HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Full Text (PDF) Free All Versions of this Article: 101/4/1162    most recent 00389.2006v1 Submit a response Alert me when this article is cited Alert me when eLetters are posted Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in ISI Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via ISI Web of Science (6) Citing Articles via Google Scholar Google Scholar Articles by Reddy, S. T. Articles by Swartz, M. A. Search for Related Content PubMed PubMed Citation Articles by Reddy, S. T. Articles by Swartz, M. A.

A sensitive in vivo model for quantifying interstitial convective transport of injected macromolecules and nanoparticles

¹Institute of Bioengineering, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland; ²Department of Biomedical Engineering, Northwestern University, Evanston, Illinois; ³School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Manchester, United Kingdom; and ⁴Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts

Submitted 2 April 2006 ; accepted in final form 30 May 2006

	ABSTRACT

TOP ABSTRACT Glossary MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX GRANTS ACKNOWLEDGMENTS REFERENCES

 
Effective interstitial transport of particles is necessary for injected drug/diagnostic agents to reach the intended target; however, quantitative methods to estimate such transport parameters are lacking. In this study, we develop an in vivo model for evaluating interstitial convection of injected macromolecules and nanoparticles. Fluorescently labeled macromolecules and particles are coinfused with a reference solute at constant infusion pressure intradermally into the mouse tail tip, and their relative convection coefficients are determined from spatial and temporal interstitial concentration profiles. Quantifying relative solute velocity with a coinfused reference solute eliminates the need to estimate interstitial fluid velocity profiles, greatly reducing experimental variability. To demonstrate sensitivity and usefulness of this model, we compare the effects of size (dextrans of 3, 40, 71, and 2,000 kDa and 40-nm diameter particles), shape (linear dextran 71 kDa vs. 69 kDa globular protein albumin), and charge (anionic vs. neutral dextran 3 kDa) on interstitial convection. We find significant differences in interstitial transport rates between each of these molecules and confirm expected transport phenomena, testifying to sensitivity of the model in comparing solutes of different size, shape, and charge. Our data show that size exclusion (within a specific size range) dominates molecular convection, while mechanical hindrance slows larger molecules and nanoparticles; proteins convect slower than linear molecules of equal molecular mass, and negative surface charges increase convection through matrix repulsion. Our in vivo model is presumably a sensitive and reliable tool for evaluating and optimizing potential drug/diagnostic vehicles that utilize interstitial and lymphatic delivery routes.

drug delivery; size exclusion; lymphatic uptake; extracellular matrix; subcutaneous

Factors such as size, shape, charge, and hydrophobicity influence the interstitial transport of macromolecules and nanoparticles, along with the complex microarchitecture of the extracellular matrix (ECM). Composed of fluid, solutes, fibrillar and bound proteins, and proteoglycans, the physical properties of the interstitial space are similar to those of a gel, and two-phase models where interstitial fluid is either free or bound are typically used to describe fluid and solute exchange in the interstitial space (5, 21, 22, 24, 25). Such models of interstitial protein transport typically consider the solutes as a single phase in examining their effects on fluid transport and thus do not attempt to describe differences in the transport between different solutes; moreover, such theoretical models are difficult to test experimentally in living tissue, and most experimental models of interstitial solute convection have been performed in very well-defined in vitro systems rather than in vivo. For example, Johnston and Deen (11, 12) investigated convection of various proteins through agarose gels, which have a porous microstructure similar to that of the interstitium and demonstrated that molecular size dominates the convective differences there. Only a few measurements of local interstitial convection have been achieved (3), including the work of Chary and Jain (8), who first directly measured albumin convection by fluorescence recovery after photobleaching in normal and neoplastic tissues; this technique is more commonly used to measure protein or macromolecular diffusion in vivo (1, 4, 7, 14).

Here we describe a new in vivo model that can directly compare the interstitial convection rates of two different solutes from the same infusion in living skin, minimizing experimental variability and thus providing a tool for optimizing interstitially injected drug vehicles and imaging agents. It expands on a previous model in mouse tail skin¹ that was developed to analyze fluid velocity in the superficial lymphatic network (3, 19, 20). Our data demonstrate the sensitivity of the model, as macromolecules and nanoparticles differing in size, shape, and charge can be differentiated with respect to their convective transport parameters; additionally known interstitial transport phenomena are further validated by the model. Of course, molecular transport behavior may be different within different tissues, since the composition and architecture, degree of hydration, degree of vascularization and lymphatic drainage, and fixed charge density of the ECM vary not only among different tissues but can also vary within the same tissue according to diet, age, etc. However, because our model relies on the differential transport behavior between two coinjected molecules, it can eliminate some of this variability and indeed may prove useful for characterizing some of these differences. This model thus exhibits sensitivity, usefulness, and reliability in evaluating and optimizing interstitial transport of potential drug vehicles and diagnostic agents that are delivered interstitially (e.g., by subcutaneous injection).

	Glossary

TOP ABSTRACT Glossary MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX GRANTS ACKNOWLEDGMENTS REFERENCES

 

K

Hydraulic conductivity (mm²·s^–1·mmHg^–1)

P_o

Interstitial fluid pressure (mmHg)

u_i

Mean solute velocity (mm/s)

v

Axial fluid velocity (mm/s)

x_i

Mean distance traveled by solute i (mm)

_i

Mean residence distance of solute i (mm)

Ratio of interstitial to lymphatic conductance (mm)

Lymphatic conductance (s^–1·mmHg^–1)

_i

Convection coefficient (ratio of solute velocity u_i to fluid velocity v)

P_o

Normalized intensity

_i

Average relative solute velocity ratio

	MATERIALS AND METHODS

TOP ABSTRACT Glossary MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX GRANTS ACKNOWLEDGMENTS REFERENCES

 
Experimental setup.   This study utilized a total of 18 female 6-wk-old mice that weighed between 20 and 30 g. All protocols were approved by the Animal Care and Use Committees of Northwestern University and Massachusetts General Hospital. Anesthesia was performed by subcutaneous injection of ketamine hydrochloride at 10 mg/kg body wt (Ketalar, Parke-Davis, Morris Plains, NY) and xylazine at 1 mg/kg (Rompun, Haver Mobay, Shawnee, KS). The tail was gently washed, and the mouse was placed on a small plate in the supine position and its tail immobilized from underneath with tape. A small heating pad was used to maintain body temperature throughout the experiment.

Infusions were accomplished using a setup described earlier (20) as shown in Fig. 1A. The injectate (a solution of fluorescently labeled macromolecules) was drawn into a catheter, which was connected to a pressure head of 33 mmHg. A 30-gauge infusion needle was inserted intradermally, in a proximal direction parallel to the tail axis, 1 mm into the tail tip. At the beginning of each experiment (time t = 0), the stopcock was opened, creating a step change in pressure at the tip from physiological baseline interstitial fluid pressure [normally 9 mmHg (20)] to the reservoir pressure and thereby initiating infusion into the tail. The rate of fluid introduced (monitored with a bubble far upstream in the tubing) averaged 0.1 µl/min into 20 mm³ of tissue, or 5 µl·g^–1·min^–1 (yielding maximal interstitial fluid velocities on the scale of 50 µm/min) and did not result in visible swelling, and edema was avoided by normal drainage into lymphatics.

View larger version (28K): [in this window] [in a new window]   Fig. 1. A: schematic of the experimental setup where P represents a fixed pressure head of 33 mmHg. At time t = 0, the infusion starts, the flow rate is monitored with a bubble in the infusion line, and the injectate is deposited interstitially. Images are captured from an epifluorescence microscope with a charge-coupled device camera (CCD). B and C: fluorescence intensity profiles from a typical coinfusion. B: images of the interstitium, taken a few seconds apart, following a coinfusion of 71-kDa dextran (71k-Dx; green)/3-kDa dextran (3k-Dx; red) show that the 71k-Dx has moved further within the interstitium, and more efficiently into the lymphatics, than the 3k-Dx. The infusion site is upstream from the left edge of the image. C: average intensity profiles corresponding to the images in A.

Image acquisition.   Fluorescence images of the tail interstitium were recorded with an epifluorescence microscope (Zeiss, Germany) and a high-performance charge-coupled device camera system (SenSys, Photometrics, Tuscon, AZ) described earlier (20). Two fluorescence channels (Omega Optical, Brattleboro, VT), consisting of fluorescein and rhodamine filters were used to measure fluorescence from the FITC- and Texas red-labeled solutes, respectively, with no signal overlap detected between the two fluorophores. In addition, a linear range of concentration intensity was verified in flat capillary tubes of 300-µm inner diameter (Vitrocom), which is approximately the thickness of the skin in the tail. Although this does not verify that the same concentration-intensity relationship will exist in tail skin, it does support the validity of the assumption of concentration-intensity linearity in tail skin since 1) the tissue thickness is approximately constant throughout the measurement region (verified histologically), and 2) the maximum intensity measured is within the linear range. Images were taken at four to seven consecutive windows moving proximally along the tail from the site of infusion (the exact position of x = 0 was arbitrary; see Theory). The background intensity was taken just before beginning the infusion, and images were captured every 2–8 min at fixed exposure. In most cases, only four consecutive windows were needed to capture the full concentration profile.

Figure 1B shows a typical image of the mouse tail under green and red fluorescence at approximately the same time (10 min, with 2 s between them) from a coinfusion of 71k-Dx/3k-Dx, demonstrating their relative concentration profiles. In this case, the larger molecule (71k-Dx in green) had traveled, on average, further than the smaller reference solute (3k-Dx in red); the analysis of such concentration profiles is addressed in the next section.

Data analysis.   The diameter of the infusion needle is relatively large with respect to the tip of the mouse tail where the infusion is made; this effectively makes the fluid transport problem one-dimensional (changes only in the axial direction), since the entire tip of the tail is uniformly infused. Therefore, we considered only the axial convective transport of fluid and solute, because fluid pressure gradients, and thus convective transport, in the radial direction were negligible in comparison (20). Each image of the tail, 3 mm wide, was divided into 60 vertical subregions (27 pixels or 0.05 mm wide), such that intensity was averaged over the height of the tail but in very small increments in the direction of flow. In this way, a virtually continuous axial concentration profile could be measured at each time point. Intensity histograms were created using Metamorph software (Universal Imaging, Downington, PA). Figure 1C shows the average intensity vs. distance profile for the corresponding image in Fig. 1B. The average intensity decreases over distance, since the concentration of the solute is at its maximum value at the site of infusion (x = 0).

Figure 2 shows average intensity vs. distance profile at different time points across the tail interstitium, and mean intensities I were normalized to :

(1)

where I_min is the initial background intensity and I_max is the intensity of the injectate (e.g., I at x = 0). Again, we assumed that the intensity was linearly related to the solute concentration such that the normalized intensity was equivalent to the normalized concentration.

View larger version (32K): [in this window] [in a new window]   Fig. 2. Typical intensity vs. distance profile from a 3k-Dx infusion.

	THEORY

TOP ABSTRACT Glossary MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX GRANTS ACKNOWLEDGMENTS REFERENCES

Several factors affect the solute convection velocity through the tissue interstitium: properties of the solute, such as size, charge, and hydrophobicity; properties of the interstitial matrix, such as porosity and fixed charge density; and the fluid velocity, which provides the driving force for convection and depends on the infusion pressure and the hydraulic resistance of the tissue. For very small solutes having no interactions with the matrix, the average solute velocity will closely approximate the average fluid velocity (u_i v). Larger molecules may be restricted to a smaller fraction of the pores (e.g., only to the larger pores with higher average fluid velocities), leading to an average solute velocity that is higher than the average fluid velocity (u_i > v), such as seen in size exclusion chromatography (6). On the other hand, large molecules may also interact with the ECM, either by mechanical hindrance or charge interactions, which could lead to an apparent solute drag and result in a lower average solute velocity than that of the fluid (u_i < v). For proteins and particles whose sizes are on the order of 1–50 nm, one would expect a combination of these effects. Our aims here were not to theoretically evaluate each of these complex interactions, but instead to simply measure and compare the average convective velocities for a variety of molecules. The fact that we coinjected meant the fluid velocity was the same for two molecules, and therefore their solute velocities could be directly compared. A measure of net solute velocity is the most relevant information needed to compare and optimize interstitial transport of an injected large molecule, particle, or drug carrier. Thus our measurement of net solute velocity relative to that of a reference molecule eliminates the need to accurately determine fluid velocity (which decreases with distance from the infusion) and reduces experimental variability. The relative solute velocity ratio also reflects the relative lymphatic uptake efficiency, since the interstitium poses a greater barrier to lymphatic uptake than the lymphatic vessels (18).

The Darcy scale axial fluid velocity v in the mouse tail skin following an interstitial infusion has been previously shown to decay exponentially with distance at steady state (20):

(2)

where is the effective lymphatic conductance (s^–1·mmHg^–1), K is the effective hydraulic conductivity (mm²·s^–1·mmHg^–1), P_o is the interstitial fluid pressure (mmHg) in the tissue (above baseline, due to the injection), and = (K/)^1/2 is the ratio of interstitial to lymphatic conductance. Each of these depends only on the specifics of the tissue and injection; thus they may differ between animals but will be the same relative to each coinjected solute.

We assumed that the mean velocity of solute i, u_i, is linearly related to the mean fluid velocity, according to a convection coefficient _i,

(3)

The assumption that fluid and solute velocities are linearly related is valid only within the convection-dominated transport region, and only within a region where tissue fluid volume fraction is relatively constant, as is the case within our measurement region (for further validation, see Ref. 20). In the case of a very small solute (relative to interstitial pore size), one can expect the solute velocity to approach the fluid velocity (_i 1). When the solute is coinjected with a reference solute r, the ratio of their velocities will equal the ratio of their convection coefficients, since v is the same for each. The term _i is introduced as the ratio of the convection coefficient of solute i with that of the reference solute r, which can thus be directly measured from their relative convection profiles without knowing the fluid velocity profile:

(4)

To determine _i, we considered that

(5)

where x_i is the mean distance convected by solute i at time t. Note that this assumes that the only contributing factor to the movement of the solute is fluid convection; in other words, the partitioning of solute from fluid uptake into blood and lymphatic capillaries is small compared with convective transport, and this assumption is explained in the APPENDIX. Upon integration, a logarithmically decaying relationship between x_i and t is seen:

(6)

The constant = P_o depends only on fluid parameters. Furthermore, the moving front of the solute is diffuse, so x_i = _i can be determined as a concentration-weighted average distance (i.e., by calculating the mean residence distance, _i) at any time point according to:

(7)

This results in a new data set of _i vs. t for each of the test and reference solutes; Fig. 3 illustrates such a data set.

View larger version (16K): [in this window] [in a new window]   Fig. 3. Typical mean residence distance vs. time ( vs. t) curve from a 2,000-kDa dextran (2M-Dx; ) and 3k-Dx (+) coinfusion. As expected, (the distance of the moving front) increases with time, since the solutes are being continuously infused at a constant pressure. Also shown are the lines that are fit for 2M-Dx (dashed line) and 3k-Dx (solid line) by nonlinear regression. From these figures, a new data set of vs. t for each particle is generated. With this data set, the difference line (xxx) is calculated (which is fit to Eq. 9 through nonlinear regression).

(8a)

and

(8b)

The values of x and x represent the true site of injection (x = 0) for the test and reference solutes, which are extrapolated from the intensity profiles (note that the exact deposit site is unknown during the experiment).

Since depends only on the fluid and not the solutes, Eqs. 8a and 8b can be collapsed into a single data set (note that x and x are equal to each other and therefore cancel out):

(9)

The original data did not contain identical time points for each of the coinjected solutes (i.e., they were seconds apart since two fluorescent channels could not be recorded simultaneously), so a new data set, the difference line (_i – _r), was generated from the best fits of each of the individual solute profiles (Eqs. 8a and 8b) using NLREG software (Phillip Sherrod, Brentwood, TN). This new data set was then fit to Eq. 9, enabling the ratio of the new fitted values of _i and _r, or the average relative test solute velocity _i, to be determined. Figure 3 shows a plot of a typical vs. t curve (from an injection of 2M-Dx and 3k-Dx as a reference), including the difference line, which was fit to Eq. 9 through nonlinear regression to determine _i.

	RESULTS

TOP ABSTRACT Glossary MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX GRANTS ACKNOWLEDGMENTS REFERENCES

 
Average relative solute velocity ratios.   Table 1 compares the average relative velocity ratio and size for each of the test solutes. Radii were estimated as follows: for dextrans, using the formula r = 0.305M^0.47 (where M = molecular mass) of Leypoldt and Henderson (13) and for albumin, from Garlick and Renkin (9). The average nanosphere radius was determined by the manufacturer to be 20 nm. Figure 4 compares the mean _i values for each of the test particles.

View larger version (10K): [in this window] [in a new window]   Fig. 4. Average relative solute velocity ratio, i, and standard deviation for each test particle. 3k-An-Dx, anionic 3-kDa dextran; 40k-Dx, 40-kDa dextran; 69k-BSA, bovine serum albumin at 69 kDa.

The statistically significant differences of _i for the various comparisons mentioned above demonstrate the sensitivity of this model. Additionally, the known and expected convective transport phenomena in the interstitium, such as the effects of size, shape, and charge, were statistically verified by this model, therefore further testifying to its sensitivity.

	DISCUSSION

TOP ABSTRACT Glossary MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX GRANTS ACKNOWLEDGMENTS REFERENCES

 
This study illustrates a new experimental tool for estimating interstitial convective properties of injected macromolecules and particles by coinfusion with a reference molecule into mouse tail skin and determining their relative interstitial velocity profiles. This addresses the need for quantifying and comparing interstitial transport parameters of macromolecules and nanoparticles in vivo for evaluating and optimizing interstitially injected drugs and drug carriers. The model is unique in both approach and capability: using robust theoretical modeling, together with a simple experimental system, it provides an effective means to evaluate small differences in interstitial transport between various types of particles by eliminating experimental differences between animals, injection conditions, and flow characteristics particular to the needle placement and specific anatomy of each mouse tail.

Several key generalizations of interstitial transport phenomena are demonstrated from our results. First, a size exclusion phenomenon apparently dominates differences in solute transport for uncharged dextrans within a molecular mass range of 3–71 kDa. Again, size exclusion refers to the phenomenon where smaller molecules convect at a slower rate than larger molecules, and such observations of macromolecules or plasma proteins through the interstitial space have been extensively reported by others (2, 6, 22, 23). For larger molecules such as 2M-Dx, we observed that mechanical hindrances due to solute interactions with the matrix counteract the size exclusion phenomena and slow convection compared with 71 kD-Dx. Furthermore, the 40-nm nanospheres convected more slowly through the interstitium than all the test molecules and reference molecules. This may be attributed to the fact that the nanospheres are rigid with a fixed radius as opposed to the dextran molecules (whose Stokes-Einstein radii represent the gross approximation of the volume that they may occupy), which are flexible and deformable chains that can easily move through pores and avoid other hindrances.

While size was important, charge and shape were also seen to affect interstitial transport. To examine the effects of charge, we compared anionic dextran (3k-An-Dx) with neutral 3k-Dx. The anionic molecule moved with a higher average velocity through the interstitium than the neutral molecule, suggesting that electrostatic repulsion may serve to reduce the interactions between a negatively charged solute and the ECM, since the latter is also negatively charged (2).

The albumin served to compare the effects of both size and shape since, although at 69 kDa it is roughly the same molecular mass as the 71k-Dx, it is a folded protein with heterogeneous charge distribution. We found that it convected nearly three times slower than the 71k-Dx (_69k-BSA = 2.4, while _71k-Dx = 7), and its convection coefficient was similar to that of 40k-Dx (Table 1). This suggests that 1) molecular mass does not affect solute transport as much as size and shape, and 2) globular proteins, with their nonuniform charge distribution, may interact more with the ECM than neutral linear molecules, leading to greater mechanical hindrance in convection.

In summary, these experimental studies demonstrate the development, utility, and sensitivity of a model for quantifying convective interstitial transport of injected macromolecules and nanoparticles. It is ideal for comparing and optimizing interstitial transport of different drug delivery vehicles such as polymer nanoparticles, micelles, or antibody-protein conjugates that utilize the interstitium and lymphatics as delivery routes. Furthermore, this model may be employed to characterize the effects of different remodeled tissue matrix on interstitial transport, especially in situations where drug delivery is important, such as in tumors or implants, or in lymphedematous conditions.

	APPENDIX

TOP ABSTRACT Glossary MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX GRANTS ACKNOWLEDGMENTS REFERENCES

 
This problem involves the transport of 1) fluid, which moves through the interstitium and can be absorbed into the blood vessels and lymphatics, 2) a smaller solute that may be absorbed into blood and lymphatics, and 3) a larger solute that can be absorbed by lymphatics but not blood vessels. All transport is assumed to be dependent only on x and t. The fluid movement is slowed by uptake into blood or lymphatics, according to the following steady-state mass balance:

(A1)

where _l and _b are the uptake rates into lymphatic and blood vessels (ml·s^–1·ml tissue^–1), respectively.

As the transport problem is one-dimensional in the x-direction (i.e., in the axial direction along the length of the tail), the resulting mass balance for solute i moving with this fluid, assuming convective transport dominates molecular diffusion, is:

(A2)

where C_i is concentration of solute i (mg/ml tissue), u_i is convective velocity of i (x-component of u), D_i is dispersion (convective) coefficient of i (here we assume convective dispersion dominates over molecular diffusion in the region of measurement, which was verified experimentally), and J and J are the fluxes of i into the blood and lymphatics, respectively.

The solute velocity varies in x and is related to the fluid velocity by a convection coefficient _i:

(A3)

J and J are described by:

(A4)

and

(A5)

where and are the solute reflection coefficients for blood and lymphatic uptake, respectively; PS_b and PS_l are the permeability coefficients multiplied by the surface areas for blood and lymphatic vessels, respectively; and C and C are the change in solute concentration between the interstitium and blood and lymphatic vessels, respectively.

We assume that the lymphatics are at least as permeable to solutes as the interstitial space (18), so that there is no concentration difference between solute in the interstitial space and that in the lymphatics:

(A6)

and

(A7)

This essentially implies that solute transport from the interstitial space into the lymphatics occurs mainly by convection, and that there is no convective partitioning of solute at the lymphatic-interstitial boundary.

Combining Eq. A1 through Eq. A7 (and noting that the term describing convective uptake into the lymphatics balances out with the decrease in overall flow rate due to lymphatic uptake),

(A8)

Thus lymphatic uptake neither concentrates nor dilutes the solute concentration in the interstitium, as expected, if we assume that the lymphatics are freely permeable to molecules within our size range.

Substituting dimensionless variables = x/L, = t/, and _i = C_i/C_o, where L is the length scale over which our solute convects in time and C_o is the maximum (injected) concentration. Assuming C is sufficiently low compared with C_i that C C_i, we obtain the dimensionless equation:

(A9)

Thus changes in solute concentration measured in the interstitium can be due to convective transport, convective dispersion, fluid uptake into the blood (which would change interstitial solute concentration only if solute is "held up" or filtered such that interstitial concentration would increase over time), and diffusion into the blood (which would decrease interstitial concentration). The validity of our model rests on the assumption that changes in interstitial solute due to blood uptake of fluid and solute (the terms grouped as "dilution/concentration" in Eq. A9) is small compared with changes due to interstitial convection (the terms grouped "convection" in Eq. A9), and that the actual interstitial solute velocity is approximately equal to the measured velocity of the moving front:

(A10)

To evaluate the scale of this ratio, we averaged the u_i for each solute within the first 0.2 cm from the injection for each experiment, and estimate _b from Starling's Law:

(A11)

where L_v is the filtration coefficient, and P – is the difference in hydrostatic and osmotic pressure, respectively, between the inside and outside of the blood vessel. In skin, L_v 0.01 ml·min^–1·mmHg^–1·100 g tissue^–1 (10), and P – is typically 0–1 mmHg (10), and so during an interstitial infusion, the infusion pressure dominates the driving force for convective fluid uptake into the blood. In our case, the infusion pressure is 33 mmHg but decays exponentially, and baseline tissue pressure in the tail skin is 9 mmHg (18). Therefore, the maximum interstitial pressure is 24 mmHg at x = 0, and the maximum convective flux from tissue into the blood vessels would be _b = 4 x 10^–5 ml·s^–1·g tissue^–1.

We estimated from the literature values for PS (9) and _b (26), according to molecular mass or approximate Stokes-Einstein radius. For u_i, we assume that this is equal to our measured solute velocity, according to the diffuse moving front of the solute (see Fig. 1, B and C), which is to be verified here a posteriori (i.e., if convection does indeed dominate interstitial dilution/concentration due to blood uptake). Thus values of maximum solute velocities were taken at x = 0 and averaged for each solute from plots of vs. t (i.e., Fig. 3). To estimate L, approximate distances at which dC/dx 0 were found to be, on average, 0.5 cm for the solutes. We do not know _i, since we can only calculate velocity ratios from our measurements (i.e., test solute velocity/reference solute velocity) and do not directly measure the fluid velocity v. However, if we assume that _r for the tracer is close to 1 since it is small, or that its limit is 1, then _i = _i (see Eq. 4). Therefore, values for _i were taken from Table 1 for this scaling exercise.

As shown in Table 2, the absolute values of the estimated ratios of interstitial convection to dilution/concentration due to uptake into the blood for solute (convection/dilution from Eq. A10) are always much greater than 1, validating a posteriori the measurement of moving solute front as approximately equal to the solute velocity. Parameter values in Table 2 were obtained or calculated from Refs. 9, 10, 23, and 24.

	GRANTS

TOP ABSTRACT Glossary MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX GRANTS ACKNOWLEDGMENTS REFERENCES

	ACKNOWLEDGMENTS

TOP ABSTRACT Glossary MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX GRANTS ACKNOWLEDGMENTS REFERENCES

 
The authors thank Dr. Larry Baxter, Howard Brenner, Fan Yuan, and Talid Sinno for helpful discussions, and Dr. Rick Boardman, Dr. Jeremy Goldman, and Eva Mika for technical assistance.

	FOOTNOTES

 

Address for reprint requests and other correspondence: M. A. Swartz, Institute of Bioengineering, Laboratory for Mechanobiology and Morphogenesis, Station 15, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland (e-mail: melody.swartz{at}epfl.ch)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

¹ Differences between mouse tail skin and human skin is likely to be on the same order of magnitude as differences in skin between different humans. Thus we feel that our results are likely generalizable to the degree that they accurately reflect differences in transport parameters in skin. However, interstitial transport properties of macromolecules in different tissues depend not only on properties of the molecule, but also on properties of the ECM. Properties of the ECM, such as composition and architecture, degree of hydration, degree of vascularization and lymphatic drainage, and fixed charge density, may all affect transport. For this reason, the relative transport parameters may differ for injections in tissues other than skin.

	REFERENCES

TOP ABSTRACT Glossary MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX GRANTS ACKNOWLEDGMENTS REFERENCES

 

1. Alexandrakis G, Brown EB, Tong RT, McKee TD, Campbell RB, Boucher Y, and Jain RK. Two-photon fluorescence correlation microscopy reveals the two-phase nature of transport in tumors. Nat Med 10: 203–207, 2004.[CrossRef][ISI][Medline]
2. Aukland K and Reed RK. Interstitial-lymphatic mechanisms in the control of extracellular fluid volume. Physiol Rev 73: 1–78, 1993.[Abstract/Free Full Text]
3. Berk DA, Swartz MA, Leu AJ, and Jain RK. Transport in lymphatic capillaries. II. Microscopic velocity measurement with fluorescence photobleaching. Am J Physiol Heart Circ Physiol 270: H330–H337, 1996.[Abstract/Free Full Text]
4. Berk DA, Yuan F, Leunig M, and Jain RK. Direct in vivo measurement of targeted binding in a human tumor xenograft. Proc Natl Acad Sci USA 94: 1785–1790, 1997.[Abstract/Free Full Text]
5. Blake TR. A theoretical view of interstitial fluid pressure–volume measurements. Microvasc Res 37: 178–187, 1989.[CrossRef][ISI][Medline]
6. Brenner H and Gaydos LJ. Constrained brownian-movement of spherical particles in cylindrical pores of comparable radius—models of diffusive and convective transport of solute molecules in membranes and porous-media. J Colloid Interface Sci 58: 312–356, 1977.[CrossRef]
7. Brown E, McKee T, diTomaso E, Pluen A, Seed B, Boucher Y, and Jain RK. Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation. Nat Med 9: 796–800, 2003.[CrossRef][ISI][Medline]
8. Chary SR and Jain RK. Direct measurement of interstitial convection and diffusion of albumin in normal and neoplastic tissues by fluorescence photobleaching. Proc Natl Acad Sci USA 86: 5385–5389, 1989.[Abstract/Free Full Text]
9. Garlick DG and Renkin EM. Transport of large molecules from plasma to interstitial fluid and lymph in dogs. Am J Physiol 219: 1595–1605, 1970.[Free Full Text]
10. Guyton AC and Hall JE. Textbook of Medical Physiology. Philadelphia, PA: Saunders, 2000.
11. Johnston ST and Deen WM. Hindered convection of ficoll and proteins in agarose gels. Ind Eng Chem Res 41: 340–346, 2002.[CrossRef]
12. Johnston ST and Deen WM. Hindered convection of proteins in agarose gels. J Memb Sci 153: 271–279, 1999.[CrossRef]
13. Leypoldt JK and Henderson LW. Molecular charge influences transperitoneal macromolecule transport. Kidney Int 43: 837–844, 1993.[ISI][Medline]
14. Netti PA, Berk DA, Swartz MA, Grodzinsky AJ, and Jain RK. Role of extracellular matrix assembly in interstitial transport in solid tumors. Cancer Res 60: 2497–2503, 2000.[Abstract/Free Full Text]
15. Nishioka Y and Yoshino H. Lymphatic targeting with nanoparticulate system. Adv Drug Delivery Res 47: 55–64, 2001.[CrossRef][ISI][Medline]
16. Oussoren C and Storm G. Liposomes to target the lymphatics by subcutaneous administration. Adv Drug Delivery Res 50: 143–156, 2001.[CrossRef][ISI][Medline]
17. Reddy ST, Rehor A, Schmoekel HG, Hubbell JA, and Swartz MA. In vivo targeting of dendritic cells in lymph nodes with poly(proplyene sulfide) nanoparticles. J Control Release: 112: 26–34, 2006.[CrossRef][ISI][Medline]
18. Swartz MA. The physiology of the lymphatic system. Adv Drug Delivery Res 50: 3–20, 2001.[CrossRef][ISI][Medline]
19. Swartz MA, Berk DA, and Jain RK. Transport in lymphatic capillaries. I. Macroscopic measurements using residence time distribution theory. Am J Physiol Heart Circ Physiol 270: H324–H329, 1996.[Abstract/Free Full Text]
20. Swartz MA, Kaipainen A, Netti PA, Brekken C, Boucher Y, Grodzinsky AJ, and Jain RK. Mechanics of interstitial-lymphatic fluid transport: theoretical foundation and experimental validation. J Biomech 32: 1297–1307, 1999.[CrossRef][ISI][Medline]
21. Taylor DG, Bert JL, and Bowen BD. A mathematical model of interstitial transport. I. Theory. Microvasc Res 39: 253–278, 1990.[CrossRef][ISI][Medline]
22. Taylor DG, Bert JL, and Bowen BD. A mathematical model of interstitial transport. II. Microvascular exchange in mesentery. Microvasc Res 39: 279–306, 1990.[CrossRef][ISI][Medline]
23. Watson PD, Bell DR, and Renkin EM. Early kinetics of large molecule transport between plasma and lymph in dogs. Am J Physiol Heart Circ Physiol 239: H525–H531, 1980.[Free Full Text]
24. Watson PD and Grodins FS. An analysis of the effects of the interstitial matrix on plasma–lymph transport. Microvasc Res 16: 19–41, 1978.[CrossRef][ISI][Medline]
25. Wiederhielm CA. Dynamics of capillary fluid exchange: a nonlinear computer simulation. Microvasc Res 18: 48–82, 1979.[CrossRef][ISI][Medline]
26. Wolf MB and Watson PD. Measurement of osmotic reflection coefficient for small molecules in cat hindlimbs. Am J Physiol Heart Circ Physiol 256: H282–H290, 1989.[Abstract/Free Full Text]

This article has been cited by other articles:

				G. Jia, C. O'Dell, J. T. Heverhagen, X. Yang, J. Liang, R. V. Jacko, S. Sammet, T. Pellas, P. Cole, and M. V. Knopp Colorectal Liver Metastases: Contrast Agent Diffusion Coefficient for Quantification of Contrast Enhancement Heterogeneity at MR Imaging Radiology, September 1, 2008; 248(3): 901 - 909. [Abstract] [Full Text] [PDF]

This Article Abstract Full Text (PDF) Free All Versions of this Article: 101/4/1162    most recent 00389.2006v1 Submit a response Alert me when this article is cited Alert me when eLetters are posted Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in ISI Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via ISI Web of Science (6) Citing Articles via Google Scholar Google Scholar Articles by Reddy, S. T. Articles by Swartz, M. A. Search for Related Content PubMed PubMed Citation Articles by Reddy, S. T.