Journal of Controlled Release 99 (2004) 293 – 300 www.elsevier.com/locate/jconrel
Evaluation of rat striatal l-dopa and DA concentration after intraperitoneal administration of l-dopa prodrugs in liposomal formulations Antonio Di Stefanoa,*, Maria Carafaa, Piera Sozioa, Francesco Pinnena, Daniela Braghirolia, Giustino Orlandoa, Giuseppe Cannazzab, Massimo Ricciutellic, Carlotta Marianeccid, Eleonora Santuccid b
a Dipartimento di Scienze del Farmaco, Universita` bG. D’AnnunzioQ, Via dei Vestini 31, 66100 Chieti, Italy Dipartimento di Scienze Farmaceutiche, Universita` degli Studi di Modena e Reggio Emilia, via Campi 183, 41100 Modena, Italy c Dipartimento di Scienze Chimiche, Universita` di Camerino, Via S. Agostino 1, 62032 Camerino (MC), Italy d Dipartimento di Studi di Chimica e Tecnologia delle Sostanze Biologicamente Attive, Universita` bLa SapienzaQ, P.le A. Moro 5, 00185 Roma, Italy
Received 9 March 2004; accepted 7 July 2004 Available online 9 August 2004
Abstract Parkinson’s disease is a neurodegenerative disease and its symptoms are relieved by administration of l-dopa (LD), which is converted by neuronal aromatic l-aminoacid decarboxylase (AADC), restoring dopamine (DA) levels in surviving neurons. In order to minimize unfavourable side effects, we studied new dimeric LD derivatives, as potential prodrugs for Parkinson’s therapeutic treatment. To improve the bioavailability of the synthesized prodrugs, they were encapsulated in unilamellar liposomes of dimiristoylphosphatidylcholine (DMPC) and cholesterol (CHOL). In vivo microdialysis was used to monitor the striatal LD and DA concentrations after i.p. administration of new delivery systems. Bioavailability evaluation was performed by means of the HPLC-EC method. The striatal levels of LD and DA were remarkably elevated after i.p. administration of liposomal formulation of prodrug (+)-1b ([(O,O-diacetyl)-l-dopa-methylester]-succinyldiamide). This formulation showed about 2.5-fold increase in the basal levels of DA in dialysate rat striatum, suggesting that liposomal formulation of (+)-1b significantly increases LD and DA concentrations with respect to equimolar administration of LD itself or free prodrug (+)-1b. D 2004 Elsevier B.V. All rights reserved. Keywords: Parkinson’s disease; l-dopa; l-dopa prodrugs; Liposomes; Microdialysis
1. Introduction * Corresponding author. Tel.: +39-871-3555338; fax: +39-8713555267. E-mail address:
[email protected] (A. Di Stefano). 0168-3659/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jconrel.2004.07.010
Parkinson’s disease (PD) is a neurodegenerative disorder associated primarily with loss of DA neurons
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in the nigrostriatal system [1]. Current therapy for PD is essentially symptomatic, and l-dopa (LD), the direct precursor of DA, is the treatment of choice for this neurodegenerative disease, despite the fact that several DA receptor agonists have been introduced for the treatment of PD [2]. LD is readily transported across the blood–brain barrier and is converted to DA by aromatic l-aminoacid decarboxylase (AADC). After a good initial response, complications are associated with long-term therapy; these include motor fluctuations, dyskinesias, mental changes and loss of efficacy [3]. The main disadvantages of LD are low water solubility, its sensitivity to chemical and enzymatic oxidation and peripheral decarboxylation. With an aim to prolonging the pharmacological activity, enhancing absorption and providing a protection against metabolism, in a previous work, we studied new dimeric LD derivatives (+)-1a, (+)-1b and (+)-1c as potential prodrugs (Scheme 1) [4]. All the new compounds showed chemical stability at acidic pH and also at the physiological pH; a relatively slow release of LD in rat and human plasma was observed. Liposomes have been used as drug carriers in an attempt to control the delivery or targeting of biologically active agents which can lead to controlled release, prolonged effect and reduced toxicity. It was demonstrated that drug encapsulation into liposomes protected against degradation, with prolonging of plasma lifetime and increasing drug therapeutic effectiveness at lower dose [5–7]. Furthermore, the constituents of phospholipidic vesicles are dimiristoylphosphatidylcholine (DMPC) and cholesterol (CHOL), which are non-toxic and non-immunogenic because they are components of human tissue [8]. Due to their high degree of biocompatibility, liposomes have been used as delivery systems for an assortment
of molecules. The entrapment of relatively lipophilic drugs or derivatives in a lipid bilayer of liposomes alters the biological activity of the drug in a number of ways. Such compounds are released from the liposomes in the biological fluids at slower rates, compared to their water-soluble counterparts, resulting in a sustained action of the drugs. Moreover, the metabolism of the drugs to their inactive metabolites is slowed down, resulting in a longer duration of action. In a previous work, it was found that the dose of LD, for correction of DA metabolism in experimental Parkinson’s syndrome in mice, can be reduced 10-fold when the preparation is incorporated into small unilamellar liposomes (60 nm) composed by PC and cholesterol [9]. The aims of the present study were to compare neostriatum LD and DA levels after i.p. administration of prodrugs (+)-1a, (+)-1b and (+)-1c with prodrugs in liposomal formulations [(+)-1a Lip, (+)-1b Lip and (+)1c Lip] and to assess whether these new liposomal formulations of described LD prodrugs were able to reach the brain and to enhance the extracellular levels of LD and DA in rat striatum of freely moving rats. A high performance liquid chromatography (HPLC) method with electrochemical detection (ED) to measure the striatal concentration of LD and DAwas utilized to determine the in vivo effects of administration of these prodrugs upon levels of LD and DA [10].
2. Materials and methods 2.1. Chemicals and reagents LD, DA, citric acid, sodium octylsulphonate, EDTA and HPLC grade solvents were obtained from
Scheme 1. Chemical formula for diamides of (O,O-diacetyl)-l-dopa-methylester.
A. Di Stefano et al. / Journal of Controlled Release 99 (2004) 293–300 Table 1 Properties of liposomal formulations of prodrugs Sample
Am
p.i.
e.e.
Permeability coefficient (cm/h)
(+)-1a Lip (+)-1b Lip (+)-1c Lip
110.3F1.2 100.5F1.3 112.2F1.2
0.15 0.17 0.16
3.22F0.10 5.28F0.07 4.31F0.05
2.83 d 105F0.05 2.77 d 105F0.07 2.86 d 105F0.05
Sigma-Aldrich (Milan, Italy). DMPC was a generous gift of Chemi (Italy). Sephadex G75 was a Pharmacia product. CHOL was a Merck product. LD prodrugs [(+)-1a, (+)-1b, (+)-1c] were synthesized by us as previously described [4]. Deionized water (Milli Q-Plus System, Millipore) was used for the preparation of all the solutions. Ringer solution consisted of 147 mM NaCl, 4 mM of KCl, 2.2 mM of CaCl2 (pH=7.4). Stock solutions (103 M) of the LD and DA were prepared in an antioxidant mixture (0.1 M NaCl, 0.01 M HCl, 5 mM Na2S2O5). Standard solutions were obtained by dilution of the stock solution to the desired concentrations with Ringer solution immediately prior to use. 2.2. Preparation of liposomal formulations The systems were composed of 3% w/v DMPC, 0.3% w/v CHOL and initially loaded with 2.5% w/v of each prodrug. Liposomes were obtained by means of the bfilmQ method as previously reported [11]. The dried film was hydrated by addition of an aqueous phase (HEPES buffer pH 7.4). The dispersion was vortexed for about 20 min and then sonicated, for 60 min at 0 8C, under N2 stream, (Vibracells-VCX400-Sonics), equipped with an exponential microprobe operating at 23 kHz and an amplitude of 6 mm. Due to the very low drug solubility in water, the drug was added to the initial organic solvent before bfilmQ formation. 2.3. Vesicles purification In order to separate loaded liposomes from untrapped substances, the vesicle dispersion was purified by gel-filtration on Sephadex G75 (glass column 501.2 cm), using HEPES buffer as eluent.
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The purified vesicles were used for size and zeta potential measurements and for evaluation of encapsulation efficiency. 2.4. Size measurements and evaluation of vesicle stability by dynamic light scattering (DLS) and zeta potential The vesicle dispersions were diluted about 100 times in the same buffer used for their preparation. Dust particles were eliminated by filtration (0.45 Am). Vesicle size distribution was measured on a Zetasizer Nano ZS90 (Malvern, UK) at 20 8C, with a scattering angle of 90.08. The polydispersity index (p.i.) was then calculated (Table 1). Vesicle stability, in terms of changes in vesicle dimensions after aggregation, was evaluated by means of the same technique on samples stored at 25 8C, for at least 1 month. The same apparatus was used for the evaluation of zeta potential using the vesicle preparation appropriately diluted (1:10) in distilled water at 25 8C (Table 2). The polidispersity index (p.i.) was directly calculated by the software of the apparatus and the values obtained are in agreement with mono disperse vesicular systems. 2.5. Drug encapsulation efficiency and in vitro release Drug entrapment within the vesicles was assessed by HPLC on purified vesicles, after their disruption with isopropanol (vesicle dispersion/isopropanol 1/1). All analyses were carried out on a Perkin-Elmer 250 liquid chromatography apparatus, equipped with a Perkin-Elmer 235 photo-diode array detector, a 20-Al Rheodyne injector and a computer integrating apparatus. Table 2 Zeta potential measurements (mV) (n=3FSD) Sample
Zeta potential
Empty liposomes (+)-1a (+)-1a Lip (+)-1b (+)-1b Lip (+)-1c (+)-1c Lip
74.00F4.00 0.25F0.03 7.06F0.42 0.36F0.04 1.29F0.06 0.30F0.02 6.70F0.35
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The column was a Supelcogel ODP-50 (15 cm 4.00 mm I.D.); the mobile phase was a 40/60 mixture of water/methanol. The flow rate was 0.9 ml/min. Table 1 shows the results of drug encapsulation efficiency (e.e.), which was calculated as follows [12]: e:e: ¼ 100
mass of incorporated drug mass used for vesicle preparation
ð1Þ
In vitro release experiments were performed in a flow-through apparatus (USP XXIV Ed) at 37 8C in water/ethanol 50/50 because of the low aqueous solubility of loaded drugs (see Table 1). Fixed volumes of vesicle samples were included in dialysis sacs (cut-off 8.000) with a fixed diffusing area (5.5 cm2). Parallel measurements, made using prodrugs without vesicles, proved that in no case was the diffusion across the dialysis membrane the limiting step of the overall diffusion process. The drug concentration was detected in the outer solution at fixed time intervals by means of the HPLC method described above, taking into account the dilution factor. The permeability coefficient of the bilayer, P bl, was determined using the linear expression [13]; valid for the period in which the amount of solute released is small. Cb ¼ Cbð0Þ þ ð3Pbl T =að1 eÞV Þt
ð2Þ
where C b and C b(0)=solute concentrations in the bulk liquid at time t and zero, respectively; T=initial amount of vesicle-entrapped solute (mg); e=volume fraction of vesicle pellet against the volume of the suspension, as determined by measurements after centrifugation (16,000 rpm, 4 8C, 20 min using a centrifuge Mod. J21-B Beckman(USA)); V=volume of the suspension (ml) and a=vesicle radius (Am). The equation is valid for the period in which the amount of solute released is small. Stability tests, carried out by Dynamic Light Scattering at 25 8C, showed that no significant variations of vesicle dimensions occurred for at least 4 weeks.
from that previously described by Abercrombie and Finlay [14]. A length of dialysis membrane (250 mm), made of cuprammonium Rayon (M.Wt. cut-off point 20,000 Da), was cut and a piece of tungsten wire threaded into the lumen to act as support during the initial preparation of the probe. The dialysis tubing was then insert into a steel cannula (30G) and secured with epoxy resin. After the epoxy resin was allowed to dry, the tungsten wire was removed and replaced with a fine fused silica-glass capillary tubing (TSP 075150). A small hole was then made in a polythene tubing (0.58 mm i.d., 0.96 mm o.d.) using a 25-gauge needle. The tubing was pushed over the end of the steel cannula without the dialysis membrane in such a way that the fused silica capillary passed trough the hole. The silica capillary was then insert in a smaller polythene tubing (0.28 mm i.d., 0.61 mm o.d.); the end of the dialysis membrane was cut to the desired length (3 mm), sealed with epoxy resin and left to dry for 4 h, as was the junction between the polythene tubing. 2.7. Microdialysis probe calibration Microdialysis probes were calibrated in vitro by placing them in a standard solution of 100 nM LD and DA in Ringer’s solution maintained at 37 8C. The probe was perfused at 2 Al/min with Ringer’s solution at least 30 min before samples are collected. Dialysate samples were collected directly into 200-ml polypropylene vials, at fixed intervals, usually every 10– 20 min. The substance concentration in the outflow was determined by HPLC analysis. The same procedure was used for in vivo experiments. The extraction efficiency (EER, relative recovery) of the microdialysis probes was calculated as: EER ¼ 1004Cd=Cs
ð3Þ
where Cd is the concentration in the dialysate and Cs is the concentration in the standard solution [15]. The average recovery for DA and LD determined in this way was 15.4F0.3% (n=47).
2.6. Microdialysis probe construction
2.8. Surgical procedure
The concentric microdialysis probes employed in this work were fabricated in house, slightly modified
Experiments were carried out on male Sprague– Dawley rats (250–300 g) purchased from Harlan Italy
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(Udine, Italy). They were housed in a climatized room with free access to food and water and kept on a 12:12-h light/dark cycle. All procedures involving animals were performed in accordance with the guidelines of the National (D.L. n. 116/1992) and European legislation (ECC n.86/609) and of the National Institute of Health on the use and care of laboratory animals. The rats were anaesthetized with chloral hydrate (400 mg/kg i.p.) and placed in a stereotaxic frame. The skull was exposed and the microdialysis probes were implanted in the centre of the right striatum with the tip located at AP 0.3 mm, ML 3.5 mm, DV 5.5 mm from bregma and dura surface, respectively. The coordinates are calculated according to the atlas of Paxinos and Watson [16]. The probe was fixed to the skull of the rat with dental cement and anchor screws. Following surgery, the rat was placed in a CMA/ 120 System for Freely-Moving Animals and the probe was connected with a peristaltic micropump (CMA 100, Carnegie Medicine, Stockholm) delivering Ringer’s solution at a flow rate of 0.2 ml/min. Experiments were carried out 24 h after probe implantation at a flow rate of 1.8 ml/min. In order to limit the breakdown and loss of endogenous compounds in the perfusate, we have mounted a socket on the head of the animal. This holds a 150-Al test tube containing 5 Al of 1M perchloric acid where the perfusate was collected. This tube was replaced manually every 30 min and 60 Al dialysate samples were collected and kept at 80 8C until analysis by HPLC with ED. Blanks were collected for 30 min and dialysis samples were collected for 7–8 h after dosing. At the end of the dialysis experiment, the animals were perfused intracardially with 0.1 M phosphatebuffered saline and 4% paraformaldehyde under deep chloral hydrate anaesthesia; brains were excised and coronal sections (30 Am) taken for assessing the correct placement of the dialysis probe.
entrapped in the vesicular structures. All animals were pretreated with the peripheral AADC inhibitor benserazide HCl (50 mg/kg i.p.) 30 min prior to i.p. administration of free prodrugs in equimolar doses: [(+)-1a (1 ml of an aqueous solution corresponding to 41.78 mg/kg and 63.5 Amol/kg), (+)-1b (1 ml of an aqueous solution corresponding to 42.67 mg/kg and 63.5 Amol/kg) and (+)-1c (1 ml of an aqueous solution corresponding to 44.45 mg/kg and 63.5 Amol/kg)] and prodrugs in liposomal formulation [(+)-1a Lip (1.67 ml corresponding to 41.78 mg/kg and 63.5 Amol/kg), (+)-1b (1.71 ml of an aqueous solution corresponding to 42.67 mg/kg and 63.5 Amol/kg) and (+)-1c (1.78 ml of an aqueous solution corresponding to 44.45 mg/kg and 63.5 Amol/kg). In the control experiments, LD (1 ml of an aqueous solution corresponding to 25 mg/kg and 127 Amol/kg) and LD Lip (1 ml of an aqueous solution corresponding to 25 mg/kg and 127 Amol/kg) were administered [17]. Dialysate samples were collected over 30-min intervals: LD and DA were measured by high HPLC coupled to an electrochemical detector [18].
2.9. Drug administration
2.11. Statistical analysis
All the formulations showed a low e.e. expressed as percentage of loading concentration (from 3.22 for (+)-1a Lip to 5.28 for (+)-1b Lip). For this reason, we performed all the experiments using non-purified vesicle preparations with the prodrugs partially
All LD and DA concentrations in dialysate are given as percentages of mean value from basal levels. Basal concentrations were determined as the mean of at least three measurements with b5% variation obtained at the beginning of the experiment. Data are expressed as a
2.10. Analytical procedure The HPLC system consisted of an L-6200A Intelligent pump (Merck-Hitachi), a Rheodyne 7295 injector with a 50-Al loop and an ESA 5100A coulometric detector. Separation was achieved on a Lichrosphere RP-C18 column (4.6250 mm, 5 Am). The mobile phase consisted of 0.05 M citric acid, 50 AM sodium EDTA, 0.4 nM sodium octylsulphonate. The pH of the mobile phase was adjusted to 2.9 by 1 M potassium hydroxide. Methanol was added to give a final concentration of 8% methanol (v/v). The mobile phase was filtered and degassed by vacuum. A flow rate of 0.7 ml/min was used in all experiments. The ED system included a model 5011 high sensitivity dual detector analytical cell: detector 1 set at +0.35 V; detector 2 set at 0.18 V.
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means with error bars for standard deviations of three rats. One-way ANOVA was used to evaluate the effect of procedures on each group of animals. If a general effect was determined by ANOVA, post-hoc analysis was performed with the Scheffe or Student’s t-test with PV0.05 used as the level of significance.
3. Results and discussion The changes in extracellular basal levels of LD and DA in rat striatum after i.p. administration of LD (127 Amol/kg), (+)-1a, (+)-1b, (+)-1c (63.5 Amol/kg) and the respective liposomal formulations LD Lip (127 Amol/kg), (+)-1a Lip, (+)-1b Lip, (+)-1c Lip (63.5 Amol/kg) are shown in Figs. 1 and 2. The e.e. for our preparations are summarized in Table 1. As reported in Section 2.9, we performed all the experiments using non-purified vesicle preparations with the prodrugs partially entrapped in the vesicular structures. Even if in the liposomal formulations, we found a high content of free drug (95–97%), the in vivo results show a great difference between drug aqueous solutions and our formulation. This can be related to the evidence that lipids constituting the liposome
Fig. 1. Dopamine levels in rat striatum dialysate after administration of equimolar doses of LD and LD Lip, prodrugs (+)-1a, (+)-1b, (+)1c and prodrugs in liposomal formulations (+)-1a Lip, (+)-1b Lip, (+)-1c Lip. Data are expressed as a means with error bars for standard deviations of three rats.
Fig. 2. l-Dopa levels in rat striatum dialysate after administration of equimolar doses of LD and LD Lip, prodrugs (+)-1a, (+)-1b, (+)-1c and prodrugs in liposomal formulations (+)-1a Lip, (+)-1b Lip, (+)1c Lip. Data are expressed as a means with error bars for standard deviations of three rats.
structures incorporate in to the plasma membrane and modulate the conformation of receptors regulating DA synthesis and secretion [19]. On the other hand in our studies the evaluation of DA and l-dopa concentration after administration of empty liposomes demonstrate that there are no significative variation in rat striatal nucleus (data not shown). The developed HPLC method proves to be useful for determination of rat striatal concentrations of DA and LD. Using this method, we can observe that i.p. injection of prodrugs (+)-1a–c, LD and liposomal formulations of prodrugs and LD influences in a different way the basal levels of LD and DA in rat striatum. Administration of (+)-1a Lip into animals did not markedly increase the LD and DA levels, while administration of free prodrug (+)-1a increased the content of DA 5.6- to 6-fold. Injection of (+)-1b Lip elevated the rat striatum basal levels of both DA and LD of about 3- and 2.3-fold respectively. Furthermore, the change induced by i.p. administration of (+)-1c Lip formulation was similar in rats given physiological salines and free prodrug (+)-1c; in this case, only DA striatal concentration was increased (about 2.5-fold). For formulation of (+)-1b Lip, the increase in DA content is probably associated with the
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fact that the bulk of compound (+)-1b was devoid of natural biotransformation and deactivation after LD had been restored from prodrug (+)-1b encapsulated in liposomes. This resulted from sustained delivery of prodrug-loaded liposomes to the brain (see Fig. 2) that protected prodrugs against degradation and increased their therapeutic effectiveness at lower dose; therefore, liposomes may provide more effective transport of prodrug into the brain and increase the LD concentration in the nigrostriatal system after its chemical and enzymatic degradation [20]. Our studies demonstrated that the molar dose of (+)-1a prodrug for standard therapy of PD can be reduced at least 3fold when liposomes are used as a vehicle. On the other hand, the increase of DA concentration in rat striatum is probably also due to stimulation of DA secretion from neuronal endings in the striatum operated by liposomal membrane constituents, as suggested by Kucheryanu et al. [21]. Since release studies from the dialysis sacs have been showed that there were no detectable differences for different prodrug-loaded formulations then our in vivo results cannot be related to different release kinetic (from Eq. (2)) from vesicular structures (Table 1). Furthermore, the differences in in vivo experiments cannot be related to vesicle dimensions because there are only slight differences among different tested formulations (Table 1). Accordingly, the presence of prodrugs in the formulation is capable to affect zeta potential values. Data were shown in Table 2. As it is possible to observe, the comparison with empty liposomes shows a significant decrease of zeta potential absolute value that approaches the value obtained with prodrug alone. This effect can be related to the chemical structure of the drug that is capable to fit well within the vesicular structure and on the surface of the bilayer. The modification of zeta potential of liposomal formulations with respect to free drug can explain the in vivo different DA and lDopa striatal levels by different interaction with biological membranes and to different absorption kinetics.
4. Conclusions In this study, neostriatum LD and DA concentration after i.p. administration of prodrugs (+)-1a,
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(+)-1b and (+)-1c vs. prodrugs in liposomal formulations was compared. Among the studied formulations, (+)-1b Lip was of particular interest because it was able to significantly enhance LD and DA levels of rat striatal dialysate with respect to equimolar administration of LD itself or free prodrug (+)-1b. These results suggest that dimeric prodrugs containing liposomes can improve the release of DA in rat brain and demonstrate the potential of these formulations as a method for the controlled delivery of antiparkinson agents. Acknowledgements Financial support from Ministero dell’Universita` e della Ricerca Scientifica e Tecnologica (Cofin 2003) (Italy). We thank Mr. Domenico Rapposelli for his skilful technical assistance. References [1] P.A. Serra, G. Esposito, P. Enrico, M.A. Mura, R. Migheli, M.R. Delogu, M. Miele, M.S. Desole, G. Grella, E. Miele, Manganese increases l-DOPA auto-oxidation in the striatum of the freely moving rat: potential implications to l-DOPA long-term therapy of Parkinson’s disease, Br. J. Pharmacol. 130 (2000) 937 – 945. [2] E. Tolosa, M.J. Marti, F. Valldeoriola, J.L. Molinuevo, History of levodopa and dopamine agonists in Parkinson’s disease treatment, Neurology 50 (1998) S2 – S10. [3] R. Pahwa, W.C. Koller, Advances in the treatment of Parkinson’s disease, Drugs Today 34 (2) (1998) 95 – 105. [4] A. Di Stefano, B. Mosciatti, G.M. Cingolani, G. Giorgioni, M. Ricciutelli, I. Cacciatore, P. Sozio, F. Claudi, Dimeric l-dopa derivatives as potential prodrugs, Bioorg. Med. Chem. Lett. 11 (2001) 1085 – 1088. [5] N. Mori, S.I. Ohta, Comparison of anticonvulsant effects of valproic acid entrapped in positively and negatively charged liposomes in amygdaloid-kindled rats, Brain Res. 593 (1992) 329 – 331. [6] H. Yokoyama, N. Mori, K. Osonoe, S. Ishida, H. Kumashiro, Anticonvulsant effect of liposome-entrapped superoxide dismutase in amygdaloid-kindled rats, Brain Res. 572 (1992) 273 – 275. [7] M. Ceruti, P. Crosasso, P. Brusa, S. Arpicco, F. Dosio, L. Cattel, Preparation, characterization, cytotoxicity and pharmacokinetics of liposomes containing water-soluble prodrugs of placitaxel, J. Control. Release 63 (2000) 141 – 153. [8] R. Langer, New methods of drug delivery, Science 249 (1990) 1527 – 1533. [9] V.V. Yurasov, V.G. Kucheryanu, V.S. Kudrin, I.V. Zhigal’tsev, E.V. Nikushkin, Y.G. Sandalov, A.P. Kaplun, V.I. Shvets,
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