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Classical Newtonian Physics and Euclidean Geometry are currently used to describe biological phenomena and the processes of drug formulation, which are characterized by homogeneity and linearity. On the other hand, at the mesoscopic level, the principles and the laws of physics are quite different from the Classical Newtonian Physics and Euclidean approach especially at nanoscale dimension. The investigation of the aggregation process of liposomes is of paramount importance due to their applications in pharmaceutical nanotechnology as drug delivery systems and as membrane models, in biosciences. The physical stability and the aggregation process of colloidal systems as well as the surface phenomena are described using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The elucidation of the dimensionality of liposome aggregates obeys the fractal approach because the aggregation phenomena are irreversible. This approach can be correlated with the extended DLVO theory, which includes the hydration energy, too.

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... Advanced Drug Delivery Systems (aDDSs) have presented fractal dimensions [6][7][8][9][10][11][12]. Liposomes, polymeric nanoparticles and micelles are in the focus of the nanotechnology field for treatment and diagnostics of chronic and incurable diseases following Mandelbrot geometry principles. ...
The morphology of drug nanocarriers correlates with their functionality, which is mainly shuttled on their surface where most of the interactions and interfacial phenomena occur. The quantification of their morphological fingerprint requires an analytical tool that should be established based on experimental data and can be correlated with their stability. The morphological quantification picture of the advanced Drug Delivery nano Systems (aDDnSs) could be achieved via fractal analysis and by introducing a novel proposed parameter, defined as ωD. This parameter is based on mathematical limits determined experimentally and on already existing theories on the colloidal fractal aggregation process which can correlate the morphological characteristics of aDDnSs with their physicochemical stability in aqueous and biological media. This review article proposes the fractal analysis and the ωD as an analytical tool and prediction parameter, respectively, which are able to promote an attractive and alternative path for studying drug delivery nanocarriers. Moreover, these approaches could facilitate the scale up process of pharmaceutical industry, and could shed more light in the quantification of drug delivery nanosystems.
Abstract The major advance of mixed liposomes (the so-called chimeric systems) is to control the size, structure, and morphology of these nanoassemblies, and therefore, system colloidal properties, with the aid of a large variety of parameters, such as chemical architecture and composition. The goal of this study is to investigate the alterations of the physicochemical and morphological characteristics of chimeric dipalmitoylphosphatidylcholine (DPPC) liposomes, caused by the incorporation of block and gradient copolymers (different macromolecular architecture) with different chemical compositions (different amounts of hydrophobic component). Light scattering techniques were utilized in order to characterize physicochemically and to delineate the fractal morphology of chimeric liposomes. In this study, we also investigated the structural differences between the prepared chimeric liposomes as are visualized by scanning electron microscopy (SEM). It could be concluded that all the chimeric liposomes have regular structure, as SEM images revealed, while their fractal dimensionality was found to be dependent on the macromolecular architecture of the polymeric guest.
Fractals have been very successful in quantifying nature's geometrical complexity, and have captured the imagination of scientific community. The development of fractal dimension and its applications have produced significant results across a wide variety of biomedical applications. This review deals with the application of fractals in pharmaceutical sciences and attempts to account the most important developments in the fields of pharmaceutical technology, especially of advanced Drug Delivery nano Systems and of biopharmaceutics and pharmacokinetics. Additionally, fractal kinetics, which has been applied to enzyme kinetics, drug metabolism and absorption, pharmacokinetics and pharmacodynamics are presented. This review also considers the potential benefits of using fractal analysis along with considerations of nonlinearity, scaling, and chaos as calibration tools to obtain information and more realistic description on different parts of pharmaceutical sciences. As a conclusion, the purpose of the present work is to highlight the presence e of fractal geometry in almost all fields of pharmaceutical research.
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Abstract Dimethoxycurcumin (DMC) is a lipophilic analog of curcumin found in Curcuma longa Linn., which is known to possess significant activity against various cancer cell lines. The purpose of this study was to develop suitable liposomal formulations in order to overcome DMC's poor water solubility and to study the aggregation kinetic profile using the fractal analysis. DMC was incorporated into liposomal formulations composed of DPPC, DPPC:DPPG:chol (9:1:1 molar ratio) and DPPC:DODAP:chol (9:1:1 molar ratio) liposomes. Light scattering techniques were used to elucidate the physicochemical parameters of the liposomal formulations with and without DMC. The structural characteristics of the incorporated molecule were found to be crucial and promote the aggregation mechanism depending also on the liposomes' composition. The results of our study contribute to the overall scientific efforts to prepare efficient carriers for DMC and could be a useful tool in order to study more efficiently the kinetics of the aggregation process of the liposomal carriers.
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Unlabelled: Colloidal nanocarriers, in their various forms, have the possibility of providing endless opportunities in the area of drug delivery. The current communication embodies an in-depth discussion of colloidal nanocarriers with respect to formulation aspects, types, and site-specific drug targeting using various forms of colloidal nanocarriers with special insights to the field of oncology. Specialized nanotechnological approaches like quantum dots, dendrimers, integrins, monoclonal antibodies, and so forth, which have been extensively researched for targeted delivery of therapeutic and diagnostic agents, are also discussed. Nanotechnological patents, issued by the U.S. Patent and Trademark Office in the area of drug delivery, are also included in this review to emphasize the importance of nanotechnology in the current research scenario. From the clinical editor: Colloidal nanocarriers provide almost endless opportunities in the area of drug delivery. While the review mainly addresses potential oncological applications, similar approaches may be applicable in other conditions with a requirement for targeted drug delivery. Technologies including quantum dots, dendrimers, integrins, monoclonal antibodies are discussed, along with US-based patents related to these methods.
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Self-similar patterns are frequently observed in Nature. Their reproduction is possible on a length scale 102–105nm with lithographic methods, but seems impossible on the nanometer length scale. It is shown that this goal may be achieved via a multiplicative variant of the multi-spacer patterning technology, in this way permitting the controlled preparation of fractal surfaces.
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The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski-Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM.
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In this work, the aggregation of charged liposomes induced by magnesium is investigated. Static and dynamic light scattering, Fourier-transform infrared spectroscopy, and cryotransmission electron microscopy are used as experimental techniques. In particular, multiple intracluster scattering is reduced to a negligible amount using a cross-correlation light scattering scheme. The analysis of the cluster structure, probed by means of static light scattering, reveals an evolution from surface fractals to mass fractals with increasing magnesium concentration. Cryotransmission electron microscopy micrographs of the aggregates are consistent with this interpretation. In addition, a comparative analysis of these results with those previously reported in the presence of calcium suggests that the different hydration energy between lipid vesicles when these divalent cations are present plays a fundamental role in the cluster morphology. This suggestion is also supported by infrared spectroscopy data. The kinetics of the aggregation processes is also analyzed through the time evolution of the mean diffusion coefficient of the aggregates.
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Two general aspects which need to be considered for the successful application of dendrimers for biomedical purposes are their availability at an acceptable cost and their suitability as regards their pharmacodynamic and pharmacokinetic properties. These two aspects are covered in this review. In the first part, synthetic strategies for the preparation of dendrimers are outlined and emphasis is given to recent work on methodologies whose aim is the development of more efficient routes to dendrimers in terms of the materials used for their synthesis as well as in terms of the procedures required for their purification. These include procedures involving double-stage and double exponential synthesis, orthogonal coupling strategies, self-assembly and solid-phase approaches, as well as particularly useful synthetic protocols such as those used in "click chemistry". The second part of the review deals with the way in which the size, chemical constitution and physicochemical properties of dendrimers used for drug delivery may affect pharmacodynamic and pharmacokinetic parameters which are important considerations for drug bioavailability. This is illustrated by an overview of examples from recent work involving non-steroidal anti-inflammatory drugs, anticancer drugs and antibacterials.
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Using time-resolved small angle neutron scattering, we have measured the wave-number-dependent structure factor S(q) of monodisperse nanoemulsions that aggregate and gel after we suddenly turn on a strong, short-range, slippery attraction between the droplets. At high q, peaks in S(q) appear as dense clusters of droplets form, and S(q) increases strongly toward low q, as these dense clusters become locked into a rigid gel network, despite the fluidity of the films between the droplets. The long-time high-q structure of nanoemulsion gels formed by slippery diffusion-limited cluster aggregation is universal in shape and remarkably independent of the droplet volume fraction, phi.
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Dynamic light scattering and electrophoretic mobility measurements have been used to characterize the size, size distribution and zeta potentials (zeta-potentials) of egg yolk phosphatidylcholine (EYPC) liposomes in the presence of monovalent ions ( Na(+) and K(+)). To study the stability of liposomes the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory has been extended by introducing the hydrated radius of the adsorbed ions onto the liposome surfaces. The decrease of liposome size is explained on the basis of the membrane impermeability to some ions which generate osmotic forces, which leads to evacuate water from liposome inside.
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We present a study of the fractal dimension of clusters of large unilamellar vesicles (LUVs) formed by egg yolk phosphatidylcholine (EYPC), dimyristoylphosphocholine (DMPC) and dipalmitoylphosphocholine (DPPC) induced by Ca2+ . Fractal dimensions were calculated by application of two methods, measuring the angular dependency of the light scattered by the clusters and following the evolution of the cluster size. In all cases, the fractal dimensions fell in the range from 2.1 to 1.8, corresponding to two regimes: diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA). Whereas DMPC clusters showed a typical transition from the RLCA to the DLCA aggregation, EYPC exhibited an unusual behaviour, since the aggregation was limited for a higher concentration than the critical aggregation concentration. The behaviour of DPPC was intermediate, with a transition from the RLCA to the DLCA regimes with cluster sizes depending on Ca2+ concentration. Studies on the reversibility of the aggregates show that EYPC and DPPC clusters can be re-dispersed by dilution with water. DMPC does not present reversibility. Reversibility is evidence of the existence of secondary minima in the DLVO potential between two liposomes. To predict these secondary minima, a correction of the DLVO model was necessary taking into account a repulsive force of hydration.
This account deals with a strategy for designing multifunctional liposomes and dendritic polymers. Such nanoparticles, although quite different in size and structure, both fulfill properties that drug carriers should exhibit, i.e. specificity or targeting ability, extended time of circulation in biological fluids and ability to be transported through cell membranes. Furthermore, having developed these multifunctional liposomal and dendritic carriers, a drug delivery model is presented that employs instead of cells multilamellar liposomes, which interact with the above mentioned multifunctional carriers. This interaction should primitively mimic the processes which occur in living cells when they interact with loaded or unloaded liposomal and dendritic nanoparticles. Multifunctionality and multivalency coupled with molecular recognition between the interacting pairs render the loaded nanoparticles effective drug delivery vehicles.
Diffusion-controlled deposition in dimension $d=2$ is studied by Monte Carlo simulation, and the number of clusters of size $s$ is found to scale as ${n}_{s}$\sim${}{s}^{$-${}$\tau${}}$ with $$\tau${}$\approx${}1.35$. The inequality $$\tau${}<2$ is shown to imply for a deposit of $N$ particles per nucleation site that the exponents in the scaling Ansatz ${n}_{s}(N)$\sim${}{s}^{$-${}$\tau${}}f(\frac{{s}^{$\sigma${}}}{N})$ satisfy the scaling law $$\sigma${}=2$-${}$\tau${}$. If the scaling properties of deposits on a surface are related to those of an aggregate grown on a seed particle, $$\tau${}=1+\frac{(d$-${}1)}{D}$ is obtained, where $D$ is the fractal dimension of the aggregate.
A relationship between the fractal surface dimension of dissolving nanoparticles and their solubility has been derived showing that fractally rough nanoparticles are expected to exhibit significantly higher solubility than predicted from the classical Ostwald–Freundlich equation. The derived relationship estimates the latent solubility increase for a given material by manipulating the surface of the particles to be dissolved, and can thus be used for developing new strategies for improving the solubility of poorly soluble drug candidates.
L'article fait une revue des résultats récents concernant les phénomènes d'agrégation de particules, notamment après l'introduction du concept de fractale pour décrire les structures obtenues. Après une introduction expérimentale et une revue des théories cinétiques de l'agrégation, la notion de « fractale » est introduite et les propriétés physiques des agrégats fractals sont discutées. Les principaux modèles d'agrégation: les modèles de collage particuleamas (notamment le modèle de Witten et Sander) et le modèle de collage amasamas sont présentés et discutés en détail. Les modèles discutés se rattachent, en particulier, aux mécanismes de la croissance des cristaux, ainsi qu'à la formation des aérosols dans l'atmosphère.
A model for diffusion-controlled aggregation in which growing clusters as well as individual particles are mobile has been investigated. Two versions of the model in which the cluster diffusion coefficient is either size independent or inversely proportional to number of particles (mass) give very similar results. In the limit of low concentration and large system size both models lead to structures with a fractal (Hausdorff) dimensionality of about 1.45-1.5 in two-dimensional lattice-based simulations.
A relatively large number (102-103) of reasonably large (about 105 particles or sites) two-dimensional Witten-Sander aggregates are simulated using new algorithms. This enables the reduction of statistical errors by an order of magnitude and provides an opportunity to determine some new quantities describing in more detail the structure of Witten-Sander clusters. A quantitate description of the distortion of large lattice-based Witten-Sander clusters into a diamond-like shape is provided. The orientational correlation in the bond directions for off-lattice Witten-Sander clusters is also measured. This quantity has a power law dependence on distance with an exponent of about -0.37.
The acid-catalyzed condensation reaction of perfluorooctyltrimethoxysilane (PFOS) and n-octyltrimethoxysilane (OTMS) in ethanol has been followed by time-resolved synchrotron radiation small-angle X-ray scattering (SAXS) on a short time scale. SAXS curves for PFOS and OTMS have been interpreted as arising from mass fractals with D f=2 (PFOS) and D f=1.7 (OTMS). The time dependence of the apparent radius of gyration, obtained from the Guinier plots, showed that the growth of fractal precursors occurs in a two-step process within 2 h for PFOS and within 1.5 h for OTMS, in which small clusters involving monomers, dimers and trimers are formed in the initial step and formation of larger clusters occurs in the second step. Furthermore, it has been suggested that the hydrophobicity and lipophobicity of the bulky alkyl groups may also contribute to the formation of these giant aggregates.
A mechanism of ion-induced acidic lipid vesicle fusion is proposed. It has been reported that fusogenic ions, e.g. Ca2+, alter acidic phospholipid membrane surfaces to be more hydrophobic. The proposed theory suggests that this alteration of the membrane surface reduces repulsive hydration interaction forces exerted on two interacting membranes and eventually induces strong adhesion of the two membranes. In vesicle systems, the strong adhesion of membranes results in deformation of vesicle membranes. At the fusion threshold concentrations of fusogenic ions, the surface hydrophobicity of the deformed area (rim area) at the boundary of adhered two vesicle membranes becomes sufficiently great according to the theory so that membrane molecular exchanges can occur through these regions (fusion sites) and the two membranes fuse. The above scheme is proposed by the theory based on the experimental results of vesicle fusion and its membrane properties. It is discussed that this fusion concept of local high hydrophobic area of the membrane surface as a fusion site is not only applicable to the cases of lipid membrane fusion, but also would be applied to the final step of membrane fusion processes occurring in most biological membrane fusion systems.
The distribution of liposomes with different membrane fluidity and vesicle size in tumors after intravenous injection was investigated in Yoshida sarcoma-bearing rats. Liposomes composed of egg phosphatidylcholine (EPC) or hydrogenated egg phosphatidylcholine (HEPC), dicetyl phosphate and cholesterol in a molar ratio of 5:1:4 were prepared. Their size was adjusted so that they had various mean diameters, ranging from 40 to 400 nm. In EPC liposomes, whose membranes were more fluid than those of HEPC liposomes, tumor accumulation increased with increasing area under the blood concentration-time curve (AUC). The size of liposomes which showed the greatest tumor accumulation and AUC was around 100 nm in diameter. In HEPC liposomes, the less fluid type, the size dependence of tumor accumulation and AUC differed. The greatest tumor accumulation or AUC were found in liposomes with a diameter of about 100 or 40 nm, respectively. This discrepancy indicates that the tumor accumulation of liposomes is not always correlated with their circulation time in the blood. To clarify the process by which these liposomes accumulate from the vascular space into the tumor, we calculated tumor uptake clearance (CLtu), which can separate the contribution of the blood concentration from the accumulation in tumor. The CLtu values for EPC and HEPC liposomes agreed at all sizes, liposomes with a diameter of 100 nm showing the highest values. These findings indicate that the accumulation of liposomes from the vascular space into the tumor is primarily governed by their size and not by their membrane fluidity or blood circulation time. When tumor blood flow was selectively enhanced by the infusion of angiotensin II, the CLtu of 100-nm liposomes decreased to the level of that in 40-nm liposomes, suggesting that some histological factor(s) in the tumor may be responsible for the localization of 100-nm liposomes in tumor. In an in vitro experiment using cultured Yoshida sarcoma cells, 59-nm HEPC liposomes were directly taken up by the tumor cells to an extent at least 2.5-times greater than larger liposomes (> 100 nm). We conclude that 100-nm liposomes may predominantly localize in the interstitial space, whereas some liposomes of smaller size may be taken up by tumor cells.
The size of liposomes has been shown to be an important factor in the efficient delivery of an antitumor agent to a tumor. In this paper, the effects of the size of liposomes on the pharmacokinetics of liposomes and liposome-encapsulated drugs are discussed with reference to: (1) the circulation amount and residence time of liposomes in the blood, (2) the accumulation of liposomes in the tumor, and (3) in vivo drug release from liposomes. In addition, the effect of size on therapeutic activity (antitumor efficacy and toxicity) of a liposomal anticancer preparation is discussed. Finally we discuss the importance of liposome size in the design of a more effective liposomal antitumor preparation.
The letter discusses the indispensable importance of Nanotechnology for the scientific and economical revival of the developing world. Similar to the nuclear age, and maybe far more so, the nanoage will be something of a Hemingway line of demarcation between the have and the have nots.
"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature
Various non-equilibrium growth models have been used to explore the development of morphology in biological systems. Here we review a class of biological growth models which exhibit fractal structures and discuss the relationship of these models to a variety of other phenomena.
A model for random aggregates is studied by computer simulation. The model is applicable to a metal-particle aggregation process whose correlations have been measured previously. Density correlations within the model aggregates fall off with distance with a fractional power law, like those of the metal aggregates. The radius of gyration of the model aggregates has power-law behavior. The model is a limit of a model of dendritic growth.
The dynamics of aggregation between electrostatically bound carboxylate and amine terminated poly(amidoamine) {PAMAM} dendrimers have been investigated in aqueous medium. Unlike the covalently connected tecto (dendrimer) analogues, aggregates of electrostatically bound PAMAM dendrimers can self-assemble in a dendritic pattern, generating fascinating fractal structures. The kinetic studies of the aggregation in water by dynamic light scattering (DLS) experiments suggest that diffusion limited colloidal aggregation (DLCA) is the prevailing mechanism for the fractal growth between 3.5 generation carboxylate terminated PAMAM dendrimer and fourth generation amine terminated PAMAM dendrimer. The fractal aggregation observed in aqueous medium was further corroborated by scanning and transmission electron microscopic studies. Furthermore, unprecedented enhancement in the intrinsic emission intensity from PAMAM dendrimer was observed associated with the dendritic aggregation of the dendrimer units. Most importantly, the present study suggests that electrostatic self-assembly can be utilized as an effective synthetic strategy to generate highly stable, nano- to microscale higher order complex structures from PAMAM dendrimers, which significantly reduces the nonradiative pathways of the excitons, resulting in many fold enhancements in the intrinsic emission intensity from the system.
The possibility of using liposomes as carriers of drugs has been investigated in three patients with metastatic cancer. The fate of liposomes injected into the circulation was followed by the removal from plasma and uptake of entrapped tracer-labelled albumin by the tissues, and by electron-microscopic observations of the localisation of liposome carrier within normal and malignant cells. With most organs a degree of preferential uptake of radioactivity was observed in the malignant deposits.
The diffusion of univalent cations and anions out of spontaneously formed liquid crystals of lecithin is remarkably similar to the diffusion of such ions across biological membranes. If the unit structure of the liquid crystal is accepted as being that of a bimolecular leaflet, then these leaflets have been shown to be many orders of magnitude more permeable to anions than to cations. The diffusion rate for cations is very significantly controlled by the sign and magnitude of the surface charge at the water/lipid interface. There is a decrease of the diffusion rate for cations as the negative charge on the lipid structure decreases—which diminishes to zero for a positively charged membrane—the diffusion rate of anions remaining very high. The exchange diffusion rate of Cl− and I− was greater than that of F−, NO3−, SO42− and HPO42− but no significant differences were detectable for the cation series, Li+, Na+, K+, Rb+ and choline. The membranes are very permeable to water.Because the diffusion rate of cations is low, the phospholipid liquid crystalline structures appear to “bind” or “capture” cations. It is found that as the surface charge of the lipid lamellae is increased, the amount of cation per μmle of lipid increases. It is argued that if the cation is sequestered in aqueous compartments between the bimolecular leaflets, and if the thickness of the aqueous compartments is determined by the surface charge density of the lipid head groups and by the ionic strength of the aqueous phase in accordance with double-layer theory, the amount of cation trapped would also be expected to vary.
Drug delivery has metamorphosed from the concept of a pill to molecular medicine in the past 100 years. Better appreciation and integration of pharmacokinetic and pharmacodynamic principles in design of drug delivery systems has led to improved therapeutic efficacy. A greater understanding of the molecular transport in relation to physico-chemical properties has led to the evolution of a biopharmaceutics classification system, which should be a future road map, governing drug design, development and delivery. While drugs belonging to class I and II will be delivered by established platform technologies, novel delivery strategies will evolve and mature to realize the potential of 'new generation' biotech and non biotech drugs belonging to class III and IV, respectively.
In the present study, the influence of vesicle size on the penetration of two fluorescently labeled substances into the human skin was investigated. For the measurements either a hydrophilic fluorescent compound [carboxyfluorescein (CF)] or a lipophilic one [1,1'-dioctadecyl-3,3,3',3'-tertramethylindocarbo-cyanine perchlorate (DiI)] were encapsulated into vesicles. Liposomal formulations were prepared by extruding the vesicles through polycarbonate membrane filters with pores of different sizes. In vitro penetration studies into human abdominal skin were performed by using the Franz diffusion cell and a standardized skin stripping technique in attempt to find an optimum size for topical drug delivery by liposomes. Confocal laser scanning microscopy (CLSM) was used to visualize the effect of penetration ability of liposomal DiI. The maximum DiI fluorescence in the skin was observed with smaller liposomes of 71 nm diameter. The liposomes with a size of 120 nm diameter showed statistically enhanced penetration of CF into the skin as compared to larger ones. The results indicated that the CF penetration was inversely related to the size of the liposomes, which was confirmed by the data of the confocal laser scanning microscopy studies.
Topical administration of cosmetics and pharmaceuticals involves a variety of different formulations of which colloidal drug carrier systems are currently of particular interest. After a short introduction of reverse micellar solutions, liquid crystals, vesicles and nanoparticles, appropriate methods of physicochemical characterization are introduced including X-ray diffraction, laser light scattering, electron microscopy, and differential scanning calorimetry. Emphasis is laid on topical applications of the colloidal drug delivery systems (DDS) covered, with the main objective of both sustained drug release and improved stability of DDS.
An "extended DLVO" approach that includes Lifshitz-van der Waals, Lewis acid-base, and electrostatic double layer interactions is used to describe interaction energies between spherical particles and rough surfaces. Favorable, unfavorable, and intermediate deposition conditions are simulated using surface properties representing common aquatic colloids and polymeric membranes. The surface element integration (SEI) technique and Derjaguin's integration method are employed to calculate interaction energy. Numerical simulations using SEI demonstrate that nanometer scale surface roughness features can produce a distribution of interaction energy profiles. Local interaction energies are statistically analyzed to define representative interaction energy profiles-minimum, average, and maximum-for various combinations of simulated particles and surfaces. In all cases, the magnitude of the average interaction energy profile is reduced, but the reduction of energy depends on particle size, asperity size, and density of asperities. In some cases, a surface that is on average unfavorable for deposition (repulsive) may possess locally favorable (attractive) sites solely due to nanoscale surface roughness. A weighted average of the analytical sphere-sphere and sphere-plate expressions of Derjaguin reasonably approximates the average interaction energy profiles predicted by the SEI model, where the weighting factor is based on the fraction of interactions involving asperities.
The fractal dimension (FD) was used to reveal brain structure irregularities in patients with schizophrenia. FD provides a unique way of quantifying the shape complexity of cortical folding of the human brain. MR images were obtained from seven patients with schizophrenia that were compared with six healthy control subjects. The MR images were first segmented, and the FD was calculated for the grey/white matter boundary for the whole brain and the hemispheres separately, using the box-counting and Minkowski-Bouligand methods. The results showed that the patients had larger FD values than the controls, for the whole brain volume and right hemisphere.
Living cells can be viewed as complex adaptive systems that exhibit non-linear dynamics and fractal features. We investigated the fractal qualities of normal and malignant hematological cells and their potential as a tool for characterizing cell phenotype and clinical behavior. A mathematical algorithm and an optic tool for fractal analysis of nuclei were developed. A total of 4,713 lymphoid cells derived from 66 patients of five distinct diagnostic groups (normal and reactive lymphocytes, low-grade lymphomas and an aggressive lymphoma) were assessed for their fractal dimension. In addition, in 19 patients fractal analysis of leukemia cells was compared to clinical endpoints. After validating our method, hematological cells possessed fractal dimensions corresponding to their clinical entity. There was a highly significant overall difference in fractal dimensions between various types of hematological malignancies. A preliminary correlation was found between the fractal dimension and the clinical outcome of leukemia patients. Hematological cells possess fractal dimensions that correlate with their biological properties. Measurement of fractal dimension seems to be a sensitive method to assess the hematological cell phenotype and to define a clinical group. This tool may be potentially useful for the evaluation of clinical behavior of hematological diseases.
Growing interest is being dedicated to soft matter because of its potential in delivering any type of drugs. Since hydrophilic, lipophilic, small and big molecules can be loaded into these colloidal systems and administered through the parenteral or nonparenteral route, soft matter systems have been used to solve many biomedical and pharmaceutical problems. In fact, they make possible to overcome difficulties in the formulation and delivery of poorly water-soluble drug molecules, settle some stability issues typical of biological drug molecules, design parenteral sustained release forms and provide functionalized soft particles that are very effective in drug targeting. This review deals with the important role that colloids play in the drug delivery and targeting, with particular attention to the more currently used systems such as microemulsions, organogels, liposomes, micelles, and dendrimers. Though significant progress has been made in drug targeting, some challenges still remain. Further efforts will be required to better understand the characteristics of targets and to discover new ones. In-depth knowledge of the physico-chemical structure and properties of the systems used for targeting is fundamental for understanding the mechanism of interaction with the biological substrate and the consequent drug release.
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