Intermolecular interactions play a role in the distribution and transport of charged contrast agents in a cartilage model

Autoři: Jenny Algotsson aff001;  Peter Jönsson aff001;  Jan Forsman aff002;  Daniel Topgaard aff001;  Olle Söderman aff001
Působiště autorů: Division of Physical Chemistry, Lund University, Lund, Sweden aff001;  Division of Theoretical Chemistry, Lund University, Lund, Sweden aff002
Vyšlo v časopise: PLoS ONE 14(10)
Kategorie: Research Article


The transport and distribution of charged molecules in polyelectrolyte solutions are of both fundamental and practical importance. A practical example, which is the specific subject addressed in the present paper, is the transport and distribution of charged species into cartilage. The charged species could be a contrast agent or a drug molecule involved in diagnosis or treatment of the widespread degenerative disease osteoarthritis, which leads to degradation of articular cartilage. Associated scientific issues include the rate of transport and the equilibrium concentrations of the charged species in the cartilage and the synovial fluid. To address these questions, we present results from magnetic resonance micro-imaging experiments on a model system of articular cartilage. The experiments yield temporally and spatially resolved data on the transport of a negatively charged contrast agent (charge = -2), used in medical examinations of cartilage, into a polyelectrolyte solution, which is designed to capture the electrostatic interactions in cartilage. Also presented is a theoretical analysis of the transport where the relevant differential equations are solved using finite element techniques as well as treated with approximate analytical expressions. In the analysis, non-ideal effects are included in the treatment of the mobile species in the system. This is made possible by using results from previous Monte Carlo simulations. The results demonstrate the importance of taking non-idealities into account when data from measurements of transport of charged solutes in a system with fixed charges from biological polyelectrolytes are analyzed.

Klíčová slova:

Cartilage – Magnetic resonance imaging – Mass diffusivity – Finite element analysis – Solute transport – Convection – Electrostatics


1. Mow VC, Ratcliffe A, Poole AR. Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures. Biomaterials 1992; 13: 67–97. doi: 10.1016/0142-9612(92)90001-5 1550898

2. Flik KR, Verma N, Cole BJ, Bach BR. In Cartilage Repair Strategies; Williams RJ. Ed.; Humana Press: Totowa, NJ, 2007; pp 1–12.

3. Buschmann MD, Grodzinsky AJ. A Molecular Model of Proteoglycan-Associated Electrostatic Forces in Cartilage Mechanics. Journal of Biomechanical Engineering 1995; 117: 179–192. doi: 10.1115/1.2796000 7666655

4. Buckwalter JA, Mankin HJ, Grodzinsky AJ. Articular Cartilage and Osteoarthritis. Instr. Course Lect. 2005; 54: 465–480. 15952258

5. Bashir A, Gray ML, Burstein D. Gd-DTPA2− as a measure of cartilage degradation. Magn. Reson. Med. 1996; 36: 665–673. doi: 10.1002/mrm.1910360504 8916016

6. Caravan P, Ellison JJ, McMurry TJ, Lauffer RB. Gadolinium(III) Chelates as MRI Contrast Agents: Structure, Dynamics, and Applications. Chem. Rev. 1999; 99: 2293–2352. doi: 10.1021/cr980440x 11749483

7. Bashir A, Gray ML, Hartke J, Burstein D. Nondestructive imaging of human cartilage glycosaminoglycan concentration by MRI. Magn. Reson. Med. 1999; 41: 857–865. doi: 10.1002/(sici)1522-2594(199905)41:5<857::aid-mrm1>;2-e 10332865

8. Trattnig S, Mlynárik V, Breitenseher M, Huber M, Zembesch A, Rand T, et al. MRI visualization of proteoglycan depletion in articular cartilage via intravenous administration of Gd-DTPA. Magn. Reson. Imaging 1999; 17: 577–583. doi: 10.1016/s0730-725x(98)00215-x 10231184

9. Nieminen MT, Töyräs J, Lassanen MS, Silvennoinen J, Helminen HJ, Jurvelin JS. Prediction of biomechanics proper ties of articular cartilage with quantitive magnetic resonance imaging. Journal of Biomechanics 2004; 37: 321–328. doi: 10.1016/s0021-9290(03)00291-4 14757451

10. Wang N, Chopin E, Xia Y. The effects of mechanical loading and gadolinium concentration on the change of T1 and quantification of glycosaminoglycans in articular cartilage by microscopic MRI. Phys. Med. Biol. 2013; 58: 4535–4547. doi: 10.1088/0031-9155/58/13/4535 23760174

11. Sigurdsson U, Siversson C, Lammentausta E, Svensson J, Tiderius CJ, Dahlberg LE. In vivo transport of Gd-DTPA2− into human meniscus and cartilage assessed with delayed gadolinium-enhanced MRI of cartilage (dGEMRIC). BMC Musculoskeletal Disorders 2014; 15: 226. doi: 10.1186/1471-2474-15-226 25005036

12. Söderman O, Algotsson J, Dahlberg LE, Svensson J. Biophysics and Biochemistry of Cartilage by NMR and MRI; The Royal Society of Chemistry, 2017; pp 176–190.

13. Salo EN, Nissi MJ, Kulmala KAM, Tiitu V, Töyräs J, Nieminen MT. Diffusion of Gd-DTPA2− into articular cartilage. Osteoarthritis and Cartilage 2012; 20: 117–126. doi: 10.1016/j.joca.2011.11.016 22179030

14. Bansal PN, Stewart RC, Entezari V, Snyder BD, Grinstaff MW. Contrast agent electrostatic attraction rather than repulsion to glycosaminoglycan affords a greater uptake ratio and improved quantitative CT imaging in cartilage. Osteoarthritis and Cartilage 2011; 19: 970–976. doi: 10.1016/j.joca.2011.04.004 21549206

15. Kulmala KAM, Karjalainen HM, Kokkonen HT, Tiitu V, Kovanen V, Lammi MJ, et al. Diffusion of ionic and non-ionic contrast agents in articular cartilage with increased cross-linking—Contribution of steric and electrostatic effects. Medical Engineering & Physics 2013; 35: 1415–1420.

16. Arbabi V, Pouran B, Weinans H, Zadpoor AA. Multiphasic modeling of charged solute transport across articular cartilage: Application of multi-zone finite-bath model. Journal of Biomechanics 2016; 49: 1510–1517. doi: 10.1016/j.jbiomech.2016.03.024 27033729

17. Pouran B, Arbabi V, Zadpoor AA, Weinans H. Isolated effects of external bath osmolality, solute concentration, and electric charge on solute transport across articular cartilage. Journal of Biomechanics 2016; 49: 1510–1517.

18. Algotsson J, Forsman J, Topgaard D, Söderman O. Electrostatic interactions are important for the distribution of Gd(DTPA)2− in articular cartilage. Magn. Reson. Med. 2016; 76: 500–509. doi: 10.1002/mrm.25889 26332213

19. Stell G, Joslin CG. The donnan equilibrium: a theoretical study of the effects of interionic forces. Biophys. J. 1986; 50: 855–859. doi: 10.1016/S0006-3495(86)83526-3 19431690

20. Dai H, Potter K, McFarland EW. Determination of ion activity coefficients and fixed charge density in cartilage with 23Na magnetic resonance microscopy. J. Chem. Eng. Data 1996; 41: 970–976. doi: 10.1021/je9600257

21. Algotsson J, Åkesson T, Forsman J. Monte Carlo Simulations of Donnan Equilibrium. Magn. Reson. Med. 2012; 68: 1298–1302. doi: 10.1002/mrm.24409 22890897

22. Hennig J, Nauerth A, Friedburg H. RARE imaging: A fast imaging method for clinical MR. Magn. Reson. Med. 1986; 3: 823–833. doi: 10.1002/mrm.1910030602 3821461

23. Alper JS, Gelb RI. Standard Errors and Confidence Intervals in Nonlinear Regression: Comparison of Monte Carlo and Parametric Statistics. J. Phys. Chem. 1990; 94: 4747–4751. doi: 10.1021/j100374a068

24. Cussler EL. Diffusion: Mass Transfer in Fluid Systems; Cambridge University Press, 2nd edn., 1997.

25. Vander Elst L, Sessoye A, Laurent S, Muller RN. Can the Theoretical Fitting of the Proton-Nuclear-Magnetic-Relaxation-Dispersion (Proton NMRD) Curves of Paramagnetic Complexes Be Improved by Independent Measurements of Their Self-Diffusion Coefficients? Helvetica Chimica Acta. 2005; 88: 574–587. doi: 10.1002/hlca.200590040

26. Ohshima H, Miyajima T. Evaluation of the Donnan Model for Polyelectrolytes Using the Composite Poisson-Boltzmann Equations. Colloid Polym. Sci. 1994; 272: 803–811. doi: 10.1007/BF00652421

27. Ohshima H. The Donnan Potential-Surface Potential Relationship for a Cylindrical Soft Particle in an Electrolyte Solution. J. Colloid Interface Sci. 2008; 323: 313–316. doi: 10.1016/j.jcis.2008.04.027 18502443

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