A mathematical model describing the kinetic of cationic liposome production from dried lipid films adsorbed in a multitubular system

BIOPROCESS ENGINEERING

A mathematical model describing the kinetic of cationic liposome production from dried lipid films adsorbed in a multitubular system

L. G. Torre, A. L. Carneiro; R. S. Rosada; C. L. Silva; M. H. A. Santana^*

Department of Biotechnological Processes, School Chemical Engineering, State University Campinas, Cx. P. 6066, 13081-970, Phone: +(55) (19) 35213921, Fax: [phone], SP, Brazil. Email: [e-mail]

ABSTRACT

Cationic liposomes are an alternative to DNA non-viral carrier in gene therapy, promoting higher efficiency for transport and delivery into the cells. Liposome production large scale is still a challenge. Among many processes, from dried film adsorbed inside multitubular system promising due its operational simplicity. this field, engineering contributions scarce no mathematical treatment literature describing type of process available. formulation proposed describe kinetic considering wetting disintegration lipid followed by lipids aggregation bilayers generating liposomes. model has fitted experimental data mass thickness, being useful predictions scaling up as well contributing development pharmaceutical products.

Keywords: Liposomes; Scale-up; Mathematical modeling.

INTRODUCTION

Liposomes are colloidal aggregates composed of self-assembled phospholipid molecules, which form one or various concentric bilayers delimiting an aqueous central nucleous. Those also named vesicles, mimetize the cell structure in composition and function, allowing incorporation hydrophilic, hydrophobic amphiphilic compounds, including nucleic acids (Lasic, 1997). Aiming to reach a specific targeting enhance interactions between surface internalization functional have been designed constructed, increasing therapeutic efficiency drugs. Transfection, is biological event DNA molecules internalized into cells, delivered cytoplasm, reaching nucleus promoting expression required protein. cationic greatly improve first steps enhancing delivery cytoplasm. order perform functions, used gene normally mixed with neutral lipids, cytoplasm cells. Additionally other lipids provide architecture spherical particle Despite benefits on medical applications commercialization liposomal products still limited. Although techniques developed for preparation laboratory scale, most them not suitable large–scale liposome manufacturing. more recent years, engineering studies different approaches proposed circumvent this problem (Kikuchi, 1991; Lasic, 1993, 1997).

Tournier et al. (1999), based on the Bangham method (Bangham al., 1965), proposed that dried lipid films formed in inner walls of tubes could be hydrated allowing self-assembling lipids generating liposomes. Carneiro and Santana (2004) demonstrated experimentally potentialities liposome production a multitubular system, useful for scaling up process. They used neutral lipids, such as soy lecithin, constructed adsorption isotherm wall glass monitored kinetic profiles generation.

Although both previous studies focused the experimental approaches, no mathematical treatment was proposed for describing this process. modeling of kinetic liposome generation from disintegration an adsorbed dried film and subsequent in aqueous solution, provides elements to design multitubular system a required production. Considering physical phenomena occurring only one tube are same set similar tubes, scaling up process is determined by number, length inner diameter tubes.

Mortha et al. (1993) derived a mathematical model to describe the penetration of water in fast disintegrating tablet. principle was that wetting capillarity front is movement from surface towards interior tablet and followed by at Such allows describing relative influence parameters inherent porous structure, terms external mass transfer internal resistance related capillary penetration.

Even though there are differences between Mortha's and the multitubular systems, dissolution of a dried lipid film is also fast controlled by resistances due to water penetration in as well transferring lipids from surface bulk solution. this case, capillarities could be provided packing hydrophilic moieties molecules, model similar that proposed derived.

This work proposes a model for describing the lipid film disintegration from inner walls of tubes, and subsequent liposome generation in water solution. first steps solubilization were described by Mortha's model. An additional term was included to formulation description self- aggregation at final step process. concentration medium written as nonlinear function time, following behavior experimental profile with kinetic parameters previously adjusted. adsorption lipids mixture considered non-competitive expressed total mass lipids.

This model was fitted to the kinetic experimental data of lipid mass disintegration and thickness adsorbed film used as a validation parameter model.

MATERIAL AND METHODS

Experimental Set Up

The flow sheet of experimental unit used for liposome production is shown in Figure 1. It was composed basically by a jacketed glass capillary tube of 1.6 mm inner diameter and 11.5 cm height (4), a lipid solution tank (1), peristaltic recycling pump (2) vacuum pump (6) and a UV detector working at 340nm (7) for absorbance measurements of lipid dispersion. The basic production steps were: (i) Adsorption of the lipids inside the capillary tube; (ii) Vacuum drying of the adsorbed lipid film; (iii) Hydration to allow lipid dissolution and liposome formation.

Materials and Experimental Methods

L-a-Phosphatidylcoline (Egg chicken, EPC), 1,2-dioleoyl-sn-Glycero-3-Phosphoethanlamine (DOPE) and 1,2-Dioleoyl-3-Trimethylammonium-Propane, Chloride salt (DOTAP) (all lipids from Avanti Lipids) were used as lipids for liposome production. The adsorption, disintegration of the dried film and liposome generation were carried out in the system described in Figure 1. Firstly the lipids (EPC/DOPE/DOTAP 50/25/25% molar) were dispersed in 3 mL of ethanol, at 35ºC, at various total lipid concentrations and recycled inside the tube for 40 min at 8 mL/min flow rate and 35ºC temperature. All the lines were previously saturated with the same type of lipid dispersion to allow that the desired adsorption occurs only inside the capillary tube. After adsorption, the lipid dispersion was drained and the film was dried by vacuum of 200 mbar at 45 ºC for 60 minutes under nitrogen flow. The dried lipid film was hydrated with 3 mL of recycling water at room temperature, at a flow rate of 8 mL/min for 40 minutes. The kinetic of liposome formation was monitored by absorbance measurements at 340 nm of the lipid dispersions. The liposomes were characterized by mean diameter and size distribution using a laser light scattering (Malvern, Autosizer 4700).

Lipid Film Thickness

The lipid film thickness was experimentally measured by scanning electron microscopy. After adsorption and drying of film, capillary removed from system subsequently cut in different heights. Micrographs pieces were done microscopy (Leica, LEO 440i) dried determined using software Leica Qwin500.

Model Formulation

The prediction of disintegration dried lipid film adsorbed in a capillary tube was based on work Mortha et al. (1993) that described a tablet disintegration in aqueous media. The principle of the model is that a wetting capillary front in movement from the surface towards the interior of the tablet and followed by a disintegrating front at the surface of the tablet. The rate of capillary penetration can be described by the well verified Washbourn's relation, (Washburn, 1921) (Equation 1).

Where L is the length of penetration liquid in capillary at time t; s is the surface tension of the liquid, q is the solid-liquid contact angle, d_H is the hydraulic diameter of the porous contained in the solid, t is the tortuosity parameter, h is the viscosity of the liquid and t is the time.

The Equation 1 is not valid in many cases due to non-stationary conditions of liquid flow. Thus, penetration constant (K) introduced as described 2.

Where m(t) may vary from 1 at the early time of penetration to 0 as total is achieved. K constant.

The disintegration or solubilization mechanism of lipids from film was considered similar to tablet proposed by Mortha et al. (1993). The criterion for similarity was the fast disintegration imparted by the capillary penetration of the water in the porous structure of the dried film.

The modifications on film thickness and in aqueous media occur as far components are being dissolved, indicating that K is not a constant value but depends time. kinetics behavior may be considered according to Equation 3.

The differentiation of Equation 3 leads to a modified for penetration rate (Equation 4).

The film disintegration is a consequence of dissolution reaction that occurs inside pores when lipids interact with liquid. This process limited by rate, internal and external mass transfer.

The external mass transfer depends on concentration differences of species, which dissolves between liquid layer near solid surface (C_s), and the concentration of the species in the external liquid medium (C_ext), as described in Equation 5.

Where k_d is the mass transfer coefficient, C_s is the concentration of the specie in the liquid layer near the solid surface, C_ext is the concentration of the specie in the external liquid medium, S_ext is the external area which is calculated by Equation 6.

Where e is the solid porosity and S₀ is the external total surface (solid + void).

The solubilized mass of lipids depends on wet surface film , reaction rate and solubility in aqueous media. This phenomenon may be described by Equation 7, where K_int is a complex rate constant, proportional to the solid disintegration, and S_int is the internal pore area that is penetrated by the liquid. S_int is a linear function of the penetrated length L, for a isotopic medium of porosity e and capillary diameter d_H, according to Equation 8. The adsorption of the cationic and neutral lipids from the mixture was considered non-competitive, and the disintegration was expressed as a total mass of lipids.

The K_int value is difficult to predict and it is assumed that it has the same magnitude as the rate of transport of dissolved species multiplied by a surface concentration.

The solubilization of the amphiphilic lipids leads to aggregation in bilayers followed by vesiculation or liposome formation. steps from film disintegration and are illustrated Figure 2, as well as the lengths of the liquid penetration (Lp) and lipid dissolution (Ld) fronts. Both, Lp and Ld vary with time and tend to reach the initial lipid film thickness L.

Equation 9 defines the liquid penetration depth at time t in non-disintegrated portion of film.

The velocity of penetration front is obtained from a differentiation Equation 9 and described in 10:

In the case of lipids in aqueous solution, an additional term may be introduced Mortha equations, describing vesiculation phenomenon. That represents a consumption individual molecules from solution due to self aggregation generating liposomes. Thus, velocity disintegrated mass is contribution internal and external transfer phenomena rate lipid necessary generate Assuming follows first order kinetics, which depends on liposome concentration, Cv, variation can defined by Equation 11.

Where C_v is the vesicles concentration and K_v is the reaction rate for liposome generation.

According to the experimental profile shape for changes of lipid concentration along time, Equation 12 was proposed describing vesicle as a non-linear function time.

Where K_t and K_t^'are the kinetic parameters of the proposed model.

The lipid film dissolution rate is also proportional to disintegration front dL_d/dt according to Equation 13.

Where r is the solid specific mass.

The mathematical model for water penetration into the lipid film, subsequent disintegration and massive liposome generation is combination of Equations 11, 12 13. constant K can be represented by an empiric described in Equation 14.

RESULTS AND DISCUSSION

The Thickness of the Dried Lipid Film Formed Inside the Capillary Glass

The micrographs obtained through scanning electron microscopy, Figure 3, show clearly the dried lipid film formed inside the capillary tube.

As it can be observed in the Figure 3, there is a great variation of lipid film thickness along the tube. This effect is due to the drying process, which may be optimized in order to get homogeneous thickness. Thus, microphotographs along different capillary tube heights were taken and a weight average thickness was calculated from the histogram distribution shown in Figure 4. The calculated average thickness was 0.47 ± 0.29 µm.

Liposomes Formation Kinetic

The kinetic of liposome formation was evaluated in two initial concentrations total lipids alcoholic dispersion used adsorption step: 50 and 60 mM. Absorbance measurements along time were performed during hydration step. obtained profiles are shown Figures 5a and 5b.

The results show a plateau of absorbance developed at initial instants, demonstrating fast formation liposomes through hydration dried lipid film. data indicate that lower concentration, faster liposome formation.

Mathematical Simulation for Massive Liposome Production

The mathematical simulation for liposome production in capillary system was obtained solving differential equations 11 to 13 using Euler method and applying a developed calculation routine software Excel 2000 Windows, Microsoft Corporation, determination of profiles massive along time.

The physico-chemical properties of aqueous lipid dispersions, internal surface area and solid specific mass used in calculations are shown Table 1. The solid specific mass was obtained, considering the internal surface area available for adsorption, the lipid film thickness and the total lipid mass adsorbed into the capillary tube, both obtained experimentally.

The Number of Lipid Molecules Per Liposome (N)

The total number of lipid molecules per liposome (N) was calculated by Equation 15, where D_H is the hydrodynamic diameter obtained by measurements of dynamic light scattering (considering spherical geometry and unimodal size distribution), (e) is the thickness of the lipid membrane, considered as 4nm for small unilamellar liposomes, according to Lasic, 1997, and a_PL is the cross-sectional area of the polar head of lipids, calculated as a weighted average of the individual lipid cross-sectional areas. The total number of lipid molecules per liposome (N) is the total cross-sectional area of the vesicle divided by the average area of one lipid molecule. The mean diameter of the produced liposomes, 280± 29 nm, allowed they were considered as small unilamellar vesicles in the calculations. The cross-sectional area for the individual lipids DOTAP, DOPE and EPC were 0.7, 0.55 and 0.71 nm², respectively (Lasic, 1997 and Israelachvili & Mitchell, 1975). In this specific case, a_PL was 0.67 nm². The value D_H considered was the experimentally measured value described before (280± 29 nm). In these conditions, a_PL was 0.67 nm² and the N value was 7.2x10⁵ lipid molecules per liposome.

Determination of K_t e K_t' Parameters

The parameters K_t e K_t' from Equation 12 depend on the vesicles concentration (C_v), that was obtained from the total lipid concentration divided by the aggregation number N. The total lipid concentration was obtained from the calibration curve of absorbance versus total lipid concentration, as described before.

According to Equation 12, K_t e K_t' were obtained through the linear, 1/K_t, and angular, K_t'/K_t, coefficients from the linear fitting of 1/C_v versus 1/t. The obtained K_t e K_t' values are presented in Table 2.

Determinations of Kv and K_ext

The parameter related to reaction rate for vesicle production, Kv, described by Equation 11, was determined at initial instants of vesicles formation, or derivation 12, as shown on Equations 16 and 17.

The vesicle concentration (C_v) to be considered in Equation 17 corresponds to the initial time of liposome formation. In this case, it was considered 5% of the maximum C_v value previously calculated.

It is known that at the final hydration step of liposomes formation there no lipid mass variation along time (dm/dt = 0) and whole extension film already penetrated disintegrated by liquid (L_p – L_d = 0). In these conditions, Equation 11 can be simplified, and K_ext can be obtained as a function of K_v and C_v, according Equation 18.

The values of parameters K_t e K_t', K_v and K_ext are presented in Table 2.

The values for other parameters of model were considered based on physical criteria and adjusted in order to fit experimental data. Table 3 shows the adjusted values.

Mathematical Simulation of Massive Liposome Formation

The liposome production model and estimated parameters allowed mathematical simulation of massive comparison with experimental data, as shown in Figure 6. The kinetic experimental data for dissolved lipid mass were obtained considering a calibration curve of absorbance at 340 nm versus total lipid concentration in aqueous media. The absorbance at 340 nm is proportional to the diameter and concentration of vesicles in the aqueous dispersion. The mean hydrodynamic diameter of the produced liposomes was 280± 29 nm.

The results show that model fits well experimental data at final hydration time, when all liposomes were formed. deviations of initial time are due to variation liposome diameter, which not considered in simulation instants hydration.

Figure 7 shows the model prediction for the penetrated and dissolved lengths profiles.

The similarity between Lp and Ld profiles indicate that lipid dissolution occurs in a fast way with no significant wet length. This behavior can be associated high capacity of hydration these lipids present, due to low phase transition temperatures (lower than room temperature).

In addition, the model predicted lipid film thickness adsorbed inside capillary tube. This corresponds to maximum value achieved by L_p and L_d in the simulated profiles (Figure 7) and can be compared to the experimental thickness. The simulated values of the lipid film thickness are presented in Table 4.

The simulated values of thickness are comparable to experimental mean value, 0.47 ± 0.29 µm for the total lipid concentration in alcoholic dispersion 50 mM, indicating that the proposed model describes the massive liposomes production.

CONCLUSIONS

The proposed mathematical model described kinetic of massive liposome production from a dried film lipids adsorbed at inner walls capillary tube. In addition, was validated by comparison between predicted and experimental thickness lipid film. can also be extended to design scaled up multitubular system for required production.

ACKNOWLEDGEMENTS

The authors are grateful to FAPESP for financial support of this work.

NOMENCLATURE

a_PL

Lipid cross-sectional area

C_ext

Concentration of the species in external liquid medium

C_s

Concentration of the specie in liquid layer near solid surface

C_v

Vesicle concentration

d_H

Hydraulic diameter of the porous contained in solid

D_H

Liposome average hydrodynamic diameter

DOPE

1,2-dioleoyl-sn-Glycer-3-Phosphoethanlamine

DOTAP

1,2-Dioleoyl-3-Trimethylammonium-Propane, Chloride salt

EPC

L-a-Phosphatidylcoline

K

penetration constant

k_d

mass transfer coefficient

K_t

parameter of the kinetic model for vesicles concentration

Kt'

parameter of the kinetic model for vesicles concentration;

K_v

Reaction rate for the vesicle production

l

Liposome shell thickness

L

Length of penetration the liquid in capillary at time t

Ld

Lipids dissolution length

Lp

Liquid penetration length

m

Parameter that may vary from 1 (early time of penetration) to 0 (penetration is completed)

M

Total mass of lipids

N

The total number of lipid molecules per liposome

S_ext

External area that is calculated by Equation 6

S₀

external total surface (solid + void)

t

Time

V

I- Vacuum indicator

Greek Letters

s

surface tension of the liquid

q

solid-liquid contact angle

t

tortuosity parameter

h

liquid viscosity

e

solid porosity

r

solid specific mass

(Received: February 01, 2007 ; Accepted: September 4, 2007)

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To whom correspondence should be addressed

Publication Dates

• Publication in this collection
  11 Feb 2008
• Date of issue
  Dec 2007

History

• Received
  01 Feb 2007
• Accepted
  04 Sept 2007