Interstitial cystitis/painful bladder pain syndrome (IC/BPS) is associated with bladder inflammation and epithelial dysfunction. Past ultrastructural studies (ref.1)  used lanthanum tracer to evince the inflammation mediated dilatation of urothelial tight junctions 
and other structural deficiencies in the cold-cup biopsies punched from bladder of IC/BPS patients.  However, for benchmarking the impact of IC/BPS on tight junctions, the normal pore size of tight junctions needs to be determined in healthy controls who may not welcome the prospect of invasive bladder biopsy and tissue processing artifacts are also liable to introduce errors in the measurement of tight junction dimensions. Therefore, we sought for alternative non-invasive methods that would be acceptable for healthy controls and IC/BPS patients. In that context, confocal laser endomicroscopy of bladder in live humans confirmed that instilled Fluorescein mimics the poor transcellular absorption of Methylene blue and other polar dyes, including Trypan blue/Evans blue dye by umbrella cells(ref.2). However, the fluorescence emitted by polygonal umbrella cell borders revealed that 30% of the bladder luminal surface covered by tight junctions expressing zonula occludens-1 (ZO-1) and claudins exhibit size dependent paracellular permeability to instilled drugs/dyes. Assuming instilled drugs and dyes squirm as spheres through tight junctions and comply with canons of Stokesian diffusion, we hypothesized that size of urothelial tight junctions can be non-invasively deciphered from the rate and extent of systemic uptake of instilled drugs and probes having known diameter because the non-deformable physical size of the drugs and probes in solution can be separately determined by electron microscopy or dynamic light scattering.

We collated the physical size or hydrodynamic diameter of 20 drugs and dyes that have been instilled into human bladder and then ran a log-linear regression between molecular weight (MW) and size. Owing to the skewed distribution, log-transformation of MW was necessary for assessing the linear relationship. The log- normality of the regression model was checked, and the significance tested by global F test. Whether the slope of least-squares line significantly different from 0 was determined by Student's t-test to determine the bands for 95% confidence limits.

Among the factors that may influence the systemic uptake of instilled drug molecules through the tortuous gap of tight junctions are the MW and geometry or size of molecules. Drug molecules are assumed to diffuse as spheres of hydrodynamic diameter (HD) through tight junctions and comply with the canons of Stokes-Einstein diffusion equation D =  kT/(6pi*r*mu). As per the equation, diffusion coefficient D with the dimensions of area/unit time is inversely proportional to the Stokes-Einstein radius (r) of the sphere as other parameters in the equation are constants as the numerator term is a fixed value with T at 310.15 Kelvin (37°C) for in vivo experiments, k is Boltzmann constant like pi (3.14) whereas viscosity symbol mu in the denominator is also determined by T.  Therefore, the  paracellular diffusion of instilled drugs in bladder is dependent on size and not on MW. Accordingly, the relationship between MW and size or HD= double of Stokes-Einstein radius r for drugs routinely instilled in bladder is not yet reported. 
Here,  we discovered a hitherto unreported log-linear relationship between MW and  with a positive regression coefficient of 9.10± 3.63 (95%CI) and the slope of least-squares line is significantly different from 0, p<0.0001. The bands for 95%CI are indicated by dotted pink lines around least squares line.  The coefficient of determination, r2= 0.61 indicates that most of the variation in hydrodynamic diameter of drugs/probes is determined by log MW and unit rise in log MW raises HD by 9.10 Angstroms (1nm= 10 Angstroms).  Since systemic uptake of drugs declines with the rise in size of drugs, we could estimate that the effective pore radius of urothelial tight junctions is 0.5-0.7nm, when bladder wall is distended ≤100mL.  This approach of indirectly assessing tight junctions have been previously tried on intestine and buccal epithelium (ref.3). While pore size of epithelium in jejunum differs from colon, the tight junctions pore size is expected to be uniform across bladder luminal surface.

The knowledge about the dimensions of urothelial tight junctions is essential for understanding the pathology of IC/BPS and intravesical therapy. A previous clinical study studied systemic levels of permeability probe, (99mtechnetium-diethylenetriaminepentaacetic acid, 99mTc-DTPA) in controls and IC/BPS patients to demonstrate the paracellular diffusion of an 11 Angstrom molecule through tight junctions. Here, we extended that work further by checking for the size of all the drugs whose systemic uptake from bladder is reported. Importantly, urothelial blood flow is intact in clinical studies, whereas studies on ex vivo experimental setup of Ussing chamber ignore the role of mucosal blood flow in washing away of diffused agents, which maintains the concentration gradient for accelerated diffusion in vivo compared to ex vivo.  Furthermore, drug molecules only have two diffuse through two-three layers of umbrella cells in richly vascularized urothelium, before diffused drugs reach urothelial capillaries for systemic uptake. Since ex vivo setup use bladder tissue thicker than two to three tissue layers, the estimated permeability of drugs ex vivo does not explain the serum levels of 0.16mg/L in human adults at 5min after instillation, coincident with the effect of lidocaine on blood pressure and lidocaine toxicity in child.  Despite being 5 times heavier than water or Na+ (Figure 1), smaller atomic size of xenon gas, the heaviest noble gas manifests that electron pairs in outer shell shrink the electron cloud and atomic size, determining HD.  We ignored the role of transcellular transport by umbrella cells in this analysis as transcellular transport is only viable for endogenous molecules: Na+ and water through Na+ and Aquaporin channels. Since most drugs are xenobiotics, they are likely to be absorped paracellularly like instilled fluorescien.  Hydrophilicity presents a challenge as the hydrophilicity of inulin, a polyfructose molecule with MW of 5000 Daltons increases its HD in aqueous solution. Higher HD of inulin compared to albumin having ten times more MW could be explained by the differences in the hydrophilicity of saccharide monomers of inulin vs amino acids monomers in albumin having variable hydrophilicity. Lipophilic drugs (Paclitaxel) are less likely to be engulfed by water molecules in aqueous medium and urothelium is  less lipophilic than octanol.

Here, we computed the evidence to support a non-invasive deterministic approach to assess the bladder permeability of IC/BPS patients and determine the dilatation of tight junctions by assessing the systemic uptake of drugs with known molecular size. This indirect approach is in stark contrast to the traditional ultrastructural studies in which tight junctions pore size is vulnerable to the errors introducced by tissue processing artifacts and not viable for benchmarking in healthy volunteers.

Eldrup, J., Thorup, J., Nielsen, S.L., Hald, T. & Hainau, B. Permeability and ultrastructure of human bladder epithelium. Br J Urol  55, 488-92 (1983).
Ganguly A, Tyagi S, Chermansky C, Kanai A, Beckel J, Hashimoto M, Cho KJ, Chancellor M, Kaufman J, Yoshimura N, Tyagi P. Treating Lower Urinary Tract Symptoms in Older Adults: Intravesical Options. Drugs Aging. 2023. doi: 10.1007/s40266-023-01009-5.
Goswami T,  Jasti B R, Li XL. Estimation of the theoretical pore sizes of the porcine oral mucosa for permeation of hydrophilic permeants. Arch Oral Biol.. 2009 Jun;54(6):577-82.