Delivery of drug macromolecules from thermally responsive gel implants to the posterior eye

Chemical Engineering Science 65 (2010) 5170–5177

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Delivery of drug macromolecules from thermally responsive gel implants to the posterior eye Pravin R. Ninawe a, Dimitri Hatziavramidis b,n, Satish J. Parulekar a a b

Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA School of Chemical Engineering, National Technical University of Athens, Zografou 15780, Athens, Greece

a r t i c l e in f o

a b s t r a c t

Article history: Received 17 December 2009 Received in revised form 22 May 2010 Accepted 14 June 2010 Available online 23 June 2010

Therapeutic modalities for posterior-eye diseases involve mostly interventions through the anterior eye, which are difficult for physicians and patients alike. Currently, sustained drug delivery to the posterior eye is gaining importance. A study for sustained delivery of an anti-VEGF agent to the posterior eye from an implant, made of poly(N-isopropylacrylamide) (NIPAM) and placed episclerally, is presented. The thermally sensitive gel is modelled as a poroelastic material with a phase transition characterized by a lower critical solution temperature (LCST). The study utilizes compartments for various eye tissues, with individual compartments considered to be completely mixed and drug transport between compartments occurring by one-dimensional diffusion. & 2010 Elsevier Ltd. All rights reserved.

Keywords: Sustained delivery Drug macromolecule Thermally responsive gel Ocular drug delivery Sclera permeability Anti-VEGF agent

1. Introduction Medical conditions in patients suffering from age-related macular degeneration (AMD) include proliferation of cells and uncontrolled cell growth in blood vessels leading to leaking of blood and proteins, scarring of the macula region, and, eventually, irreversible loss of vision. Uncontrolled expression of vascular endothelial growth factor (VEGF) is responsible for this disease condition. Various anti-VEGF drugs, best known among them Macugen, a pegylated aptamer that inhibits VEGF isoform 165, and Lucentis, an IgG1 Fab fragment, have been identified, and administered for AMD treatment, the best known by intravitreal injection (Olejnik and Hughes, 2005). However, delivering these drugs to the target, the choroid, retinal pigmented epithelium (RPE), and vitreoretinal space is a challenge. An effective and less vision-threatening than intravitreal injection route of administration is transscleral delivery using hydrogels (Hoare and Kohane, 2008; Lee et al., 2004; Yu and Ding, 2008; Woldum et al., 2008; Xinming et al., 2004), particularly for sustained delivery of anti-VEGF macromolecular drugs. Unlike implants of conventional polymer networks and matrix reservoirs of degradable polymers, hydrogels have a macroporous structure, which makes them efficient for transport of

n

Corresponding author. Tel.: +30 210 772 3125. E-mail address: [email protected] (D. Hatziavramidis).

0009-2509/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2010.06.014

macromolecular drugs. Of particular interest for sustained delivery of macromolecular drugs are gels of fast response. An example of a fast-response gel is a poly(N-isopolyacrylamide) ¨ (NIPAM) (Fanger et al., 2006) gel, which is loaded with the drug prior to its implantation in the sclera. A certain time after its implantation, the gel reaches the temperature of the body and undergoes deswelling. The lower critical solution temperature (LCST) for this phase transition of the NIPAM gel is 32 1C. A significant amount of drug is released during deswelling of the gel, with the remainder being released by diffusion after termination of deswelling. As a result of macro-porosity, the amount of solvent and drug left in the gel after deswelling is substantial to qualify the delivery as sustained. The released drug diffuses through the sclera and reaches the choroid and the retinal pigmented epithelium (RPE), where it is needed at therapeutic levels. A fragment of IgG, IgG1 Fab, with properties as those of Lucentis as detailed in a CHMP review (2007), is chosen as the drug of interest in this study. A composite mathematical model is presented in Section 2. Estimation of transport parameters, description of deswelling and drug release from the hydrogel, and description of the fate of the released drug are considered in Section 2. The results of model simulations pertaining to profiles of pressure, porosity, and drug concentration in the hydrogel, as well as drug release from the hydrogel into post-ocular tissues and profiles of drug concentration in the latter are presented and discussed in Section 3 followed by concluding remarks.

P.R. Ninawe et al. / Chemical Engineering Science 65 (2010) 5170–5177

2. Mathematical model 2.1. Transport parameters 2.1.1. Tissue permeabilities The drug, IgG1 Fab fragment, needs to permeate the sclera and choroid and overcome the RPE to reach the site of action. The function, structure, and composition of these tissues are different and so are their transport properties. Wherever possible, in addition to obtaining values for various transport parameters from the literature, these values were estimated in this study, as in the case of the sclera, the composition, and structure of which are well known. The transport coefficients in each of the three tissues of the posterior eye are isotropic (Irvine and Weissman, 1992). Edwards and Prausnitz (1998) proposed a fiber-matrix model at three scales; microscale, mesoscale, and macroscale. On a microscale, the sclera is composed of ground substance which is an aqueous solution of proteoglycans (0.0292 vol%), glycosaminoglycans (GAGs, 0.282 vol%), salts, and proteins. Collagen fibrils (18.4 vol%), which constitute the mesoscale, are arranged into regular hexagonal arrays of cylinders in the ground substance to form collagen lamellae. On the macroscale, the collagen lamellae are also arranged regularly as hexagonal arrays of cylinders in the ground substance. Using the fiber-matrix model, the effective diffusivity of IgG in the ground substance, Deff,gs, was calculated starting at microscale and proceeding in succession to mesoscale and macroscale (Perrins et al., 1979). Knowing the molecular weights and equivalent molecular radii of IgG and IgG1 Fab fragment, and the effective diffusivity of IgG in the sclera, the effective diffusivity of the IgG1 Fab fragment in the sclera can be estimated. The permeability of a tissue, such as sclera, choroid, and retina, to IgG1 Fab fragment is obtained from the effective diffusivity of the fragment in that tissue and the thickness of the tissue. The permeability of the choroid-RPE to molecules of various sizes has been measured using fluorescent probes and the results ¨ have been correlated with the molecular radius (Pitakanen et al., 2005). The permeability of the choroid-RPE to IgG, whose molecular radius is 5.23 nm, is estimated to be 6.3  10  7 cm/s, much lower than the permeability of the sclera and retina to IgG. This is expected as RPE is a single layer of epithelium cells, which are compactly packed and have very low intercellular spacing to allow macromolecules, such as IgG, to permeate. In a study of transcleral delivery of bioactive protein FITC-IgG to choroid and retina (Ambati et al., 2000b), the permeability of retina to FITCIgG was estimated to be 6.2  10  6 cm/s. The permeability of the choroid and retina to IgG1 Fab fragment is estimated accordingly. 2.1.2. Elimination constants While there is no drug elimination in the sclera, there is elimination in the choroid, because of the vasculature, and the retina, because of systemic absorption. In-vivo studies indicate that the average half-lives of IgG in choroid and retina are 2.89 and 3.36 days, respectively. Drug elimination in the choroid and retina follows first-order kinetics, with rate constants being 0.2398 and 0.2063 day  1, respectively (Ambati et al., 2000b). 2.2. Hydrogel deswelling 2.2.1. Equilibrium properties The NIPAM hydrogel composition is 12.79 wt% N-isopropylacrylamide (NIPA), 30 wt% PEG (pore-forming agent, molecular weight¼400), 2 wt% N, N0 –methylenebisacrylamide (BIS, cross¨ linking agent), and the remainder water (Fanger et al., 2006). The

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30% weight fraction of PEG (any PEG weight fraction higher than 20%) assures macro-pore formation in the hydrogel. At a temperature lower than its LCST (  32 1C), the hydrogel swells and is loaded with the drug, anti-VEGF agent IgG1 Fab fragment in the present case. When the hydrogel is implanted in the eye, it is subjected to the body temperature which is above its LCST, and it undergoes deswelling. With a PEG weight fraction of 30%, the hydrogel undergoes the least change in volume upon phase transition. Thus, a significant amount of solvent and drug is retained in the hydrogel after deswelling to qualify for the sustained drug delivery to the posterior eye. The equilibrium swelling/deswelling of the hydrogel is determined from the properties of the crosslinked polymer network, as per the relation (Queslel and Mark, 1985 and 1986).   x m 2=3 lnð1u2m Þ þ u2m þ wu22m ¼  V1 u2m 1=3 1 þ Ku2m ð1Þ V0 x In Eq. (1), u2m is the volume fraction of the polymer at equilibrium swelling and V1 the molar volume of the solvent. The reader is advised to refer to Nomenclature section for complete list of variables. The solvent–polymer interaction parameter, w, is given by

w¼

1 u2m þ 2 3

ð2Þ

and the junction density, m, and cycle rank, x, are given by     rV0 3Mc rV0 Mc , m¼ x¼ 1 1 2Mc Mn 2Mc Mn

ð3Þ

In Eq. (3), r is the density of the polymer, Mn the number average molecular weight of the monomer, and Mc the average molecular weight of the crosslink, which is obtained from Mc ¼

nNIPA MNIPA þMBIS nBIS

ð4Þ

with MJ and nJ being the molecular weight and the number of moles of J, J¼NIPA, BIS, respectively. The parameter K in Eq. (1) is completely described as (Flory and Erman, 1982)     B @B gB @ðgBÞ 2 1 K¼ þ þ zðl1Þ , , g¼l 2 2 ðB þ1Þ @l ðgB þ 1Þ @l g 2 ðl1Þð1þ lzl Þ 1=3 , l ¼ u2m ð5Þ B¼ ð1 þ gÞ2

In Eq. (5), z is a parameter accounting for the non-affine transformation of the domain of constraint with strain, and g the measure of severity of entanglement of polymer network. From equilibrium swelling calculations done in this work, z is estimated to be 0.2. 2.2.2. Deswelling model The hydrogel is considered to be a poroelastic medium and its free deswelling is described by the model of Yamaue and Doi (2005). The displacement vector, u, satisfies the equations   G Ku þ rðr:uÞ þGr2 u ¼ rp ð6Þ 3 for the gel, and

r:u_ ¼ kr2 p, u_ ¼

@u @t

ð7Þ

for the solvent. In Eq. (6), K0 and G are the osmotic bulk modulus and shear modulus, respectively, and p the pressure. In Eq. (7), u_

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is the rate of deformation vector and k the Darcy’s coefficient, estimation of which is addressed elsewhere (Tanaka et al., 1973). We consider here a cylindrical hydrogel. In cylindrical coordinates, under the assumption that the radial displacement ur is a function only of r and t and the axial displacement uz is a function only of z and t and linearly proportional to z (Yamaue and Doi, 2005), viz., ur ðr, y,z,tÞ ¼ uðr,tÞ;

uz ðr, y,z,tÞ ¼ aðtÞz

ð8Þ

Eqs. (6) and (7) can be combined to yield (Yamaue and Doi, 2005)   @u 1 da @ 1 @ðurÞ þ ð9Þ r¼D @t 2 dt @r r @r

hydrogel also changes according to (Truskey et al., 2004) @fp _ ¼ r:ðfp uÞ @t

ð16Þ

2.3. Drug release The hydrogel implanted in the posterior eye is exposed to body temperature, which is above its LCST, and undergoes deswelling during which the solvent, water, together with the anti-VEGF drug, IgG1 Fab fragment, will be transported out of the hydrogel. A mass balance for the drug in the hydrogel is written as @C þ t:rC ¼ r:ðDIgG1 rCÞ @t

ð17Þ

subject to boundary conditions uðr,tÞ ¼ 0

at

The solvent velocity t is obtained as

r¼0

@u u þ 2ð12RÞ ¼ ð34RÞae @t r

t¼ at

r¼a

ð10Þ

where a is the initial radius of the cylindrical hydrogel and the parameters D and R are given by   4 G  ð11Þ D ¼ k Ku þ G , R ¼  3 Ku þ 43 G At equilibrium, the following are valid uðr,1Þ ¼ ae r,

að1Þ ¼ ae

ð12Þ

Eq. (9) is solved analytically to obtain the displacement components in the radial and axial directions, u(r, t) and a(t)z, respectively, as uðr,tÞ ¼ ae r þ

1 X

wn ðrÞexpðqn tÞ;

aðtÞ ¼ ae þ

n¼0

wn ðrÞ ¼ cn J1

rffiffiffiffiffiffiffi! qn r ; D

1 X

wn ðaÞ ; a

rp

with k being the hydraulic permeability of the polymer network, which is provided by the relation (Jackson and James, 1986) k¼

3a2p 20fp

ðlnðfp Þ0:931Þ

ð19Þ

In Eq. (19), ap is the radius of the polyacrylamide chain. In Eq. (17), DIgG1 is given by (De et al., 2002) !2 1fp DIgG1 ¼ Do ð20Þ 1þ fp with Do being the diffusivity of IgG1 Fab fragment in water. The boundary conditions for pressure, velocity, porosity, and drug concentration in the cylindrical gel are well established (Yamaue and Doi, 2005, Crank, 1997) and therefore are not restated here. 2.4. Compartmental model

u2 qn ¼ D n2 a

ð13Þ

with cn’s being constants determined using initial conditions, conditions for u(r,0) and a(0), and un’s being solutions of   dJ1 ðxÞ 8 þ 1 R J1 ðxÞ ¼ 0 x ð14Þ dx 3 In the above, J1(x) is the Bessel function of the first kind and first order. With the displacement known, the pressure is calculated as (Yamaue and Doi, 2005)      4 @uðr,tÞ @uðr,tÞ uðr,tÞ uða,tÞ   þ pðr,tÞ ¼ pi þ Ku þ G 3 @r @r r a r¼a ð15Þ where pi is the intraocular pressure (IOP), which is 16.5 mm Hg in normal human eye. During deswelling, the porosity of the

The compartmental model that describes delivery of the drug from the hydrogel to the posterior eye tissues is shown in Fig. 1. The subscripts s, c, and r denote the three compartments, sclera, choroid, and retina, respectively. The volume of a compartment, Vj, equals Ajdj, with Aj being the average cross-sectional area across which drug molecules are transported within a compartment and dj being the depth of the compartment, j ¼s, c, and r. Once the drug is released from the hydrogel, it is delivered to the tissues of the posterior eye. It is assumed that all drug released from the cylindrical hydrogel in contact with the sclera is directed to the sclera. From sclera, the drug is transferred to the choroid across the sclera–choroid interface and from choroid to retina across the choroid–retina interface. The transfer is accompanied by elimination of the drug, which follows firstorder kinetics (kec and ker constants). The compartmental model assumes complete mixing in each of the three tissues of the posterior eye. It also considers the

Ker

Kec Pc, Acr

Ps, Asc Drug release by hydrogel

ð18Þ

bn expðqn tÞ;

n¼0

bn ¼

k

Zs fp

Choroid, Vc

Sclera, Vs Pc, Asc

Pr, Acr Retina, Vr

Vitreous chamber

Pr, Acr

Fig. 1. Compartmental model for transscleral delivery of anti-VEGF drug from hydrogel to retina.

P.R. Ninawe et al. / Chemical Engineering Science 65 (2010) 5170–5177

interfaces between various compartments to be surfaces with infinitesimal capacity, thus posing no resistance to drug transport. In reality, this may be true for the sclera–choroid but not for the choroid–retina interface which acts as the blood–retina barrier. In keeping up with tradition, we consider the three compartments to be lumped parameter systems. The conservation equations for the drug in the three compartments are Vs

dcs _ ¼ RA sc ðPs cs Pc cc Þ, dt

dcc ¼ Asc ðPs cs Pc cc Þ þAcr ðPr cr Pc cc Þkec Vc cc , cc ð0Þ ¼ 0 dt dcr ¼ Acr ðPc cc Pr cr ÞAr Pr cr ker Vr cr , cr ð0Þ ¼ 0 Vr dt

ð21Þ

with R_ being the rate of drug release from the hydrogel and Pj the permeability of compartment j to drug, j ¼s, c, and r. The permeability is defined as Hj D j dj

,

j ¼ s,c,r

with Hj being the partition coefficient for the drug, Dj the drug diffusivity in compartment j, and dj the thickness of the tissue (compartment). It is important to know the fate of the drug once it is released from the hydrogel. Addition of mass balances of Eq. (21) and integration of the resulting mass balance for the three-compartment system leads to Z t Vs cs ðtÞ þ Vc cc ðtÞ þ Vr cr ðtÞ þ ðker Vr þ Ar Pr Þ cr ðtuÞdtu t

cc ðtuÞdtu ¼ 0

3. Results and discussion

The hydrogel is considered to have a volume of 1 cm3 and a radius of 0.312 cm at a temperature of drug loading lower than the LCST and contains solvent (water) and drug. When the hydrogel implant is placed on the sclera in the posterior eye, it is assumed that it reaches the body temperature (37 1C) almost instantaneously. The change in the hydrogel radius, ah [¼a{1+ u(a,t)}], for initial (drug loading) temperatures of 30 and 20 1C is shown in Fig. 2. The simulations reveal that the time for hydrogel to undergo volume change as the temperature changes from its initial value (drug-loading temperature, below the LCST) to body temperature (above the LCST), and for the pressure and porosity of the hydrogel to equilibrate compares well with the ¨ observed time of 3–4 h (Fanger et al., 2006). The profiles of pressure and porosity in the hydrogel are displayed in Figs. 3 and

0.32

0

Z

t

_ RðtuÞdtu:

0.28

ð22Þ ah (cm)

þ kec Vc

Z

deswelling and drug release into the three tissues are presented next. The values of key parameters used for the simulations are listed in Table 1.

3.1. Hydrogel deswelling

cs ð0Þ ¼ 0

Vc

Pj ¼

0

The fractions of the drug released which are accumulated in the sclera (fs), choroid (fc), and retina (fr), and the fraction of drug released that is eliminated (fe) is then defined as Vj cj ðtÞ , j ¼ s,c,r; DðtÞ Z t 1 ½k V c ðtuÞ þ ðker Vr þ Ar Pr Þcr ðtuÞdtu; fe ðtÞ ¼ DðtÞ 0 ec c c Z t _ 0 Þdt0 : Rðt DðtÞ ¼

b 0.2 0

ð23Þ

0

2 t (hr)

3

4

x 104 10

8

Table 1 Values of parameters used in simulations. Value

Source

K0 (@37 1C) G (@37 1C) ae (37–20 1C) ae (37–30 1C)

Hirotsu, 1990 Hirotsu, 1990

Do (IgG1) Ps (IgG1)

150,000 N/m2 20,000 N/m2  0.325a  0.226b 3.68  10  11 cm2/N s 5.2  10  7 cm2/s 7.66  10  6 cm/s

Pc (IgG1)

1.13  10  6 cm/s

Pr (IgG1)

1.11  10  5 cm/s

Tanaka et al., 1973 Ambati et Ambati et ¨ Pitakanen Ambati et

al., 2000a al., 2000b, et al., 2005 al., 2000b

¨ Calculated using swelling ratio at 20 and 37 1C (Fanger et al., 2006). ¨ Calculated using swelling ratio at 30 and 37 1C (Fanger et al., 2006).

p (N/m2)

0.5 h

Parameter

b

1

Fig. 2. Change in radius of the hydrogel (of volume 1 cm3) with time for change in temperature from (a) 30–37 1C and (b) 20–37 1C.

In view of Eq. (22), the four fractions in Eq. (23) must sum up to unity, with fr being an important parameter in designing the drug delivery system. The results of simulations on hydrogel

a

a 0.24

fj ðtÞ ¼

k

5173

6 1h 4

2

2h 3.5 h

0 0

0.2

0.4 0.6 Normalized radius (r/a)

0.8

Fig. 3. Profiles of pressure in hydrogel. Initial temperature 30 1C.

1

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P.R. Ninawe et al. / Chemical Engineering Science 65 (2010) 5170–5177

0.6 0.95

0.5

0.5 h

C (mg/cm3)

(1 - φp)

4h 0.94 1h 0.93 2h

0.92

0.4

8h 12 h

0.3

0.2 24 h

3.5 h 0.91

0.1 0

0.2

0.4 0.6 Normalized radius (r/a)

0.8

1

Fig. 4. Profiles of hydrogel porosity in hydrogel. Initial temperature 30 1C.

0

0.4 0.6 Normalized radius (r/a)

0.8

1

Fig. 6. Drug concentration profiles in the hydrogel after deswelling. Initial temperature 30 1C.

0.6

1

0.5

0.5 h

0.4

0.8

3.5 h

0.6 2h

0.3

Diffusion

f

C (mg/cm3)

0.2

0.4 0.2

Deswelling

1h

0.2

0.1

0

0 0

0.2

0.4 0.6 Normalized radius (r/a)

0.8

0

1

Fig. 5. Drug concentration profiles in the hydrogel during deswelling. Initial temperature 30 1C.

18

24

1

Ti = 20°C, Dload = 1 mg

0.8 Drug released (mg)

The profiles of drug (IgG1 Fab fragment) concentration in the hydrogel during (short times) and after (long times) deswelling are presented in Figs. 5 and 6, respectively, and the profile of the fraction of the drug released from the hydrogel is shown in Fig. 7. One can observe that by the end of deswelling, during which the hydrogel volume decreases from 1 cm3 at initial temperature to its equilibrium value at body temperature, roughly 70% of the drug load is released. The remainder 30% of the drug is released from the hydrogel by diffusion over a period of approximately more than 2 days. The variation in the amount of the released drug with time, for initial hydrogel temperatures of 20 and 30 1C and drug loads of 0.5 and 1 mg, is displayed in Fig. 8. The values of drug load were those for which clinical tests were made, and 0.5 mg was the recommended monthly dose of Lucentiss(CHMP review, 2007). It is observed that neither the initial hydrogel temperature nor the drug load has a noticeable effect on the rate of drug release.

12 t (hr)

Fig. 7. Fraction of drug released with time during and after hydrogel deswelling. Initial temperature 30 1C.

4. While the hydrogel reaches the equilibrium volume in less than 4 h, the decline in pressure and porosity (solvent volume fraction) is continuous. There are substantial spatial variations in pressure and porosity as hydrogel volume is reduced.

3.2. Drug release from hydrogel

6

Ti = 30°C, Dload = 1 mg

0.6

0.4

Ti = 20 °C, Dload = 0.5 mg

0.2

Ti = 30 °C, Dload = 0.5 mg

0 0

8

16

24 t (hr)

32

40

48

Fig. 8. Total drug released from hydrogel with time.

3.3. Drug distribution in posterior eye The profiles of the drug (IgG1 Fab fragment) concentration in the tissues of the posterior eye, sclera, choroid, retina, for initial hydrogel temperatures of 20 and 30 1C and drug loads of 0.5 and 1 mg, are given in Figs. 9–12. The concentration profiles in these

P.R. Ninawe et al. / Chemical Engineering Science 65 (2010) 5170–5177

5175

105

106

c

Cj/Ccalb

s

c

s Cj/Ccalb

104

r

r

102

100

100 0

2

4

6

0

8

2

4

6

8

t (week)

t (week) Fig. 9. Profiles of drug concentration in sclera (s), choroid (s), and retina (r). Initial temperature of hydrogel 30 1C and drug load 1 mg.

Fig. 12. Profiles of drug concentration in sclera (s), choroid (s), and retina (r). Initial temperature of hydrogel 20 1C and drug load 0.5 mg.

106

1

0.8

fc

fs

4

10

c

0.6 fj

Cj/Ccalb

s

r

0.4 fe

102

0.2 fr 0

100 0

2

4

6

8

t (week) Fig. 10. Profiles of drug concentration in sclera (s), choroid (s), and retina (r). Initial temperature of hydrogel 30 1C and drug load 0.5 mg.

105

c

Cj/Ccalb

s

r

100 0

2

4

6

8

t (week) Fig. 11. Profiles of drug concentration in sclera (s), choroid (s), and retina (r). Initial temperature of hydrogel 20 1C and drug load 1 mg.

figures are in agreement with our expectations of performance of rate processes in series. In Figs. 9–12, the drug concentration was normalized with the value of the concentration which results in

0

6

12 t (hr)

18

24

Fig. 13. Profiles of various fractions of drug released from hydrogel at short times. Initial temperature of hydrogel 30 1C and drug load 1 mg.

total inhibition of neovascularization, 150 mg/L. Again, neither the initial temperature nor the drug load seems to make a noticeable difference. In Figs. 9–12, a maximum in drug concentration occurs in every compartment some time close to the end of deswelling. The drug concentration profile in the retina is a little lower than but close to that in the sclera, while the concentration profile in the choroid is significantly higher than those in the sclera and retina. It should be noticed that it takes at least 8 weeks or 2 months before the concentration in the choroid and the retina reaches the value which is associated with total inhibition of neovascularization (150 mg/L) which is the recommended dosage for Lucentiss. The profiles of drug fraction in the three compartments, sclera, choroid, and retina, for short and long times, initial hydrogel temperature of 30 1C and drug load 0.5 mg, are displayed in Figs. 13 and 14. The bulk of the drug load is released during deswelling where also the maximum in the drug fraction in the sclera, fs, occurs. The drug fractions in the choroid and retina, fc and fr, reach their maxima approximately 5 h after fs has reached its maximum. For a more realistic simulation of macromolecular drug delivery, one needs an anatomically correct model for the eye. With such a model, one can study the effect on drug delivery of the shape, size, and site of placement of the episcleral hydrogel implant. This work is currently in progress.

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the retina to reach the value which results in total inhibition of neovascularization, 150 mg/L.

1 fe

0.8

Nomenclature fc

fj

0.6

0.4

0.2 fs

fr

0 0

2

4 t (week)

6

8

Fig. 14. Profiles of various fractions of drug released from hydrogel over long times. Initial temperature of hydrogel 30 1C and drug load 0.5 mg.

The purpose of this study was to predict the efficiency of a combined drug-release-from-hydrogel and tissue-compartmental model for sustained drug delivery. The experimental results used for comparison are from intravenous injections of known amounts of the IgG-segment. The predictions made in this study do not match exactly the experimental results, but the difference can be attributed in part to the difference in the nature of the drug delivery methods. The goal of this study was to estimate the timeline for which a specific mode of drug administration would be effective when compared to the available results of another mode. Even the roughest estimate, using a simple compartmental model, shows an effective drug concentration in the retina for twice the duration than the experimental values. Therefore, in case of a disease such as wet AMD, which requires frequent administration of the drug, the current study predicts half the dose or less frequent administration of the drug as compared to the currently available intravenous treatment.

4. Conclusions The model developed in this study describes deswelling of a thermally responsive hydrogel, made out of poly(N-isopropylacrylamide) (NIPAM), release of a macromolecular anti-VEGF drug, IgG1 Fab fragment, from the hydrogel, and delivery of the drug to the posterior eye. Based on the results of the simulations done with this model, the following conclusions can be drawn:

 The NIPAM hydrogel is modelled as a poroelastic material and





the time for its deswelling from an equilibrium state at an initial temperature to an equilibrium state at the body temperature is predicted to be 3–4 h, in agreement with the experimental findings. Most of the drug, close to 70% by weight, is released from the hydrogel, by convection (Darcy flow of the solvent through the macro-pores of the hydrogel), during deswelling. The remaining 30% is released from the hydrogel by diffusion over a period of at least 25 h. The compartmental model for drug delivery to the posterior eye tissues, in spite of its inherent weakness (assumption of complete mixing over the entire volume of each tissue), predicts realistic sustained delivery times of the order of 8 weeks, in agreement with clinical trials. The recommended monthly dose for Lucentiss is 0.5 mg. More specifically, it takes 8 weeks for the drug concentration in the choroid and

a ah ap Asc Acr Ar As B, g cc cr cs C Ccalb dj D, R Do Dj DIgG1 Dload f ff fj G Hj k kec ker K K0 MBIS MNIPA Mc Mn nBIS nNIPA p pi Pc Ps Pr R_ r t Ti u u_ ur, u uz v v2m V0

initial radius of cylindrical hydrogel, m radius of cylindrical hydrogel, m acrylamide polymer chain radius, m interfacial area between sclera and choroid, m2 interfacial area between choroid and retina, m2 surface area of retina, m2 surface area of sclera, m2 defined in Eq. (5) concentration of drug in choroid, kg m  3 concentration of drug in retina, kg m  3 concentration of drug in sclera, kg m  3 concentration of drug in the hydrogel, kg m  3 calibration concentration of drug (equivalent to minimum therapeutic level), kg m  3 depth of compartment j (j ¼s, c, r), m defined in Eq. (11) diffusion coefficient of drug in water, m2 s  1 drug diffusivity in compartment j (j¼ s, c, r), m2 s  1 diffusion coefficient of drug (IgG1 Fab fragment) in hydrogel, m2 s  1 amount of drug loaded in hydrogel, kg fraction of drug load released from the hydrogel into sclera friction constant between polymer and solvent system, N s m4 j ¼s, c, r, defined in Eq. (24) shear modulus of elasticity of acrylamide chain network, Pa partition coefficient for the drug on compartment j, j ¼s, c, r hydrodynamic permeability of acrylamide polymer network, m s  1 first-order drug elimination constant in choroid, s  1 first-order drug elimination constant in retina, s  1 parameter defined in Eq. (5) bulk modulus of elasticity of acrylamide chain network, Pa molecular weight of BIS, kg mol  1 molecular weight of NIPA, kg mol  1 average molecular weight of crosslink, kg mol  1 number average molecular weight of monomeric material, kg mol  1 number of moles of BIS, mol number of moles of NIPA, mol pressure, N m  2 intraocular pressure, N m  2 permeability of choroid to drug, m s  1 permeability of sclera to drug, m s  1 permeability of retina to drug, m s  1 rate of drug release by the hydrogel, kg s  1 radial coordinate, m time, s temperature of hydrogel before implantation, 1C displacement vector, m rate of deformation vector, m/s radial displacement, m axial displacement, m solvent velocity defined in Eq. (18), m s  1 volume fraction of polymer at equilibrium swelling degree reference volume (here, volume of polymerizing mixture), m3

P.R. Ninawe et al. / Chemical Engineering Science 65 (2010) 5170–5177

V1 Vc Vr Vs z

molar volume of solvent, m3 mol  1 volume of choroid, m3 volume of retina, m3 volume of sclera, m3 axial coordinate, m

Greek letters

a(t) g w dc

Zs k l

m fp z

r x y

r

defined in Eq. (13) measure of severity of entanglement of polymer network, used in Eq. (5) solvent–polymer interaction parameter, defined in Eq. (2) thickness, m viscosity of the solvent, Pa s Darcy’s coefficient defined in Eq. (8), N  1 s  2 m4 related to v2m in Eq. (5) number of junctions in the polymer network defined in Eq. (3) polymer volume fraction parameter accounting for non-affine transformation of domain of constraint with strain polymer density, kg m  3 cycle rank or number of independent circuits in the network defined in Eq. (3) angular coordinate, rad differential operator

Subscript e

equilibrium

Superscript .

time derivative

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