Designing and mathematical modeling of pH responsive biopolymer hydrogels for targeted drug delivery in controlled release systems

Kopač, Tilen (avtor), Ručigaj, Aleš (mentor)

Targeted drug delivery to the desired site and controlled release rate increase treatment efficacy, reduce side effects and patient burden, protect the drug from degrading factors in the body, and reduce treatment costs. In this field, hydrogels are most commonly used as drug delivery systems. Fabrication and design of appropriate hydrogel properties to encapsulate and protect the drug, transport it to the desired location, and changing the structure of the hydrogel to cause drug release at a specific rate requires a series of complex studies and experiments. In this dissertation, mathematical modeling of hydrogel properties is presented to predict key parameters for designing the desired properties of hydrogels, such as shear modulus, crosslink density, mesh size, and drug release rate. The proposed approach could be useful in all hydrogel applications where the design of desired hydrogel properties is crucial. The developed mathematical model could reduce the number of experiments required for hydrogel development, thereby shortening research time, reducing research costs, and reducing the consumption of chemicals and energy, contributing to more environmentally friendly research. The polymer concentration, the mass fraction of polymers in the mixture, and the concentration and type of crosslinking agent are crucial when designing hydrogels with desired properties. For the purpose of targeted delivery and biocompatibility, pH-sensitive biopolymers were used. Hydrogels were prepared from modified nanocellulose, alginate, and scleroglucan, which represent the biopolymeric base of the systems studied. In order to extend the pH range of the hydrogels, the cationic functionalization of cellulose nanofibrils was carried out to extend the number of pH-responsive biopolymers. The research area was complemented by the preparation of hydrogels from different blends of basic biopolymers, expanding the possibilities to design the properties of the hydrogel network (mesh size, charge, hydrophilicity) to meet the requirements of a wide range of applications. The final part of the network modification was the use of the rheological modifier Laponite, which was incorporated into the network to influence the barrier properties of the hydrogel. Additional control over the crosslink density and thus the mesh size was achieved by using a crosslinking agent. In most cases, ionic crosslinkers such as calcium ions were used to maintain biocompatibility. Mathematical modeling of the drug release technology involves a detailed analysis of two key mechanisms, namely diffusion and the kinetics of adsorption and desorption of the drug in the case of electrostatic interactions with the hydrogel surface. The mass transfer by diffusion is directly related to the mesh sizes, as they allow complete encapsulation of the drug when the hydrodynamic radius of the drug is larger than the mesh size. On the other hand, increasing the mesh size allows diffusion of the drug. The release rate can be controlled by adjusting the mesh size, which acts as steric barrier. Therefore, the first part of the dissertation aims to develop a mathematical model to predict the mesh size in a hydrogel network as a function of the concentration of biopolymers and crosslinking agents. The mesh size was determined by oscillatory rheology measurements. The mechanical properties of hydrogels determine the shear modulus and crosslink density, which are the most important parameters for determining mesh size. In the dissertation, the theory of polymer-polymer interactions was introduced, which allows the analysis of the mechanical properties of hydrogels as a consequence of the interactions between the polymer chains that occur during the crosslinking process. In addition, the crosslink density was defined as the number of interactions between the polymer chains per hydrogel volume. It was shown that the number of bonds formed during crosslinking depends on the concentration of functional groups on the polymer surface, the concentration of the polymer and the crosslinking agent, and the tendency to form interactions between the polymer chains. Based on the observed predominant effect of hydrogen and ionic interactions, we developed a generalized mathematical model to predict the shear modulus, crosslink density, and mesh size in the hydrogel as a function of polymer and crosslinking agent concentration. The model was further modified to respond to hydrogels in an environment with different pH and temperature values. Using the developed model in already known correlations between mesh size and diffusion coefficient, the drug release rate was predicted in cases where diffusion is the predominant transport phenomenon and drugs do not form interactions with hydrogels. The model was verified by numerous release tests in a medium with different pH and temperature. Theophylline and FITC-dextran with different molecular weights were used as modeldrugs. In this way, the effect of the size of the drug (hydrodynamic radius) on the release rate was also mathematically evaluated. The second part of the dissertation deals with the comprehensive characterization of hydrogels and the search for material properties that influence the design of hydrogels as drug delivery systems. In addition to the rotational oscillation measurements mentioned earlier, rheological rotation tests with continuous rotation were performed, which are particularly important from the point of view of the application properties of hydrogels. A comprehensive study of various hydrogel systems based on biopolymer blends with the addition of Laponite as a rheological modifier was published. Detailed analysis of flow behavior and determination of zero-shear viscosities and yield stresses led to the exploration of the direct relationship between mechanical and flow properties. This study also allowed us to modify the mathematical model for predicting crosslink density with a correlation factor so that we could also mathematically predict the yield stress of hydrogels. The approach to determine the correlation between mechanical and flow properties has led to a better understanding of the crosslinking process in complex hydrogel systems. On the other hand, the inhomogeneity of the hydrogel network was demonstrated by low-field nuclear magnetic resonance (LF-NMR) studies. In this way, we obtained information about the crosslink density based on various measurements and were able to further verify the written mathematical model. At the same time, certain deviations of the model from the experimental values were easier to explain. In the field of hydrogel characterization, we focused mainly on the study of nanocellulose, which represents a new period of research in the field of hydrogels. As mentioned earlier, we successfully modified nanocellulose with cationic character, further increasing the number of biopolymers for the development of pH-dependent hydrogels. We also carefully studied the effects of fiber size on the rheological behavior of nanocellulose. Ultimately, it was found that knowledge of the morphological and topographical properties of the hydrogel surface is crucial for the accurate design of hydrogels as delivery systems. The latter is particularly crucial for the mechanisms of adsorption and desorption of drugs on the surface, which was the subject of the last part of the PhD thesis. The third part of the research involves a detailed analysis of the kinetics of adsorption and desorption of proteins on or from the hydrogel surfaces. Lysozyme was used as a model protein. In the last publication presented, the kinetics of adsorption as a function of temperature and ionic strength of the release medium was studied by mathematical modeling of lysozyme release in addition to the already well-developed model for predicting the diffusivity of lysozyme. For the first time, we presented the mechanism for determining the initial (maximum) rate of protein adsorption on the hydrogel surface. At the same time, it was possible to similarly determine the initial (minimum) rate of protein desorption from the surface. The slowing of the adsorption rate and the acceleration of the desorption rate with increasing ionic strength were accurately evaluated mathematically with appropriate parameters. Implementation of the mathematical model for studying adsorption and desorption kinetics into the previously developed model for predicting drug release by the diffusion mechanism allows development of a generalized mathematical model for predicting targeted drug delivery with controlled release as a function of hydrogel design parameters (concentration and type of polymers and crosslinking agents, and understanding of the theory of polymer-polymer interactions during the crosslinking process).

• Jezik: Angleški jezik
• Ključne besede: hydrogel, rheology, crosslink density, polymer interactions, controlled drug release, mathematical modelling
• Vrsta gradiva: Doktorsko delo/naloga
• Tipologija: 2.08 - Doktorska disertacija
• Organizacija: FKKT - Fakulteta za kemijo in kemijsko tehnologijo
• Leto izida: 2022
• PID: 20.500.12556/RUL-141693
• COBISS.SI-ID: 126021635
• Datum objave v RUL: 05.10.2022

Sekundarni jezik

• Jezik: Slovenski jezik
• Naslov: Načrtovanje in matematično modeliranje pH odzivnih biopolimernih hidrogelov za ciljno dostavo učinkovin s kontroliranim sproščanjem

Izvleček

Tarčna dostava zdravilnih učinkovin na želeno mesto in sprošþanje s kontrolirano hitrostjo povečujejo učinkovitost zdravljenja, zmanjšujejo stranske učinke in obremenitev na pacienta, varujejo učinkovino pred razkrojevalnimi dejavniki v telesu ter znižujejo ceno zdravljenja. Na tem področju se kot dostavni sistemi učinkovin najpogosteje uporabljajo hidrogeli. Priprava in načrtovanje primernih lastnosti hidrogelov za enkapsulacijo in zaščito učinkovine, transport na želeno mesto in sprememba v strukturi hidrogela, ki povzroči sproščanje učinkovine z natančno določeno hitrostjo, zahteva številne kompleksne študije in eksperimente. V disertaciji je skladno s tem predstavljeno matematično modeliranje hidrogelnih lastnosti za napoved ključnih parametrov za načrtovanje zahtevanih lastnosti hidrogelov, kot so strižni modul, gostota zamreženja, povprečna velikost por v hidrogelni mreži in napoved hitrosti sproščanja učinkovine. Predlagan pristop bi lahko bil potencialno uporaben v vseh aplikacijah hidrogelov, kjer je načrtovanje želenih lastnosti ključnega pomena. Razvit matematični model bi lahko zmanjšal število eksperimentov potrebnih pri načrtovanju hidrogelov in na ta način skrajšal čas raziskav, zmanjšal stroške raziskav in zmanjšal porabo kemikalij in energentov ter tako prispeval k bolj okolju prijaznim raziskavam. Pri načrtovanju hidrogelov z želenimi lastnostmi ima ključno vlogo koncentracija polimerov, masni delež polimerov v mešanici in koncentracija ter vrsta zamreževala. Za namen tarčne dostave in biokompatibilnosti so bili uporabljeni pH odzivni biopolimeri. Hidrogele smo pripravljali iz modificirane nanoceloluloze, alginata in skleroglukana, ki predstavljajo biopolimerno osnovo preuþevanih sistemov. Z namenom razširitve pH območja odzivnosti hidrogelov smo nanofibrilno celulozo funkcionalizirali, s ciljem doseči kationsko naravo nanoceluloznega hidrogela. Območje raziskav smo dopolnili s pripravo hidrogelov iz različnih mešanic osnovnih biopolimerov, kar je povečalo možnosti načrtovanja lastnosti hidrogelne mreže (velikost por, naboj, hidrofilnost) za potrebe širokega območja uporabnosti. V sklepnem delu modifikacije hidrogelne mreže smo uporabili reološki modifikator Laponit, ki je bil vključen v biopolimerno mešanico in tako vplival na mejne lastnosti hidrogela (vpliv na sposobnost zadrževanja in migracijo učinkovine). Dodatno kontrolo nad gostoto zamreženja in s tem velikostjo por smo dosegli z uporabo zamreževalnega sredstva, pri čemer so se v luči ohranjanja biokompatibilnosti v večini primerov uporabljali ionski zamreževalci (kalcijevi ioni). Matematično modeliranje sproščanja različnih učinkovin zajema natančno analizo dve ključnih mehanizmov, difuzije ter kinetike adsorpcije in desorpcije učinkovine v primeru elektrostatskih interakcij s hidrogelno površino. Prenos snovi z difuzijo je neposredno povezan z velikostjo por v hidrogelni mreži, saj le te omogočajo popolno enkapsulacijo učinkovine, ko je njen hidrodinamični radij večji od velikosti por. Po drugi strani pa povečanje por vodi v difuzijo učinkovine. Pore delujejo kot sterične ovire, pri čemer lahko s spreminjanjem velikosti por nadzorujemo hitrost sproščanja. Prvi del doktorske disertacije je zato ciljno usmerjen v razvoj matematičnega modela za napoved povprečne velikosti por v hidrogelni mreži glede na koncentracijo biopolimerov in zamreževala. Velikost por smo določali z reološkimi oscilatornimi meritvami, saj mehanske lastnosti hidrogelov določajo strižni modul in gostoto zamreženja. Predstavili smo teorijo polimer-polimer interakcij, ki omogoča analizo mehanskih lastnosti hidrogelov kot posledico interakcij med polimernimi verigami, ki nastanejo med procesom zamreževanja. Gostota zamreženja smo definirali kot število povezav med polimernimi verigami na volumen hidrogela. Dokazali smo, da je število povezav, ki nastanejo med zamreževanjem, odvisno od koncentracije funkcionalnih skupin na površini polimera, koncentracije polimera in zamreževala ter od težnje zamreževala k ustvarjanju interakcij med polimeri. Na podlagi ugotovljenih prevladujočih vodikovih in ionskih interakcij smo razvili matematični model za napoved strižnega modula, gostote zamreženja in povprečne velikosti por v hidrogelu v odvisnosti od koncentracije polimera in zamreževala. Model je bil modificiran za odziv hidrogelov v okolju z različno temperaturo in pH vrednostjo. Z uporabo razvitega modela v že znanih korelacijah med povprečno velikostjo por in difuzijskim koeficientom smo napovedali hitrost sproščanja učinkovin v primerih, kjer je difuzija prevladujoč transportni pojav in učinkovine s hidrogeli ne tvorijo interakcij. Veljavnost modela smo preverili s številnimi testi sproščanja v mediju z različno pH vrednostjo in temperaturo. Kot modelne učinkovine smo uporabili teofilin in FITC dekstran z različnimi molekulskimi masami. Na ta način smo matematično ovrednotili tudi vpliv velikosti učinkovine na hitrost sproščanja. Drugi del disertacije se nanaša na karakterizacijo hidrogelov in iskanje materialnih lastnosti, ki vplivajo na načrtovanje hidrogelov kot dostavnih sistemov učinkovin. Poleg že omenjenih reoloških oscilatornih meritev smo izvedli še reološke rotacijske meritve, ki so pomembne predvsem z vidika aplikativnih lastnosti hidrogelov. Objavljena je bila obširna študija različnih hidrogelnih sistemov na osnovi biopolimernih mešanic ob dodatku Laponita kot reološkega modifikatorja. Natančna analiza tokovnega obnašanja in določitev viskoznosti prvega newtonskega območja ter mejne napetosti je vodila do raziskovanja neposredne povezave med mehanskimi in tokovnimi lastnostmi. Ta študija je omogočila modifikacijo matematičnega modela za napoved gostote zamreženja s korelacijskim faktorjem in tako smo matematično napovedali tudi mejne napetosti hidrogelnih sistemov. Pristop ugotavljanja korelacije med mehanskimi in tokovnimi lastnostmi je vodil do lažjega razumevanja procesa zamreževanja v kompleksnih hidrogelnih sistemih. Po drugi strani smo s testi nuklearne magnetne resonance z nizkim poljem (LF-NMR) dokazali nehomogenost hidrogelne mreže. Na ta način smo dobili podrobnejše informacije o gostoti zamreženja in matematični model posledično še dodatno potrdili. Hkrati smo določena odstopanja modela od eksperimentalnih vrednosti lahko ustrezno obrazložili. Na področju karakterizacije hidrogelov smo se osredotočili predvsem na študijo nanoceluloze, ki postaja vse bolj zanimiva za raziskovanja na področju hidrogelov. Kot že omenjeno, smo v disertaciji uspešno modificirali nanocelulozo s kationskim značajem in tako še razširili število biopolimerov za načrtovanje pH odzivnih hidrogelov. Poleg tega smo preučili vpliv velikosti vlaken na reološke lastnosti. Ugotovili smo tudi, da je za natančno načrtovanje hidrogelov kot dostavnih sistemov ključno poznavanje morfoloških in topografskih lastnosti hidrogelne površine. Slednje je še posebej pomembno pri mehanizmih adsorpcije in desorpcije učinkovin na površino. Tretji del raziskovalnega dela obsega natančno analizo kinetike adsorpcije in desorpcije proteinov na oziroma s površine hidrogelov. Kot modelni protein smo izbrali lizocim. V zadnji predstavljeni publikaciji smo z matematičnim modeliranjem sproščanja lizocima ob že vnaprej dobro razvitem modelu za napoved difuzivnosti lizocima natančno opisali kinetiko adsorpcije v odvisnosti od temperature in ionske moči medija za sproščanje. Prvič smo predstavili mehanizem določitve začetne (maksimalne) hitrosti adsorpcije proteina na površino hidrogela. Hkrati je bilo mogoče podobno določiti tudi začetno (minimalno) hitrost desorpcije proteina s površine. Upočasnjevanje hitrosti adsorpcije in povečevanje hitrosti desorpcije ob povišani ionski moči sta bila natančno matematično ovrednotena z optimizacijskimi parametri prileganja funkcije k eksperimentalnim podatkom. Implementacija matematičnega modela študije kinetike adsorpcije in desorpcije v že predhodno razviti model za napoved sproščanja učinkovine po difuzijskem mehanizmu omogoča razvoj splošnega matematičnega modela za napoved tarčne dostave učinkovin s kontroliranim sproščanjem v odvisnosti od parametrov za načrtovanje hidrogelov (koncentracija in vrsta polimerov in zamreževal ob razumevanju teorije interakcij polimer-polimer med procesom zamreževanja).

• Ključne besede: hidrogel, reologija, gostota zamreženja, interakcije polimerov, kontrolirano sproščanje, matematično modeliranje