Abdulwaheed Ògúnsàmì
email: abdulwaheed.ogunsami@anu.edu.au

Ian Jackson

Jan V M Borgomano

Jérôme Fortin

Hasan Sidi

Andre Gerhardt

Boris Gurevich

Vassili Mikhaltsevitch

Maxim Lebedev

Hasan

Vassily Mikhaltsevitch

Elastic properties of a reservoir sandstone: a broadband inter-laboratory benchmarking exercise

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

 [START_REF] King | Recent developments in seismic rock physics[END_REF]. The technology involves the 35 acquisition, processing and interpretation of repeated three-dimensional (3D) seismic surveys over a 1 producing field in order to understand production-related changes and their impact on the elastic 2 properties of the reservoir. The success of such technology depends partially on the sensitivity of 3 measured seismic attributes (such as acoustic impedance and V P to V S ratio) to changes in reservoir 4 conditions such as effective pressure and fluid saturation (e.g. [START_REF] Lumley | Assessing the technical risk of a 4D seismic 4 project[END_REF][START_REF] Wang | Feasibility of time-lapse seismic reservoir monitoring: The physical basis[END_REF]. The 5 sensitivity can be established by laboratory testing of the elastic properties of core samples as a function 6

of effective pressure and fluid saturation. 7 8 Conventionally, laboratory testing is done using the ultrasonic wave-propagation techniques (Gregory & 9 Podio, 1970;Birch,1960;[START_REF] Han | The effects of porosity and clay content on wave velocities in 17 sandstones[END_REF].At ultrasonic (MHz) frequencies, however, the pressure 10 dependence of elastic moduli of fluid saturated rocks may be much weaker than at seismic frequencies 11 due velocity dispersion (Mavko & Jizba, 1991;[START_REF] Gurevich | A simple model for squirt-flow 15 dispersion and attenuation in fluid-saturated granular rocks[END_REF][START_REF] Müller | Seismic wave attenuation and dispersion resulting 32 from wave-induced flow in porous rocks -A review[END_REF]. In dry granular 12 rocks such as sandstones, the pressure dependence of elastic moduli of the rock is primarily controlled by 13 pressure-dependent compliance of grain-to-grain contacts, which are usually much softer than the grain 14 mineral itself. In a fluid-saturated rock, the pore fluid may stiffen these contacts, and this stiffening is 15 frequency-dependent. At seismic frequencies, there is enough time in one wave period for the fluid to 16 squeeze out of the contact area into the larger pore space, and hence the contacts are almost as compliant 17 as in the dry rock. Conversely, at ultrasonic frequencies, the wave period is insufficient for the fluid to 18 squeeze out, so that the fluid is effectively trapped in the contact area, reducing the compliance of the 19 contact to almost zero. Thus, the ultrasonic moduli of a fluid-saturated rock are often much less sensitive 20 to confining or fluid pressure than the moduli measured at seismic frequencies. This effect, known as 21 squirt flow dispersion (e.g. [START_REF] Mavko | Melt squirt in the asthenosphere[END_REF][START_REF] O'connell | Viscoelastic properties of fluid-saturated cracked solids[END_REF], is one of the reasons as 22 to why ultrasonic measurements on fluid-saturated samples are often inadequate for calibration of seismic 23 measurements. to pressure and saturation using measurements on dry cores combined with the Gassmann theory. 3

However, the process of drying reservoir samples may potentially modify the property of the rock matrix 4 and introduce additional complications. 5 6 Forced-oscillation technique of the 'stress-strain type' (Spencer, 1981;[START_REF] Batzle | Fluid mobility and frequency-dependent seismic velocity -13 Direct measurements[END_REF]) constitutes a 7 promising alternative approach. The technique provides for the measurement of the elastic properties of 8 rocks under low-frequency, low strain loading conditions that broadly simulate those of typical porous 9 reservoirs. In recent decades, there have been several laboratory investigations using the forced-10 oscillation technique (e.g. [START_REF] Adam | Gassmann's fluid substitution and shear modulus variability in 2 carbonates at laboratory seismic and ultrasonic frequencies[END_REF][START_REF] Adam | Seismic wave attenuation in carbonates[END_REF][START_REF] Adelinet | Frequency and fluid effects 7 on elastic properties of basalt: Experimental investigations[END_REF]Li et al., 2014;11 Pimienta et al. 2015[START_REF] Mikhaltsevitch | A laboratory study of low-frequency wave 26 dispersion and attenuation in water-saturated sandstones[END_REF]. However, the technique is relatively new, rapidly 12 developing, and further studies are required to validate its reliability (see overview in Subramaniyan et 13 al.,2014). Furthermore, different studies use different measurement systems or tested different reservoir 14 rocks. To the best of our knowledge, no effort has been made to cross-validate the various results. 15 16 The study presented in this paper fills this gap. For a single cylindrical core specimen, we performed a 17 systematic inter-laboratory testing of elastic properties of a porous reservoir sandstone using three 18 different forced-oscillation measurement devices. The specimen was tested both in dry and decane-19 saturated conditions to document the fluid-saturated and pressure-dependent elastic properties of the 20 reservoir specimen. Results from the different measurement devices were compared and interpreted using 21 rock physics theories. Our findings demonstrate the consistency of the results between the three 22 measurement devices within a reasonable measurement error. 23 2.0 Methods 1

Specimen

2

The test specimen is a homogenous reservoir sandstone sampled from a depth of 2660 m from an oil field 3 offshore from NW Africa. Petrographic and XRD analyses of rocks from the relevant depth interval 4 within this formation indicate moderately well sorted but poorly compacted sandstone comprising 60.5-5 70% detrital minerals (mainly quartz), 18.5-29.5% diagenetic infill (mainly the carbonates dawsonite, 6 calcite and dolomite), and 4.5-12% clay. We obtained a cylindrical core-plug specimen -initially 79.5 7 mm in length and 38.5 mm in diameter -for tests at Curtin University and the École Normale Supérieure 8 (ENS). Later this sample was re-cored to a smaller dimension (75 mm in length and 15 mm in diameter) 9

for testing at the Australian National University (ANU). The porosity and permeability estimated from 10 petrophysical logs are ~ 30% and 120 mD (1.2 ×10-13 m2), respectively. To study the fabric and crack-11 related microstructure, we obtained X-ray tomographic images of the specimen at ambient conditions. To 12 evaluate the possible matrix damage and extent of microstructural changes during the test possibly due to 13 the drying, we measured the porosity from the weight of the dry and fully saturated specimen (as 29%) 1: Physical properties of the test specimen and the pore fluid. K matrix is the bulk modulus for the 1 mineral skeleton required to reconcile the observed fluid-related stiffening of the bulk modulus with the 2 Gassmann model. K f is the fluid bulk modulus. 3

The elastic properties were measured both in dry and fully-saturated conditions with n-decane, a well-4 characterised liquid hydrocarbon. Table 1 summarises the physical properties of the specimen as well as 5 the physical properties of the n-decane pore fluid, obtained from the webbook of the National Institute of 6

Standards and Technology (NIST). 7 8

Experimental Set-up 9

We used three complementary forced-oscillation techniques in different rock physics laboratories: Axial 10 stress oscillation both at Curtin and ENS, confining pressure oscillation at ENS, and torsional oscillation 11 at the ANU. We also measured the elastic properties of the specimen using the ultrasonic wave 12

propagation method both at Curtin and ENS. 13

Oscillation of axial stress and confining pressure -Young's modulus, Poisson's 14 ratio, and bulk modulus 15

We measured Young's modulus and associated dissipation, along with Poisson's ratio of the reservoir 16 sandstone specimen with the low-frequency axial stress oscillation apparatus (Figure 1) both at the Curtin 17 University and ENS [START_REF] Borgomano | Dispersion and attenuation 23 measurements of the elastic moduli of a dual-porosity limestone[END_REF][START_REF] Mikhaltsevitch | A laboratory study of low-frequency wave 26 dispersion and attenuation in water-saturated sandstones[END_REF]. The working principle for the 18 set up at both laboratories is similar except that the apparatus at ENS has additional capacity for 19 measurements involving oscillation of the hydrostatic pressureallowing the direct measurement of the 20 bulk modulus. The confining medium for each apparatus is hydraulic oil. Pore pressure within the 21 cylindrical test specimen, for each set-up, can be independently applied and controlled. By applying a 22 sinusoidally time-varying axial stress or confining-pressure perturbation to the rock, we estimate the 23 dynamic moduli (Young's and bulk), Poisson's ratio and associated dissipation by measuring the resulting 24 axial and circumferential strains on the rock sample and the axial strain in the reference aluminium 1 material [START_REF] Borgomano | Dispersion and attenuation 23 measurements of the elastic moduli of a dual-porosity limestone[END_REF][START_REF] Mikhaltsevitch | A laboratory study of low-frequency wave 26 dispersion and attenuation in water-saturated sandstones[END_REF]. The essential parts are a force generator, a 2 force sensor to measure the applied stress and a displacement sensor to measure the resulting strain. In 3 both set-ups, aluminium cylinders 38.5 mm in diameter constitute the end platens which serve as the 4 elastic reference. A piezoelectric actuator, mounted between the axial piston of the cell and the top end 5 platen, is used to apply the oscillating axial force to the jacketed cylindrical specimen. For the test 6 involving oscillation of the confining pressure (e.g. [START_REF] Adelinet | Frequency and fluid effects 7 on elastic properties of basalt: Experimental investigations[END_REF][START_REF] David | Laboratory 39 measurements of low-and high-frequency elastic moduli in Fontainebleau sandstone[END_REF]Pimienta et 7 al., 2015), the pressure-control system is used to perturb the confining pressure, providing low-amplitude 8 hydrostatic stress oscillation around a mean value of confining pressure. The amplitude of pressure 9 oscillation 𝛥𝑃 𝑐 , and the resulting volumetric strain, are sufficiently low that the material's response to 10 stress is linear [START_REF] Pimienta | Bulk modulus dispersion and attenuation in sandstones[END_REF]. 11

The aluminium platen, used as the reference material, is equipped with two axial (and four at ENS) strain 12 gauges which act as the axial stress sensor [START_REF] Mikhaltsevitch | A laboratory study of low-frequency wave 26 dispersion and attenuation in water-saturated sandstones[END_REF][START_REF] Borgomano | Dispersion and attenuation 23 measurements of the elastic moduli of a dual-porosity limestone[END_REF]. The 13 average of the strains ( al,av ) obtained from these gauges is used, together with the known Young's 14 modulus of aluminium ( E al,av = 72GPa, [START_REF] Mavko | The Rock Physics Handbook: Tools for Seismic Analysis of 19 Porous Media[END_REF] to obtain the axial stress, 𝜎 x = E.  al,av . The 15 axial ( ax ) and circumferential (radial) ( rad ) strains in the test specimen are obtained from the axial and 16 circumferential strain gauges glued directly onto the specimen. This gives Young's modulus E of the 17 specimen as the ratio of the axial stress to the specimen's axial strain. Poisson's ratio  is obtained as the 18 ratio of the amplitudes of the radial and axial strains, For the forced-oscillation of the confining pressure, the ratio of the hydrostatic stress to the resulting 1 volumetric strain Ɛ 𝑣𝑜𝑙 = Ɛ 𝑎𝑥 + 2Ɛ 𝑟𝑎𝑑 provides the bulk modulus K as:

2 K = - ∆𝑃 𝑐 𝜀 𝑣𝑜𝑙 (5) 3
We then obtained the associated dissipation 𝑄 -1 from the phase difference  between the applied stress 4 𝜙 stress and resulting strain 𝜙 strain (i.e.  =  stress - strain ). The Young's dissipation is obtained from the 5 phase shift between the axial stress  ax and axial strain  ax , 𝑄 𝐸 -1 = tan ( ax - ax). The bulk dissipation 6 (𝑄 𝐾 -1 ) for the hydrostatic oscillation is obtained from the phase shift between the hydrostatic stress P c 7 and the volumetric strain Ɛ 𝑣𝑜𝑙 , as 𝑄 𝐾 -1 = tan ( -Pc - ɛ vol ).

8

At ENS, the specimen was tested for different amounts of so-called dead volume. The dead volume (i.e. 9 the volume of fluid in the reservoir drainage system or pipelines connected to the ends of the sample) has 10 an important implication on the interpretation of drainage regime of laboratory tests and must be carefully 11 considered [START_REF] Pimienta | Modelling the drained/undrained 40 transition: effect of the measuring method and the boundary conditions[END_REF][START_REF] Mikhaltsevitch | A laboratory study of the effect 29 of boundary conditions on the elastic moduli measurements[END_REF]. Indeed, the apparent elastic modulus of the 12 sample will depend on the dead volume for frequencies below the drained/undrained transition. Thus, the 13 valves, which control the dead volume, were kept open for adjustment of confining and pore pressures but 14 are closed during forced-oscillation measurements. 15

Torsional forced oscillations -Shear modulus 4

Torsional forced-oscillation tests have been conducted on the specimen in dry and saturated (n-decane) 5 conditions using the attenuation apparatus at the Australian National University (Jackson & Paterson, 6 1993;[START_REF] Lu | Seismic-frequency laboratory measurements of shear mode viscoelasticity in 36 crustal rocks I: competition between cracking and plastic flow in thermally cycled Carrara marble[END_REF]. This apparatus is a gas-medium rig with capacity for high-pressure We obtained the shear modulus and associated dissipation of the sandstone specimen at mHz -Hz 3 frequencies from the analysis of the response of the composite beam of Fig. 2 to the application of an 4 oscillating torque. The beam consists of the test specimen that is connected in series to an elastic standard 5 of known mechanical properties. Displacements associated with the twist of the beam, upon application of 6 torque, are measured by two pairs of three-plate capacitance transducers. The distortion of the specimen 7 assembly, containing the specimen of interest along with steel connecting rods, relative to that of the 8 hollow steel elastic element, provides an interim indication of the complex compliance (including the 9 phase lag between applied torque and resulting distortion). The shear modulus and dissipation (𝑄 𝐺 -1 ) for 10 the test specimen are computed from the complex compliance differential between the specimen and 11 reference assemblies (containing a control specimen of intact glass), along with the known shear moduli 12 for the control specimen and enclosing annealed copper jacket [START_REF] Jackson | A high-pressure, high-temperature apparatus for studies of seismic 26 wave dispersion and attenuation[END_REF]Lu & Jackson, 13 2006). 14 10

Ultrasonic measurements 1

Ultrasonic tests were performed both at Curtin University and ENS using the standard pulse transmission 2 techniques [START_REF] Birch | The velocity of compressional waves in rocks to 10 kilobars: 1[END_REF]. At Curtin University, we used an apparatus with a slightly modified set of units 3 placed between the steel platens (Figure 3). The transducers are inserted in steel end-caps where they are 4 fixed on the end butts facing a sample by steel springs. At ENS, the ultrasonic transducers embedded in 5 each end platen of the axial oscillation set up described in section 2.2.1 were used for measurement of the 6 ultrasonic velocities in conjunction with the low-frequency oscillation of axial stress or confining 7 pressure. The central frequencies for the P-and S-wave ultrasonic transducers are 1 MHz and 0.5 MHz, 8

respectively. The errors for the measured P-wave and S-wave velocities are less than 2% and 5%, 9 respectively, originating from the uncertainties in sample's length and the determination of the first 10 arrival time of P-and S-waves. 11

Experimental protocols 12

The low-frequency tests at both Curtin and ENS were first performed on a dry specimen at confining 13 pressure P c = 10 MPa before testing the decane-saturated specimen at 10 MPa differential pressure (P eff = 14 P c -P f ). The experimental assemblies have different dead volumes: 2 cm 3 at Curtin, optionally 3.3 cm 3 or 15 50 cm 3 at ENS, and 42 cm 3 at ANU. Standard industry practice is to clean reservoir core specimens 16 before any laboratory testing. Such cleaning involves the use of solvents, e.g. 50/50 mixture of 17 toluene/methanol with 1% of ammonium hydroxide, to remove any contaminant/residue from the in-situ 18 hydrocarbon. For this test, however, no such cleaning was performed to minimise the change of the 19 specimen's properties. So dry conditions for the test at Curtin implies 'as received' without any 20 desiccation or oven-drying. The specimen was only oven-dried in other laboratories, prior to testing to 21 reduce the effect of moisture. At ENS, for example, the specimen was oven-dried for two days at 60-70°C 22 before measurement. In both laboratories, the ultrasonic measurements were made at a 0-15 MPa range of 23 confining pressures for the dry conditions and at a 0-15 MPa range of differential pressure for the 24 saturated conditions. For both ultrasonic and low-frequency test, pore fluid pressure P f was fixed at 5 1 At the ANU, we first investigated the oven-dried specimen at a range of confining pressures before 7 testing the decane-saturated specimen. For the saturated conditions the pore fluid pressure was held 8 constant at 5 MPa and we varied the confining pressure to achieve differential pressures of 4 -15 MPa. 9

We charged the pore fluid line with n-decane and the pore-fluid pressure within the specimen was 10 allowed to equilibrate for more than 24 hours to ensure uniform pore pressure in the specimens, before 11 testing the mechanical properties. Between successive measurements of mechanical properties at varied 12 12 differential pressures, we explored the possibility of taking permeability measurements, using the 1 transient-flow approach, to further guarantee that the reservoir sandstone specimen was saturated 2 correctly and that the pore pressure is in equilibrium. No permeability data, however, were successfully 3 obtainedas we shall discuss later. Nonetheless, our saturation procedures are designed to achieve the 4 closest possible approach to conditions of full saturation. For instance, the saturation and fluid charging 5 procedure at ANU, involving a protocol of sustained evacuation of the entire pore fluid system and 6 bleeding of any residual gas, is terminated upon a sudden rise of pore pressure with incremental advance 7 of the piston within the pore-fluid intensifier -indicative of saturation of the pore space with an 8 incompressible pore fluid. At ENS, the specimen was fully-saturated using a specific procedure described 9 as follows; a vacuum was generated throughout the whole sample from a vacuum pump connected on the 10 top pore line. The pore fluid is then injected from the bottom of the sample. The vacuum pump is 11 connected to the top pore line via a transparent tube which enables us to see the fluid movement from one 12 end of the sample to the other. Moreover, the volume injected by the fluid pumps can be monitored. 13

Finally, a volume of fluid of at least 2-3 times the pore volume, is drained through the sample to ensure 14 the absence of air bubbles. 15 16 3.0 Results A broadly similar Young's Modulus, averaging 13.5 ± 0.5 GPa, is measured for the dry conditions in both 8 labs, without any systematic frequency dependence. In addition, for the dry specimen, the Poisson's ratio 9 are found constant with frequency with a value of 0.17 ± 0.02. 10

The fluid-saturated specimen shows systematically higher values of Young's modulus than for dry 11 conditions (except for ENS with large dead volume). The Young's modulus suggests a mild frequency 12 dependencemost clearly with the results of the test at Curtintending to increase with increasing 13 frequency. Substantial strain-energy dissipation consistently matches the observed dispersion of Young's 14 modulus. Note that the difference between the dry and saturated Young's modulus (Curtin and small dead 15 volume of ENS) is similar in both labs and equal ~ 0.6 ± 0.2 GPa. 16

The Poisson's ratio of the saturated sample is higher than for a dry sample. Thus, the results of Young's 1 modulus and Poisson's ratio from the two independently conducted tests at both labs are broadly 2 consistent both in terms of the fluid and frequency dependence. The results show a systematic sensitivity of shear modulus to increasing pressure both in dry and 1 saturated conditions. Dry shear modulus of 4.2 GPa measured at P c = 4 MPa increases progressively to 2 5.6 GPa at 15 MPa. 3

The shear modulus for both dry and saturated specimens shows only mild dispersion across the frequency 4 range of the test. On decane-saturation, the shear modulus of the reservoir specimen remains essentially 5 unchanged. Subtle differences between the dry and decane-saturated shear moduli at the lowest values of 6 confining/differential pressure may not be resolvable given the uncertainties of order 0.5 MPa in pressure. 7

For both dry and saturated-conditions, the shear dissipation shows no systematic frequency dependence. 8

Pressure and fluid sensitivity of the shear dissipation is observed only for measurement at P ⩽ 7 MPa, 9

where values of 𝑸 𝑮 -𝟏 range between 0.02 and 0.06. Overall, shear modulus and dissipation are concluded 10 to be essentially frequency -independent. 11 The bulk modulus of ~7 GPa is observed for the dry conditions. The modulus and dissipation for the dry 11 specimen are essentially frequency-independent. Upon saturation with n-decane, the bulk modulus is 12 markedly increased by ~7 % and ~ 27 % relative to bulk modulus of the dry condition for the large and 13 small dead volumes, respectively. 14

The observed dissipation 𝑄 𝐾 -1 of ~ 0.01 is broadly similar for both dry and saturated-conditions. Besides, 1 the bulk modulus and dissipation 𝑄 𝐾 -1 for the decane-saturated conditions show no systematic frequency 2 -dependence.

Ultrasonic measurements 12

To provide further information on the frequency dependence of the elastic properties beyond the 13 frequency covered by the forced-oscillation techniques, ultrasonic measurements of the velocities were 14 performed in both the Curtin and ENS labs using the pulse transmission technique. Here we summarise 15 the pressure dependence of the ultrasonic velocities for dry and decane-saturated conditions (Figure 7). 16

With a fixed pore pressure at 5 MPa, the confining pressure was varied to enable testing at a range of 1 differential pressure for the decane-saturated conditions. 2

Overall, the results obtained from both labs are broadly consistent in that they show a consistent pressure 3 sensitivity of the velocity both in dry and saturated conditions. For example, the P-wave velocity at 4 ambient (bench-top) pressure conditions of ~2300 m/s measured at Curtin for the dry specimen 5 systematically increases to 3000 m/s at 15 MPa confining pressurea trend consistently similar with the 6 results for n-decane-saturated conditions, tested both at Curtin and ENS. However, the values of the P-7

wave velocities for the dry conditions, measured at both labs, are somewhat different. At P c = 10 MPa, for 8 example, the measured velocity for the dry conditions at ENS lab (2600 m/s) is lower than the one 9 obtained at Curtin (2800 m/s). 10

Whereas the measured velocities for the decane-saturated conditions from both labs are broadly 11 consistent, the fluid sensitivity is differentpossibly because the specimen tested at ENS was oven-dried 12 whereas the same specimen was tested 'as received' at Curtin University. Overall, the high-frequency 13 velocity results from both tests indicate consistent, systematic pressure sensitivities for both in dry and 14 fluid-saturated conditions, with somewhat diminished pressure sensitivity for decane pore fluid saturation. 15 The systematic increase in shear modulus and ultrasonic velocities with increasing pressure observed for 19 both the dry and decane-saturated conditions is consistent with the expectation of the effect of pressure-20 related closure of compliant (crack-like) porosity in a porous medium [START_REF] Walsh | The effect of cracks on the uniaxial elastic compression of rocks[END_REF][START_REF] Sayers | Sensitivity of elastic-wave velocities to stress changes in sandstones[END_REF]Fortin 21 et al., 2005). Such compliant porosity in sandstones is primarily associated with the grain-to-grain 22 contacts. We interpret the pressure sensitivity as related to the deformation of the compliant grain-to-grain 23 contacts which is consistent with the weakly-cemented nature of the reservoir sandstone facies. The 24 implication from the theory of Walsh (1965) using P = Eα -with dry Young's modulus E of 13.8 GPa 1 and a closure pressure, P of 10 MPais that the inter-granular contacts must have an indicative aspect 2 ratio  < 7  10 -4 . Such inference is broadly consistent with published values of aspect ratio for 3 sandstones (e.g. [START_REF] Cheng | Pore Aspect Ratio Spectrum of a Rock[END_REF][START_REF] Siggins | Saturation, pore pressure and effective stress from sandstone 18 acoustic properties[END_REF][START_REF] Pimienta | Bulk modulus dispersion and attenuation in sandstones[END_REF]. Note that 4 features with such low-aspect-ratio cannot be detected by X-ray micro-CT, which has a matrix on the 5 order of 1000 3 voxels. However, the observed pressure sensitivity of the directly measured shear modulus 6 might also include a contribution arising from finite compliance of the interfaces between the specimens 7 and loading pistonsparticularly for P < 10 MPa. 8

Discussion

Dispersion and dissipation in the dry specimen 9

The elastic properties of the 'dry' reservoir sandstone specimen indicate a modest level of dispersion of 10 both the Young's and shear moduli and associated strain-energy dissipation. For rocks under dry 11 conditions, no (fluid-related) modulus dispersion and dissipation is expected. So such modest dispersion 12 and dissipation for the nominally dry conditions are conceivably a manifestation of the presence of 13 moisture in the pore spaces (e.g. [START_REF] Clark | Effect of volatiles on attenuation ( Q -1 ) and 31 velocity in sedimentary rocks[END_REF]Vigil et al., 1994;[START_REF] Pimienta | Investigation of elastic weakening in limestone and 5 sandstone samples from moisture adsorption[END_REF]Yurikov et al., 14 2018) or frictional effects (e.g. Walsh,1966;[START_REF] Mavko | Frictional Attenuation : An Inherent Amplitude Dependence[END_REF]. That moisture could be responsible for such 15 observation is consistent with the findings of Vigil et al., (1994) on the nature of silica-water interfaces. 16

They showed that a thin gel-like layer results from the effect of adhesion of moisture and frictional 17 behaviour of the amorphous silica surface. Under those conditions, the frequency-dependence of the 18 mechanical properties of porous material of predominantly quartz, especially with moisture on the 19 siliceous surfaces at the intra-granular contacts, could be strongly favoured. For example, similar effects 20 on nominally dry Navajo sandstone -initially vacuum-dried and then allowed to equilibrate for 28 days in 21 100% relative humidity airdocumented by Spencer (1981) was interpreted as related to the presence of 22

non-negligible moisture content. 23

There are possible sources of moisture in our reservoir sandstone specimen. We tested the specimen at the 24 Curtin University 'as is' without any thorough drying protocol in an attempt to avoid undesirable 25 modification of the microstructure or the fluid-sensitive properties of the clay. So the remaining fluid (i.e. 1 hydrocarbon and moisture) in this original sample may be described as "residual" from the fully saturated 2 in-situ conditions. The strongest evidence of the influence of residual moisture is provided by comparing 3 the 'dry' measurements of Young's modulus and ultrasonic compressional wave velocities, V p measured 4 at Curtin University and ENS. Both Young's modulus and ultrasonic V p are substantially lower for the 5 oven-dried than for the 'as-received' dry specimen, suggesting that the residual moisture stiffens the grain 6 contacts. Effect of volatiles plausibly from the re-exposure to laboratory atmosphere during re-jacketing 7 of the smaller-sized specimen tested at ANU could also partly be responsible for the non-negligible 8 strain-energy dissipation observed in torsional oscillation under dry conditions (Fig. 5). 9

Frictional effects due to relative motions at the compliant inter-granular contacts [START_REF] Mavko | Frictional Attenuation : An Inherent Amplitude Dependence[END_REF]Walsh, 10 1966) may also explain the observed Young's and shear dissipation for the dry reservoir sandstone 11 specimen. Such frictional effect is consistent with the observation (in Figure 7) that the dissipation 12 diminishes with increasing pressure and also likely contributed by interfacial compliance, particularly 13 below 10 MPa. where k is the permeability of the medium, K f is the bulk modulus of the pore-fluid, Φ is the porosity of 5 the sample, η is the viscosity of the fluid, and l is the length scale over which pore fluid diffusion occurs, 6 typically taken as between the half-and whole-length of the specimen. 7

At higher frequency, a critical frequency for squirt-flow f sq describes the transition between saturated-8 isobaric and saturated-isolated fluid regimes. With K, α, 𝜂 as the bulk modulus of the medium, crack 9 aspect ratio and viscosity respectively, the squirt frequency [START_REF] Jones | Pore fluids and frequency-dependent wave propagation in rocks[END_REF][START_REF] O'connell | Viscoelastic properties of fluid-saturated cracked solids[END_REF]) 10 is given as

11 fsq = 𝐾𝛼 3 2𝜋𝜂 (7) 12
Using the data of Table 1, the characteristic length (80 mm) of the rock sample and aspect ratio,  of ~ 7 13  10 -4 , the draining and squirt frequencies for the decane-saturated conditions of the reservoir sandstone 14 specimen are estimated as ~ 80 -300 Hz and 2 kHz respectively. 15

Experimental boundary conditions 16

An important consideration in the comparison of inter-laboratory results on fluid-saturated porous media 17 is the boundary condition imposed by the fluid drainage and control system on each experimental 18 apparatus. The conditions of the fluid-saturated specimen are often assumed to be undrained. However, 19 this is not always the case [START_REF] Bishop | The influence of system compressibility on the observed pore-pressure response to 17 an undrained in stress in saturated rock[END_REF] imposed on a typical experiment with dead volume in the fluid drainage system at each end of the test 3 specimen. Indeed, the dead volumes need to be taken into account in laboratory tests as it can strongly 4 affect the measured dispersion and dissipation of a porous specimen because of its participation in the 5 draining of the specimen. Rather than the measured dispersion and dissipation being genuinely related to 6 the fluid within the pore network of the specimen, the measured properties also include the effect of 7 possible fluid flow between the pore space of the specimen and the external pore-fluid reservoirs. 8

Therefore the dead volume must be effectively zero or at least much smaller than the rock pore volume, to 9 access the undrained conditions. So to compare and interpret the fluid flow regimes on the test reservoir 10 sandstone specimen, it is critical to review the possible effect of the boundary conditions. Pore volumes of 11 the specimen tested at ANU, and the other labs are ~ 4 cm 3 and 28 cm 3 respectivelyreflecting the 12 dimensional differences. For the test conducted at ENS, two drainage arrangements were usedone with 13 3.3 cm 3 (small) and the other with > 50 cm 3 (large) dead volume. For the test conducted at ANU and 14

Curtin University, the dead volumes were 41.5 cm 3 and 2 cm 3 respectively. As all forced-oscillation tests 15 were conducted at frequencies lower than f dr , those involving the larger dead volumes will therefore probe 16 drained conditions. Only the measurements with the lesser dead volumes of 2 cm 3 and 3.3 cm 3 at Curtin 17 and ENS, respectively, could be expected to probe essentially undrained conditions for the reservoir 18 sandstone specimen. 19 20 Accordingly, the stiffening by fluid saturation of the bulk modulus directly measured with oscillation of 21 confining pressure must represent the (undrained) saturated isobaric regime -consistent with the expected 22 effect of the presence of a relatively incompressible pore fluid such as decane, in the pore space. For such 23 saturated-isobaric conditions, no fluid-related stiffening is expected for the shear modulus which is 24 therefore expected to be the same as for drained conditions. However, given the sizeable dead volume 25 relative to pore volume for the ANU apparatus as configured for this study, the forced torsional 26 oscillation tests at sub-Hz frequencies should have probed drained conditions with a shear modulus 1 essentially unaffected by fluid saturation as observed. The possibility that the shear modulus might 2 actually be reduced slightly by decane saturation at the lowest differential pressures (Fig. 5) might reflect 3 lubrication of the inter-granular contacts. A much smaller dead volume of 1.5 cm 3 , also available on the 4 ANU apparatus, might be used to access undrained conditions in future measurements on highly 5 permeable materials. 6 7 Reconciliation with the Gassmann model 8

The fact that the bulk modulus, whether directly measured at ENS or inferred from the axial-oscillation 9 tests with small dead volume (Fig. 8), is systematically increased by decane saturation (Fig. 8), provides 10 qualitative confirmation that the undrained regime was probed by these tests. Modelling the fluid-related 11 stiffening of K and E for the saturated conditions allows an additional, more quantitative assessment. The 12 well-known, low-frequency Gassmann equation [START_REF] Gassmann | Über die Elastizität poröser Medien[END_REF] predicts the effects of pore fluids on 13 the bulk and shear moduli of an isotropic homogenous medium within the saturated isobaric regime as 14 follows 15

𝐾 u = 𝐾 d + ΔK; (8) 16
µ u = µ d (9) 17
where 𝐾 u is the undrained modulus, 𝐾 d the modulus of the dry rock frame, µ d the shear modulus of the 18 dry rock, µ u the shear modulus of the saturated rock and ΔK is the increase in the bulk modulus due to 19 fluid saturation of the dry rock, given as 20

ΔK = (1- 𝐾 d 𝐾 m ) 2 𝐾 f 𝜙+ ((1 - 𝐾 d 𝐾 m ) -𝜙) 𝐾 f 𝐾 m (10) 21
where 𝐾 m is the bulk modulus of the mineral matrix, 𝐾 f the bulk modulus of the pore fluid, 𝐾 d the bulk 22 modulus of the dry rock medium, (drained of any pore-filling fluid), and 𝜙 the porosity. The observed 23 increase of bulk modulus upon decane saturation is well described by the Gassmann model with a bulk 1 modulus of 33.1 GPa (Table 1) for the mineral skeleton (Fig. 8). This value is substantially less than that 2 (37.6 GPa, McSkimin et al.,1965) for quartz alone, and hence is plausible for this impure sandstone (see 3 e.g., [START_REF] Vernik | Acoustic velocity and porosity systematics in siliciclastics[END_REF]. For a specimen with such a heterogeneous matrix (containing quartz and clay), the 4 application of Gassmann's equation is not strictly rigorous. Indeed, the generalised equations of The dry bulk modulus is ~ 7.1 GPa (as directly measured with the confining pressure oscillation test), the 1 bulk modulus of decane pore fluid is 1.21 GPa (Table 1). The bulk modulus directly measured (at ENS) 2 with small dead volume closely approaches the Gassmann's K u . The fact that K directly measured with 3 large dead volume is, reasonably, intermediate between K d and K u (Figure 8) suggests incomplete 4 draininghighlighting the role of experimental boundary conditions. The fluid stiffening effect, 5 represented by the spacing of the values of K inferred from axial stress oscillation tests dry and decane-6 saturated conditions with small dead volume is accurately predicted by the Gassmann model, but less so 7 the absolute values of modulus at least for the ENS data. 8

The Gassmann value of K u and the directly measured value of shear modulus 𝜇 = 𝜇 d = 𝜇 u can be combined 9 (E = 9K𝜇/(3K+𝜇) and 𝜈 =(3K -2𝜇)/(2(3K+ 𝜇)) to obtain E u and 𝜈 u respectively. We compared the 10 obtained values of E u and 𝜈 u with the measurements in Fig. 4. Both the difference between values of E 11 measured in the Curtin lab dry and decane-saturated, and the absolute values of the modulus are well 12 described by the Gassmann model. For the ENS data, the same is true of the difference, but the absolute 13 values are systematically lower. The Poisson's ratio for the fluid-saturated conditions, especially from 14 results with the least dead volume (Curtin University), agrees quite well with Gassmann's 𝜈 u. Therefore, 15 it is reasonable to conclude that the elastic properties of the decane-saturated reservoir sandstone 16 specimen are those of the undrained (saturated isobaric) conditions. 17

Broadband wave speeds 18

The broadband comparison in Fig. 9 indicates an only modest dispersion (2-6 %) in P-wave velocity 19 across the four decades of frequency separating the forced-oscillation and ultrasonic data (~ 2-6 % 20 relative to the ultrasonic value) -suggesting that the pressure dependence of wavespeeds or moduli from 21 ultrasonic data would be broadly applicable at seismic frequencies. 22

For the S-wave velocities, however, the dispersion between the ultrasonic velocity and those inferred 23 from the shear modulus directly measured at 0.01 Hz with the ANU apparatus is greater (~ 10-12 %). 24 Such dispersion is not unexpected given the pressure-dependent behaviour of both the shear modulus and 1 ultrasonic velocity (Fig. 5 &7) for the dry specimen, attributed to the closure of compliant inter-granular 2 contacts. The presence of such compliant inter-granular contacts creates conditions favourable for squirt 3 flow (with estimated characteristic frequency f sq ~ 2 kHz) of the pore fluids between the inter-granular 4 contacts and porespossibly explaining the observed dispersion of the shear modulus but also 5 contributing to dispersion of the bulk modulus. specimen and P d = 10 MPa for saturation with the n-decane. Young's modulus and Poisson's ratio were 1 measured using axial forced-oscillation technique, shear modulus with torsional forced-oscillation and 2 bulk modulus using oscillation of confining pressure. 3

The stiffening of the moduli (K and E) and Poisson's ratio observed on decane saturation of the specimen 4 can be reconciled with the Gassmann model, suggesting that low-frequency testing with sufficiently small 5 dead volume probes the undrained (saturated isobaric) conditions. Such fluid-related stiffening is more 6 limited or absent for low-frequency measurements with dead volumes comparable with the pore volume 7 of the specimen. Such measurements probe the systematically lower and frequency-dependent moduli 8 associated with the transition towards drained conditions. Direct measurement of bulk modulus and shear 9 modulus using approaches involving oscillation of confining pressure and the torsional forced-oscillation 10 measurements, respectively, are consistent with those deduced from (E and 𝜈, obtained ) axial forced-11 oscillation measurements. We have attributed the pressure dependence of both the ultrasonic velocities 12 and low-frequency shear modulus of the dry specimen to the progressive closure of compliant inter-13 granular contacts within the sandstone specimen. The presence of such compliant inter-granular contacts 14 creates conditions favourable for squirt flow predicted at frequencies ~ 2 kHz, potentially responsible for 15 the dispersion of shear and bulk moduli and compressional and shear velocity between forced-oscillation 16 and ultrasonic frequencies. 17

33

  Time-lapse (4D) seismic technology is an important reservoir monitoring tool for the oil and gas industry 34 (e.g. Capello &Batzle, 1997;[START_REF] Lumley | Practical Issues of 4D Seismic Reservoir Monitoring: What an 1 Engineer Needs to Know[END_REF]

24 25 3

 25 Due to strong velocity dispersion in fluid saturated rocks, time-lapse seismic feasibility studies (e.g. 1 MacBeth, 2004; Holt et al., 2005; Asaka et al., 2018) commonly assess the sensitivity of elastic properties 2

20 Furthermore

 20 , given the Poisson's ratio and Young's modulus, the bulk K ax and shear G ax moduli of the 21 (isotropic) medium can be inferred as follows: 22

16 1Figure 1 :

 161 Figure 1: A schematic of the low-frequency laboratory apparatus, on the left for Curtin University 2 (Mikhaltsevitch et al., 2014) and on the right for ENS ( Borgomano et al., 2020) 3

7 1 Figure 2 :

 712 Figure 2: A schematic of the attenuation apparatus at the ANU.

  2

Figure 3 .

 3 Figure 3. The arrangement for ultrasonic measurements at Curtin University (Mikhaltsevitch et al., 2014) 5

17 3. 1 1 Figure 4 :

 17114 Figure 4: Frequency-dependent elastic properties (E, 𝑄 𝐸 -1 and Poisson's ratio) of the reservoir specimen 2 at dry (black symbol) and decane-saturated (red symbol) conditions assessed under axial forced-3 oscillation at Curtin University (open circle symbols) and ENS (filled circle symbols for small dead 4 volume and filled triangle symbols for large dead volume). Dashed straight lines show the predictions 5 based on Gassmann's theory. Differential pressure at 10 MPa. 6 7

5 11 Figure 5 :

 115 Figure 5: Shear modulus and dissipation of the dry (black symbol), and decane-saturated (red symbols) 12specimen measured with torsional forced-oscillations using the Jackson -Paterson apparatus at the ANU. 13Pore pressure fixed at 5MPa and confining pressure varied accordingly. The uncertainty associated with 14 the determined modulus is ± 3% 1516

1

 1

Figure 6 : 6 Figure 6

 666 Figure 6: Bulk modulus and dissipation of the dry (black symbol) and decane-saturated specimen (red 2 symbols, small dead volume with a solid line and large dead volume with the dashed line) measured with 3 a test involving the oscillation of the confining pressure at ENS. Differential pressure at 10 MPa. 4 5

3 4 5Figure 7 :

 47 Figure 7: Pressure-dependent ultrasonic velocities of the specimen obtained by the pulse transmission 6 techniques for the dry (in black) and decane-saturated conditions (in red symbols) both at Curtin 7 University (denoted with circles) and ENS (denoted with square). Filled symbols for V P , and open 8 symbols, for V S . 9 10

16 4. 1

 161 Dry conditions 17 Pressure sensitivity of elastic properties 18

14

 14

4. 2 &

 2 Decane-saturated conditions 15 Fluid flow regimes and characteristic frequencies 16 It is well established that pore fluids strongly modify the mechanical properties of shallow crustal rocks 17 to be frequency-dependent (Cleary, 1978; O'Connell & Budiansky, 1977). Such frequency-dependent 18 behaviour can be described in terms of three fluid-flow regimes that are separated by transitionseach 19 with a different relaxation mechanism. These transitions manifest as modulus dispersion and dissipation 20 in the mechanical properties of fluid-saturated porous media (O'Connell & Budiansky, 1977). 21At low-frequency conditions, pore fluid pressure perturbation within a homogenous porous medium has 22 sufficient time to reach local equilibriummeaning that any representative elementary volume of the 23 porous medium has same pore fluid pressure and thus poroelastic theories apply. Such state of local 24 equilibrium of pore pressure is referred to as the saturated isobaric ( O'Connell & Budiansky, 1977). The 25 saturated isobaric regime is an undrained condition which is separated from the drained conditions at even 1 lower frequencies by a transition characterised by a critical frequency given as[START_REF] Cleary | Elastic and dynamic response regimes of fluid-impregnated solids with diverse 34 microstructures[END_REF] Detournay 2

  ; Ghabezloo & Sulem, 2010; Pimienta et al., 2015; 20 Mikhaltsevitch et al., 2019). The nature and design of the pore pressure drainage and control system are 21 essential. For example, Mikhaltsevitch et al. (2019) illustrated the effect of dead volume on the frequency 22 dependences of the elastic moduli of n-decane-saturated Savonnieres limestone specimens. In Pimienta et 1 al., (2016) a one-dimensional poroelastic model was used to quantify the effect of boundary conditions 2

Brown 5 & 9 10Figure 8 :

 598 Figure 8: Frequency-dependence of the directly measured (square/triangle symbol = small/large dead

6 7Figure 9 : 12 5.0 Conclusion 13

 691213 Figure 9: Broadband velocities for the decane-saturated specimen using results from axial oscillation, 8 torsional oscillation and pulse transmission test, both at Curtin University (filled and open circle for Vp 9 and Vs respectively) and ENS (filled and open square for Vp and Vs respectively) at 10 MPa differential 10 pressure. Vs inferred from ANU measurements in open triangles. 11 12

  Overall, the results of the inter-laboratory testing are consistent in terms of the effect of frequency and 18 fluid saturation for the reservoir sandstone specimen. Such broad consistency illustrates the validity of 19 forced-oscillation techniques and constitutes an important benchmarking study on elastic properties 20 testing of a porous medium. 21Data Availability Statement 22The data supporting the findings in this paper belong to Woodside Energy Ltd and are not publicly 23 available. 24

  14following completion of the first phase of the experimental work at Curtin University.

	Table
	15
	16		Test specimen
	17	Porosity,𝜱	Permeability (mD)	Density (kg/m 3 )	K matrix (GPa)
	18	29%	120	1933.2	33.1
			n-Decane pore fluid
	19	Temp. ( o C)	Viscosity (Pa.s)	Density (kg/m 3 )	K f (GPa)
	20	20	9.68 × 10 -4	734.2	1.21


Ling Ding

Zhenbin Lyu

Beatrice Louis

Aura Tintaru

Erik Laurini

Domenico Marson

Mengjie Zhang

Wanxuan Shao

Yifan Jiang

Ahlem Bouhlel

Laure Balasse

Philippe Garrigue

Eric Mas

Suzanne Giorgio

Juan Iovanna

Yuanyu Huang

Sabrina Pricl

Benjamin Guillet

Dr Ling Peng
email: ling.peng@univ-amu.fr

Surface charge of supramolecular nanosystems for in vivo biodistribution: a microSPECT/CT imaging study

Keywords: supramolecular nanosystems, dendrimer, self-assembling, surface charge, metal chelators, SPECT imaging

Bioimaging has revolutionized medicine by providing accurate information for disease diagnosis and treatment. Nanotechnology-based bioimaging is expected to further improve imaging sensitivity and specificity. In this context, we have developed supramolecular nanosystems based on self-assembly of amphiphilic dendrimers for single photon emission computed tomography (SPECT) bioimaging. These dendrimers bear multiple In 3+ radionuclides at their terminals as SPECT reporters. By replacing the macrocyclic DOTA cage with the smaller NOTA scaffold as the In 3+ chelator, the corresponding dendrimer exhibited neutral In 3+complex terminals in place of negatively charged In 3+ -complex terminals. This negative-toneutral surface charge alteration completely reversed the zeta-potential of the nanosystems from negative to positive. As a consequence, the resulting SPECT nanoprobe generated a highly sought-after biodistribution profile accompanied by a drastically reduced uptake in liver, leading to significantly improved tumor imaging. This finding contrasts with current literature reporting that positively charged nanoparticles have preferential accumulation in the liver. As such, this study provides new perspectives for improving the biodistribution of positively charged nanosystems for biomedical applications.

Introduction

Molecular imaging has revolutionized cancer management by providing precise information relating to tumor detection, grading, staging, and diagnosis, as well as monitoring treatment response and efficacy for personalized medicine. [1,2] Nevertheless, there is high demand for further improvements in terms of sensitivity, specificity, and spatial resolution.

Nanotechnology is expected to overcome these limitations by further improving imaging sensitivity and specificity via the so-called 'enhanced permeability and retention (EPR)' effect, also termed passive tumor targeting. [3][4][5] EPR allows nanosized macromolecules or particles to preferentially accumulate in tumor tissue because of the leaky vasculature and disabled lymphatic system characterizing the tumor microenvironment. [6] As a result, the local concentration of imaging agents in tumor lesions can be significantly increased, leading to better imaging outcomes. Moreover, nanosystems can carry multiple or hundreds of imaging reporters, which can significantly enhance the contrast signal for more accurate imaging and diagnosis. Consequently, different nanosystems have been explored and studied for tumor imaging. [3][4][5] Dendrimer nanosystems are of particular interest for the delivery of imaging agents because of the unique dendritic structure and multivalent cooperativity confined within the nanoscale dimension. [7][8][9][10][11][START_REF] Zhao | Nanotechnology Characterization Tools for Biosensing and Medical Diagnosis[END_REF] We have recently established small amphiphilic dendrimers that are able to self-assemble into supramolecular nanosystems for effective tumor imaging using positron emission tomography (PET) and single photon emission computed tomography (SPECT) (Figure 1). [START_REF] Garrigue | Proc. Natl. Acad. Sci[END_REF][START_REF] Ding | [END_REF] Both PET and SPECT are radio-imaging techniques that have a high sensitivity yet unlimited tissue penetration, and are able to visualize functional information quantitatively. [15,16] Notably, SPECT is the most prevalent clinical imaging modality, accounting for >75% of all nuclear imaging procedures. [17] Thus, we have focused our recent efforts on optimizing our supramolecular dendrimer systems for SPECT imaging. tetraazacyclododececane-1-(glutaric acid)-4,7,10-triacetic acid) at the terminals (In-1 in Figure 1). [START_REF] Ding | [END_REF] By virtue of its amphiphilic nature, In-1 self-assembled into small and stable supramolecular nanomicelles for effective SPECT imaging of tumors based on the favorable combination of EPR-based passive tumor targeting and the dendrimeric structure bearing multivalent SPECT reporters. Nevertheless, In-1 also displayed high liver retention, which represents a severe limitation for its future clinical translation. It is well known that different chelators can significantly impact the biodistribution of radiotracers based on their size, charge, geometry, and lipophilicity when complexed with radionuclide metal ions. [18][19][20] As the macrocycle DOTA ring in the DOTAGA chelator forms a negatively charged complex with In 3+ , we suspected that, despite the small nanosize of the corresponding In-1 nanomicelle, the overall surface charge of the In-1 nanoparticle might cause the high liver uptake and retention. Thus, we hypothesized that suppressing the negative surface charge of the dendrimer could limit this unfavorable liver retention.

We previously developed an amphiphilic dendrimer

Accordingly, we replaced the macrocyclic DOTA cage with the NOTA (1,4,7triazacyclononane-1,4,7-triacetic acid) scaffold by conjugating the chelator NODAGA

(1,4,7-triazacyclononane,1-glutaric acid-4,7-acetic acid) at the dendrimer terminals, because the NOTA ring can form a neutral complex when chelating the trivalent metal ion In 3+ (In-2 in Figure 1). [21] Also, the macrocycle NOTA scaffold is smaller than the DOTA cage, and hence generates more stable complexes with small metal ions such as Ga 3+ , In 3+ , and Cu 2+ . [22] It should be noted that here we use DOTA and NOTA cages or rings as macrocyclic scaffolds for complexing with metal ions, rather than as the specific chelators in this work.

Their corresponding chelators used in this work, DOTAGA and NODAGA, are, respectively, DOTA and NOTA-derivatives, often used for convenient conjugation with other chemical entities to present DOTA and NOTA scaffolds, thus maintaining the full denticity of DOTA and NOTA when chelating with metal ions.

Indeed, changing the DOTA cage to the NOTA ring at the amphiphilic dendrimer terminals had a profound impact on the surface charge of the resulting dendrimer, completely reversing the zeta potential from negative to positive when complexing with the trivalent metal ion In 3+ . As a consequence of this alteration, the radioactive In 3+ -labelled imaging nanoprobe

In-2 led to a highly favorable biodistribution with drastically reduced uptake in liver, generating significantly improved tumor imaging. Although current literature reports that positively charged nanoparticles preferentially accumulate in the liver, [3][4][5] our results clearly show that the presence of neutral surface regions of nanosystem with overall positively charged zeta potential could also result in drastically reduced liver uptake. Therefore, our findings provide new perspectives for improving the safety and biodistribution of various nanosystems for biomedical applications. Herein, we present and discuss our work in establishing In-2 as a promising agent for SPECT imaging of tumors, highlighting the importance of surface charge for the biodistribution of nanoparticles as a general concept.

Results and discussion

We prepared the dendrimer 2 bearing the macrocyclic NOTA cages at the terminals according to our previously reported synthesis. [START_REF] Garrigue | Proc. Natl. Acad. Sci[END_REF] However, in the present study, we reduced the quantity of the reagent NODA-GA(tBu)3 by half in order to facilitate the purification procedures while maintaining the chemical integrity and high yield of product 2 (Figure 2A and Scheme S1). Chelation of the stable isotope 115 In 3+ by 2 was performed using 115 InCl3 at 25°C

for 10 min at pH 4.0-4.5 (Figure 2A). These conditions contrasted with those used for the synthesis of In-1, which required substantially higher temperatures (55°C) and longer times (120 min). The successful complexation of four 115 In 3+ ions by the macrocyclic NOTA scaffolds in 2 was confirmed using high-resolution mass spectroscopy, which revealed the isotopic pattern characteristic of the triply charged species [ 115 In-2+3H] 3+ of the expected molecular structure (Figure 2C, Figure S1). [START_REF]We were unable to obtain well-resolved NMR spectra for In-2 because of the highly quadrupolar effect of the 115[END_REF] Previously, we also supported the synthesis of the dendrimer In-1 carrying the DOTA cages through isothermal titration calorimetry (ITC). [START_REF] Ding | [END_REF] We used the same approach to study the thermodynamics of the interaction between In 3+ and the dendrimer 2 bearing the NOTA cages for generating In-2 (Figure 2B). The titration of both dendrimers 1 and 2 with the trivalent cation In 3+ presented very similar calorimetric behaviors. The spontaneous formation of In-2

was promoted by a favorable binding free energy (ΔG) of -7.64 kcal mol -1 . This value arises from the balanced and favorable contributions of both the entropic (-TΔS = -2.21 kcal mol -1 ) and the enthalpic (ΔH = -5.43 kcal mol -1 ) components, which are similar to the binding thermodynamic parameters for In-1 (ΔG = -7.86 kcal mol -1 , -TΔS = -2.61, and ΔH = -5.25 kcal mol -1 ). A 4:1 stoichiometry was also determined for the In-2 complex by the ITC-derived number of occupied sites (n = 3.95), corroborating the results obtained using high-resolution mass spectroscopy (Figure 2C).

With the synthesized In-2 in hand, we then examined the spontaneously self-assembling features of In-2 in water. Using transmission electron microscopy, we observed the formation of small and spherical nanoparticles of an average size of 18 nm by In-2 in water (Figure 3A), similar to those generated by the self-assembly of In-1 (Figure 3F). Furthermore, dynamic light scattering analysis confirmed the presence of nanoparticles of similar sizes for both dendrimers

In-1 and In-2 in water and in phosphate buffer at pH 7.4 (Figure 3B, G, and Figure S3). This highlighted that, like In-1, In-2 also self-assembled into nanomicelles. We then used a fluorescent spectroscopic assay with Nile Red to estimate the critical micelle concentration (CMC) of In-2, which was around 40 µM, similar to the CMC value for In-1 (49 µM) (Figure S4). In addition, we measured the surface zeta potential of the In-2 nanomicelles, and obtained a positive value of +11 mV (Figure 3C), which could be ascribed to the interior tertiary amine functionality, since the In 3+ complex with the NOTA ring in the NODAGA chelator at the dendrimer terminal is neutral. This is distinctly different from that of In-1, where each DOTA cage within the DOTAGA terminal in complex with In 3+ has a net negative charge, thereby generating In-1 nanomicelles with an overall negative zeta potential of -8 mV (Figure 3H). To further confirm the spontaneous self-assembly of In-1 and In-2 into nanomicelles, we performed molecular dynamics simulations following a consolidated procedure. [START_REF] Garrigue | Proc. Natl. Acad. Sci[END_REF][START_REF] Ding | [END_REF] Starting from randomly distributed monomers, we obtained stable spherical micelles for both systems during the timescale of the simulations (1.0 µs) (Figures 3D,F,I,J). The corresponding average micelle diameters computed from the equilibrated molecular dynamics simulations were 15 nm and 13 nm for the In-1 and In-2 systems, respectively, which were in good agreement with the experimental results obtained using both dynamic light scattering and transmission electron microscopy. By inspecting the conformational structures of both micelles, no back-folding of the terminal groups was detected, in line with our previous findings obtained for similar systems [13, 14] . Accordingly, the In 3+ -bearing terminal units are all located at the periphery of the micelles in both the In-1 and In-2 systems. Further analysis of the electrostatic surface potential confirmed the foreseen effect of replacing the DOTA cage with the NOTA scaffold, with a negative electrostatic potential observed for In-1 (Figure 3I) and a positive potential for In-2 3D), in agreement with the experimentally-determined surface zeta potentials (Figures 3C,H). Moreover, the surface of the In-1 micelle was characterized by the presence of localized negatively charged regions, corresponding to the trivalent In 3+ ions in complex with the DOTA cages at the DOTAGA terminals (Figure 3J), while the In-2 nanoparticles presented patches of neutral charge, corresponding to In 3+ ions in complex with NOTA rings at the NODAGA terminals (Figure 3E).

(Figure
Next, we prepared the radioactive dendrimer complex [ 111 In]In-2 for SPECT imaging.

Radiolabeling was performed using [ 111 In]In 3+ in ammonium acetate buffer, and the obtained [ 111 In]In-2 complex had an excellent radiochemical purity of over 93%, which was remarkably stable and maintained up for at least 48 h at 37°C in human serum (Figure 4A). SPECT imaging In line with our original hypothesis, we tentatively rationalized the discrepancies in biodistribution to the difference in chelators and the resulting alteration in surface charge of In-1 and In-2, since the size variation between the In-1 and In-2 nanomicelles was very small (Figure 3). As discussed above, after changing the DOTA cage in In-1 to the NOTA scaffold in In-2 at the dendrimer terminals, the zeta potential of the corresponding In 3+ -labelled nanomicelles formed by these dendrimers changed accordingly (Figures 3E and3J), leading to a more than 2-fold reduced accumulation of [ 111 In]In-2 in the liver. Of note, the majority of published studies report that positively-charged nanoparticles are more likely to accumulate in the liver than their negatively charged counterparts. [3][4][5] Our results, however, demonstrate that overall positively charged nanosystems exhibiting neutral regions on their surface can also exhibit reduced liver uptake. As a consequence, a significantly improved biodistribution and imaging profile was obtained with [ 111 In]In-2 compared to [ 111 In]In-1. Our findings highlight that the impact on pharmacokinetics and biodistribution is dependent not only on the choice of chelator, [22,[START_REF] Strand | [END_REF] but also on the nature of the whole imaging probes. This overall feature may impact the ability of probes to bind to proteins in body fluids, depending on the different surface charges, and hence impacting the overall biodistribution. [25] In addition, lowering the liver uptake can also help to improve the safety and biodistribution profiles of the supramolecular nanosystems that have been developed for biomedical applications in general. Moreover, the dendrimer In-2 enabled better tumor imaging, which was significantly enhanced (up to 2.0fold) and long-lasting (up to 48 h after injection) for both-tumor-to-muscle and tumor-to-liver ratios (Figures 5C and5D). This feature is particular interesting in developing imaging-guided internal radiotherapy.

It is noteworthy that the mice receiving the radioactive [ 111 In]In-2 did not display any abnormal behaviors or adverse effects during all experimental imaging procedures.

Furthermore, healthy mice that received the nonradioactive In-2 did not exhibit any organ damage or blood biochemistry defects, even when the administered dose of In-2 was 10 times higher than that required for SPECT imaging (Figure 6). As shown in Figure 6A, histological analysis of organs from mice treated with In-2 revealed no gross lesions or significant underlying pathologies in any organ tissue sections. Also, several major blood biochemistry parameters including alanine transaminase, aspartate transaminase, total bilirubin, creatinine, urea, total protein, alkaline phosphatase, triacylglycerol and total cholesterol, remained at the levels comparable to those found in untreated mice (Figure 6B). This highlighted that no acute events were associated with In-2 in terms of normal liver, kidney, and muscle function, further confirming that the main organs functioned well after treatment with In-2. All these data demonstrate that [ 111 In]In-2 produces no adverse effects, but delivers effective SPECT imaging quality.

Conclusion

By replacing the DOTA cage with the NOTA scaffold to chelate the radionuclide In 3+ , we established a new amphiphilic dendrimer In-2 bearing neutral coordination complexes with the trivalent In 3+ ions at the dendrimer terminals for SPECT imaging. This modification had a drastic impact, generating significantly improved tumor imaging and a beneficial biodistribution profile. Notably, the uptake of In-2 in the liver was reduced significantly, by more than 2-fold compared with that of In-1; at the same time, the imaging contrast was also considerably enhanced up to 2-fold and sustained even up to 48 h after injection. This study presents not only the supramolecular dendrimer nanosystem In-2 for safe and effective SPECT imaging of tumors, but also new perspectives for improving the safety and biodistribution of supramolecular nanosystems for biomedical applications such as theranostics based on imaging-guided internal radiotherapy.

In- 1

 1 composed of a long hydrophobic alkyl chain and a hydrophilic poly(amidoamine) dendron bearing the SPECT radionuclide 10-tetraacetic acid) ring in the chelator DOTAGA(1,4,7,10-

Figure 1 .

 1 Figure 1. Schematic illustration of the supramolecular dendrimer nanosystems, based on the

Figure 2 . 2 .

 22 Figure 2. Synthesis of the amphiphilic dendrimer 2 and its chelation with the nonradioactive

Figure 3 . 1 and

 31 Figure 3. Comparison of the spontaneous self-assembling of the amphiphilic dendrimers In-1

using [ 111

 111 In]In-2 was first performed in orthotopically xenografted mice bearing human pancreatic adenocarcinoma SOJ-6 tumors, and the results obtained with [ 111 In]In-1 were used as control for comparison. Co-registration with computed tomography (CT) enabled anatomical localization of the SPECT signals for further quantification. As seen in Figure 4B, a significantly improved image contrast for tumor visualization was obtained with [ 111 In]In-2 compared to [ 111 In]In-1.

Figure 4 .[

 4 Figure 4. Radiolabeled dendrimers [ 111 In]In-1 and [ 111 In]In-2 for SPECT imaging in a mouse

Figure 5 .

 5 Figure 5. Radiolabeled dendrimer [ 111 In]In-1 and [ 111 In]In-2 for SPECT imaging in a patient-

Figure 6 . 2 .

 62 Figure 6. In vivo toxicity assessment of In-2 in healthy mice at different doses. 1×, 5×, and 10×

Acknowledgments

We thank Michel Skandalovski (CERIMED, Aix-Marseille University), Samy Vigier, and Sandrine Pons (Faculty of Pharmacy, Aix-Marseille University) for technical support. This work was supported by the Ligue Nationale Contre le Cancer (LP, ZL), China Scholarship Council (LD), Italian Association for Cancer Research (IG17413) (SP), the French National Research Agency under the frame of the Era-Net EURONANOMED European Research projects 'NANOGLIO', 'TARBRAINFECT', and 'NAN-4-TUM' (LP), H2020 NMBP 'SAFE-N-MEDTECH' (LP), the National Natural Science Foundation of China (31871003, 31901053) (YH), and Ecole Doctorale 62 Sciences de la vie et de la santé, Aix-Marseille Université (BL). This article is based upon work from COST Action CA 17140 'Cancer Nanomedicine from the Bench to the Bedside' supported by COST (European Cooperation in Science and Technology).

Author contribution

LP coordinated the project. LD, ZL, AB and PG synthesized the agents, LD, ZL, AT, SG, AB, and PG made the characterization of the agents, EL, DM, and SP provided ITC and molecular modeling data, EM and PG prepared the SOJ-6 animal model, LD, YJ, and JL prepared the LIPC animal model, PG, BL, LB, and SF performed imaging experiments, MZ, WS, and YH performed toxicity study, LD, ZL, AT, PG, BL, AB, BG, YH, EL, SP, and LP analyzed data; LP wrote the paper with contribution from LD, ZL, AT, EL, SP, PG, BG, and YH. All authors proofed the manuscript.

Surface charge of supramolecular nanosystems for in vivo biodistribution: a microSPECT/CT imaging study

Replacing the DOTA cage with the NOTA scaffold to chelate the radionuclide In 3+ , the corresponding dendrimer nanosystem completely reversed the zeta-potential from negative to positive, generated a highly favorable biodistribution profile with a drastically reduced uptake in liver, and exhibited significantly improved tumor imaging.