Modeling Diffusivity Through Alginate-Based Microfibers: A Comparison of Numerical and Analytical Models Based on Empirical Spectrophotometric Data

Authors

  • Sabra Djomehri Department of Biomedical, Chemical and Materials Engineering, San Jose State University, San Jose CA 95192-0082, USA
  • Maryam Mobed-Miremadi Department of Biomedical, Chemical and Materials Engineering, San Jose State University, San Jose CA 95192-0082, USA
  • Mallika Keralapura Department of Electrical Engineering, San Jose State University, San Jose CA 95192-0082, USA

DOI:

https://doi.org/10.6000/1929-6037.2013.02.01.8

Keywords:

Alginate, diffusivity, modeling, hollow fiber, cylindrical

Abstract

The study of mass transport across hollow and solid 3D microfibers to study metabolic profiles is a key aspect of tissue engineering approach. A new modified numerical mathematical model based on Fickian equations in cylindrical coordinates has been proposed for determining the membrane diffusivity of 2% (w/v) alginate-based stents cross-linked with 10% CaCl2. Based on the economical and direct spectrophotometric measurements, using this model, inward diffusivities ranging from 5.2x10-14 m2/s 2.93x10-12m2/s were computed for solutes with Stokes radii ranging between 0.36 to 3.5 nm, diffusing through bare alginate and alginate-chitosan-alginate microfibers. In parallel an analytical solution to the cylindrical Fickian equation was derived to validate the numerical solution using experimental diffusion data from a solid stent. Excellent agreement was found between the numerical and analytical models with a maximum calculated residual value of 4%. Using these models, a flexible computational platform is proposed to conduct custom diffusion and MW cut-off characterization across micro-porous microfibers not limited to alginate in composition.

References

Park JH, Shin US, Kim HW. Alginate-microfibers produced by self-assembly in cell culture medium. Bull Korean Chem Soc 2011; 32 (2): 431-3. http://dx.doi.org/10.5012/bkcs.2011.32.2.431 DOI: https://doi.org/10.5012/bkcs.2011.32.2.431

Zhu X, Pack DW, Braatz RD. Modelling intravascular delivery from drug-elutingstents with biodurable coating: investigation of anisotropic vascular drug diffusivity and arterial drug distribution. Comput Method Biomechs 2012; 1-12. DOI: https://doi.org/10.1080/10255842.2012.672815

Moroni L, Wijn JR, van Blitterswijk CA. Polymer hollow fiber three-dimensional matrices with controllable cavity and shell thickness. Biomaterials 2006; 27(5): 5918-26. http://dx.doi.org/10.1016/j.biomaterials.2006.08.015 DOI: https://doi.org/10.1016/j.biomaterials.2006.08.015

Tamayol A, Akbari M, Annabi N, Paul A, Khadamhosseini A, Juncker D. Fiber-based tissue engineering: progress, challenges, and opportunities. Biotechnology Advances 2012 [serial on the internet]. Available from:doi 10.1016/j.biotechadv.2012.11.007 DOI: https://doi.org/10.1016/j.biotechadv.2012.11.007

Zhang S, Liu T, Chen L, Ren M, Zhang B, Wang Z, et al. Bifunctionalpolyethersulfone hollow fiber with a porous,

single-layer skin for use as a bioartificial liver bioreactor. J Mater Sci Mater Med 2012; 23: 2001-11. http://dx.doi.org/10.1007/s10856-012-4673-8 DOI: https://doi.org/10.1007/s10856-012-4673-8

Asthana A, Lee KH, Shun SJ, Perumal J, Butker L, Lee SH, et al. Bromo-oxidation reaction in enzyme-entrapped alginate hollow microfibers. Biomicrofluidics 2011 [serial on the internet]. http://dx.doi.org/10.10631/1.3605512 DOI: https://doi.org/10.1063/1.3605512

Wan J. Microfluidic-based synthesis of hydrogel particles for cell microencapsulation and cell-based drug delivery. Polymers 2012; 4(2): 1084-108. http://dx.doi.org/10.3390/polym4021084 DOI: https://doi.org/10.3390/polym4021084

Luo Y, Lode A, Gelinsky M. Direct Plotting of Three-Dimensional Hollow Fiber Scaffolds Based on Concentrated Alginate Pastes for Tissue Engineering. AdvHealthc Mater 2012 [serial on the internet]. Available from: doi:10.1002/adhm.201200303 http://dx.doi.org/10.1002/adhm.201200303 DOI: https://doi.org/10.1002/adhm.201200303

Amin S, Rajabnezhad S, Kohli K. Hydrogels as potential drug delivery systems. Sci Res Essays 2009; 3(11): 175-83.

Takka S, Gürel A. Evaluation of Chitosan/Alginate Beads Using Experimental Design: Formulation and In vitro Characterization. AAPS PharmSciTech 2010; 11(1): 460-6. http://dx.doi.org/10.1208/s12249-010-9406-z DOI: https://doi.org/10.1208/s12249-010-9406-z

Barralet JE, Wang L, Lawson M, Triffitt JT, Cooper PR, Shekton RM. Comparison of bone marrow cell growth on 2D and 3D alginate hydrogels. J Mater Sci Mater Med 2005; 16: 515-19. http://dx.doi.org/10.1007/s10856-005-0526-z DOI: https://doi.org/10.1007/s10856-005-0526-z

Mobed-Miremadi M, Asthi A, Nagendra R, Varma R. Alginate-Chitosan-Alginate Microcapsules for Oral Administration: 2009. Proceedings of the American Institute of Chemical Engineering Conference; Nashville, Tenessee, USA. Available from: www3.aiche.org/Proceedings/Extended Abstract.aspc?PaperID=170186

Kwok WY, Kiparissides C, Yuet P, Harrris JT, Goosen MFA. Mathematical modelling of protein diffusion in microcapsules: A comparison with results. Can J Chem Eng 1991; 69(1): 361-70. http://dx.doi.org/10.1002/cjce.5450690144 DOI: https://doi.org/10.1002/cjce.5450690144

Goosen MFA. Fundamentals of Animal Cell Encapsulation and Immobilization. 1st ed. Boca Raton: CRC Press 1992.

Westrin B, Axelsson A, Zacchi G. Diffusion measurement in gels - A review. J Controlled Release 1994; 30: 189. http://dx.doi.org/10.1016/0168-3659(94)90025-6 DOI: https://doi.org/10.1016/0168-3659(94)90025-6

Wang N, Adams G, Buttery L, Falcone FH, Stolnik S. Alginate encapsulation technology supports embryonic stem cells differentiation into insulin-producing cells. J Biotechnol 2009; 144(4): 304-12. http://dx.doi.org/10.1016/j.jbiotec.2009.08.008 DOI: https://doi.org/10.1016/j.jbiotec.2009.08.008

Yu G, Fan Y. Preparation of poly(D,L-lactic acid) scaffolds using alginate particles. J Biomater Sci - Polym Ed 2008; 19(1): 87-98. http://dx.doi.org/10.1163/156856208783227703 DOI: https://doi.org/10.1163/156856208783227703

Hsiong SX, Cooke PH, Kong H, Fishman ML, Ericsson M, Mooney DJ. AFM Imaging of RGD Presenting Synthetic Extracellular Matrix Using Gold Nanoparticles. Macromol Biosci 2008; 8(6): 469-77. http://dx.doi.org/10.1002/mabi.200700313 DOI: https://doi.org/10.1002/mabi.200700313

McGinty S, McKee S. Modelling drug-eluting stents. Math Med Biol 2011; 28: 1-29. http://dx.doi.org/10.1093/imammb/dqq003 DOI: https://doi.org/10.1093/imammb/dqq003

Li RH, Altreuter DH, Gentile FT. Transport characterization of hydrogel matrices for cell encapsulation. Biotech Bioeng 1995; 50: 365-73. http://dx.doi.org/10.1002/(SICI)1097-0290(19960520)50:4<365::AID-BIT3>3.0.CO;2-J DOI: https://doi.org/10.1002/(SICI)1097-0290(19960520)50:4<365::AID-BIT3>3.0.CO;2-J

Russo R, Malinconico M, Santagata G. Effect of Cross-Linking with Calcium Ions on the Physical Properties of Alginate Flms. Biomacromolecules 2007; 8(10): 3193. http://dx.doi.org/10.1021/bm700565h DOI: https://doi.org/10.1021/bm700565h

Flynn G, Yalkowsky S, Roseman T. Mass transport phenomena and models: theoretical concepts. J Pharm Sci 1974; 63(4): 479-10. http://dx.doi.org/10.1002/jps.2600630403 DOI: https://doi.org/10.1002/jps.2600630403

Tanaka H, Matsumara M, Veliky IA. Diffusion characteristics of substrates in Ca-alginate gel beads. Biotech Bioeng 1984; 26(1): 53-8. http://dx.doi.org/10.1002/bit.260260111 DOI: https://doi.org/10.1002/bit.260260111

Carslaw H, Jaeger J. Conduction of Heat in Solids. 2nd ed. Oxford: Oxford University Press 1959.

Fick A. Ṹber diffusion. Ann Physik Leipzig 1855; 170: 59-86. http://dx.doi.org/10.1002/andp.18551700105 DOI: https://doi.org/10.1002/andp.18551700105

Carnahan B, Luther HA, Wilkes JO. Applied Numerical Methods. New York: Wiley&Son 1969.

Crank J. The Mathematics of Diffusion, 2nd ed. Oxford: Clarendon Press 1975.

Lakshminarayanakh N. Transport Phenomena in Membranes. New York: Academic Press 1969.

Wang Q, Zhang N, Hu X, Yang J, Du Y. Alginate/polyethylene glycol blend fibers and their properties for drug controlled release. J Biomed Mater Res A 2007; 82A(1): 122-28. http://dx.doi.org/10.1002/jbm.a.31075 DOI: https://doi.org/10.1002/jbm.a.31075

Lin YS, Huang KS, Yang CH, Wang CY, Yang YS, Hsu HS, et al. Microfluidic Synthesis of Microfibers for Magnetic-Responsive Controlled Drug Release and Cell Culture. PLoS One 2012 [serial on the internet]. Available from: doi: 10.1371/journal.pone.0033184. http://dx.doi.org/10.1371/journal.pone.0033184 DOI: https://doi.org/10.1371/journal.pone.0033184

Meyer U, Meyer T, Handschel J, W HP. Fundamentals of Tissue Engineering and Regenerative Medicine. 1st ed. New York: Springer Verlag 2009. http://dx.doi.org/10.1007/978-3-540-77755-7 DOI: https://doi.org/10.1007/978-3-540-77755-7

Mobed-Miremadi M, Asi B, Parasseril J, Wong E, Tat M, Shan Y. Comparative diffusivity measurments for alginate-based atomized and inkjet-bioprinted artificial cells using fluorescence microscopy. Artif Cells Nanomed Biotech 2012. [serial on the internet]. Available from: doi 10.3109/10731199.2012.716064. http://dx.doi.org/10.3109/10731199.2012.716064 DOI: https://doi.org/10.3109/10731199.2012.716064

Andersen T, Strand BL, Formo K, Alsberg E, Christensen BE. Alginates as biomaterials in tissue engineering. Carbohydrate Chem: Chem Biol Approach 2012; 37: 227-58. http://dx.doi.org/10.1039/9781849732765-00227 DOI: https://doi.org/10.1039/9781849732765-00227

Zheng SJ, Wu H. Generation of alginate microfibers with a roller-assisted microfluidic system. Lab Chip 2009; 9(7): 996-1001. http://dx.doi.org/10.1039/b813518e DOI: https://doi.org/10.1039/B813518E

Takei T, Sakai S, Yokonuma T, Ijima H, Kawakami K. Fabrication of artificial endothelialized tubes with predetermined three-dimensional configuration from flexible cell-enclosing alginate fibers. Biotech Prog 2007; 23(1): 182-6. http://dx.doi.org/10.1021/bp060152j DOI: https://doi.org/10.1021/bp060152j

Lee KH, Shin SJ, Park Y, Leee SH. Synthesis of cell-laden alginate hollow fibers using microfluidic chips and microvascularized tissue-engineering applications. Small Volume 2009; 5: 1264-68. http://dx.doi.org/10.1002/smll.200801667 DOI: https://doi.org/10.1002/smll.200801667

Riggio C, Ciofani G, Raffa V, Bossi S, Micera S, Cushieri A. Polymeric Thin Film Technology for Neural Interfaces: review and Perspectives. In: Hashim AA editor. Polymeric Thin

Films. Intech 2010. Available for free access at: http/www.intechopen.com/books/polymeric-thin-films/polymeric-thin-film-technology-for-neural interfaces-review-and-perspectives.

Pontrelli G, de Monte F. A multi-layer porous wall model for coronary drug-eluting stents. Int J Heat Mass Transfer 2010; 53(19-20): 3629-37. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.03.031 DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2010.03.031

Wehry EL. Molecular Fluorescence and Phosphorescence Spectrometry. In: Settle FA. Handbook of Instrumental Techniques for Analytical Chemistry. 1st ed. National Science Foundation, Arlington, Virginia: Prentice Hall PTR (ECS Professional) 1997; pp. 507-536.

Downloads

Published

2013-02-27

How to Cite

Djomehri, S., Mobed-Miremadi, M., & Keralapura, M. (2013). Modeling Diffusivity Through Alginate-Based Microfibers: A Comparison of Numerical and Analytical Models Based on Empirical Spectrophotometric Data. Journal of Membrane and Separation Technology, 2(1), 74–87. https://doi.org/10.6000/1929-6037.2013.02.01.8

Issue

Section

Articles