Chitosan-Based Particulate Carriers: Structure, Production and Corresponding Controlled Release

The state of the art in the use of chitosan (CS) for preparing particulate carriers for drug delivery applications is reviewed. After evidencing the scientific and commercial potentials of CS, the links between targeted controlled activity, the preparation process and the kinetics of release are detailed, focusing on two types of particulate carriers: matrix particles and capsules. More precisely, the relationship between the size/structure of CS-based particles as multifunctional delivery systems and drug release kinetics (models) is emphasized. The preparation method and conditions greatly influence particle structure and size, which affect release properties. Various techniques available for characterizing particle structural properties and size distribution are reviewed. CS particulate carriers with different structures can achieve various release patterns, including zero-order, multi-pulsed, and pulse-triggered. Mathematical models have an unavoidable role in understanding release mechanisms and their interrelationships. Moreover, models help identify the key structural characteristics, thus saving experimental time. Furthermore, by investigating the close relation between preparation process parameters and particulate structural characteristics as well as their effect on release properties, a novel “on-demand” strategy for the design of drug delivery devices may be developed. This reverse strategy involves designing the production process and the related particles’ structure based on the targeted release pattern.


Introduction
Chitosan (CS), derived from chitin through deacetylation, is a natural polymer with enormous potential applications in biotechnology and food engineering. Chitin is a longchain polymer of N-acetyl glucosamine and the second most abundant natural biopolymer after cellulose on the planet [1][2][3][4][5]. The estimated annual biosynthesis of chitin is roughly 1010 tons in the biosphere [6]. It is a sustainable natural resource that is omnipresent but still underexploited commercially. Chitin and cellulose belong to the same class of biopolymers, i.e., polysaccharides. The two other main classes of biopolymers include proteins and nucleic acids.
CS is a linear polysaccharide composed of amino groups, with its structure containing D-glucosamine (deacetylated units) and N-acetyl-D-glucosamine (acetylated units) linked randomly through β-(1→4) bonds ( Figure 1) [7]. Due to its repeatedly reported beneficial characteristics, such as the absence of toxicity, biocompatibility and biodegradability, CS has found considerable applications in various fields, including environmental engineering, agriculture, aquaculture, agrochemistry, the food industry and the medical/pharmaceutical and cosmetic industries [8][9][10][11].
Chitin can be extracted from algae, fungi, arthropods (crabs, shrimp, crayfish and insects), plankton and mollusks (squids). Nowadays, the main commercial sources of chitin and its derivatives are shells and the exoskeleton of crustaceans, which used to be considered low-value marine wastes. The global annual production of shrimp or Chitin can be extracted from algae, fungi, arthropods (crabs, shrimp, crayfis insects), plankton and mollusks (squids). Nowadays, the main commercial sources tin and its derivatives are shells and the exoskeleton of crustaceans, which used to b sidered low-value marine wastes. The global annual production of shrimp or lobster and crab waste was reported to be between 6 and 8 million tons [12]. For instance, c cean shells contain roughly 15-40 wt% of chitin [13]. The powder of this grounded m byproduct can serve as an animal-feed supplement, but with very limited profit compared with its refined, high-value chemicals ( Table 1). The transformation of from marine waste is not complex, but the process requires considerable amounts of and chemical components such as strong acids and bases. Additionally, the final pr quality varies a lot depending on the raw material (species of shellfish as well as typ quantities of impurities). i Annual production of chitin is probably under 10,000 tons, whereas more recent figures available [14]. ii Global industrial production of chitosan is estimated to reach 173.9 thousan by 2027 [9]. iii Data from Alibaba (March 2023) [16].
The industrial production of refined chitin/chitosan and their derivatives rem low by 2016. Indeed, it was reported that less than half of the global demand was sa [15,17]. Both demand and production for CS have kept growing in various indu  ii Global industrial production of chitosan is estimated to reach 173.9 thousand tons by 2027 [9]. iii Data from Alibaba (March 2023) [16].
The industrial production of refined chitin/chitosan and their derivatives remained low by 2016. Indeed, it was reported that less than half of the global demand was satisfied [15,17]. Both demand and production for CS have kept growing in various industries worldwide during the last few years. The global market volume of chitin and its derivatives was valued at nearly USD 7.1 billion by 2021 [18], was estimated at USD 7.9 billion in 2022 and is foreseen to reach a revised size of USD 24.9 billion by 2030 [19].

Emerging Research and Industrial Interest for Chitosan
The first interest in commercializing chitin was held back in the 1930s because of the strong competition with synthesized polymers at that time. Large-scale production of chitin regained attention in the mid-1970s, when regulations aiming to reduce the dumping of shellfish waste were introduced. Regarding research interest, 108,025 references concerning "chitin/chitosan" were found using SciFinder (years between 1970 and 2022). A remarkable increase in the number of publications was evidenced at the beginning of the 1990s, indicating a real emerging research interest in the academic world ( Figure 2). On the other hand, according to statistics from WIPO's database, PATENTSCOPE, the potential commercial applications of CS have grown steadily since the late twentieth century, whereas the number of patent applications concerning CS has exploded in the last three decades. A total of 51,274 patent application records in English were found from all offices ( Figure 3).

A Multiple-Application Biopolymer
Chitosan's multiple utilities originate from its relatively specific chemical and physical properties. Indeed, it is the unique example of a cationic polyelectrolyte among known

A Multiple-Application Biopolymer
Chitosan's multiple utilities originate from its relatively specific chemical and physical properties. Indeed, it is the unique example of a cationic polyelectrolyte among known

A Multiple-Application Biopolymer
Chitosan's multiple utilities originate from its relatively specific chemical and physical properties. Indeed, it is the unique example of a cationic polyelectrolyte among known natural polysaccharides. Thus, complexes, or coacervates, can be produced through electrostatic interactions between chitosan and other negatively charged compounds. Because of its beneficial biological properties, such as non-toxicity, biodegradability, biocompatibility, mucoadhesive behavior and antimicrobial activities, it is apt to bind with electronegative mucous membranes, and it shows low in vitro toxicity as well as in the case of some in vivo models [20]. CS is also a pH-sensitive material whose dissolution in water is possible only under mildly acidic conditions (pH < 6.5). This may sometimes be considered a limitation. CS derivatives with extended water solubility can be obtained through chemical modification of the chains, such as carboxymethylation, quaternization and hydroxypropylation [21]. There are many examples of functional groups that have been introduced onto the CS chain to form water-soluble derivatives [22], e.g., thiolated CS [23], glycol CS [24,25], quaternized CS [26], carboxymethyl CS [27], isobutyl CS [28] and oligoethylene oxide sulfonate CS [29]. In addition to its well-known applications in various fields (Figure 3), CS has significant potential for managing hyperlipidemia [30]. Recently, there have been reports on the beneficial effects of CS in controlling the COVID-19 pandemic [31,32]. To conclude, CS's availability (relying on abundant reserves in nature), benign properties and versatile applications rationalize the ongoing research enthusiasm from both academia and industry.

Terminology of Particulate Carriers
Due to chitosan's versatile properties mentioned above, its application as a delivery system has been reported in numerous papers. At the level of the particulate carrier, CS is commonly used as the principal polymer to build up the carrier's core material as well as the peripheral material to coat or/and impart novel functionality to the vector.
Within the scope of this review, particulate carriers are defined as micro-or nano-sized particulate dispersions of liquid or solid particles. The size range is first related to the route of administration. In addition, the nanometric size range endows this type of object with interesting properties as a delivery system because of the large specific area, which usually facilitates the release of active molecules. Alternatively, their surface is available for further functionalization, providing specific interaction properties potentially leading to targeting. Understanding and characterizing the nature/morphology/size of particles is important for designing and optimizing particle-based systems for specific applications ( Figure 4). Additionally, a particle's shape can have a significant influence on its physical, chemical and biological properties, e.g., surface area, packing properties, flow behavior, mechanical properties, drug release kinetics and efficiency [33][34][35][36].
A complex nomenclature of particulate carriers exists in the literature [37,38]. Within the scope of this review, prefixes indicate the size of the carrier, such as micro-/nano-. Micro-/nanospheres refer to spherical particles with diameters in the micrometer/nanometer range ( Figure 5). According to the International Union of Pure and Applied Chemistry (IUPAC), the lower limit between micro-and nano-sizing is still a matter of debate. This review adapted the terminology of IUPAC (Table 2). A nanoparticle refers to a particle of any shape with at least one dimension between 10 −9 and 10 −7 m. The upper limit is chosen as 100 nm because novel properties that distinguish particles from bulk material normally show up at a critical dimension scale lower than 100 nm [39]. Nevertheless, due to certain phenomena (transparency, ultrafiltration, stable dispersion, etc.), the upper limit can be acceptably extended up to 500 nm. Nanoparticles can be divided into two categories: homogeneous nanoparticles, also known as "nanospheres," and core-shell structured nanoparticles, known as "nanocapsules" (Figure 6) [40][41][42][43].

Terminology Concise Definition
Nanoparticle Particle of any shape with at least one characteristic dimension between 10 −9 and 10 −7 m Nanocapsule Hollow nanoparticle consisting of a solid shell encircling a core-forming area Nanosphere Spherical-shaped nanoparticle without membrane or any distinct outer layer

Microparticle
Particle with at least one dimension between 10 −7 and 10 −4 m Microcapsule Hollow microparticle composed of a solid shell surrounding a core-forming space Microsphere Microparticle of spherical shape without membrane or any distinct outer layer A nano-/microsphere is composed of a matrix where substances can be permanently or temporarily embedded, dissolved or covalently bound. Nano-/microcapsules are submicroscopic colloidal drug carrier systems composed of an oily/aqueous core surrounded by a thin membrane, which is usually, but not necessarily, made of polymer [39].
From a toxicological and pharmaceutical perspective, vesicular capsules possess an advantage over matrix spheres because of their lower polymer content and high loading capacity for both hydrophilic and lipophilic active molecules [41].
Due to its mild reaction conditions and simple process, the crosslinking gelation method has been extensively studied. The gelation method usually generates the polymer matrix structure, the coating/shell or the core region of core-shell capsules. There are several CS crosslinking gelation mechanisms that offer numerous possibilities for preparing fine-tuned particulate carriers ( Figure 7) [62]. Apart from the required experimental conditions, the various gelation methods differ by the nature of the inter-chain crosslinks (ionic, hydrophobic association, covalent, etc.) and, consequently, their stability, reversibility and timescale, among others.
Schematically, spray drying and supercritical processes can produce monolithic matrix (sphere)-structured particles, while capsule structures can be produced via emulsification (emulsion-alkali coacervation/precipitation, emulsion-emulsion coacervation method), electrospraying and microfluidic processes. Table 3 summarizes frequently used methods for the preparation of CS-involved particulate carriers, their main advantages and shortcomings, the size range of the obtained particles and, when available, a rough estimation of the particle concentration at the process outlet.
The structure of a particulate carrier is strongly related to its preparation method. Therefore, selecting the most suitable preparation process is strongly related to the required structural characteristics and, thus, the targeted application. Process parameters, including pH, temperature, concentration of reagents, mass ratio of polymer and crosslinker/surfactants, nature of colloidal stabilizers and agitation speed, have a strong effect on the carrier's structural properties, such as particle average size, particle size distribution, particle shape, porosity, swelling capacity, degradation rate and diffusivity of the drug through the carrier material [63]. Numerous research studies have explored examples of this relationship using the Design of Experiments (DoE) method [64][65][66].  The parameter "particle concentration" was defined as the concentration fabricated particles in their dispersing medium after formation but before any e ations such as separation or dilution. This concentration was calculated or whenever allowed by the provided experimental data. This parameter may be regarding the scale-up or transfer to industrial processes of lab-scale preparat   The parameter "particle concentration" was defined as the concentratio fabricated particles in their dispersing medium after formation but before an ations such as separation or dilution. This concentration was calculated o whenever allowed by the provided experimental data. This parameter may b regarding the scale-up or transfer to industrial processes of lab-scale prepar dures. Indeed, when very dilute suspensions of particles are produced, furth be necessary to increase particle concentration before application. The parameter "particle concentration" was defined as the concentration of newlyfabricated particles in their dispersing medium after formation but before any extra operations such as separation or dilution. This concentration was calculated or estimated whenever allowed by the provided experimental data. This parameter may be important regarding the scale-up or transfer to industrial processes of lab-scale preparation procedures. Indeed, when very dilute suspensions of particles are produced, further steps may be necessary to increase particle concentration before application.  The process is convenient, cost-effective and devoid of high temperatures and use of solvent. Also usable for living-cell encapsulation.
Limited size control/size reduction. Difficulties in largescale production.
90 µm-7 mm -Polymer concentration; viscosity of polymer solution; flow rate; geometry of extrusion device; type and concentration of nonsolvent bath.

Crosslinking gelation
Electrostatic interaction between polyelectrolytes and polyvalent ions is often used as the driving force to form micro-/nanoparticles. The positively charged natural polymer CS has been broadly investigated to form composites with negative electrolytes by ionic crosslinking (ionotropic gelation). Alternatively, covalent crosslinking has been used.
Mild processing conditions. Simple equipment. Ionotropic gelation: low toxicity, limited risk of altering the encapsulated drug.

Crosslinking gelation
Electrostatic interaction between polyelectrolytes and polyvalent ions is often used as the driving force to form micro-/nanoparticles. The positively charged natural polymer CS has been broadly investigated to form composites with negative electrolytes by ionic crosslinking (ionotropic gelation). Alternatively, covalent crosslinking has been used.
Mild processing conditions. Simple equipment. Ionotropic gelation: low toxicity, limited risk of altering the encapsulated drug.
Poor stability in non-acidic conditions. Difficulty in encapsulating high-molecular-weight drugs. Toxicity of certain covalent crosslinkers (aldehydes, for instance). The process is convenient, cost-effective and devoid of high temperatures and use of solvent. Also usable for living-cell encapsulation.
Limited size control/size reduction. Difficulties in largescale production.
90 µm-7 mm -Polymer concentration; viscosity of polymer solution; flow rate; geometry of extrusion device; type and concentration of nonsolvent bath.

Crosslinking gelation
Electrostatic interaction between polyelectrolytes and polyvalent ions is often used as the driving force to form micro-/nanoparticles. The positively charged natural polymer CS has been broadly investigated to form composites with negative electrolytes by ionic crosslinking (ionotropic gelation). Alternatively, covalent crosslinking has been used.
Mild processing conditions. Simple equipment. Ionotropic gelation: low toxicity, limited risk of altering the encapsulated drug.
Electrospraying CS is dispersed/dissolved into a mixture of solvent and blend with drug solution/suspension.
The conductive liquids are atomized under high voltage to form drug-encapsulated particles. The flow rate, voltage and distance between needle tip and collector are crucial process parameters.
Low production cost; narrow particle size distribution; easy-to-control surface properties and rapid preparation; high drug-loading efficiency; gentle conditions without use of harsh solvents.
Further investigation needed for upscaling; potential toxicity due to certain solvents. Low production cost; narrow particle size distribution; easy-to-control surface properties and rapid preparation; high drug-loading efficiency; gentle conditions without use of harsh solvents.

Further investigation
needed for upscaling; potential toxicity due to certain solvents. Low production cost; narrow particle size distribution; easy-to-control surface properties and rapid preparation; high drug-loading efficiency; gentle conditions without use of harsh solvents.

Further investigation
needed for upscaling; potential toxicity due to certain solvents.

0.1-1.3 µm -
Flow rate; solvent evaporation rate; collector distance; electrical conductivity; nature of polymer, solvent and molecules being used in the process.

Reverse microemulsion/micellar method
Organic solvent (containing surfactant) is mixed with acidic CS solution to form reverse micelles. Then, drug conjugate and CS attach to the micelles via glutaraldehyde (crosslinker) to form nanoparticles. Residual solvent and surfactant and excess crosslinking agent need to be removed.
Application of organic solvent; timeconsuming preparation process; complex washing step.  Sieving method A drug-loaded CS jelly mass is crosslinked and then manually passed through a sieve to obtain nonsticky particles.
Simple and commercially viable; easy scale-up; devoid of tedious processes; high drug loading.

Irregular particle
shape. 500-600 µm -Mesh size of the sieve; amplitude and frequency of vibration; duration of the sieving process; properties of the material.
ually passed through a sieve to obtain nonsticky particles. devoid of tedious processes; high drug loading. shape.
tion of the sieving process; properties of the material.
ually passed through a sieve to obtain nonsticky particles. devoid of tedious processes; high drug loading. shape.
tion of the sieving process; properties of the material.
-Flow rate; viscosity; temperature; device geometry; electrical and magnetic fields.

Characteristics of Chitosan-Involved Particulate Carrier
The morphology of sub-microparticles is a fundamental characteristic that significantly affects their properties. Several characteristics of nano-/microparticles are essential to know, such as average size and size distribution, shape, surface properties (area, charge, functionalization), porosity, etc. These properties are desirable for assessing safety, ensuring consistent product quality control and ensuring regulatory compliance.
The size distribution of spherical partials is a subject that has been well illustrated and developed. Briefly, it is generally required to combine light-scattering techniques (DLS, LS) with microscopic characterization using TEM, SEM and AFM [115][116][117][118]. However, for non-spherical particles, the diffusion coefficient also depends on the shape of the particles [119,120]. A combination of several techniques is recommended to obtain precise information on particle size and shape. For example, particles with irregular shapes obtained from the sieving method have been characterized by the laser light diffusion method and SEM micrographs. LS was used to determine the size and distribution of spherical particles equal in volume to the samples [61]. As for rod-shaped and cylindrical particles, the aspect ratio was introduced to describe the elongation of the particle shape [119]. The characterization of fiber-shaped particles requires more complex techniques as they have an elongated shape and cannot be adequately described by a single dimension. Size characterization of fiber-shaped particles can be conducted based on various dimensions such as diameter, length, aspect ratio and specific surface area [120][121][122][123]. Finally, it must be reminded that average values of particle size may differ from one technique to another simply because "averages" are not calculated in the same way (number, surface, volume, intensity, etc.).
Additionally, Small-angle X-ray scattering (SAXS) is a technique that can be used to determine the size, size distribution, shape and organization of hierarchal structures [124]. SAXS is based on the interaction of X-rays with the electrons in the material, producing scattering patterns that can interpret particle shapes such as spheres, rods, discs, hollow spheres and dumbbells [125]. However, SAXS is limited to analyzing samples in the range of 1-100 nanometers, and interpreting SAXS data, especially when the sample is complex or contains multiple components, could be challenging.
As to capsule and multilayer particles, besides the size of the particle (the diameter of the outermost shell), the thickness of the layer(s) (including shell thickness) is also an interesting characteristic to know since the properties of layers made of different materials can be pretty diverse. However, this characteristic has not been abundantly discussed in the literature.
Microscopy techniques (SEM, TEM, CLSM) play a significant role not only by visualizing the surface morphology, shape and size of sub-microparticles but also their internal structure (cross-section, porosity, crystallinity) [113,[126][127][128][129]. Additionally, the structural evolution of particles during the release process can be monitored by consecutive micrographs, which can reveal and confirm the release mechanism over time [130]. SEM and TEM can provide high-resolution images of the particle structure and morphology, allowing for direct visualization of the particles at the nanoscale. Confocal microscopy uses a focused laser beam to scan a sample and create a series of optical sections at different depths. Confocal slices can provide detailed information about the internal structure and organization of the sample at a particular depth or plane (Figure 9). By using fluorescent labeling, the oil phase inside the core of microcapsules was localized and quantified [130]. The fluorescence signals of polymers allow the visualization of their distribution within the polymeric shell. Furthermore, the oil phase is distinguished unambiguously from air bubbles by comparing optical and fluorescent images. With the help of computational image analysis, the layer thickness and the volumes of different phases can be estimated.

Particulate Structure and Controlled Release Kinetics
Drug release refers to the process by which entrapped drugs dissolve and diffuse into the outer medium by diffusing within bulk core material and/or shell material or passing through pores or fractures within the particles. Drug release kinetics depend greatly on the particulate building materials, drug properties and structural properties of composites, including shape, particle size, surface roughness, porosity, shell thickness, etc. Additionally, along the release process, carrier structure may evolve under the effect of stimuli in the release environment. The assumed principal drug release mechanisms include dissolution, erosion, swelling and diffusion [20,134]. Release mechanisms and the corresponding release profiles dominated by each were summarized in Ref. [62]. To simplify the analysis of the experimental release results, it is generally crucial to identify the limiting phenomena.
As the drug release process results from interactions between entrapped molecules, encapsulating particles and the releasing environment, the particulate structure and its evolution over a definite release time have a great effect on release kinetics. Elucidating the corresponding relations between composite structures and potential release mechanisms enables researchers to predict the release trend of certain loaded active ingredients from a specific structured vehicle. Figure 10 summarizes graphically several typical CSinvolved particulate carriers with relevant release profiles found in the literature. In Figure 10a, which illustrates CS polymeric matrix particles, drug molecules are distributed

Particulate Structure and Controlled Release Kinetics
Drug release refers to the process by which entrapped drugs dissolve and diffuse into the outer medium by diffusing within bulk core material and/or shell material or passing through pores or fractures within the particles. Drug release kinetics depend greatly on the particulate building materials, drug properties and structural properties of composites, including shape, particle size, surface roughness, porosity, shell thickness, etc. Additionally, along the release process, carrier structure may evolve under the effect of stimuli in the release environment. The assumed principal drug release mechanisms include dissolution, erosion, swelling and diffusion [20,134]. Release mechanisms and the corresponding release profiles dominated by each were summarized in Ref. [62]. To simplify the analysis of the experimental release results, it is generally crucial to identify the limiting phenomena.
As the drug release process results from interactions between entrapped molecules, encapsulating particles and the releasing environment, the particulate structure and its evolution over a definite release time have a great effect on release kinetics. Elucidating the corresponding relations between composite structures and potential release mechanisms enables researchers to predict the release trend of certain loaded active ingredients from a specific structured vehicle. Figure 10 summarizes graphically several typical CS-involved particulate carriers with relevant release profiles found in the literature. In Figure 10a, which illustrates CS polymeric matrix particles, drug molecules are distributed on the particle surface as well as inside the matrix. The diffusion of molecules located superficially may lead to a burst release, i.e., the fast release of a significant number of loaded molecules before the further and slower release of the remaining substance. Medium permeation inward the carrier causes erosion, swelling and diffusion, which are mainly responsible for the following sustained release, which may last from hours to days [83,111]. Figure 10b represents a core-shell capsule case. The core region could be solid or liquid (oil phase), which encapsulates dissolved active ingredients or dispersed systems such as emulsion droplets, nano-/microparticles or liposomes [82,112,135]. The outer wall-like shell prevents leakage and the degradation of the inner contents from harsh conditions inside the internal environment, such as pH, enzymes, etc. Structural incompleteness due to fracture or breakage of the shell leads to the liberation of inside molecules. Figure 10c is a core-shellstructured microcapsule encapsulating drug-loaded nanoparticles in an oily core enclosed by a CS shell. Both drug molecules and drug-loaded poly-(lactic-co-glycolic acid) (PLGA) nanoparticles were enclosed in a stimulus-responsive microcapsule [110]. The CS shell prevented the leakage of the entrapped cargo in a neutral medium and broke down in an acidic site, thus providing sustained drug delivery through the diffusion of free drug and nanoparticle degradation. Additionally, enzyme intestinal delivery was reported to be localized by alginate nanoparticles incorporated into CS-shelled microcapsules [113]. Figure 10d is a CS-based microsphere with an alginate coating. The coating can protect the loaded substance from degradation and hydrolysis in acidic conditions for hours and can modulate the release rate by suppressing burst release [103]. In addition, in some other core-shell cases, the external shell is able to respond to certain stimuli, e.g., pH and ionic strength [82], and achieve targeting effects through the addition of biological ligands [84]. Figure 10e,f are both multilayered CS hydrogel capsules. The drug is loaded homogenously in each layer of the carrier in Figure 10e, while the one in Figure 10f contains sequentially alternating drug-loaded and void layers. It is possible to customize the number of layers and tailor their thickness [136]. The former achieves approximately a zero-order release, while the latter is supposed to attain a pulsatile drug release [81]. Apart from CS-based carriers alone, the encapsulated ingredient is also a dimension that can enrich the utility of these functional carriers. For example, Figure 10g represents a core-shell nanosphere system that was developed for co-delivering drugs (oleanolic acid and doxorubicin) as a strategy to treat multi-drug-resistant breast cancer. This novel dualdrug-loaded DDS was proven effective as a breast-tumor targeting strategy in in vitro and ex vivo evaluations [137]. Below are some typical CS-relevant carriers with their release profiles found in the literature. Particularly worth mentioning is the fact that certain release profiles may be attained by diverse carriers. Inversely, a carrier may possess different release profiles under different dissolution conditions (pH, ionic strength, light, temperature, magnetic field, etc.).
To sum up, further investigations into the correlation between carrier structure and the associated release profile are worth the effort. By achieving this goal, in turn, it would be possible to design on-demand drug delivery systems that can regulate, in an expected way, more precisely the release rate of certain drugs at a specific time interval and location.

Release Kinetics, Mechanisms and Modeling
The use of kinetic models can aid in describing the release rate of drugs, lea increased efficiency, accuracy and safety of the dose. This, in turn, can help optim design of drug delivery devices [138]. With an appropriate understanding of the l phenomena that govern drug release from a given system, it is possible to descri release behavior by applying proper mathematical models. As known, various greatly influence this complex process, such as matrix geometry, matrix swelling rium and kinetics, matrix erosion, drug dissolution and partitioning, drug di drug-matrix interaction, initial drug distribution, etc. (Figure 11). Based on spe sumptions and hypotheses, certain mathematical models enable the simulation of kinetics under certain conditions. Some of these mathematical models have bee monly used to identify dominant release mechanisms on the basis of the compar tween experimental and theoretical time variations in cumulated released amoun

Release Kinetics, Mechanisms and Modeling
The use of kinetic models can aid in describing the release rate of drugs, leading to increased efficiency, accuracy and safety of the dose. This, in turn, can help optimize the design of drug delivery devices [138]. With an appropriate understanding of the limiting phenomena that govern drug release from a given system, it is possible to describe drug release behavior by applying proper mathematical models. As known, various factors greatly influence this complex process, such as matrix geometry, matrix swelling equilibrium and kinetics, matrix erosion, drug dissolution and partitioning, drug diffusion, drug-matrix interaction, initial drug distribution, etc. (Figure 11). Based on specific assumptions and hypotheses, certain mathematical models enable the simulation of release kinetics under certain conditions. Some of these mathematical models have been commonly used to identify dominant release mechanisms on the basis of the comparison between experimental and theoretical time variations in cumulated released amounts [138]. Trying to develop a general and unifying model would consequently result in an increase in the complexity of the model's expression and make it difficult to obtain analytical and/or numerical solutions. Although achieving a highly general model may be challenging, researchers have explored the potential of using empirical/semi-empirica models to describe the release kinetic characteristics, prioritizing various aspects that make up the release phenomenon. Mathematical models used to fit the drug release profile from CS-based particles include the Higuchi square root, Korsmeyer-Peppas', Hixon-Crowell's, Baker-Lonsdale's, Peppas-Sahlin's, Kopcha's, Hopfenberg's and Gallagher-Corrigan (GC) models. According to the systems, zero-order or first-order kinetics may be observed.
For zero-order kinetics, the release of an active agent is only a function of time, and the process takes place at a constant rate independent of active agent concentration: where Mt is the amount of drug released at time t and k is the zero-order constant.
The first-order release kinetics model assumes that the rate of drug release is proportional to the amount of drug remaining in the dosage form [139,140]: where k′ is the first-order rate constant and M0 is the initial amount of drug in the dosage form. The Higuchi model explains the release of a drug as a diffusion process, which is governed by Fick's law and has a time-dependent square root relationship [141]: Trying to develop a general and unifying model would consequently result in an increase in the complexity of the model's expression and make it difficult to obtain analytical and/or numerical solutions. Although achieving a highly general model may be challenging, researchers have explored the potential of using empirical/semi-empirical models to describe the release kinetic characteristics, prioritizing various aspects that make up the release phenomenon. Mathematical models used to fit the drug release profile from CS-based particles include the Higuchi square root, Korsmeyer-Peppas', Hixon-Crowell's, Baker-Lonsdale's, Peppas-Sahlin's, Kopcha's, Hopfenberg's and Gallagher-Corrigan (GC) models. According to the systems, zero-order or first-order kinetics may be observed.
For zero-order kinetics, the release of an active agent is only a function of time, and the process takes place at a constant rate independent of active agent concentration: where M t is the amount of drug released at time t and k is the zero-order constant. The first-order release kinetics model assumes that the rate of drug release is proportional to the amount of drug remaining in the dosage form [139,140]: where k is the first-order rate constant and M 0 is the initial amount of drug in the dosage form. The Higuchi model explains the release of a drug as a diffusion process, which is governed by Fick's law and has a time-dependent square root relationship [141]: where M ∞ is the absolute amount of drug released over infinite time and k H is a release rate constant.
The Korsmeyer-Peppas model is a semi-empirical model that establishes the exponential relationship between the amount released and the time and provides indications about the mechanism of drug release [142][143][144]: where K is a rate constant and n is the exponent that incorporates the effects of the release mechanism and the geometrical characteristics of the system. The Hixson-Crowell model was initially derived from a work dealing with agitation [145]: The GC model is particularly useful for predicting drug release profiles under different conditions [152]. Additionally, it can be adapted to describe dual-phased drug release [152][153][154]. The experimental data on the release of curcumin from MnFe 2 O 4 magnetic nanoparticles with multilayered CS-alginate (ALG) shells were a good fit to the GC model. The CS-ALG coating was reported to be useful in inhibiting burst release, and the increase in the number of layers could delay the dissolution rate, thus achieving sustained release [154].
The distinguishing aspect of the last three models from others is their incorporation of two discrete phenomena that occur during drug release: diffusion and relaxation in the Peppas-Sahlin and Gallagher-Corrigan models and diffusion and erosion in Kopcha's model.
Frequently used models are adopted to describe the release characteristics and mechanisms of drugs from CS-based systems, prioritizing different factors (Table 4). Table 4. Mathematical models to reveal the release mechanisms of reported chitosan-based particulate systems. It is important to note that good-fitting experimental data are necessary but may not be sufficient to identify the best model among different models devoted to correctly describing complex release kinetics. Mathematical hypotheses are supposed to take experimental observation of phenomena into consideration. However, in practice, it may not always be feasible. For instance, swelling and erosion of the CS matrix also contributed to the release of vitamins, but the best model chosen was the Peppas-Sahlin model, which privileges more diffusion and relaxation [158]. By synthetically analyzing characteristic constants of diverse models, researchers can better understand the underlying mechanisms of drug release and predict the release kinetics more accurately [1].

Mechanism (s) Description of Systems Model Equation(s) References
Furthermore, considering the overall size distribution of particles rather than just the unitary average diameter may be crucial in developing more accurate models, as heterogeneity in samples is a common occurrence in practical applications [162,163].
It is noteworthy that the systematic implementation of mathematical modeling in the development of active ingredient delivery systems can enhance R&D efficiency, save time and reduce expenses. Additionally, the advanced utilization of this approach can enable the advancement of precision medicine. Instead of an undifferentiated regular dosage regimen, personalized medicine can afford a better therapeutic effect and lower toxicity by considering patients' individual characteristics.

Conclusive Remarks and Prospective Research
Tremendous interest in CS from both academic and diverse industrial fields has emerged over the past few decades. Innovative carriers have been developed with unique properties such as sustained release, responsiveness to environmental factors and multiphase release.
An improved understanding of the close relationship between the preparation process and particle structure would enable the prediction of formulation and preparation strategies for drug delivery systems to achieve the desired release kinetics [152,164]. Additionally, modeling capacity is a powerful tool to increase the efficiency of developing new systems, which is crucial for the industry to turn the idea of on-demand drug delivery systems (DDS) into a reality.
Efforts should be focused on investigating in a more specific manner how the preparation process affects the structure of the vehicle and subsequent release behaviors from the polymeric network. By gaining more insight into these aspects, it is possible to design DDSs that release drugs in a controlled manner, such as sustained release, pulsatile release or targeted release, depending on the specific therapeutic needs. Funding: This is work supported by the "Impact Biomolecules" project of the "Lorraine Université d'Excellence" (Investissements d'avenir-ANR project number 15-004).

Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.