Transport in Porous Media

, Volume 92, Issue 1, pp 119–143

Modeling Concentration Distribution and Deformation During Convection-Enhanced Drug Delivery into Brain Tissue

  • Karen H. Støverud
  • Melanie Darcis
  • Rainer Helmig
  • S. Majid Hassanizadeh
Article

Abstract

Convection-enhanced drug delivery is a technique where a therapeutic agent is infused under positive pressure directly into the brain tissue. For predicting the final concentration distribution and optimizing infusion rate and catheter placement, numerical models can be of great help. However, despite advances in modeling this process, often the infused agent does not reach the targeted region prescribed in the modeling phase. In this study, patient-specific brain structure and parameters, obtained from diffusion tensor imaging (DTI), are implemented in a numerical model which describes the flow and transport in an elastic deformable matrix. To our knowledge, this is the first time that information from DTI is used in a numerical model which includes both transport of a therapeutic agent and tissue deformation. Fractional anisotropy (FA) is used to distinguish between gray and white matter and tortuosity to differentiate between inside and outside the brain tissue. One voxel in the DT-image is represented by one element of the numerical grid. The DT-images were in addition used to determine the orientation of the white matter fiber tracts and calibrate permeability and diffusion coefficients found in the literature. Values chosen for the porosity and Lamé parameters are also based on those found in the literature. Given realistic literature values, the calibration of the permeability and diffusion tensors are shown to be successful. Our result shows that preferential flow occur in direction of the white matter fiber tracts. The current model assumes linear deformation, corresponding to small porosity changes. But, because large porosity changes occur that may adversely affect drug transport, non-linear deformations should be included in the future.

Keywords

Convection-enhanced delivery Poro-elasticity Diffusion tensor imaging Brain tissue 

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References

  1. Baish J.W., Netti P.A., Jain R.K.: Transmural coupling of fluid flow in microcirculatory network and interstitium in tumors. Microvasc. Res. 53, 128–141 (1997)CrossRefGoogle Scholar
  2. Basser P.: Interstitial pressure, volume, and flow during infusion into brain tissue. Microvas. Res. 44, 143–165 (1992)CrossRefGoogle Scholar
  3. Basser P., Pierpaoli C.: Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor mri. J. Magn. Reson. B 111, 209–219 (1996)CrossRefGoogle Scholar
  4. Basser P., Mattiello J., Lebihan D.: Mr diffusion tensor spectroscopy and imaging. Biophys. J. 66, 259–267 (1994a)CrossRefGoogle Scholar
  5. Basser P., Mattielo J., Lebihan D.: Estimation of the effective self-diffusion tensor from the nmr spin-echo. J. Magn. Reson. B 103, 247–254 (1994b)CrossRefGoogle Scholar
  6. Baxter L., Jain R.: Transport of fluid and macromolecules in tumors; the role of interstitial pressure and convection. Microvasc. Res. 37, 77–104 (1989)CrossRefGoogle Scholar
  7. Bender B., Klose U.: Cerebrospinal fluid and interstitial fluid volume measurements in the human brain at 3t with epi. Magn. Reson. Med. 61, 834–841 (2009)CrossRefGoogle Scholar
  8. Biot M.: Theory of elasticity and consolidation for a porous anisotropic solid. J. Appl. Phys. 25, 182–185 (1955)CrossRefGoogle Scholar
  9. Bobo R., Akbasak D.W.A.L., Morrison P., Dedrick R., Oldfield E.: Convection-enhanced delivery of macromolecules in the brain. Proc. Natl Acad. Sci. USA 91, 2076–2080 (1994)CrossRefGoogle Scholar
  10. Brown W.: Solid mixture permittivities. J. Chem. Phys. 23, 1514–1517 (1955)CrossRefGoogle Scholar
  11. Chen X., Sarntinoranont M.: Biphasic finite element model of solute transport for direct infusion into nervous tissue. Ann. Biomed. Eng. 35, 2145–2158 (2007)CrossRefGoogle Scholar
  12. Chen Z., Broaddus W., Viswanathan R., Raghavan R., Gillies G.: Intraparenchymal drug delivery via positive-pressure infusion: Experimental and modeling studies of poroelasticity in brain phantom gels. IEEE Trans. Biomed. Eng. 49(2), 85–96 (2002)CrossRefGoogle Scholar
  13. Cheng S., Bilston L.E.: Unconfined compression of white matter. J. Biomech. 40, 117–124 (2007)CrossRefGoogle Scholar
  14. Cheng S., Clarke E., Bilston L.: Rheological properties of the tissues of the central nervous system: a review. Med. Eng. Phys. 30, 1318–1337 (2008)CrossRefGoogle Scholar
  15. Cowin S., Cardoso L.: Fabric dependence of wave propagation in anisotropic porous media. Biomech. Model. Mechanobiol. 10, 39–65 (2011)CrossRefGoogle Scholar
  16. Dutta-Roy T., Wittek A., Miller K.: Biomechanical modelling of normal pressure hydrocephalus. J. Biomech. 41, 2263–2271 (2008)CrossRefGoogle Scholar
  17. Flemisch, B., Darcis, M., Erbertseder, K., Faigle, B., Lauser, A., Mosthaf, K., Muthing, S., Nuske, P., Tatomir, A., Wolff, M., Helmig, R.: DuMux: DUNE for multi-{phase, component, scale, physics, ...} flow and transport in porous media. Adv. Water Resour. Corrected Proofs, doi:10.1016/j.advwatres.2011.03.007 (2011)
  18. Garcia J., Smith J.: A biphasic hyperelastic model for the analysis of fluid and mass transport in brain tissue. Ann. Biomed. Eng. 37, 375–386 (2009)CrossRefGoogle Scholar
  19. Gillies G., Smith J., Humphrey J., Broaddus W.: Positive pressure infusion of therapeutic agents into brain tissues: Mathematical and experimental simulations. Technol. Health Care 13, 235–243 (2005)Google Scholar
  20. Groothuis R.: The blood-brain and blood-tumor barriers: a review of stragies for increasing drug delivery. Neuro-Oncology 2, 45–59 (2000)Google Scholar
  21. Hagmann P., Jonasson L., Maeder P., Thiran J., Wedeen V., Meuli R.: Understanding diffusion mr imaging techniques: From scalar diffusion weighted imagin to diffusion tensor imaging and beyond. RadioGraphics 26, S205–S223 (2006)CrossRefGoogle Scholar
  22. Hassanizadeh M., Gray W.: General conservation equations for multi phase systems: 3. constitutive theory for porous media flow. Adv. Water Resour. 3, 25–40 (1980)CrossRefGoogle Scholar
  23. Helmig R.: Multiphase Flow and Transport Processes in the Subsurface. Springer, Heidelberg (1997)Google Scholar
  24. Holz M., Hei S., Sacco A.: Temperature-dependent self-diffusion coefficients of water and six selected molecular liquids for calibration in accurate 1h nmr pfg measurements. Phys. Chem. Chem. Phys. 2, 4740–4742 (2000)CrossRefGoogle Scholar
  25. Kaczmarek M., Subramaniam R., Neff S.: The hydromechanics of hydrocephalus: steady-state solutions for cylindrical geometry. Bull. Math. Biol. 59(2), 295–323 (1997)CrossRefGoogle Scholar
  26. Kalyanasundaram S., Calhoun V., Leong K.: A finite element model for predicting the distribution of drugs intracranially to the brain. Am. J. Physiol. 273, R1810–R1821 (1997)Google Scholar
  27. Kim H., Lizak M., Tansey G., Csaky K., Robinson M., Yuan P., Wang N., Lutz R.: Study of ocular transport of drugs released from an intravitreal implant using magnetic resonance imaging. Ann. Biomed. Eng. 33(2), 150–164 (2005)CrossRefGoogle Scholar
  28. Kim J., Garett G., Chen X., Mareci T., Sarntinoranont M.: Voxelized model of interstitial transport in the rat spinal cord following direct infusion into white matter. J. Biomech. Eng. 131, 071,007 (2009)Google Scholar
  29. Kim J.H., Mareci T., Sarntinoranont M.: A voxelized model of direct infusion into the corpus callosum and hippocampus of the rat brain: model development and parameter analysis. Med. Biol. Eng. Comput. 48, 203–214 (2010)CrossRefGoogle Scholar
  30. Klatt D., Hamhaber U., Asbach P., Braun J., Sack I.: Noninvasive assessment of the rheological behavior of human organs using multifrequency mr elastography: a study of brain and liver viscoelasticity. Phys. Med. Biol. 52, 7281–7294 (2007)CrossRefGoogle Scholar
  31. Lai W., Mow W.: Drag-induced compression of articular cartilage during a permeation experiment. Biorheology 17(1–2), 111–123 (1980)Google Scholar
  32. Linninger A., Somayaji M., Erickson T., Guo X., Penn R.: Computational methods for predicting drug transport. J. Biomech. 41, 2176–2178 (2008a)CrossRefGoogle Scholar
  33. Linninger A., Somayaji M., Mekarsk M., Zhang L.: Prediction of convection-enhanced drug delivery to the human brain. J. Theor. Biol. 250, 125–138 (2008b)CrossRefGoogle Scholar
  34. McGuire S., Zaharoff D., Yuan F.: Nonlinear dependence of hydraulic conductivity on tissue deformation during intratumoral infusion. AnnBiomedEng 37(7), 1173–1181 (2006)Google Scholar
  35. Miller K., Chinzei K.: Mechanical properties of brain tissue in tension. J. Biomech. 35, 483–490 (2002)CrossRefGoogle Scholar
  36. Morrison P.F., Laske D.W., Bobo H., Oldfield E., Dedrick R.: High-flow microinfusion: tissue penetration and pharmacodynamics. Am. J. Physiol. Regul. Integr. Comp. Physiol. 266, 292–305 (1994)Google Scholar
  37. Netti P., Baxter L., Boucher Y., Skalak R., Rakesh K.: Time-dependent behavior of interstitial fluid pressure in solid tumors: implications for drug delivery. Cancer Res. 55, 5451–5458 (1995)Google Scholar
  38. Netti P., Baxter L., Boucher Y., Skalak R., Jain R.: Macro- and microscopic fluid transport in living tissues: applications to solid tumors. AIChE J. 43(3), 818–831 (1997)CrossRefGoogle Scholar
  39. Nicholson C.: Diffusion and related transport mechanisms in the brain tissue. Rep. Progr. Phys. 64, 815–884 (2001)CrossRefGoogle Scholar
  40. Odgaard A.: Three-dimensional methods for quantification of cancellous bone architecture. Bone 20(4), 315–328 (1997)CrossRefGoogle Scholar
  41. Odgaard A., Kabel J., van Rietbergen B., Dalstra M., Huiskes R.: Fabric and elastic principal directions of cancellous bone are closely related. J. Biomech. 30(5), 487–495 (1997)CrossRefGoogle Scholar
  42. Prabhu S., Broaddus W., Gillies G., Loudon W., Chen Z.J., Smith B.: Distribution of macromolecular dyes in brain using positivepressure infusion: a model for direct controlled delivery of therapeutic agents. Surg. Neurol. 50, 367–375 (1998)CrossRefGoogle Scholar
  43. Raghavan R., Brady M., Rodriguez-Ponze M., Hartlep A., Pedain C., Sampson J.: Convection-enhanced delivery of therapeutics for brain disease, and its optimization. Neurosurg. Focus 20(3), E12 (2006)CrossRefGoogle Scholar
  44. Sarntinoranont M., Banerjee R., Lonser R., Morrison P.: A computational model of direct interstitial infusion of macromolecules into spinal cord. Ann. Biomed. Eng. 31(4), 448–461 (2003)CrossRefGoogle Scholar
  45. Sarntinoranont M., Chen X., Zhao J., Mareci T.: Computational model of interstitial transport in the spinal cord using diffusion tensor imaging. Ann. Biomed. Eng. 34, 1304–1321 (2006)CrossRefGoogle Scholar
  46. Sen A., Torquato S.: Effective conductivity of anisotropic two-phase composite media. Phys. Rev. B 39, 4504–4515 (1988)CrossRefGoogle Scholar
  47. Smith J., Humphrey A.: Interstitial transport and transvascular fluid exchange during infusion into brain and tumor tissue. Microvasc. Res. 73, 58–73 (2007)CrossRefGoogle Scholar
  48. Smith J.A., Garcia J.A.: A nonlinear biphasic model of flow-controlled infusion in brain: fluid transport and tissue deformation analyses. J. Biomech. 42, 2017–2025 (2009)CrossRefGoogle Scholar
  49. Smith J., Garcia J.: A nonlinear biphasic model of flow-controlled infusions in brain: mass transport analyses. J. Biomech. 44, 524–531 (2011)CrossRefGoogle Scholar
  50. Taylor Z., Miller K.: Reassessment of brain elasticity for analyses of biomechanisms of hydocephalus. J. Biomech. 37, 1263–1269 (2004)CrossRefGoogle Scholar
  51. Tuch D., Wedeen V., Dale A., George J., Belliveau J.: Conductivity tensor mapping of the human brain using diffusion tensor mri. Proc. Natl Acad. Sci. 98, 11697–11701 (2001)CrossRefGoogle Scholar
  52. Vorisek I., Sykova E.: Measuring diffusion parameters in the brain: comparing the real-time iontophoretic method and diffusion-weighted magnetic resonance. Acta Physiol. 195, 101–110 (2009)CrossRefGoogle Scholar
  53. Zhang X.Y., Luck J., Dewhirst W., Yuan F.: Interstitial hydraulic conductivity in a fibrosarcoma. Am. J. Physiol. 279, H2726–H2734 (2000)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Karen H. Støverud
    • 1
  • Melanie Darcis
    • 2
  • Rainer Helmig
    • 2
  • S. Majid Hassanizadeh
    • 3
  1. 1.Center for Biomedical ComputingSimula Research LaboratoryLysakerNorway
  2. 2.Department of Hydromechanics and Modeling of HydrosystemsUniversity of StuttgartStuttgartGermany
  3. 3.Environmental HydrogeologyUtrecht UniversityUtrechtThe Netherlands

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