On the ubiquitous presence of fractals and fractal concepts in pharmaceutical sciences: A review

Ten years of the manufacturing classification system: a review of literature applications and an extension of the framework to continuous manufacture

The MCS initiative was first introduced in 2013. Since then, two MCS papers have been published: the first proposing a structured approach to consider the impact of drug substance physical properties on manufacturability and the second outlining real world examples of MCS principles. By 2023, both publications had been extensively cited by over 240 publications. This article firstly reviews this citing work and considers how the MCS concepts have been received and are being applied. Secondly, we will extend the MCS framework to continuous manufacture. The review structure follows the flow of drug product development focussing first on optimisation of API properties. The exploitation of links between API particle properties and manufacturability using large datasets seems particularly promising. Subsequently, applications of the MCS for formulation design include a detailed look at the impact of percolation threshold, the role of excipients and how other classification systems can be of assistance. The final review section focusses on manufacturing process development, covering the impact of strain rate sensitivity and modelling applications. The second part of the paper focuses on continuous processing proposing a parallel MCS framework alongside the existing batch manufacturing guidance. Specifically, we propose that continuous direct compression can accommodate a wider range of API properties compared to its batch equivalent.

Extrusion-based technologies for 3D printing: a comparative study of the processability of thermoplastic polyurethane-based formulations

Thermoplastic polyurethanes (TPU) offer excellent properties for a wide range of dosage forms. These polymers have been successfully utilized in personalized medicine production using fused deposition modeling (FDM) 3D printing (3DP). However, direct powder extrusion (DPE) has been introduced recently as a challenging technique since it eliminates filament production before 3DP, reducing thermal stress, production time, and costs. This study compares DPE and single-screw extrusion for binary (drug-TPU) and ternary (drug-TPU-magnesium stearate [MS]) mixtures containing from 20 to 60% w/w of theophylline. Powder flow, mechanical properties, fractal analysis, and percolation theory were utilized to analyze critical properties of the extrudates. All the mixtures could be processed at a temperature range between 130 and 160 °C. Extrudates containing up to 50% w/w of drug (up to 30% w/w of drug in the case of single-screw extrusion binary filaments) showed toughness values above the critical threshold of 80 kg/mm2. MS improved flow in mixtures where the drug is the only percolating component, reduced until 25 °C the DPE temperature and decreased the extrudate roughness in high drug content systems. The potential of DPE as an efficient one-step additive manufacturing technique in healthcare environments to produce TPU-based tailored on-demand medicines has been demonstrated.

The Fractal Viewpoint of Tumors and Nanoparticles

Even though the promising therapies against cancer are rapidly improved, the oncology patients population has seen exponential growth, placing cancer in 5th place among the ten deadliest diseases. Efficient drug delivery systems must overcome multiple barriers and maximize drug delivery to the target tumors, simultaneously limiting side effects. Since the first observation of the quantum tunneling phenomenon, many multidisciplinary studies have offered quantum-inspired solutions to optimized tumor mapping and efficient nanodrug design. The property of a wave function to propagate through a potential barrier offer the capability of obtaining 3D surface profiles using imaging of individual atoms on the surface of a material. The application of quantum tunneling on a scanning tunneling microscope offers an exact surface roughness mapping of tumors and pharmaceutical particles. Critical elements to cancer nanotherapeutics apply the fractal theory and calculate the fractal dimension for efficient tumor surface imaging at the atomic level. This review study presents the latest biological approaches to cancer management based on fractal geometry.

Lyotropic Liquid Crystalline Nanostructures as Drug Delivery Systems and Vaccine Platforms

Lyotropic liquid crystals result from the self-assembly process of amphiphilic molecules, such as lipids, into water, being organized in different mesophases. The non-lamellar formed mesophases, such as bicontinuous cubic (cubosomes) and inverse hexagonal (hexosomes), attract great scientific interest in the field of pharmaceutical nanotechnology. In the present review, an overview of the engineering and characterization of non-lamellar lyotropic liquid crystalline nanosystems (LLCN) is provided, focusing on their advantages as drug delivery nanocarriers and innovative vaccine platforms. It is described that non-lamellar LLCN can be utilized as drug delivery nanosystems, as well as for protein, peptide, and nucleic acid delivery. They exhibit major advantages, including stimuli-responsive properties for the “on demand” drug release delivery and the ability for controlled release by manipulating their internal conformation properties and their administration by different routes. Moreover, non-lamellar LLCN exhibit unique adjuvant properties to activate the immune system, being ideal for the development of novel vaccines. This review outlines the recent advances in lipid-based liquid crystalline technology and highlights the unique features of such systems, with a hopeful scope to contribute to the rational design of future nanosystems.

Anti-migraine effect of wine-processed Radix scutellariae: Pharmacodynamic verification in nitroglycerin-induced rats and correlation study between compounds dissolution and the fractal dimension

ETHNOPHARMACOLOGICAL RELEVANCE

Wine-processed Radix scutellariae (RS) is the processed product of RS, which is the dried root of Scutellaria baicalensis Georgi. It is recorded in Chinese traditional formula that wine-processed RS has the effect of anti-migraine, while the effect has not been confirmed and the possible mechanism remains unclear.

AIM OF THE STUDY

To verify the anti-migraine effect of wine-processed RS in nitroglycerin (NTG)-induced rats and explore the correlation between compounds dissolution and the pore structure based on fractal theory.

MATERIALS AND METHODS

In the validation of pharmacodynamics, the effects of wine-processed RS on migraines were firstly evaluated by observing the number of head-scratching of rats, then investigated by determining the levels of nitric oxide (NO), calcitonin gene-related peptide (CGRP) and the expression of c-Fos in the brain of NTG-induced rat models using ELISA and immunohistochemical assessments. In the correlation study, the stir-frying time of RS was set to 5 min, 10 min and 15 min. The scanning electron microscope (SEM) and mercury intrusion method were used to explore the pore structure and main parameters of the pore structure including pore size distribution, pore volume, porosity, surface area and fractal dimension. The compounds dissolution of total flavonoids and five major components containing baicalein, baicalin, scutellarin, wogonin and wogonoside was determined by UV-Vis spectrophotometry and HPLC separately.

RESULTS

The animal experiments had shown that wine-processed RS could significantly reduce the head-scratching times of NTG-induced rat models (p < 0.01) and markedly decrease the levels of NO (p < 0.01), CGRP (p < 0.05) and the expression of c-Fos (p < 0.01) compared with model group. The data indicated that wine-processing would affect the dissolution of compounds by changing the pore structure of RS. The order of positive correlation between pore structure parameters and compounds' dissolution was total surface area > fractal dimension (r > 0) and the order of negative correlation was average pore size > total porosity > total volume (r < 0). Compared with the other sample groups (p < 0.05), the wine-processed RS stir-fried for 10 min had a pore structure which was more favorable for compounds dissolution.

CONCLUSIONS

Wine-processing could strengthen the anti-migraine effect of RS by changing the pore structure of RS, which is linked to the dissolution of compounds. The RS stir-fried for 10 min may be more effective in treating migraine.

A Langevin dynamics approach for multi-layer mass transfer problems

We use Langevin dynamics simulations to study the mass diffusion problem across two adjacent porous layers of different transport properties. At the interface between the layers, we impose the Kedem-Katchalsky (KK) interfacial boundary condition that is well suited in a general situation. A detailed algorithm for the implementation of the KK interfacial condition in the Langevin dynamics framework is presented. As a case study, we consider a two-layer diffusion model of a drug-eluting stent. The simulation results are compared with those obtained from the solution of the corresponding continuum diffusion equation, and an excellent agreement is shown.

Nanomedicines and Nanosimilars: Looking for a New and Dynamic Regulatory "Astrolabe" Inspired System

The application of the nanotechnology in medicine and pharmaceutics opens new horizons in therapeutics. Several nanomedicines are in the market and an increasing number is in clinical trials. But which is the advantage of the medicines in nanoscale? The scientists and the regulatory authorities agree that the size and consequently the physiochemical/biological properties of nanomaterials play a key role in their safety and effectiveness. Additionally, all of them agree that a new scientific-based regulatory landscape is required for the establishment of nanomedicines in the market. The aim of this review is to investigate the parameters that the scientists and the regulatory authorities should take into account in order to build up a dynamic regulatory landscape for nanomedicines. For this reason, we propose an "astrolabe-like system" as the guide for establishing the regulatory approval process. Its function is based on the different physicochemical/biological properties in comparison to low molecular weight drugs.

Benefits of Fractal Approaches in Solid Dosage Form Development

Pharmaceutical formulations are complex systems consisting of active pharmaceutical ingredient(s) and a number of excipients selected to provide the intended performance of the product. The understanding of materials' properties and technological processes is a requirement for building quality into pharmaceutical products. Such understanding is gained mostly from empirical correlations of material and process factors with quality attributes of the final product. However, it seems also important to gain knowledge based on mechanistic considerations. Promising is here to study morphological and/or topological characteristics of particles and their aggregates. These geometric aspects must be taken into account to better understand how product attributes emerge from raw materials, which includes, for example, mechanical tablet properties, disintegration or dissolution behavior. Regulatory agencies worldwide are promoting the use of physical models in pharmaceutics to design quality into a final product. This review deals with pharmaceutical applications of theoretical models, focusing on percolation theory, fractal, and multifractal geometry. The use of these so-called fractal approaches improves the understanding of different aspects in the development of solid dosage forms, for example by identifying critical drug and excipient concentrations, as well as to study effects of heterogeneity on dosage form performance. The aim is to link micro- and macrostructure to the emerging quality attributes of the pharmaceutical solid dosage forms as a strategy to enhance mechanistic understanding and to advance pharmaceutical development and manufacturing processes.

Achieving High Excipient Efficiency with Elastic Thermoplastic Polyurethane by Ultrasound Assisted Direct Compression

Ultrasound assisted compression (USAC) is a manufacturing technique which applies thermal and mechanical energy to the powder bed, producing tablets with improved characteristics compared to the direct compression process. This technology is ideal for thermoplastic materials, as polyurethanes, whose particles usually undergo a sintering process. Thermoplastic polyurethanes are widely used in sustained drug release systems but rarely seen in tablets due to their elastic properties. The aim of this work is to investigate the ability of USAC to manufacture sustained release matrix tablets based on elastic thermoplastic polyurethanes (TPU), overcoming the limitations of direct compression. The technological and biopharmaceutical characteristics of the TPU matrices have been evaluated, with special focus on the porous structure due to the implications on drug release. For the first time, USAC has been successfully employed for manufacturing elastic thermoplastic polyurethanes-based matrices. TPU tablets show an inert character with a sustained drug release governed by a diffusional mechanism. Initial porosity of matrices was similar in all batches studied, with no influence of drug particle size, and a fractal nature of the pore network has been observed. SEM microphotographs show the continuum medium created by the sintering of the polymer, responsible for the high excipient efficiency.

Panos Macheras: a pioneering scientist in pharmaceutical science

Professor Panos Macheras is a pioneering scientist in pharmacokinetics, pharmacodynamics and biopharmaceutics. His many important contributions to pharmaceutical science are reviewed.

Mathematical Modeling of Release Kinetics from Supramolecular Drug Delivery Systems

Embedding of active substances in supramolecular systems has as the main goal to ensure the controlled release of the active ingredients. Whatever the final architecture or entrapment mechanism, modeling of release is challenging due to the moving boundary conditions and complex initial conditions. Despite huge diversity of formulations, diffusion phenomena are involved in practically all release processes. The approach in this paper starts, therefore, from mathematical methods for solving the diffusion equation in initial and boundary conditions, which are further connected with phenomenological conditions, simplified and idealized in order to lead to problems which can be analytically solved. Consequently, the release models are classified starting from the geometry of diffusion domain, initial conditions, and conditions on frontiers. Taking into account that practically all solutions of the models use the separation of variables method and integral transformation method, two specific applications of these methods are included. This paper suggests that "good modeling practice" of release kinetics consists essentially of identifying the most appropriate mathematical conditions corresponding to implied physicochemical phenomena. However, in most of the cases, models can be written but analytical solutions for these models cannot be obtained. Consequently, empiric models remain the first choice, and they receive an important place in the review.

Biosensor Applications of Electrodeposited Nanostructures

The development of biosensors for a range of analytes from small molecules to proteins to oligonucleotides is an intensely active field. Detection methods based on electrochemistry or on localized surface plasmon responses have advanced through using nanostructured electrodes prepared by electrodeposition, which is capable of preparing a wide range of different structures. Supported nanoparticles can be prepared by electrodeposition through applying fixed potentials, cycling potentials, and fixed current methods. Nanoparticle sizes, shapes, and surface densities can be controlled, and regular structures can be prepared by electrodeposition through templates. The incorporation of multiple nanomaterials into composite films can take advantage of the superior and potentially synergistic properties of each component. Nanostructured electrodes can provide supports for enzymes, antibodies, or oligonucleotides for creating sensors against many targets in areas such as genomic analysis, the detection of protein antigens, or the detection of small molecule metabolites. Detection can also be performed using electrochemical methods, and the nanostructured electrodes can greatly enhance electrochemical responses by carefully designed schemes. Biosensors based on electrodeposited nanostructures can contribute to the advancement of many goals in bioanalytical and clinical chemistry.

Electron microscopy/energy dispersive X-ray spectroscopy of drug distribution in solid dispersions and interpretation by multifractal geometry

Much contemporary research of poorly water-soluble drugs focuses on amorphous solid dispersions (SDs) for oral drug delivery. Recently, a multifractal formalism has been introduced to describe the distribution of an inorganic carrier in SDs. The present work attempts to directly image model drugs by means of scanning electron microscopy and energy dispersive X-ray spectroscopy. The compounds amlodipine, felodipine, glyburide, and indomethacine, which include halogens to enable sufficient scattering in energy dispersive X-ray spectroscopy, were employed to prepare SDs with hydroxypropyl methylcellulose acetate succinate (HPMCAS) by using a microwave method. Following chemical imaging, it was demonstrated that drug distribution was best described by multifractals, which was clearly superior to a monofractal assumption. The obtained fractal dimensions were influenced by drug loading and it was possible to detect microstructural changes upon addition of the plasticizer urea. Accordingly, the multifractal approach bears much potential to better explore the analytical results of chemical formulation imaging. Insights can be gained from the microstructural organization of SDs, which is interesting to further study formulation and process factors as well as physical stability.

Improving the prediction of environmental fate of engineered nanomaterials by fractal modelling

A critical analysis of the available engineered nanomaterials (ENMs) environmental fate modelling approaches indicates that existing tools do not satisfactorily account for the complexities of nanoscale phenomena. Fractal modelling (FM) can complement existing kinetic fate models by including more accurate interpretations of shape and structure, density and collision efficiency parameters to better describe homo- and heteroaggregation. Pathways to including hierarchical symmetry concepts and a route to establishing a structural classification of nanomaterials based on FM are proposed.

Biopharmaceutic classification of drugs revisited

The biopharmaceutics classification system (BCS) was based on the tube model of the intestinal lumen. This model considers constant drug permeability along the intestines, a plug flow fluid with the suspended drug particles moving with the fluid, and dissolution in the small particle limit. Since then the research work focusing on drug gastrointestinal (GI) absorption phenomena and processes rely on the classical laws of transport, diffusion and kinetics; however, the homogeneous assumptions associated with the well-stirred Euclidean media, where the classical laws of diffusion and kinetics apply, have been questioned in the past. In this work we explore the biopharmaceutic classification of drugs using a heterogeneous pseudo steady-state model of oral drug absorption. The fraction of dose absorbed (F_abs) was expressed as a function of two time-dependent processes where time dependent coefficients govern drug absorption and non-absorption processes. Fundamental drug properties like the absorption potential are correlated with F_abs and allow the biopharmaceutic classification of drugs taking into account the heterogeneous aspects of oral drug absorption. This analysis reveals that for Class I drugs no time dependency is expected for both absorption and non absorption processes since the gastric emptying is controlling the absorption of Class I drugs while the completion of absorption (F_abs>90%) is terminated along the first part of the jejunum. Due to the biopharmaceutical properties of Class II, III and IV drugs, these drugs travel throughout the GI tract and therefore both absorption and non absorption processes will exhibit time dependency. Thus, the calculation of F_abs (<90%) for Class II, III and IV is dependent on the estimates of the time exponents of time dependent coefficients controlling drug absorption e.g. dissolution, uptake or non absorption e.g. precipitation.

A multiscale mechanism of drug release from polymeric matrices: confirmation through a nonlinear theoretical model

In this paper, we propose a new approach for the dynamics of drug delivery systems, assimilated to complex systems, an approach based on concepts like fractality, non-differentiability, and multiscale evolution. The main advantage of using these concepts is the possibility of eliminating the approximations used in the standard approach by replacing complexity with fractality, that imposes, in mathematical terms, the mandatory use of the non-differential character of defined physical quantities. The theoretical model presented, validated for other physical systems, demonstrates its functionality also for drug delivery systems, highlighting, in addition, new insights into the complexity of this system. The spatio-temporal scales of system evolution are characterized through the fractality degree, as a measure of the complexity of the phenomena occurring at each scale. Numerical analysis of the experiment showed that the overall drug release kinetics can be obtained by composing "smaller release kinetics" occurring at scales appropriate for each phase of the drug release mechanism, phases whose expansion depends on the system density. Moreover, the uncertainties in establishing the exact limits of the phases were removed by applying the principle of scale superposition, resulting in a global fractality degree corresponding to the entire release kinetics. Even if the theoretical model is perfectible by identifying constants specific to each delivery system, this paper is intended to be the beginning of an alternative approach to drug delivery mechanisms.

In Situ Characterization of Bak Clusters Responsible for Cell Death Using Single Molecule Localization Microscopy

Apoptosis plays a pivotal role in development and tissue homeostasis in multicellular organisms. Clustering of Bak proteins on the mitochondrial outer membrane is responsible for the induction of apoptosis by evoking a release of pro-apoptotic proteins from mitochondria into cytosol. However, how the protein cluster permeabilizes the mitochondrial membrane remains unclear because elucidation of the cluster characteristics such as size and protein density has been hampered by the diffraction-limited resolution of light microscopy. Here, we describe an approach to quantitatively characterize Bak clusters in situ based on single molecule localization. We showed that Bak proteins form densely packed clusters at the nanoscale on mitochondria during apoptosis. Quantitative analysis based on the localization of each Bak protein revealed that the density of Bak protein is uniform among clusters although the cluster size is highly heterogeneous. Our approach provides unprecedented information on the size and protein density of Bak clusters possibly critical for the permeabilization and is applicable for the analysis of different cluster formations.

Structural and thermal analysis of a hyper-branched exopolysaccharide produced by submerged fermentation of mushroom mycelium

An exopolysaccharide (PTR-EPS1) purified from the culture medium of the mycelial fermentation of Pleurotus tuber-regium had a weight-average molecular mass of 173.6 kDa and a radius of 55.6 nm.

Fractal geometry as a new approach for proving nanosimilarity: a reflection note

Nanosimilars are considered as new medicinal outcomes combining the generic drugs and the nanocarrier as an innovative excipient, in order to evaluate them as final products. They belong to the grey area - concerning the evaluation process - between generic drugs and biosimilar medicinal products. Generic drugs are well documented and a huge number of them are in market, replacing effectively the off-patent drugs. The scientific approach for releasing them to the market is based on bioequivalence studies, which are well documented and accepted by the regulatory agencies. On the other hand, the structural complexity of biological/biotechnology-derived products demands a new approach for the approval process taking into consideration that bioequivalence studies are not considered as sufficient as in generic drugs, and new clinical trials are needed to support their approval process of the product to the market. In proportion, due to technological complexity of nanomedicines, the approaches for proving the statistical identity or the similarity for generic and biosimilar products, respectively, with those of prototypes, are not considered as effective for nanosimilar products. The aim of this note is to propose a complementary approach which can provide realistic evidences concerning the nanosimilarity, based on fractal analysis. This approach is well fit with the structural complexity of nanomedicines and smooths the difficulties for proving the similarity between off-patent and nanosimilar products. Fractal analysis could be considered as the approach that completely characterizes the physicochemical/morphological characteristics of nanosimilar products and could be proposed as a start point for a deep discussion on nanosimilarity.

Biorelevant dissolution of poorly soluble weak acids studied by UV imaging reveals ranges of fractal-like kinetics

Much pharmaceutical research has been invested into drug dissolution testing and its mathematical modeling. Even today, there is no complete understanding of the dissolution process but novel imaging tools have been introduced into pharmaceutics that may spur further scientific advancement. We used UV imaging to study the intrinsic dissolution of various poorly soluble acidic model drugs to understand the effects of heterogeneity on early intrinsic drug dissolution using a biorelevant medium: celecoxib, ketoprofen, naproxen, and sulfathiazole. All compounds were characterized using X-ray powder diffraction and thermal analysis. Raman spectroscopy and scanning electron microscopy were employed before and after the initial dissolution phase. As a result, ranges of fractal-like dissolution behavior were found with all model compounds. Intrinsic dissolution rate exhibited a power law mainly at early time points. Subsequently, after several minutes, pseudo-equilibrium was reached with a nearly constant dissolution rate. Further research should investigate whether compounds other than acids demonstrate similar early dissolution kinetics in biorelevant media. The observed fractal-like intrinsic dissolution behavior has several pharmaceutical implications. This study primarily helps us to better understand in vitro dissolution testing, particularly on a miniaturized scale. This improved understanding of early dissolution events may advance future correlations with in vivo data. Therefore, fractal-like dissolution should be considered during biopharmaceutical modeling.