total thickness of L = 600 μm. Values for D _i were varied to be 10%, 1%, and 0.1% of the D _eff estimated for subintimal tissues from numerical optimization described earlier. In a second series of parametric studies, the effects of intimal thickness (L _i) were studied by varying L _i=10 μm, 20 μm, 60 μm, and 120 μm for a constant thickness of L = 600 μm and constant D _i to be 10% of D _eff.

Fig. 3.

Model predictions of urea transport through a multilayered synovium construct in the 1D unsteady diffusion problem. (a) FEM model showing the meshing of two zones corresponding to subintima synovium (yellow) and intimal layer (see inset). Here, the tissue bath is also incorporated into the FEM model with dimensions much larger than the 600 μm thick synovium (b) Effects of intimal diffusivity for urea on donor bath clearance modeled with a base value for D _eff = 3.05 × 10⁴ mm²/s and a 10 μm thick intimal layer (c) Effects of intimal thickness upon donor bath clearance of urea modeled with a base value for (D _eff)_i = 0.1D _eff.

Results

Sample Collection and Preparation.

A total of 5 porcine and 2 human synovial explants were procured from joints as described earlier. Visual inspection revealed a great deal of variation in the thickness and color of the intact synovium prior to harvest and sample preparation (Fig. 1(b)), suggesting the existence of multiple synovial subtypes as described previously. Samples were trimmed to dimensions of approximately 10 × 10 mm and thicknesses ranging from 200 to 800 μm.

Diffusion Experiments.

Values for urea concentration measured in the donor bath exhibited a monotonic decay over time for all samples (Fig. 1(d)). In all cases, the donor bath concentration of urea normalized by initial values, fell to less than 5% of initial values by 72 h (Figs. 2(c) and 2(d)). Average values for normalized donor bath concentration at 72 h were 2.37 ± 1.59% (mean ± SD) for porcine (n = 5), and 3.27% (mean) for human (n = 2).

Measurement of Solid Volume Fraction.

Water volume fractions were measured to be ϕ_w = 0.87±0.0159 (mean ± SD) in porcine samples and an average of 0.75 in human samples. For the purposes of FEM, an average value for ${\mathrm{\varphi }}_{\mathrm{s}}=0.19\hspace{0.17em}$ was used in all mesh development for ϕ_w + ϕ_s = 1. Tissue swelling was not observed in porcine explants, with thickness after a 72-h experiment measured to be 94.5±28.5% (mean ± SD) of thickness measured immediately after harvest (n = 5).

Model Verification for Free Diffusion of a Solute Under Steady-State Transport Conditions.

Excellent agreement (RSS < 0.001) was obtained between the numerical solution for steady-state transport of a solute through the construct and the analytical solution given in Eq. (3) (see Fig. 2(b)). Following expectations for Fick's law governing transport under these conditions, the equilibrium conditions for solute concentration approached fixed values on both C(x = 0) and C(x = L).

FE Model Simulation of Unsteady Transport and Optimization to Determine D_eff.

Good agreement was obtained between experimental measures of urea in the donor bath and FE model simulations for all samples, regardless of thickness. While the time to equilibrium varied among explants (Figs. 2(c) and 2(d)), the residual sum of squares fell below 0.18 for all samples (Table 1). Numerical optimization gave effective diffusivities for urea in tissue (D _eff) that were an order of magnitude lower than the diffusion coefficient for urea in water D _free = 1.34 × 10⁻³ mm²/s, with porcine values ranging between 2.09 × 10⁻⁴ and 5.19 × 10⁻⁴ mm²/s (Fig. 2(c)) and human samples between 2.44 × 10⁻⁴ and 5.17 × 10⁻⁴ mm²/s (Fig. 2(d)).

Table 1.

Values for the effective diffusion coefficients (D _eff) obtained by numerical fitting of the FEM to experimental data along with RSS and thickness values are shown for porcine and human synovium

Sample	Source	Deff (mm2/s)	RSS	Thickness (μm)
A	Porcine	2.09 × 10−4	0.0363	800
B	Porcine	2.47 × 10−4	0.0297	300
C	Porcine	5.19 × 10−4	0.0118	840
D	Porcine	2.36 × 10−4	0.00996	400
E	Porcine	3.16 × 10−4	0.183	690
Average	Porcine	3.05 × 10−4	—	606
A	Human	5.36 × 10−4	0.0631	700
B	Human	2.44 × 10−4	0.0655	870
Average	Human	3.90 × 10−4	—	785

Parametric Studies of D _eff in Synovial Intima.

In the multilayer FE model of synovium explants, the effective diffusivity in the intimal layer D _i as well as thickness of the intimal layer L _i was varied to examine their effects on urea clearance from the donor bath. Altering D _I over three orders of magnitude was associated with dramatic differences in the time to solute clearance as shown in Fig. 3(b). While a ten-fold decrease in D _i over D _eff produced little effect for an intimal layer of 10 μm thickness, the time to solute clearance were substantially reduced for the cases when D _i = 0.01D _eff and 0.001D _eff (Fig. 3(b)). In a second parametric variation, increasing the thickness of the intima with D _i = 0.1D _eff had the effect of decreasing the kinetics of solute clearance from the bath (Fig. 3(c)).

Discussion

In this study, we determined the diffusion coefficients for a single, low molecular weight solute through both porcine and human synovium using a combined experimental and multiphasic modeling approach. The resulting values for effective diffusivity of urea in porcine and human synovium samples were found to be much lower than the free diffusivity in both porcine and human samples. In comparison to previous in vitro studies of solute transport in bovine synovium for a 70 kDa dextran molecule [31], the lower molecular weight urea was observed to have a shorter time to clearance than the time to clearance shown for 70 kDa dextran, consistent with the anticipated behavior for a larger molecule [31]. While the prior study reported transport in a living synovium explant, a solute diffusivity was not obtained. Comparisons for unsteady transport across studies are difficult without reporting of diffusivities due to an intrinsic dependence on sample and test geometry including size of baths and tissue used in the experiments. Further, our studies of de-vitalized tissue were necessary here to distinguish parameters of passive transport from those that would occur due to cellular uptake; however, while the cryopreservation method used here reduces the formation of large ice crystals, freezing and thawing explants may still alter transport. Across all samples in this study, solute concentration in the donor bath consistently decreased to less than 5% of initial values by 72 h. The use of devitalized tissue ensured cellular uptake did not play a role in the transport of urea and that diffusion through extracellular space was not impaired by the presence of cells in the intima. The impaired transport cannot be explained from volume exclusion effects alone, however, and would indicate a decreased effective diffusivity in the tissue. These results suggest that matrix components could impede diffusion as evidenced by the lower effective diffusivities, but that there was negligible or no irreversible solute-matrix binding.

This study is the first to model synovium mass transport using a multiphasic mixture model. While cartilage, disk, meniscus, and other connective tissues have been represented using fluid-solid mixture models, this represents the first time the mixture assumption has been applied to synovium [34,48]. The model presented here was adapted from previous models developed for cartilage and was effective for describing both the analytical solution and experimental measures [36]. Moreover the FE model has the capability to incorporate matrix-solute binding, mechanical loading, cellular uptake and synthesis, and charge interactions as may be necessary for accurately modeling the transport of therapeutic drugs [44,45,48–51]. Indeed, this FE model-based approach will be useful for incorporating observed heterogeneities in tissue morphometry and eventually, tissue composition. Here, results from tissue experiments were averaged despite our intuition that synovium is heterogeneous depending on location of harvest. Future work will focus on stratifying the synovium into subcategories as has been suggested for fibrillar, areolar, and adipose synovium [23] and incorporating heterogeneity in tissue morphometry and solute diffusivity into the FE model.

The clearance kinetics of urea from the bath observed in the explant studies here are markedly slower than reported results and half-life from in vivo studies of larger molecules [52–54]. The discrepancy in half-life can be partially explained due to measurement uncertainty inherent in measures of serum concentrations from living subjects, due to the very large blood volume and very low sensitivity detection methods. It is plausible that drug concentrations measured in vivo would be estimated to be below detection limits far sooner than in the finite volume test bath used here. Another key difference between the experimental findings reported here and previously reported in vivo drug clearance is the mismatch of boundary conditions: in this study, the thickness of tissue is taken to be the path-length of diffusion, but a distributed network of lymphatic vessels is dispersed in the subintima, primarily located in the first 500 μm from the joint surface, that continually drains intra-articularly delivered compounds. This would have the effect of decreasing the apparent path-length in our model although the FE model could be constructed to represent the morphometric complexity corresponding to these lymphatic vessel structures [55]. Further, the drugs used in the in vivo studies have much larger molecular weights than that of urea; prior work has identified a correlation between solute molecular weight and residence times in the joint so that additional studies of varying molecular weight solutes are necessary for a more accurate comparison with the in vivo studies [19].

The developed FE model of synovium verified with experimental data has the potential to predict the effects of varying molecular weight drugs and their delivery via carrier vehicles and other modifications in future work. In attempts to increase drug residence times and efficacy, a wide range of drug delivery depots have been developed to provide a steady and sustained release. These depots include encapsulation of small-molecule drugs for treating arthritis in microspheres made from natural and polymeric materials [56–58]. The microspheres have been shown to increase drug residence times in the joint through a controlled drug release rate and subsequent transport through the synovium as well as increased residence of the microspheres themselves due to their large molecular weight [59]. By critically identifying the primary transport mechanisms influencing IA drug clearance, the FE model has the potential to discover optimal treatment strategies for maximal presentation of therapeutic drug doses within the joint.

Clearance of macromolecules from the joint is known to change with onset of disease through multiple mechanisms. Pathologic changes in the synovium associated with joint diseases potentially contribute to the decreased transport including the formation of a pannus-like structure with increased thickness and cellularity [60]. The increase in thickness and altered cellularity may decrease drug transport through the synovium, an issue further compounded by the formation of a boundary layer of large molecular weight molecules which leads to a reflectance of the large macromolecules back into the joint fluid [61]. While increased synovial vascularity is associated with joint disease, studies have shown a corresponding decrease in lymphatic function due to inflammation impeding an ability for solutes to clear out from synovium [62,63]. Additionally, the intra-articular pressure may be elevated with disease and is another factor to consider when evaluating transport in pathological drug passage [21,64]. A modified version of the FE model presented here could find value as a predictor of the effects of individual pathological mechanisms and their anticipated contribution to drug transport.

In this study, parameters were chosen to exclude the possibility for deformation of the solid matrix, although experimental conditions may allow for solid matrix [36,50,65]; however, the material properties pertinent to deformation are poorly characterized in the synovium. Additionally, the model used in our study makes use of a constant value for the effective diffusion coefficient, and thus is independent of solute concentration unlike that shown in prior studies [66]. Even with these limitations, this combined experimental-computational study is able to demonstrate the processes of drug transport through synovium.

Conclusion

Experimental data for unsteady transport of a small molecular weight drug were obtained in both human and porcine synovial explants. Combined with a validated FE model of joint synovium, this study determined for the first time, effective diffusivities for solute transport in synovium. Parametric studies modeling a role for the intima indicate that both intimal thickness and effective diffusivity are important for transport, but that varying effective diffusivity in both the intimal and subintimal layer will have a profound impact on drug clearance kinetics from the joint space.

Funding Data

• This work was supported with funds from the National Institutes of Health (R01 AR070975, R01 AR074415, R01 AR069588, R01 AR067491, R01 AG15768, R01 AG46927; Funder ID: 10.13039/100000002).

• CS, POB and JAJF gratefully acknowledge support from the Washington University Center for Cellular Imaging (WUCCI) which is funded by Washington University School of Medicine, the Children's Discovery Institute of Washington University and St. Louis Children's Hospital (CDI-CORE-2015-505), The Foundation for Barnes-Jewish Hospital (3770 and 4642), the Washington University Rheumatic Diseases Resource-based Research Center (RDRRC) (NIH P30AR073752; Funder ID: 10.13039/100007268).