Dr Line Pourtau

Dr Hugo Oliveira

Dr Julie Thevenot

Yali Wan

Prof Alain Brisson

Dr Olivier Sandre

Sylvain Miraux

Eric Thiaudière
email: eric.thiaudiere@rmsb.u-bordeaux2.fr

Sébastien Lecommandoux
email: lecommandoux@enscbp.fr

Prof. Sébastien Lecommandoux

Yali Wan Five

Author-Four

Antibody-functionalized magnetic polymersomes: in vivo targeting and imaging of bone metastases using high resolution MRI

Keywords: Magnetic Resonance Imaging, Polymersome, Targeting, Bone Tumor Magnetic Resonance Imaging, Polymersome, Targeting, Bone Tumor

Multifunctional polymersomes loaded with maghemite nanoparticles and grafted with an antibody, directed against human endothelial receptor 2, are developed as novel MRI contrast agents for bone metastasis imaging. Upon administration, in mice bearing orthotopic metastatic breast cancer, MR images show targeting and enhanced retention of antibodylabeled polymersomes at the tumor site.

Breast cancer is the most prevalent cancer and second leading cause of cancer mortality in women. [1] In nearly 50% of primary cancers, and 80% of recurring metastases, this type of cancer preferentially metastasizes to the skeleton, e.g. femur, pelvis, vertebrae and skull [2] , leading to poor vital prognosis. [3] . Due to their body location (profound tissue surrounded by a mineralized bone matrix) and the heterogeneity of pathological tissue, the use of new tools, allowing specific detection of these malignant cells, may result in better treatment outcome and patient survival. High-performance imaging, providing spatial resolution in three dimensions, is required for the detection of small-sized tumors (such as early metastatic stages). In this context, magnetic resonance imaging (MRI) is a good candidate for noninvasive characterization of tumor development in vivo. Widely implemented in clinical practice, MRI provides a sensitive method for the detection of bone marrow metastases. [4] Tumor detection is usually carried out using the natural or gadolinium-enhanced contrast between healthy tissue and tumor tissue, but specifically targeted contrast agents can ensure precise tumor delineation and allow a more accurate diagnostic.

During the past two decades, magnetic nanoparticles and particularly ultrasmall superparamagnetic iron oxide nanoparticles (USPIOs) and clusters of the later (generally assembled using organic material and designated as superparamagnetic iron oxides, SPIOs) [5] have been widely investigated as MRI contrast agents owing to their unique characteristics: efficient contrast effects (as negative (T 2 ) contrast agents), biocompatibility, and possible surface functionalization. [5,6] Recent work has indeed demonstrated the utility of targeting iron oxide particles towards the development of pathology-specific MRI contrast agents. [7,8,9,10] On the other hand, polymersomes, vesicular structures generated by self-assembly of amphiphilic copolymers, are promising drug carriers that can accommodate both hydrophobic and hydrophilic cargo within their membrane and aqueous core, respectively. [11] Recently, several authors have shown that high amounts of USPIOs could be incorporated within these structures with a good control over their morphology and size and, at the same time, superior transverse relaxometric properties (high r 2 values). [12] Our group previously developed such hybrid polymersomes where the embedded USPIOs acted as both MRI contrast agents (with r 2 up to 182 s -1 .mM Fe -1 ) and actuators for magnetic field induced drug release (magnetochemotherapy). [13] Another interesting development of polymersomes in the recent years is their functionalization with targeting molecules (protein, peptide or small molecule). Indeed, targeted polymersomes have been successfully implemented for vascular targeting and receptor-mediated endocytosis [14] , leading to improved drug efficiency, especially with antibodies as ligand [15] .

Here, by means of polymersome surface functionalization using cell specific targeting ligands (antibodies), we demonstrate hybrid polymersomes application as T 2 * MRI contrast agents for specific targeting of a breast cancer bone metastases model. The overexpression of the membrane tyrosine kinase Human Epidermal Growth Factor Receptor-2 (HER2), found in approximately 20% of breast cancers [16] , is associated with a poor prognosis, making this receptor a potential target for guided therapy. Indeed, several examples of successful HER2 targeting have been recently described. [7, 8, 17, 18] [18] Hence, trastuzumab, the first monoclonal humanized antibody targeting HER2, approved by FDA in 1998, and currently applied in the clinical field, [19] was used as ligand to target breast cancer cells in a bone metastasis model.

Polymersomes were prepared from a blend of amphiphilic block copolymers:

poly(trimethylene carbonate)-b-poly(glutamic acid), the same copolymer end-capped with either a maleimide group or fluorescein, and hydrophobically coated USPIOs (30 wt% to polymer). After nanoprecipitation in buffer, maleimide-bearing polymersomes were reacted with thiol-derivatized trastuzumab to obtain the targeted multifunctional polymer vesicles (Figure 1A, experimental procedures are detailed in Supporting Information).

These multifunctional polymersomes were further tested in a clinically relevant model. A majority of studies focused in large subcutaneous xenograft cancer models [7,8,18] , presenting poor relevance in a metastasis detection scenario. Indeed, in some cases, the tumor volume reached 1 cm 3 , representing a significant percentage of the mice body weight. The size of the tumors can influence tumor vascularization and dramatically change its microenvironment, with a drastic impact on the contrast agent overall performances. [20] Recently, a more realistic animal model was presented by Kievit et al. [21] : transgenic mice with intact immune system were used, developing tumors in a natural manner, with metastases appearing in lungs, liver and bone. Unfortunately, due to their small size, bone metastases were not detected by MRI in this study. Here, focusing on a diagnostic clinical scenario, we propose an animal model bearing small tumors (12-15µl), mimicking a relevant metastasis environment. Spontaneous bone metastases, arising from primary breast tumor, are uncommon and this has prompted the wide use of bone tumor models based on local or systemic injection of tumor cells. One of the main disadvantages of the systemic injection resides on the lack of control of the tumor final localization and pathogenesis. [22] In that sense, we developed a bone cancer model by As observed in Figure 1C, naked and antibody-grafted polymersomes presented similar size and zeta potential, consistent with previous reports. [13,23] Using the previously determined aggregation number, [23] we estimated an average number of antibody per vesicle of 31, corresponding to a grafting efficiency of 86% (Supporting Information). The developed systems relaxivity (r 2 ) was evaluated at 4.7 T (200 MHz operating frequency) and values were found consistent with previous reports using similar USPIOs. [9,24] The targeting potential of the developed system was first tested in an in vitro setting. After exposure to the polymer vesicles, cells were analyzed by flow cytometry: polymersomes fluorescently labeled and functionalized with trastuzumab showed a clear targeting (six fold increase of the number of FITC positive cells) towards BT-474 cells (HER2 positive) as compared with naked particles (Figure 1D). Moreover, when cells expressing low levels of HER2 (i.e. MDA-MB-231 breast cancer cell line [25] ) were used, no significant differences were observed for the two formulations tested (Figure 1D), demonstrating the specificity of the targeting. Interestingly, thanks to the polymersomes high USPIOs content, MRI also evidenced the targeting towards BT-474 cells. Indeed, as observed in Figure 1E, cells incubated with targeted polymersomes and embedded in a transparent gel appeared with a negative contrast (T 2 * effect in gradient echo images), accounting for the uptake of polymersomes, whereas cells incubated with naked polymersomes showed no change in contrast as compared to control cells.

MRI was also used to perform real time whole body biodistribution [26] (4.7 Tesla; Figure 2A).

Figure 2B presents signal-to-noise ratio (SNR) as a function of time (pre-contrast minus postcontrast values, ∆SNR) for 3 tissues (i.e. blood, liver and muscle). Despite a quick uptake by the liver, blood data show that the injected polymersomes persist in circulation for at least 20 min (Figure 2A and2B). Similar results where found after naked polymersomes administration (data not shown) and for other nanoparticles with similar sizes. [27] Interestingly, MRI signal analysis of the tumor tissue showed that naked polymersomes are less retained than the targeted ones (Figure 2E). Additionally, superior contrast was observed in the tumor bone, when compared with the contralateral femur tissue (Figure 2C This behavior can be explained by the small size of the internal lesions without fully developed vascularization in the bone. Indeed, larger tumors generally contain leaky vasculature associated with insufficient lymph drainage that is correlated with an enhanced permeability and retention (EPR) effect of nanoparticles also referred to as passive targeting. [28] In the case of smaller tumor structures, where angiogenesis might be less influenced by anoxic conditions, this EPR effect is very limited. In such a context, the development of nanoparticles with an "active targeting" (grafting of a specific ligand) is necessary to reach the tumor and maintain a high concentration at the tumor site. As a result, this was only when targeted polymersomes were used that a more persistent T 2 * contrast effect was observed at the tumor site, associated with an increased residence time of the contrast agent.

To our knowledge, this is the first report of USPIO-loaded polymeric vesicles used as MRI contrast agent and able to target cancer cells in vivo, in a relevant animal model for bone metastasis. This approach opens new avenues for the development of more powerful diagnostic tools developed on the basis of higher specificity. Indeed, to avoid any loss in binding affinity, only a limited number of contrast agent structures can be grafted onto one antibody. For common MRI contrast agents such as gadolinium complexes, the concentration of contrast agent at the targeted site achieved with such labeled antibodies is usually insufficient to generate detectable MRI contrast. [29] In the case of magnetic polymersomes however, the high relaxivity provided by the USPIOs clustering effect associated with the binding of several antibodies per particle potentiate the efficiency as targeted MRI contrast agent.

Thanks to the versatility of the polymersome structure, other -or complex mixtures oftargeting moieties can be used in order to assess other tissues or pathological situations, broadening their application as diagnostic tools. Moreover, as previously reported by our group, the developed systems are able to load high amounts of drug and USPIOs (i.e. 12%

(w/w) of doxorubicin while also encapsulating 50% (w/w) of USPIOs). [13,23] In comparison with other reported vesicular systems, where a doxorubicin loading of only 3.3% (w/w) was reached, [7] these polymersomes open new perspectives for the development of targeted tools for a dual diagnostic and therapy purpose.

Experimental Section

A detailed description of experimental procedures can be found in the supporting information.

Supporting Information

Supporting Information is available online from Wiley InterScience or from the author.

antibody concentration was determined by OD280 (corrected to 1 mg/mL), snap frozen and kept at -20ºC until further use. The number of thiols per antibody was determined using Ellman's assay [32] . The influence of thiolation in the antibody dispersion stability was followed by DLS, with no aggregation being observed (Figure S1,A). Tratuzumab antibody presented a hydrodynamic diameter of 12.3±1.1 and 12.9±0.4 nm, with a polydispersity index of 0.18 and 0.17, for native and thiolated, respectively.

Superparamagnetic iron oxide nanoparticles (USPIOs; γ-Fe 2 O 3 ) were synthesized as previously described [33] , sorted according to their size by fractionated phase separations and characterized along the sorting process by vibrating sample magnetometry (VSM) and on the final sample by scattering techniques (SLS, DLS and SANS). Then they were grafted with the anionic surfactant Beycostat NB09 (CECA, Arkema group, France) as described elsewhere [34] , in order to allow their inclusion in the polymersome hydrophobic reservoir.

Polymersomes were obtained by the nanoprecipitation method (solvent assisted dispersion).

Briefly, a mixture of diblock:triblock:FITC-grafted-diblock (PTMC-PGA : PTMC-PGA-PEG : PTMC-PGA-FITC; 60:20:20) solution (10 mg/mL final, in DMSO) and USPIOs (at 30% feed weight ratio) was vortexed with phosphate buffer (50 mM, pH 6.5) solution.

Nanoparticle were purified via ultrafiltration (3 x) using a filter cut off of 100 kDa, with phosphate buffer, 50 mM, pH 6.5. Total mass of the dispersion was determined using gravimetry and total iron content was assessed as described elsewhere [35] . The density of reactive maleimide groups was determined by using a competition Ellman's assay. Briefly, the dispersion (200 uL) was mixed to a same volume of a 250 uM, L-cysteine (Sigma) solution. This mixture was let to react for 1 hr, 1100 rpm, at room temperature. A control was performed using polymersomes based on PTMC-b-PGA alone. In a 96 well plate, each sample (50 uL) was pipetted, together with Tris Buffer (200 uL, 30mM, pH 8.9) and DTNB (20uL, 29.7 mg DTNB in methanol). The absorption of the formed product was measured at 412 nm. The number of maleimide groups was determined by the loss of thiol concentration, against a L-cysteine calibration curve.

In order to produce targeted polymersomes the thiolated trastuzumab was added to the nanoparticle dispersion at 55 µg of antibody per mg of total copolymer and left to react, overnight, at room temperature. Unreacted antibody was removed by means of ultrafiltration (3 x) with phosphate buffer, 50 mM, pH=7.4, using a filter cut-off of 25 nm (Millipore).

Antibody content was determined by means of BCA protein assay. The number of grafted antibodies per nanoparticle was estimated by dividing the number of antibody molecules (measured after final step of purification) by the number of polymersomes in dispersion (estimated using the previously determined aggregation number [36] ). The grafting efficiency was expressed as the percentage of grafted antibody (quantified after final step of purification by means of the BCA assay) in relation to the total amount initially reacted with polymersomes. In view of comproving the efficient antibody grafting a small amount of the nanoparticle dispersion, before and after the final step of purification, where loaded in a 7% SDS PAGE gel (lacking reducing agents). Free trastuzumab was run alongside grafted nanoparticles. As observed in figure S1,B, when the antibody is grafted to the nanoparticles it is unable to enter the gel and appears solely in the well of the stacking gel. Before the last step of purification a faint band is observed at the correspondent size of the free thiolated antibody, corresponding to the small fraction of unreacted antibody (Figure S1,B,column 4).

Conversely, after the last step of purification (Figure S1, B, column 5) no free antibody can be detected asserting for the purification procedure.

Figure S1-Dynamic light scattering characterization of native and thiolated trastuzumab antibody (trastuzumab and trastuzumab-SH, respectively) (A). Native PAGE 7% gel of trastuzumab grafted nanoparticles before and after last purification step (B).

Size and zeta potential of the NPs was measured by Dynamic Light Scattering using the NanoZS90 apparatus from Malvern Instrument. Measurement was carried out at 90°. The sample was kept at constant temperature (25°C) during all the experiment. The Smoluchowski model was applied for zeta potential determination and cumulant analysis was used for mean particle size determination.

Relaxation rate R 2 (1/T 2 ) measurements of polymersomes were performed as follows.

Experiments were carried out at 4.7 T (200 MHz operating frequency) on a Bruker Biospec system (Bruker, Ettlingen, Germany) at 20°C. T2 measurements were performed at 25ºC with a CPMG (Carr-Purcell-Meiboon-Gill) imaging sequence (TR, 5000 or 10000 ms; inter echotime: 5 ms; number of echo images: 256; FOV: 50 x 50 mm; matrix: 128 x 128; slice thickness: 2 mm).

Cryo-Transmission Electron Microscopy (cryo-TEM). Polymersomes (2 mg/mL in water)

were deposited on an EM grid coated with a perforated carbon film. After draining the excess liquid with a filter paper, grids were quickly plunged into liquid ethane cooled down by liquid nitrogen and mounted onto a Gatan 626 cryoholder (Gatan, USA). TEM was performed with a Tecnai F20 microscope (FEI, USA) operated at 200 kV. Images were recorded with a 2k x 2k USC1000-SSCCD camera (Gatan). (scale bar 50 nm).

In vitro experiments

Cell culture:

Human breast cancer cell lines BT474 and MDA-MB-231 were purchased from the American Type Culture Collection. Tumor cells were cultured routinely in RPMI 1640 and DMEM/F12 (Invitrogen, Carlsblad, CA, USA) respectively, supplemented with 10% foetal calf serum (Invitrogen, Carlsblad, CA, USA). Cultures were kept under standard conditions (37°C, humidified atmosphere, 5% CO2) and passaged twice a week to keep them in logarithmic growth.

Cytometry:

Breast cancer cell lines BT474 and MDA-MB-231 were incubated with NPs (naked or targeted) at 0.2mg of copolymer per mL in complete medium and at 37°C. After 4hrs incubation with NPs, cells were washed three times with phosphate-buffered saline (PBS), collected and analyzed by flow cytometry Incyte software (Millipore, Billerica, MA, USA).

MRI:

Breast cancer cell lines BT474 and MDA-MB-231 were incubated with NPs (naked or targeted) at 0.2mg of copolymer per mL in complete medium and at 37°C. After 24 hr incubation with NPs, cells were washed three times with phosphate-buffered saline (PBS), collected and trapped in agarose gels (1% w/v in H 2 O) for MRI analysis. All experimental procedures were approved by the local institutional ethics committee (approval n° 33010001-A).

Mice were followed for several months, using MRI, in order to assess tumor progression (Figure S3). Presence of HER2 expression in newly formed tumor tissue in bone was confirmed ex vivo before nanoparticle administration (Figure S4).

In vivo MRI:

Animal preparation for MRI:

Mice were anesthetized using isoflurane (1-1.5% in air). Gradient insert temperature was maintained at 37°C and a system for monitoring physiological parameters used to control respiration rate (SA Instruments, Inc., Stony Brook, NY, USA).

Biodistribution measurement:

For scanning the whole mouse in one shot, a mouse whole body coil was used. Keyhole reconstruction and image analysis were performed with homemade software developed on Igor Pro [37] .

MRI tumor progression monitoring:

MRI was performed in a vertical bore spectrometer at 9. x 83 x 83 μm 3 , receiver bandwidth: 52 kHz. The final 3D TrueFISP image was made from the combination of eight acquisitions sets. Each set was acquired with a specific difference in phase between consecutive radio frequency pulses. The differences in phase were ΔΦ= 180°, 0°, 90°, 270°, 45°, 135°, 225°, 315° [38] . Reconstructions were performed with Igor Pro data processing software (Wavemetrics, Lake Oswego, OR, USA). The final TrueFISP images were calculated as the square root of the sum-of-the-square of the eight images. The total acquisition time was 34 minutes.

Tumor volume quantification:

Tumor volume analysis was performed with a semi-automatic segmentation procedure on Amira software (Visage Imaging GmbH, Berlin, Germany). First a volume that encompassed femur was preselected in the MR image. Inside this preselected volume, minimal value of tumor signal was defined by thresholding the signal intensity at 4 times the bone marrow value.

Ex vivo HER2 immunohistochemistry:

Excised bone were decalcified 4 days in ethylene diamine tetraacetic acid 0.5M (Sigma-Aldrich, St. Louis, MO, USA), dehydrated, embedded in paraffin and sectioned with a Jung model K microtome (Carl Zeiss, Heidelberg, Germany). Ten-micrometer thick sections were used for HER2 immunochemistry. HER2 immunohistochemical detection was performed on slides using an indirect streptavidin-biotin-peroxidase approach (Histostain-SP kit, Invitrogen, Carlsbad, CA, USA). The primary antibody mouse anti HER2/Neu (9G6): sc-08 (Santa Cruz biotechnology, Santa Cruz, CA, USA) was diluted 1:200 in PBS and added for 2h at room temperature. After several rinses in PBS, cells were incubated with biotinylated secondary antibody for 10 min and streptavidin-peroxidase conjugate for 10 min with intermittent washes in PBS. Slides were stained using 3-amino-9-ethylcarbazole as chromogen in the presence of hydrogen peroxide. Bone sections were mounted and examined by optical microscopy (Zeiss, Le Pecq, France). TrueFISP image was made of the combination of four acquisitions sets. Each set was acquired with a specific difference in phase between consecutive radio frequency pulses. The differences in phase were ΔΦ= 180°, 0°, 90°, 270° [38] . Reconstructions were performed with Igor Pro data processing software (Wavemetrics, Lake Oswego, OR, USA). The final TrueFISP images were calculated as the square root of the sum-of-square of the four images.

The total acquisition time was 20 minutes.

A reference image was acquired with these parameters before nanoparticle intra venous bolus injection (100 μL).

  injecting BT-474 cells (HER2-positive cell line) directly in the femoral bone of NOD/SCID mice. (Figure 1B, experimental procedures are detailed in Supporting Information).

  , D), attesting the targeting specificity in a clinically relevant in vivo scenario.

Figure 2 -

 2 Figure 2 -(A) Biodistribution of T 2 * targeted polymersome in tumor bearing mice. Normalized 3D volume rendering of contrast agent accumulation throughout time. (B) ΔSNR, in relevant organs, after targeted polymersome administration and as a function of time (20 min). (C) Pre-contrast whole body MR images before targeted polymersome administration. (D) Pre-contrast minus post-contrast whole body MR images 5 min post polymersome administration. (E) ΔSNR in the tumor site after naked or targeted polymersome administration, as a function of time (20 min).

Figure 3 -

 3 Figure 3 -Extracted longitudinal MRI views of bone in vivo. 3D TrueFISP image before (A, B) and after (C, D) naked (n=4) or targeted (n=6) polymersome administration (respectively) to tumor-bearing mice. Percentage signal change at the tumor site after naked or targeted polymersome injection, (E) and (F) respectively. Experiments were performed when the tumors reached a volume of 12 to 15 µl. Red arrows on MR images denote tumor tissue. White arrows on MR images denote contrast variations on tumor boundaries.

Figure S2 -

 S2 Figure S2 -Gallery of cryo-TEM images showing polymersomes embedded in a thin film of amorphous ice, homogenously distributed and densely coated with magnetic particles.

A

  T2*-weighted image was performed at 4.7 Tesla with a FLASH sequence (TE/ TR: 15/40 ms; FOV: 25 x 25 x 25 mm; matrix: 384 x 128 x 128; spatial resolution: 65 x 195 x 195 μm 3 , receiver bandwidth: 6 kHzIn vivo experimentsBone tumor model: BT474 breast cancer cells were harvested, counted with a Malassez cell counter and transferred into RPMI medium without serum before injection in NOD/SCID mice (8 week old, body weight =18-22 g). Mice were anesthetized with isoflurane (1-1.5% in air). After shaving the limb, the femur was exposed and a 0.6 mm hole was generated with a driller (Harvard Apparatus, Les Ulis, France). Mice were injected with 10 μL, containing one million tumor cells, into the intramedullary canal of the femur in the epiphysis region with Hamilton syringe. Bone wax was used to obturate the injection hole.

  It was an eight-leg high-pass birdcage resonator with a resonator diameter of 28 mm and a resonator length of 100 mm. The housing allows for a maximum outer diameter of the animal including mouse holder of 25 mm. These dimensions ensure the full coverage of a mouse with a weight up to 25 g. The resonator was made from flexible printed circuit board with chip capacitors in the endrings for tuning the resonator to the NMR system's frequency of 200.3MHz. Two capacitive coupling schemes including cable traps were used for providing circular polarization during both transmission and reception. Trim capacitors were used for adjusting tune and match when changing loads. A four-pole quadrature hybrid connected the two resonator ports to transmitter and receiver. The resonator shows a Q drop from 300 to 100 when loaded, which indicates that sample losses are dominating. For the reference image for keyhole reconstruction, two whole-body 3D FISP T2*-weighted images were acquired before and after dynamic contrast enhancement imaging to complete the k-space of dynamic images: TE/TR: 4/8 ms; flip angle: 10°; bandwidth: 39 kHz, FOV: 95 x 22 x 22 mm; matrix: 256 x 80 x 64; spatial resolution, 371 x 275 x 344 (μm) 3 ; number of averages: 8; total acquisition time: 5 min 3s. For dynamic contrast enhancement (DCE), dynamic 3D FISP T2*-weighted was performed with the following parameters: TE/TR: 4/8 ms; flip angle: 10°; bandwidth: 39 kHz; FOV: 95 x 22 x 22 mm; matrix: 256 x 44 x 40; spatial resolution, 371 x 500 x 550 (μm) 3 ; number of averages, 1; temporal resolution: 14 s/image; number of dynamic images: 96; experimental time, 23 min. A bolus of 100 µL of NPs at a dose of 15 mg of copolymer per mL was injected in the tail vein 1min after the beginning of the contrast-enhanced imaging experiment.

Figure S3 -

 S3 Figure S3-In vivo 3D TrueFISP MRI of the femoral bone of tumor-bearing mice 14 days (A), 41 days (B), 48 days (C), and 83 days after tumor cells injection (D). Red arrows on MR images show tumor locations. Tumor volume (µl) as a function of the elapsed time following BT474 cells implantation (E). Curves fit to a model of exponential growthand are shown for clarity. Letters (B, C, D) correspond to the displayed MR images.

Figure S4 -

 S4 Figure S4-MRI and HER2 immunohistochemistry of an healthy bone mouse (A,C) and bone of tumor bearing mouse 87 days post-surgery (B,D). (A,B) Extracted slice from 3D TrueFISP MRI data. (C,D) Her2 immunochemistry of the corresponding region where presence of HER2 on tumor cells membranes is revealed in red (D).

  4 Tesla (Bruker, Ettingen, Germany) without contrast agent injection. The RF coil was a dedicated 8-mm diameter surface probe tuned at 400 MHz (Doty, Columbia, SC, USA). The 3D TrueFISP sequence parameters were: TE/TR: 3.48/6.96 ms; FOV: 20 x 16 x 16 mm 3 ; matrix: 256 x 192 x 192; spatial resolution: 78

Acknowledgements

This work was supported by funding from the European Commission under the seventh framework program within the frame of the NanoTher project (Integration of novel NANOparticle based technology for THERapeutics and diagnosis of different types of cancer CP-IP 213631-2). The authors would also like to thanks European Science Foundation P2M program for support and Prof. J. Robert from Institut Bergonié for antibodies. Received: December 18, 2012 Revised: February 10, 2013 Published online: April 19, 2013

Supporting Information for

Antibody-functionalized magnetic polymersomes: in vivo targeting and imaging of bone metastases using high resolution MRI

By Line Pourtau + , Hugo Oliveira + , Julie Thevenot, Yali Wan, Alain Brisson, Olivier Sandre, Sylvain Miraux, Eric Thiaudière* and Sébastien Lecommandoux*

Experimental Section

Polymersomes formulation and characterization:

Poly(trimethylene carbonate)-b-poly(l-glutamic acid) (PTMC-b-PGA) copolymer was synthesized by ring-opening polymerization as previously described [30] . In order to form thiol-reactive vesicles, based on PTMC-b-PGA copolymer, a triblock formation strategy was followed. In that sense a bifunctional (i.e. N-Hydroxysuccinimide and maleimide) 2kDa PEG (JenkemUSA, China) was grafted to the diblock copolymer. Briefly, PTMC 26 -PGA 20 (0.65 g) was dissolved in anhydrous DMSO (13 mL) in the presence of 1 equivalent of N,Ndiisopropylethylamine (DIPEA) per acid group. Then bifunctional PEG (0.25 g) was dissolved in anhydrous DMSO (5 mL) and mixed to the previous solution. The reaction continued for 24 hrs in a N 2 atmosphere, at room temperature. The solution was concentrated by means of ultrafiltration (1 kDa) to a final volume of 5 mL and the copolymer precipitated by the addition of cold dichloromethane: diethyl ether (1:2) (150 mL). The obtained solid was extensively washed with diethyl ether, vacuum dried overnight and stored at -20 ºC until further use.

For fluorescent labeling, PTMC-b-PGA was modified in bulk using FITC. Briefly, copolymer (250 mg) was dissolved in anhydrous DMSO (5 mL) and DIPEA (100µL; 1 eq. per acid function) was added. After 5 min stirring, FITC (18 mg; 1 eq.) was added and the mixture was stirred overnight at room temperature. The resulting product was dialyzed against ultrapure water for three days and freeze dried.

The strategy of the antibody grafting to the polymersome surface consisted in the reaction of the thiolated protein to the active maleimide groups in the polymersome surface. In that sense the antibody was thiolated in a controlled fashion, as follows. Trastuzumab (purified from Herceptin®, Roche) was dispersed in 50 mM phosphate buffer pH 8.0 (at 5 mg/mL) and a 50fold molar excess of 2-iminothiolane (Sigma) was added and left to react for 2 hrs at room temperature, as described elsewhere [31] . Unreacted 2-iminothiolane was removed using ultrafiltration (50 kDa, Spinx-UF20, Corning) with 50 mM phosphate buffer pH 6.5. The


Eneko Garaio
email: eneko.garayo@ehu.es

Olivier Sandre
email: olivier.sandre@enscbp.fr

Juan-Mari Collantes

Jose Angel

Stéphane Mornet

Fernando Plazaola

Specific Absorption Rate Dependence on Temperature in Magnetic Field Hyperthermia Measured by Dynamic Hysteresis Losses (AC Magnetometry)

Magnetic nanoparticles are intensively studied for their potential use for magnetic hyperthermia, a treatment that has passed a phase II clinical trial against severe brain cancer (glioblastoma) at the end of 2011. Their heating power, characterized by the "specific absorption rate (SAR)", is often considered temperature independent in the literature, mainly because of the difficulties that arise from the measurement methodology. Using a dynamic magnetometer presented in a recent paper, we measure here the thermal dependence of SAR for superparamagnetic iron oxide (maghemite) nanoparticles (NPs) of four different

size-ranges corresponding to mean diameters around 12 nm, 14 nm, 15 nm and 16 nm. The article reports a parametrical study extending from 10 to 60 • C in temperature, from 75 to 1031 kHz in frequency, and from 2 to 24 kA•m -1 in magnetic field strength. It was observed that SAR values of smaller NPs decrease with temperature whereas for the larger sample (16 nm) SAR values increase with temperature. The measured variation of SAR with temperature is frequency dependent. This behaviour is fully explained within the scope of linear response theory based on Néel and Brown relaxation processes, using independent magnetic measurements of the specific magnetization and the magnetic anisotropy constant. A good quantitative agreement between experimental values and theoretical values is confirmed in a tri-dimensional space that uses as coordinates the field strength, the frequency and the temperature.

Introduction

The SAR value, sometimes also denoted specific loss power (SLP), defined as the power transformed into heat per unit of mass of nanoparticles, drastically depends on external parameters such as the frequency and intensity of the applied magnetic field, as well as on the internal characteristics of the nanoparticles, i.e. size, shape, material, agglomeration state and even on properties (e.g. viscosity or thermal conductivity) of the dispersion medium [START_REF] Hergt | Physical limits of hyperthermia using magnetite fine particles[END_REF][START_REF] Rosenweig | Heating magnetic fluid with alternating magnetic field[END_REF][START_REF] Ma | Size dependence of specific power absorption of fe3o4 particles in ac magnetic field[END_REF][START_REF] Lima | Size dependence of the magnetic relaxation and specific power absorption in iron oxide nanoparticles[END_REF]. Moreover, a much less known fact is that SAR can also depend on temperature for superparamagnetic nanoparticles (NPs). But although temperature explicitly appears in the linear approximated relaxation equations classically used to model magnetic field hyperthermia [START_REF] Rosenweig | Heating magnetic fluid with alternating magnetic field[END_REF], experimental studies of the temperature-dependency of SAR are rather scarce.

Until now, SAR values of magnetic nanoparticles were measured most often by calorimetric methods [START_REF] Hergt | Physical limits of hyperthermia using magnetite fine particles[END_REF][START_REF] Ma | Size dependence of specific power absorption of fe3o4 particles in ac magnetic field[END_REF][START_REF] Fortin | Size-sorted anionic iron oxide nanomagnets as colloidal mediators for magnetic hyperthermia[END_REF][START_REF] Kita | Heating characteristics of ferromagnetic iron oxide nanoparticles for magnetic hyperthermia[END_REF]. For a suspension of nanoparticles in a fluid carrier, the SAR is obtained experimentally from the slope of the temperature curve by the formula [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF]:

SAR = m d •C p,d m NP • dT dt t=0 (1)
where m d and C p,d are the mass and heat capacity of the dispersion medium respectively, while m NP is the mass of nanoparticles (including all the elements of the magnetic material, such as oxygen for oxides). However, the calorimetric methods present serious difficulties to measure the temperature dependency of given magnetic nanoparticle's heating power. Only when the sample holder is quasi-adiabatic and the surrounding temperature is properly controlled, it is possible to obtain the initial time slope in equation (1) at different temperatures. Natividad et al. measured by these means temperature-dependent SAR of commercial magnetite [START_REF] Natividad | Adiabatic magnetothermia makes possible the study of the temperature dependence of the heat dissipated by magnetic nanoparticles under alternating magnetic fields[END_REF] and manganite perovskite [START_REF] Natividad | New insights into the heating mechanisms and selfregulating abilities of manganite perovskite nanoparticles suitable for magnetic fluid hyperthermia[END_REF] nanoparticles respectively in the 120 -250 and 253 -343 K temperature ranges, i.e. around the blocking temperature T B for iron oxide and near to the Curie temperature T C for manganite. Regmi et al. [START_REF] Regmi | Temperature dependent dissipation in magnetic nanoparticles[END_REF] measured by calorimetry the temperature dependent magnetic dissipation of iron oxide nanoparticles suspended in frozen and liquid water at a single frequency of 395 kHz. They provided qualitative confirmation for the linear response theory based on Néel relaxation process.

There are several more convenient methods than the calorimetry one to measure SAR values as a function of temperature. They are based on Faraday's law of induction to obtain M(t), the dynamic magnetization [START_REF] Mehdaoui | Influence of a transverse static magnetic field on the magnetic hyperthermia properties and high-frequency hysteresis loops of ferromagnetic feco nanoparticles[END_REF][START_REF] Gudoshnikov | Hysteresis losses in a dense superparamagnetic nanoparticle assembly[END_REF][START_REF] Gudoshnikov | Ac magnetic technique to measure specific absorption rate of magnetic nanoparticles[END_REF]. The loss power values can be obtained directly from AC hysteresis loops area at different temperatures. Veverka et al. measured by this method the specific loss power of cobalt ferrite NPs in agarose gel at the single frequency of 50 kHz and at 28 kA•m -1 (35 mT) intensity [START_REF] Veverka | Magnetic heating by cobalt ferrite nanoparticles[END_REF]. The temperature range was from 25 • C to 80 • C. Bekovic et al. obtained SAR values for maghemite NPs 10.9 nm in size dispersed in mineral oil in the temperature range of 20 to 80 • C at the single frequency of 100 kHz [START_REF] Bekovik | An experimental study of magnetic-field and temperature dependence on magnetic fluid's heating power[END_REF].

In the present work, a previously tested lab-made AC magnetometer giving results compatible with the calorimetric method but with a higher sensitivity [START_REF] Garaio | A wide-frequency range ac magnetometer to measure the specific absorption rate in nanoparticles for magnetic hyperthermia[END_REF], is used to study the thermal dependence of SAR values of different nanoparticle batches dispersed in water. The SAR variations with temperature (∆SAR T ) of superparamagnetic maghemite nanoparticles of different size distributions have been measured in a wide applied magnetic field frequency range (from 75 to 1030 kHz). The observed thermal behaviour is clearly size dependent: for small samples, absorption rate decreases with temperature whereas for the largest sample, it increases. The change rate of SAR with temperature is also frequency dependent, except for the smallest sized sample. The measured derivative of SAR versus temperature becomes more negative with frequency increase. We successfully explain the thermal behaviour of superparamagnetic samples considering Brown and Néel relaxation times. In that case we show a relationship between the thermal dependence of SAR (either decrease or increase) and the mean (number-average) diameter compared to the optimal value obtained by simulation of the conventional relaxation equations of magnetic moment [START_REF] Rosenweig | Heating magnetic fluid with alternating magnetic field[END_REF].

Experimental

Synthesis of Iron oxide NPs.

Four samples made of superparamagnetic iron oxide were used in this study. Those denoted I, II, III were synthesized by alkaline co-precipitation of ferrous and ferric salts followed by different size sorting and coating steps, whereas sample IV was a gift of the Nanotex R company. Sample I has the broader size ranges, with the polydispersity of magnetic cores typical of the aqueous co-precipitation route. Then it was coated by citrate ligands in order to be stable in aqueous media around pH ∼ 7. For samples II and III, the maghemite nanoparticles right after the co-precipitation were dispersed in nitric acid. Then they were submitted to a size-sorting procedure based on the liquid-liquid phase-separation obtained by screening the electrostatic repulsions with an excess of electrolyte (HNO 3 ) concentration. The principle of this sorting is that the concentrated phase (denoted C) is enriched with the larger nanoparticles, whereas the dilute phase (denoted S) contains the smaller nanoparticles. After repeating several phase separation and washing steps, samples II and III originate from fractions C1C2C3 and C1C2S3, corresponding respectively to the pellet and the supernatant phases obtained by adding HNO 3 electrolyte to the previous C1C2 fraction and washing of the ions in excess. While sample II was kept in dilute HNO 3 at pH ∼ 2, sample III was coated by Dextran in order to be dispersible in neutral aqueous media, in particular biological ones. For all samples, the iron oxide concentration was measured precisely by thermogravimetry analysis (TGA) and UV-visible spectroscopy, giving comparable results within few percents.

Broad size-distribution citrate-coated maghemite NPs (Sample I)

Superparamagnetic iron oxide nanoparticles were synthesized by the Massart's synthesis of alkaline co-precipitation in water [START_REF] Massart | Preparation of aqueous magnetic liquids in alkaline and acid media[END_REF]. The resulting nanoparticles of magnetite (Fe 3 O 4 ) were oxidized into maghemite (γ-Fe 2 O 3 ) [START_REF] Tourinho | Synthesis and magnetic-properties of manganese and cobalt ferrite ferrofluids[END_REF]. Then they were coated by tri-sodium citrate in order to obtain a stable colloidal suspension at pH ≈ 7 [START_REF] Dubois | Structural analogy between aqueous and oily magnetic fluids[END_REF]. The hydrodynamic diameter measured by dynamic light scattering with a Malvern NanoZS90 instrument was 33 nm, with a polydispersity index PDI = 0.30 as determined by the 2nd order cumulants fitting method of the auto-correlogram. The size-dispersity of these nanoparticles was assessed by automated particle-counting on TEM images (figure 1). Later the size distribution of the magnetic cores will also be obtained by another way, namely by fitting the static (DC) magnetization curve measured by a vibrating sample magnetometer (VSM), with the Langevin formalism of superparamagnetism. In both cases (TEM and VSM), a Log-normal distribution law was chosen to represent the inherent size-dispersity of the sample.

Larger and narrower size-distribution maghemite NPs (Sample II)

In order to obtain maghemite NPs with a higher heating efficiency, a size-grading method based on successive phase separation by added electrolyte was applied to isolate a fraction with a narrower size-distribution and a larger average diameter [START_REF] Massart | reparation and properties of monodisperse magnetic fluids[END_REF]. Contrary to Sample I, this refined fraction (Sample II) remained uncoated, i.e. dispersed in acidic medium (HNO 3 pH ∼ 2) thank to the cationic charges of their surface brought by adsorbed protons. The successive separation of the initial suspension by a series of addition of HNO 3 to screen the electrostatic repulsions and washing steps to obtain fractions of refined size-grade is detailed in the supporting information of several references [START_REF] Arosio | Hybrid iron oxidecopolymer micelles and vesicles as contrast agents for mri: impact of the nanostructure on the relaxometric properties[END_REF][START_REF] Vuong | A universal scaling law to predict the efficiency of magnetic nanoparticles as mri t2-contrast agents[END_REF]. The hydrodynamic diameter of Sample II diluted 400 times in HNO 3 at pH ∼ 2 is 32 nm (from 5 successive measurements by dynamic light scattering at 25 • C and 90 • scattering angle with a NanoZS90 instrument, Malvern, UK), with a low polydispersity index PDI = 0.14.

The weight concentration of iron oxide in sample II is c 0 II = 99 g•L -1 = 9.9×10 4 g•m -3 as measured by UV-Vis spectroscopy (Fig. 2a). It was diluted by a factor 8 (c II = 12.3 g•L -1 ) to perform dynamic hysteresis measurements at varying temperature. Proper SAR measurements need an accurate determination of concentration of iron oxide in the suspensions. For that we used the comparison of the UV-Vis absorption spectrum from 240 to 800 nm to a calibration curve [START_REF] Safi | Interactions between sub-10nm iron and cerium oxide nanoparticles and 3t3 fibroblasts: the role of the coating and aggregation state[END_REF].

Larger and narrower size-distribution maghemite NPs coated by Dextran (Sample III)

The fraction C1C2S3 that contains magnetic cores slightly smaller than C1C2C3 (Sample II) was coated by neutral hydrophilic polysaccharide chains of Dextran T70 (molar mass 70000 g•mol -1 ), that is a common method to disperse iron oxide nanoparticles in aqueous media at pH 7, especially biological buffers [START_REF] Robert | Magnetic iron-Dextran microspheres[END_REF][START_REF] Mornet | A method for synthesis and functionalization of ultrasmall superparamagnetic covalent carriers based on maghemite and dextran[END_REF]. After incubation with the polymer at 60 • C, the nanoparticles were washed with ethanol to remove un-adsorbed polymer chains. The alcohol was eliminated by rotatory evaporation and the MNPs were readily re-dispersed in water. The concentration measured by TGA was c 0 III = 114 g•L -1 . The hydrodynamic diameter of Sample III diluted 300 times in water is 56 nm with a PDI = 0.13. It was diluted to c III = 20.5 g•L -1 for the SAR measurements.

Commercial iron oxide NPs coated by poly(acrylate) chains (Sample IV)

A commercial batch of water-based Fe 3 O 4 nanoparticles was kindly provided by the Nanotex R Company (reference: NanoMag-32). However, this sample partially sedimented. Several attempts were made unsuccessfully to re-suspend the nanoparticles in water by hydrophilic polymer coatings. But due to their large magnetic core sizes, another strategy was adopted to impede the sedimentation. Instead of stabilization, gelation of the aqueous phase was obtained by adding the suspension into 2 wt. % Agar (dissolved at 60 • C), then letting it cool down to room temperature.

SAR measurements by AC magnetometry

The radiofrequency (RF) magnetic field was generated by an air coil connected in parallel with a resonant circuit fed by a linear power amplifier [START_REF] Plazaola | Specific absorption rate of magnetite nanoparticle powders with and without surrounding organic ligands[END_REF][START_REF] Garaio | A multifrequency eletromagnetic applicator with an integrated AC magnetometer for magnetic hyperthermia experiments[END_REF]. Then, the dynamic magnetization of the sample, M t , and AC hysteresis loops were measured by a system of three pickup coils previously described in [START_REF] Garaio | A wide-frequency range ac magnetometer to measure the specific absorption rate in nanoparticles for magnetic hyperthermia[END_REF][START_REF] Garaio | A multifrequency eletromagnetic applicator with an integrated AC magnetometer for magnetic hyperthermia experiments[END_REF]. Afterward, the specific absorption rate values were obtained from the following integral of the dynamic magnetization vs. applied field strength H t :

SAR = f c M t • d H t ( 2
)
where f is the frequency and c the weight concentration of iron oxide (not iron metal). The integration is done over the period of the oscillating magnetic field [START_REF] Garaio | A wide-frequency range ac magnetometer to measure the specific absorption rate in nanoparticles for magnetic hyperthermia[END_REF].

To measure the thermal dependence of SAR, the temperature of the sample was previously raised by a hot air gun heater or decreased by using a circulating water chiller. Then, M t was measured continuously while sample was reaching room temperature (25 • C), each measure-ment of a whole hysteresis loop lasting around 5 sec (thus in quasi isothermal conditions within ± 0.5 • C).. A fiber optic thermometer insensitive to RF magnetic fields (Opsens, Quebec, QC, Canada) with an outer diameter of 0.4 mm recorded temperature inside the vial filled with 1.5 mL of sample. Diameter by TEM (nm) 9) and ( 10) were used to compute the number-averages and standard deviations of diameters: d TEM = 8.7 ± 3.3 nm for sample I, d TEM = 14.9 ± 6.4nm for sample II, d TEM = 12.9 ± 4.6 nm for sample III, and d TEM = 16.9 ± 1.7 nm for sample IV; For sample III, the inflection point near 280 • C corresponds to the degradation of Dextran under N 2 atmosphere, while the second inflection point at 450 • C is ascribed to the introduction of O 2 and the burning of all the remaining organic coating. The weight ratio of polymer to iron oxide is 52 %. In the case of sample IV, no degradation of polymer coating is observed, which explains the weak colloidal stability of this sample (supposedly stabilized by poly(acrylic acid), according to Nanotex R ).

Results and discussion

Hysteresis-loops for γ-Fe 2 O 3 samples were measured at magnetic field intensities below 20 kA•m -1 , frequencies of 75, 532, 1030 kHz, and at different sample temperatures ranging from 10 to 60 • C. Figure 3 shows the measured hysteresis cycles at different frequencies for samples I, II, III and IV. The DC magnetization curves at room temperature plotted on figure 3 have been obtained using a vibrating sample magnetometer (VSM). As expected, for all samples, the hysteresis area broadens from a single line at DC to a wide hysteresis loop as the frequency increases. This broadening is less pronounced in sample IV. In table 1, the colloidal properties of each sample are written. The corresponding volume fractions are given by φ = c/ρ where the mass density of maghemite is ρ = 5000 kg•m -3 . For each frequency, field intensity and temperature, the SAR values were obtained by equation (2). Figure 2 shows the measured SAR values for the maghemite samples, within the temperature range from 10 to 60 • C. The different applied magnetic field frequencies are 75, 532 and 1030 kHz whereas the field intensity is 20 kA•m -1 for samples I and II, 15 kA•m -1 for sample III and 5 kA•m -1 for sample IV. An almost linear drop of the specific heating power with temperature is observed in the case of samples I, II and III. Similar behaviour has been found by Bekovic et al. [START_REF] Bekovik | An experimental study of magnetic-field and temperature dependence on magnetic fluid's heating power[END_REF] who reported a decrease of SAR values by 50 % from 10 to 60 • C for 11 nm size maghemite nanoparticles measured by AC magnetometry at applied magnetic field frequency of 100 kHz. For sample IV, however, an increment of SAR with temperature is observed at 532 and 1030 kHz frequencies.

Figure 5 and6 show the relative change of SAR with temperature (in %) called here ∆SAR T and calculated by equation [START_REF] Ma | Size dependence of specific power absorption of fe3o4 particles in ac magnetic field[END_REF]. As it can be appreciated, each sample presents a different thermal behaviour of its absorption rate: In sample IV ∆SAR T is positive at 532 and 1030 kHz frequencies whereas it is negative at 75 kHz. In samples II and III ∆SAR T also depends on frequency but it is negative at all frequencies. ∆SAR T is negative too in sample I although in this case, it is frequency independent.

∆SAR T = SAR(T ) -SAR(T = 10 • C) SAR(T = 10 • C) (3) (a) Sample I -2 0 -1 0 0 1 0 2 0 -2 0 -1 0 1 0 2 0 D C 7 5 k H z 5 3 2 k H z 1 0 3 0 k H z M ( A ⋅m -1
)

H a p p ( k A ⋅m -1 ) (b) Sample II -2 0 -1 0 0 1 0 2 0 -4 0 0 -2 0 0 0 2 0 0 4 0 0 D C 7 5 k H z 5 3 2 k H z 1 0 3 0 k H z M ( A ⋅m -1
)

H a p p ( k A ⋅m -1 ) (c) Sample III -2 0 -1 0 0 1 0 2 0 -8 0 -6 0 -4 0 -2 0 2 0 4 0 6 0 8 0 D C 7 5 k H z 5 3 2 k H z 1 0 3 0 k H z M ( A ⋅m -1
)

H a p p ( k A ⋅m -1 ) (d) Sample IV -2 0 -1 0 0 1 0 2 0 -5 0 0 5 0 D C 7 5 k H z 5 3 2 k H z 1 0 3 0 k H z M ( A ⋅m -1
)

H a p p ( k A ⋅m -1 )
Figure 3: Hysteresis-loops measured at different frequencies for sample I, II , III and IV. DC magnetization curves (black line) were measured by VSM. For sample IV, the minor loops at 5 kA•m -1 are plotted. Note that as the frequency increases, the loops broaden, except for sample IV, for which the area remains quasi-constant, leading to a SAR proportional to frequency (see figure 10d). The loops were measured at room temperature (25 • C).

The magnitude ∆SAR T has shown to be independent of applied magnetic field intensity for samples I, II and III. However, ∆SAR T is quite dependent on intensity in the case of sample IV. Figure 6 shows the measured ∆SAR T values for sample IV at low (5 kA•m -1 ) and high (15 kA•m -1 ) field intensities. As it can be appreciated, at 75 kHz SAR decreases more rapidly with temperature. At higher frequency (532 and 1030 kHz), ∆SAR T becomes negative when a larger magnetic field is applied.

Linear response theory

The linear-response theory is used to fit the measured experimental data and to explain the behaviour of SAR with frequency, field strength and temperature observed in superparamagnetic γ-Fe 2 O 3 nanoparticles. To do so, the effective relaxation time, τ eff , is computed by the combination of Néel relaxation time, τ N , and Brownian time constant, τ B , that is smaller than the shorter time between the two [START_REF] Rosenweig | Heating magnetic fluid with alternating magnetic field[END_REF][START_REF] Obeada | The temperature effect on the combined brownian and neel relaxation processes in a water-based magnetic fluid[END_REF]:

τ B = 3ηV H k B T (4)
τ N = τ 0,N • exp KV M k B T (5
)

τ e f f = τ N • τ B τ N + τ B ( 6
)
where K is the anisotropy constant (in J•m -3 ),

V M = π • d 3 /6 the magnetic core volume, V H = π • d 3
H /6 the hydrodynamic volume, T the temperature, k B the Boltzmann constant and η the viscosity coefficient of water (in Pa•s). In [START_REF] Fortin | Size-sorted anionic iron oxide nanomagnets as colloidal mediators for magnetic hyperthermia[END_REF], τ 0,N is a characteristic attempt time with magnitude order of 10 -13 -10 -8 s [START_REF] Jl Dorman | Le phénomène de superparamagnétisme[END_REF][START_REF] Wohlfarth | Magnetic properties of single domain ferromagnetic particles[END_REF]. A more complicated equation for the Néel time was introduced by R. Rosenweig [START_REF] Rosenweig | Heating magnetic fluid with alternating magnetic field[END_REF], but we checked that it leads to similar results for the fitting of the experimental SAR data. Afterwards, the theoretical SAR values (in W•g -1 ) are obtained by the following expression [START_REF] Rosenweig | Heating magnetic fluid with alternating magnetic field[END_REF]:

SAR = 1 ρ µ 0 π f H 2 app ∞ 0 dr • g d 0 ,σ (2r) • χ 0 • 2π • f • τ eff 1 + (2π • f • τ eff ) 2 (7)
where µ 0 is the magnetic permeability of vacuum, f is the frequency, H app the intensity of applied magnetic field, ρ the nanoparticle mass density (in g•m -3 ) and τ eff the relaxation time given by equation [START_REF] Kita | Heating characteristics of ferromagnetic iron oxide nanoparticles for magnetic hyperthermia[END_REF]. The integral of equation ( 7) is performed for all nanoparticle size distribution g d 0 ,σ (d), which is assumed to have a log-normal distribution:

g d 0 ,σ (d) = 1 d • β √ 2π • exp -ln(d/α) 2 2β 2 (8)
with α the median value of the distribution and β the standard width of the Log values. Then the mean diameter (number-average) d 0 is given by:

d 0 = α • exp β 2 /2 (9)
and the standard deviation σ is computed by:

σ = d 0 exp (β 2 ) -1 (10)
The parameter χ 0 on equation ( 7) is the equilibrium susceptibility of these superparamagnetic samples. As an approximation [START_REF] Rosenweig | Heating magnetic fluid with alternating magnetic field[END_REF], it can be considered as the static volume susceptibility per nanoparticle given by the Langevin function L(x):

χ 0 = M d H app • L µ 0 M d V M k B T (11)
where M d is the magnetic domain magnetization of the nanoparticles (in A•m -1 ). Note that the parameter χ 0 is size dependent and thus, it is placed into the integral of equation [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF]. The domain magnetization M d in equation ( 11) is related to the saturation magnetization of the suspension, M sat , and the volume fraction of the suspension, φ , by:

M sat = φ • M d ( 12
)
In order to calculate SAR by means of equation ( 7), adequate values have to be used to estimate the two characteristic times. For the Brown's relaxation mechanism of the particles, temperature-dependent water viscosity η listed in table 2 and hydrodynamic volume V H computed from the hydrodynamic diameter (d H ) measured by DLS (see table 1) were used. In the case of sample IV, the nanoparticles exhibit much less rotational mobility because the agarose gel impedes particle rotation and hence, Brown time constant τ B can be considered infinite and the effective relaxation time τ eff equals to Néel relaxation time τ N (see eq. 6). Also, the adequate values of log normal distribution parameters (d 0 and σ ), mono-domain magnetization M d and crystal anisotropy K have to be used to estimate Néel relaxation time for each sample. Moreover, in order to calculate the absorbed power at different temperatures, the thermal behaviour of magnetic properties must be known. In order to obtain these values and their thermal evolution, we have realized the following measurements: room temperature DC magnetization, field-cooled (FC) and zero-field cooled (ZFC) magnetization as a function of temperature. More precisely, temperature was initially decreased down to T=5 K under zero field (ZFC) or under H=795.8 A•m -1 (10 Oe) (FC) and then magnetization was recorded while raising back to room temperature under a weak magnetic field H=795.8 A•m -1 (10 Oe).

Room temperature DC magnetization curves

Figure 5 shows DC magnetization curves measured at room temperature by vibrating sample magnetometer (VSM) for samples I and II dispersed in water with nanoparticle concentrations written on table 1 (same as for the SAR measurements). The absence of coercive field indicates that they are in the superparamagnetic (SPM) regime and hence, the magnetization, M SPM can be described by the Langevin function (see equation 13) integrated for all sizes [START_REF] Chantrell | Measurements of particle size distribution parameters in ferrofluids[END_REF][START_REF] Chen | Size determination of superparamagnetic nanoparticles from magnetization curve[END_REF]: Fitting the experimental data to equation ( 13), the values of mean nanoparticle sizes d 0 VSM and the standard deviations σ VSM can be obtained (note the superscript VSM). From the saturation magnetization M sat and the measured volume fractions, the domain magnetization M d can be obtained by means of equation [START_REF] Gudoshnikov | Hysteresis losses in a dense superparamagnetic nanoparticle assembly[END_REF]. Table 3 shows the so obtained values at room temperature for samples I, II, III and IV. These values are compatible, within the experimental uncertainty, with the mean diameters and standard deviations measured by TEM: d 0 TEM = 8.7

M SPM = M sat ∞ 0 dr • g d 0 ,σ (2r) • L µ 0 M d V M k B T H app (13)
nm with σ TEM = 3.3 nm for sample I, d 0 TEM = 14.9 nm with σ TEM = 6.4 nm for sample II, d 0 TEM = 12.9 nm with σ TEM = 4.6 nm for sample III, and d 0 TEM = 16.9 nm with σ TEM = 1.7nm for sample IV. Diameters of SPM nanoparticles measured by TEM are indeed always slightly larger than the diameters deduced by magnetometry, as ascribed to a usual nonmagnetic dead layer around ferrite cores [START_REF] Haneda | Magnetic-structure at gamma-fe2o3-organic interfaces[END_REF]. The tiny differences between diameters deduced from VSM and TEM measurements may arise from the fact that in microscopy, despite the high number N of particles analysed by automated particle counting (from 270 to 2060), only a fraction of nanoparticles in the sample contributes to the final values of the diameter, whereas in VSM, the contribution of all the nanoparticles in the sample are averaged. The standard deviation σ VSM is too large in the case of sample IV, which might be the sign of the presence of ferromagnetic nanoparticles in the suspension. In fact, it will be shown that the standard deviation σ that best fit experimental SAR values is always bellow σ VSM .

Zero-field cooled (ZFC) magnetization as a function of temperature

The magnetization versus temperature curve of a sample of nanoparticles at small applied field is a source of valuable information about its magnetic properties. The experimental data can be described by a simple non-interacting model and hence, parameters like the anisotropy constant, between others, can be obtained. Here, in order to obtain the effective anisotropy constants (K eff ), the ZFC-FC magnetization curves of the nanoparticle samples were measured. Afterward, the ZFC branches were fitted to a non-interacting moments linear model. This procedure was used by Denardin et al. [START_REF] Jc Denardin | Thermoremanence and zero-field-cooled/field-cooled magnetization study of Co x (SiO 2 ) 1-x granular films[END_REF] for the evaluation of effective anisotropy constant (K eff ) in Co x (SiO 2 ) 1-x particles and by Nadeem et al. [START_REF] Nadeem | Spin-glass freezing of maghemite nanoparticles prepared by microwave plasma synthesis[END_REF]. Because the model involves non-interacting moments, small concentrations of nanoparticles are preferred and hence, the samples were diluted 10 times when measuring ZFC magnetization curves. Due to the low magnetization of the diluted samples, a rf-SQUID based [START_REF] Clarke | The SQUID Handbook: Fundamentals and Technology of SQUIDs and SQUID Systems[END_REF] commercial magnetometer (Quantum Designs MPMS-7T) was used. A resolution of 10 -7 emu is commonly achieved with this type of commercial magnetometers [START_REF] Cabassi | Differential method for sample holder background subtraction in superconducting quantum interference device (SQUID) magnetometry[END_REF]. In particular, the sensitivity of the MPMS-7T magnetometer, as specified by the manufacturers, is 6×10 -7 emu; enough to measure the magnetization of diluted samples, which was always larger than 5×10 -4 emu. This magnetometer was previously calibrated by Yttrium Iron Garnet 1 mm in diameter Sphere (Standard Reference Materials 2853) and reset after each measurement.

The magnetization of polydisperse non-interacting superparamagnetic nanoparticles, M SPM is given by equation ( 13) in the previous section. For small applied magnetic field H app typical of FC/ZFC experiments, the Langevin function can be simplified to L(x) ≈ x/3. Above a critical nanoparticle volume, V B , the thermal energy is not enough to spontaneously reverse the magnetic moment and hence nanoparticles are no longer superparamagnetic (their magnetic moments are blocked). The value of V B is given by the following well known phenomenological equation [START_REF] Knobel | Superparamagnetism and other magnetic features in granular materials: A review on ideal and real systems[END_REF]:

V B = k B T K • ln τ m τ 0 ≈ 23 • k B T K ( 14
)
where τ 0 is a time constant (10 -9 s), K the magnetic anisotropy constant (at T = T B ) and τ m is the characteristic measurement time which, for SQUID magnetometer measurements, has an order of magnitude of 10 s (explaining the prefactor 23 = 10 • ln 10 in the numerical application). Now, the contribution of blocked (BL) particles to the sample magnetization is [START_REF] Knobel | Superparamagnetism and other magnetic features in granular materials: A review on ideal and real systems[END_REF]:

M BL = φ µ 0 • M 2 d 3K H app ( 15
)
where φ is the volume fraction of the sample. Then, the total magnetization of the sample M(T ) is given by the sum of M BL and M SPM [START_REF] Knobel | Superparamagnetism and other magnetic features in granular materials: A review on ideal and real systems[END_REF]:

M BL = ∞ V B dr • g d 0 ,σ (2r) • φ • µ 0 • M 2 d 3K H app ( 16
)
M SPM = V B 0 dr • g d 0 ,σ (2r) • φ • µ 0 • M 2 d •V M 3k B T H app ( 17
)
M(T ) = M BL + M SPM ( 18
)
In a normal ZFC experiment, the temperature is varied from 5 to 300 K and hence, in equation ( 18), the domain magnetization M d and anisotropy constant K cannot be considered temperature independent. The domain magnetization is assumed to change with temperature according to a modified Bloch's law [START_REF] Wang | Temperature dependence of magnetic anisotropy constant in iron chalcogenide fe3se4: Excellent agreement with theories[END_REF]:

M d (T ) = M d,T=0 • (1 -f e • T 2 ) (19)
where, f e is an empirical parameter. The exponent 2 in equation ( 19) arises from finite size effects. Then for NPs with uniaxial symmetry, the crystal anisotropy constant has to vary with temperature according to the following formula [START_REF] Wang | Temperature dependence of magnetic anisotropy constant in iron chalcogenide fe3se4: Excellent agreement with theories[END_REF][START_REF] Chikazumi | Physics of Ferromagnetism[END_REF]:

K(T ) = K T=0 • (1 -f e • T 2 ) 3 ( 20
)
In order to fit equation ( 19) to the experimental data, it is necessary to know the saturation magnetization M sat (T = 0) (or equivalently the nanoparticle domain magnetization M d,T=0 which is just proportional) at zero temperature. Moreover, the phenomenological parameter f e has to be known in order to calculate the temperature dependence of SAR. Therefore, the saturation magnetization (at 7 Tesla) was measured at different temperatures from 5 to 300 K. These measurements were performed by the same commercial magnetometer (Quantum Designs MPMS-7T) as in ZFC. Figure 8a represents the so obtained M d values obtained by dividing M sat by the volume fraction φ at different temperatures, properly fitted by equation [START_REF] Dubois | Structural analogy between aqueous and oily magnetic fluids[END_REF]. The f e values that best fit experimental data to equation [START_REF] Dubois | Structural analogy between aqueous and oily magnetic fluids[END_REF] are written in table 4. Figure 9 shows ZFC-FC curves for the four samples from 50 to 300 K measured by SQUID magnetometer. The samples were diluted 10 times to reduce inter-particle interactions. The ZFC branches were fitted by eq. ( 18), which is the sum of the magnetization M BL of blocked moments (eq. 16) and M SPM of unblocked moments (eq. 17). The two integrals on the size distribution have a lower (respectively upper) size limit (equivalently volume V B ) taken as fit-Table 4: f e parameters that best fit to equation [START_REF] Dubois | Structural analogy between aqueous and oily magnetic fluids[END_REF].

Sample f e (K -2 ×10 -6 ) I 1.7 ± 0.1 II 1.6 ± 0.1 III 1.6 ± 0.1 IV 0.9 ± 0.1 ting parameter, whereas the domain magnetization M d (T ) was fitted previously with eq. ( 19), of parameters M d,T=0 and f e . By this method, the fitted volume V B gave the anisotropy constant at T = T B through eq. ( 14). The anisotropy constant at T = 0 K and at room temperature (T = 300 K) was obtained by eq. ( 20) with the f e value already determined. It must be noted that the temperature dependence of M d and of the anisotropy constant K given respectively by eq. ( 19) and ( 20) are necessary to achieve a good agreement between experimental data and theory. Figure 8b shows the variation of the obtained anisotropy constant with the temperature according to equation [START_REF] Massart | reparation and properties of monodisperse magnetic fluids[END_REF]. Table 5 summarises the obtained M d and anisotropy constant K values at T = 0 and at room temperature.

The anisotropy constants at room temperature respectively below (samples I, II, III) and above (sample IV) 10 4 J•m -3 are compatible with values from literature on similar iron oxide nanoparticles measured by several methods such as SQUID magnetometry [START_REF] Lartigue | Water-dispersible sugar-coated iron oxide nanoparticles: An evaluation of their relaxometric and magnetic hyperthermia properties[END_REF][START_REF] Demortiere | Size-dependent properties of magnetic iron oxide nanocrystals[END_REF] or ferromagnetic resonance [START_REF] Gazeau | Magnetic resonance of ferrite nanoparticles: evidence of surface effects[END_REF].

Fitting of the experimentally measured Specific Absorption Rate

The measured SAR values were fitted to the non-interacting relaxation model previously described. The average size d 0 VSM and M sat (or equivalently M d ) values deduced from static M-H curves (see section 3.2), were used as parameters determined independently. Also the anisotropy constant values previously obtained from the fits of the ZFC curves (see section 3.3) were used as fixed parameters. To obtain the theoretical thermal dependence of SAR, the temperature dependence of M d and K deduced in previous section (equations 19 and 20) were assumed with the corresponding f e parameter. Regarding to hydrodynamic diameter, d H , the values obtained by DLS were used (see table 1). However, due to the short Néel relaxation time compared to the Brownian time constant calculated by eq. ( 4), the main relaxation mechanism is Néel relaxation process and the predicted SAR value did not vary significantly with d H . It justifies the approximation made when considering the ferrofluid viscosity equal to the carrier fluid viscosity (water viscosity on table 2), in addition to the fact that volume fraction remains below 0.4 % in all cases, therefore viscosity estimated by the Einstein relationship for solid suspension varies by less than 1 %. Finally, by means of the Levenberg-Marquardt non-linear fitting method, the standard size deviation σ and precession time τ 0 were varied to find out their respective values that best fit the experimental SAR data to the set of equations ( 4), ( 5), ( 6) and [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF]. Table 6 shows the so obtained standard size deviations σ and τ 0 values. The standard deviation values in table 6 that best fit experimental data to equation ( 7) are different from the standard deviation values obtained from DC magnetization curves σ VSM ; they are smaller, especially for sample IV. It was indeed impossible to properly adjust the experimental SAR curve with the σ VSM values, which were too large.

Figure 10 represents measured SAR versus frequency curves for samples I, II, III and IV. This figure also shows the fitting of the experimental data using eq. [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF]. As it can be appreciated, the experimental data are in good agreement with the curves predicted by eq. ( 7) for all samples. On the other hand, graphs on figure 11 represent the measured thermal dependence ∆SAR T at 75, 532 and 1030 kHz as well as the fitting using equation [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF] for each frequency. Experimental and theoretical data are in good agreement in the measured temperature range, from 10 • C to 60 • C. To verify the linear relaxation model and especially to check the method to obtain the equilibrium χ 0 from the static susceptibility of Langevin law, (see eq. 11), the SAR values measured at different applied magnetic field intensities where compared whit the values predicted by eq. [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF]. As it can be appreciated on figure 12, the experimental data are well fitted by the predicted values and hence, the method to calculate χ 0 is adequate. In the case of sample IV dispersed in agarose gel, however, when magnetic field intensity rises above 6 kA•m -1 , the lineal response theory fails to predict the absorption rate. Finally, the variation of SAR with temperature can be interpreted qualitatively from the theoretical increment with temperature of the optimum NP size, d m , which maximizes the specific loss power (see figure 13). The shifts are mainly ascribed to a change of relaxation times and, at a minor extend, to the decrease of the equilibrium susceptibility χ 0 with a raise of temperature. According to eq. ( 7), SAR values must decrease with temperature when the experimental NP sizes are distributed below the optimal diameter d m . However, this situation reverses when the mean diameter becomes larger than d m , and thus, in that case, the thermal loss power should rather increase with temperature for a given frequency and field strength (see figure 13). The optimum diameter d m also changes with the magnetic field frequency, explaining the reversal of the thermal behaviour for sample IV between f = 75 Hz and f = 1 MHz (see the explanations in the legend of figure 13).

Out of linear theory

In the case of sample IV, ∆SAR T depends on the applied magnetic field intensity H app as shown in figure 14, contrary to samples I, II and III. The linear response theory used to explain measured SAR data in the previous section fails to explain this behaviour (see figure 14). Moreover, the measured SAR values do not adjust to the theoretical curve predicted by the model when the field intensity H app exceeds 6 kA•m -1 in sample IV. Therefore, a two-level model proposed by Carrey et al. [START_REF] Carrey | Simple models for dynamic hysteresis loop calculations of magnetic single-domain nanoparticles: Application to magnetic hyperthermia optimization[END_REF] was used to explain the observed thermal behaviour. First, the dynamic time evolution of magnetization was calculated numerically for randomly oriented single domain nanoparticles. Then, when the simulated hysteresis loops converged [START_REF] Carrey | Simple models for dynamic hysteresis loop calculations of magnetic single-domain nanoparticles: Application to magnetic hyperthermia optimization[END_REF], which happens after 5 periods, the SAR was calculated by means of equation ( 2) for each temperature.

To carry out the numerical calculations, the values of anisotropy constant K, attempt of time τ 0 , domain magnetization M d and size distribution parameters (d 0 , σ ) obtained for sample IV in the previous sections were considered as parameters. Figure 15 shows the so obtained theoretical ∆SAR T values at 1 MHz frequency. As it can be appreciated in figure 15, there is a good qualitative agreement between experimental and simulated data, although a quantitative discrepancy exists. One possible reason for the observed discrepancy is the assumption made in the two-level model: all the possible states are restricted to two discrete levels only [START_REF] Carrey | Simple models for dynamic hysteresis loop calculations of magnetic single-domain nanoparticles: Application to magnetic hyperthermia optimization[END_REF][START_REF] Yu | Dynamic hysteresis of a superparamagnetic nanoparticle at low-to-intermediate frequencies[END_REF]. The measured behaviour of ∆SAR T can be additionally interpreted as a reduction of ∆E barrier that separates two possible energy levels (1 and 2 in figure 16). Figure 16a shows the energy barrier ∆E when an external low magnetic field (5 kA•m -1 ) is applied. Figure 16b, however, shows the energy barrier ∆E when an external stronger magnetic field is applied (15 kA•m -1 ). The barrier ∆E gets smaller when increasing the magnetic field intensity. On the other hand, the time that the magnetization needs to recover the equilibrium state, defined as Néel relaxation time, strongly depends on ∆E. Indeed, the term KV M in equation ( 5) can be understood as the energy barrier ∆E [START_REF] Carrey | Simple models for dynamic hysteresis loop calculations of magnetic single-domain nanoparticles: Application to magnetic hyperthermia optimization[END_REF][START_REF] Yu | Dynamic hysteresis of a superparamagnetic nanoparticle at low-to-intermediate frequencies[END_REF] in figure 16. Hence, Néel relaxation time τ N shortens when increasing the externally applied magnetic field intensity, resulting in a change of ∆SAR T behaviour with field intensity. E n e r g y ( a . u . )

ؑ | ( r a d ) | 2 1 ∆E (b) -4 -2 0 2 -1 0 -5 0 5 1 0 1 5 2 0 ∆E < K ٷ V H a p p = 1 5 k ⋅A m -1

∆E

E n e r g y ( a . u . )

ؑ | ( r a d ) | 2 1

Figure 16: Energy as function of θ , the angle between an easy magnetization-axis and the magnetic moment of the single domain nanoparticle with uniaxial anisotropy [START_REF] Carrey | Simple models for dynamic hysteresis loop calculations of magnetic single-domain nanoparticles: Application to magnetic hyperthermia optimization[END_REF] (K = 10 kJ•m -3 ). For simplicity the applied magnetic field is supposed parallel to easy magnetization-axis. The magnetic field intensity is a) 5 kA•m -1 and b) 15 kA•m -1 .

The obtained results indicate clearly that SAR values are dependent on temperature. The temperature dependence of SAR implies some experimental impact on medical practice for tumour ablation. The heating efficiency of iron oxide nanoparticles can vary by up to 16 % between 25 • C and 45 • C, as reported in the present work. Therefore, in order to design more adequately magnetic hyperthermia treatments, the SAR values measured at typical hyperthermia temperatures above the physiological temperature (from 41 to 46 • C) have to be considered, rather than SAR values measured at room temperature (25 • C). Although the difference is moderate, it can induce an error in the estimate final temperature of tissues under hyperthermia treatment, which can lead to undesired effects. On the other hand, the thermal dependence of SAR could explain some discrepancies between values reported in the literature by different groups on analogous samples, especially when SAR was obtained by calorimetric methods and assumed to be temperature independent. The present work aims at understanding the nature and causes of these SAR variations with temperature in iron oxide nanoparticles, which are the most commonly used magnetic nanoparticles in view of their proven biocompatibility.

Conclusions

The specific heating efficiency (SAR value) of water-dispersed maghemite nanoparticles were measured at different temperatures and varying field strengths by AC magnetometry in a wide frequency range from 75 to 1030 kHz. From this study, we can conclude that it is possible to measure and to explain both qualitatively and quantitatively the temperature dependence of SAR for superparamagnetic iron oxide (maghemite) nanoparticles.

It has been observed that the SAR values of maghemite nanoparticles decrease with temperature when their sizes range mainly below d m , the optimum size that maximises SAR. This is the case of the smaller sizes samples I, II and III. However, when the nanoparticle sizes are distributed above d m , SAR increases with temperature. This is the case of the largest size sample IV at low magnetic field (5 kA•m -1 ) and high frequency (532 and 1030 kHz), but not at low frequency (75 kHz). The linear response theory involving Néel relaxation and Brownian time constants was used to fully explain the measured SAR values. To do so, independent magnetic measurements of nanoparticle average sizes, domain magnetization and anisotropy constants were made before fitting theoretical SAR curves to experimental data. A good agreement between the linear relaxation model and measured data was confirmed in a tri-dimensional space (magnetic field frequency, intensity and sample temperature)

The linear model, however, fails to explain the thermal dependence of SAR at larger magnetic field (H app > 6 kA•m -1 ) for sample IV. A recent paper [START_REF] Hergt | Validity limits of the Neel relaxation model of magnetic nanoparticles for hyperthermia[END_REF] reported indeed that for large sized magnetic nanoparticles, such failure of the linear model is observed beyond a threshold magnetic field value. It was observed that the variation rate of SAR with temperature changes of sign depending on the applied magnetic field intensity: it is positive at low field (H app = 5 kA•m -1 ) whereas it is negative at lower field (H app = 15 kA•m -1 ). At this point, a two-level energy model developed by J. Carrey et al. was used to explain the measured SAR dependence with temperature. A good qualitative and semi-quantitative agreement between experimental values and the values predicted by the model was achieved.

In conclusion, the presented AC magnetometer offers a practical method to directly measure SAR values of magnetic nanoparticles at different temperatures and dispersed in various media, including water. This instrument can be particularly interesting to study subtle effects reported recently in the literature, such as the concentration-dependence of SAR, ascribed to magnetic dipolar interactions [START_REF] Pineiro-Redondo | The influence of colloidal parameters on the specific power absorption of PAA-coated magnetite nanoparticles[END_REF], or the effect of a thermally insulating materials wrapping the iron oxide cores, as evidenced with lipid bilayers [START_REF] Bealle | Ultra magnetic liposomes for mr imaging, targeting, and hyperthermia[END_REF]. The precise assessment of SAR is of utmost importance when preparing experiments of magnetic hyperthermia in vitro or in vivo, where the intrinsic properties of the utilized magnetic NPs need to be known beforehand in order to find out the necessary concentration of NPs and magnetic field conditions to deposit a given thermal dose. The obtained temperature dependence of SAR values can induce an error in the final temperature estimation on tissues under hyperthermia treatment, which can lead to undesired effects. Moreover, the thermal dependence of SAR could explain some discrepancies between values reported in the literature by different groups on analogous samples, especially when SAR was obtained by calorimetric methods and assumed to be temperature independent. Until now in the literature, the most precise parametrical studies of SAR values of SPM nanoparticles were two-dimensional (i.e. with only the field strength and frequency as coordinates) [START_REF] Di Corato | Magnetic hyperthermia efficiency in the cellular environment for different nanoparticle designs[END_REF]. To our knowledge, this is the first tri-dimensional parametrical study (i.e., versus field strength, frequency and temperature), that shows total quantitative agreement between the experiments

Figure 1 :

 1 Figure 1: TEM images of the unsorted maghemite sample I (a), of the size-sorted fractions samples II (b) and III (c), and of the magnetite provided by Nanotex R , sample IV (d). The scale bars represent respectively 50 nm for sample I and 100 nm for the others. The images were processed with the ImageJ software (http://rsb.info.nih.gov/ij/) with background subtract, threshold, binary and watershed filters to detect the border lines of the nanoparticles and enable an automatic counting; e) Histograms of diameters for sample I (filled diamonds), sample II (filled triangles), sample III (empty squares) and sample IV (open circles). The statistics was built by processing 2 TEM images of sample I (N∼840 nanoparticles), 5 images of sample II (N∼1600), 3 images of sample III (N∼2060), and 1 image of sample IV (N∼270). The dotted and continuous lines are Log-normal fits of parameters α (median) and β (standard width of the logarithms). Then equations (9) and[START_REF] Regmi | Temperature dependent dissipation in magnetic nanoparticles[END_REF] were used to compute the number-averages and standard deviations of diameters: d TEM = 8.7 ± 3.3 nm for sample I, d TEM = 14.9 ± 6.4nm for sample II, d TEM = 12.9 ± 4.6 nm for sample III, and d TEM = 16.9 ± 1.7 nm for sample IV;

Figure 2 :

 2 Figure 2: Non-destructive determination of the iron oxide concentration by UV-Vis spectroscopy. The spectra of the samples diluted respectively 80 times in water (sample I) and 400 times in HNO 3 at pH∼2 (sample II) were recorded between 240 and 800 nm. The extinction coefficient ε(λ ) calculated after normalization by the light path L (cm) and the equivalent iron concentration (respectively [Fe] I = 1.0 mol•L -1 , [Fe] II = 1.24 mol•L -1 , and [Fe] III = 1.26 mol•L -1 as determined here) was fitted to a calibration curve obtained from measurements on samples at concentrations titrated by atomic emission spectroscopy. Then the weight concentration was simply deduced by multiplying by 80 mol•L -1 (∼ half the molar mass of γ-Fe 2 O 3 ), yielding c I 0 = 80 g•L -1 for sample I, c II 0 = 99 g•L -1 for sample II, and c III 0 = 100.6 g•L -1 for sample III. This method was not possible for sample IV because of its poor colloidal stability (inducing a strong scattering baseline to the spectrum); b) Thermogravimetry analysis (TGA) of samples III and IV leading to the inorganic dry weight concentrations, c III 0 = 114.3 g•L -1 for sample III and c IV 0 = 7.1 g•L -1 for sample IV.For sample III, the inflection point near 280 • C corresponds to the degradation of Dextran under N 2 atmosphere, while the second inflection point at 450 • C is ascribed to the introduction of O 2 and the burning of all the remaining organic coating. The weight ratio of polymer to iron oxide is 52 %. In the case of sample IV, no degradation of polymer coating is observed, which explains the weak colloidal stability of this sample (supposedly stabilized by poly(acrylic acid), according to Nanotex R ).

Figure 4 :

 4 Figure 4: Measured SAR values dependence with temperature. The magnetic field intensity is 20 kA•m -1 for samples I and II, 15 kA•m -1 for sample III and 5 kA•m -1 for sample IV. The magnetic field frequencies are 75, 531 and 1031 kHz.

H

  app = 15 kA⋅m -1 פSAR T (%) T (ºC)

Figure 5 :

 5 Figure 5: Measured ∆SAR T values (see equation 3). The magnetic field intensity, H app , is 20 kA•m -1 for samples I and II whereas it is 15 kA•m -1 for sample III. The magnetic field frequencies are 75, 531 and 1031 kHz (square, circle and triangle symbols respectively).

Figure 6 :

 6 Figure 6: Measured ∆SAR T values for sample IV at 5 kA•m -1 (left) and 15 kA•m -1 (right).

Figure 7 :

 7 Figure 7: DC magnetization curves measured by VSM. Solid lines indicate the fitting of experimental data to equation (13).

Figure 8 :

 8 Figure 8: Measured M d at different sample temperatures. The curves are fitted with eq. (19) (see text); b) Temperature evolution of anisotropy constant K according to eq. (20).

Figure 9 :

 9 Figure 9: ZFC-FC curves of samples I, II, III and IV and their corresponding fitting of ZFC branch to equation (18) (solid lines). The magnetization was measured while applied field was 795.8 A•m -1 (10 Oe).

Figure 10 :

 10 Figure 10: Measured SAR at a given field intensity versus frequency. Solid lines represent fitting with the curves predicted by the linear relaxation model using the magnetic parameters d 0 , K and M d measured independently.

Figure 11 :

 11 Figure 11: Measured ∆SAR T at a given field intensity versus temperature. Solid lines represent the curves predicted by the linear relaxation model using the magnetic parameters d 0 , K and M d measured independently.

- 1 )H app (kA⋅m - 1 )Figure 12 :

 1112 Figure 12: Measured SAR versus field intensity fitted by the predicted values (solid lines). Note that the lower SAR values in sample IV are due to lower H app values (x-axis).

Figure 13 :

 13 Figure 13: Predicted SAR values by eq. (7) versus monodisperse nanoparticle size for sample IV at a) 75 kHz and b) 1 MHz. The magnetic field intensity is H app = 5 kA•m -1 . At both frequencies, the optimal diameter d m shifts towards larger values when T increases. For sample IV, the NPs are distributed in a range of sizes 16.1 ± 3.4 nm. These sizes are located mainly below d m at f = 75 kHz and above d m at f = 1 MHz. Thus one expects a decrease of SAR with T at f = 75 kHz and an increase of SAR with T at f = 1 MHz, as experimentally observed (figure 11).

Figure 14 :

 14 Figure 14: Measured ∆SAR T of sample IV at a)5 kA•m -1 and b)15 kA•m -1 . Solid lines represent the theoretical curves predicted by the linear response model explained in the previous sections. For large field, the model fails to predict the experimental ∆SAR T .

Figure 15 :

 15 Figure 15: ∆SAR T values predicted by the two-level model at 1030 kHz frequency for sample IV (solid lines) and the corresponding experimental values.

  ٷ V H a p p = 5 k ⋅A m -1

Table 1 :

 1 Colloidal properties of the measured samples. For sample IV in agar-gel d H is assumed to be infinity.

	Sample Concentration Volume fraction	Hydrodynamic
		c (mg•mL -1 )	φ (%)	diameter d H (nm)
	I	8	0.16	33
	II	12.3	0.245	32
	III	20	0.4	56
	IV	2	0.04	∞

Table 2 :

 2 Water viscosity coefficient at different temperatures[START_REF] Haynes | CRC Handbook of Chemistry and Physics[END_REF] T ( • C) η (mPa•s -1 )

	10	1.307
	20	1.002
	30	0.797
	40	0.653
	50	0.547
	60	0.467

Table 3 :

 3 Parameters that best fit the measured DC magnetization curves in figure7using equation[START_REF] Gudoshnikov | Ac magnetic technique to measure specific absorption rate of magnetic nanoparticles[END_REF]. Next

		M d	d 0	VSM σ VSM p.i. VSM d 0	TEM σ TEM p.i. TEM
		(kA•m -1 )	(nm)	(nm)		(nm)	(nm)
	Sample I	254	12.9	4.9	0.38	8.7	3.3	0.38
	Sample II	283	14.9	4.4	0.29	14.9	6.4	0.41
	Sample III 295	14.5	4.3	0.29	12.9	4.6	0.30
	Sample IV 276	16.1	9.0	0.52	16.9	1.7	0.10

columns: Average sizes, standard size deviation and polydispersity index (p.i. TEM ) obtained by TEM. For both techniques, the p.i. is equal to the beta parameter in the Log-normal distribution law (eq. 8).

Table 5 :

 5 Measured anisotropy constant K values deduced from curve fittings of the ZFC curve with eq. (18).

		K (kJ•m -3 )
		T = 0 K T = 300 K
	sample I	13.2	8.3
	sample II	13.9	8.8
	sample III	13.7	8.6
	sample IV	20.0	15.5

Table 6 :

 6 Standard deviation of diameters σ and characteristic τ 0 values that best fit to the experimental SAR data with the combination of equations 4-20, in which all the other parameters were determined independently.

		σ (nm) τ 0 (ns)
	sample I	4.0	1.07
	sample II	3.1	2.05
	sample III	3.2	2.00
	sample IV	3.4	0.43

Acknowledgments

We thank the Nanotex Company in Madrid for providing us with sample IV. We also want to acknowledge the Basque government for financial support under grant IT-443-10.

and the linear (Debye-type) model of magnetic moments relaxation.