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Abstract

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. ...
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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.
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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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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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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.
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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.
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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.
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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.
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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.
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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.
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"...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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
Article
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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Fractal dimension analysis of MR images reveals grey matter structure irregularities in schizophrenia
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