Bioconjugate Chem. 2007, 18, 2115–2121
2115
Conjugation to Increase Treatment Volume during Local Therapy: A Case Study with PEGylated Camptothecin Kraig Haverstick,† Alison Fleming,‡ and W. Mark Saltzman*,‡ Department of Chemical and Biomolecular Engineering, Cornell University, and Department of Biomedical Engineering, Yale University. Received June 16, 2007
Controlled release of chemotherapy drugs from polymer implants placed directly at the tumor site is a proven method for treatment of cancers of the brain. Although this method provides high doses of drug at the tumor site, the drug does not penetrate far enough into the brain for optimum treatment in most cases. Rapid drug elimination leads to more than a 10-fold drop in concentration within 2 mm of the implant. Conjugation to water-soluble polymers, such as poly(ethylene glycol) (PEG) or dextran, has the potential to increase drug distribution in the brain. We have recently PEGylated the chemotherapy drug camptothecin and found a large increase in the extent of distribution of camptothecin in the rat brain, but most of the drug in tissue was in the less-active conjugated form. Stability of the conjugation bond, activity of the drug–polymer conjugate, solubility of the conjugate relative to the drug, and molecular weight of the polymer must all be considered in the design of a conjugate to maximize drug distribution. Therefore, to optimize the PEGylated system, we have developed a pharmacokinetic model to determine the relative importance of parameters involved in the distribution of drug–polymer conjugates after release from a polymer implant. Our modeling shows that PEGylation has the potential to increase treatment distances to more than a centimeter, which may be sufficient to prevent the recurrence of human brain tumors.
INTRODUCTION Drug–polymer conjugation is a promising approach for improving systemic and targeted drug delivery. Systemic delivery of camptothecin, an antitumor, topoisomerase I inhibiting drug, has been enhanced by conjugation to dextran (1), poly(2-hydroxypropyl) methacrylamide (2, 3), and poly(ethylene glycol) (4). Conjugation extends circulation time in the bloodstream, and additional attachment of protease-specific sequences can target release of the free drug. Recently, we have shown that conjugation of camptothecin to PEG can dramatically improve solubility and penetration through tissue (5). Drug delivery to the brain faces challenges not present for delivery to other parts of the body. The blood–brain barrier limits systemic delivery of most drugs (6). Local administration by direct injection or controlled-release implantation overcomes this obstacle, but since diffusion becomes the primary means of distribution in the brain, the drug moves slowly from the initial injection or implantation site (7). The treatment volume is limited by rapid drug elimination, primarily through capillaries for small, hydrophobic molecules, relative to the rate of diffusion. The pharmacokinetics of a number of therapeutic drugs in the brain has been studied with the general result being that rapid elimination quickly produces a steady-state profile, where drug concentration decreases sharply with distance from the implant site: the extent of penetration—or the characteristic distance for the drop in concentration—depends on the rate of diffusion of drug in the brain and the rate of elimination (for a review of this literature, see (8)). Diffusion and elimination properties in brain tissue have previously been reported for a variety of compounds, including our recent measurements for * Address correspondence to Professor W. Mark Saltzman, Department of Biomedical Engineering, P.O. Box 208260, Yale University, New Haven, CT 06520, E-mail:
[email protected], Phone: 203432-4262, Fax:203-432-0030. † Cornell University. ‡ Yale University.
camptothecin (5). These drugs have low molecular weights (below 500, except for paclitaxel), and are fairly hydrophobic (except sucrose), making them susceptible to rapid elimination through capillaries. The dimensionless coefficient, φ, analogous to the Thiele modulus in reaction catalysis (9), has been previously defined as
√ Dk
φ)a
(1)
where a is the radius of porous catalyst particles, k is the firstorder reaction rate, and D is the rate of diffusion of reactant in the catalyst pores. For low values of φ, reactant penetrates throughout the catalyst, and reaction efficiency is high; for high values of φ, reactant does not penetrate, and the reaction efficiency is low. This same coefficient can be used to predict the extent of penetration in the brain; in this case, a is the characteristic implant length, k is the first-order rate of elimination in the brain, and D is the effective diffusion coefficient in the brain (7). For most drugs, the value for φ is greater than 1 (see (8)). Previous modeling results, which assume the presence of only diffusion and first-order elimination, predict that φ values in this range lead to a distribution where the drug does not penetrate very far from the surface of a spherical implant. Figure 1 illustrates the steady-state concentration profile of drug around a spherical implant. As φ decreases, drug distribution improves, but for φ greater than 1, drug concentrations decrease by an order of magnitude within 2 mm of the implant. To improve the distribution of a particular drug, its φ value in the brain must be reduced. Since the rate of diffusion cannot be increased, it is necessary to find a way to slow the rate of drug elimination. This can be accomplished by attachment of a polymer. Another factor working against many drugs is their low solubility in water; conjugation to a water-soluble polymer has an additional advantage, since it can significantly increase the maximum achievable concentration of a poorly soluble drug in the brain. Although elimination is not solely driven by molecular size, larger molecules tend to be retained in the brain for longer
10.1021/bc700214h CCC: $37.00 2007 American Chemical Society Published on Web 10/13/2007
2116 Bioconjugate Chem., Vol. 18, No. 6, 2007
Haverstick et al.
Figure 1. Steady state profiles of drug concentration as a function of distance from the implant.
Figure 3. Camptothecin–poly(ethylene glycol) drug–polymer conjugates. (A) PEG-CPT. (B) PEG-Gly CPT. (C) PEG-Sar-CPT. (D) R ) R′ ) H, Camptothecin: Drug is conjugated at the R site to PEG. R′ ) OH, 10-hydroxycamptothecin: Drug is conjugated at the R′ site to PEG.
Figure 2. Drug delivery systems. (A) Drug is released in its free state. (B) Moderate-activity conjugate is released and remains in its conjugated form. (C) Inactive conjugate is released, and drug is fully active after hydrolysis. (D) Low-activity conjugate is released, and drug is fully active after hydrolysis. Circles represent drug with shading indicative of the degree of activity.
periods of time. While most drugs have half-lives in the ranges of minutes, larger polymers such as dextran are retained with half-lives of 15 h or more (10). Since poly(ethylene glycol) is known for its biocompatibility and its ability to solubilize hydrophobic molecules in water, we believe that PEG–drug conjugates show great potential for improving the brain distribution of drug released from controlled-release polymers. Since the ultimate goal in improving the distribution of chemotherapy drug is to increase the volume of tissue treated, the potency of the drug must also be considered. The form of the drug is often critical to its potency. When paclitaxel, methotrexate, and doxorubicin were permanently modified with PEG, the toxicity of the conjugates was found to be lower than the toxicity of the free drugs by a factor of 50 to 1000 (11). Therefore, as drug–polymer conjugates are evaluated, the toxicity of the conjugate in comparison to the free drug must also be considered in order to determine the relative value of conjugation. Finally, the time of exposure can be just as important as the level of exposure in the treatment of tumors. A low dose of drug over a long period of time can be more effective than a high dose for a short period for certain kinds of agents. Use of a controlled release implant can provide low levels of chemotherapy drug for periods of weeks or longer. Since conjugation of drug to a polymer will reduce the rate of elimination, residence time in the brain will increase, and dosing with conjugates over a longer time course may be possible. We have investigated three different types of model drug– polymer systems to compare to a free drug system (Figure 2). In the first case, we looked at release of drug alone as a basis for comparison with conjugates. In the second case, the drug is attached permanently to the diffusable polymer, but the potency of the drug is reduced in conjugated form. In the third case, the drug is coupled by an ester bond, which hydrolyzes under physiological conditions with a half-life of 1 to 3 days. While the drug is attached to the polymer, it is not active. After
hydrolysis, the free drug is released and biologically active. Therefore, we initially implant an inactive species, which travels away from the implant site, becomes hydrolyzed in water, and releases the free drug in its active form. In the final case, the drug–polymer conjugate is active but at a lower level than the free drug, and the bond can be hydrolyzed to release the free drug. Each of these systems has the potential to improve distribution of active drug in the brain; our goal in this present study was to determine essential characteristics of PEGylated camptothecin and to model each of these cases to determine which system would be more effective.
EXPERIMENTAL SECTION Materials. Carboxymethyl poly(ethylene glycol), molecular weight 3400, was purchased from Shearwater Polymers. 10hydroxycamptothecin was purchased from NetQem. All other reagents and solvents were acquired from Aldrich Chemical Company. Methods. Synthesis of Poly(ethylene glycol)–Camptothecin Conjugates. These procedures were modified from previously published protocols (12), as described completely earlier (5). The structures of these conjugates appear in Figure 3, and their physical properties are listed in Table 1. Determination of Solubility. For CPT, excess CPT was added to a PBS solution (pH 7.4). The container was sealed and placed at 37 °C overnight. The UV absorbance of the solution at 369 nm was measured and compared to a calibration curve for CPT to determine the saturated concentration. A Hitachi U-2001 spectrophotometer was used for all UV measurements. For conjugates, approximately 10 mg of conjugate was weighed in a vial. PBS was added in 10 µL increments until all conjugate was dissolved. Determination of Hydrolysis Rate. Conjugate was weighed and dissolved at a concentration of 9 mg/L in phosphate-buffered saline at 37 °C. The solution was capped and stored in a 37 °C shaker. At increasing intervals of 1 h to a half-day, a 1 mL sample was taken for HPLC analysis. A Waters 2690 Separation module with photodiode array detector was used with a Zorbax 300SB-CN column. A 10 µL volume was injected into a solvent gradient of 80:0:20 to 40:40:20 (water/acetonitrile/0.5% TFA in water) over 20 min to elute the free camptothecin in 12.9 min. The areas under the absorbance curve at 254 nm, 354 nm, and 369 nm were compared to a calibration curve from injected known concentrations of camptothecin to determine the concentration of free camptothecin in the sample. Concentrations
Conjugation to Increase Treatment Volume
Bioconjugate Chem., Vol. 18, No. 6, 2007 2117
Table 1. Model Parameters from Drug-Polymer Conjugatesa drug form
solubility (mg/L)
Camptothecin PEG3400-CPT PEG3400-Gly CPT PEG3400-Sar-CPT a
IC50, 72 h (µg/L)
kh (h-1)
ke (h-1)
D (mm2/hr)
φ (a ) 1.5 mm)
12.9 ND ND ND
N/A 0.018 0.012 0.0085
1.28 0.017 0.017 0.017
0.282 0.14 0.14 0.14
3.20 0.75 0.68 0.64
27.5 >1000 >1000 >1000
ND ) not determined. N/A ) not applicable.
were plotted versus time and fitted to a first-order curve to determine the hydrolysis rate and initial loading of CPT. Determination of IC50 Values. IC50 values were determined for free CPT, PEG3400-Sar-CPT, and PEG3400-Gly CPT using rat 9L glioma cells. Values were based on different exposure times in culture. Experiments were repeated four times for each condition. Conjugates showed activity that was time-delayed by the hydrolysis required to produce active free drug. Determination of Elimination Rate. Elimination rate was assumed to be first-order. For camptothecin, the elimination rate was determined in rat brains by measuring the total amount of CPT released from a biodegradable polymer implant and remaining in the brain at various time points after implantation. Elimination of PEG4000 and PEG900 has been previously studied in the rat brain (13). We have estimated the conjugate elimination rate in a human brain based on these rat data. The overall rate of 1.5 × 10-5 s-1 includes 0.2 × 10-5 s-1 across the blood–brain barrier and 1.3 × 10-5 s-1 from elimination at structural boundaries. Since the length scale of the human brain is ten times that of the rat brain, we estimated conservatively a boundary rate 1/5 the rate in the rat. This gives a total human elimination rate of (0.2 + 0.26) × 10-5 s-1 or 0.017 h-1, which we have used in our modeling. Determination of EffectiVe Diffusion Coefficient. Diffusion coefficients in the brain were calculated empirically using the Wilke–Chang equation (14) and multiplying by 0.4 to account for tortuosity in the brain (7).Brain diffusion coefficients were also determined experimentally in a previous report (5). For CPT, this experimentally determined diffusion coefficient (0.282 mm2/h) was significantly lower than what we empirically calculated (0.825 mm2/h) both from Wilke–Chang and from molecules of comparable molecular weights (15). Lower-thanexpected experimental diffusion coefficients have been reported for other small molecules such as paclitaxel (16) and fluorescein (10). Experimental PEG3400 conjugate diffusion coefficients (0.14 mm2/h) in rat brains, assuming an elimination rate of 1.5 × 10-5 s-1, were also found to be lower than expected for PEG based on Wilke–Chang and aqueous experimental values (17) (0.18 mm2/h) for equivalent PEG molecular weight. We have chosen to use the more conservative experimentally determined values. Model. To predict the effect of different conjugate parameters on distribution of drug in the brain, we have modified a previously established model (7) to estimate the treatment volume surrounding a conjugate-loaded polymer implant. This model assumes that drug moves only by simple diffusion and is removed by first-order elimination. Treatment distance and volume will be defined as the brain space, which receives an IC50 concentration of chemotherapy drug for 72 h. Treatment distance is measured from the surface of the implant, which is assumed to be stationary and to maintain a constant conjugate concentration. Since drug–polymer conjugates in cases 3 and 4 can be hydrolyzed to release free drug, the model is designed to monitor the distribution of both conjugate and free drug. For the conjugate, the governing equation in spherical coordinates for distribution after release from a sphere is
(
)
∂2Cc 2 ∂Cc ∂Cc ) Dc + - (ke,c + kh)Cc ∂t r ∂r ∂r2
(2)
and for the free drug, when it is generated only by hydrolysis of the conjugate
(
)
∂Cd ∂2Cd 2 ∂Cd ) Dd + + khCc - ke,dCd (3) ∂t r ∂r ∂r2 where Cc ) concentration of the conjugate; Cd ) concentration of the free drug; Dc ) effective diffusion coefficient of the conjugate; Dd ) effective diffusion coefficient of the drug; ke,c ) elimination rate of the conjugate; ke,d ) elimination rate of the drug; kh ) hydrolysis rate of the conjugate; t ) time; r ) radial distance from the center of the implant. These equations were implemented with the following initial and boundary conditions: When t ) 0, C ) 0 for all r > a. When t > 0, C f 0 as r f ∞. For the conjugate: When t > 0, C ) C0 at r ) ∞. For the free drug: When t > 0, ∂C / ∂r ) 0 at r ) a where a is the radius of the implant. When we are simply releasing free drug or stable drugpolymer conjugate from a polymer, the governing equation is
(
)
∂2Cd 2 ∂Cd ∂Cd ) Dd + - ke,dCd (4) ∂t r ∂r ∂r2 where the same boundary conditions are applied as for eq 2 for the hydrolyzing conjugate. The transient solution to eqs 2 and 4 has been obtained and published previously
{ [
√ ] [1 - erf( r2√-Dta - √kt)] + exp[(r - a) √ Dk ][ 1 - erf( r2√-Dta + √kt)]} (5)
k a C ) exp -(r - a) C0 2r D
where k ) ke,c + kh for the released conjugate and k ) ke,d for the released drug (18). Therefore, in both of these cases we can easily calculate the distribution of the released material at a given time. Since eq 3 is coupled to eq 2 by a conjugate concentration term, hydrolyzed drug distribution cannot be determined explicitly. We have used two different approximations to calculate the distribution of drug that has been hydrolyzed from the conjugate. For one approximation, the drug does not diffuse after hydrolysis and goes to steady state. Therefore, eq 3 reduces to ∂Cd ) khCc - ke,dCd ) 0 (3a) ∂t A second way to simplify eq (3 is to assume that the drug does diffuse and goes rapidly to steady state, or 0 ) Dd
(
∂2Cd
+
)
2 ∂Cd + khCc - ke,dCd r ∂r
(3b) ∂r Both approximations simplify calculation of the profile of hydrolyzed drug concentration. Equation 3a greatly overestimates drug concentration close to the implant but slightly underestimates drug concentration far from the site. Equation 3b slightly overestimates drug concentration far from the site. The true transient concentration at the treatment distance should 2
2118 Bioconjugate Chem., Vol. 18, No. 6, 2007
Haverstick et al.
Table 2. Modeling Values for Determination of Treatment Distances conjugate case case case case
1 2 3 3
free CPT
C0 mg/L
D (mm2/hr)
ke (hr-1)
1/A
1–25 1–1000 1–1000 1–1000
0.14–0.18 0.14–0.18 0.14–0.18
0.017 0.017 0.017
0.002–0.02 0 0.002–0.02
fall between the treatment distances estimated by eqs 3a and 3b. In practice, we found a minimal difference between calculated treatment distances from eqs 3a and 3b for the model parameters used for CPT and PEG-CPT, and therefore eq 3a was used to give the results presented.
RESULTS Three PEG-camptothecin conjugates were synthesized as described in the Experimental Section. They differed in the stability of the linkage between the polymer and the 20-hydroxyl group of camptothecin. In a previous report, we provided analysis by MALDI-TOF to confirm the chemical modifications (5); those results were verified for all of the preparations used here. Table 1 lists the relevant physical properties in the brain for these three compounds in comparison to camptothecin. Solubilities were measured in phosphate-buffered saline at 37 °C, and the CPT solubility is consistent with a previously reported value of 25 mg/L (18). An additional benefit of CPT conjugation is stabilization of the active lactone form to higher pH values (19). Conjugate concentrations in Table 1 and future discussions refer to the free drug equivalent concentration of the conjugate. For example, 1 mg/L of conjugate has 1 mg/L of CPT attached to PEG. Diffusion coefficients were determined experimentally for CPT and conjugates and are slightly lower than empirically expected. Hydrolysis rates, elimination rates, and IC50 values were determined as described in the Experimental Section. Modeling incorporated simple diffusion, first-order hydrolysis and elimination, and several constraints on the physical system. A spherical polymer implant 3 mm in diameter was assumed. This is the average size of the implants used in typical experiments. PEGs of molecular weights 2000 and 3400 were modeled with the assumption that PEG 2000 will have the same rate of elimination and solubility as PEG 3400. Our model assumes that release from the implant occurs with a constant concentration maintained at the implant surface. Since a homogenous environment was assumed, the concentration of drug varied only with radial distance from the center of the implant. The treatment area, therefore, was a sphere surrounding the implant site. Four different systems were modeled. Relevant parameters and variables for modeling of these systems are listed in Table 2. In the first case, unconjugated drug is released. A permanent conjugate with reduced cytotoxicity of the conjugate relative to the drug itself is released in case 2. In case 3, the conjugate is assumed to have no toxicity, and the hydrolysis-released drug has the same properties as the drug itself. Case 4 is identical to case 3, except that the conjugate form has cytotoxicity in the range 50–500 times less than the free drug. Variables for the different cases consisted of the C0 value, hydrolysis rate (0.05–0.035 h-1), conjugate diffusion coefficient (PEG2000 or PEG3400), and IC50 value of the conjugate. The drug and conjugate profiles at 96 h, with a C0,CPT of 25 and a C0,conj of 500 mg/L, appear in Figure 4. These profiles assume a conjugate diffusion coefficient of 0.14 mm2/h (PEG3400) and, for case 3 (lines 3a and 3b), a hydrolysis rate of 0.018 h-1. The slope of the CPT (line 1) in the semilog plot is very steep, as the drug is eliminated quickly. Released CPT
kh (hr-1)
0.005–0.035 0.005–0.035
D (mm2/hr)
ke (hr-1)
IC50 (µg/L)
0.282
1.28
12.9
0.282 0.282
1.28 1.28
12.9 12.9
in Figure 4 (line 3b) was calculated using a numerical solution to eq (3b. Although the concentration of CPT released from conjugate (line 3b) is clearly lower at the implant surface than what can be achieved with CPT alone, drug concentration has a much smaller slope in the semilog plot. With no hydrolysis (line 2), the conjugate can reach higher concentrations farther from the implant, but this is offset by the lower cytotoxicity of the conjugate relative to the free drug. Optimization of treatment becomes a balance of these effects. For all cases, concentration profiles were computed at 96 h after implantation. At this time, concentration profiles were close to steady-state values, and enough drug was present to maintain C0 values for at least 72 more hours. “Treatment distances” were determined as the farthest distances from the implant surface at which the concentration at 96 h was above the IC50 value. For unconjugated drug, this IC50 value was 0.0129 mg/L. For conjugated drug, it was A multiplied by 0.0129 mg/L, where A is the toxicity reduction factor for the conjugated form. When both unconjugated and conjugated forms of the drug were present and active (case 4), they were assumed to have an additive effect toward achieving an IC50 concentration. Samples of treatment distance results for cases 2, 3, and 4 appear in Figures 5, 6, and 7, where C0 ) 500 mg/L for all curves in Figure 7. Treatment distances for case 1 were 0.235, 0.264, 0.281, 0.293, and 0.303 cm for C0 values of 5, 10, 15, 20, and 25 mg/L, respectively. Concentration profiles, and hence treatment distances, for the first two cases were determined exactly using eq 5. Figure 5 shows that increasing the toxicity
Figure 4. Concentration profiles at 96 h. 1 ) CPT (case 1, C0 ) 25 mg/L); 2 ) PEG3400dCPT (case 2, C0 ) 500 mg/L); 3a ) PEG3400—CPT (case 3/4, C0 ) 500 mg/L); and 3b ) CPT released (case 3/4, from PEG3400—CPT). (A) Direct plot. (B) Semilog plot.
Conjugation to Increase Treatment Volume
Bioconjugate Chem., Vol. 18, No. 6, 2007 2119
gives the largest treatment distance. The optimal hydrolysis rate increases as A increases to 200 and higher.
DISCUSSION
Figure 5. Treatment distances of permanent conjugates (case 2). Thin ) PEG2000. Bold ) PEG3400.
Figure 6. Treatment distances of inert hydrolyzable conjugates (case 3). Thin ) PEG2000. Bold ) PEG3400.
Figure 7. Treatment distances of active, hydrolyzable conjugates (case 4, C0 ) 500 mg/L). (A) PEG2000. (B) PEG3400.
of the conjugate, the C0 concentration, and the effective diffusion coefficient all lead to larger treatment distances for a case 2 conjugate. For cases 3 and 4, concentration profiles of conjugate were determined exactly with eq 5. Equation 3a was used to get drug concentrations for treatment distance calculations for cases 3 and 4. The results of these calculations appear in Figures 6 and 7. Figure 6 illustrates that, as C0 decreases for a case 3 conjugate, the optimal hydrolysis rate increases from about 0.018 h-1 for C0 ) 500 to about 0.035 h-1 for C0 ) 50 mg/L. Finally, in Figure 7, if A is 100 or less, a nearly permanent conjugate
PEG–CPT conjugates were synthesized and characterized as drug–polymer conjugates to determine appropriate parameters for modeling of drug distribution in the human brain. Our goal was to determine the potential advantage of a drug–polymer conjugate over drug alone in terms of distribution from a controlled-release polymer and tumor treatment. This would allow rational design of future conjugates with optimal physical properties for treatment of a cancer site. Although these equations can be applied to other drug conjugate systems, our results are specific for PEG–camptothecin conjugates. Case 1 serves as a baseline for comparison to conjugate systems. The C0 value for camptothecin is severely limited by low water solubility, and camptothecin is rapidly eliminated from the brain. If a saturated concentration can be maintained at the implant surface, a treatment distance of 0.3 cm is achieved. Experimentally, C0 values as high as 20 mg/L have been maintained in a rat brain for several days after implantation. (5) Although the IC50 value may not be the critical concentration necessary for effective tumor site treatment, we believe it to be a more appropriate choice than the C0/10 value often used, since it does account for the toxicity of the drug. As a result of the high diffusion and elimination rates, free drug approaches a steady-state profile within a matter of minutes. The two major advantages of the PEG conjugates are a much greater solubility in water than the drug itself and a much slower rate of elimination. Obviously, increasing the C0 value increases the treatment distance. Additionally, since we assume PEG2000 differs from PEG3400 only in having a larger diffusion coefficient, a PEG2000 system will give a larger treatment distance than an otherwise equivalent PEG3400 system. Finally, a decrease in A, the toxicity reduction factor, always leads to an increase in treatment distance. The most interesting of the variables is the hydrolysis rate of the conjugate, which will show an internal optimum for treatment distance under most of our conditions. While a conjugate system allows for considerably more design freedom than a drug alone, we still face physical limitations. We assume that PEG2000 stands at the low molecular weight end for conjugate, or else we risk lower conjugate solubility. Although PEG as low as 900 has been shown to have the same elimination rate as PEG4000, (13) we expect the solubilizing power, and hence potential C0, to be reduced. Therefore, diffusivity of the conjugate has an upward bound of ∼0.18 mm2/ h. Depending on the drug, some flexibility in the A factor of the conjugate is possible by using different linkages, such as a 10-hydroxy linkage for CPT, but it is unlikely that a factor less than 50 will be achieved. Additionally, variation of the linkage can be used to produce a range of hydrolysis rates. Within the parameter space we investigated, the largest treatment distance was 1.343 cm for a case 2 PEG2000 conjugate with A ) 50 and C0 ) 1000 mg/L. We have found it difficult to determine A experimentally for our conjugates, because the experimental error is greater than the difference we would predict in the cytotoxicity assays between A ) ∞ and A ) 50. The modeling results can be applied to the CPT conjugates that we synthesized, assuming C0 ) 500 mg/L and 1/A ) 0. These cases led to treatment distances of 0.817 cm for the sarcosine conjugate, 0.842 cm for the glycine conjugate, and 0.855 cm for the ester conjugate. The ester conjugate had the optimal hydrolysis rate for these conditions. Although these conjugates already show a significant improvement over the 0.3 cm treatment distance of camptothecin alone, we discuss approaches that might increase treatment distances further in the next few paragraphs.
2120 Bioconjugate Chem., Vol. 18, No. 6, 2007
Decreasing the surface concentration, C0, decreases the treatment distance. The treatment distance relative to that for C0 ) 1000 seems to be fairly independent of the other variables, and doubling C0 from 500 to 1000 increases the treatment distance an average of 14% for case 2 and 12% for cases 3 and 4. We set 500 mg/L as a practical C0 limit, which should be achievable in ViVo. Advantages for further increases are tempered with a very high conjugate loading requirement and concentrations that may be difficult to sustain. Although drug conjugates have a greatly reduced cytotoxicity relative to the native drug, they have been found to be active at concentrations 50 to 1000 times greater than their parent drug. We assumed an initial 1/A value of zero, meaning that the conjugate is completely inert. Increasing conjugate activity in our models with A values of 500, 200, 100, and 50 will lead to an increase in treatment distance and will also decrease the optimum hydrolysis rate. We have found that increases in treatment distance with decreasing A are approximately independent of C0. As the hydrolysis rate increases, the benefit of increasing 1/A to 0.02 decreases from 0.31 to 0.075 cm for PEG3400 and from 0.35 to 0.085 cm for PEG2000. Increasing the rate of diffusion will also increase the treatment distance. This can only be done by decreasing the molecular weight of PEG, which may have implications for the solubility and elimination rate. Decreasing PEG from 3400 to 2000 increases the conjugate diffusion coefficient from 0.14 to 0.18 mm2/h. This leads to an average increase of 10.9% in the treatment distance for cases 3 and 4 and an average increase of 9.5% for case 2. Finally, we can control the hydrolysis rate through the conjugation linkage, so that this variable can be adjusted to maximize treatment distance for a given set of conditions. The optimal hydrolysis rate balances the properties of the conjugate with the properties of the released drug. Increasing the cytotoxicity of the conjugate shifts the optimum hydrolysis rate to lower values, as does increasing the implant surface concentration. Optimizing over the range 0–0.035 h-1 can increase treatment distance by as much as 0.287 cm. As conjugate toxicity decreases, increasing the C0 value leads to an improvement in the treatment distance. On the basis of our modeling results, the PEG3400–CPT conjugate version gives the greatest treatment distance of the conjugates we have synthesized. On the assumption that it is a case 3 conjugate with no cytotoxicity in the conjugated form and a C0 value of 500 mg/L, this version gives a treatment distance of 0.855 cm. This value is significantly greater than the 0.3 cm that we calculate for release of unconjugated drug. Released conjugate should treat a volume of 4.24 cm3, which is 11 times the 0.37 cm3 treated by unconjugated drug. Reducing to PEG2000–CPT improves the treatment distance to 0.950 cm. Producing an implant that can sustain a C0 value as high as 500 mg/L requires some special consideration. As an estimate of total conjugate required, a steady-state profile of PEG3400–CPT with C0 ) 500 mg/L contains 0.44 mg of conjugate (with 15 wt % CPT/conjugate). Therefore, the rate of loss of conjugate is 0.44 mg × 0.035 h-1, or 0.0154 mg/h, for 168 h requires 2.59 mg of conjugate. Placing this mass into a 0.15 cm radius pellet at a density of 1.5 g/cm3 requires a loading of 12.2%. Several controlled-release polymers have been used for implants of this kind including nonbiodegradable EVAc (polyethyleneco-vinyl acetate) (20, 21) and biodegradable p(CPP:SA) (poly(1,3bis(p-carboxyphenoxy)propane/sebacic acid)). (16, 22) On the basis of our experience, both EVAc and p(CPP:SA) could be loaded at 15% (or more) and could be designed to maintain such a high C0. Since PEG–CPT conjugate could be thought of as a “controlled release” device on its own, another possibility would be to create an implant of pure conjugate. A final
Haverstick et al.
consideration would be to include free CPT along with conjugate in the loaded implant. This free CPT should be more soluble in the presence of conjugate and may slow hydrolysis when present in high concentrations near the implant. These calculations help in the interpretation of our previous experimental results with conjugate penetration in the brain (5) and also point toward approaches that might improve conjugate design for this application. We note that this study has limitations: in particular, we have made assumptions about the rate of elimination of PEG from the brain and about the relationship between conjugate diffusion and PEG diffusion that need to be verified. In addition, we note that it is difficult to estimate actual values for the parameter A.
CONCLUSIONS Low solubility and rapid elimination in the brain prevent most drugs from diffusing more than a few millimeters away from an implant site. Poly(ethylene glycol)–drug conjugates have much longer residence times and higher solubilities than their free drug counterparts. For the chemotherapy drug camptothecin, these improvements allow greater distribution of the drug in the brain. This translates into a greater volume of tissue receiving a therapeutic dose of drug and, therefore, a greater likelihood of prevention of tumor recurrence. Specifically, if a therapeutic dose is defined as the IC50 concentration of 0.0129 mg/L for 72 h, we predict a 3 mm diameter PEG3400–CPT implant to treat 4.24 cm3, more than 11 times the volume treated by a CPT implant of the same diameter. This increase in treatment volume may be sufficient to improve the clinical effectiveness of controlled-release implants on human brain tumors.
ACKNOWLEDGMENT This work was supported by grants from NIH (CA52857 and NS045236).
LITERATURE CITED (1) Harada, M., Murata, J., Sakamura, Y., Sakakibara, H., Okuno, S., and Suzuki, T. (2001) Carrier and dose effects on the pharmacokinetics of T-0128, a camptothecin analog-carboxymethyl dextran conjugate, in non-tumor and tumor-bearing rats. J. Controlled Release 71, 71–86. (2) Caiolfa, V. R., Zamai, M., Fiorino, A., Frigerio, E., Pellizzoni, C., d’Argy, R., Ghiglieri, A., Castelli, M. G., Farao, M., Pesenti, E., Gigli, M., Angelucci, F., and Suarato, A. (2000) Polymerbound camptothecin: initial biodistribution and antitumour activity studies. J. Controlled Release 65, 105–119. (3) Sakuma, S., Lu, Z. R., Kopeckova, P., and Kopecek, J. (2001) Biorecognizable HPMA copolymer-drug conjugates for colonspecific delivery of 9-aminocamptothecin. J. Controlled Release 75, 365–379. (4) Conover, C. D., Pendri, A., Lee, C., Gilbert, C. W., Shum, K. L., and Greenwald, R. B. (1997) Camptothecin delivery systems: the antitumor activity of a camptothecin 20-0polyethylene glycol ester transport form. Anticancer Res. 17, 3361–3368. (5) Fleming, A. B., Haverstick, K., and Saltzman, W. M. (2004) In vitro cytotoxicity and in vivo distribution after direct delivery of PEG-camptothecin conjugates to the rat brain. Bioconjugate Chem. 15, 1364–75. (6) Begley, D. J., Bradbury, M. W., and Kreuter, J. (2000) The Blood-Brain Barrier and Drug DeliVery to the CNS, Dekker, New York. (7) Saltzman, W. M., and Radomsky, M. L. (1991) Drugs released from polymers: diffusion and elimination in brain tissue. Chem. Eng. Sci. 46, 2429–2444. (8) Saltzman, W. M. (2000) Interstitial transport in the brain: principles for local drug delivery, In Handbook of Biomedical
Conjugation to Increase Treatment Volume Engineering (Bronzino, J., Ed.)pp 99–1 to 99–14, CRC Press, Boca Raton, FL. (9) Thiele, E. W. (1939) Relation between catalytic activity and size of particle. Ind. Eng. Chem. 31, 916–920. (10) Dang, W., and Saltzman, W. M. (1992) Dextran retention in the rat brain following controlled release from a polymer. Biotechnol. Prog. 8, 527–532. (11) Pendri, A., Gilbert, C. W., Soundararajan, S., Bolikal, D., Shorr, R. G. L., and Greenwald, R. B. (1996) PEG Modified Anticancer Drugs: Synthesis and Biological Activity. J. BioactiVe Compat. Polym. 11, 122–135. (12) Greenwald, R., Pendri, A., Conover, C., Lee, C., Choe, Y., Gilbert, C., Martinez, A., Xia, J., Wu, D., and Hsue, M. (1998) Camptothecin-20-PEG ester transport forms: the effect of spacer groups on antitumor activity. Bioorg. Med. Chem. 6, 551–562. (13) Cserr, H. F., Cooper, D. N., Suri, P. K., and Patlak, C. S. (1981) Efflux of radiolabeled polyethylene glycols and albumin from rat brain. Am. J. Physiol. 240, F319–F328. (14) Wilke, C. R., and Chang, P. (1955) Correlation of diffusion coefficients in dilute solutions. AIChE J. 1, 264–270. (15) Yaws, C. W. (1995) Handbook of Transport Property Data: Viscosity, Thermal ConductiVity, and Diffusion Coefficients of Liquids and Gases, Gulf Publishing Company, Houston. (16) Fung, L. K., Ewend, M. G., Sills, A., Sipos, E. P., Thompson, R., Watts, M., Colvin, O. M., Brem, H., and Saltzman, W. M.
Bioconjugate Chem., Vol. 18, No. 6, 2007 2121 (1998) Pharmacokinetics of interstitial delivery of carmustine, 4-hydroperoxycyclophosphamide, and paclitaxel from a biodegradable polymer implant in the monkey brain. Cancer Res. 58, 672–684. (17) Waggoner, R., Blum, F., and Lang, J. (1995) Diffusion in aqueous solutions of poly(ethylene glycol) at low concentrations. Macromolecules 28, 2658–2664. (18) Mahoney, M. J., and Saltzman, W. M. (1996) Controlled release of proteins to tissue transplants for the treatment of neurodegenerative disorders. J. Pharm. Sci. 85, 1276–1281. (19) Zhao, H., Lee, C., Sai, P. K., Choe, Y. H., Boro, M., Pendri, A., Guan, S. Y., and Greenwald, R. B. (2000) 20-O-acylcamptothecin derivatives: evidence for lactone stabilization. J. Org. Chem. 65, 4601–4606. (20) Powell, E. M., Sobarzo, M. R., and Saltzman, W. M. (1990) Controlled release of nerve growth factor from a polymeric implant. Brain Res. 515, 309–311. (21) Reinhard, C., Radomsky, M. L., Saltzman, W. M., Hilton, J., and Brem, H. (1991) Polymeric controlled release of dexamethasone in normal rat brain. J. Controlled Release 16, 331– 340. (22) Fung, L., Shin, M., Tyler, B., Brem, H., and Saltzman, W. M. (1996) Chemotherapeutic drugs released from polymers: distribution of 1,3-bis(2-chloroethyl)-1-nitrosourea in the rat brain. Pharm. Res. 13, 671–682. BC700214H
