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1.
Int J Mol Sci ; 24(21)2023 Oct 24.
Artículo en Inglés | MEDLINE | ID: mdl-37958495

RESUMEN

Positron emission tomography (PET) radioligands that bind with high-affinity to α4ß2-type nicotinic receptors (α4ß2Rs) allow for in vivo investigations of the mechanisms underlying nicotine addiction and smoking cessation. Here, we investigate the use of an image-derived arterial input function and the cerebellum for kinetic analysis of radioligand binding in mice. Two radioligands were explored: 2-[18F]FA85380 (2-FA), displaying similar pKa and binding affinity to the smoking cessation drug varenicline (Chantix), and [18F]Nifene, displaying similar pKa and binding affinity to nicotine. Time-activity curves of the left ventricle of the heart displayed similar distribution across wild type mice, mice lacking the ß2-subunit for ligand binding, and acute nicotine-treated mice, whereas reference tissue binding displayed high variation between groups. Binding potential estimated from a two-tissue compartment model fit of the data with the image-derived input function were higher than estimates from reference tissue-based estimations. Rate constants of radioligand dissociation were very slow for 2-FA and very fast for Nifene. We conclude that using an image-derived input function for kinetic modeling of nicotinic PET ligands provides suitable results compared to reference tissue-based methods and that the chemical properties of 2-FA and Nifene are suitable to study receptor response to nicotine addiction and smoking cessation therapies.


Asunto(s)
Receptores Nicotínicos , Tabaquismo , Ratones , Animales , Nicotina/farmacología , Nicotina/metabolismo , Encéfalo/metabolismo , Tabaquismo/metabolismo , Cinética , Ligandos , Tomografía de Emisión de Positrones/métodos , Receptores Nicotínicos/genética , Receptores Nicotínicos/metabolismo
2.
Molecules ; 28(16)2023 Aug 13.
Artículo en Inglés | MEDLINE | ID: mdl-37630292

RESUMEN

In the field of nuclear medicine, the ß+ -emitting 43Sc and ß- -emitting 47Sc are promising candidates in cancer diagnosis and targeted radionuclide therapy (TRT) due to their favorable decay schema and shared pharmacokinetics as a true theranostic pair. Additionally, scandium is a group-3 transition metal (like 177Lu) and exhibits affinity for DOTA-based chelators, which have been studied in depth, making the barrier to implementation lower for 43/47Sc than for other proposed true theranostics. Before 43/47Sc can see widespread pre-clinical evaluation, however, an accessible production methodology must be established and each isotope's radiolabeling and animal imaging capabilities studied with a widely utilized tracer. As such, a simple means of converting an 18 MeV biomedical cyclotron to support solid targets and produce 43Sc via the 42Ca(d,n)43Sc reaction has been devised, exhibiting reasonable yields. The NatTi(γ,p)47Sc reaction is also investigated along with the successful implementation of chemical separation and purification methods for 43/47Sc. The conjugation of 43/47Sc with PSMA-617 at specific activities of up to 8.94 MBq/nmol and the subsequent imaging of LNCaP-ENZaR tumor xenografts in mouse models with both 43/47Sc-PSMA-617 are also presented.


Asunto(s)
Medicina Nuclear , Neoplasias de la Próstata , Humanos , Animales , Ratones , Masculino , Escandio , Medicina de Precisión , Neoplasias de la Próstata/diagnóstico por imagen , Neoplasias de la Próstata/radioterapia , Radioisótopos/uso terapéutico
3.
Eur J Nucl Med Mol Imaging ; 49(12): 4014-4024, 2022 Oct.
Artículo en Inglés | MEDLINE | ID: mdl-35792927

RESUMEN

PURPOSE: To identify the optimal threshold in 18F-fluoromisonidazole (FMISO) PET images to accurately locate tumor hypoxia by using electron paramagnetic resonance imaging (pO2 EPRI) as ground truth for hypoxia, defined by pO2 [Formula: see text] 10 mmHg. METHODS: Tumor hypoxia images in mouse models of SCCVII squamous cell carcinoma (n = 16) were acquired in a hybrid PET/EPRI imaging system 2 h post-injection of FMISO. T2-weighted MRI was used to delineate tumor and muscle tissue. Dynamic contrast enhanced (DCE) MRI parametric images of Ktrans and ve were generated to model tumor vascular properties. Images from PET/EPR/MRI were co-registered and resampled to isotropic 0.5 mm voxel resolution for analysis. PET images were converted to standardized uptake value (SUV) and tumor-to-muscle ratio (TMR) units. FMISO uptake thresholds were evaluated using receiver operating characteristic (ROC) curve analysis to find the optimal FMISO threshold and unit with maximum overall hypoxia similarity (OHS) with pO2 EPRI, where OHS = 1 shows perfect overlap and OHS = 0 shows no overlap. The means of dice similarity coefficient, normalized Hausdorff distance, and accuracy were used to define the OHS. Monotonic relationships between EPRI/PET/DCE-MRI were evaluated with the Spearman correlation coefficient ([Formula: see text]) to quantify association of vasculature on hypoxia imaged with both FMISO PET and pO2 EPRI. RESULTS: FMISO PET thresholds to define hypoxia with maximum OHS (both OHS = 0.728 [Formula: see text] 0.2) were SUV [Formula: see text] 1.4 [Formula: see text] SUVmean and SUV [Formula: see text] 0.6 [Formula: see text] SUVmax. Weak-to-moderate correlations (|[Formula: see text]|< 0.70) were observed between PET/EPRI hypoxia images with vascular permeability (Ktrans) or fractional extracellular-extravascular space (ve) from DCE-MRI. CONCLUSION: This is the first in vivo comparison of FMISO uptake with pO2 EPRI to identify the optimal FMISO threshold to define tumor hypoxia, which may successfully direct hypoxic tumor boosts in patients, thereby enhancing tumor control.


Asunto(s)
Carcinoma de Células Escamosas , Hipoxia Tumoral , Animales , Carcinoma de Células Escamosas/diagnóstico por imagen , Carcinoma de Células Escamosas/patología , Hipoxia de la Célula , Espectroscopía de Resonancia por Spin del Electrón , Hipoxia/diagnóstico por imagen , Ratones , Misonidazol/análogos & derivados , Tomografía de Emisión de Positrones/métodos , Radiofármacos , Tomografía Computarizada por Rayos X
4.
Neurocrit Care ; 34(1): 64-72, 2021 02.
Artículo en Inglés | MEDLINE | ID: mdl-32358767

RESUMEN

BACKGROUND: Cardiac arrest (CA) patients who survived by cardiopulmonary resuscitation (CPR) can present different levels of neurological deficits ranging from minor cognitive impairments to persistent vegetative state and brain death. The pathophysiology of the resulting brain injury is poorly understood, and whether changes in post-CA brain metabolism contribute to the injury are unknown. Here we utilized [18F]fluorodeoxyglucose (FDG)-Positron emission tomography (PET) to study in vivo cerebral glucose metabolism 72 h following CA in a murine CA model. METHODS: Anesthetized and ventilated adult C57BL/6 mice underwent 12-min KCl-induced CA followed by CPR. Seventy-two hours following CA, surviving mice were intraperitoneally injected with [18F]FDG (~ 186 µCi/200 µL) and imaged on Molecubes preclinical micro-PET/computed tomography (CT) imaging systems after a 30-min awake uptake period. Brain [18F]FDG uptake was determined by the VivoQuant software on fused PET/CT images with the 3D brain atlas. Upon completion of Positron emission tomography (PET) imaging, remaining [18F]FDG radioactivity in the brain, heart, and liver was determined using a gamma counter. RESULTS: Global increases in brain [18F]FDG uptake in post-CA mice were observed compared to shams and controls. The median standardized uptake value of [18F]FDG for CA animals was 1.79 versus sham 1.25 (p < 0.05) and control animals 0.78 (p < 0.01). This increased uptake was consistent throughout the 60-min imaging period and across all brain regions reaching statistical significance in the midbrain, pons, and medulla. Biodistribution analyses of various key organs yielded similar observations that the median [18F]FDG uptake for brain was 7.04%ID/g tissue for CA mice versus 5.537%ID/g tissue for sham animals, p < 0.05). CONCLUSIONS: This study has successfully applied [18F]FDG-PET/CT to measure changes in brain metabolism in a murine model of asystolic CA. Our results demonstrate increased [18F]FDG uptake in the brain 72 h following CA, suggesting increased metabolic demand in the case of severe neurological injury. Further study is warranted to determine the etiology of these changes.


Asunto(s)
Fluorodesoxiglucosa F18 , Paro Cardíaco , Animales , Encéfalo/diagnóstico por imagen , Glucosa , Paro Cardíaco/diagnóstico por imagen , Humanos , Ratones , Ratones Endogámicos C57BL , Tomografía Computarizada por Tomografía de Emisión de Positrones , Tomografía de Emisión de Positrones , Radiofármacos , Distribución Tisular
5.
Angew Chem Int Ed Engl ; 59(35): 15161-15165, 2020 08 24.
Artículo en Inglés | MEDLINE | ID: mdl-32415874

RESUMEN

Herein, we report the development of an 18 F-labeled, activity-based small-molecule probe targeting the cancer-associated serine hydrolase NCEH1. We undertook a focused medicinal chemistry campaign to simultaneously preserve potent and specific NCEH1 labeling in live cells and animals, while permitting facile 18 F radionuclide incorporation required for PET imaging. The resulting molecule, [18 F]JW199, labels active NCEH1 in live cells at nanomolar concentrations and greater than 1000-fold selectivity relative to other serine hydrolases. [18 F]JW199 displays rapid, NCEH1-dependent accumulation in mouse tissues. Finally, we demonstrate that [18 F]JW199 labels aggressive cancer tumor cells in vivo, which uncovered localized NCEH1 activity at the leading edge of triple-negative breast cancer tumors, suggesting roles for NCEH1 in tumor aggressiveness and metastasis.


Asunto(s)
Radioisótopos de Flúor/uso terapéutico , Tomografía de Emisión de Positrones/métodos , Esterol Esterasa/metabolismo , Animales , Femenino , Humanos , Ratones
6.
Nanomaterials (Basel) ; 13(4)2023 Feb 09.
Artículo en Inglés | MEDLINE | ID: mdl-36839041

RESUMEN

Photodynamic therapy (PDT), the use of light to excite photosensitive molecules whose electronic relaxation drives the production of highly cytotoxic reactive oxygen species (ROS), has proven an effective means of oncotherapy. However, its application has been severely constrained to superficial tissues and those readily accessed either endoscopically or laparoscopically, due to the intrinsic scattering and absorption of photons by intervening tissues. Recent advances in the design of nanoparticle-based X-ray scintillators and photosensitizers have enabled hybridization of these moieties into single nanocomposite particles. These nanoplatforms, when irradiated with diagnostic doses and energies of X-rays, produce large quantities of ROS and permit, for the first time, non-invasive deep tissue PDT of tumors with few of the therapeutic limitations or side effects of conventional PDT. In this review we examine the underlying principles and evolution of PDT: from its initial and still dominant use of light-activated, small molecule photosensitizers that passively accumulate in tumors, to its latest development of X-ray-activated, scintillator-photosensitizer hybrid nanoplatforms that actively target cancer biomarkers. Challenges and potential remedies for the clinical translation of these hybrid nanoplatforms and X-ray PDT are also presented.

7.
Nat Chem ; 15(1): 119-128, 2023 01.
Artículo en Inglés | MEDLINE | ID: mdl-36280766

RESUMEN

Interactions between the microbiota and their colonized environments mediate critical pathways from biogeochemical cycles to homeostasis in human health. Here we report a soil-inspired chemical system that consists of nanostructured minerals, starch granules and liquid metals. Fabricated via a bottom-up synthesis, the soil-inspired chemical system can enable chemical redistribution and modulation of microbial communities. We characterize the composite, confirming its structural similarity to the soil, with three-dimensional X-ray fluorescence and ptychographic tomography and electron microscopy imaging. We also demonstrate that post-synthetic modifications formed by laser irradiation led to chemical heterogeneities from the atomic to the macroscopic level. The soil-inspired material possesses chemical, optical and mechanical responsiveness to yield write-erase functions in electrical performance. The composite can also enhance microbial culture/biofilm growth and biofuel production in vitro. Finally, we show that the soil-inspired system enriches gut bacteria diversity, rectifies tetracycline-induced gut microbiome dysbiosis and ameliorates dextran sulfate sodium-induced rodent colitis symptoms within in vivo rodent models.


Asunto(s)
Colitis , Microbioma Gastrointestinal , Humanos , Animales , Suelo/química , Colitis/inducido químicamente , Colitis/metabolismo , Homeostasis , Modelos Animales de Enfermedad
8.
Nat Biomed Eng ; 7(11): 1514-1529, 2023 Nov.
Artículo en Inglés | MEDLINE | ID: mdl-37308586

RESUMEN

Topographical cues on cells can, through contact guidance, alter cellular plasticity and accelerate the regeneration of cultured tissue. Here we show how changes in the nuclear and cellular morphologies of human mesenchymal stromal cells induced by micropillar patterns via contact guidance influence the conformation of the cells' chromatin and their osteogenic differentiation in vitro and in vivo. The micropillars impacted nuclear architecture, lamin A/C multimerization and 3D chromatin conformation, and the ensuing transcriptional reprogramming enhanced the cells' responsiveness to osteogenic differentiation factors and decreased their plasticity and off-target differentiation. In mice with critical-size cranial defects, implants with micropillar patterns inducing nuclear constriction altered the cells' chromatin conformation and enhanced bone regeneration without the need for exogenous signalling molecules. Our findings suggest that medical device topographies could be designed to facilitate bone regeneration via chromatin reprogramming.


Asunto(s)
Células Madre Mesenquimatosas , Osteogénesis , Ratones , Humanos , Animales , Cromatina , Constricción , Regeneración Ósea
9.
Sci Adv ; 7(24)2021 06.
Artículo en Inglés | MEDLINE | ID: mdl-34117071

RESUMEN

The revolutionizing efficacy of recombinant human bone morphogenetic protein (rhBMP-2) for clinical spinal fusion is hindered by safety issues associated with the high dose required. However, it continues to be widely used, for example, in InFUSE Bone Graft (Medtronic). Here, we developed a translational protein engineering-based approach to reduce the dose and thereby improve the safety of rhBMP-2 delivered in a collagen sponge, as in InFUSE Bone Graft. We engineered a bridge protein with high affinity for rhBMP-2 and collagen that can be simply added to the product's formulation, demonstrating improved efficacy at low dose of rhBMP-2 in two mouse models of bone regeneration, including a newly developed spinal fusion model. Moreover, the bridge protein can control the retention of rhBMP-2 from endogenous collagenous extracellular matrix of tissue. Our approach may be generalizable to other growth factors and collagen-based materials, for use in many other applications in regenerative medicine.


Asunto(s)
Fusión Vertebral , Animales , Proteína Morfogenética Ósea 2/farmacología , Proteínas Morfogenéticas Óseas , Regeneración Ósea , Colágeno , Ratones , Proteínas Recombinantes/farmacología , Factor de Crecimiento Transformador beta
10.
Radiol Imaging Cancer ; 3(2): e200104, 2021 03.
Artículo en Inglés | MEDLINE | ID: mdl-33817651

RESUMEN

Purpose: To enhance the spatial accuracy of fluorine 18 (18F) misonidazole (MISO) PET imaging of hypoxia by using dynamic contrast-enhanced (DCE) MR images as a basis for modifying PET images and by using electron paramagnetic resonance (EPR) partial oxygen pressure (pO2) as the reference standard. Materials and Methods: Mice (n = 10) with leg-borne MCa4 mammary carcinomas underwent EPR imaging, T2-weighted and DCE MRI, and 18F-MISO PET/CT. Images were registered to the same space for analysis. The thresholds of hypoxia for PET and EPR images were tumor-to-muscle ratios greater than or equal to 2.2 mm Hg and less than or equal to 14 mm Hg, respectively. The Dice similarity coefficient (DSC) and Hausdorff distance (d H ) were used to quantify the three-dimensional overlap of hypoxia between pO2 EPR and 18F-MISO PET images. A training subset (n = 6) was used to calculate optimal DCE MRI weighting coefficients to relate EPR to the PET signal; the group average weights were then applied to all tumors (from six training mice and four test mice). The DSC and d H were calculated before and after DCE MRI-corrected PET images were obtained to quantify the improvement in overlap with EPR pO2 images for measuring tumor hypoxia. Results: The means and standard deviations of the DSC and d H between hypoxic regions in original PET and EPR images were 0.35 mm ± 0.23 and 5.70 mm ± 1.7, respectively, for images of all 10 mice. After implementing a preliminary DCE MRI correction to PET data, the DSC increased to 0.86 mm ± 0.18 and the d H decreased to 2.29 mm ± 0.70, showing significant improvement (P < .001) for images of all 10 mice. Specifically, for images of the four independent test mice, the DSC improved with correction from 0.19 ± 0.28 to 0.80 ± 0.29 (P = .02), and the d H improved from 6.40 mm ± 2.5 to 1.95 mm ± 0.63 (P = .01). Conclusion: Using EPR information as a reference standard, DCE MRI information can be used to correct 18F-MISO PET information to more accurately reflect areas of hypoxia.Keywords: Animal Studies, Molecular Imaging, Molecular Imaging-Cancer, PET/CT, MR-Dynamic Contrast Enhanced, MR-Imaging, PET/MR, Breast, Oncology, Tumor Mircoenvironment, Electron Paramagnetic ResonanceSupplemental material is available for this article.© RSNA, 2021.


Asunto(s)
Misonidazol , Hipoxia Tumoral , Animales , Espectroscopía de Resonancia por Spin del Electrón , Hipoxia/diagnóstico por imagen , Imagen por Resonancia Magnética , Ratones , Oxígeno , Tomografía Computarizada por Tomografía de Emisión de Positrones , Tomografía de Emisión de Positrones
11.
Sci Rep ; 8(1): 607, 2018 01 12.
Artículo en Inglés | MEDLINE | ID: mdl-29330383

RESUMEN

Central nervous system (CNS) demyelination represents the pathological hallmark of multiple sclerosis (MS) and contributes to other neurological conditions. Quantitative and specific imaging of demyelination would thus provide critical clinical insight. Here, we investigated the possibility of targeting axonal potassium channels to image demyelination by positron emission tomography (PET). These channels, which normally reside beneath the myelin sheath, become exposed upon demyelination and are the target of the MS drug, 4-aminopyridine (4-AP). We demonstrate using autoradiography that 4-AP has higher binding in non-myelinated and demyelinated versus well-myelinated CNS regions, and describe a fluorine-containing derivative, 3-F-4-AP, that has similar pharmacological properties and can be labeled with 18F for PET imaging. Additionally, we demonstrate that [18F]3-F-4-AP can be used to detect demyelination in rodents by PET. Further evaluation in Rhesus macaques shows higher binding in non-myelinated versus myelinated areas and excellent properties for brain imaging. Together, these data indicate that [18F]3-F-4-AP may be a valuable PET tracer for detecting CNS demyelination noninvasively.


Asunto(s)
4-Aminopiridina/administración & dosificación , Enfermedades Desmielinizantes/diagnóstico por imagen , Radioisótopos de Flúor/química , Tomografía de Emisión de Positrones/métodos , Canales de Potasio/metabolismo , 4-Aminopiridina/química , 4-Aminopiridina/farmacología , Animales , Enfermedades Desmielinizantes/metabolismo , Femenino , Humanos , Macaca mulatta , Masculino , Ratones , Trazadores Radiactivos , Ratas
12.
Nat Biomed Eng ; 2(7): 508-521, 2018 Jul.
Artículo en Inglés | MEDLINE | ID: mdl-30906646

RESUMEN

Silicon-based materials have been widely used. However, remotely controlled and interconnect-free silicon configurations have been rarely explored, because of limited fundamental understanding of the complex physicochemical processes that occur at interfaces between silicon and biological materials. Here, we describe rational design principles, guided by biology, for establishing intracellular, intercellular and extracellular silicon-based interfaces, where the silicon and the biological targets have matched properties. We focused on light-induced processes at these interfaces, and developed a set of matrices to quantify and differentiate the capacitive, Faradaic and thermal outputs from about 30 different silicon materials in saline. We show that these interfaces are useful for the light-controlled non-genetic modulation of intracellular calcium dynamics, of cytoskeletal structures and transport, of cellular excitability, of neurotransmitter release from brain slices, and of brain activity in vivo.

13.
J Nucl Med ; 57(2): 279-84, 2016 Feb.
Artículo en Inglés | MEDLINE | ID: mdl-26564318

RESUMEN

UNLABELLED: There is strong clinical interest in using neural stem cells (NSCs) as carriers for targeted delivery of therapeutics to glioblastoma. Multimodal dynamic in vivo imaging of NSC behaviors in the brain is necessary for developing such tailored therapies; however, such technology is lacking. Here we report a novel strategy for mesoporous silica nanoparticle (MSN)-facilitated NSC tracking in the brain via SPECT. METHODS: (111)In was conjugated to MSNs, taking advantage of the large surface area of their unique porous feature. A series of nanomaterial characterization assays was performed to assess the modified MSN. Loading efficiency and viability of NSCs with (111)In-MSN complex were optimized. Radiolabeled NSCs were administered to glioma-bearing mice via either intracranial or systemic injection. SPECT imaging and bioluminescence imaging were performed daily up to 48 h after NSC injection. Histology and immunocytochemistry were used to confirm the findings. RESULTS: (111)In-MSN complexes show minimal toxicity to NSCs and robust in vitro and in vivo stability. Phantom studies demonstrate feasibility of this platform for NSC imaging. Of significance, we discovered that decayed (111)In-MSN complexes exhibit strong fluorescent profiles in preloaded NSCs, allowing for ex vivo validation of the in vivo data. In vivo, SPECT visualizes actively migrating NSCs toward glioma xenografts in real time after both intracranial and systemic administrations. This is in agreement with bioluminescence live imaging, confocal microscopy, and histology. CONCLUSION: These advancements warrant further development and integration of this technology with MRI for multimodal noninvasive tracking of therapeutic NSCs toward various brain malignancies.


Asunto(s)
Neoplasias Encefálicas/diagnóstico por imagen , Glioblastoma/diagnóstico por imagen , Células-Madre Neurales/diagnóstico por imagen , Tomografía Computarizada de Emisión de Fotón Único/métodos , Animales , Línea Celular Tumoral , Humanos , Radioisótopos de Indio/efectos adversos , Radioisótopos de Indio/farmacocinética , Marcaje Isotópico , Imagen por Resonancia Magnética , Ratones , Ratones Desnudos , Imagen Multimodal , Nanopartículas , Fantasmas de Imagen , Radiofármacos/efectos adversos , Radiofármacos/farmacocinética , Distribución Tisular
14.
Rev Sci Instrum ; 82(3): 035117, 2011 Mar.
Artículo en Inglés | MEDLINE | ID: mdl-21456798

RESUMEN

In addition to operating the imaging ellipsometric measurements by four-specific temporal phases in the photoelastic modulated ellipsometry, we added the fifth one to solve the initial phase of the photoelastic modulator. This methodology has been developed to conquer the slow imaging processing of charge-coupled device camera for the stroboscopic illumination in the polarization modulated imaging ellipsometry. Without any calibration in its initial phase, we can perform the ellipsometric measurement by the measurements of intensity at five-specific temporal phases. The intensities of a full cycle for a point on SiO(2)∕Si thin film were measured and analyzed for verifying this algorithm. The five stroboscopic illuminations were performed to measure the two-dimensional distribution of the same SiO(2)∕Si thin film.

15.
Opt Lett ; 34(15): 2279-81, 2009 Aug 01.
Artículo en Inglés | MEDLINE | ID: mdl-19649070

RESUMEN

A set of four-temporal phases in photoelastic-modulated polarimetry is proposed to measure the Stokes parameters. In comparison with the conventional polarimetry, which uses a set of four-spatial angles by rotating a quarter-wave plate to obtain the polarimetric parameters, this temporal type polarimetry not only can reduce the time consumption but also can avoid the measurement error from the beam deviation. In addition, based on singular value decomposition, the figure of merit of this temporal phase technique can improve its signal-to-noise ratio by a factor of 2 in comparison with the rotating quarter-wave plate.

16.
Appl Opt ; 45(16): 3733-9, 2006 Jun 01.
Artículo en Inglés | MEDLINE | ID: mdl-16724130

RESUMEN

What we believe to be a novel amplitude sensitive optical heterodyne polarimeter in which a Zeeman laser is associated with balanced detector detection was set up. The aim was to measure the optical activity of a quartz crystal with a Cornu depolarizer at high accuracy. The features of this novel polarimeter, which include the use of a two-frequency laser that ensures the accuracy of the measurement, are discussed. Furthermore, the detection sensitivity of the optical activity of a quartz crystal was measured as 8.5x10(-10). To our knowledge, this is the highest sensitivity obtained for optical activity measurement of a quartz crystal when the error of the measurement is also analyzed.

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