This is the first comprehensive analysis of the instilled drug’s serum levels to support the principle that systemic uptake is preceded by passive diffusion which is determined by physicochemical properties. The restricted diffusion of drugs across the bladder epithelium (ex vivo) lends credence to the concept of the blood-urine barrier, a counterpart of the blood-brain barrier. However, inferences drawn from ex vivo setup are often challenged by a pronounced variability in the serum levels of instilled drugs due to extensive dilution in the systemic circulation and rapid hepatic clearance of the absorbed drug fraction in pre-clinical and clinical studies (ref.1-3). Since serum levels of instilled drugs are the sum total of absorption and elimination (kinetic steps),  we sought to anchor the concept of bladder permeability to the physiochemical properties of drugs for resolving the confusion in evidence-based medicine by intravesical therapy.

We critically analyzed the absorption of 24 drugs and dyes that are commonly instilled into mammalian bladder to construct a first-order, multiple linear regression model using the physicochemical properties, also factored in the Lipinski's rule for absorption of drugs across cellular membranes:  molecular weight (MW), hydrodynamic diameter, partition coefficient (P), polar surface area (area of the polar atom- nitrogen and oxygen in a molecule) and dissociation constant (pKa). A skew in the systemic uptake data of drugs required log transformation of MW and P for deriving a linear relationship and the significance and the 95% confidence limits of the least-squares line was determined by the F test and Student's t-test, respectively.

A linear increase in the hydrodynamic diameter with the ascendancy of MW for drugs/probes tabulated in Table 1 reaffirms the deterministic relationship between MW and hydrodynamic diameter. Both Table 1 and scatter plot of Fig.1  reinforce that systemic uptake of disparate drugs is inversely related to their log MW, determined by a  negative regression coefficient of  -12.77 and conforms to Stokesian Diffusion, according to which drugs diffuse as spheres of Stokes-Einstein radius (r= half of the hydrodynamic diameter)  into the tissue medium of viscosity (u) according to the diffusivity equation: D= kT/6pi*r*u;  where k and T in the numerator are the Boltzmann constant (k) and temperature (T) of 37°C for in vivo experiments adds another constant and makes u also constant in the denominator.  Therefore, except for ‘r’, all other terms in the diffusivity (D) equation are constants for intravesical drug delivery. 
Fig.1 highlights that factors other than molecular size also influence the systemic uptake of instilled drugs. However, a correlation coefficient, r of 0.371 between log P and the polar surface area of plotted drugs sheds light on the problem of multicollinearity in their physicochemical properties. Since parsimony of variables increases the predictive power of the model, only  regression coefficients for log MW and log P were incorporated in the First-order linear-log multiple regression model:  % systemic uptake = 52.15-12.77 log MW +0.52 log P
The least-squares slope for log MW = -12.77 ± 9.29 (95% CI) is thrice in magnitude to the standard error of 4.403 and the t-statistic of -2.9 is significantly different from 0 (p<0.01) and the same is true for intercept.  Our predictive model passes the Kolmogorov-Smirnov log normality test and global F test for significance (p<0.05). The coefficient of determination (r2) = 0.38 implies that log MW predicts 38% variation in systemic uptake and a unit increase in log MW reduces the uptake by 12.77% for drugs having MW ranging from 24 to 66000 Daltons.  The impact of the covariate, log P, and the number of observations in our model is indexed by
adjusted r2 = 0.32.  While a rise in MW reduces the systemic uptake, a rise in log P increases the systemic uptake as illustrated by the higher uptake of Methylene blue compared to Evans blue and of amphiphilic molecules like lidocaine (log P 1.64) over mitomycin (log P -0.38).  However, the t-statistic for log P did not reach significance with available data.

Our predictive equation is attested by >50% of the instilled dose for small MW of salicylate (137 Daltons) and thiotepa (189.23 Daltons) reaching serum compared to just <0.01% dose for iodinated albumin due to its large MW (66500 Daltons) (ref. 1-3). Our analysis affirms that MW is a suitable proxy for hydrodynamic diameter because both exhibit an inverse relationship with the systemic uptake, whose positive relationship with log P is evident from a >3fold higher systemic uptake of lipophilic oxybutynin (log P 4.2, 357 Daltons; ref.3) over hydrophilic mitomycin (log P-0.38, 334.33 Daltons). Log P indexes the solubility ratio between water and 1-octanol mixture with the hydrophilic, ionized fraction of drug partitioning into the water and the partitioning of the lipophilic, unionized fraction into 1-octanol representing the ease of drug's diffusion into the lipid bilayer of cell membranes. Drugs that strike a balance on the hydrophilic and lipophilic scale or are amphiphilic exhibit higher systemic uptake than drugs that lie on the extremes of the hydrophilic and lipophilic scale.  With regard to the entry routes for drugs, the energy-dependent active transport by umbrella cells (transcellular route) is generally reserved for endogenous substances (Na+, urea) instilled in the bladder but most of the instilled xenobiotics can only reach systemic circulation via passive paracellular diffusion across tight junctions as highlighted by instilled fluorescein uptake in preclinical and clinical studies (Table 1; ref.2). Therefore, an increase in MW increases the hydrodynamic diameter which ends up hindering the diffusion of drug "spheres" through the tortuous gap of tight junctions (ref.3) while the inflammation-driven dilation of urothelial tight junctions increases the systemic uptake of instilled urea, salicylate, and lidocaine. It appears that toxicokinetic information on xenobiotics:  Formalin and DMSO especially their elimination and distribution half-life of <2min, respectively was overlooked by researchers seeking to determine their systemic uptake by erroneously drawing the first blood sample at the standard timepoint of 15min after instillation, when 7 half-lives have elapsed or 97-99% of the absorbed formalin and DMSO have been either eliminated or diluted in the systemic distribution, respectively to ensure homeostasis. In fact, garlic odor sensed immediately in the exhaled air of subjects instilled with 50% DMSO is generated by dimethyl sulfide, a DMSO metabolite generated in the liver within 2min of instillation and the odor-causing metabolite represents just 3% of DMSO dose absorbed from bladder (~40%).

These findings anchor the concept of bladder permeability of instilled drugs to their physicochemical properties, namely, log MW and log P  for addressing the gross mismatch between the limited ingress of Evans Blue dye (960.8 Daltons) in rodent bladder and significant systemic uptake (>20% of instilled dose) of smaller MW drugs, lidocaine, and oxybutynin in healthy human volunteers. While how larger MW retards passive paracellular diffusion is self-explanatory,  our predictive equation also brings the log P of instilled drugs into the limelight and explains why the amphiphilic nature of phospholipids in liposomes facilitates endocytosis-mediated bladder uptake above and beyond the paracellular diffusion of polar drugs like heparin.  Log P indexes the positive impact of non-polarity on diffusion across cell membranes, which gets manifested in the limited ingress of polar Evans Blue relative to ingress of less polar Methylene blue /fluorescein, when instilled at volumes that are  >90% and < 10% of maximum bladder capacity, respectively.

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