High-energy-density lithium sulfur (Li-S) batteries suffer heavily from the polysulfide shuttle effect, a result of the dissolution and transport of intermediate polysulfides from the cathode, into the electrolyte, and onto the anode, leading to rapid cell degradation. If this primary mechanism of cell failure is to be overcome, the distribution, dynamics, and degree of polysulfide transport must first be understood in depth. In this work, operando optical fluorescence microscope imaging of optically accessible Li-S cells is shown to enable real-time qualitative visualization of the spatial distribution of lithium polysulfides, both within the electrolyte and porous cathode. Quantitative determinations of spatial concentration are also possible at a low enough concentration. The distribution throughout cycling is monitored, including direct observation of polysulfide shuttling to the anode and consequent dendrite formation. This was enabled through the optimization of a selective fluorescent dye, verified to fluoresce proportionally with concentration of polysulfides within Li-S cells. This ability to directly and conveniently track the spatial distribution of soluble polysulfide intermediates in Li-S battery electrolytes, while the cell operates, has the potential to have a widespread impact across the field, for example, by enabling the influence of a variety of polysulfide mitigation strategies to be assessed and optimized, including in this work the LiNO3 additive.
Degradation of cathode materials in lithium-ion batteries results in the presence of transition metal ions in the electrolyte, and these ions are known to play a major role in capacity fade and cell failure. Yet, while it is known that transition metal ions migrate from the metal oxide cathode and deposit on the graphite anode, their specific influence on anode reactions and structures, such as the solid electrolyte interphase (SEI), is still quite poorly understood due to the complexity in studying this interface in operational cells. In this work we combine operando electrochemical atomic force microscopy (EC-AFM), electrochemical quartz crystal microbalance (EQCM), and electrochemical impedance spectroscopy (EIS) measurements to probe the influence of a range of transition metal ions on the morphological, mechanical, chemical, and electrical properties of the SEI. By adding representative concentrations of Ni2+, Mn2+, and Co2+ ions into a commercially relevant battery electrolyte, the impacts of each on the formation and stability of the anode interface layer is revealed; all are shown to pose a threat to battery performance and stability. Mn2+, in particular, is shown to induce a thick, soft, and unstable SEI layer, which is known to cause severe degradation of batteries, while Co2+ and Ni2+ significantly impact interfacial conductivity. When transition metal ions are mixed, SEI degradation is amplified, suggesting a synergistic effect on the cell stability. Hence, by uncovering the roles these cathode degradation products play in operational batteries, we have provided a foundation upon which strategies to mitigate or eliminate these degradation products can be developed.
Cardiac disease progression reflects the dynamic interaction between adversely remodeled neurohumoral control systems and an abnormal cardiac substrate. Vagal nerve stimulation (VNS) is an attractive neuromodulatory option to dampen this dynamic interaction; however, it is limited by off-target effects. Spatially-selective VNS (sVNS) offers a promising solution to induce cardioprotection while mitigating off-target effects by specifically targeting pre-ganglionic parasympathetic efferent cardiac fibers. This approach also has the potential to enhance therapeutic outcomes by eliminating time-consuming titration required for optimal VNS. Recent studies have demonstrated the independent modulation of breathing rate, heart rate, and laryngeal contraction through sVNS. However, the spatial organization of afferent and efferent cardiac-related fibers within the vagus nerve remains unexplored. By using trial-and-error sVNS in vivo in combination with ex vivo micro-computed tomography fascicle tracing, we show the significant spatial separation of cardiac afferent and efferent fibers (179±55° SD microCT, p<0.05 and 200±137° SD, p<0.05 sVNS - degrees of separation across a cross-section of nerve) at the mid-cervical level. We also show that cardiac afferent fibers are located in proximity to pulmonary fibers consistent with recent findings of cardiopulmonary convergent neurons and circuits. We demonstrate the ability of sVNS to selectively elicit desired scalable heart rate decrease without stimulating afferent-related reflexes. By elucidating the spatial organization of cardiac-related fibers within the vagus nerve, our findings pave the way for more targeted neuromodulation, thereby reducing off-target effects and eliminating the need for titration. This, in turn, will enhance the precision and efficacy of VNS therapy in treating cardiac pathology, allowing for improved therapeutic efficacy.
Aqueous zinc-ion batteries (AZIBs) have experienced a rapid surge in popularity, as evident from the extensive research with over 30 000 articles published in the past 5 years. Previous studies on AZIBs have showcased impressive long-cycle stability at high current densities, achieving thousands or tens of thousands of cycles. However, the practical stability of AZIBs at low current densities (<1C) is restricted to merely 50-100 cycles due to intensified cathode dissolution. This genuine limitation poses a considerable challenge to their transition from the laboratory to the industry. In this study, leveraging density functional theory (DFT) calculations, an artificial interphase that achieves both hydrophobicity and restriction of the outward penetration of dissolved vanadium cations, thereby shifting the reaction equilibrium and suppressing the vanadium dissolution following Le Chatelier's principle, is described. The approach has resulted in one of the best cycling stabilities to date, with no noticeable capacity fading after more than 200 cycles (≈720 h) at 200 mA g-1 (0.47C). These findings represent a significant advance in the design of ultrastable cathodes for aqueous batteries and accelerate the industrialization of aqueous zinc-ion batteries.
Solid-state batteries (SSBs) are promising alternatives to the incumbent lithium-ion technology; however, they face a unique set of challenges that must be overcome to enable their widespread adoption. These challenges include solid-solid interfaces that are highly resistive, with slow kinetics, and a tendency to form interfacial voids causing diminished cycle life due to fracture and delamination. This modeling study probes the evolution of stresses at the solid electrolyte (SE) solid-solid interfaces, by linking the chemical and mechanical material properties to their electrochemical response, which can be used as a guide to optimize the design and manufacture of silicon (Si) based SSBs. A thin-film solid-state battery consisting of an amorphous Si negative electrode (NE) is studied, which exerts compressive stress on the SE, caused by the lithiation-induced expansion of the Si. By using a 2D chemo-mechanical model, continuum scale simulations are used to probe the effect of applied pressure and C-rate on the stress-strain response of the cell and their impacts on the overall cell capacity. A complex concentration gradient is generated within the Si electrode due to slow diffusion of Li through Si, which leads to localized strains. To reduce the interfacial stress and strain at 100% SOC, operation at moderate C-rates with low applied pressure is desirable. Alternatively, the mechanical properties of the SE could be tailored to optimize cell performance. To reduce Si stress, a SE with a moderate Young's modulus similar to that of lithium phosphorous oxynitride (â¼77 GPa) with a low yield strength comparable to sulfides (â¼0.67 GPa) should be selected. However, if the reduction in SE stress is of greater concern, then a compliant Young's modulus (â¼29 GPa) with a moderate yield strength (1-3 GPa) should be targeted. This study emphasizes the need for SE material selection and the consideration of other cell components in order to optimize the performance of thin film solid-state batteries.
For zinc-ion batteries (ZIBs), the non-uniform Zn plating/stripping results in a high polarization and low Coulombic efficiency (CE), hindering the large-scale application of ZIBs. Here, inspired by biomass seaweed plants, an anionic polyelectrolyte alginate acid (SA) was used to initiate the in situ formation of the high-performance solid electrolyte interphase (SEI) layer on the Zn anode. Attribute to the anionic groups of -COO- , the affinity of Zn2+ ions to alginate acid induces a well-aligned accelerating channel for uniform plating. This SEI regulates the desolvation structure of Zn2+ and facilitates the formation of compact Zn (002) crystal planes. Even under high depth of discharge conditions (DOD), the SA-coated Zn anode still maintains a stable Zn stripping/plating behavior with a low potential difference (0.114â V). According to the classical nucleation theory, the nucleation energy for SA-coated Zn is 97 % less than that of bare Zn, resulting in a faster nucleation rate. The Zn||Cu cell assembled with the SA-coated electrode exhibits an outstanding average CE of 99.8 % over 1,400 cycles. The design is successfully demonstrated in pouch cells, where the SA-coated Zn exhibits capacity retention of 96.9 % compared to 59.1 % for bare Zn anode, even under the high cathode mass loading (>10â mg/cm2 ).
The phase separation dynamics in graphitic anodes significantly affects lithium plating propensity, which is the major degradation mechanism that impairs the safety and fast charge capabilities of automotive lithium-ion batteries. In this study, we present comprehensive investigation employing operando high-resolution optical microscopy combined with non-equilibrium thermodynamics implemented in a multi-dimensional (1D+1D to 3D) phase-field modeling framework to reveal the rate-dependent spatial dynamics of phase separation and plating in graphite electrodes. Here we visualize and provide mechanistic understanding of the multistage phase separation, plating, inter/intra-particle lithium exchange and plated lithium back-intercalation phenomena. A strong dependence of intra-particle lithiation heterogeneity on the particle size, shape, orientation, surface condition and C-rate at the particle level is observed, which leads to early onset of plating spatially resolved by a 3D image-based phase-field model. Moreover, we highlight the distinct relaxation processes at different state-of-charges (SOCs), wherein thermodynamically unstable graphite particles undergo a drastic intra-particle lithium redistribution and inter-particle lithium exchange at intermediate SOCs, whereas the electrode equilibrates much slower at low and high SOCs. These physics-based insights into the distinct SOC-dependent relaxation efficiency provide new perspective towards developing advanced fast charge protocols to suppress plating and shorten the constant voltage regime.
X-ray computed tomography was applied in imaging 3D-printed gyroids used for bioseparation in order to visualize and characterize structures from the entire geometry down to individual nanopores. Methacrylate prints were fabricated with feature sizes of 500 µm, 300 µm, and 200 µm, with the material phase exhibiting a porous substructure in all cases. Two X-ray scanners achieved pixel sizes from 5 µm to 16 nm to produce digital representations of samples across multiple length scales as the basis for geometric analysis and flow simulation. At the gyroid scale, imaged samples were visually compared to the original computed-aided designs to analyze printing fidelity across all feature sizes. An individual 500 µm feature, part of the overall gyroid structure, was compared and overlaid between design and imaged volumes, identifying individual printed layers. Internal subvolumes of all feature sizes were segmented into material and void phases for permeable flow analysis. Small pieces of 3D-printed material were optimized for nanotomographic imaging at a pixel size of 63 nm, with all three gyroid samples exhibiting similar geometric characteristics when measured. An average porosity of 45% was obtained that was within the expected design range, and a tortuosity factor of 2.52 was measured. Applying a voidage network map enabled the size, location, and connectivity of pores to be identified, obtaining an average pore size of 793 nm. Using Avizo XLAB at a bulk diffusivity of 7.00 × 10-11 m2s-1 resulted in a simulated material diffusivity of 2.17 × 10-11 m2s-1 ± 0.16 × 10-11 m2s-1.
It is widely accepted that the commercial application of lithium-sulfur batteries is inhibited by their short cycle life, which is primarily caused by a combination of Li dendrite formation and active material loss due to polysulfide shuttling. Unfortunately, while numerous approaches to overcome these problems have been reported, most are unscalable and hence further hinder Li-S battery commercialization. Most approaches suggested also only tackle one of the primary mechanisms of cell degradation and failure. Here, we demonstrate that the use of a simple protein, fibroin, as an electrolyte additive can both prevent Li dendrite formation and minimize active material loss to enable high capacity and long cycle life (up to 500 cycles) in Li-S batteries, without inhibiting the rate performance of the cell. Through a combination of experiments and molecular dynamics (MD) simulations, it is demonstrated that the fibroin plays a dual role, both binding to polysulfides to hinder their transport from the cathode and passivating the Li anode to minimize dendrite nucleation and growth. Most importantly, as fibroin is inexpensive and can be simply introduced to the cell via the electrolyte, this work offers a route toward practical industrial applications of a viable Li-S battery system.
Introduction: Despite detailed characterization of fascicular organization of somatic nerves, the functional anatomy of fascicles evident in human and large mammal cervical vagus nerve is unknown. The vagus nerve is a prime target for intervention in the field of electroceuticals due to its extensive distribution to the heart, larynx, lungs, and abdominal viscera. However, current practice of the approved vagus nerve stimulation (VNS) technique is to stimulate the entire nerve. This produces indiscriminate stimulation of non-targeted effectors and undesired side effects. Selective neuromodulation is now a possibility with a spatially-selective vagal nerve cuff. However, this requires the knowledge of the fascicular organization at the level of cuff placement to inform selectivity of only the desired target organ or function. Methods and results: We imaged function over milliseconds with fast neural electrical impedance tomography and selective stimulation, and found consistent spatially separated regions within the nerve correlating with the three fascicular groups of interest, suggesting organotopy. This was independently verified with structural imaging by tracing anatomical connections from the end organ with microCT and the development of an anatomical map of the vagus nerve. This confirmed organotopic organization. Discussion: Here we show, for the first time, localized fascicles in the porcine cervical vagus nerve which map to cardiac, pulmonary and recurrent laryngeal function (N = 4). These findings pave the way for improved outcomes in VNS as unwanted side effects could be reduced by targeted selective stimulation of identified organ-specific fiber-containing fascicles and the extension of this technique clinically beyond the currently approved disorders to treat heart failure, chronic inflammatory disorders, and more.
Lithium-ion battery (LIB) performance can be significantly affected by the nature of the complex electrode microstructure. The carbon binder domain (CBD) present in almost all LIB electrodes is used to enhance mechanical stability and facilitate electronic conduction, and understanding the CBD phase microstructure and how it affects the complex coupled transport processes is crucial to LIB performance optimization. In this work, the influence of microporosity in the CBD phase has been studied in detail for the first time, enabling insight into the relationships between the CBD microstructure and the battery performance. To investigate the effect of the CBD pore size distributions, a random field method is used to generate in silico a multiple-phase electrode structure, including bimodal pore size distributions seen in practice and microporous CBD with a tunable pore size and variable transport properties. The distribution of macropores and the microporous CBD phase substantially affected simulated battery performance, where battery specific capacity improved as the microporosity of the CBD phase increased.
Reduced graphene-oxide (RGO)-based electrodes in supercapacitors deliver high energy/power capacities compared to typical nanoporous carbon materials. However, extensive critical analysis of literature reveals enormous discrepancies (up to 250 F g-1 ) in the reported capacitance (variation of 100-350 F g-1 ) of RGO materials synthesized under seemingly similar methods, inhibiting an understanding of capacitance variation. Here, the key factors that control the capacitance performance of RGO electrodes are demonstrated by analyzing and optimizing various types of commonly applied electrode fabrication methods. Beyond usual data acquisition parameters and oxidation/reduction properties of RGO, a substantial difference of more than 100% in capacitance values (with change from 190 ± 20 to 340 ± 10 F g-1 ) is found depending on the electrode preparation method. For this demonstration, ≈40 RGO-based electrodes are fabricated from numerous distinctly different RGO materials via typically applied methods of solution (aqueous and organic) casting and compressed powders. The influence of data acquisition conditions and capacitance estimation practices are also discussed. Furthermore, by optimizing electrode processing method, a direct surface area governed capacitance relationship for RGO structures is revealed.
The growing interest in the development of next-generation net zero energy systems has led to the expansion of molybdenum disulfide (MoS2) research in this area. This activity has resulted in a wide range of manufacturing/synthesis methods, controllable morphologies, diverse carbonaceous composite structures, a multitude of applicable characterization techniques, and multiple energy applications for MoS2. To assess the literature trends, 37,347 MoS2 research articles from Web of Science were text scanned to classify articles according to energy application research and characterization techniques employed. Within the review, characterization techniques are grouped under the following categories: morphology, crystal structure, composition, and chemistry. The most common characterization techniques identified through text scanning are recommended as the base fingerprint for MoS2 samples. These include: scanning electron microscopy (SEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and Raman spectroscopy. Similarly, XPS and Raman spectroscopy are suggested for 2H or 1T MoS2 phase confirmation. We provide guidance on the collection and presentation of MoS2 characterization data. This includes how to effectively combine multiple characterization techniques, considering the sample area probed by each technique and their statistical significance, and the benefit of using reference samples. For ease of access for future experimental comparison, key numeric MoS2 characterization values are tabulated and major literature discrepancies or currently debated characterization disputes are highlighted.
The zinc-ion battery is one of the promising candidates for next-generation energy storage devices beyond lithium technology due to the earth's abundance of Zn materials and their high volumetric energy density (5855 mA h cm-3). To date, the formation of Zn dendrites during charge-discharge cycling still hinders the practical application of zinc-ion batteries. It is, therefore, crucial to understand the formation mechanism of the zinc dendritic structure before effectively suppressing its growth. Here, the application of operando digital optical microscopy and in situ lab-based X-ray computed tomography (X-ray CT) is demonstrated to probe and quantify the morphologies of zinc electrodeposition/dissolution under multiple galvanostatic plating/stripping conditions in symmetric Zn||Zn cells. With the combined microscopy approaches, we directly observed the dynamic nucleation and subsequent growth of Zn deposits, the heterogeneous transportation of charged clusters/particles, and the evolution of 'dead' Zn particles via partial dissolution. Zn electrodeposition at the early stage is mainly attributed to activation, while the subsequent dendrite growth is driven by diffusion. The high current not only facilitates the formation of sharp dendrites with a larger mean curvature at their tips but also leads to dendritic tip splitting and the creation of a hyper-branching morphology. This approach offers a direct opportunity to characterize dendrite formation in batteries with a metal anode in the laboratory.
The electrochemical synthesis of hydrogen peroxide (H2 O2 ) via a two-electron (2 e- ) oxygen reduction reaction (ORR) process provides a promising alternative to replace the energy-intensive anthraquinone process. Herein, we develop a facile template-protected strategy to synthesize a highly active quinone-rich porous carbon catalyst for H2 O2 electrochemical production. The optimized PCC900 material exhibits remarkable activity and selectivity, of which the onset potential reaches 0.83â V vs. reversible hydrogen electrode in 0.1â M KOH and the H2 O2 selectivity is over 95 % in a wide potential range. Comprehensive synchrotron-based near-edge X-ray absorption fine structure (NEXAFS) spectroscopy combined with electrocatalytic characterizations reveals the positive correlation between quinone content and 2 e- ORR performance. The effectiveness of chair-form quinone groups as the most efficient active sites is highlighted by the molecule-mimic strategy and theoretical analysis.
Chronic kidney disease (CKD) increases the risk of cardiovascular disease, including vascular calcification, leading to higher mortality. The release of calcifying extracellular vesicles (EVs) by vascular smooth muscle cells (VSMCs) promotes ectopic mineralization of vessel walls. Caveolin-1 (CAV1), a structural protein in the plasma membrane, plays a major role in calcifying EV biogenesis in VSMCs. Epidermal growth factor receptor (EGFR) colocalizes with and influences the intracellular trafficking of CAV1. Using a diet-induced mouse model of CKD followed by a high-phosphate diet to promote vascular calcification, we assessed the potential of EGFR inhibition to prevent vascular calcification. Furthermore, we computationally analyzed 7,651 individuals in the Multi-Ethnic Study of Atherosclerosis (MESA) and Framingham cohorts to assess potential correlations between coronary artery calcium and single-nucleotide polymorphisms (SNPs) associated with elevated serum levels of EGFR. Mice with CKD developed widespread vascular calcification, associated with increased serum levels of EGFR. In both the CKD mice and human VSMC culture, EGFR inhibition significantly reduced vascular calcification by mitigating the release of CAV1-positive calcifying EVs. EGFR inhibition also increased bone mineral density in CKD mice. Individuals in the MESA and Framingham cohorts with SNPs associated with increased serum EGFR exhibit elevated coronary artery calcium. Given that EGFR inhibitors exhibit clinical safety and efficacy in other pathologies, the current data suggest that EGFR may represent an ideal target to prevent pathological vascular calcification in CKD.NEW & NOTEWORTHY Here, we investigate the potential of epidermal growth factor receptor (EGFR) inhibition to prevent vascular calcification, a leading indicator of and contributor to cardiovascular morbidity and mortality. EGFR interacts and affects the trafficking of the plasma membrane scaffolding protein caveolin-1. Previous studies reported a key role for caveolin-1 in the development of specialized extracellular vesicles that mediate vascular calcification; however, no role of EGFR has been reported. We demonstrated that EGFR inhibition modulates caveolin-1 trafficking and hinders calcifying extracellular vesicle formation, which prevents vascular calcification. Given that EGFR inhibitors are clinically approved for other indications, this may represent a novel therapeutic strategy for vascular calcification.
Atherosclerosis , Extracellular Vesicles , Renal Insufficiency, Chronic , Vascular Calcification , Humans , Mice , Animals , Caveolin 1/metabolism , Calcium/metabolism , Muscle, Smooth, Vascular/metabolism , Vascular Calcification/genetics , Vascular Calcification/prevention & control , ErbB Receptors/genetics , ErbB Receptors/metabolism , Extracellular Vesicles/metabolism , Membrane Proteins/metabolism , Atherosclerosis/metabolism , Myocytes, Smooth Muscle/metabolism
Proton exchange membrane fuel cells, consuming hydrogen and oxygen to generate clean electricity and water, suffer acute liquid water challenges. Accurate liquid water modelling is inherently challenging due to the multi-phase, multi-component, reactive dynamics within multi-scale, multi-layered porous media. In addition, currently inadequate imaging and modelling capabilities are limiting simulations to small areas (<1 mm2) or simplified architectures. Herein, an advancement in water modelling is achieved using X-ray micro-computed tomography, deep learned super-resolution, multi-label segmentation, and direct multi-phase simulation. The resulting image is the most resolved domain (16 mm2 with 700 nm voxel resolution) and the largest direct multi-phase flow simulation of a fuel cell. This generalisable approach unveils multi-scale water clustering and transport mechanisms over large dry and flooded areas in the gas diffusion layer and flow fields, paving the way for next generation proton exchange membrane fuel cells with optimised structures and wettabilities.
The investigation of lithium-ion battery failures is a major challenge for personnel and equipment due to the associated hazards (thermal reaction, toxic gases and explosions). To perform such experiments safely, a battery abuse-test chamber has been developed and installed at the microtomography beamline ID19 of the European Synchrotron Radiation Facility (ESRF). The chamber provides the capability to robustly perform inâ situ abuse tests through the heat-resistant and gas-tight design for flexible battery geometries and configurations, including single-cell and multi-cell assemblies. High-speed X-ray imaging can be complemented by supplementary equipment, including additional probes (voltage, pressure and temperature) and thermal imaging. Together with the test chamber, a synchronization graphical user interface was developed, which allows an initial interpretation by time-synchronous visualization of the acquired data. Enabled by this setup, new meaningful insights can be gained into the internal processes of a thermal runaway of current and future energy-storage devices such as lithium-ion cells.
X-ray computed tomography (X-ray CT) is a non-destructive characterization technique that in recent years has been adopted to study the microstructure of battery electrodes. However, the often manual and laborious data analysis process hinders the extraction of useful metrics that can ultimately inform the mechanisms behind cycle life degradation. This work presents a novel approach that combines two convolutional neural networks to first locate and segment each particle in a nano-CT LiNiMnCoO2 (NMC) electrode dataset, and successively classifies each particle according to the presence of flaws or cracks within its internal structure. Metrics extracted from the computer vision segmentation are validated with respect to traditional threshold-based segmentation, confirming that flawed particles are correctly identified as single entities. Successively, slices from each particle are analyzed by a pre-trained classifier to detect the presence of flaws or cracks. The models are used to quantify microstructural evolution in uncycled and cycled NMC811 electrodes, as well as the number of flawed particles in a NMC622 electrode. As a proof-of-concept, a 3-phase segmentation is also presented, whereby each individual flaw is segmented as a separate pixel label. It is anticipated that this analysis pipeline will be widely used in the field of battery research and beyond.
Image Processing, Computer-Assisted , Neural Networks, Computer , Image Processing, Computer-Assisted/methods , Tomography, X-Ray Computed/methods , Computers , Electrodes
Atherosclerotic plaque calcification directly contributes to the leading cause of morbidity and mortality by affecting plaque vulnerability and rupture risk. Small microcalcifications can increase plaque stress and promote rupture, whereas large calcifications can stabilize plaques. Drugs that target bone mineralization may lead to unintended consequences on ectopic plaque calcification and cardiovascular outcomes. Bisphosphonates, common anti-osteoporotic agents, have elicited unexpected cardiovascular events in clinical trials. Here, we investigated the role of bisphosphonate treatment and timing on the disruption or promotion of vascular calcification and bone minerals in a mouse model of atherosclerosis. We started the bisphosphonate treatment either before plaque formation, at early plaque formation times associated with the onset of calcification, or at late stages of plaque development. Our data indicated that long-term bisphosphonate treatment (beginning prior to plaque development) leads to higher levels of plaque calcification, with a narrower mineral size distribution. When given later in plaque development, we measured a wider distribution of mineral size. These morphological alterations might be associated with a higher risk of plaque rupture by creating stress foci. Yet, bone mineral density positively correlated with the duration of the bisphosphonate treatment.
