Relative vascular permeability and vascularity across different regions of the rat nasal mucosa: implications for nasal physiology and drug delivery

Intranasal administration provides a non-invasive drug delivery route that has been proposed to target macromolecules either to the brain via direct extracellular cranial nerve-associated pathways or to the periphery via absorption into the systemic circulation. Delivering drugs to nasal regions that have lower vascular density and/or permeability may allow more drug to access the extracellular cranial nerve-associated pathways and therefore favor delivery to the brain. However, relative vascular permeabilities of the different nasal mucosal sites have not yet been reported. Here, we determined that the relative capillary permeability to hydrophilic macromolecule tracers is significantly greater in nasal respiratory regions than in olfactory regions. Mean capillary density in the nasal mucosa was also approximately 5-fold higher in nasal respiratory regions than in olfactory regions. Applying capillary pore theory and normalization to our permeability data yielded mean pore diameter estimates ranging from 13–17 nm for the nasal respiratory vasculature compared to <10 nm for the vasculature in olfactory regions. The results suggest lymphatic drainage for CNS immune responses may be favored in olfactory regions due to relatively lower clearance to the bloodstream. Lower blood clearance may also provide a reason to target the olfactory area for drug delivery to the brain.

2 Supplementary section 1. Rationale for the method used for capillary wall pore size estimation.
An established method to quantify the upper limit of vascular permeability of capillaries for hydrophilic macromolecules based on the pore theory 2 is to systemically administer exogenous tracers of various sizes and compare accumulation of the tracers in the tissue interstitium that occurs as a result of transcapillary diffusion 3,4 . Transport of a hydrophilic molecule through a fluid-filled pore is expected to become increasingly 'hindered' or 'restricted' when the hydrodynamic diameter (d H ) of the molecule approaches the pore diameter and analytical expressions for this behavior have been described for different pore geometries 5 . Here, we quantitatively investigated extravasation of a broad size range of systemically administered hydrophilic macromolecule tracers to assess whether significant regional differences in vascular permeability characteristics exist across and within the nasal respiratory and olfactory mucosae. This experimentally observed quantitative data showing size-dependent extravasation of tracers in different regions of the nasal mucosa was then fit to a model for 'motion of a closely-fitting sphere in a fluid filled tube' (equation (1)) 1 to estimate a diameter for capillary wall pores in different regions of the nasal mucosa.

Supplementary section 2.
Fitting the cylindrical pore model to the observed fluorescence intensity data in the nasal mucosa predicts capillary wall pore size in the mucosa.
To obtain our experimental data reflecting relative permeability to hydrophilic macromolecules in different regions of the nasal mucosa, four fluorescent Texas Red (TR) labeled hydrophilic macromolecular tracers of increasing hydrodynamic diameters (TR-Dex3 < TR-Dex10 < TR-BSA < TR-Dex70) ( Table 1) were administered systemically in separate animals. In each case, the tracer was allowed to circulate for 30 minutes following which the animal was exsanguinated by perfusion with phosphate buffered saline (PBS) to eliminate blood borne signal and fixative to prevent post-mortem movement of the extravasated tracer in the tissue interstitium. The nasal passages were then exposed and tracer extravasation into the nasal mucosa was quantified by measuring Texas Red fluorescence signal (Fig. 3). Auto-fluorescence was determined and subtracted by carrying out control experiments where saline alone was systemically administered in place of tracer. Since tracers were conjugated to different amounts of Texas Red, tracer doses were selected so as to constrain the moles of Texas Red in each experiment (Table 1).
We have previously derived the relationship: where D' is the effective diffusion coefficient through a capillary wall pore, D is the free diffusion coefficient of each tracer, FL, the arbitrary fluorescence intensity units (i.e. Texas redassociated signal) obtained for each tracer in a given region of the nasal lamina propria minus background auto-fluorescence intensity measured for the same region in saline control experiments (i.e. the colored bars in Fig. 3b-k), and  (Supplementary table S1).
We calculated the right hand side of equation (10) i.e., the Y value for each tracer in different regions of the nasal mucosa using our experimental data as shown in Supplementary table S1. Y 1 , Y 2 , Y 3 , and Y 4 are known from experimental data for different regions of the nasal mucosa, where subscript 1 corresponds to TR-Dex3, 2 corresponds to TR-Dex10, 3 corresponds to TR-BSA and 4 corresponds to TR-Dex70 (Supplementary table S1). X 1 , X 2 , X 3 , and X 4 can be evaluated explicitly using the cylindrical pore model (equation (1)) by assuming a value for d pore .
Assuming a cylindrical geometry typical of many vascular pores 2,6 , the cylindrical pore model provides the following relationship 1 : For a specific tracer with a fixed diameter (d tracer ) the X terms (i.e., D'/D) are a function of d pore . Our objective was to determine the value of X and thus d pore for a given nasal region that best fit our experimental data (Y value) across multiple tracers. When evaluating X terms using the cylindrical pore model, the lower limit for the d pore values was set to the hydrodynamic diameter (d H ) of the tracer since the cylindrical pore model is applicable only when d tracer < d pore (equation (1)). The upper limit for d pore values was arbitrarily set to 100 nm, since the largest fenestrations would be expected to have an upper limit of permeability below this value 6 . X values were obtained using MATLAB for all d pore values within the aforementioned range with a resolution of 0.0001 nm.
The constant of proportionality in equation (10) does not allow a direct comparison between the cylindrical pore model predicted X terms (left hand side of equation (10)) and the experimentally measured Y terms (right hand side of equation (10)). However, since we have data for multiple tracers in a given nasal mucosal region, we were able to marginalize out this constant of proportionality by a normalization operation. The method was to normalize each of the Y 2 , Y 3 , and Y 4 values by Y 1 to obtain the normalized Y terms Y 2 /Y 1 , Y 3 /Y 1 , and Y 4 /Y 1 (where subscript 1 corresponds to TR-Dex3, 2 corresponds to TR-Dex10, 3 corresponds to TR-BSA and 4 corresponds to TR-Dex70). We then directly compared the normalized Y terms to cylindrical pore model predicted X terms normalized in a similar way i.e. (X 2 /X 1 , X 3 /X 1 , and X 4 /X 1 ) for the aforementioned range of d pore values. The process was repeated using each of the tracers as the normalization reference for a given nasal region (e.g. normalizing by Y 2 yielded terms Y 1 /Y 2 , Y 3 /Y 2 , and Y 4 /Y 2 and so on). Experimental data (Y) following normalization is provided in Supplementary table S2. Normalization of cylindrical pore model predicted X terms and fitting the model predicted terms to our experimental data (Y terms) was carried out using MATLAB. First, the squared differences between the normalized experimental (Y) values and corresponding normalized cylindrical pore model predicted (X) values over the aforementioned range of d pore values was calculated. An example of squared differences across the entire range of d pore values for each tracer normalization is shown for the Nasoturbinate site 1 (NT1) area of the respiratory region ( Supplementary Fig. S1).
We found that normalization with data from the smaller two tracers (TR-Dex3 and TR-Dex10) yielded more robust estimates. Normalization by TR-Dex70 for all regions and additionally by TR-BSA for the third dorsal rostral ethmoturbinate (3EDR) olfactory region resulted in much larger estimated d pore values (Supplementary Fig. S1d). Based on the value ranges of the predicted X for the four different normalizations, it was observed that the 'ranges' of the squared differences between normalized predicted (X) and normalized experimental (Y) values increased with the size of the tracer, i.e. the squared differences were smallest for TR-Dex3 and largest for TR-Dex70 normalization (see y-axis values from Supplementary Fig. S1). The very large squared difference ranges were close to the MATLAB numerical limits (Supplementary Fig. S1d) and caused the resolution of predicted d pore to be poor. Hence TR-Dex70 normalization was neglected for reporting the best estimates in the respiratory region and NALT while TR-BSA and TR-Dex70 normalization was neglected for reporting the putative best estimates for the olfactory region 3EDR.
Finally, a determination of the best fit average d pore for different nasal regions was obtained by minimizing the mean-of-the-squared-differences (MSD) between X and Y values for a particular tracer normalization in each nasal region (Supplementary Fig. S2). The final estimated capillary wall pore size for a particular region of the nasal passage was then the d pore value corresponding to the average MSD value across all tracer normalizations (   (Fig.  3), the free diffusion coefficient (D) (Table 1), and the area under the plasma concentration versus time curve from 0 to 30 minutes for the Texas Red signal corresponding to each tracer ( 30 0 AUC ) were used to calculate a term Y. As explained in supplementary section 2, Y corresponds to the right hand side of equation (10). a The 3 rd dorsal rostral ethmoturbinate (3EDR) region had the highest extravasation of all four systemically administered tracers within the olfactory region. We therefore use the tracer fluorescence intensity above background in this area as representative of the olfactory region. In 3EDR fluorescence intensity was significantly above background only for TR-Dex3, while fluorescence intensity above background for TR-Dex10 and TR-BSA showed a trend towards significance. We therefore, provide the results for the 3EDR region as a putative estimate that is used for comparison to other regions in our discussion but exclude it from our results in Table 2. 6 Supplementary table S2: Normalizing experimentally observed fluorescence intensity data in different regions of the nasal mucosa to allow comparison to the cylindrical pore model.