Monte Carlo simulation methods-based models for analyzing the kinetics of drug delivery from controlled release systems

Authors

  • Saúl Jiménez-Jiménez Laboratorio de Investigación y Posgrado en Tecnología Farmacéutica, Facultad de Estudios Superiores Cuautitlán, Universidad Nacional Autónoma de México https://orcid.org/0000-0001-9969-2155
  • Salomón Cordero-Sánchez Departamento de Química, Universidad Autónoma Metropolitana, Unidad Iztapalapa, México
  • José-Gerardo Mejía-Hernández Laboratorio de Investigación y Posgrado en Tecnología Farmacéutica, Facultad de Estudios Superiores Cuautitlán, Universidad Nacional Autónoma de México
  • David Quintanar-Guerrero Laboratorio de Investigación y Posgrado en Tecnología Farmacéutica, Facultad de Estudios Superiores Cuautitlán, Universidad Nacional Autónoma de México
  • Luz-María Melgoza-Contreras Departamento de Sistemas Biológicos, Universidad Autónoma Metropolitana, Unidad Xochimilco, México
  • Rafael Villalobos-García Laboratorio de Investigación y Posgrado en Tecnología Farmacéutica, Facultad de Estudios Superiores Cuautitlán, Universidad Nacional Autónoma de México

DOI:

https://doi.org/10.1590/

Keywords:

Monte Carlo simulation, Diffusion, Drug-controlled release, Percolation threshold, Nanotechnology, Simulation, Swelling

Abstract

Pharmaceutical controlled-release formulations are systems developed by a set of unit operations to achieve a satisfactory combination between a drug and excipients to allow its gradual release. These devices must simultaneously meet criteria for stability, biocompatibility, safety, efficacy, scalability at industrial volumes, and technological efficiency for drug release. Controlled-release systems (CRSs) must release drugs in a way that maintains an adequate concentration in the organism, a requirement that is challenging to meet in practice. Even though novel CRSs may be designed with new materials as excipients, new drugs, or emerging manufacturing technologies, the mechanisms for drug release continue to be governed by a set of similar physicochemical phenomena such as diffusion, swelling, or erosion. These phenomena are too complex to be analyzed by numerical methods; however, they are relatively accessible by probabilistic models especially the Monte Carlo simulation. In this review, we discuss key findings related to the use of this probabilistic method for analyzing the drug-controlled release process in different pharmaceutical devices. Based on this evidence, we propose their potential application in the characterization of new drug-controlled release systems, synergy with other computational methods, and their capability to be adapted for in vivo or in vitro kinetic analysis.

Downloads

References

Adamczyk P, Polanowski P, Sikorski A. Percolation in polymer-solvent systems: A Monte Carlo study. J Chem Phys. 2009 Dec 21;131(23).

Adepu S, Ramakrishna S. Controlled drug delivery systems: current status and future directions. Molecules. 2021 Sep 29;26(19):5905.

Aguilar-De-Leyva A, Gonçalves-Araujo T, Daza V, Caraballo I. A new deferiprone controlled release system obtained by ultrasound-assisted compression. Pharmaceutical Development and Technology. 2014 Sep 1;19(6):728-34.

Ahualli S, Martin-Molina A, Maroto-Centeno JA, Quesada-Perez M. Interaction between ideal neutral nanogels: A monte carlo simulation study. Macromolecules. 2017 Mar 14;50(5):2229-38.

Al-Tabakha MM, Alomar MJ. In vitro dissolution and in silico modeling shortcuts in bioequivalence testing. Pharmaceutics. 2020 Jan 4;12(1):45.

Andreadis II, Gioumouxouzis CI, Eleftheriadis GK, Fatouros DG. The advent of a new era in digital healthcare: a role for 3D printing technologies in drug manufacturing?. Pharmaceutics . 2022 Mar 10;14(3):609.

Avalle P, Pygall SR, Pritchard J, Jastrzemska A. Interrogating erosion-based drug liberation phenomena from hydrophilic matrices using near infrared (NIR) spectroscopy. Eur J Pharm Sci. 2013 Jan 23;48(1-2):72-9.

Axpe E, Chan D, Offeddu GS, Chang Y, Merida D, Hernandez HL, et al. A multiscale model for solute diffusion in hydrogels. Macromolecules . 2019 Sep 3;52(18):6889-97.

Bannigan, P., Bao, Z., Hickman, R.J. et al. Machine learning models to accelerate the design of polymeric long-acting injectables. Nat Commun. 2023;14:35.

Barry BW. Drug delivery routes in skin: a novel approach. Adv Drug Delivery Rev. 2002 Nov 1;54:S31-40.

Benkő E, Ilič IG, Kristó K, Regdon Jr G, Csóka I, Pintye-Hódi K, et al. Predicting drug release rate of implantable matrices and better understanding of the underlying mechanisms through experimental design and artificial neural network-based modelling. Pharmaceutics . 2022 Jan 19;14(2):228.

Bertrand N, Leclair G, Hildgen P. Modeling drug release from bioerodible microspheres using a cellular automaton. Int J Pharm. 2007 Oct 1;343(1-2):196-207.

Beugeling M, Grasmeijer N, Born PA, van der Meulen M, van der Kooij RS, Schwengle K, et al. The mechanism behind the biphasic pulsatile drug release from physically mixed poly (dl-lactic (-co-glycolic) acid)-based compacts. Int J Pharm . 2018 Nov 15;551(1-2):195-202.

Bouzo BL, Calvelo M, Martin-Pastor M, Garcia-Fandino R, de la Fuente M. In vitro-in silico modeling approach to rationally designed simple and versatile drug delivery systems. J Phys Chem B. 2020 Jun 11;124(28):5788-800.

Bozzuto G, Molinari A. Liposomes as nanomedical devices. Int J Nanomed. 2015 Feb 2:975-99.

Bruschi ML. Strategies to modify the drug release from pharmaceutical systems. Woodhead Publisher. 2015 Jun 16.

Bunde A, Havlin S, Nossal R, Stanley HE, Weiss GH. On controlled diffusion‐limited drug release from a leaky matrix. The Journal of chemical physics. 1985 Dec 1;83(11):5909-13

Campiñez MD, Benito E, Romero-Azogil L, Aguilar-de-Leyva A, de Gracia Garcia-Martin M, Galbis JA, Caraballo I. Development and characterization of new functionalized polyurethanes for sustained and site-specific drug release in the gastrointestinal tract. European journal of pharmaceutical sciences. 2017 Mar 30;100:285-95.

Cao J, Liu T, Han Z, Tu B. Sulfate ions diffusion in concrete under coupled effect of compression load and dry-wet circulation. Math Biosci and Engineering. 2023 Mar 1;20(6):9965-91.

Caraballo I, Melgoza LM, Alvarez-Fuentes J, Soriano MC, Rabasco AM. Design of controlled release inert matrices of naltrexone hydrochloride based on percolation concepts. International journal of pharmaceutics. 1999 Apr 20;181(1):23-30.

Caraballo I. Critical points in the formulation of pharmaceutical swellable controlled release dosage forms-Influence of particle size. Particuology. 2009 Dec 1;7(6):421-5.

Casalini T. Not only in silico drug discovery: Molecular modeling towards in silico drug delivery formulations. J Controlled Release. 2021 Apr 10;332:390-417.

Turnbull D, Cohen MH. On the free‐volume model of the liquid‐glass transition. The Journal of chemical physics . 1970 Mar 15;52(6):3038-41.

Coleman K. The ICH Q9 Revision and a Renewed Focus on Quality Risk Management Fundamentals. Pharm Technol. 2023 Dec 2;47(12):28-30.

Colombo P, Bettini R, Massimo G, Catellani PL, Santi P, Peppas NA. Drug diffusion front movement is important in drug release control from swellable matrix tablets. J Pharm Sci. 1995 Aug;84(8):991-7.

Corsaro C, Neri G, Mezzasalma AM, Fazio E. Weibull modeling of controlled drug release from Ag-PMA Nanosystems. Polymers. 2021 Aug 27;13(17):2897.

Cukier RI. Diffusion of Brownian spheres in semidilute polymer solutions. Macromolecules . 1984 Mar;17(2):252-5.

Dan N. Drug release through liposome pores. Colloids Surf B. 2015 Feb 1;126:80-6.

Davanço MG, Campos DR, de Oliveira Carvalho P. In vitro-In vivo correlation in the development of oral drug formulation: A screenshot of the last two decades. Int J Pharm . 2020 Apr 30;580:119210.

Davit BM, Kanfer I, Tsang YC, Cardot JM. BCS biowaivers: similarities and differences among EMA, FDA, and WHO requirements. The AAPS J. 2016 May;18:612-8.

De Izarra A, Jang YH, Lansac Y. DNA-assisted assembly of cationic gold nanoparticles: Monte Carlo simulation. Soft Matter. 2021;17(41):9315-25.

Draksler P, Mikac U, Laggner P, Paudel A, Janković B. Polyethylene oxide matrix tablet swelling evolution: The impact of molecular weight and tablet composition. Acta Pharmaceutica. 2021 Jun 30;71(2):215-43.

Du J, Strenzke G, Bück A, Tsotsas E. Monte Carlo modeling of spray agglomeration in a cylindrical fluidized bed: From batch-wise to continuous processes. Powder Technol. 2022 Jan 1;396:113-26.

Fan H, Lin Q, Morrissey GR, Khavari PA. Immunization via hair follicles by topical application of naked DNA to normal skin. Nat Biotechnol. 1999 Sep;17(9):870-2.

Fathi M, Mohebbi M, Varshosaz J, Shahidi F. Cellular automata modeling of hesperetin release phenomenon from lipid nanocarriers. Food Bioprocess Technol. 2013 Nov;6:3134-42.

Feller W. An introduction to probability theory and its applications, Volume 2. John Wiley & Sons; 1991 Jan 8.

Fernandez-Lopez L, Roda S, Robles-Martín A, Muñoz-Tafalla R, Almendral D, Ferrer M, et al. Enhancing the Hydrolytic Activity of a Lipase towards Larger Triglycerides through Lid Domain Engineering. Int J Mol Sci. 2023 Sep 6;24(18):13768.

Fishman G. Monte Carlo: concepts, algorithms, and applications. Springer Science & Business Media; 2013 Mar 9.

Fu Y, Kao WJ. Drug release kinetics and transport mechanisms of non-degradable and degradable polymeric delivery systems. Expert Opin Drug Delivery. 2010 Apr 1;7(4):429-44.

Fuertes I, Miranda A, Millán M, Caraballo I. Estimation of the percolation thresholds in acyclovir hydrophilic matrix tablets. European journal of pharmaceutics and biopharmaceutics. 2006 Nov 1;64(3):336-42.

Fuertes I, Caraballo I, Miranda A, Millán M. Study of critical points of drugs with different solubilities in hydrophilic matrices. International journal of pharmaceutics . 2010 Jan 4;383(1-2):138-46.

Fukś H, Mudiyanselage SA. Deterministic cellular automata resembling diffusion. International Journal of Modern Physics C. 2022 Nov 21;33(11):2250148.

Galdón E, Millán-Jiménez M, Mora-Castaño G, de Ilarduya AM, Caraballo I. A Biodegradable Copolyester, Poly (butylene succinate-co-ε-caprolactone), as a High Efficiency Matrix Former for Controlled Release of Drugs. Pharmaceutics . 2021 Jul 10;13(7):1057.

Gao J, Karp JM, Langer R, Joshi N. The future of drug delivery. Chem Mater. 2023 Jan 24;35(2):359-63.

Gao L, Guo Q, Lin H, Pan D, Huang X, Lin J, et al. Modeling of lactose enzymatic hydrolysis using Monte Carlo method. Electron J Biotechnol. 2019 Jul 1;40:78-83.

Geraili A, Xing M, Mequanint K. Design and fabrication of drug‐delivery systems toward adjustable release profiles for personalized treatment. View. 2021 Oct;2(5):20200126.

Gonçalves-Araújo T, Rajabi-Siahboomi AR, Caraballo I. Polymer percolation threshold in HPMC extended release formulation of carbamazepine and verapamil HCl. AAPS PharmSciTech. 2010 Jun;11:558-62.

Gomes Filho MS, Oliveira FA, Barbosa MA. A statistical mechanical model for drug release: Investigations on size and porosity dependence. Phys A: Statistical Mechanics and its Applications. 2016 Oct 15;460:29-37.

Grund J, Koerber M, Walther M, Bodmeier R. The effect of polymer properties on direct compression and drug release from water-insoluble controlled release matrix tablets. International journal of pharmaceutics . 2014 Jul 20;469(1):94-101.

Han R, Xiong H, Ye Z, Yang Y, Huang T, Jing Q, et al. Predicting physical stability of solid dispersions by machine learning techniques. J Controlled Release . 2019 Oct 1;311:16-25.

Han Y, Shchukin D, Fernandes P, Mutihac RC, Möhwald H. Mechanism and kinetics of controlled drug release by temperature stimuli responsive protein nanocontainers. Soft Matter . 2010;6(19):4942-7.

Herrmann IK, Wood MJ, Fuhrmann G. Extracellular vesicles as a next-generation drug delivery platform. Nat Nanotechnol. 2021 Jul;16(7):748-59.

Hoffman RM. The hair follicle as a gene therapy target. Nat Biotechnol . 2000 Jan;18(1):20-1.

Hu Y, Kim Y, Jeong JP, Park S, Shin Y, Hong IK, et al. Novel temperature/pH-responsive hydrogels based on succinoglycan/poly (N-isopropylacrylamide) with improved mechanical and swelling properties. Eur Polym J. 2022 Jul 5;174:111308.

Huang J, Goolcharran C, Ghosh K. A quality by design approach to investigate tablet dissolution shift upon accelerated stability by multivariate methods. European Journal of Pharmaceutics and Biopharmaceutics. 2011 May 1;78(1):141-50.

Hughes BD. Random walks and random environments. Oxford University Press; 1996 Jun 13.

Hwang KM, Cho CH, Tung NT, Kim JY, Rhee YS, Park ES. Release kinetics of highly porous floating tablets containing cilostazol.European Journal of Pharmaceutics and Biopharmaceutics. 2017 Jun 1;115:39-51.

Islam MA, Barua S, Barua D. A multiscale modeling study of particle size effects on the tissue penetration efficacy of drug-delivery nanoparticles. BMC Syst Biol. 2017 Dec;11:1-3.

Jagusiak A, Chlopas K, Zemanek G, Wolski P, Panczyk T. Controlled release of doxorubicin from the drug delivery formulation composed of single-walled carbon nanotubes and congo red: A molecular dynamics study and dynamic light scattering analysis. Pharmaceutics. 2020 Jul 3;12(7):622. Pharmaceutics , 12. https://api.semanticscholar.org/CorpusID:220412589

» https://api.semanticscholar.org/CorpusID:220412589

Jiang X, Abedi K, Shi J. Polymeric nanoparticles for RNA delivery. Reference Module in Mater Sci Mater Eng. 2021.

Jimenez-Jimenez S, Hashimoto K, Santana O, Aguirre J, Kuchitsu K, Cárdenas L. Emerging roles of tetraspanins in plant inter-cellular and inter-kingdom communication. Plant signaling & behavior. 2019 Apr 3;14(4):e1581559.

Juszczyk E, Kulinowski P, Baran E, Birczyński A, Klaja J, Majda D, et al. Hydration Patterns in Sodium Alginate Polymeric Matrix Tablets-The Result of Drug Substance Incorporation. Materials. 2021 Jan;14(21):6531.

Khizer Z, Nirwan JS, Conway BR, Ghori MU. Okra (Hibiscus esculentus) gum based hydrophilic matrices for controlled drug delivery applications: Estimation of percolation threshold. International journal of biological macromolecules. 2020 Jul 15;155:835-45.

Kambayashi A. In Silico Modeling Approaches Coupled with In Vitro Characterization in Predicting In Vivo Performance of Drug Delivery System Formulations. Mol Pharm. 2023 Jul 31;20(9):4344-53.

Kaoui B. Computer simulations of drug release from a liposome into the bloodstream. Eur Phys J E. 2018 Feb;41:1-6.

Kashkooli FM, Soltani M, Souri M. Controlled anti-cancer drug release through advanced nano-drug delivery systems: Static and dynamic targeting strategies. J Controlled Release . 2020 Nov 10;327:316-49

Kaur P, Jiang X, Duan J, Stier E. Applications of in vitro-in vivo correlations in generic drug development: case studies. The AAPS Journal. 2015 Jul;17:1035-9.

Kimura G, Puchkov M, Leuenberger H. An attempt to calculate in silico disintegration time of tablets containing mefenamic acid, a low water-soluble drug. Journal of pharmaceutical sciences. 2013 Jul 1;102(7):2166-78.

Kobryń J, Sowa S, Gasztych M, Dryś A, Musiał W. Influence of hydrophilic polymers on the factor in weibull equation applied to the release kinetics of a biologically active complex of Aesculus hippocastanum. Int J Polym Sci. 2017;2017.

Kocaaga B, Guner FS, Kurkcuoglu O. Molecular dynamics simulations can predict the optimum drug loading amount in pectin hydrogels for controlled release. Mater Today Commun. 2022 Jun 1;31:103268.

Koomullil R, Tehrani B, Goliwas K, Wang Y, Ponnazhagan S, Berry J, Deshane J. Computational simulation of exosome transport in tumor microenvironment. Frontiers in Medicine. 2021 Apr 13;8:643793.

Kosmidis K, Argyrakis P, Macheras P. A reappraisal of drug release laws using Monte Carlo simulations: the prevalence of the Weibull function. Pharm Res. 2003a Jul;20:988-95.

Kosmidis K, Argyrakis P, Macheras P. Fractal kinetics in drug release from finite fractal matrices. J Chem Phys. 2003b Sep 22;119(12):6373-7.

Kosmidis K, Dassios G. Monte Carlo simulations in drug release. J Pharmacokinet Pharmacodyn. 2019 Apr 1;46:165-72.

Kosmidis K, Macheras P. Monte Carlo simulations for the study of drug release from matrices with high and low diffusivity areas. Int J Pharm . 2007 Oct 1;343(1-2):166-72.

Kosmidis K, Rinaki E, Argyrakis P, Macheras P. Analysis of Case II drug transport with radial and axial release from cylinders. Int J Pharm . 2003 Mar 26;254(2):183-8.

Kroese DP, Taimre T, Botev ZI. Handbook of monte carlo methods. John Wiley & Sons; 2013 Jun 6.

Kulagin AE, Shapovalov AV. Analytical description of the diffusion in a cellular automaton with the Margolus neighbourhood in terms of the two-dimensional Markov chain. Mathematics. 2023 Jan 22;11(3):584.

Kulinowski P, Hudy W, Mendyk A, Juszczyk E, Węglarz WP, Jachowicz R, et al. The relationship between the evolution of an internal structure and drug dissolution from controlled-release matrix tablets. Aaps Pharmscitech. 2016 Jun;17:735-42

Kulinowski P, Młynarczyk A, Jasiński K, Talik P, Gruwel ML, Tomanek B, et al. Magnetic resonance microscopy for assessment of morphological changes in hydrating hydroxypropylmethylcellulose matrix tablets in situ-is it possible to detect phenomena related to drug dissolution within the hydrated matrices? Pharm Res . 2014 Sep;31:2383-92.

Laaksonen H, Hirvonen J, Laaksonen T. Cellular automata model for swelling-controlled drug release. Int J Pharm . 2009 Oct 1;380(1-2):25-32.

Landau D, Binder K. A guide to Monte Carlo simulations in statistical physics. Cambridge University Press. 2021 Jul 29.

Langer R. New methods of drug delivery. Science. 1990 Sep 28;249(4976):1527-33.

Lemos HD, Prado LD, Rocha HV. Use of biorelevant dissolution media in dissolution tests as a predictive method of oral bioavailability. Braz J Pharm Sci . 2022 Jul 13;58:e19759.

Lenzini S, Bargi R, Chung G, Shin JW. Matrix mechanics and water permeation regulate extracellular vesicle transport. Nat Nanotechnol . 2020 Mar;15(3):217-23.

Liang J, Pitsillou E, Ververis K, Guallar V, Hung A, Karagiannis TC. Small molecule interactions with the SARS-CoV-2 main protease: In silico all-atom microsecond MD simulations, PELE Monte Carlo simulations, and determination of in vitro activity inhibition. J Mol Graphics Modell. 2022 Jan 1;110:108050.

Liang X, Bos C, Hermans M, Richardson I. An improved cellular automata solidification model considering kinetic undercooling. Metall Mater Trans B. 2023 Jun;54(3):1088-98.

Liao J, Hou B, Huang H. Preparation, properties and drug controlled release of chitin-based hydrogels: An updated review. Carbohydr Polym. 2022 May 1;283:119177.

Liu Y, Bravo KM, Liu J. Targeted liposomal drug delivery: a nanoscience and biophysical perspective. Nanoscale Horiz. 2021;6(2):78-94.

Ma J, Lin P. Simulation approach for random diffusion of chloride in concrete under sustained load with cellular automata. Materials. 2022 Jun 21;15(13):4384.

Macha IJ, Ben-Nissan B, Vilchevskaya EN, Morozova AS, Abali BE, Müller WH, et al. Drug delivery from polymer-based nanopharmaceuticals-an experimental study complemented by simulations of selected diffusion processes. Frontiers in bioengineering and biotechnology. 2019 Mar 8;7:37.

Mackie JS, Meares P. The diffusion of electrolytes in a cation-exchange resin membrane I. Theoretical. Proceedings of the Royal Society of London. Series A. Math Phys Sci. 1955 Nov 22;232(1191):498-509.

Maghsoodi M, Barghi L. Polymer percolation threshold in multi-component HPMC matrices tablets. Advanced Pharmaceutical Bulletin. 2011 Jun;1(1):27.

Manaia EB, Abuçafy MP, Chiari-Andréo BG, Silva BL, Oshiro Junior JA, Chiavacci LA. Physicochemical characterization of drug nanocarriers. Int J Nanomed . 2017 Jul 13:4991-5011.

Mandal AS, Biswas N, Karim KM, Guha A, Chatterjee S, Behera M, et al. Drug delivery system based on chronobiology-A review. J Controlled Release . 2010 Nov 1;147(3):314-25.

Malonis P, Lagaros ND. Reliability-based structural optimization using neural networks and Monte Carlo simulation. Computer Methods in Applied Mechanics and Engineering. 2002 Jun 7;191(32):3491-507.

Martín-Camacho UJ, Rodríguez-Barajas N, Sánchez-Burgos JA, Pérez-Larios A. Weibull β value for the discernment of drug release mechanism of PLGA particles. Int J Pharm . 2023 Jun 10;640:123017.

Martínez L, Betz G, Villalobos R, Melgoza L, Young PM. Correlation between compactibility values and excipient cluster size using an in silico approach. Drug Development and Industrial Pharmacy. 2013 Feb 1;39(2):374-81.

Martínez L, Villalobos R, Sánchez M, Cruz J, Ganem A, Melgoza LM. Monte Carlo simulations for the study of drug release from cylindrical matrix systems with an inert nucleus. Int J Pharm . 2009 Mar 18;369(1-2):38-46.

Mason LM, Campiñez MD, Pygall SR, Burley JC, Gupta P, Storey DE, et al. The influence of polymer content on early gel-layer formation in HPMC matrices: The use of CLSM visualisation to identify the percolation threshold. Eur J Pharm Biopharm. 2015 Aug 1;94:485-92.

Medina P, Carrasco SC, Jofré MS, Rogan J, Valdivia JA. Characterizing diffusion processes in city traffic. Chaos, Solitons & Fractals. 2022 Dec 1;165:112846.

O’Farrell C, Simmons MJ, Batchelor HK, Stamatopoulos K. The effect of biorelevant hydrodynamic conditions on drug dissolution from extended-release tablets in the dynamic colon model. Pharmaceutics . 2022 Oct 14;14(10):2193.

Pannier AK, Shea LD. Controlled release systems for DNA delivery. Mol Ther. 2004 Jul 1;10(1):19-26.

Papadopoulou V, Kosmidis K, Vlachou M, Macheras P. On the use of the Weibull function for the discernment of drug release mechanisms. Int J Pharm . 2006 Feb 17;309(1-2):44-50.

Park H, Otte A, Park K. Evolution of drug delivery systems: From 1950 to 2020 and beyond. J Controlled Release . 2022 Feb 1;342:53-65.

Park K. Controlled drug delivery systems: past forward and future back. J Controlled Release . 2014 Sep 28;190:3-8.

Pawłowska M, Sikorski A. Monte carlo study of the percolation in two-dimensional polymer systems. J Mol Model. 2013 Oct;19:4251-8.

Peppas NA, Franson NM. The swelling interface number as a criterion for prediction of diffusional solute release mechanisms in swellable polymers. J Polym Sci, Polym Phys Ed. 1983 Jun;21(6):983-97.

Peraman R, Bhadraya K, Padmanabha Reddy Y. Analytical quality by design: a tool for regulatory flexibility and robust analytics. Int J Anal Chem. 2015 Feb 2;2015.

Pérez-Mas L, Martín-Molina A, Quesada-Pérez M, Moncho-Jordá A. Maximizing the absorption of small cosolutes inside neutral hydrogels: steric exclusion versus hydrophobic adhesion. Phys Chem Chem Phys. 2018;20(4):2814-25.

Polanowski P, Sikorski A. Diffusion of small particles in polymer films. J Chem Phys . 2017 Jul 7;147(1).

Politis SN, Colombo P, Colombo G, Rekkas DM. Design of experiments (DoE) in pharmaceutical development. Drug Dev Ind Pharm. 2017 Jun 3;43(6):889-901.

Poornima G, Harini K, Pallavi P, Gowtham P, Girigoswami K, Girigoswami A. RNA-A choice of potential drug delivery system. Int J Polym Mater Polym Biomater. 2023 Jul 3;72(10):778-92.

Pramanik A, Garg S. Design of diffusion‐controlled drug delivery devices for controlled release of Paclitaxel. Chem Biol Drug Des. 2019 Aug;94(2):1478-87.

Pramod K, Tahir MA, Charoo NA, Ansari SH, Ali J. Pharmaceutical product development: A quality by design approach. Int J Pharm Invest. 2016 Jul;6(3): 129.

Queiroz AL, Wood B, Faisal W, Farag F, Garvie-Cook H, Glennon B, Vucen S, Crean AM. Application of percolation threshold to disintegration and dissolution of ibuprofen tablets with different microcrystalline cellulose grades. International Journal of Pharmaceutics . 2020 Nov 15;589:119838.

Quesada-Pérez M, Maroto-Centeno JA, Ramos-Tejada MD, Martín-Molina A. Coarse-grained simulations of solute diffusion in crosslinked flexible hydrogels. Macromolecules . 2022 Feb

Quesada-Pérez M, Martín-Molina A. Monte Carlo simulation of thermo-responsive charged nanogels in salt-free solutions. Soft Matter . 2013;9(29):7086-94.

Quesada-Pérez M, Martín-Molina A. Solute diffusion in gels: thirty years of simulations. Adv Colloid Interface Sci. 2021 Jan 1;287:102320.

Ranjan A, Jha PK. Studying drug release through polymeric controlled release formulations in United States pharmacopoeia 2 apparatus using multiphysics simulation and experiments. Mol Pharm . 2021 May 31;18(7):2600-11.

Reichl LE. A modern course in statistical physics. John Wiley & Sons; 2016 May 31.

Robert CP, Casella G, Casella G. Monte Carlo statistical methods. New York: Springer; 1999 Aug.

Romischke J, Scherkus A, Saemann M, Krueger S, Bader R, Kragl U, et al. Swelling and mechanical characterization of polyelectrolyte hydrogels as potential synthetic cartilage substitute materials. Gels. 2022 May 12;8 (5) : 296.

Russo V, Grénman H, Salmi T, Tesser R. A novel approach to inulin depolymerization: A Monte Carlo based model. Chem Eng Sci. 2022 Jul 20;256:117712.

Ryu JY, Won EJ, Lee HA, Kim JH, Hui E, Kim HP, et al. Ultrasound-activated particles as CRISPR/Cas9 delivery system for androgenic alopecia therapy. Biomaterials. 2020 Feb 1;232:119736.

Santana R, Zuluaga R, Gañán P, Arrasate S, Onieva E, González-Díaz H. Predicting coated-nanoparticle drug release systems with perturbation-theory machine learning (PTML) models. Nanoscale. 2020;12(25):13471-83.

Sarrut D, Etxebeste A, Munoz E, Krah N, Letang JM. Artificial intelligence for Monte Carlo simulation in medical physics. Front Phys. 2021 Oct 28;9:738112.

Sawilowsky SS. You think you’ve got trivials?. Journal of Modern Applied Statistical Methods. 2003;2: 218-225.

Senapati S, Upadhyaya A, Dhruw S, Giri D, Maiti P. Controlled DNA delivery using poly (lactide) nanoparticles and understanding the binding interactions. J Phys Chem B . 2021 Aug 26;125(35):10009-17.

Seo JH, Mittal R. Computational modeling of drug dissolution in the human stomach. Front Phys . 2022 Jan 10;12:755997.

Sercombe L, Veerati T, Moheimani F, Wu SY, Sood AK, Hua S. Advances and challenges of liposome assisted drug delivery. Front Pharm. 2015 Dec 1;6:163819.

Siepmann J, Siegel RA, Rathbone MJ. Fundamentals and applications of controlled release drug delivery. New York: Springer; 2012 Jan 1.

Tolia G, Li SK. Study of drug release and tablet characteristics of silicone adhesive matrix tablets. European journal of pharmaceutics and biopharmaceutics . 2012 Nov 1;82(3):518-25.

Tracy T, Wu L, Liu X, Cheng S, Li X. 3D printing: Innovative solutions for patients and pharmaceutical industry. Int J Pharm . 2023 Jan 25;631:122480.

Vaitukaitis P, Maggiolo D, Remmelgas J, Abrahmsén-Alami S, Bernin D, Siiskonen M, et al. Water transport and absorption in pharmaceutical tablets-a numerical study. Meccanica. 2020 Feb;55:421-33.

Vernon-Carter EJ, Meraz M, Bello-Perez LA, Alvarez-Ramirez J. Analysis of starch digestograms using Monte Carlo simulations. Carbohydr Polym . 2022 Sep 1;291:119589.

Villalobos R, V Garcia E, Quintanar D, M Young P. Drug release from inert spherical matrix systems using Monte Carlo simulations. Curr Drug Delivery. 2017 Feb 1;14(1):65-72.

Wahab M, Mögel HJ, Schiller P. Monte Carlo Simulations of Lipid Bilayers and Liposomes Using Coarse-Grained Models. Adv Planar Lipid Bilayers Liposomes. 2011 Jan 1 (Vol. 14, pp. 157-200). Academic Press.

Weiss GH. Random walks and their applications: Widely used as mathematical models, random walks play an important role in several areas of physics, chemistry, and biology. Am Sci. 1983 Jan 1;71(1):65-71.

Wenzel T, Stillhart C, Kleinebudde P, Szepes A. Influence of drug load on dissolution behavior of tablets containing a poorly water-soluble drug: estimation of the percolation threshold. Drug Development and Industrial Pharmacy . 2017 Aug 3;43(8):1265-75.

Wu IY, Bala S, Škalko-Basnet N, Di Cagno MP. Interpreting non-linear drug diffusion data: Utilizing Korsmeyer-Peppas model to study drug release from liposomes. Eur J Pharm Sci . 2019 Oct 1;138:105026.

Wu S, Chen Y, Qi C, Liu C, Li G, Zhu H. A 3D Monte Carlo simulation of convective diffusional deposition of ultrafine particles on fiber surfaces. Atmosphere. 2022 Aug 18;13(8):1319.

El Yacoubi S, El Jai A. Cellular automata modelling and spreadability. Mathematical and Computer Modelling. 2002 Dec 1;36(9-10):1059-74.

Yassin S, Su K, Lin H, Gladden LF, Zeitler JA. Diffusion and swelling measurements in pharmaceutical powder compacts using terahertz pulsed imaging. J Pharm Sci . 2015 May 1;104(5):1658-67.

Yekpe K, Abatzoglou N, Bataille B, Gosselin R, Sharkawi T, Simard JS, et al. Developing a quality by design approach to model tablet dissolution testing: an industrial case study. Pharm Dev Technol. 2018 Jul 3;23(6):646-54.

Yu LX, Amidon G, Khan MA, Hoag SW, Polli J, Raju GK, et al. Understanding pharmaceutical quality by design. The AAPS Journal. 2014 Jul;16:771-83.

Zhang K, Qian S, Liu Z, Liu H, Lin Z, Heng W, Gao Y, Zhang J, Wei Y. Specific surface area of mannitol rather than particle size dominant the dissolution rate of poorly water-soluble drug tablets: A study of binary mixture. International Journal of Pharmaceutics . 2024 Jul 20;660:124280.

Downloads

Published

2025-02-11

Issue

Section

Review

How to Cite

Monte Carlo simulation methods-based models for analyzing the kinetics of drug delivery from controlled release systems. (2025). Brazilian Journal of Pharmaceutical Sciences, 61. https://doi.org/10.1590/