Magnetic Relaxometry: A Comparison to Magnetoencephalography

  • Edward R. FlynnEmail author
Living reference work entry


Magnetic relaxometry is a technology utilizing SQUID sensors and superparamagnetic nanoparticles to target various diseases using antibodies or other biomolecules specific to disease cells. The nanoparticles are magnetized in a small field, and the SQUID sensors are used to detect the nanoparticle decaying field. The method has high sensitivity, more than 1000 times a mammogram for breast cancer, high contrast as only nanoparticles bound to cells are measured, and high specificity using specific biomarkers conjugated to the nanoparticles. Future directions of magnetic relaxometry include diagnosis of neural diseases using biomarkers specific to these diseases coupled to nanoparticles; this will complement ongoing diagnostic programs using magnetoencephalography.


SQUID Magnetic relaxometry Nanoparticles Cancer 

1 Introduction

The development of superconducting quantum interference detector (SQUID) sensor technology (Zimmerman 1966) opened up a number of new research areas where the measurement of ultralow magnetic fields provided new illumination into underlying phenomenon. Some of the earliest of these programs were in the area of measurement of magnetic fields from the heart (MCG) and brain (MEG) by (Cohen 1968) followed by the measurement of evoked responses in the brain by Brenner et al. (1975). These early efforts have been summarized in the review of Hämäläinen et al. (1993) where the details of the SQUID sensors and applications are described. These applications are based on the measurements of biomagnetic magnetic fields emanating from currents involved in living tissue.

Magnetic relaxometry, or as defined here as superparamagnetic relaxometry (SPMR), is a more recent emerging technology (Flynn and Bryant 2005; Kötitz 1995; Romanus et al. 2001) that is similar in many respects to MEG and MCG in its application and in the procedures used to analyze the data. At Senior Scientific, SPMR has been used to investigate various disease states, in particular cancer through the use of biomarkers conjugated to the nanoparticles [NP]. The method has been shown to be very sensitive for detecting cancer; for example, it is more than 1000 times more sensitive than a mammogram for detecting breast cancer. Because of the unique nature of superparamagnetic NP, very high contrast can be obtained between bound and unbound NP and high specificity to disease using biomarkers. As in MEG, SPMR typically uses SQUID sensors to measure the low magnitude fields emitted by the NP during their magnetic relaxation. Similarly, SPMR uses arrays of SQUID sensors to localize sources of magnetic activity with the analysis normally performed with inverse theory algorithms of the same type as in MEG and MCG (see, e.g., the inverse theory described by Huang et al. (1998) for MEG). The resulting data are also subject to filtering and noise-suppression methods developed for biomagnetism measurements. As in MEG, the use of phantoms to calibrate and test the sensor systems and develop the software analysis methods is directly applicable to SPMR; both MEG and SPMR take advantage of the basic principles of electromagnetism.

The principal difference is that SPMR measures the relaxing magnetic fields from magnetic nanoparticles (NP) that have been briefly magnetized in a magnetic field and are not biomagnetic in nature. In MEG and MCG, the sources are described in terms of current dipoles with units corresponding to picoamps, whereas in SPMR, the sources are described in terms of magnetic moments with units corresponding to pJ/T (picoJoule/Tesla). However many of the applications of SPMR are directly related to biological phenomena. In the following discussions, SPMR is applied to the measurement of specificity and sensitivity of various antibodies to various cell types – in particular cancer cells – to the study of incubation rates for attachment of NP to cells, to localization of tumors in living animals, and to measurement of percentage of injected material delivered to tumors and other targeted organs in living animals.

There are two important principals that SPMR methods utilize in their measurements: (1) the high sensitivity of SQUID sensors for detecting extremely small amounts of magnetite – the principal ingredients of NP used – and (2) the special properties of superparamagnetic NP that yield high magnetic moments and high contrast for bound NP. In this regard, the SQUID sensors are exactly the same as used in MEG and the prototype system described here was originally used for MEG measurements. The sensitivity required is somewhat less than MEG, and this fact combined with the method of measurement allows most SPMR measurements to be made without the need for shielded rooms. As in MEG, it is typical to use gradiometers for the sensor configuration. An important difference between MEG and SPMR in the SQUID sensor configuration considerations is that the magnetic NP must be magnetized and this requires the presence of a pulsed magnetic field. This magnetizing field needs be only some tens of gauss due to the intrinsic saturation properties of the NP, and the magnetizing field is only applied for a fraction of a second. However, this requires that the SQUID sensor system be turned on and off during the pulsing and that the components of the system do not respond to this magnetic pulse for any extended duration. The coil configuration producing this magnetizing field also limits the configuration of the sensors such that this field is relatively uniform in strength and direction over the sensor array; thus, a whole-head MEG system is not amenable to SPMR measurements, whereas a relatively flat array such as used in MCG works quite well.

2 The SPMR Method

In Fig. 1, the system used for SPMR measurements at Senior Scientific is illustrated. The SQUID sensor system, seen here as the dewar at the top with the sensor snout below, is a replica of an early seven-channel second-order gradiometer system used in early MEG studies (Supek et al. 1999) and is operated here in an unshielded environment without any background compensation; this condition along with artifacts induced by the pulsing limits the sensitivity to 20pT. As described later, this system is being improved by several orders-of-magnitude in sensitivity. The magnetizing field of 50 gauss is applied by the Helmholtz coils seen in this photo and is in the direction parallel to the central gradiometer and relatively uniform over the measurement volume of interest. Samples to be measured are placed on a stage seen just below the sensor snout and can be moved in three dimensions. Samples may consist of live cell cultures, phantom sources, and live animals (normally mice). For single-source samples, the seven-channel system is adequate for determining the position and magnetic moment strength of the sample. For multiple sources, such as with animals or phantoms, the stage is moved in the x-y plane in order to obtain sufficient field measurements to solve the inverse problem. An important difference here between MEG and SPMR is that the sources are aligned along the z-direction (along the axis of the central sensor) so that only the coordinates and the magnitude of the moments need be calculated and not the directions. This not only simplifies the inverse-problem calculations but results in a significant increase in spatial resolution over MEG (Flynn 1994) with localizations better than 0.5 mm observed. The field from a magnetic dipole is given by
$$ \mathbf{B}\left(\boldsymbol{\mu}, \mathbf{r}\right)=\left({\mu}_0/4\pi \right)\left[\left(3\left(\boldsymbol{\mu} \cdot \mathbf{r}\right)\mathbf{r}\right)/{\mathrm{r}}^5-\boldsymbol{\mu} /{\mathrm{r}}^3\right] $$
and since both μ and r lie along the z-axis, this reduces to
$$ {\mathrm{B}}_{\mathrm{z}}=\left({\mu}_0/2\pi \right)\left(\mu /{\mathrm{z}}^3\right) $$
where μ is the magnetic moment which may be expressed in units of pJ/T. A typical value of μ observed for high-quality NP is 1.27 × 10 −07 pJ/T/np.
Fig. 1

Photograph of magnetic relaxometry system used at senior scientific for studying disease using cell cultures and small animals. The upper structure is the dewar containing the SQUID sensors with gradiometers in the protruding snout. The Helmholtz coils are shown above and below the measurement stage

To measure the moments using the SPMR method, the sample is placed under the SQUID sensor system, and a magnetizing field of approximately 50 gauss is applied for 0.75 s during which time the sensors are turned off. After a short delay, 0.035 s, to allow any induced currents in the system to dissipate, the decaying magnetic moment of the sample is measured by the SQUID sensor array. An example of such a decaying moment is shown in Fig. 2. The initial decay follows an exponential curve as predicted by Néel (1955). The field decay curve is measured for several seconds and the field magnitude calculated at the end of the magnetizing pulse. The field from each sensor position is then used to derive the source positions and magnitudes.
Fig. 2

Magnetic relaxation decay curves for NP bound to cells through antibody interactions and the same NP without cells present

An important attribute of SPMR is that the decay time constants differ substantially between NP that are bound to a cell or some other substance and thus not able to freely rotate and NP that are unhindered (Adolphi et al. 2009, 2010). This is shown clearly in Fig. 2 where the curve for NP bound to cells decays in seconds, whereas effectively no signal is seen for the same NP but not bound to cells. Néel relaxation occurs due to thermal fluctuations of the direction of the magnetic moment relative to the crystal orientation. The rate for Néel is given by
$$ {\tau}_N={\tau}_0{e}^{KV/ kT} $$
where K is a characteristic of the magnetic material, V is the volume of the NP, k is the Boltzmann constant, and τ 0 has a value of 10 −9 s. In contrast, if the NP are not bound, they decay by Brownian motion given by the rate
$$ {\tau}_B=3\eta {V}_h/{k}_BT $$
where η is the viscosity of the medium, Vh is the hydrodynamic volume, and kB is Boltzmann’s constant. The desired decay time for bound NP is several seconds which according to the Néel formula requires a NP with a diameter of 25 nm. Unbound NP of this diameter decaying by Brownian motion decay in less than 1 msec. This very important feature of SPMR means that very high contrast is achieved in imaging cancer cells in vivo that are targeted by the NP that have been conjugated to antibodies specific to the cancer cells as NP circulating in the blood give no signal in the SQUID sensor time window. There are some similarities in this property of SPMR and MEG. PET is often used for both cancer detection and for brain activity through targeting metabolic activity. However, PET isotopes are decaying whether at the targeted site or anywhere in the blood stream. As stated above this is not true of SPMR and also not true in MEG where only active neuronal clusters are producing measurable magnetic fields.
The first important attribute of SPMR is the high sensitivity of the method for detecting minute amounts of NP, less than ng of Fe required, because of the SQUID sensor capabilities. The second important attribute are the characteristics of the superparamagnetic NP that yield high magnetic moments, substantial difference between bound and unbound NP, and are not ferromagnetic so do not cluster. The Néel time dependence on volume severely restricts the size of the NP that can be used in SPMR since a diameter of just a few nm in either direction from the ideal of 25 nm can be many orders-of-magnitude difference in decay time. For this reason, substantial effort has gone into methods of producing NP with minimal dispersity in size. Figure 3 is a recent result obtained at the Center for Integrative Nanotechnology (CINT) (Vreeland 2015).
Fig. 3

Plot of NP diameter distribution as obtained from analyzing a transmission electron microscope photo of NP placed on a slide

3 Applications of SPMR to Nanomedicine

The methodology of SPMR has been applied to a number of diseases in the area of nanomedicine. T-cells have been labeled with NP conjugated to an antibody for the specific T-cells responsible for rejecting transplanted organs and used to measure transplant rejection in a mouse model (Flynn et al. 2007; Butler et al. 2013). A study of leukemia minimal residual disease (MRD) has been carried out using NP with antibodies (CD-34) specific to a number of leukemia types (Jaetao et al. 2009). SPMR has also been applied to the study of solid tumors in breast cancer (Hathaway et al. 2011; Adolphi et al. 2012), ovarian cancer (Flynn et al. 2014), and prostate cancer. The results have also been compared to MRI imaging in some detail using an animal model (Adolphi et al. 2012). A further advantage of the SPMR technique over many other biomedical methods is the transparency of tissue and bone to low-frequency magnetic fields. This implies, just as in the case of MEG, that source localization is not affected by intervening tissue. For animal studies this is quite important and is unlike the scattering that occurs in the use of fluorescent markers resulting in loss of localization of source accuracy with depth.

3.1 Linearity of Response

Because the strength of the magnetic field is completely linear in relationship to the source magnetic moment, the SPMR results are directly proportional to the number of bound NP in the source. Again, a similarity to MEG where the magnetic field strength observed can be directly related to the number of neurons involved. This linearity is demonstrated in Fig. 4 for the case of ovarian cancer cells (Flynn et al. 2014). Here the number of live ovarian cells in an in vitro sample was varied with the strength of the magnetic moment measured. The inset to this figure shows that the sensitivity with the present SPMR system shown in Fig. 1 is 40,000 cells. The present standard for detecting ovarian cancer is trans-vaginal sonography (TVS) which requires over one billion cells indicating the excellent sensitivity of the SPMR method. The linearity shown in this figure is useful for in vivo animal studies of therapy. By using known amounts of cells and NP, it is possible to convert magnetic moments to numbers of cells and then monitor the number of cancer cells in a tumor as a function of applied therapy to see if the therapy is working or not. This is not possible in MRI where saturation of signal occurs and the response is not linear.
Fig. 4

Plot of the magnetic moment of cell cultures versus the number of cells illustrating the moment is linear with the cell number. The insert is the lower cell count indicating the sensitivity of the SPMR method for these cells

3.2 Specificity

There are many types of antibodies, proteins, and other bioagents that can be linked to the NP used in SPMR through conjugation procedures. By using various live cell lines of cancer or T-cells, it is possible to determine the specificity of these various agents to different cell lines by measuring the magnetic moment as a function of time after mixing the conjugated NP with the cells. The resulting incubation curve can be used for a variety of purposes. From a dynamic perspective, the rate of binding of the antibody to the cells can be used to understand the chemical processes involved. The relative magnitudes of the moments observed indicate the specificity of the particular antibody for the cell line and can be used to determine biomarker efficacy. The results also can be used as a calibration for in vivo studies to determine what type of cancer is present. Figure 5 is an example of such a study using several breast cancer cell lines and the antibody Her2 (Hathaway et al. 2011). The results at the top of the figure show that the cell line MCF7/Her2–18 is significantly more specific to the Her2 antibody than the MDA-MB-231 cell line and even more so than the non-specific cell line CHO. This comparison is verified by the microscopic examination of the cells in the lower part of the figure where Prussian blue staining has stained the NP on the cell surface. The MCF7.Her2–18 cell line shows considerable more NP are on the surface than the other cell lines. Fitting these curves with a rate equation (Flynn et al. 2014) yields the number of NP/cell which may be several million NP. The sensitivity for detecting these breast cancer cells in the present SPMR system is about 100,000 cells. This may be compared to a mammogram that requires 100 million cells. Because of the specific action of the antibody on the NP, only cancer cells are targeted and not benign tumors.
Fig. 5

Specificity of the SPMR method is shown for different cell types in breast cancer depending on the antibody chosen, Her2. The upper part of the figure shows incubation curves for three different cell lines and no cells with the magnitude of each curve representing the specificity of the Her2 antibody for that cell line. The lower part of the figure verifies this finding by showing that the cells with the highest specificity are covered more completely with the NP as visualized through Prussian Blue staiing

3.3 In Vivo Detection and Localization

Living animals containing tumors may be placed under the SPMR system and the tumors localized and the number of cells determined. In Fig. 6, an example of such an experiment is shown. The mouse is a xenograft mouse containing two human breast cancer tumors. For this case, the NP + Her2 have been intra-tumorally injected although intravenous injections also may be used. The mouse was placed under the system and the stage moved to obtain a total of 35 sensor positions. The inverse problem was solved using a Levenberg-Marquardt algorithm similar to that used in MEG (Huang et al. 1998) and the source locations and magnetic moments extracted. The resulting confidence limits are then superimposed on a photograph of the mouse using a grid to establish the correct geometric relationship. The upper left-hand corner of the figure shows the two tumors growing on the mouse; the lower left corner shows the resulting confidence limits x and y coordinates, and the right photo shows the superposition of these two measurements.
Fig. 6

Superposition of SPMR magnetic moment confidence limits on photographs of small animals showing localization in animals containing xenograft human tumors. A shows the tumors on the animal and C the superposition

Through the use of phantoms containing vials of live cells, it has been shown that spatial resolutions of approximately 0.5 mm for multiple sources can be obtained (Hathaway et al. 2011). This is better than the resolution normally obtained in MEG experiments. The principal reason for this is that in the inverse problem only the coordinates and the magnitude of the source have to be determined since the sources are all aligned with the magnetizing field. In MEG, two more factors are needed that determine the orientation of the source.

4 Future SPMR Systems

The SPMR system described here, and shown in Fig. 1, is limited in sensitivity and resolution capabilities. It has no background sensors and operates in an unshielded environment and is thus subject to considerable interference. It is currently operating at a 20 pT sensitivity level, whereas the SQUID sensitivity is better than 5 f T/√Hz. System-performing MCG measurements in unshielded environments often exceed 10 f T/√Hz noise thresholds so it is possible to improve the present system by several orders of magnitude by addition of background sensors. Other considerations to improve the performance of the system are removal of all metal components and induced currents in the system due to the pulsing of the Helmholtz coils which can be accomplished by reengineering the SQUID probe. Finally, improvements in the NP themselves offer additional sensitivity increases due to the dispersity of the size of the NP. Because of the narrow range of NP diameters that fall in the SPMR window, many of the NP coupled to cells fall outside of the window but occupy sites on the cell thus reducing the effective magnetic moment of the cell. Reduced dispersity of the NP is a major goal in the development of SPMR. Figure 7 is an illustration of the next-generation system performance for detecting cells. In this T-cells are shown but the performance increase is representative of all of the cell lines for the various cancers being investigated.
Fig. 7

Extrapolation of the linearity curve for cells versus moment to a SPMR system of much higher sensitivity demonstrating <100 cell detection capability

5 Conclusions

Although the primary thrust of this manuscript has been on cancer and similar diseases, there are many other diseases with biomarkers known that SPMR can be applied to. These include several diseases of the brain, and in the future the combination of MEG and SPMR in the diagnosis and treatment of neural diseases will be quite promising. There are a number of biomarkers known for the tau and amyloid plaque that build up in the brain of Alzheimer’s patients. There is also increasing evidence for the role of tau in PTSD and CTE, and it will be possible to identify this with SPMR using the known biomarkers for tau. Recent MEG research in these areas have identified methods for MEG biomarkers in brain disorders (Georgopoulos et al. 2007), PTSD (Georgopoulos et al. 2010) and traumatic brain injury (Huang et al. 2009). The combination of these approaches could be a significant advance in understanding these increasingly common neural diseases.


  1. Adolphi NL, Huber DL, Jaetao JE, Bryant HC, Lovato DM, Fegan DL, Venturini EL, Monson TC, Tessier TE, Hathaway HJ, Bergemann C, Larson RS, Flynn ER (2009) Characterization of magnetite nanoparticles for SQUID-relaxometry and magnetic needle biopsy. JMMM 321:1459–1464CrossRefGoogle Scholar
  2. Adolphi NL, Huber DL, Bryant HC, Monson TC, Fegan DL, Lim JK, Jaetao JE, Tessier TE, Lovato DM, Butler KS, Provencio PC, Hathaway HJ, Majetich SA, Larson RS, Flynn ER (2010) Characterization of single-core magnetite nanoparticles for magnetic imaging by SQUID-relaxometry. PMB 55:5985–6012Google Scholar
  3. Adolphi NA, Butler KS, Lovato DM, Tessier TE, Trujillo JE, Hathaway HJ, Fegan DM, Monson TC, Stevens TE, Huber DL, Ramu J, Milne ML, Conradi MS, Altobelli SA, Larson RS, Flynn ER (2012) Imaging of Her2-targeted magnetic nanoparticles for breast cancer detection, comparison of SQUID-detected magnetic relaxometry and MRI. Contrast Media Mol Imaging 7(3):308–319CrossRefGoogle Scholar
  4. Brenner D, Williamson SJ, Kaufman L (1975) Visually evoked magnetic fields of the human brain. Science 190:480–482CrossRefGoogle Scholar
  5. Butler KS, Lovato DM, Adolphi NA, Belfon R, Fegan DM, Monson TC, Hathaway HJ, Huber DL, Tessier TE, Bryant HC, Flynn ER, Larson RS (2013) Development of antibody-tagged nanoparticles for noninvasive detection of transplant rejection using biomagnetic sensors. Cell Transplant 22:1943–1954CrossRefGoogle Scholar
  6. Cohen D (1968) Magnetoencephalography: evidence of magnetic fields produced by alpha-rhythm currents. Science 161:784–786CrossRefGoogle Scholar
  7. Flynn ER, Bryant HC (2005) A SQUID based system for in vivo cancer imaging. Phys Med Biol 50:1273–1293CrossRefGoogle Scholar
  8. Flynn ER (1994) Factors which affect spatial resolving power in large array biomagnetic sensors. Rev Sci Instrum 65:922CrossRefGoogle Scholar
  9. Flynn ER, Bryant HC, Bergemann C, Larson RS, Lovato D, Sergatskov DA (2007) Use of a SQUID array to detect T-cells with magnetic nanoparticles in determining transplant rejection. JMMM 311:429–435CrossRefGoogle Scholar
  10. Flynn ER, Adolphi NL, Bryant HC, Butler KS, Hathaway HJ, Huber DL, Lovato DM, Tessier TE, Trujillo JE, Larson RS (2014) Applications of magnetic relaxometry in ovarian cancer. To be publishedGoogle Scholar
  11. Georgopoulos AP, Karageorgiou E, Leuthold AC, Lewis SM, Lynch JK, Alonso AA, Aslam Z, Carpenter AF, Georgopoulos A, Hemmy LS, Koutlas IG, Langheim FJP, McCarten JR, McPherson SE, Pardo JV, Pardo PJ, Parry GJ, Rottunda SJ, Segal BM, Sponheim SR, Stanwyck JJ, Stephane M, Westermeyer JJ (2007) Synchronous neural interactions assessed by magnetoencephalography: a functional biomarker for brain disorders. J Neural Eng 4:349–355CrossRefGoogle Scholar
  12. Georgopoulos AP, Tan HRM, Lewis SM, Leuthold AC, Winskowski AM, Lynch JK, Engdahl B (2010) The synchronous neural interactions test as a functional neuromarker for post-traumatic stress disorder (PTSD): a robust classification method based on the bootstrap. J Neural Eng 7:016011CrossRefGoogle Scholar
  13. Hämäläinen M, Hari R, Ilmoniemi RJ, Knuutila J, Lounasmaa OV (1993) Magnetoencephalography – theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev Mod Phys 65:413–497CrossRefGoogle Scholar
  14. Hathaway HJ, Butler KS, Adolphi NA, Lovato DM, Belfon R, Fegan DL, Monson TC, Trujillo JE, Tessier TE, Bryant HC, Huber DL, Larson RS, Flynn ER (2011) A novel method for early detection of breast cancer using magnetic nanoparticles and ultra-sensitive magnetic field sensors. Breast Cancer Res 13:R108CrossRefGoogle Scholar
  15. Huang M, Aine CJ, Supek S, Best E, Ranken D, Flynn ER (1998) Multi-start downhill simplex methods for spatio-temporal source localization in magnetoencephalography. Electroencephalogr Clin Neurophysiol 108:32–44CrossRefGoogle Scholar
  16. Huang MX, Theilmann RJ, Robb A, Angeles A, Nichols S, Drake A, D’Andrea J, Levy M, Holland M, Song T, Sheng G, Hwang E, Yoo K, Cui L, Baker D, Trauner T, Coimbra R, Lee R (2009) Integrated imaging approach with MEG and DTI to detect mild traumatic brain injury in military and civilian patients. J Neurotrauma 26:1213–1226CrossRefGoogle Scholar
  17. Kötitz R (1995) Ferrofluid relaxation for biomagnetic imaging, biomagnetism: fundamental research and clinical applications. In: Baumgartner C et al.(eds) Elsevier science. IOS Press, Amsterdam, p 785Google Scholar
  18. Néel L (1955) Some theoretical aspects of rock-magnetism. Adv Phys 4:191–243CrossRefGoogle Scholar
  19. Romanus E, Huckel M, Gross C, Prass S, Brauer R, Weitsches W, Weber P (2001) Magnetic nanoparticles as a novel tool in vivo diagnostics. ICMF9 MRX posterGoogle Scholar
  20. Supek S, Aine C, Ranken D, Best E, Flynn ER, Wood C (1999) Single versus paired visual stimulation: superposition of early neuromagnetic responses and retinotopy in extrastriate cortex in humans. Brain Res 830:43–55CrossRefGoogle Scholar
  21. Vreeland EC (2015) Enhanced nanoparticle size control by extended LaMer’s mechanism, Chem. Mater. 27:6059–6066CrossRefGoogle Scholar
  22. Jaetao JE, Butler KS, Adolphi NL, Lovato DM, Bryant HC, HC RI, Winter SS, Tessier TE, Hathaway HJ, Bergemann C, Flynn ER, Larson RS (2009) Enhanced leukemia cell detection using a novel magnetic needle and nanoparticles. Cancer Res 69(21):8310–8316CrossRefGoogle Scholar
  23. Zimmerman JE (1966) Macroscopic quantum interference effects through superconducting point contacts. Phys Rev 141:367–375CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Senior Scientific LLCAlbuquerqueUSA

Section editors and affiliations

  • Risto Ilmoniemi
    • 1
  1. 1.Department of Neuroscience and Biomedical EngineeringAalto UniversityEspooFinland

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