Annals of Biomedical Engineering

, Volume 41, Issue 1, pp 100–111 | Cite as

An Inverse Problem Approach to Recovery of In Vivo Nanoparticle Concentrations from Thermal Image Monitoring of MR-Guided Laser Induced Thermal Therapy

  • D. Fuentes
  • A. Elliott
  • J. S. Weinberg
  • A. Shetty
  • J. D. Hazle
  • R. J. Stafford
Article

Abstract

Quantification of local variations in the optical properties of tumor tissue introduced by the presence of gold–silica nanoparticles (NP) presents significant opportunities in monitoring and control of NP-mediated laser induced thermal therapy (LITT) procedures. Finite element methods of inverse parameter recovery constrained by a Pennes bioheat transfer model were applied to estimate the optical parameters. Magnetic resonance temperature imaging (MRTI) acquired during a NP-mediated LITT of a canine transmissible venereal tumor in brain was used in the presented statistical inverse problem formulation. The maximum likelihood (ML) value of the optical parameters illustrated a marked change in the periphery of the tumor corresponding with the expected location of NP and area of selective heating observed on MRTI. Parameter recovery information became increasingly difficult to infer in distal regions of tissue where photon fluence had been significantly attenuated. Finite element temperature predictions using the ML parameter values obtained from the solution of the inverse problem are able to reproduce the NP selective heating within 5 °C of measured MRTI estimations along selected temperature profiles. Results indicate the ML solution found is able to sufficiently reproduce the selectivity of the NP mediated laser induced heating and therefore the ML solution is likely to return useful optical parameters within the region of significant laser fluence.

Keywords

Bioheat transfer Laser induced thermal therapy Statistical inverse Nanoparticle selective heating MR temperature imaging PDE constrained optimization 

References

  1. 1.
    Babaian, R. J., B. Donnelly, D. Bahn, J. G. Baust, M. Dineen, D. Ellis, A. Katz, L. Pisters, D. Rukstalis, K. Shinohara, et al. Best practice statement on cryosurgery for the treatment of localized prostate cancer. J. Urol. 180(5):1993–2004, 2008.PubMedCrossRefGoogle Scholar
  2. 2.
    Balay, S., W. D. Gropp, L. C. McInnes, and B. F. Smith. PETSc Users Manual. Technical Report ANL-95/11-Revision 2.1.5, Argonne National Laboratory, 2003.Google Scholar
  3. 3.
    Barry, S. E. Challenges in the development of magnetic particles for therapeutic applications. Int. J. Hyperther. 24:451–466, 2009.Google Scholar
  4. 4.
    Baumgarten, D., M. Liehr, F. Wiekhorst, U. Steinhoff, P. Munster, P. Miethe, L. Trahms, and J. Haueisen. Magnetic nanoparticle imaging by means of minimum norm estimates from remanence measurements. Med. Biol. Eng. Comput. 46(12):1177–1185, 2008.PubMedCrossRefGoogle Scholar
  5. 5.
    Bekas, C., E. Kokiopoulou, and Y. Saad. An estimator for the diagonal of a matrix. Appl. Numer. Math. 57(11–12):1214–1229, 2007.CrossRefGoogle Scholar
  6. 6.
    Benson, S. J., L. C. McInnes, J. Moré, and J. Sarich. TAO user manual (revision 1. 8). Technical Report ANL/MCS-TM-242, Mathematics and Computer Science Division, Argonne National Laboratory, 2005. http://www.mcs.anl.gov/tao.
  7. 7.
    Biros, G., and O. Ghattas. Parallel Lagrange-Newton-Krylov-Schur methods for PDE-constrained optimization. Part I: the Krylov-Schur solver. SIAM J. Sci. Comput. 27(2):687–713, 2006.CrossRefGoogle Scholar
  8. 8.
    Blacker, T., et al. Cubit Users Manual, 2008. http://cubit.sandia.gov/documentation.
  9. 9.
    Carp, S. A., S. A. Prahl, and V. Venugopalan. Radiative transport in the delta-[bold P] approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media. J. Biomed. Opt. 9:632, 2004.PubMedCrossRefGoogle Scholar
  10. 10.
    Carpentier, A., R. J. McNichols, R. J. Stafford, J. Itzcovitz, J. P. Guichard, D. Reizine, S. Delaloge, E. Vicaut, D. Payen, A. Gowda, et al. Real-time magnetic resonance-guided laser thermal therapy for focal metastatic brain tumors. Neurosurgery 63(1 Suppl 1):8, 2008.Google Scholar
  11. 11.
    Cherukuri, P., S. A. Curley, and S. R. Grobmyer: Use of nanoparticles for targeted, noninvasive thermal destruction of malignant cells. Methods Mol. Biol. 624:359–373, 2010.PubMedCrossRefGoogle Scholar
  12. 12.
    Cookson, M. S., G. Aus, A. L. Burnett, E. D. Canby-Hagino, A. V. DAmico, R. R. Dmochowski, D. T. Eton, J. D. Forman, S. L. Goldenberg, J. Hernandez, et al. Variation in the definition of biochemical recurrence in patients treated for localized prostate cancer: the American Urological Association prostate guidelines for localized prostate cancer update panel report and recommendations for a standard in the reporting of surgical outcomes. J. Urol. 177(2):540–545, 2007.PubMedCrossRefGoogle Scholar
  13. 13.
    Detre, J. A., J. S. Leigh, D. S. Williams, and A. P. Koretsky. Perfusion imaging. Magn. Reson. Med. 23(1):37–45, 2005.CrossRefGoogle Scholar
  14. 14.
    Diagaradjane, P., A. Shetty, J. C. Wang, A. M. Elliott, J. Schwartz, S. Shentu, H. C. Park, A. Deorukhkar, R. J. Stafford, S. H. Cho, et al. Modulation of in vivo tumor radiation response via gold nanoshell-mediated vascular-focused hyperthermia: characterizing an integrated antihypoxic and localized vascular disrupting targeting strategy. Nano Lett. 8(5):1492, 2008.PubMedCrossRefGoogle Scholar
  15. 15.
    Diller, K. R., J. W. Valvano, and J. A. Pearce. Bioheat transfer. In: The CRC Handbook of Mechanical Engineering, edited by F. Kreith and Y. Goswami, 2nd edn. Boca Raton: CRC Press, 2005, pp. 4-278–4-357.Google Scholar
  16. 16.
    dosSantos, I., D. Haemmerich, D. Schutt, A. F. da Rocha, and L. R. Menezes. Probabilistic finite element analysis of radiofrequency liver ablation using the unscented transform. Phys. Med. Biol. 54:627–640, 2009.PubMedCrossRefGoogle Scholar
  17. 17.
    Duck, F. A. Physical Properties of Tissue: A Comprehensive Reference Book. New York: Academic Press, 1990.Google Scholar
  18. 18.
    El-Sayed, I. H. Nanotechnology in head and neck cancer: the race is on. Curr. Oncol. Rep. 12(2):121–128, 2010.PubMedCrossRefGoogle Scholar
  19. 19.
    Emelianov, S. Y., P. C. Li, and M. ODonnell. Photoacoustics for molecular imaging and therapy. Phys. Today 62(8):34, 2009.PubMedCrossRefGoogle Scholar
  20. 20.
    Feng, Y., D. Fuentes, A. Hawkins, J. Bass, M. N. Rylander, A. Elliott, A. Shetty, R. J. Stafford, and J. T. Oden. Nanoshell-mediated laser surgery simulation for prostate cancer treatment. Eng. Comput. 25(1):3–13, 2009.PubMedCrossRefGoogle Scholar
  21. 21.
    Fisher, M., J. Nocedal, Y. Trémolet, and S. J. Wright. Data assimilation in weather forecasting: a case study in PDE-constrained optimization. Optim. Eng. 10(3):409–426, 2009.CrossRefGoogle Scholar
  22. 22.
    Flath, H. P., L. C. Wilcox, V. Akçelik, J. Hill, B. van Bloemen Waanders, and O. Ghattas. Fast algorithms for Bayesian uncertainty quantification in large-scale linear inverse problems based on low-rank partial Hessian approximations. SIAM J. Sci. Comput. 33(1):407, 2011.CrossRefGoogle Scholar
  23. 23.
    Fuentes, D., Y. Feng, A. Elliott, A. Shetty, R. J. McNichols, J. T. Oden, and R. J. Stafford. Adaptive real-time bioheat transfer models for computer driven MR-guided laser induced thermal therapy. IEEE Trans. Biomed. Eng. 57(5), 2010. Cover Page.Google Scholar
  24. 24.
    Fuentes, D., J. T. Oden, K. R. Diller, J. Hazle, A. Elliott, A. Shetty, and R. J. Stafford. Computational modeling and real-time control of patient-specific laser treatment cancer. Ann. BME 37(4):763, 2009.Google Scholar
  25. 25.
    Fuentes, D., C. Walker, A. Elliott, A. Shetty, J. Hazle, and R. J. Stafford. MR temperature imaging validation of a bioheat transfer model for LITT. Int. J. Hyperth. 27(5):453–464, 2011. Cover Page.CrossRefGoogle Scholar
  26. 26.
    Fuentes, D., J. Yung, J. D. Hazle, J. S. Weinberg, and R. J. Stafford. Kalman filtered MR temperature imaging for laser induced thermal therapies. Trans. Med. Imaging 31(4):984–994, 2012. Special Issue on Interventional Imaging.CrossRefGoogle Scholar
  27. 27.
    Ghanem, R. G., and P. D. Spanos. Stochastic Finite Elements: A Spectral Approach. New York: Dover Publications, 2003.Google Scholar
  28. 28.
    Gonzalgo, M. L., N. Patil, L. M. Su, and V. R. Patel. Minimally invasive surgical approaches and management of prostate cancer. Urol. Clin. N. Am. 35(3):489–504, 2008.CrossRefGoogle Scholar
  29. 29.
    Haario, H., M. Laine, A. Mira, and E. Saksman. DRAM: efficient adaptive MCMC. Stat. Comput. 16(4):339–354, 2006.CrossRefGoogle Scholar
  30. 30.
    Henderson, A., and J. Ahrens. The ParaView Guide. Colombia: Kitware, 2004.Google Scholar
  31. 31.
    Hirsch, L. R., R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E. Price, J. D. Hazle, N. J. Halas, and J. L. West. Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance. Proc. Natl Acad. Sci. 100(23):13549, 2003.PubMedCrossRefGoogle Scholar
  32. 32.
    Huttunen, J. M. J., T. Huttunen, M. Malinen, and J. P. Kaipio. Determination of heterogeneous thermal parameters using ultrasound induced heating and mr thermal mapping. Phys. Med. Biol. 51:1011, 2006.PubMedCrossRefGoogle Scholar
  33. 33.
    Ibanez, L., W. Schroeder, L. Ng, and J. Cates. The ITK Software Guide. Colombia: Kitware, Inc. ISBN 1-930934-15-7, http://www.itk.org/ItkSoftwareGuide.pdf, 2nd edition, 2005.
  34. 34.
    Jaynes, E. T., and G. L. Bretthorst. Probability Theory: The Logic of Science. Cambridge: Cambridge University Press, 2003.Google Scholar
  35. 35.
    Jones, S., G. Barnett, J. L. Sunshine, M. Griswold, A. Sloan, M. D. Phillips, R. Tyc, and M. Torchia. First human application of laser interstitial thermal therapy in GBM using MR guided autolitt system. In: Proceedings of the 17th Scientific Meeting, International Society for Magnetic Resonance in Medicine, 2009.Google Scholar
  36. 36.
    Kaipio, J., and E. Somersalo. Statistical and Computational Inverse Problems, Vol. 160. New York: Springer, 2005.Google Scholar
  37. 37.
    Kirk, B. S., and J. W. Peterson. libMesh-a C++ Finite Element Library. CFDLab. URL http://libmesh.sourceforge.net, 2003.
  38. 38.
    LeMaître, O. P., and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. New York: Springer, 2010.Google Scholar
  39. 39.
    Liu, S. Y., Z. S. Liang, F. Gao, S. F. Luo, and G. Q. Lu. In vitro photothermal study of gold nanoshells functionalized with small targeting peptides to liver cancer cells. J. Mater. Sci. Mater. Med. 21(2):665–674, 2010.PubMedCrossRefGoogle Scholar
  40. 40.
    McNichols, R. J., M. Kangasniemi, A. Gowda, J. A. Bankson, R. E. Price, and J. D. Hazle. Technical developments for cerebral thermal treatment: water-cooled diffusing laser fibre tips and temperature-sensitive MRI using intersecting image planes. Int. J. Hyperth. 20(1):45–56, 2004.CrossRefGoogle Scholar
  41. 41.
    Melancon, M., W. Lu, and C. Li. Gold-based magneto/optical nanostructures: challenges for in vivo applications in cancer diagnostics and therapy. Mater. Res. Bull. 34(6):415, 2009.PubMedCrossRefGoogle Scholar
  42. 42.
    Minden, V., B. F. Smith, and M. G. Knepley. Preliminary implementation of PETSC using GPUS. In: Proceedings of the 2010 International Workshop of GPU Solutions to Multiscale Problems in Science and Engineering, 2010.Google Scholar
  43. 43.
    Pennes, H. H. Analysis of tissue and arterial blood temperatures in the resting forearm. J. Appl. Physiol. 1:93–122, 1948.PubMedGoogle Scholar
  44. 44.
    Prudencio, E., and X. C. Cai. Parallel multilevel restricted Schwarz preconditioners with pollution removing for pde-constrained optimization. SIAM J. Sci. Comput. 29:964–985, 2007.CrossRefGoogle Scholar
  45. 45.
    Prudencio, E., and S. H. Cheung. Parallel adaptive multilevel sampling algorithms for the Bayesian analysis of mathematical models. Int. J. Uncertain. Quantif. 2(3):215–237, 2012.CrossRefGoogle Scholar
  46. 46.
    Prudencio, E., and K. Schulz. The parallel C++ statistical library queso: quantification of uncertainty for estimation, simulation and optimization. In: Euro-Par 2011: Parallel Processing Workshops. New YorK: Springer, 2012, pp. 398–407.Google Scholar
  47. 47.
    Roemer, R. B., A. M. Fletcher, and T. C. Cetas. Obtaining local SAR and blood perfusion data from temperature measurements: steady state and transient techniques compared. Int. J. Radiat. Oncol. Biol. Phys. 11(8):1539–1550, 1985.PubMedCrossRefGoogle Scholar
  48. 48.
    Salloum, M., R. Ma, and L. Zhu. Enhancement in treatment planning for magnetic nanoparticle hyperthermia: optimization of the heat absorption pattern. Int. J. Hyperth. 25(4):309–321, 2009.Google Scholar
  49. 49.
    Schwartz, J. A., A. M. Shetty, R. E. Price, R. J. Stafford, J. C. Wang, R. K. Uthamanthil, K. Pham, R. J. McNichols, C. L. Coleman, and J. D. Payne. Feasibility study of particle-assisted laser ablation of brain tumors in orthotopic canine model. Cancer Res. 69(4):1659, 2009.PubMedCrossRefGoogle Scholar
  50. 50.
    Shafirstein, G., W. Baumler, M. Lapidoth, S. Ferguson, P. E. North, and M. Waner. A new mathematical approach to the diffusion approximation theory for selective photothermolysis modeling and its implication in laser treatment of port-wine stains. Lasers Surg. Med. 34(4):335–347, 2004.Google Scholar
  51. 51.
    Shah, J., S. Park, S. Aglyamov, T. Larson, L. Ma, K. Sokolov, K. Johnston, T. Milner, and S. Y. Emelianov. Photoacoustic imaging and temperature measurement for photothermal cancer therapy. J. Biomed. Opt. 13:034024, 2008.PubMedCrossRefGoogle Scholar
  52. 52.
    Stafford, R. J., D. Fuentes, A. E. Elliott, J. S. Weinberg, and K. Ahrar. Laser-induced thermal therapy for tumor ablation. Crit. Rev. Biomed. Eng. 38(1):79, 2010.PubMedCrossRefGoogle Scholar
  53. 53.
    Stafford, R. J., R. E. Price, C. J. Diederich, M. Kangasniemi, L. E. Olsson, and J. D. Hazle. Interleaved echo-planar imaging for fast multiplanar magnetic resonance temperature imaging of ultrasound thermal ablation therapy. J. Magn. Reson. Imaging 20(4):706–714, 2004.PubMedCrossRefGoogle Scholar
  54. 54.
    Stern, J. M., J. Stanfield, W. Kabbani, J. T. Hsieh, and J. A. Cadeddu: Selective prostate cancer thermal ablation with laser activated gold nanoshells. J. Urol. 179(2):748–753, 2008.PubMedCrossRefGoogle Scholar
  55. 55.
    Tarantola, A. Inverse Problem Theory and Methods for Model Parameter Estimation. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2005.Google Scholar
  56. 56.
    Ward, J. F., H. Nakanishi, L. Pisters, R. J. Babaian, and P. Troncoso. Cancer ablation with regional templates applied to prostatectomy specimens from men who were eligible for focal therapy. BJU Int. 104(4):490–497, 2009.PubMedCrossRefGoogle Scholar
  57. 57.
    Welch, A. J., and M. J. C. van Gemert. Optical-Thermal Response of Laser-Irradiated Tissue. New York: Plenum Press, 1995.Google Scholar
  58. 58.
    Xiu, D. Fast numerical methods for stochastic computations: a review. Commun. Comput. Phys. 5(2–4):242–272, 2009.Google Scholar

Copyright information

© Biomedical Engineering Society 2012

Authors and Affiliations

  • D. Fuentes
    • 1
  • A. Elliott
    • 1
  • J. S. Weinberg
    • 2
  • A. Shetty
    • 3
  • J. D. Hazle
    • 1
  • R. J. Stafford
    • 1
  1. 1.Department of Imaging PhysicsThe University of Texas M.D. Anderson Cancer CenterHoustonUSA
  2. 2.Department of NeurosurgeryThe University of Texas M.D. Anderson Cancer CenterHoustonUSA
  3. 3.BioTex, Inc.HoustonUSA

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