Theoretical Application of Irreversible (Nonequilibrium) Thermodynamic Principles to Enhance Solute Fluxes across Nanofabricated Hemodialysis Membranes
Objective. Nanotechnology has the potential to improve hemodialysis membrane technology. Thus, a major objective is to understand how to enhance toxic solute fluxes across these membranes. The aim of this concept building study is to review the application of irreversible thermodynamic (IT) to solute fluxes. Methods. We expanded the application of the Nernst-Planck equation to include the Kedem-Katchalsky equation, pH, membrane thickness, pore size, and electric potential as variables. Results. (1) Reducing the membrane’s thickness from 25？μm to 25？nm increased the flux of creatinine, -microglobulin, and tumor necrosis factor-α (TNF-α) by a thousand times but prevented completely albumin flux, (2) applying an electric potential of 50–400？mV across the membrane enhanced the flux of the respective molecules by , , and ？mol/s, and (3) changing the pH from 7.35 to 7.42 altered the fluxes minimally. Conclusions. The results supported an argument to investigate the application of IT to study forces of fluxes across membranes. Reducing the membrane’s thickness—together with the application of an electrical potential—qualities achievable by nanotechnology, can enhance the removal of uremic toxins by many folds. However, changing the pH at a specific membrane thickness does not affect the flux significantly. 1. Introduction Irreversible (nonequilibrium) thermodynamics (IT) is a descriptive and powerful tool to delineate the contribution of forces responsible for fluid movements across membranes. Both Soltanieh and Gill [1] and Sievertsen [2] presented excellent reviews summarizing the differences between IT and kinetic transport models. Kedem and Katchalsky [3] stressed that kinetic equations describing volume and solute flow do not fully describe a membrane’s physical behavior. They also pointed out to the quantitatively incomparable results of permeability data obtained by different methods. Kedem and Katchalsky resolved this issue by applying IT methods to address membrane transport processes. The principle is to identify the constituent, independent, and elemental processes within the system (diffusion, convection, and so forth…). Then, each process is represented by a set of flux and conjugate force, where there is a relationship between the flux (flow) and the force (free energy gradient) causing it. All these parallel processes of fluxes and conjugate forces can be summed up [4, 5]. Hemodialysis is a life-saving procedure to treat patients with kidney failure. During hemodialysis treatment, the human blood is filtered through a semipermeable membrane to
References
[1]
M. Soltanieh and W. N. Gill, “Review of reverse osmosis membranes and transport models,” Chemical Engineering Communications, vol. 12, no. 4–6, pp. 279–363, 1981.
[2]
E. Sivertsen, Membrane separation of anions in concentrated electrolytes [Ph.D. thesis], Department of Chemical Engineering, Norwegian University of Science and Technology, Trondheim, Norway, September 2001.
[3]
O. Kedem and A. Katchalsky, “Thermodynamic analysis of the permeability of biological membranes to non-electrolytes,” Biochimica et Biophysica Acta, vol. 27, pp. 229–246, 1958.
[4]
M. H. Friedman, Principles and Models of Biological Transport, Springer, New York, NY, USA, 2nd edition, 2008.
[5]
H. V. Westerhoff, K. J. Hellingwerf, J. C. Arents, B. J. Scholte, and K. Van Dam, “Mosaic nonequilibrium thermodynamics describes biological energy transduction,” Proceedings of the National Academy of Sciences of the United States of America, vol. 78, no. 6, pp. 3554–3558, 1981.
[6]
J. T. Daugirdas, P. G. Black, and T. S. Ing, Handbook of Dialysis, Lippincott Williams & Wilkins, Philadelphia, Pa, USA, 4th edition, 2007.
[7]
G. Eknoyan, G. J. Beck, A. K. Cheung et al., “Effect of dialysis dose and membrane flux in maintenance hemodialysis,” The New England Journal of Medicine, vol. 347, no. 25, pp. 2010–2019, 2002.
[8]
F. Locatelli, A. Martin-Malo, T. Hannedouche et al., “Effect of membrane permeability on survival of hemodialysis patients,” Journal of the American Society of Nephrology, vol. 20, no. 3, pp. 645–654, 2009.
[9]
J. Himmelfarb and T. A. Ikizler, “Medical progress: hemodialysis,” The New England Journal of Medicine, vol. 363, no. 19, pp. 1833–1845, 2010.
[10]
F. Lacotelli, A. Cavalli, S. M. Vigano, and G. Pontoriero, “Lessons from recent trials on hemodialysis,” in Hemodialysis: New Metods and Future Technology, C. Ronco and M. H. Rosner, Eds., vol. 171, pp. 30–38, S. Karger AG, Basel, Switzerland, 2011.
[11]
S. T. Hwang, “Nonequilibrium thermodynamics of membrane transport,” AIChE Journal, vol. 50, no. 4, pp. 862–870, 2004.
[12]
V. Nikonenko, V. Zabolotsky, C. Larchet, B. Auclair, and G. Pourcelly, “Mathematical description of ion transport in membrane systems,” Desalination, vol. 147, no. 1–3, pp. 369–374, 2002.
[13]
J. Waniewski, “Mathematical modeling of fluid and solute transport in hemodialysis and peritoneal dialysis,” Journal of Membrane Science, vol. 274, no. 1-2, pp. 24–37, 2006.
[14]
W. M. Deen, “Hindered transport of large molecules in liquid filled pores,” AIChE Journal, vol. 33, no. 9, pp. 1409–1425, 1987.
[15]
K. B. G. Sprenger, W. Kratz, A. E. Lewis, and U. Stadtmuller, “Kinetic modeling of hemodialysis, hemofiltration, and hemodiafiltration,” Kidney International, vol. 24, no. 2, pp. 143–151, 1983.
[16]
W. R. Bowen and A. W. Mohammad, “Characterization and prediction of nanofiltration membrane performance-A general assessment,” Chemical Engineering Research and Design, vol. 76, no. 8, pp. 885–893, 1998.
[17]
C. C. Striemer, T. R. Gaborski, J. L. McGrath, and P. M. Fauchet, “Charge- and size-based separation of macromolecules using ultrathin silicon membranes,” Nature, vol. 445, no. 7129, pp. 749–753, 2007.
[18]
A. Van den Berg and M. Wessling, “Nanofluidics: silicon for the perfect membrane,” Nature, vol. 445, no. 7129, p. 726, 2007.
[19]
A. C. Attaluri, Z. Huang, A. Belwalkar, W. V. Geertruyden, D. Gao, and W. Misiolek, “Evaluation of nano-porous alumina membranes for hemodialysis application,” ASAIO Journal, vol. 55, no. 3, pp. 217–223, 2009.
[20]
A. Szymczyk, C. Labbez, P. Fievet, A. Vidonne, A. Foissy, and J. Pagetti, “Contribution of convection, diffusion and migration to electrolyte transport through nanofiltration membranes,” Advances in Colloid and Interface Science, vol. 103, no. 1, pp. 77–94, 2003.
[21]
P. Dechadilok and W. M. Deen, “Hindrance factors for diffusion and convection in pores,” Industrial & Engineering Chemistry Research, vol. 45, no. 21, pp. 6953–6959, 2006.
[22]
Y. Gu and N. Miki, “A microfilter utilizing a polyethersulfone porous membrane with nanopores,” Journal of Micromechanics and Microengineering, vol. 17, no. 11, pp. 2308–2315, 2007.
[23]
W. Sparreboom, A. Van Den Berg, and J. C. T. Eijkel, “Principles and applications of nanofluidic transport,” Nature Nanotechnology, vol. 4, no. 11, pp. 713–720, 2009.
[24]
A. Power, N. Duncan, and C. Goodlad, “Advances and innovations in dialysis in the 21st century,” Postgraduate Medical Journal, vol. 85, no. 1000, pp. 102–107, 2009.
[25]
R. A. Ward, “Protein-leaking membranes for hemodialysis: a new class of membranes in search of an application?” Journal of the American Society of Nephrology, vol. 16, no. 8, pp. 2421–2430, 2005.
[26]
W. H. Fissell, H. D. Humes, A. J. Fleischman, and S. Roy, “Dialysis and nanotechnology: now, 10 years, or never?” Blood Purification, vol. 25, no. 1, pp. 12–17, 2007.
[27]
M. A. Knepper and J. A. Mindell, “Structural biology: molecular coin slots for urea,” Nature, vol. 462, no. 7274, pp. 733–734, 2009.
[28]
J. Karlsson, A. L. Ungell, J. Gr？sj？, and P. Artursson, “Paracellular drug transport across intestinal epithelia: influence of charge and induced water flux,” European Journal of Pharmaceutical Sciences, vol. 9, no. 1, pp. 47–56, 1999.
[29]
D. Perret, F. Rousseau, V. Tran, and H. Gascan, “Reversal of some viral IL-6 electrostatic properties compared to IL-6 contributes to a loss of alpha receptor component recruitment,” Proteins, vol. 60, no. 1, pp. 14–26, 2005.
[30]
N. Ferraz, D. O. Carlsson, J. Hong, et al., “Haemocompatibility and ion exchange capability of nanocellulose polypyrrole membranes intended for blood purification,” Journal of the Royal Society Interface, vol. 9, pp. 1943–1955, 2012.
[31]
K. V. Peinemann and S. Pereira-Nunes, Membrane Technology: Membranes for Life, vol. 1, Wiley, Weinheim, Germany, 2008.
[32]
K. Opatrny, “Clinical importance of biocompatibility and its effect on haemodialysis treatment,” Nephrology Dialysis Transplantation, vol. 18, no. 5, pp. V41–V44, 2003.
[33]
H. Klinkmann, P. Ivanovich, and D. Falkenhagen, “Biocompatibility: the need for a systems approach,” Nephrology Dialysis Transplantation, vol. 8, no. 2, pp. 40–42, 1993.
[34]
R. Vanholder, “Biocompatibility issues in hemodialysis,” Clinical Materials, vol. 10, no. 1-2, pp. 87–133, 1992.
[35]
W. E. Bloembergen, R. M. Hakim, D. C. Stannard et al., “Relationship of dialysis membrane and cause-specific mortality,” American Journal of Kidney Diseases, vol. 33, no. 1, pp. 1–10, 1999.
[36]
A. Santoro and E. Mancini, “Cardiac effects of chronic inflammation in dialysis patients,” Nephrology Dialysis Transplantation, vol. 17, supplement 8, pp. 10–15, 2002.
[37]
A. Hedayat, S. Yannacopoulos, and J. Postlethwaite, “Conjoint action of CO2 corrosion and reciprocating sliding wear on plain carbon steel part I—effect of contact pressure and amine inhibitor,” Corrosion, vol. 48, no. 11, pp. 953–959, 1992.
[38]
J. K. Leypoldt, “Solute fluxes in different treatment modalities,” Nephrology Dialysis Transplantation, vol. 15, no. 1, pp. 3–9, 2000.
[39]
J. Han, J. Fu, and R. B. Schoch, “Molecular sieving using nanofilters: past, present and future,” Lab on a Chip, vol. 8, no. 1, pp. 23–33, 2008.
[40]
J. C. T. Eijkel and A. V. D. Berg, “Nanotechnology for membranes, filters, and sieves. A series of mini reviews covering new trends in fundamental and applied research, and potential applications of miniaturized technologies,” Lab on a Chip, vol. 6, pp. 19–23, 2006.
[41]
K. Meyer-Rosberg, D. R. Scott, D. Rex, K. Melchers, and G. Sachs, “The effect of environmental pH on the proton motive force of Helicobacter pylori,” Gastroenterology, vol. 111, no. 4, pp. 886–900, 1996.
[42]
A. Matin, B. Wilson, E. Zychlinsky, and M. Matin, “Proton motive force and the physiological basis of delta pH maintenance in thiobacillus acidophilus,” Journal of Bacteriology, vol. 150, no. 2, pp. 582–591, 1982.
[43]
A. L. Koch, “The pH in the neighborhood of membranes generating a protonmotive force,” Journal of Theoretical Biology, vol. 120, no. 1, pp. 73–84, 1986.
[44]
O. H. Setty, R. W. Hendler, and R. I. Shrager, “Simultaneous measurements of proton motive force, delta pH, membrane potential, and H+/O ratios in intact Escherichia coli,” Biophysical Journal, vol. 43, no. 3, pp. 371–381, 1983.
[45]
S. P. Sun, K. Y. Wang, D. Rajarathman, et al., “Polyamide—imide nanofiltration hollow fiber membranes with elongation induced nano-pore evolution,” AICHE Journal, vol. 56, no. 6, pp. 1481–1494, 2010.
[46]
H. Gurland, W. Samtleben, M. J. Lysaght, and J. F. Winchester, “Extracorporeal blood purification techniques: plasmaspheres and hemoperfusion,” in Replacement of Renal Function by Dialysis, C. Jacobs, C. M. Kjellstrand, K. M. Koch, and J. F. Winchester, Eds., pp. 472–500, Kluwer Academic, Dodrecht, The Netherlands, 4th edition, 1996.
[47]
S. S. H. Rizvi, “Membrane applications in biotechnology, food processing, life sciences, and energy conversion: introduction,” in Handbook of Membrane Separations Chemical, Pharmaceutical, Food, and Biotechnological Applications, A. K. Pabby, S. S. H. Rizvi, and A. M. Sastre, Eds., p. 503, CRC Press, Boca Raton, Fla, USA, 2009.
[48]
M. A. La-Scalea, C. M. S. Menezes, and E. I. Ferreira, “Molecular volume calculation using AM1 semi-empirical method toward diffusion coefficients and electrophoretic mobility estimates in aqueous solution,” Journal of Molecular Structure, vol. 730, no. 1–3, pp. 111–120, 2005.
[49]
W. Hayduk and H. Laudie, “Prediction of diffusion coefficients for nonelectrolytes in dilute aqueous solutions,” AIChE Journal, vol. 20, pp. 611–615, 1974.
[50]
Y. Kiso, K. Muroshige, T. Oguchi et al., “Effect of molecular shape on rejection of uncharged organic compounds by nanofiltration membranes and on calculated pore radii,” Journal of Membrane Science, vol. 358, no. 1-2, pp. 101–113, 2010.
[51]
E. Barrett and T. Addis, “The Serum creatinine concentration for normal individuals,” The Journal of Clinical Investigation, vol. 26, no. 5, pp. 875–878, 1947.
[52]
M. Chelamcharla, J. K. Leypoldt, and A. K. Cheung, “Dialyzer membranes as determinants of the adequacy of dialysis,” Seminars in Nephrology, vol. 25, no. 2, pp. 81–89, 2005.
