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Theoretical modeling of long-time drug release from nitrosalicyl-imine-chitosan hydrogels through multifractal logistic type laws. (English) Zbl 1423.92065

Summary: Drug release is a complex phenomenon due to the large number of interdependent side effects that occur simultaneously, involving strong nonlinear dynamics. Therefore, since their theoretical description is difficult in the classical mathematics modelling, we have built a theoretical model based on logistic type laws, validated by the correlations with the experimental data, in a special case of drug release from hydrogels. The novelty of our approach is the implementation of multifractality in logistic type laws, situation in which any chaotic system, characterized by a small number of nonlinear interactions, gets memory and, implicitly, characterization through a large number of nonlinear interactions. In other words, the complex system polymer-drug matrix becomes “pseudo-intelligent”.

MSC:

92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
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[1] Naseri-Nosar, M.; Ziora, Z. M., Wound dressings from naturally-occurring polymers: a review on homopolysaccharide-based composites, Carbohydrate Polymers, 189, 379-398 (2018) · doi:10.1016/j.carbpol.2018.02.003
[2] Cheng, B.; Pei, B.; Wang, Z.; Hu, Q., Advances in chitosan-based superabsorbent hydrogels, RSC Advances, 7, 67, 42036-42046 (2017) · doi:10.1039/c7ra07104c
[3] Rotaru, A.; Cojocaru, C.; Cretescu, I.; Pinteala, M., Performances of clay aerogel polymer composites for oil spill sorption: experimental design and modeling, Separation and Purification Technology, 133, 260-275 (2014) · doi:10.1016/j.seppur.2014.06.059
[4] Timpu, M.-M.; Morariu, S.; Marin, L., Salicyl-imine-chitosan hydrogels: supramolecular architecturing as a crosslinking method toward multifunctional hydrogels, Carbohydrate Polymers, 165, 39-50 (2017) · doi:10.1016/j.carbpol.2017.02.027
[5] Chabbi, J.; Jennah, O.; Katir, N.; Lahcini, M.; Bousmina, M.; El Kadib, A., Aldehyde-functionalized chitosan-montmorillonite films as dynamically-assembled, switchable-chemical release bioplastics, Carbohydrate Polymers, 183, 287-293 (2018) · doi:10.1016/j.carbpol.2017.12.036
[6] Marin, L.; Ailincai, D.; Morariu, S.; Tartau-Mititelu, L., Development of biocompatible glycodynameric hydrogels joining two natural motifs by dynamic constitutional chemistry, Carbohydrate Polymers, 170, 60-71 (2017) · doi:10.1016/j.carbpol.2017.04.055
[7] Laroche, C.; Delattre, C.; Mati-Baouche, N., Bioactivity of chitosan and its derivatives, Current Organic Chemistry, 22, 7, 641-667 (2018) · doi:10.2174/1385272821666170811114145
[8] Pellá, M. C. G.; Lima-Tenório, M. K.; Tenório-Neto, E. T.; Guilherme, M. R.; Muniz, E. C.; Rubira, A. F., Chitosan-based hydrogels: from preparation to biomedical applications, Carbohydrate Polymers, 196, 233-245 (2018) · doi:10.1016/j.carbpol.2018.05.033
[9] Ailincai, D.; Tartau Mititelu, L.; Marin, L., Drug delivery systems based on biocompatible imino-chitosan hydrogels for local anticancer therapy, Drug Delivery, 25, 1, 1080-1090 (2018) · doi:10.1080/10717544.2018.1466937
[10] Marin, L.; Ailincai, D.; Mares, M., Imino-chitosan biopolymeric films: obtaining, self-assembling, surface and antimicrobial properties, Carbohydrate Polymers, 117, 762-770 (2015) · doi:10.1016/j.carbpol.2014.10.050
[11] Olaru, A.-M.; Marin, L.; Morariu, S.; Pricope, G.; Pinteala, M.; Tartau-Mititelu, L., Biocompatible chitosan based hydrogels for potential application in local tumour therapy, Carbohydrate Polymers, 179, 59-70 (2018) · doi:10.1016/j.carbpol.2017.09.066
[12] Ailincai, D.; Marin, L.; Morariu, S., Dual crosslinked iminoboronate-chitosan hydrogels with strong antifungal activity against Candida planktonic yeasts and biofilms, Carbohydrate Polymers, 152, 306-316 (2016) · doi:10.1016/j.carbpol.2016.07.007
[13] Bejan, A.; Ailincai, D.; Simionescu, B. C.; Marin, L., Chitosan hydrogelation with a phenothiazine based aldehyde: a synthetic approach toward highly luminescent biomaterials, Polymer Chemistry, 9, 18, 2359-2369 (2018) · doi:10.1039/c7py01678f
[14] Iftime, M. M.; Marin, L., Chiral betulin-imino-chitosan hydrogels by dynamic covalent sonochemistry, Ultrasonics Sonochemistry, 45, 238-247 (2018) · doi:10.1016/j.ultsonch.2018.03.022
[15] Marin, L.; Moraru, S.; Popescu, M.-C., Out-of-water constitutional self-organization of chitosan-cinnamaldehyde dynagels, Chemistry—A European Journal, 20, 16, 4814-4821 (2014) · doi:10.1002/chem.201304714
[16] Kovács, R.; Csenki, Z.; Bakos, K., Assessment of toxicity and genotoxicity of low doses of 5-fluorouracil in zebrafish ( Danio rerio) two-generation study, Water Research, 77, 201-212 (2015) · doi:10.1016/j.watres.2015.03.025
[17] Gajski, A. M.; Mititelu Tartau, L.; Pinteala, M.; Marin, L., Nitrosalicyl-imine-chitosan hydrogels based drug delivery systems for long term sustained release in local therapy, Journal of Colloid and Interface Science, 536, 196-207 (2019) · doi:10.1016/j.jcis.2018.10.048
[18] Fifere, A.; Marangoci, N.; Maier, S.; Coroaba, A.; Maftei, D.; Pinteala, M., Theoretical study on \(β\)-cyclodextrin inclusion complexes with propiconazole and protonated propiconazole, Beilstein Journal of Organic Chemistry, 8, 2191-2201 (2012) · doi:10.3762/bjoc.8.247
[19] Mandelbrot, B., The Fractal Geometry of Nature (1983), New York, NY, USA: W. H. Freeman, New York, NY, USA · Zbl 1194.30028
[20] Nottale, L., Scale Relativity and Fractal Space-Time. A New Approach to Unifying Relativity and Quantum Mechanics (2011), London, UK: Imperial College Press, London, UK · Zbl 1222.83004
[21] Merches, I.; Agop, M., Differentiability and Fractality in Dynamics of Physical Systems (2016), Singapore: World Scientific, Singapore · Zbl 1338.70001
[22] Magop, D.; Bacaita, S.; Peptu, C.; Popa, M.; Agop, M., Non-differentiability at mesoscopic scale in drug release processes from polymer microparticles, Materiale Plastice, 49, 2, 101-105 (2012)
[23] Durdureanu-Angheluta, A.; Bacaita, S.; Radu, V., Mathematical modelling of the release profile of anthraquinone-derived drugs encapsulated on magnetite nanoparticles, Revue Roumaine de Chimie, 58, 2-3, 217-221 (2013)
[24] Cioca, G.; Pinteala, M.; Bacaita, E. S., Nonlinear behaviors in gene therapy theoretical and experimental aspects, Materiale Plastice, 55, 3, 340-343 (2018)
[25] Cioca, G.; Bacaita, E. S.; Agop, M.; Lupascu Ursulescu, C., Anisotropy influences on the drug delivery mechanisms by means of joint invariant functions, Computational and Mathematical Methods in Medicine, 2017 (2017) · Zbl 1397.92278 · doi:10.1155/2017/5748273
[26] Gurlui, S.; Agop, M.; Strat, M.; Strat, G.; Bācāiţā, S., Experimental and theoretical investigations of anode double layer, Japanese Journal of Applied Physics, 44, 5, 3253-3259 (2005) · doi:10.1143/jjap.44.3253
[27] Agop, M.; Alexandroaie, D.; Cerepaniuc, A.; Bacaita, S., El Naschie’s \(ε^{(∞)}\) space-time and patterns in plasma discharge, Chaos, Solitons & Fractals, 30, 2, 470-489 (2006) · doi:10.1016/j.chaos.2005.11.072
[28] Ursu, C.; Pompilian, O. G.; Gurlui, S., \(Al_2 O_3\) ceramics under high-fluence irradiation: plasma plume dynamics through space-and time-resolved optical emission spectroscopy, Applied Physics A, 101, 1, 153-159 (2010) · doi:10.1007/s00339-010-5775-0
[29] Nica, O.; Dimitriu, D. G.; Paun, V. P.; Matasaru, P. D.; Scurtu, D.; Agop, M., Experimental and theoretical investigations of a plasma fireball dynamics, Physics of Plasma, 17, 4 (2010) · doi:10.1063/1.3381067
[30] Agop, M.; Paun, V.; Harabagiu, A., El Naschie’s \(ε^{(∞)}\) theory and effects of nanoparticle clustering on the heat transport in nanofluids, Chaos, Solitons & Fractals, 37, 5, 1269-1278 (2008) · doi:10.1016/j.chaos.2008.01.006
[31] Colotin, M.; Pompilian, G. O.; Nica, P.; Gurlui, S.; Paun, V.; Agop, M., Fractal transport phenomena through the scale relativity model, Acta Physica Polonica A, 116, 2, 157-164 (2009) · doi:10.12693/aphyspola.116.157
[32] Gurlui, G. V.; Paun, V.-P.; Casian-Botez, I.; Agop, M., The microscopic-macroscopic scale transformation through a chaos scenario in the fractal space-time theory, International Journal of Bifurcation and Chaos, 21, 2, 603-618 (2011) · doi:10.1142/s021812741102888x
[33] Gottlieb, I.; Agop, M.; Ciobanu, G.; Stroe, A., El Naschie’s \(ε^{(∞)}\) space-time and new results in scale relativity theories, Chaos, Solitons & Fractals, 30, 2, 380-398 (2006) · doi:10.1016/j.chaos.2005.11.018
[34] Stroe, M.; Nica, P.; Ioannou, P. D.; Malandraki, O.; Gavanas-Pahomi, I., El Naschie’s \(ε^{(∞)}\) space-time, hydrodynamic model of scale relativity theory and some applications, Chaos, Solitons & Fractals, 34, 5, 1704-1723 (2007) · doi:10.1016/j.chaos.2006.05.014
[35] Malandraki, C.; Nicuta, A.; Constantin, B., Dynamics control of the complex systems via nondifferentiability, Journal of Applied Mathematics, 2013 (2013) · Zbl 1397.35338 · doi:10.1155/2013/137056
[36] Nedeff, V.; Moşneguţu, E.; Panainte, M., Dynamics in the boundary layer of a flat particle, Powder Technology, 221, 312-317 (2012) · doi:10.1016/j.powtec.2012.01.019
[37] Agop, M.; Nica, P.; Gîrţu, M., On the vacuum status in Weyl-Dirac theory, General Relativity and Gravitation, 40, 1, 35-55 (2008) · Zbl 1136.83320 · doi:10.1007/s10714-007-0519-y
[38] Agop, M.; Murgulet, C., El Naschie’s \(ε^{(∞)}\) space-time and scale relativity theory in the topological dimension D = 4, Chaos, Solitons & Fractals, 32, 3, 1231-1240 (2007) · doi:10.1016/j.chaos.2006.09.038
[39] Gottlieb, I.; Agop, M.; Jarcǎu, M., El Naschie’s cantorian space-time and general relativity by means of Barbilian’s group, Chaos, Solitons & Fractals, 19, 4, 705-730 (2004) · Zbl 1064.83538 · doi:10.1016/s0960-0779(03)00244-3
[40] Agop, M.; Ioannou, P.; Nica, P.; Radu, C.; Alexandru, A.; Vizureanu, P., Fractal characteristics of the solidification process, Materials Transactions, 45, 3, 972-975 (2004) · doi:10.2320/matertrans.45.972
[41] Agop, M.; Griga, V.; Ciobanu, B., Gravity and cantorian space-time, Chaos, Solitons & Fractals, 9, 7, 1143-1181 (1998) · Zbl 0976.83027 · doi:10.1016/s0960-0779(98)80005-2
[42] Ciubotariu, C.; Agop, M., Absence of a gravitational analog to the Meissner effect, General Relativity and Gravitation, 28, 4, 405-412 (1996) · Zbl 0851.53070 · doi:10.1007/bf02105084
[43] Agop, M.; Nica, P. E.; Gurlui, S.; Focsa, C.; Paun, V. P.; Colotin, M., Implications of an extended fractal hydrodynamic model, European Physical Journal D, 56, 3, 405-419 (2010) · doi:10.1140/epjd/e2009-00304-5
[44] Szajdzinska-Pietek, E.; Pinteala, M.; Schlick, S., Monitoring pH-dependent conformational changes in aqueous solutions of poly(methacrylic acid)-b-polydimethylsiloxane copolymer based on fluorescence spectra of pyrene and 1,3-bis(1-pyrenyl)propane, Polymer, 45, 12, 4113-4120 (2004) · doi:10.1016/j.polymer.2004.03.101
[45] Marin, L.; Popescu, M. C.; Zabulica, A.; Uji-I, H.; Fron, E., Chitosan as matrix for bio-polymer dispersed liquid crystal systems, Carbohydrate Polymers, 95, 1, 16-24 (2013) · doi:10.1016/j.carbpol.2013.02.028
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