Complementation testing identifies genes mediating effects at quantitative trait loci underlying fear-related behavior.

Knowing the genes involved in quantitative traits provides an entry point to understanding the biological bases of behavior, but there are very few examples where the pathway from genetic locus to behavioral change is known. To explore the role of specific genes in fear behavior, we mapped three fear-related traits, tested fourteen genes at six quantitative trait loci (QTLs) by quantitative complementation, and identified six genes. Four genes, Lamp, Ptprd, Nptx2, and Sh3gl, have known roles in synapse function; the fifth, Psip1, was not previously implicated in behavior; and the sixth is a long non-coding RNA, 4933413L06Rik, of unknown function. Variation in transcriptome and epigenetic modalities occurred preferentially in excitatory neurons, suggesting that genetic variation is more permissible in excitatory than inhibitory neuronal circuits. Our results relieve a bottleneck in using genetic mapping of QTLs to uncover biology underlying behavior and prompt a reconsideration of expected relationships between genetic and functional variation.

Changes of PM2.5 and O3 and their impact on human health in the Guangdong-Hong Kong-Macao Greater Bay Area.

In recent years, the combined pollution of PM2.5 and O3 in China, particularly in economically developed regions such as the Guangdong-Hong Kong-Macao Greater Bay Area (GBA), has garnered significant attention due to its potential implications. This study systematically investigated the changes of PM2.5 and O3 and their associated human health effects in the GBA, utilizing observational data spanning from 2015 to 2019. The findings revealed a spatial trend indicating a gradual decrease in PM2.5 levels from the northwest to the southeast, while the spatial distribution of MDA8 O3 demonstrated an opposing pattern to that of PM2.5. The monthly fluctuations of PM2.5 and MDA8 O3 exhibited V-shaped and M-shaped patterns, respectively. Higher MDA8 O3 concentrations were observed in autumn, followed by summer and spring. Over the five-year period, PM2.5 concentrations exhibited a general decline, with an annual reduction rate of 1.7 µg m-3/year, while MDA8 O3 concentrations displayed an annual increase of 3.2 µg m-3. Among the GBA regions, Macao, Foshan, Guangzhou, and Jiangmen demonstrated notable decreases in PM2.5, whereas Jiangmen, Zhongshan, and Guangzhou experienced substantial increases in MDA8 O3 levels. Long-term exposure to PM2.5 in 2019 was associated with 21,113 (95% CI 4968-31,048) all-cause deaths (AD), 1333 (95% CI 762-1714) cardiovascular deaths (CD), and 1424 (95% CI 0-2848) respiratory deaths (RD), respectively, reflecting declines of 27.6%, 28.0%, and 28.4%, respectively, compared to 2015. Conversely, in 2019, estimated AD, CD, and RD attributable to O3 were 16,286 (95% CI 8143-32,572), 7321 (95% CI 2440-14,155), and 6314 (95% CI 0-13,576), respectively, representing increases of 45.9%, 46.2%, and 44.2% over 2015, respectively. Taken together, these findings underscored a shifting focus in air pollution control in the GBA, emphasizing the imperative for coordinated control strategies targeting both PM2.5 and O3.

Complementation testing identifies causal genes at quantitative trait loci underlying fear related behavior.

Knowing the genes involved in quantitative traits provides a critical entry point to understanding the biological bases of behavior, but there are very few examples where the pathway from genetic locus to behavioral change is known. Here we address a key step towards that goal by deploying a test that directly queries whether a gene mediates the effect of a quantitative trait locus (QTL). To explore the role of specific genes in fear behavior, we mapped three fear-related traits, tested fourteen genes at six QTLs, and identified six genes. Four genes, Lsamp, Ptprd, Nptx2 and Sh3gl, have known roles in synapse function; the fifth gene, Psip1, is a transcriptional co-activator not previously implicated in behavior; the sixth is a long non-coding RNA 4933413L06Rik with no known function. Single nucleus transcriptomic and epigenetic analyses implicated excitatory neurons as likely mediating the genetic effects. Surprisingly, variation in transcriptome and epigenetic modalities between inbred strains occurred preferentially in excitatory neurons, suggesting that genetic variation is more permissible in excitatory than inhibitory neuronal circuits. Our results open a bottleneck in using genetic mapping of QTLs to find novel biology underlying behavior and prompt a reconsideration of expected relationships between genetic and functional variation.

Regulating the Heme Active Site by Covalent Modifications: Two Case Studies of Myoglobin.

Using myoglobin (Mb) as a model protein, we herein developed a facial approach to modifying the heme active site. A cavity was first generated in the heme distal site by F46 C mutation, and the thiol group of Cys46 was then used for covalently linked to exogenous ligands, 1H-1,2,4-triazole-3-thiol and 1-(4-hydroxyphenyl)-1H-pyrrole-2,5-dione. The engineered proteins, termed F46C-triazole Mb and F46C-phenol Mb, respectively, were characterized by X-ray crystallography, spectroscopic and stopped-flow kinetic studies. The results showed that both the heme coordination state and the protein function such as H2 O2 activation and peroxidase activity could be efficiently regulated, which suggests that this approach might be generally applied to the design of functional heme proteins.

TransMatch: A Transformer-Based Multilevel Dual-Stream Feature Matching Network for Unsupervised Deformable Image Registration.

Feature matching, which refers to establishing the correspondence of regions between two images (usually voxel features), is a crucial prerequisite of feature-based registration. For deformable image registration tasks, traditional feature-based registration methods typically use an iterative matching strategy for interest region matching, where feature selection and matching are explicit, but specific feature selection schemes are often useful in solving application-specific problems and require several minutes for each registration. In the past few years, the feasibility of learning-based methods, such as VoxelMorph and TransMorph, has been proven, and their performance has been shown to be competitive compared to traditional methods. However, these methods are usually single-stream, where the two images to be registered are concatenated into a 2-channel whole, and then the deformation field is output directly. The transformation of image features into interimage matching relationships is implicit. In this paper, we propose a novel end-to-end dual-stream unsupervised framework, named TransMatch, where each image is fed into a separate stream branch, and each branch performs feature extraction independently. Then, we implement explicit multilevel feature matching between image pairs via the query-key matching idea of the self-attention mechanism in the Transformer model. Comprehensive experiments are conducted on three 3D brain MR datasets, LPBA40, IXI, and OASIS, and the results show that the proposed method achieves state-of-the-art performance in several evaluation metrics compared to the commonly utilized registration methods, including SyN, NiftyReg, VoxelMorph, CycleMorph, ViT-V-Net, and TransMorph, demonstrating the effectiveness of our model in deformable medical image registration.

Eosin Y-Based Metal-Organic Framework Synergistic with Cobalt(II) Complex for Hydrogen Evolution through Photoinduced Intermolecular Electron Transfer.

Photocatalytic hydrogen evolution reaction (HER) is a promising approach for producing clean energy and has the potential to play an important role in the transition toward a more sustainable and environmentally friendly energy system. Optimizing the photoinduced electron transfer (PET) process and increasing visible-light utilization play a central role in photocatalysis. Herein, we built a novel Eosin Y-based metal-organic framework (Zn-EYTP) by synergizing a cobalt(II) complex for boosting the H2 evolution efficiency through photoinduced intermolecular electron transfer. Under optimized conditions, the maximum H2 evolution efficiency for Zn-EYTP was determined to be a turnover number (TON) value of 11,100 under green LED irradiation. And the synthesized Zn-EYTP photocatalysts could be easily recycled to restore the initial photocatalytic activity even after 3 cycles. Detailed studies reveal that the significantly enhanced HER activity in Zn-EYTP could be ascribed to the effective separation of photogenerated charges and the synergistic intermolecular interaction between Zn-EYTP and [Co(bpy)3]Cl2. The present work enables a deeper understanding of the importance of the PET process for enhanced HER photocatalytic activities, which will provide a viable strategy for the development of highly efficient photocatalysts.

Single-cell methylation analysis of brain tissue prioritizes mutations that alter transcription.

Relating genetic variants to behavior remains a fundamental challenge. To assess the utility of DNA methylation marks in discovering causative variants, we examined their relationship to genetic variation by generating single-nucleus methylomes from the hippocampus of eight inbred mouse strains. At CpG sequence densities under 40 CpG/Kb, cells compensate for loss of methylated sites by methylating additional sites to maintain methylation levels. At higher CpG sequence densities, the exact location of a methylated site becomes more important, suggesting that variants affecting methylation will have a greater effect when occurring in higher CpG densities than in lower. We found this to be true for a variant's effect on transcript abundance, indicating that candidate variants can be prioritized based on CpG sequence density. Our findings imply that DNA methylation influences the likelihood that mutations occur at specific sites in the genome, supporting the view that the distribution of mutations is not random.

Research on a New Intelligent and Rapid Screening Method for Depression Risk in Young People Based on Eye Tracking Technology.

Depression is a prevalent mental disorder, with young people being particularly vulnerable to it. Therefore, we propose a new intelligent and rapid screening method for depression risk in young people based on eye tracking technology. We hypothesized that the "emotional perception of eye movement" could characterize defects in emotional perception, recognition, processing, and regulation in young people at high risk for depression. Based on this hypothesis, we designed the "eye movement emotional perception evaluation paradigm" and extracted digital biomarkers that could objectively and accurately evaluate "facial feature perception" and "facial emotional perception" characteristics of young people at high risk of depression. Using stepwise regression analysis, we identified seven digital biomarkers that could characterize emotional perception, recognition, processing, and regulation deficiencies in young people at high risk for depression. The combined effectiveness of an early warning can reach 0.974. Our proposed technique for rapid screening has significant advantages, including high speed, high early warning efficiency, low cost, and high intelligence. This new method provides a new approach to help effectively screen high-risk individuals for depression.

A new early warning method for mild cognitive impairment due to Alzheimer's disease based on dynamic evaluation of the "spatial executive process".

Objective: Mild cognitive impairment (MCI) due to Alzheimer's disease (AD), as an early stage of AD, is an important point for early warning of AD. Neuropathological studies have shown that AD pathology in pre-dementia patients involves the hippocampus and caudate nucleus, which are responsible for controlling cognitive mechanisms such as the spatial executive process (SEP). The aim of this study is to design a new method for early warning of MCI due to AD by dynamically evaluating SEP. Methods: We designed fingertip interaction handwriting digital evaluation paradigms and analyzed the dynamic trajectory of fingertip interaction and image data during "clock drawing" and "repetitive writing" tasks. Extracted fingertip interaction digital biomarkers were used to assess participants' SEP disorders, ultimately enabling intelligent diagnosis of MCI due to AD. A cross-sectional study demonstrated the predictive performance of this new method. Results: We enrolled 30 normal cognitive (NC) elderly and 30 MCI due to AD patients, and clinical research results showed that there may be neurobehavioral differences between the two groups in digital biomarkers captured during SEP. The early warning performance for MCI due to AD of this new method (areas under the curve (AUC) = 0.880) is better than that of the Minimum Mental State Examination (MMSE) neuropsychological scale (AUC = 0.856) assessed by physicians. Conclusion: Patients with MCI due to AD may have SEP disorders, and this new method based on dynamic evaluation of SEP will provide a novel human-computer interaction and intelligent early warning method for home and community screening of MCI due to AD.

Rural pensions, intra-household bargaining, and elderly medical expenditure in China.

China's rural elderly spend less on medical expenditures as they age despite declining health, raising welfare concerns. This paper investigates the role of intrahousehold bargaining power on health expenditures of the elderly by evaluating the impact of cash transfers from a new social pension program. The program provided windfall payments to those above age 60, making it possible to employ a regression discontinuity design based on age of eligibility to estimate causal effects. Using data from the 2011 and 2013 waves of the China Health and Retirement Longitudinal Study, we find that receiving pension payments increases both the utilization of outpatient care and outpatient expenditures by the elderly who experienced illness. This result is robust to controlling for total household expenditures per capita, ruling out income effects as the main channel. Consistent with pensions increasing elderly bargaining power, we find that pensions significantly increase medical expenditures only for those elderly who co-reside with children or grandchildren but have no effect on those who live independently.

Brain intrinsic magnetic susceptibility mapping depicts whole-brain functional connectivity balance of normal aging in lifespan.

We hypothesized that brain normal aging maintains a balanced whole-brain functional connectivity (FC) in lifetime: some connections decline while other connections increase or retain, in a summation balance as a result of the cancellation of positive and negative connections. We validated this hypothesis through the use of the brain intrinsic magnetic susceptibility source (denoted by χ) as reconstructed from fMRI phase data. In implementation, we first acquired brain fMRI magnitude (m) and phase (p) data from a cohort of 245 healthy subjects in an age span of 20-60 years, then sought MRI-free brain χ source data by computationally solving an inverse mapping problem, thereby obtained triple datasets {χ, m, p} as brain images in different measurements. We performed GIG-ICA for brain function decomposition and constructed the FC matrices (χFC, mFC, pFC} (in size of 50 × 50 for a selection of 50 ICA nodes), followed by a comparative analysis on brain FC agings using {χ, m, p} data. In the results, we found that: (i) χFC aging upholds a FC balance in life span, in an intermediator between mFC and pFC agings by: mean(pFC) = -0.011 < mean(χFC) = 0.015 < mean(mFC) = 0.036; and (ii) the χFC aging exhibits a slight decline with a slightly downward fitting line in intermediation between the two slightly upward fitting lines for the mFC and pFC agings. On the rationale of the χ-depicted MRI-free brain functional state, the brain χFC aging is closer to the brain FC aging truth than the MRI-borne mFC and pFC agings.

Ferroptosis and multi-organ complications in COVID-19: mechanisms and potential therapies.

COVID-19 is an infectious disease caused by SARS-CoV-2, with respiratory symptoms as primary manifestations. It can progress to severe illness, leading to respiratory failure and multiple organ dysfunction. Recovered patients may experience persistent neurological, respiratory, or cardiovascular symptoms. Mitigating the multi-organ complications of COVID-19 has been highlighted as a crucial part of fighting the epidemic. Ferroptosis is a type of cell death linked to altered iron metabolism, glutathione depletion, glutathione peroxidase 4 (GPX4) inactivation, and increased oxidative stress. Cell death can prevent virus replication, but uncontrolled cell death can also harm the body. COVID-19 patients with multi-organ complications often exhibit factors related to ferroptosis, suggesting a possible connection. Ferroptosis inhibitors can resist SARS-CoV-2 infection from damaging vital organs and potentially reduce COVID-19 complications. In this paper, we outline the molecular mechanisms of ferroptosis and, based on this, discuss multi-organ complications in COVID-19, then explore the potential of ferroptosis inhibitors as a supplementary intervention for COVID-19. This paper will provide a reference for the possible treatment of SARS-CoV-2 infected disease to reduce the severity of COVID-19 and its subsequent impact.

Computed cancer magnetic susceptibility imaging (canχ): Computational inverse mappings of cancer MRI.

PURPOSE: We report a new cancer imaging modality in the contrast of tissue intrinsic susceptibility property by computed inverse magnetic resonance imaging (CIMRI). METHODS: In MRI physics, an MRI signal is formed from tissue magnetism source (primarily magnetic susceptibility χ) through a cascade of MRI-introduced transformations (e.g. dipole-convolved magnetization) involving MRI setting parameters (e.g. echo time). In two-step computational inverse mappings (from phase image to internal fieldmap to susceptibility source), we could remove the MRI transformations and imaging parameters, thereby obtaining χ-depicted cancer images (canχ) from MRI phase images. Canχ is computationally implemented from clinical cancer MRI phase image by CIMRI. RESULTS: As a result of MRI effect removal through computational inverse mappings, the reconstructed χ map (canχ) could provide a new cancerous tissue depiction in contrast of tissue intrinsic magnetism property (i.e. diamagnetism vs paramagnetism) as in an off-scanner state (e.g. in absence of main field B0). CONCLUSION: Through retrospective clinical cancer MRI data analysis, we reported on the canχ method in technical details and demonstrated its feasibility of innovating cancer imaging in the contrast of tissue intrinsic paramagnetism/diamagnetism property (in a cancer tissue state free from MRI effect).

Tilted quantitative susceptibility mapping at oblique MRI (tiltQSM).

OBJECTIVE: If the phase image matrix was acquired from oblique MRI, it is needed to deal with the oblique effect for quantitative susceptibility mapping (QSM), as addressed in this paper. METHODS: We proposed two methods for QSM reconstruction from slice-tilted MRI phase image (tiltQSM): 1) rotData per anti-tilting phase image rotation back into the B0-upright system, and 2) rotKernel per pro-tilting dipole kernel rotation into the same oblique setting as defined by the tilted phase image. Both matrix methods were implemented in an additional preprocessing subroutine to ensure that the phase image and the dipole kernel were represented in the same coordinate system (either in B0-upright system or in B0-tilted system); thereafter tiltQSM could be completed through a regular QSM procedure. Besides the oblique effect, tiltQSM also suffers from MRI anisotropy. We provided numeric simulations, phantom tests and in vivo brain experiments on tiltQSM with oblique MRI (axial slice tilting at 3T). RESULTS: The tiltQSM reconstruction could attain a performance corr > 0.90 (spatial correlation conformance) for small tilting angles <10°. The tiltQSM performance could be further degraded by voxel anisotropy due to image matrix rotation (digital geometry error). CONCLUSIONS: To seek inverse solutions of MRI phase images acquired at oblique MRI (e.g. in axial slice tilting), we proposed tiltQSM to deal with the oblique effect per matrix rotation (either rotData or rotKernel) in a preprocessing subroutine prior to a regular QSM procedure. In practice, it is always recommended to acquire MRI phase images in isotropic matrix at zero obliqueness (or limited to small tilting angles <10°) for maximal (optimal) QSM reconstruction.

High-Branched Organosilicon Epoxy Resin with Low Viscosity, Excellent Toughness, Hydrophobicity, and Dielectric Property.

Rapidly developing technology places higher demands on materials, thus the simultaneous improvement of materials' multiple properties is a hot research topic. In this work, a high-branched silicone epoxy resin (QSiE) was synthesized and applied to the curing system of bisphenol A epoxy resin (DGEBA) for modification investigations. When 6 wt% QSiE was added to the system, the viscosity dropped by 51.8%. The mechanical property testing results indicated that QSiE could significantly enhance the material's toughness while preserving good rigidity. The impact strength was enhanced by 1.31 times when 6wt% of QSiE was introduced. Additionally, the silicon skeleton in QSiE has low surface energy and low polarizability, which could endow the material with good hydrophobic and dielectric properties. This work provided a new idea for the preparation of high-performance epoxy resin additives, and provided a broad prospect for cutting-edge applications of epoxy resins.

Understanding the zigzags of multi-echo phase signals by numerical simulations.

Understanding the multi-echo phase zigzag signals is instrumental to assuring the quality of MRI phase data acquisition for ensuing phase exploration and exploitation. This paper provides a theoretical and computational mechanism for understanding the zigzag multi-echo phase formation that has been observed in numerical multi-echo gradient-recalled (GRE) simulations of clinical complex-valued brain MRI images. Based on intravoxel dephasing mechanism, we calculated a train of multi-GRE complex-valued voxel signals by simulating field gradient reversals under perturbations in either gradient strength (G±Î´G) or gradient duration (Δ±Î´Δ), as well as the simultaneous bi-variable gradient perturbations (δGδΔ). In this theoretical experiment, we observed a zigzag line of one-shot multi-echo phase signals at a voxel with respect to linear stepwise field gradient variations inδG ∝ n andÎ´Δ âˆ n (where n denotes the echo index). However, the multi-echo magnitude signals were invariant to field gradient reversal, i.e. no multi-echo magnitude zigzags. To support our simulations, we analyzed the clinical one-shot multi-echo T2*-weighted MRI phase images and found similar multi-echo phase zigzags. In this way, we provide a theoretical and computational understanding of multi-echo phase zigzag artifacts, specifically for the eddy current effect on one-shot multi-GRE signals in practice.

Pulmonate slug evolution is reflected in the de novo genome of Arion vulgaris Moquin-Tandon, 1855.

Stylommatophoran pulmonate land slugs and snails successfully completed the water-to-land transition from an aquatic ancestor and flourished on land. Of the 30,000 estimated species, very few genomes have so far been published. Here, we assembled and characterized a chromosome-level genome of the "Spanish" slug, Arion vulgaris Moquin-Tandon, 1855, a notorious pest land slug in Europe. Using this reference genome, we conclude that a whole-genome duplication event occurred approximately 93-109 Mya at the base of Stylommatophora and might have promoted land invasion and adaptive radiation. Comparative genomic analyses reveal that genes related to the development of kidney, blood vessels, muscle, and nervous systems had expanded in the last common ancestor of land pulmonates, likely an evolutionary response to the terrestrial challenges of gravity and water loss. Analyses of A. vulgaris gene families and positively selected genes show the slug has evolved a stronger ability to counteract the greater threats of external damage, radiation, and water loss lacking a protective shell. Furthermore, a recent burst of long interspersed elements in the genome of A. vulgaris might affect gene regulation and contribute to rapid phenotype changes in A. vulgaris, which might be conducive to its rapid adaptation and invasiveness.

CERL: A Unified Optimization Framework for Light Enhancement With Realistic Noise.

Low-light images captured in the real world are inevitably corrupted by sensor noise. Such noise is spatially variant and highly dependent on the underlying pixel intensity, deviating from the oversimplified assumptions in conventional denoising. Existing light enhancement methods either overlook the important impact of real-world noise during enhancement, or treat noise removal as a separate pre- or post-processing step. We present Coordinated Enhancement for Real-world Low-light Noisy Images (CERL), that seamlessly integrates light enhancement and noise suppression parts into a unified and physics-grounded optimization framework. For the real low-light noise removal part, we customize a self-supervised denoising model that can easily be adapted without referring to clean ground-truth images. For the light enhancement part, we also improve the design of a state-of-the-art backbone. The two parts are then joint formulated into one principled plug-and-play optimization. Our approach is compared against state-of-the-art low-light enhancement methods both qualitatively and quantitatively. Besides standard benchmarks, we further collect and test on a new realistic low-light mobile photography dataset (RLMP), whose mobile-captured photos display heavier realistic noise than those taken by high-quality cameras. CERL consistently produces the most visually pleasing and artifact-free results across all experiments. Our RLMP dataset and codes are available at: https://github.com/VITA-Group/CERL.

How many single-copy orthologous genes from whole genomes reveal deep gastropod relationships?

The Gastropoda contains 80% of existing mollusks and is the most diverse animal class second only to the Insecta. However, the deep phylogeny of gastropods has been controversial for a long time. Especially the position of Patellogastropoda is a major uncertainty. Morphology and some mitochondria studies concluded that Patellogastropoda is likely to be sister to all other gastropods (Orthogastropoda hypothesis), while transcriptomic and other mitogenomic studies indicated that Patellogastropoda and Vetigastropoda are sister taxa (Psilogastropoda). With the release of high-quality genomes, orthologous genes can be better identified and serve as powerful candidates for phylogenetic analysis. The question is, given the current limitations on the taxon sampling side, how many markers are needed to provide robust results. Here, we identified single-copy orthologous genes (SOGs) from 14 gastropods species with whole genomes available which cover five main gastropod subclasses. We generated different datasets from 395 to 1610 SOGs by allowing species missing in different levels. We constructed gene trees of each SOG, and inferred species trees from different collections of gene trees. We found as the number of SOGs increased, the inferred topology changed from Patellogastropoda being sister to all other gastropods to Patellogastropoda being sister to Vetigastropoda + Neomphalina (Psilogastropoda s.l.), with considerable support. Our study thus rejects the Orthogastropoda concept showing that the selection of the representative species and use of sufficient informative sites greatly influence the analysis of deep gastropod phylogeny.

Proof of linear MRI phase imaging from an internal fieldmap.

PURPOSE: Brain MRI phase imaging assumes a linear spatial mapping of the internal fieldmap that continues to lack theoretical proof. We herein present one proof by replacing the arithmetic mean (in MRI signal formation from the intravoxel spin precession dephasing mechanism) with the geometric mean. METHODS: By replacing the complex arithmetic mean of intravoxel dephasing isochromats with a complex geometric mean, we readily derive a linear spatial mapping of MRI phase imaging from an internal fieldmap without any restriction in phase angles. To justify the replacement of the complex arithmetic mean with the complex geometric mean for realistic brain MRI, we provide numerical T2*MRI simulations to observe the similarity and difference between arithmetic- and geometric-mean phase images in diverse settings with respect to spatial resolution and echo time, with or without proton density weighting. RESULTS: Theoretically, the complex geometric mean model offers a theoretical proof of linear spatial mapping for MRI phase imaging. Numerical simulations of T2*MRI phase imaging show that the geometric mean conforms to the arithmetic mean at a high similarity in the small phase condition (e.g., corr > 0.90 in phase pre-wrapping status at TE  < 10 ms) and the similarity falls at large phase angles (e.g., corr ≈ 0.80 in phase-wrapped status at TE  = 30 ms). CONCLUSION: By replacing the arithmetic mean of intravoxel spin precession dephasing with the geometric mean, we find a theoretical proof for linear MRI phase imaging beyond the small phase condition on spin precession angles.