Skip to main content

Advertisement

SpringerLink
Log in

Magnetic nanoparticle imaging by means of minimum norm estimates from remanence measurements

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

In magnetic nanoparticle imaging, magnetic nanoparticles are coated and functionalized to bind to specific targets. After measuring their magnetic relaxation or remanence, their distribution can be determined by means of inverse methods. The reconstruction algorithm presented in this paper includes first a dipole fit using a Levenberg–Marquardt optimizer to determine the reconstruction plane. Secondly, a minimum norm estimate is obtained on a regular grid placed in that plane. Computer simulations involving different parameter sets and conditions show that the used approach allows for the reconstruction of distributed sources, although the reconstructed shapes are distorted by blurring effects. The reconstruction quality depends on the signal-to-noise ratio of the measurements and decreases with larger sensor-source distances and higher grid spacings. In phantom measurements, the magnetic remanence of nanoparticle columns with clinical relevant sizes is determined with two common measurement systems. The reconstructions from these measurements indicate that the approach is applicable for clinical measurements. Our results provide parameter sets for successful application of minimum norm approaches to Magnetic Nanoparticle Imaging.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. A generic environment for bio-numerical simulation. ist-program of the european commission, project no. 10378 (2000) http://www.simbio.de

  2. Alexiou C, Schmid R, Jurgons R, Bergemann C, Arnold W, Parak F (2002) Ferrofluids—magnetically controllable fluids and their applications, Lecture Notes in Physics, vol 594. Targeted tumor therapy with “Magnetic Drug Targeting": therapeutic efficacy of ferrofluid bound mitoxantrone. Springer, Berlin, pp 233–251

    Google Scholar 

  3. Apel M, Heinlein UA, Miltenyi S, Schmitz J, Campbell JD (2007) Magnetism in medicine, 2 edn. Magnetic cell separation for research and clinical applications. Wiley-VCH, Berlin, pp 571–595. doi:10.1002/9783527610174.ch4g

    Google Scholar 

  4. Brauer H, Haueisen J, Ziolkowski M, Tenner U, Nowak H (2000) Reconstruction of extended current sources in a human body phantom applying biomagnetic measuring techniques. IEEE Trans Magn 36(4):1700–1705. doi:10.1109/20.877770

    Article  Google Scholar 

  5. Bulte JWM, Kraitchman DL (2004) Iron oxide mr contrast agents for molecular and cellular imaging. NMR Biomed 17(7):484–499. doi:10.1002/nbm.924

    Article  Google Scholar 

  6. Dames P, Gleich B, Flemmer A, Hajek K, Seidl N, Wiekhorst F, Eberbeck D, Bittmann I, Bergemann C, Weyh T, Trahms L, Rosenecker J, Rudolph C (2007) Targeted delivery of magnetic aerosol droplets to the lung. Nat Nano 2(8):495–499. doi:10.1038/nnano.2007.217

    Article  Google Scholar 

  7. Di Rienzo L, Haueisen J (2006) Theoretical lower error bound for comparative evaluation of sensor arrays in magnetostatic linear inverse problems. IEEE Trans Magn 42(11):3669–3673. doi:10.1109/TMAG.2006.882338

    Article  Google Scholar 

  8. Enpuku K, Soejima K, Nishimoto T, Tokumitsu H, Kuma H, Hamasaki N, Yoshinaga K (2006) Liquid phase immunoassay utilizing magnetic marker and high t-c superconducting quantum interference device. J Appl Phys 100(5). doi:10.1063/1.2337384

  9. Flynn ER, Bryant HC (2005) A biomagnetic system for in vivo cancer imaging. Phys Med Biol 50:1273–1293. doi:10.1088/0031-9155/50/6/016

    Article  Google Scholar 

  10. Gleich B, Weizenecker J (2005) Tomographic imaging using the nonlinear response of magnetic particles. Nature 435(7046):1214–1217. doi:10.1038/nature03808

    Article  Google Scholar 

  11. Hämäläinen MS, Ilmoniemi RJ (1994) Interpreting magnetic-fields of the brain—minimum norm estimates. Med Biol Eng Comput 32(1):35–42. doi:10.1007/BF02512476

    Article  Google Scholar 

  12. Hansen PC (1987) The truncated svd as a method for regularization. BIT 27(4):534–553. doi:10.1007/BF01937276

    Article  MATH  MathSciNet  Google Scholar 

  13. Haueisen J, Unger R, Beuker T, Bellemann M (2002) Evaluation of inverse algorithms in the analysis of magnetic flux leakage data. IEEE Trans Magn 38(3):1481–1488. doi:10.1109/20.999121

    Article  Google Scholar 

  14. Hergt R, Dutz S, Mller R, Zeisberger M (2006) Magnetic particle hyperthermia: nanoparticle magnetism and materials development for cancer therapy. J Phys Condens Matter 18(38):2919–2934. doi:10.1088/0953-8984/18/38/S26

    Article  Google Scholar 

  15. Ito A, Shinkai M, Honda H, Kobayashi T (2005) Medical application of functionalized magnetic nanoparticles. J Biosci Bioeng 100(1):1–11

    Article  Google Scholar 

  16. Johannsen M, Gneveckow U, Thiesen B, Taymoorian K, Cho C, Waldoefner N, Scholz R, Jordan A, Loening S, Wust P (2007) Thermotherapy of prostate cancer using magnetic nanoparticles: feasibility, imaging, and three-dimensional temperature distribution. Eur Urol 52(6):1653–1662. doi:10.1016/j.eururo.2006.11.023

    Article  Google Scholar 

  17. Jordan A, Scholz R, Wust P, Fahling H, Krause J, Wlodarczyk W, Sander B, Vogl T, Felix R (1997) Effects of magnetic fluid hyperthermia (mfh) on c3h mammary carcinoma in vivo. Int J Hyperther 13(6):587–605

    Article  Google Scholar 

  18. Leder U, Haueisen J, Huck M, Nowak H (1998) Non-invasive imaging of arrhythmogenic left-ventricular myocardium after infarction. Lancet 352(9143):1825–1825. doi:10.1016/S0140-6736(98)00082-8

    Article  Google Scholar 

  19. Pankhurst Q, Connolly J, Jones S, Dobson J (2003) Applications of magnetic nanoparticles in biomedicine. J Phys Appl Phys 36(13):R167–R181(1). doi:10.1088/0022-3727/36/13/201

    Google Scholar 

  20. Pinto B, Silva C (2007) A simple method for calculating the depth of eeg sources using minimum norm estimates (mne). Med Biol Eng Comput 45(7):643–652. doi:10.1007/s11517-007-0204-z

    Article  Google Scholar 

  21. Rad A, Arbab A, Iskander A, Jiang Q, Soltanian-Zadeh H (2007) Quantification of superparamagnetic iron oxide (spio)-labeled cells using mri. J Magn Reson Imag 26(2):366–374. doi:10.1002/jmri.20978

    Article  Google Scholar 

  22. Salata OV (2004) Applications of nanoparticles in biology and medicine. J Nanobiotechnol 2:3. doi:10.1186/1477-3155-2-3

    Article  Google Scholar 

  23. Schnabel A, Burghoff M, Hartwig S, Petsche F, Steinhoff U, Drung D, Koch H (2004) A sensor configuration for a 304 squid vector magnetometer. Neurol Clin Neurophysiol 70

  24. Smith WE, Dallas WJ, Kullmann WH, Schlitt HA (1990) Linear estimation theory applied to the reconstruction of a 3-d vector current distribution. Appl Opt 29(5):658–667

    Article  Google Scholar 

  25. Thiel F, Schnabel A, Knappe-Grüneberg S, Stollfu D, Burghoff M (2007) Demagnetization of magnetically shielded rooms. Rev Sci Instrum 78(3):035,106. doi:10.1063/1.2713433

    Google Scholar 

  26. Thorek D, Chen A, Czupryna J, Tsourkas A (2006) Superparamagnetic iron oxide nanoparticle probes for molecular imaging. Ann Biomed Eng 34(1):23–38. doi:10.1007/s10439-005-9002-7

    Article  Google Scholar 

  27. Tikhonov AN (1963) Resolution of ill-posed problems and the regularization method (in russian). Dokl Akad Nauk SSSR 151:501–504

    MathSciNet  Google Scholar 

  28. Uchida S, Iramina K, Goto K, Ueno S (2000) A comparison of iterative minimum norm estimation and current dipole estimation for magnetic field measurements from small animals. IEEE Trans Magn 36(5):3724–3726. doi:10.1109/20.908953

    Article  Google Scholar 

  29. Varah JM (1973) On the numerical solution of ill-conditioned linear systems with applications to ill-posed problems. SIAM J Numer Anal 10(2):257–267. doi:10.1137/0710025

    Article  MATH  MathSciNet  Google Scholar 

  30. Weitschies W, Ktitz R, Bunte T, Trahms L (1997) Determination of relaxing or remanent nanoparticle magnetization provides a novel binding specific technique for the evaluation of immunosassays. Pharm Pharmacol Lett 7:5–8

    Google Scholar 

  31. Wiekhorst F, Jurgons R, Eberbeck D, Seliger C, Steinhoff U, Trahms L, Alexiou C (2006) Quantification of magnetic nanoparticles by magnetorelaxometry after local cancer therapy with magnetic drug targeting. J Nanosci Nanotechnol 6(9–10):3222–3225. doi:10.1166/jnn.2006.477

    Article  Google Scholar 

Download references

Acknowledgments

This work was funded by the E. C. Sixth Framework Programme (STREP project “Biodiagnostics”, contract no. NMP4-CT-2005-017002) and in part supported by the the German Federal Ministry of Education and Research (FKZ 13N9150) and the state of Thuringia under participation of the European Funds for Regional Development (TAB project 2006FE0096).

Author information

Authors and Affiliations

  1. Institute of Biomedical Engineering and Informatics, Technische Universität Ilmenau, P.O. Box 100565, 98684, Ilmenau, Germany

    Daniel Baumgarten & Jens Haueisen

  2. Department of Internal Medicine I and Biomagnetic Center, Department of Neurology, Friedrich Schiller University Jena, 07745, Jena, Germany

    Mario Liehr

  3. Physikalisch-Technische Bundesanstalt, 10587, Berlin, Germany

    Frank Wiekhorst, Uwe Steinhoff & Lutz Trahms

  4. Senova GmbH, 07745, Jena, Germany

    Peter Münster

  5. fzmb GmbH, Research Centre of Medical Technology and Biotechnology, Geranienweg 7, 99947, Bad Langensalza, Germany

    Peter Miethe

Authors
  1. Daniel Baumgarten
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mario Liehr
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Frank Wiekhorst
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Uwe Steinhoff
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Peter Münster
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Peter Miethe
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Lutz Trahms
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Jens Haueisen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Baumgarten.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baumgarten, D., Liehr, M., Wiekhorst, F. et al. Magnetic nanoparticle imaging by means of minimum norm estimates from remanence measurements. Med Biol Eng Comput 46, 1177–1185 (2008). https://doi.org/10.1007/s11517-008-0404-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-008-0404-1

Keywords

Search

Navigation