www.elsevier.com/locate/jconrel

Journal of Controlled Releas

Tailoring width of microfabricated nanochannels to solute size can

be used to control diffusion kinetics

Frank Martina,*, Robbie Walczaka, Anthony Boiarskia, Michael Cohena, Teri Westa,

Carlo Cosentinob, Mauro Ferraric

aiMEDD Inc., Columbus, OH, USAbDepartment of Experimental and Clinical Medicine, University of Catanzaro bMagna Gr&ciaQ, Catanzaro, Italy

cDepartment of Internal Medicine, Ohio State University, Columbus, OH, USA

Received 17 June 2004; accepted 28 September 2004

Abstract

Top–down microfabrication techniques were used to create silicon-based membranes consisting of arrays of uniform

channels having a width as small as 7 nm. The measurement of diffusion kinetics of solutes across these membranes under sink

conditions reveals non-Fickian behavior as the nanopore width approaches the hydrodynamic diameter of the solute. Zero-order

diffusion of interferon is observed at channel width of 20 nm, and the same phenomenon occurs with albumin and 13-nm-wide

channels, whereas Fickian diffusion kinetics is seen at 26 nm and larger pore sizes. A prototypical drug delivery device is

described that is fitted with a 13-nm nanopore membrane and loaded with radio-labeled BSA. Following subcutaneous

implantation in rats, diffusion from the device provided prolonged levels of BSA in the blood. Such a nonmechanical device

offers important advantages in drug delivery applications, including zero-order release and high loading capacity.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Nanochannels; Nanopore membranes; Silicon membranes; Microfabrication

1. Introduction

Fick’s laws of diffusion are usually adequate to

describe the kinetics of solutes from a region of higher

concentration to a region of lower concentration

0168-3659/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jconrel.2004.09.024

* Corresponding author.

E-mail address: fmartin@imeddinc.com (F. Martin).

through a thin, semipermeable membrane. As the size

of the membrane pores approaches that of the solute,

however, unexpected effects can occur, which cause

substantial deviations from the kinetics predicted by

Fick’s laws. The diffusion of molecules in micro-

porous media such as zeolites has led to experimental

evidence of such unusual phenomena as molecular

traffic control and single file diffusion (SFD; [1–6]).

Theoretical treatments and simulations suggest that, in

e 102 (2005) 123–133

F. Martin et al. / Journal of Controlled Release 102 (2005) 123–133124

the case of SFD, solute molecules of equal size cannot

pass each other in pores that approximate the

dimensions of the molecule itself, regardless of the

influence of concentration gradient, and thus, their

initial rate of movement (or flux) is overestimated by

Fick’s law [7–12].

Top–down microfabrication methods have been

used to create nanopore membranes consisting of

arrays of parallel rectangular channels, which, in their

smallest aspect, range from 7 to 50 nm (Fig. 1). The

original method pioneered by Chu et al. [14] consists

of two basic steps: (1) surface micromachining of

nanochannels in a thin film on the top of a silicon

wafer, and (2) forming the nanopore membrane by

etching away the bulk of the silicon wafer underneath

the thin-film structure. The overall fabrication process

is shown schematically in Fig. 2.

Fig. 1. Photographic images of nanopore membranes. (A) Appearance of

dies before being cut into individual units. (B) SEM cross-sectional view

material. (C) SEM top view of membrane with pores at 1000� magnifi

regions. (D) Top SEM view of membrane, 6000�, showing details of po

Several factors hinder controlled diffusion for

current commercial membrane fabrication techniques.

Solvent-casting process, which is the most common,

typically exhibits large variations in the pore size; ion-

track etching yields better results concerning the pore

size distribution, but low porosities, while the pore

configurations and arrangements in porous alumina

membranes, which exhibit an high uniformity, are

difficult to control. On the other hand, Desai et al. [13]

showed that, by the same silicon microfabrication

technique exploited in this work, it is possible to

create nanoporous silicon membranes exhibiting con-

trolled diffusion and rejection performance compara-

ble with current commercially available ones, such as

those by Whatman and Millipore.

Given the absolute pore sizes in the 7- to 50-nm

range possible with silicon microfabrication technol-

4 inches silicon wafer showing 120 small and 100 large membranes

of membrane with 50-nm pores separated by silicon and polysilicon

cation showing 45-Am-long pores separated by 10-Am-long anchor

re and anchor structures.

Fig. 2. Schematic of key steps in silicon nanopore membrane fabrication process. Details are given in Materials and methods.

F. Martin et al. / Journal of Controlled Release 102 (2005) 123–133 125

ogy, nanopore membranes were first applied to create

capsules for the immunoisolation of transplanted islet

cells [15]. In this setting, the nanopore membrane is

designed to serve as the only connection between the

reservoir containing the cells and the external

medium. The membrane size is selected to allow the

passage of insulin, glucose, oxygen, and carbon

dioxide, molecules required for the proper function

of the cell feedback system, while blocking elements

of the immune system which might attack the graft.

Although it is relatively easy to prevent the passage of

cytotoxic cells, macrophages, and other cellular

immune molecules through the biocapsule, it is more

challenging to block humoral immune components

such as antibodies and cytokines, as well as cell-

secreted antigens. Previous studies have indicated that

a membrane with maximum pore diameter of 30 nm

can retain immunoglobulin and complement mole-

cules [16]. Microfabricated nanopore membranes with

pores of about 15 nm appear well suited for this

purpose [17,18].

During the development of the immunoisolating

biocapsule, it was noted that diffusion through nano-

pore membranes was slower than predicted from

Fick’s law when using smaller pore sizes. To explore

this phenomenon, the relationship between diffusion

rates of various solutes and the width of nanopore

membranes was investigated in more detail and is

presented in this paper.

2. Materials and methods

2.1. Materials

All laboratory reagents and chemicals were

obtained from Sigma (St. Louis, MO) or Fisher

Biochemicals (Pittsburgh, PA), unless otherwise noted.

2.2. Nanopore membrane fabrication

The first major process step involves etching

channels in the silicon substrate over its entire surface

to define the overall shape of the pores (Fig. 2A). The

etched channels are 2 Am wide, separated by 2 Am,

and they are 5 Am deep. These channels are formed

using a plasma-etch procedure with a thermally grown

oxide layer as an etch-mask.

F. Martin et al. / Journal of Controlled Release 102 (2005) 123–133126

The next major step involves growing a sacrificial

oxide layer over the entire wafer surface, including

the surface area of the channels (Fig. 2B). The

sacrificial-oxide layer thickness defines the channel

width in the final membrane. The proper selection of

the time and temperature of this thermal oxidation

step allows for the control of the sacrificial layer

thickness to tolerances of less than 0.5 nm across the

entire wafer.

Anchor points are created within the channels to

define the pore length (45 Am distance). These anchor

points are 10 Am long and are formed between each

45-Am-long pore region. The anchors provide rigidity

to the membrane structure because there are no pores

in the anchor regions. The anchor points are formed

across the entire wafer by selectively etching through

the sacrificial layer in a series of 10-Am-wide strips

perpendicular to the channel direction.

The next fabrication step involves filling the

channels using a polysilicon deposition process

(Fig. 2C). This filling step forms the membrane

structure by providing silicon material on each side of

the sacrificial oxide layers. The deposition also

provides solid silicon–polysilicon areas in the anchor

regions to stabilize the membrane. The deposited

polysilicon layer is then bplanarizedQ ( Fig. 2D) usinga plasma-etch process, leaving a smooth surface

structure with the pores exposed. An SEM photo-

graph image of the planarized membrane surface is

shown in Fig. 1.

Following planarization, a boron-doping step is

performed, where boron ions are diffused into the

surface of the silicon–polysilicon material to a depth

of 3 Am (see dashed line in Fig. 2E). Boron-doped

silicon etches in KOH at a much lower rate than

undoped silicon does, thus, the boron doping provides

an etch stop that will later define the membrane

thickness.

A protective nitride mask layer is then deposited on

the wafer that completely covers both sides. This layer

is impervious to the KOH chemical etch that will be

used to form the membranes out of the silicon

substrate. On the backside of the wafer, windows

are plasma etched in the nitride layer to define the

membrane dimensions (i.e., a series of 1�2 mm

windows for the small membrane dies and 2�3.5 mm

windows for the large-membrane dies in Fig. 1A).

These windows in the protective nitride layer expose

the silicon wafer to KOH etchant in the desired

regions (Fig. 2F).

The wafer is then placed in a 55 8C KOH bath to

etch the unprotected silicon through the windows in

the nitride and up to the boron etch-stop to form the

membrane (Fig. 2G). After the silicon is removed, the

protective nitride etch mask (Fig. 2H) and sacrificial

oxide (Fig. 2I) are removed using an HF etchant. This

final etching step opens the pores and provides the

desired nanopore membrane structure.

2.3. In vitro human recombinant interferon a2bdiffusion

A 1.17 mg/mL human recombinant interferon a2b

solution containing 315 mM sodium chloride and 25

mM sodium acetate (pH 4.5–5.0) was obtained from

PC-Gen (Buenos Aires, Argentina). The interferon

solution was concentrated to 4.68 mg/mL using a

Microcon YM-3 concentrator (Millipore, Bedford,

MA) as per manufacturer instructions. Approximately

1.6 mg interferon was placed into the donor chamber

using a volume of 0.33 mL and was allowed to diffuse

into an acceptor chamber containing 10 mL phosphate

buffered saline (PBS, pH 7.4) with 0.1% bovine

serum albumin (BSA) and 0.2% sodium azide. All

interferon diffusion experiments were carried out at 37

8C using silicon membranes containing 20 nm pores.

At various time intervals, the donor chamber was

placed in a new acceptor chamber containing 10 mL

fresh buffer. Samples containing diffused interferon

were analyzed for interferon concentration using a

standardized ELISA kit (Research Diagnostics, Flan-

ders, NJ).

2.4. In vitro BSA diffusion

Nanopore membranes of two sizes, 13 and 26 nm,

were fitted to implant housings (see Fig. 4) and filled

with FITC-labeled BSA at a concentration of 5 mg/

mL. The implants were submerged in 15-mL conical-

bottom centrifuge tubes containing 10 mL PBS buffer

with 0.2% w/v sodium azide, and samples were

removed periodically for fluorescence analysis using

a Packard FluoroCount fluorescence detector (Perkin

Elmer, Boston, MA). The external medium was

changed periodically to insure maintenance of sink

conditions.

Fig. 3. In vitro interferon diffusion through nanopore membrane (20

nm pore size) under sink conditions: experimental data (o), Fick’s

law prediction (–), and model-based simulation (– –).

F. Martin et al. / Journal of Controlled Release 102 (2005) 123–133 127

2.5. In vivo pharmacokinetics of BSA

Implants fitted with appropriate nanopore mem-

branes were assembled and loaded with 125I-BSA

(ICN Biochemicals, Irvine, CA). Implants were

sterilized prior to loading by either autoclaving or

chemically sterilizing by soaking in a standard

phosphate-buffered saline solution (PBS) containing

0.2% (w/v) sodium azide. The implant formulation

was generated by diluting the appropriate amount of125I-labeled BSA (determined from the specific

activity reported by the manufacturer for each lot

obtained) with a 25 mg/mL stock solution of

unlabeled BSA and was filter sterilized. The final

formulation solution contained BSA at a concentra-

tion of 5 mg/mL and a 125I-labeled BSA concentration

of 60–65 ACi, in a final volume of 300 AL, the currentapproximate loading capacity of each implant. After

aseptically loading the implants with the BSA

formulation, each implant was washed by dipping

into 25 mL PBS and transferred to 25 mL fresh PBS,

both contained in sterile 50-mL conical tubes. Any

residual air bubbles trapped in the grate opening

above the membrane area were dislodged by flowing

a stream of liquid containing PBS over the grating

with a 1-mL syringe containing a 27-gauge luer-lock

needle. Once a day for 3 to 6 days, or until the

expected constant rate of diffusion was achieved, 100

AL aliquot was removed. The aliquot was transferred

to a 5-mL polypropylene serum tube and counted on a

gamma counter (Packard Biosciences). For each

treatment group, three 10- to 12-week-old female

Sprague–Dawley rats (Harlan, Indianapolis, IN) were

anesthetized with isoflurane (Minrad, Buffalo, NY).

After shaving and sterilizing the implant site, a 1.5-cm

incision was made parallel to and 1 cm from the

backbone through the skin layer midway on the

animal’s flank. A pocket was made for the implant

under the skin by opening and closing a pair of

hemostats to the front and back of the incision. The

incision bpocketQ was made in this way to ensure that

the ends of the implant did migrate to a position over

the incision, thereby improving implant retention. The

entire implant was rinsed in two changes of PBS, then

the grate of the implant was wetted with 10 AL of

PBS. A small amount (100 AL) of PBS was

introduced into the incision for wetting purposes,

and the implants were inserted into the incision pocket

and centered under the incision site. A small plastic

ring at one end of the implant was used to orient the

membrane downward and in the proper direction

relative to the animals’ flesh and skin. Release in the

proper direction insured that the implant diffusion was

not impeded in any way by physical blockage. The

incision was sutured and the animal was allowed to

recover.

For pharmacokinetic analysis, blood samples were

obtained. Animals were anesthetized with isoflurane,

the tails warmed for 2 min, and 0.2 ml samples of

blood were collected from the lateral tail veins. The

blood was allowed to clot for 45 min, spun at

10,000�g for 1 min, and then a 50 AL aliquot

removed for gamma counting.

3. Results

3.1. Human recombinant interferon a2b release data

The interferon release profile is shown in Fig. 3.

The membrane used in the experiment had a 20-nm

pore size; the initial concentration in the donor well

was 4.68 mg/ml. The solid line has been obtained by

simply combining the first Fick’s law with the mass

conservation principle and multiplying the mass flux

times the total nominal pore area: The resulting

diffusion profile is exponential, as expected. The

steady-state value is close to 100% of the amount of

F. Martin et al. / Journal of Controlled Release 102 (2005) 123–133128

drug loaded into the donor well because the acceptor

well volume is much larger than that of the donor

well. Therefore, to make the concentration homoge-

neous on both sides of the membrane, only a small

amount of drug has to be retained in the donor well.

Looking at the experimental measurements (circle

markers), it is fairly clear that, even if the nominal

experimental parameter values are varied, Fick’s law

could not explain the nonexponential measured

diffusion profile. On the contrary, the release rate

remains constant (zero-order kinetics) for a long

period (about 25 days), until 75% of the total amount

has been released. Later on, a possible interpretation

for this result will be provided, and a suitable

theoretical diffusion model fitting the data (dashed

line) will be devised.

Fig. 4. Implant device fitted with nanopore membrane. (Top) Drawing ill

possible diffusion path of a drug molecule held within the device reservoir.

in relation to a U.S. 1 cent piece. All implant housing components were

cylindrical methacrylate inset carrier is fitted with two rubber O-rings. A 2�within the insert carrier using general-purpose silicone adhesive and allow

titanium encasement until the nanopore membrane region is fully aligned u

rubber septa are sealed at each end of the titanium encasement using si

vertically, and a 27-gauge luer-lock needle is inserted into the upper septa f

implant via the lower septa until all the air within the implant is removed, a

The needles are removed under gentle liquid injection pressure to avoid an

by immersion in appropriate buffer prior to either placement into a testing

3.2. In vitro BSA release data

Experiments like the one described in the previous

section indicate that nanopore membranes can be

engineered to control diffusion rates and kinetic order

by bfine tuningQ the channel width in relation to the

size of the solutes. Moreover, when the proper balance

is struck, zero-order diffusion kinetics is possible.

Implantable zero-order output devices are useful to

deliver drugs that are not orally bioavailable, partic-

ularly in clinical settings where the maintenance of a

steady-state level in the blood stream for long periods

is desirable [19]. The nanopore membrane offers a

nonmechanical means to achieve such release

kinetics. These considerations encouraged the devel-

opment of a prototypical drug delivery device (Fig. 4).

ustrating key features of the device. The dashed arrow represents a

(Bottom) Photograph of prototype implant device illustrating its size

obtained from Manufacturing Technical Solutions (Carroll, OH). A

3 mm nanopore membrane die is affixed over a small-bore opening

ed to cure 3 h at 55 8C. The completed carrier is inserted into the

nder the grate opening. Methacrylate end caps containing resealable

licone adhesive and were allowed to cure. The implant is oriented

or use as an air vent. The liquid suspension is slowly injected into the

s indicated by the presence of liquid exuding from the upper needle.

y concomitant influx of air upon withdrawal. The implants are rinsed

vessel or surgical implantation.

Fig. 6. In vitro diffusion kinetics of fluorescein isothiocyanate

(FITC)-labeled BSA through 26-nm pore size membrane under sink

conditions: experimental data (o), Fick’s law prediction (–), and

model-based simulation (– –).

F. Martin et al. / Journal of Controlled Release 102 (2005) 123–133 129

The device consists of a reservoir formed from a

cylindrical titanium alloy enclosure (45�5 mm)

capped at both ends with molded polymer plugs.

The device is fitted with a nanopore membrane as the

only connection between the internal reservoir and the

external medium. The nanopore membrane serves to

control the release rates of drugs loaded into the

reservoir. It was reckoned that the device would be

useful for delivering small-molecular-weight organic

drugs, as well as larger peptide- and protein-based

biopharmaceuticals.

As a point of reference, the hydrodynamic diameter

of a typical biopharmaceutical ranges between about 4

and 15 nm, and a typical small organic drug may be 3

to 5 nm in size [20]. Thus, the widths of these

nanopore channels can be made to approximate

molecular dimensions. To test the system, bovine

serum albumin (BSA) MW 66,000 Da) has been

selected as a surrogate of a fairly large protein

biopharmaceutical. Virtually no BSA diffusion is seen

through nanopore membranes of 7 nm (data not

shown), which would be expected because the hydro-

dynamic diameter of BSA is about 8 nm. The in vitro

release of fluorescent-labeled BSA loaded into

implants fitted with nanopore membranes of two

sizes, 13 and 26 nm, under sink conditions is shown in

Figs. 5 and 6, respectively.

Fig. 5. In vitro diffusion kinetics of fluorescein isothiocyanate

(FITC)-labeled BSA through 13-nm pore size membrane under sink

conditions: experimental data (o), Fick’s law prediction (–), and

model-based simulation (– –).

The expected diffusion behavior predicted by

Fick’s law is depicted in the figures and compared

with an interpolation, obtained from a dynamic

diffusion model, which will be discussed later on.

The mass flux is constant in the 13-nm case (Fig.

5), and zero-order kinetics is maintained for the entire

duration of the experiment, while the 26-nm test data

(Fig. 6) show an approximate exponential release

profile. Note that, in the latter case, there is a second-

order effect, which creates a kind of inertia in the

initial days: The release rate starts from a very low

value, then increases until the curve assumes a slope

close to that predicted by Fick’s law. This phenom-

enon occurs in some experiments and is likely caused

by an unsuccessful prewetting of the pores. Thus, it

has to be neglected and classified as experimental

error.

As one would intuitively expect, even with pore

sizes greater than 26 nm, BSA diffusion remains

Fickian (data not shown). These data indicate that flux

can be controlled by porosity, and the diffusion

kinetics controlled by channel width.

3.3. In vivo tests

To capitalize on the constrained diffusion feature

offered by these nanopore membranes, some tests

were conducted to assess their utility as a means of

Fig. 7. Pharmacokinetics of 125I-BSA in rats given as a single bolus

subcutaneous injection (n) or following implantation of nanopore

devices with an in vitro output rate of 15 Ag/day (E). Mean values

for three implants and standard deviation are plotted.

Table 1

BSA release of different kinds of membranes

Whatman Millipore iMEDD

Nominal pore size (nm) 20 25 13

Membrane thickness (Am) 1 105 4

Effective area (mm2) 4 5.6 0.0111

Release rate (mg/day) 17.1 13.7 0.9

Release rate/Effective area

(mg/day/mm2)

4.28 2.45 81.1

F. Martin et al. / Journal of Controlled Release 102 (2005) 123–133130

controlling the bioavailability of a protein in vivo.

Devices fitted with 13-nm membranes and filled with

300 AL of a solution containing 0.15 mg of 125I-BSA

were implanted dorsally and subcutaneously in three

rats. The devices were adjusted to have an in vitro

output rate of 15 Ag/day and, thus, were designed to

release the albumin for about 100 days. The pharma-

cokinetics of the labeled BSA in blood was measured

and compared with a dose of BSA delivered by a

standard subcutaneous bolus injection. Fig. 7 shows

the mean values for blood levels over a period of 45

days after implantation. In the case of the nanopore

implant group, following an initial period of rapid

decline (during the first 9 days), the rate of clearance

of BSA from the central compartment slowed,

maintaining measurable levels for the ensuing 4

weeks. The initial decline is attributed to the

equilibration of the radiolabeled BSA appearing in

the blood with the albumin pool in the interstitial fluid

volume. This equilibration has been reported to have a

half-life of about 3–7 days, which is in line with the

results obtained [23]. In comparison with the standard

subcutaneous injection, BSA delivered in the nano-

pore device was detectable for a substantially longer

period. As expected, when the devices were recovered

from experimental animals, they were encapsulated in

a fibrous capsule, but upon visual inspection, the

nanopore membrane itself was free of any tissue

intrusion. The encapsulation response did not appear

to retard the bioavailability of the albumin released

from the device; about half the labeled albumin was

recovered from the nanopore device, which conforms

to the expectation that half the drug was released

during the 7-week implantation period.

4. Discussion

4.1. Performance analysis

The performance of iMEDD membranes, in terms

of drug release, can be compared with that of other

commercially available membranes, based on differ-

ent fabrication processes. To this aim, data reported in

Ref. [13] can be exploited, where Desai et al.

compared a silicon microfabricated membrane with

two commercially available filter membranes by

Whatman (made from porous alumina) and Millipore

(fabricated by ion-track etching). They analyzed the

diffusive transport of BSA between two vessels across

the membranes; to assess the rejection performances

of the membranes, they used a diffusion chamber with

two compartments, A and B, containing 2 ml of

solutions at different concentrations, divided by the

membrane. The initial concentrations in the two

compartments were 4 and 0 g/dL, respectively. The

BSA concentration in the sink was measured after 7 h.

These results have been translated in a daily release

rate and compared with the measurements from the

release test on 13-nm pore size membranes (Table 1).

From Table 1, it can be noted that nanoporous silicon

membranes exhibit a much larger release rate per unit

effective area with respect to other membranes based

on different technologies.

A particular attention must be paid to the issue of

protein fouling/sticking on the membrane surface. In

Ref. [13], for example, microscopy imaging of

F. Martin et al. / Journal of Controlled Release 102 (2005) 123–133 131

membranes before and after the diffusion experiments

revealed that Whatman and Millipore membranes had

undergone significant changes in morphology, while

micromachined silicon membranes did not exhibit any

change and the pores were free from biofouling and

any agglomeration of protein. This results suggest that

silicon membranes suffer much less from biofouling

than other kind of membranes do.

Zhang et al. [21] devised a method to significantly

reduce nonspecific protein (such as albumin, fibrino-

gen, and IgG) adsorption and cell adhesion, modify-

ing silicon surfaces by the covalent attachment of a

self-assembled polyethylene glycol (PEG) film. How-

ever, the need for this surface treatment in the drug-

delivery applications explored in this paper was not

encountered. Biofouling by nonspecific molecular

adsorption is, indeed, a great concern in the context

of convective mass transport, as is the case in delivery

systems activated by osmotic pressure-driven or

mechanical pumps. It is, however, of lesser impor-

tance in diffusive nanoscale systems, where the

reversible and dynamic nature of noncovalent adsorp-

tion appears to interfere, to a lesser extent, with the

desired transport and release phenomena.

4.2. Results interpretation

The situation presented here differs from the SFD

observed for adsorbate molecules, such as methane or

CF4, in crystalline zeolites. The microfabricated

nanopore channels used here are of molecular size

in only one dimension, and the solutes themselves do

not tend to adsorb to the silicon surface. The

observations reported in this paper are consistent with

the diffusion reported for colloidal particles confined

in closed one-dimensional channels of micrometer

scale, where particle self-diffusion is non-Fickian for

long time periods and the distribution of particle

displacements is a Gaussian function [3]. In the case

presented here, zero-order flux is observed when a

chamber filled with a solute is separated from a

solute-free external medium by channels that are only

several times wider than the hydrodynamic diameter

of the individual molecules. The basic principle of

diffusion as a mixing process with solutes free to

undergo Brownian motion in three dimensions does

not apply because, in at least one dimension, solute

movement within the nanopore is physically con-

strained by the channel walls. Experimental observa-

tions of colloidal particles in a density matched fluid

confined between two flat plates reveal that particle

diffusion becomes anisotropic near the interface, in

this case, leading to hindered diffusion as a conse-

quence of constrained Brownian motion and hydro-

dynamic drag effects at distances close to the walls

[22]. In the case of iMEDD membranes, it is not

entirely certain that the ordering of solutes imposed by

the nanopore geometry will be as strict as true

cylindrical pores, nor that the sequence of particles

passing through the nanopores under the influence of

the concentration gradient will remain unchanged

over the time required to travel the 4 Am length of the

channel; particles could conceivably pass each other

laterally. Whether a consequence of a SFD-like

phenomenon or drag effects (or a combination of

both), the nanopore membrane used here is rate

limiting and, if properly tuned, restricts solute

diffusion to a point that flux rates across the

membrane are entirely independent of concentration

gradient.

4.3. Modeling and data fitting

To achieve a further insight in the mechanisms

involved in nanochannel diffusion, the experimental

phenomena have been described in mathematical

terms, thus yielding a dynamic model. The model

allows to simulate the diffusion experiments and fit

the related data.

A detailed description of such a model is beyond

the scope of this work, thus, the description will be

limited to the main concepts. Basically, the core of the

model is constituted by combining Fick’s first law

with the mass conservation principle. The model relies

upon the basic hypothesis that the membrane effect

can be mathematically described by means of a

saturation value for the mass flux, where the threshold

is intuitively dependent on the nanochannel width and

the molecular dimensions.

This hypothesis can be better understood if one

looks at the results from the interferon diffusion test.

Referring to Fig. 3, the release profile depicted by the

dashed line can be obtained by simply simulating the

experiment with the nominal parameters values and

optimizing the mass flux saturation level (which is

therefore the only free parameter) on the basis of the

Fig. 8. Interferon mass flux through a 20-nm pore size membrane:

Fick’s law prediction (–) and model-based simulation (– –).

F. Martin et al. / Journal of Controlled Release 102 (2005) 123–133132

available data. The simulated mass flux is depicted in

Fig. 8, along with the same quantity obtained from a

simulation of the free (Fickian) diffusion case, with

the same parameters values. Clearly, the flux at the

beginning achieves the highest value because the

concentration gradient is maximum. Assuming a

saturation level below this maximum value results in

a constant flux for a certain time interval, in this case,

about 20 days. The switch from constant to exponen-

tially decreasing profile occurs when the concentra-

tion gradient becomes so low that the flux value is less

or equal than the fixed threshold.

In light of the good fit that the model provides to

diffusion data, it can be argued that the hypothesis

about the flux saturation effect is reasonable, although

deeper understanding must be achieved, concerning

the basic molecular mechanisms causing it. Besides

the theoretical value, this interpretation of the phe-

nomenon, along with the computational model,

proves very useful as a tool for the tuning of the

release device, allowing to substitute long and

expensive experimental tests by simulation with

different parameters values.

5. Conclusion

The experimental and mathematical results pre-

sented in this work lead to believe that the devices

outfitted with silicon nanopore membranes can regu-

late the delivery kinetics of a wide range of drugs.

Moreover, because the mechanism of release is

attributable to a novel constrained diffusion mecha-

nism provided by the precise geometry of the nanopore

membrane itself, and no moving parts, such as pistons,

are required, the drugs can likely be loaded into the

device reservoir in a range of physical states, including

solutions and crystalline or micronized suspensions.

Flexibility with respect to the physical form of

encapsulated drugs provides options to substantially

increase the loaded dose and duration of therapy, as

well as approaches to increase the stability of proteins,

which are intrinsically unstable in an aqueous solution

at body temperature.

References

[1] L.A. Clark, G.T. Ye, R.Q. Snurr, Molecular traffic control in a

nanoscale system, Physical Review Letters 84 (2000) 2893–2896.

[2] T. Meersmann, et al., Exploring single-file diffusion in one-

dimensional nanochannels by laser-polarized 129Xe NMR

spectroscopy, Journal of Physical Chemistry A 104 (2000)

11665–11670.

[3] Q. Wei, C. Bechinger, P. Leiderer, Single-file diffusion of

colloids in one-dimensional channels, Science 287 (2000)

625–627.

[4] V. Kukla, et al., NMR studies of single-file diffusion in

unidimensional channel zeolites, Science 272 (1996 (May 3))

702–704.

[5] V. Gupta, S.S. Nivarthi, D. Keffer, A.V. McCormick, D. H.T.,

Evidence of single-file diffusion in zeolites, Science 274

(1996) 164.

[6] K. Hahn, J. Karger, V.V. Kukla, Single file-diffusion observa-

tion, Physical Review Letters 76 (1996) 2762–2765.

[7] S.M. Auerbach, Theory and simulation of jump dynamics,

diffusion and phase equilibrium in nanopores, International

Reviews in Physical Chemistry 19 (2000) 155–198.

[8] Z. Mao, S.B. Sinnott, A computational study of molecular

diffusion and dynamic flow through carbon nanotubes, Journal

of Physical Chemistry B 104 (2000) 4618–4624.

[9] P. Nelson, S. Auerbach, Self-diffusion in single-file zeolite

membranes is Fickian at long times, Journal of Chemical

Physics 110 (1999) 9235–9244.

[10] J.M.D. MacElroy, S.H. Suh, Self-diffusion in single-file pores

of finite length, Journal of Chemical Physics 106 (1997)

8595–8597.

[11] S.K. Aityan, V.I. Portnov, General Physiology and Biophysics

5 (1986 (Aug)) 351–364.

[12] D.G. Levitt, Dynamics of a single-file pore: non-Fickian

behavior, Physical Review. A, General Physics 8 (1973)

3050–3054.

F. Martin et al. / Journal of Controlled Release 102 (2005) 123–133 133

[13] T.A. Desai, D.J. Hansford, L. Leoni, M. Essenpreis, M.

Ferrari, Nanoporous anti-fouling silicon membranes for bio-

sensors applications, Biosensors and Bioelectronics 15 (2000)

453–462.

[14] W.H. Chu, R. Chin, T. Huen, M. Ferrari, Silicon membrane

nanofilters from sacrificial oxide removal, Journal of Micro-

electromechanical Systems 8 (1999) 34–42.

[15] T.A. Desai, Microfabrication technology for pancreatic cell

encapsulation, Expert Opinion in Biological Therapeutics 2

(2002 (Aug)) 633–646.

[16] R.P. Lanza, et al., Transplantation of encapsulated canine islets

into spontaneously diabetic BB/W or rats without immuno-

suppression, Endocrinology 131 (1992) 637–642.

[17] T.A. Desai, et al., Microfabricated immunoisolating bio-

capsules, Biotechnology and Bioengineering 57 (1998)

118–120.

[18] T.A. Desai, D. Hansford, M. Ferrari, Characterization of

micromachined silicon membranes for immunoisolation and

bioseparation applications, Journal of Membrane Science 159

(1999) 221–231.

[19] J.C. Wright, et al., An in vivo/in vitro comparison with a

leuprolide osmotic implant for the treatment of prostate cancer,

Journal of Controlled Release 75 (2001) 1–10.

[20] E.M. Johnson, D.A. Berk, R.K. Jain, W.M. Deen, Hindered

diffusion in agarose gels: test of effective medium model,

Journal of Biophysics 70 (1996) 1017–1023.

[21] M. Zhang, T.A. Desai, M. Ferrari, Proteins and cells on

peg immobilized silicon surfaces, Biomaterials 19 (1998)

953–960.

[22] B. Lin, J. Yu, S. Rice, Direct measurements of constrained

Brownian motion of an isolated sphere between two walls,

Physical Review E 62 (2000) 3909–3919.

[23] A. Spiess, V. Mikalunas, S. Carlson, M. Zimmer, R.M. Craig,

Albumin kinetics in hypoalbuminemic patients receiving total

parenteral nutrition, Journal of Parenteral and Enteral Nutrition

20 (1996 (Nov–Dec)) 424–428.