Modulation of Phase Shift between Wnt and Notch Signaling Oscillations Controls Mesoderm Segmentation.

How signaling dynamics encode information is a central question in biology. During vertebrate development, dynamic Notch signaling oscillations control segmentation of the presomitic mesoderm (PSM). In mouse embryos, this molecular clock comprises signaling oscillations of several pathways, i.e., Notch, Wnt, and FGF signaling. Here, we directly address the role of the relative timing between Wnt and Notch signaling oscillations during PSM patterning. To this end, we developed a new experimental strategy using microfluidics-based entrainment that enables specific control of the rhythm of segmentation clock oscillations. Using this approach, we find that Wnt and Notch signaling are coupled at the level of their oscillation dynamics. Furthermore, we provide functional evidence that the oscillation phase shift between Wnt and Notch signaling is critical for PSM segmentation. Our work hence reveals that dynamic signaling, i.e., the relative timing between oscillatory signals, encodes essential information during multicellular development.

Quantum interference in superposed lattices.

Charge transport in solids at low temperature reveals a material's mesoscopic properties and structure. Under a magnetic field, Shubnikov-de Haas (SdH) oscillations inform complex quantum transport phenomena that are not limited by the ground state characteristics and have facilitated extensive explorations of quantum and topological interest in two- and three-dimensional materials. Here, in elemental metal Cr with two incommensurately superposed lattices of ions and a spin-density-wave ground state, we reveal that the phases of several low-frequency SdH oscillations in [Formula: see text] and [Formula: see text] are no longer identical but opposite. These relationships contrast with the SdH oscillations from normal cyclotron orbits that maintain identical phases between [Formula: see text] and [Formula: see text] . We trace the origin of the low-frequency SdH oscillations to quantum interference effects arising from the incommensurate orbits of Cr's superposed reciprocal lattices and explain the observed [Formula: see text]-phase shift by the reconnection of anisotropic joint open and closed orbits.

Rise of Ruppia in Chesapeake Bay: Climate change-driven turnover of foundation species creates new threats and management opportunities.

Global change has converted many structurally complex and ecologically and economically valuable coastlines to bare substrate. In the structural habitats that remain, climate-tolerant and opportunistic species are increasing in response to environmental extremes and variability. The shifting of dominant foundation species identity with climate change poses a unique conservation challenge because species vary in their responses to environmental stressors and to management. Here, we combine 35 y of watershed modeling and biogeochemical water quality data with species comprehensive aerial surveys to describe causes and consequences of turnover in seagrass foundation species across 26,000 ha of habitat in the Chesapeake Bay. Repeated marine heatwaves have caused 54% retraction of the formerly dominant eelgrass (Zostera marina) since 1991, allowing 171% expansion of the temperature-tolerant widgeongrass (Ruppia maritima) that has likewise benefited from large-scale nutrient reductions. However, this phase shift in dominant seagrass identity now presents two significant shifts for management: Widgeongrass meadows are not only responsible for rapid, extensive recoveries but also for the largest crashes over the last four decades; and, while adapted to high temperatures, are much more susceptible than eelgrass to nutrient pulses driven by springtime runoff. Thus, by selecting for rapid post-disturbance recolonization but low resistance to punctuated freshwater flow disturbance, climate change could threaten the Chesapeake Bay seagrass' ability to provide consistent fishery habitat and sustain functioning over time. We demonstrate that understanding the dynamics of the next generation of foundation species is a critical management priority, because shifts from relatively stable habitat to high interannual variability can have far-reaching consequences across marine and terrestrial ecosystems.

Unveiling Invariant Optical Properties of Dielectric Meta-Atoms.

The phase-shift, transmittance, and polarization properties of meta-atoms are investigated, motivated by their use as building blocks of metasurfaces used in metalenses, holograms, and beam shaping. We studied dielectric nanorod meta-atoms of several geometries, which included cylinders, triangles, squares, hexagons, octagons, and truncated cones. By analyzing light propagation through these meta-atoms for three different wavelengths (632.8, 545, and 50 nm), we show that the phase-shift introduced is independent of their cross-section shape, contrary to the expected behavior. Additionally, we show that the polarization response is independent of the shape and that the transmittance is partially shape-independent. We identify a novel dependence of phase-shift on the effective cross-sectional area of meta-atoms. These meta-atom optical properties are independent of its shape if its geometry has a C3 or larger rotational symmetry. This optical invariance has significant implications for the topological optimization of flat optics.

Understanding change in benthic marine systems.

BACKGROUND: The unprecedented influence of human activities on natural ecosystems in the 21st century has resulted in increasingly frequent large-scale changes in ecological communities. This has heightened interest in understanding such changes and effective means to manage them. Accurate interpretation of state changes is challenging because of difficulties translating theory to empirical study, and most theory emphasizes systems near equilibrium, which may not be relevant in rapidly changing environments. SCOPE: We review concepts of long-transient stages and phase shifts between stable community states, both smooth, continuous and discontinuous shifts, and the relationships among them. Three principal challenges emerge when applying these concepts. The first is how to interpret observed change in communities - distinguishing multiple stable states from long transients, or reversible shifts in the phase portrait of single attractor systems. The second is how to quantify the magnitudes of three sources of variability that cause switches between community states: (1) 'noise' in species' abundances, (2) 'wiggle' in system parameters and (3) trends in parameters that affect the topography of the basin of attraction. The third challenge is how variability of the system shapes evidence used to interpret community changes. We outline a novel approach using critical length scales to potentially address these challenges. These concepts are highlighted by a review of recent examples involving macroalgae as key players in marine benthic ecosystems. CONCLUSIONS: Real-world examples show three or more stable configurations of ecological communities may exist for a given set of parameters, and transient stages may persist for long periods necessitating their respective consideration. The characteristic length scale (CLS) is a useful metric that uniquely identifies a community 'basin of attraction', enabling phase shifts to be distinguished from long transients. Variabilities of CLSs and time series data may likewise provide proactive management measures to mitigate phase shifts and loss of ecosystem services. Continued challenges remain in distinguishing continuous from discontinuous phase shifts because their respective dynamics lack unique signatures.

Melatonin in energy control: Circadian time-giver and homeostatic monitor.

Melatonin is a neurohormone synthesized from dietary tryptophan in various organs, including the pineal gland and the retina. In the pineal gland, melatonin is produced at night under the control of the master clock located in the suprachiasmatic nuclei of the hypothalamus. Under physiological conditions, the pineal gland seems to constitute the unique source of circulating melatonin. Melatonin is involved in cellular metabolism in different ways. First, the circadian rhythm of melatonin helps the maintenance of proper internal timing, the disruption of which has deleterious effects on metabolic health. Second, melatonin modulates lipid metabolism, notably through diminished lipogenesis, and it has an antidiabetic effect, at least in several animal models. Third, pharmacological doses of melatonin have antioxidative, free radical-scavenging, and anti-inflammatory properties in various in vitro cellular models. As a result, melatonin can be considered both a circadian time-giver and a homeostatic monitor of cellular metabolism, via multiple mechanisms of action that are not all fully characterized. Aging, circadian disruption, and artificial light at night are conditions combining increased metabolic risks with diminished circulating levels of melatonin. Accordingly, melatonin supplementation could be of potential therapeutic value in the treatment or prevention of metabolic disorders. More clinical trials in controlled conditions are needed, notably taking greater account of circadian rhythmicity.

Mouse Models in Circadian Rhythm and Melatonin Research.

This contribution reviews the role of inbred and transgenic mouse strains for deciphering the mammalian melatoninergic and circadian system. It focusses on the pineal organ as melatonin factory and two major targets of the melatoninergic system, the suprachiasmatic nuclei (SCN) and the hypophysial pars tuberalis (PT). Mammalian pinealocytes sharing molecular characteristics with true pineal and retinal photoreceptors synthesize and secrete melatonin into the blood and cerebrospinal fluid night by night. Notably, neuron-like connections exist between the deep pinealocytes and the habenular/pretectal region suggesting direct pineal-brain communication. Control of melatonin biosynthesis in rodents involves transcriptional regulation including phosphorylation of CREB and upregulation of mPer1. In the SCN, melatonin acts upon MT1 and MT2 receptors. Melatonin is not necessary to maintain the rhythm of the SCN molecular clockwork, but it has distinct effects on the synchronization of the circadian rhythm by light, facilitates re-entrainment of the circadian system to phase advances in the level of the SCN molecular clockwork by acting upon MT2 receptors and plays a stabilizing role in the circadian system as evidenced from locomotor activity recordings. While the effects in the SCN are subtle, melatonin is essential for PT functions. Via the MT1 receptor it drives the PT-intrinsic molecular clockwork and the retrograde and anterograde output pathways controlling seasonal rhythmicity. Although inbred and transgenic mice do not show seasonal reproduction, the pathways from the PT are fully intact if the animals are melatonin proficient. Thus, only melatonin-proficient strains are suited to investigate the circadian and melatoninergic systems.

Viral predation pressure on coral reefs.

BACKGROUND: Predation pressure and herbivory exert cascading effects on coral reef health and stability. However, the extent of these cascading effects can vary considerably across space and time. This variability is likely a result of the complex interactions between coral reefs' biotic and abiotic dimensions. A major biological component that has been poorly integrated into the reefs' trophic studies is the microbial community, despite its role in coral death and bleaching susceptibility. Viruses that infect bacteria can control microbial densities and may positively affect coral health by controlling microbialization. We hypothesize that viral predation of bacteria has analogous effects to the top-down pressure of macroorganisms on the trophic structure and reef health. RESULTS: Here, we investigated the relationships between live coral cover and viruses, bacteria, benthic algae, fish biomass, and water chemistry in 110 reefs spanning inhabited and uninhabited islands and atolls across the Pacific Ocean. Statistical learning showed that the abundance of turf algae, viruses, and bacteria, in that order, were the variables best predicting the variance in coral cover. While fish biomass was not a strong predictor of coral cover, the relationship between fish and corals became apparent when analyzed in the context of viral predation: high coral cover (> 50%) occurred on reefs with a combination of high predator fish biomass (sum of sharks and piscivores > 200 g m-2) and high virus-to-bacteria ratios (> 10), an indicator of viral predation pressure. However, these relationships were non-linear, with reefs at the higher and lower ends of the coral cover continuum displaying a narrow combination of abiotic and biotic variables, while reefs at intermediate coral cover showed a wider range of parameter combinations. CONCLUSIONS: The results presented here support the hypothesis that viral predation of bacteria is associated with high coral cover and, thus, coral health and stability. We propose that combined predation pressures from fishes and viruses control energy fluxes, inhibiting the detrimental accumulation of ecosystem energy in the microbial food web.

Ultrasonic Imaging of Deeper Bone Defect Using Virtual Source Synthetic Aperture with Phased Shift Migration: A Phantom Study.

Ultrasound imaging for bone is a difficult task in the field of medical ultrasound. Compared with other phase array techniques, the synthetic aperture (SA) has a better lateral resolution but a limited imaging depth due to the limited ultrasonic energy emitted by the single emitter in each transmission. In contrast, the virtual source (VS) synthetic aperture allows a simultaneous multi-element emission and could provide a higher ultrasonic incident energy in each transmission. Therefore, the VS might achieve a high imaging quality at a deeper depth for bone imaging than the traditional SA. In this study, we proposed the virtual source phase shift migration (VS-PSM) method to achieve ultrasonic imaging of the deeper bone defect featured in the multilayer structure. The proposed VS-PSM method was validated using standard soft tissue phantom and printed bone phantom with artificial defects. The image quality was evaluated in terms of contrast-to-noise ratios (CNR) and amplitudes of scatters and defects at different imaging depths. The results showed that the VS-PSM method could achieve a high imaging quality of the soft tissues with a significant improvement in the scattering amplitude and without a significant sacrifice of the lateral and axial resolution. The PSM was superior to the DAS in suppressing the background noise in the images. Compared with the traditional SA-PSM, the VS-PSM method could image deeper bone defects at different ultrasonic frequencies, with an average improvement of 50% in CNR. In conclusion, this study demonstrated that the proposed VS-PSM method could image deeper bone defects and might help the diagnosis of bone disease using ultrasonic imaging.

Cluster-Based Strategy for Maximizing the Sum-Rate of a Distributed Reconfigurable Intelligent Surface (RIS)-Assisted Coordinated Multi-Point Non-Orthogonal Multiple-Access (CoMP-NOMA) System.

This article proposes a distributed intelligent Coordinated Multi-Point Non-Orthogonal Multiple-Access (CoMP-NOMA) collaborative transmission model with the assistance of reconfigurable intelligent surfaces (RISs) to address the issues of poor communication quality, low fairness, and high system power consumption for edge users in multi-cellular networks. By analyzing the interaction mechanisms and influencing factors among RIS signal enhancement, NOMA user scheduling, and multi-point collaborative transmission, the model establishes RIS-enhanced edge user grouping and coordinates NOMA user clusters based on this. In the multi-cell RIS-assisted JT-CoMP NOMA downlink transmission, joint optimization of the power allocation (PA), user clustering (UC), and RIS phase-shift matrix design (PS) poses a challenging Mixed-Integer Non-Linear Programming (MINLP) problem. The original problem is decomposed by optimizing the formulas into joint sub-problems of PA, UC, and PA and PS, and solved using an alternating optimization approach. Simulation results demonstrate that the proposed scheme effectively reduces the system's power consumption while significantly improving the system's throughput and rates.

Grating (Moiré) Microinterferometric Displacement/Strain Sensor with Polarization Phase Shift.

Grating (moiré) interferometry is one of the well-known methods for full-field in-plane displacement and strain measurement. There are many design solutions for grating interferometers, including systems with a microinterferometric waveguide head. This article proposes a modification to the conventional waveguide interferometer head, enabling the implementation of a polarization fringe phase shift for automatic fringe pattern analysis. This article presents both the theoretical considerations associated with the proposed solution and its experimental verification, along with the concept of in-plane displacement/strain sensing using the described head.

Exploring Safety-Stability Tradeoffs in Cooperative CAV Platoon Controls with Bidirectional Impacts.

Advanced sensing technologies and communication capabilities of Connected and Autonomous Vehicles (CAVs) empower them to capture the dynamics of surrounding vehicles, including speeds and positions of those behind, enabling judicious responsive maneuvers. The acquired dynamics information of vehicles spurred the development of various cooperative platoon controls, particularly designed to enhance platoon stability with reduced spacing for reliable roadway capacity increase. These controls leverage abundant information transmitted through various communication topologies. Despite these advancements, the impact of different vehicle dynamics information on platoon safety remains underexplored, as current research predominantly focuses on stability analysis. This knowledge gap highlights the critical need for further investigation into how diverse vehicle dynamics information influences platoon safety. To address this gap, this research introduces a novel framework based on the concept of phase shift, aiming to scrutinize the tradeoffs between the safety and stability of CAV platoons formed upon bidirectional information flow topology. Our investigation focuses on platoon controls built upon bidirectional information flow topologies using diverse dynamics information of vehicles. Our research findings emphasize that the integration of various types of information into CAV platoon controls does not universally yield benefits. Specifically, incorporating spacing information can enhance both platoon safety and string stability. In contrast, velocity difference information can improve either safety or string stability, but not both simultaneously. These findings offer valuable insights into the formulation of CAV platoon control principles built upon diverse communication topologies. This research contributes a nuanced understanding of the intricate interplay between safety and stability in CAV platoons, emphasizing the importance of information dynamics in shaping effective control strategies.

A Performance Comparison of 3D Survey Instruments for Their Application in the Cultural Heritage Field.

Thanks to the recent development of innovative instruments and software with high accuracy and resolution, 3D modelling provides useful insights in several sectors (from industrial metrology to cultural heritage). Moreover, the 3D reconstruction of objects of artistic interest is becoming mandatory, not only because of the risks to which works of art are increasingly exposed (e.g., wars and climatic disasters) but also because of the leading role that the virtual fruition of art is taking. In this work, we compared the performance of four 3D instruments based on different working principles and techniques (laser micro-profilometry, structured-light topography and the phase-shifting method) by measuring four samples of different sizes, dimensions and surface characteristics. We aimed to assess the capabilities and limitations of these instruments to verify their accuracy and the technical specifications given in the suppliers' data sheets. To this end, we calculated the point densities and extracted several profiles from the models to evaluate both their lateral (XY) and axial (Z) resolution. A comparison between the nominal resolution values and those calculated on samples representative of cultural artefacts was used to predict the performance of the instruments in real case studies. Overall, the purpose of this comparison is to provide a quantitative assessment of the performance of the instruments that allows for their correct application to works of art according to their specific characteristics.

Ergodic Rate Analysis of Simultaneous Transmitting and Reflecting Reconfigurable Intelligent Surface-Assisted Rate-Splitting Multiple Access Systems Based on Discrete Phase Shifts.

In this paper, we combine simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) with rate-splitting multiple access (RSMA) technology and investigate the ergodic rate performance of an STAR-assisted RSMA system. Considering the discrete phase shifts of the STAR-RIS in practice, the downlink performance of STAR-RIS-assisted RSMA with discrete phase shifts is compared to that with continuous phase shifts. Firstly, the cumulative distribution function of signal-to-interference-plus-noise ratio (SINR) of users is analyzed. Then, the total ergodic rate of the system and its approximate closed-form solution are, respectively, derived based on the cumulative distribution function of users. The simulation results validate the effectiveness of the theoretical analysis, showing good agreement between the derived theoretical ergodic rate and the corresponding simulations. Although the system performance with discrete phase shifts is inferior to that with continuous phase shifts due to quantization errors, the performance of the continuous phase shift system is well approximated when the quantization bit of the phase shift system reaches 3 in the simulations. Additionally, the impact of the number of STAR-RIS elements on the system's performance is analyzed.

Self-Biased Magneto-Electric Antenna for Very-Low-Frequency Communications: Exploiting Magnetization Grading and Asymmetric Structure-Induced Resonance.

VLF magneto-electric (ME) antennas have gained attention for their compact size and high radiation efficiency in lossy conductive environments. However, the need for a large DC magnetic field bias presents challenges for miniaturization, limiting portability. This study introduces a self-biased ME antenna with an asymmetric design using two magneto materials, inducing a magnetization grading effect that reduces the resonant frequency during bending. Operating principles are explored, and performance parameters, including the radiation mechanism, intensity and driving power, are experimentally assessed. Leveraging its excellent direct and converse magneto-electric effect, the antenna proves adept at serving as both a transmitter and a receiver. The results indicate that, at 2.09 mW and a frequency of 24.47 kHz, the antenna has the potential to achieve a 2.44 pT magnetic flux density at a 3 m distance. A custom modulation-demodulation circuit is employed, applying 2ASK and 2PSK to validate communication capability at baseband signals of 10 Hz and 100 Hz. This approach offers a practical strategy for the lightweight and compact design of VLF communication systems.

Precise Error Performance of BPSK Modulated Coherent Terahertz Wireless LOS Links with Pointing Errors.

One of the key advantages of terahertz (THz) communication is its potential for energy efficiency, making it an attractive option for green communication systems. Coherent THz transmission technology has recently been explored in the literature. However, there exist few error performance results for such a wireless link employing coherent THz technology. In this paper, we explore a comprehensive terrestrial channel model designed for wireless line-of-sight communication using THz frequencies. The performance of coherent THz links is analyzed, and it is found to be notably affected by two significant factors, atmospheric turbulence and pointing errors. These could occur between the terahertz transmitter and receiver in terrestrial links. The exact and asymptotic solutions are derived for bit error rate and interrupt probability for binary phase-shift keying coherent THz systems, respectively, over log-normal and Gamma-Gamma turbulent channels. The asymptotic outage probability analysis is also performed. It is shown that the presented results offer a precise estimation of coherent THz transmission performance and its link budget.

[Magnetic induced phase shift detection system based on a novel sensor for cerebral hemorrhage].

The main magnetic field, generated by the excitation coil of the magnetic induction phase shift technology detection system, is mostly dispersed field with small field strength, and the offset effect needs to be further improved, which makes the detection signal weak and the detection system difficult to achieve quantitative detection, thus the technology is rarely used in vivo experiments and clinical trials. In order to improve problems mentioned above, a new Helmholtz birdcage sensor was designed. Stimulation experiment was carried out to analyze the main magnetic field in aspects of intensity and magnetic distribution, then different bleeding volume and bleeding rates experiments were conducted to compared with traditional sensors. The results showed that magnetic field intensity in detection region was 2.5 times than that of traditional sensors, cancellation effect of the main magnetic field was achieved, the mean value of phase difference of 10 mL rabbit blood was (-3.34 ± 0.21)°, and exponential fitting adjusted R 2 between phase difference and bleeding volumes and bleeding rates were both 0.99. The proposed Helmholtz birdcage sensor has a uniform magnetic field with a higher field strength, enable more accurate quantification of hemorrhage and monitored change of bleeding rates, providing significance in magnetic induced technology research for cerebral hemorrhage detection.

Identification of the global diurnal rhythmic transcripts, transcription factors and time-of-day specific cis elements in Chenopodium quinoa.

BACKGROUND: Photoperiod is an important environmental cue interacting with circadian clock pathway to optimize the local adaption and yield of crops. Quinoa (Chenopodium quinoa) in family Amaranthaceae has been known as superfood due to the nutritious elements. As quinoa was originated from the low-latitude Andes, most of the quinoa accessions are short-day type. Short-day type quinoa usually displays altered growth and yield status when introduced into higher latitude regions. Thus, deciphering the photoperiodic regulation on circadian clock pathway will help breed adaptable and high yielding quinoa cultivars. RESULTS: In this study, we conducted RNA-seq analysis of the diurnally collected leaves of quinoa plants treated by short-day (SD) and long-day conditions (LD), respectively. We identified 19,818 (44% of global genes) rhythmic genes in quinoa using HAYSTACK analysis. We identified the putative circadian clock architecture and investigated the photoperiodic regulatory effects on the expression phase and amplitude of global rhythmic genes, core clock components and transcription factors. The global rhythmic transcripts were involved in time-of-day specific biological processes. A higher percentage of rhythmic genes had advanced phases and strengthened amplitudes when switched from LD to SD. The transcription factors of CO-like, DBB, EIL, ERF, NAC, TALE and WRKY families were sensitive to the day length changes. We speculated that those transcription factors may function as key mediators for the circadian clock output in quinoa. Besides, we identified 15 novel time-of-day specific motifs that may be key cis elements for rhythm-keeping in quinoa. CONCLUSIONS: Collectively, this study lays a foundation for understanding the circadian clock pathway and provides useful molecular resources for adaptable elites breeding in quinoa.

Circadian rhythm entrainment of the jewel wasp, Nasonia vitripennis, by antagonistic interactions of multiple spectral inputs.

Circadian light entrainment in some insects is regulated by blue-light-sensitive cryptochrome (CRY) protein that is expressed in the clock neurons, but this is not the case in hymenopterans. The hymenopteran clock does contain CRY, but it appears to be light-insensitive. Therefore, we investigated the role of retinal photoreceptors in the photic entrainment of the jewel wasp Nasonia vitripennis. Application of monochromatic light stimuli at different light intensities caused phase shifts in the wasp's circadian activity from which an action spectrum with three distinct peaks was derived. Electrophysiological recordings from the compound eyes and ocelli revealed the presence of three photoreceptor classes, with peak sensitivities at 340 nm (ultraviolet), 450 nm (blue) and 530 nm (green). An additional photoreceptor class in the ocelli with sensitivity maximum at 560-580 nm (red) was found. Whereas a simple sum of photoreceptor spectral sensitivities could not explain the action spectrum of the circadian phase shifts, modelling of the action spectrum indicates antagonistic interactions between pairs of spectral photoreceptors, residing in the compound eyes and the ocelli. Our findings imply that the photic entrainment mechanism in N. vitripennis encompasses the neural pathways for measuring the absolute luminance as well as the circuits mediating colour opponency.

Phase-shifted transverse relaxation orientation dependences in human brain white matter.

This work aimed to demonstrate an essential phase shift ε 0 for better quantifying R 2 and R 2 * in human brain white matter (WM), and to further elucidate its origin related to the directional diffusivities from standard diffusion tensor imaging (DTI). ε 0 was integrated into a proposed generalized transverse relaxation model for characterizing previously published R 2 and R 2 * orientation dependence profiles in brain WM, and then comparisons were made with those without ε 0 . It was theorized that anisotropic diffusivity direction ε was collinear with an axon fiber subject to all eigenvalues and eigenvectors from an apparent diffusion tensor. To corroborate the origin of ε 0 , R 2 orientation dependences referenced by ε were compared with those referenced by the standard principal diffusivity direction Φ at b-values of 1000 and 2500 (s/mm2 ). These R 2 orientation dependences were obtained from T 2 -weighted images (b = 0) of ultrahigh-resolution Connectome DTI datasets in the public domain. A normalized root-mean-square error ( NRMSE % ) and an F -test were used for evaluating curve-fittings, and statistical significance was considered to be a p of 0.05 or less. A phase-shifted model resulted in significantly reduced NRMSE % compared with that without ε 0 in quantifying various R 2 and R 2 * profiles, both in vivo and ex vivo at multiple B 0 fields. The R 2 profiles based on Φ manifested a right-shifted phase ( ε 0 > 0 ) at two b-values, while those based on ε became free from ε 0 . For all phase-shifted R 2 and R 2 * profiles, ε 0 generally depended on the directional diffusivities by tan - 1 D ⊥ / D ∥ , as predicted. In summary, a ubiquitous phase shift ε 0 has been demonstrated as a prerequisite for better quantifying transverse relaxation orientation dependences in human brain WM. Furthermore, the origin of ε 0 associated with the directional diffusivities from DTI has been elucidated. These findings could have a significant impact on interpretations of prior R 2 and R 2 * datasets and on future research.