Rational approximation of golden angles: Accelerated reconstructions for radial MRI.

PURPOSE: To develop a generic radial sampling scheme that combines the advantages of golden ratio sampling with simplicity of equidistant angular patterns. The irrational angle between consecutive spokes in golden ratio-based sampling schemes enables a flexible retrospective choice of temporal resolution, while preserving good coverage of k-space for each individual bin. Nevertheless, irrational increments prohibit precomputation of the point-spread function (PSF), can lead to numerical problems, and require more complex processing steps. To avoid these problems, a new sampling scheme based on a rational approximation of golden angles (RAGA) is developed. METHODS: The theoretical properties of RAGA sampling are mathematically derived. Sidelobe-to-peak ratios (SPR) are numerically computed and compared to the corresponding golden ratio sampling schemes. The sampling scheme is implemented in the BART toolbox and in a radial gradient-echo sequence. Feasibility is shown for quantitative imaging in a phantom and a cardiac scan of a healthy volunteer. RESULTS: RAGA sampling can accurately approximate golden ratio sampling and has almost identical PSF and SPR. In contrast to golden ratio sampling, each frame can be reconstructed with the same equidistant trajectory using different sampling masks, and the angle of each acquired spoke can be encoded as a small index, which simplifies processing of the acquired data. CONCLUSION: RAGA sampling provides the advantages of golden ratio sampling while simplifying data processing, rendering it a valuable tool for dynamic and quantitative MRI.

Is human height based on a Lucas sequence relationship between the foot height, tibial length, femur length and upper body length?

This is a retrospective chart and radiographic review of 145 patients who underwent full-body EOS imaging; 109 males and 36 females. The mean ages of the female and male subsets are 28.8 (SD = 11.6) years and 29.5 (SD = 11.8) years, respectively. The sum of the foot height (Ft) and the tibial length (T) for each subject was compared to their femur length (Fe). Subsequently, the sum of the tibial (T) and femoral lengths (Fe) were compared to their respective upper body lengths (UB), as measured from the tops of the femoral heads. A linear regression test was performed to determine whether a Lucas sequence-based relationship exists between Ft + T and Fe, and between T + Fe and UB. The regression for the relationship between Ft + T and Fe for the entire cohort (R = 0.82, R2 = 0.70), the female subset (R = 0.94, R2 = 0.88) and the male subset (R = 0.75, R2 = 0.57), all demonstrated a strong positive correlation between Ft + T and Fe and showed that Ft + T is a likely predictor of Fe. The regression test for the entire cohort demonstrated a moderately positive correlation between T + Fe and UB (R = 0.41, R2 = 0.17, F(1, 145) = 29.42, p = 2.4E-07). A stronger correlation was found for the relationship between T + Fe and UB (R = 0.57, R2 = 0.32, F(1, 35) = 16.64, p = 2.5E-05) for the female subset relative to the male subset (R = 0.20, R2 = 0.038, F(1, 35) = 4.37, p = 0.04). There appears to be a Lucas sequence relationship between the lengths of the foot height, tibial length, femoral length and upper body length, which together make up standing height. This mathematical proportion relationship is stronger in females than males.

There Is no Universal Standard of Beauty.

This article discusses the various factors that contribute to facial beauty and the different contexts in which they are significant. The authors examine the roles of the golden ratio, ideal proportions, symmetry, and specific facial features in what constitutes an attractive face. They also investigate the influence of cultural and evolutionary perspectives on facial beauty and the impact of social media on our perception of beauty. The article provides a comprehensive overview of the topic and emphasises the significance of facial beauty and its impact on our lives. The authors acknowledge that the concept of beauty is difficult to define with absolute precision, and that the objective-subjective argument regarding facial beauty remains unsolved. However, they argue that physical attributes undoubtedly influence perceptions of attractiveness, but beauty extends beyond surface-level features. They also suggest that embracing diversity in beauty standards fosters a more inclusive society that celebrates the unique qualities of every person.Level of Evidence V This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

Determining the widths of the maxillary anterior teeth for esthetics: comparison of the Mondelli and Albers formulas, esthetic proportion, and golden ratio.

The purpose of this study was to compare various formulas for idealized proportions of the maxillary incisors to the actual dimensions of natural teeth. The Mondelli formula 1 (MF1), Mondelli formula 2 (MF2), Albers formula (AF), esthetic proportion (EP) for width and height of anterior teeth, and golden ratio (GR) were calculated for a total of 50 dental students (30 women and 20 men) who participated in the study. The following measurements were obtained directly in the participant's mouth with a digital caliper: the mesiodistal and incisogingival dimensions of the maxillary central incisors, lateral incisors, and canines; the intercanine distance; and the smile width. The participants were photographed, and the smile width was also measured on the photographs. The MF1 and MF2 were each calculated twice, using both direct measurements and photographic measurements. The projected central incisor widths calculated using the MF1, MF2, and AF were compared among themselves and against the actual measurements using analysis of variance and Fisher test for multiple comparisons (α = 0.05). The EP and GR were analyzed using descriptive statistics. There was a statistically significant difference between all of the widths projected by the formulas and the actual widths of the central incisors (P < 0.05). Whether calculated from a direct or a photographic measurement, the incisor widths projected by the MF1 and MF2 were statistically similar to each other (P > 0.05). The EP values were similar to those reported in the literature. Only 2% of the participants had an incisor width ratio (central incisor/lateral incisor) that matched the GR of 1.618, while 86% fell within the range of 1.2 to 1.4. Overall, the proportions calculated with the MF1, MF2, AF, EP, and GR did not exactly match the actual dimensions of natural teeth. The formulas and the proportions available in the literature can assist in esthetic planning, but the individual characteristics of each patient and expertise of the dentist should guide treatment for each case.

W. D. Hamilton and the golden sex ratio.

In his famous two-part paper, published in Journal of Theoretical Biology in 1964, W. D. Hamilton predicted that natural selection acting in male-haploid populations favours a ratio of males to females that is in accordance with the golden ratio. This prediction has found its way into the pages of one of the best-selling books of all time, Dan Brown's 2003 novel The da Vinci Code, and is therefore in the running for the most widely known quantitative result in the history of evolutionary biology. Unfortunately, this golden-ratio result is wrong, and was later corrected by Hamilton, who showed that natural selection actually favours an unbiased sex ratio in this setting. But it has been unclear exactly how Hamilton arrived at the golden-ratio result in the first place. Here I show that the solution to this puzzle is found in unpublished work held in the British Library's W. D. Hamilton Archive. Specifically, in addition to employing a faulty method for calculating relatedness, Hamilton had also employed a faulty method for calculating reproductive value, considering only genetic contributions to the next generation rather than to the distant future. Repeating both mistakes recovers his erroneous golden-ratio result.

Sandwich-Kernelled AgCu Nanoclusters with Golden Ratio Geometry and Promising Photothermal Efficiency.

Metal nanoclusters have recently attracted extensive interest from the scientific community. However, unlike carbon-based materials and metal nanocrystals, they rarely exhibit a sheet kernel structure, probably owing to the instability caused by the high exposure of metal atoms (particularly in the relatively less noble Ag or Cu nanoclusters) in such a structure. Herein, we synthesized a novel AgCu nanocluster with a sandwich-like kernel (diameter≈0.9 nm and length≈0.25 nm) by introducing the furfuryl mercaptan ligand (FUR) and the alloying strategy. Interestingly, the kernel consists of a centered silver atom and two planar Ag10 pentacle units with completely mirrored symmetry after a rotation of 36 degrees. The two Ag10 pentacles and some extended structures show an unreported golden ratio geometry, and the two inner five-membered rings and the centered Ag atom form an unanticipated full-metal ferrocene-like structure. The featured kernel structure causes the dominant radial direction transition of excitation electrons, as determined via time-dependent density functional theory calculations, which affords the protruding absorption at 612 nm and contributes to the promising photothermal conversion efficiency of 67.6 % of the as-obtained nanocluster, having important implications for structure-property correlation and the development of nanocluser-based photothermal materials.

Optimal Diffusion Gradient Encoding Scheme for Diffusion Tensor Imaging Based on Golden Ratio.

BACKGROUND: The accuracy of the estimated diffusion tensor elements can be improved by using a well-chosen magnetic resonance imaging (MRI) diffusion gradient encoding scheme (DGES). Conversely, diffusion tensor imaging (DTI) is typically challenged by the subject's motion during data acquisition and results in corrupted image data. PURPOSE: To identify a reliable DGES based on the golden ratio (GR) that can generate an arbitrary number of uniformly distributed directions to precisely estimate the DTI parameters of partially acquired datasets owing to subject motion. STUDY TYPE: Prospective. POPULATION: Simulations study; three healthy volunteers. FIELD STRENGTH/SEQUENCE: 3 T/DTI data were obtained using a single-shot echo planar imaging sequence. STATISTICAL TESTS: A paired sample t-test and the Wilcoxon test were used, P < 0.05 was considered statistically significant. ASSESSMENT: Two corrupted scenarios A and B were considered and evaluated. For the simulation study, the GR DGES and generated subsets were compared with the Jones and spiral DGESs by electric potential (EP) and condition number (CN). For the human study, the specific subsets A and B selected from scenarios A and B were used for MRI to evaluate fractional anisotropic (FA) map. RESULTS: For the simulation study, the EPs of the GR (14034.25 ± 12957.24) DGES were significantly lower than the Jones (15112.81 ± 13926.08) and spiral (14297.49 ± 13232.94) DGESs. CN variations of GR (1.633 ± 0.024) DGES were significantly lower than Jones (1.688 ± 0.119) and spiral (4.387 ± 2.915) DGESs. For the human study, GR (0.008 ± 0.020) DGES performed similarly with Jones (0.008 ± 0.022) DGES and was superior to spiral (0.022 ± 0.054) DGES in the FA map error. DATA CONCLUSION: The GR DGES ensured that directions of the complete sets and subsets were uniform. The GR DGES had lower error propagation sensitivity, which can help image infants or patients who cannot stay still during scanning. LEVEL OF EVIDENCE: 2 TECHNICAL EFFICACY: Stage 1.

Artificial Neural Network Detects Hip Muscle Forces as Determinant for Harmonic Walking in People after Stroke.

Many recent studies have highlighted that the harmony of physiological walking is based on a specific proportion between the durations of the phases of the gait cycle. When this proportion is close to the so-called golden ratio (about 1.618), the gait cycle assumes an autosimilar fractal structure. In stroke patients this harmony is altered, but it is unclear which factor is associated with the ratios between gait phases because these relationships are probably not linear. We used an artificial neural network to determine the weights associable to each factor for determining the ratio between gait phases and hence the harmony of walking. As expected, the gait ratio obtained as the ratio between stride duration and stance duration was found to be associated with walking speed and stride length, but also with hip muscle forces. These muscles could be important for exploiting the recovery of energy typical of the pendular mechanism of walking. Our study also highlighted that the results of an artificial neural network should be associated with a reliability analysis, being a non-deterministic approach. A good level of reliability was found for the findings of our study.

Chinese Aesthetic Mask: Three Forehead and Five Eyes-Holistic Processing and Facial Attractiveness.

Human face processing has been attributed to holistic processing. Here, we ask whether humans are sensitive to configural information when perceiving facial attractiveness. By referring to a traditional Chinese aesthetic theory-Three Forehead and Five Eyes-we generated a series of faces that differed in spacing between facial features. We adopted a two-alternative forced-choice task in Experiment 1 and a rating task in Experiment 2 to assess attractiveness. Both tasks showed a consistent result: The faces which fit the Chinese aesthetic theory were chosen or rated as most attractive. This effect of configural information on facial attractiveness was larger for faces with highly attractive features than for faces with low attractive features. These findings provide experimental evidence for the traditional Chinese aesthetic theory. This issue can be further explored from the perspective of culture in the future.

CArtesian sampling with Variable density and Adjustable temporal resolution (CAVA).

PURPOSE: To develop a variable density Cartesian sampling method that allows retrospective adjustment of temporal resolution for dynamic MRI applications and to validate it in real-time phase contrast MRI (PC-MRI). THEORY AND METHODS: The proposed method, called CArtesian sampling with Variable density and Adjustable temporal resolution (CAVA), begins by producing a sequence of phase encoding indices based on the golden ratio increment. Then, variable density is introduced by nonlinear stretching of the indices. Finally, the elements of the resulting sequence are rounded up to the nearest integer. The performance of CAVA is evaluated using PC-MRI data from a pulsatile flow phantom and real-time, free-breathing data from ten healthy volunteers. RESULTS: CAVA enabled image recovery at various temporal resolutions that were selected retrospectively. For the pulsatile flow phantom, image quality and flow quantification accuracy from CAVA were comparable to that from another pseudo-random sampling pattern with fixed temporal resolution. In addition, flow quantification results based on CAVA were in good agreement with a breath-held segmented acquisition. CONCLUSIONS: By allowing retrospective binning of the MRI data, CAVA provides an avenue to retrospectively adjust the temporal resolution of PC-MRI.

A universal mathematical model applied to the congenital ventral penile curvature.

INTRODUCTION: The macroscopic dynamic of fetal penis development presents a pattern resembling the unfolding of a spiral, so congenital ventral penile curvature could indicate that this natural sequence has been interrupted. Our aim in this article is to offer a mathematical model of congenital ventral curvature of the penis. MATERIALS AND METHODS: Five individuals who presented with congenital ventral penile curvature and three who presented with acquired penile ventral curvature due to Peyronie's disease were evaluated. The penises were photographed during an induced erection test and the penile curvature patterns were compared with an equiangular spiral. When an association was found, a potential relationship to the golden spiral-a type of equiangular spiral-was also assessed. The mathematical spiral relationships were analyzed using Wolfram CDF Player® (Logarithmic Spiral) and PhiMatrix® software. The Wolfram software generated logarithmic spirals equivalent to the penile curvature with appropriate mathematical values. The PhiMatrix software, which builds any golden spirals from golden rectangles, was used to check whether the spiral was golden as well as equiangular. RESULTS: An equiangular spiral that was also golden was found in all cases of congenital ventral penile curvature. In contrast, none of the acquired penile ventral curvature cases showed a specific pattern. CONCLUSION: Congenital ventral penile curvature has the mathematical pattern of a golden spiral. Our results offer a mathematical algorithm for potential use in surgical reconstruction procedures, regenerative medicine, tissue engineering, robotics, and body-machine interfaces.

Transverse Ridge of Premolars and Oblique Ridge of Maxillary Molars are in Divine Golden Ratio.

AIMS: In premolars and molars, transverse ridge (TR) and oblique ridge (OR) play major roles in providing strength and stability to the cusps in particular and tooth as a whole. Hence, they could be divided at the central groove or the transverse groove in a divine golden ratio. MATERIALS AND METHODS: Twenty pairs of maxillary and mandibular casts were retrieved from the Department of Orthodontics. The lengths of buccal triangular ridge (BTR), lingual triangular ridge (LTR) and TR of maxillary and mandibular first and second premolars were measured. Similarly, lengths of distal cuspal ridge of mesiopalatal cusp, triangular ridge of distobuccal cusp (DBTR) and OR of the maxillary first and second molars were measured using a brass wire and a Vernier caliper. The TR:BTR, BTR:LTR, OR:distal ridge of mesiopalatal cusp (MPDR), and MPDR:DBTR ratios were calculated to find out the possibility of golden ratio. RESULTS: Transverse ridges of the premolars and OR of the maxillary first and second molars were divided at the central groove in a divine golden ratio. The mean TR/BTR ratio for maxillary first premolar was 1.61 ± 0.007, whereas the mean BTR/LTR ratio was 1.63 ± 0.02. The mean TR/BTR ratio for maxillary second premolar was 1.61 ± 0.01, whereas the mean BTR/LTR ratio was 1.62 ± 0.04. The TR/BTR and BTR/LTR ratios for mandibular first premolar were 1.6 ± 0.008 and 1.64 ± 0.02, respectively. Similarly, the mean TR/BTR ratio for mandibular second premolar was 1.61 ± 0.01, whereas the mean BTR/LTR ratio was 1.63 ± 0.02. CONCLUSION: The ORs of maxillary first molar ridge and TR of maxillary and mandibular premolars are divided into two parts at transverse and central grooves, respectively, in a divine ratio. CLINICAL RELEVANCE: The ORs of maxillary first molar ridge and TR of maxillary and mandibular premolars are divided into two parts at transverse and central grooves, respectively, in a divine ratio. This signifies the strength and stability of the occlusal table in the posterior teeth, as the golden ratio is the mark of functional excellence. Golden ratio should be taken into consideration while restoration or fabrication of the posterior teeth.

Golden ratio stack of spirals for flexible angiographic imaging: Proof of concept in congenital heart disease.

PURPOSE: In this study, a golden ratio stack of spiral (GRASS) sequence that used both golden step and golden angle ordering was implemented. The aim was to demonstrate that GRASS acquisitions could be flexibly reconstructed as both cardiac-gated and time-resolved angiograms. METHODS: Image quality of time-resolved and cardiac-gated reconstructions of the GRASS sequence were compared to 3 conventional stack of spirals (SoS) acquisitions in an in silico model. In 10 patients, the GRASS sequence was compared to conventional breath hold angiography (BH-MRA) in terms of image quality and for vessel measurement. Vessel measurements were also compared to cine images. RESULTS: In the cardiac-gated in silico model, the image quality of GRASS was superior to regular and golden-angle with regular step SoS approaches. In the time-resolved model, GRASS image quality was comparable to the golden-angle with regular step technique and superior to regular SoS acquisitions. In patients, there was no difference in qualitative image scores between GRASS and BH-MRA, but SNR was lower. There was good agreement in vessel measurements between the GRASS reconstructions and conventional MR techniques (BH-MRA: 29.8 ± 5.6 mm, time-resolved GRASS-MRA: 29.9 ± 5.4 mm, SSFP diastolic: 29.4 ± 5.8 mm, cardiac-gated GRASS-MRA diastolic: 29.5 ± 5.5 mm, P > 0.87). CONCLUSION: We have demonstrated that the GRASS acquisition enables flexible reconstruction of the same raw data as both time-resolved and cardiac-gated volumes. This may enable better interrogation of anatomy in congenital heart disease.

Golden ratio and phyllotaxis, a clear mathematical link.

Exploiting Markoff's theory for rational approximations of real numbers, we explicitly link how hard it is to approximate a given number to an idealized notion of growth capacity for plants which we express as a modular invariant function depending on this number. Assuming that our growth capacity is biologically relevant, this allows us to explain in a satisfying mathematical way why the golden ratio occurs in nature.

High-resolution dynamic oxygen-17 MR imaging of mouse brain with golden-ratio-based radial sampling and k-space-weighted image reconstruction.

PURPOSE: The current study aimed to develop a three-dimensional (3D) dynamic oxygen-17 (17 O) MR imaging method with high temporal and spatial resolution to delineate the kinetics of 17 O water uptake and washout in the brains of mice with glioblastoma (GBM). METHODS: A 3D imaging method with a stack-of-stars golden-ratio-based radial sampling scheme was employed to acquire 17 O signal in vivo. A k-space-weighted image reconstruction method was used to improve the temporal resolution while preserving spatial resolution. Simulation studies were performed to validate the method. Using this method, the kinetics of 17 O water uptake and washout in the brains of mice with GBM were delineated after an intravenous bolus injection of 17 O water. RESULTS: The proposed 17 O imaging method achieved an effective temporal resolution of 7.56 s with a nominal voxel size of 5.625 µL in the mouse brain at 9.4 T. Reduced uptake and prolonged washout of 17 O water were observed in tumor tissue, suggesting compromised cerebral perfusion. CONCLUSION: This study demonstrated a promising dynamic 17 O imaging approach that can delineate 17 O water kinetics in vivo with high temporal and spatial resolution. It can also be used to image cerebral oxygen consumption rate in oxygen-17 inhalation studies. Magn Reson Med 79:256-263, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Two-Stage Processing of Aesthetic Information in the Human Brain Revealed by Neural Adaptation Paradigm.

Some researchers in aesthetics assume visual features related to aesthetic perception (e.g. golden ratio and symmetry) commonly embedded in masterpieces. If this is true, an intriguing hypothesis is that the human brain has neural circuitry specialized for the processing of visual beauty. We presently tested this hypothesis by combining a neuroimaging technique with the repetition suppression (RS) paradigm. Subjects (non-experts in art) viewed two images of sculptures sequentially presented. Some sculptures obeyed the golden ratio (canonical images), while the golden proportion were impaired in other sculptures (deformed images). We found that the occipito-temporal cortex in the right hemisphere showed the RS when a canonical sculpture (e.g. Venus de Milo) was repeatedly presented, but not when its deformed version was repeated. Furthermore, the right parietal cortex showed the RS to the canonical proportion even when two sculptures had different identities (e.g. Venus de Milo as the first stimulus and David di Michelangelo as the second), indicating that this region encodes the golden ratio as an abstract rule shared by different sculptures. Those results suggest two separate stages of neural processing for aesthetic information (one in the occipito-temporal and another in the parietal regions) that are hierarchically arranged in the human brain.

Hand grip strength as a physical biomarker of aging from the perspective of a Fibonacci mathematical modeling.

BACKGROUND: The Golden Ratio (GR) and the Fibonacci sequence have wide applications in biodiversity research, and recent studies indicate that the GR can be highlighted in the organization and physiological functioning of many body systems. The aim of this cross-sectional descriptive study is to determine the applicability of a mathematical model derived from the Fibonacci sequence to investigate the changes in hand grip strength (HGS) induced by the aging process. METHODS: We assessed the HGS for both hands, using a Saehan hydraulic hand dynamometer in a group of autonomous elderly subjects. One hundred twenty 55-year-old subjects (58 males and 62 females) and seventy 89-year-old subjects (31 men and 39 women) were included in the study group. All subjects were completely independent or independent with minimal assistance in activities of daily living (ADL), as determined after applying the Barthel index of ADL. The data series were statistically processed using descriptive statistics (univariate analysis) and inferential statistical methods (the t test for unpaired groups, with effect size measure - Cohen's d and the ratio of the means method). RESULTS: The decline of the relative HGS between the two age groups can be expressed by values close to the GR value (p < 0.001), both in relation to body symmetry (left hand/right hand evaluation) and laterality (dominant hand/non-dominant hand evaluation), for both sexes. For the whole group of men and women, the rhythm of HGS decline may be expressed by a value (1.61) notably close to the GR, regardless of body symmetry or laterality. CONCLUSIONS: The common pattern of the relative HGS reduction between 55 and 89 years, as expressed by a value notably close to GR, can be considered to be an expression of a specific and predictable manifestation of the aging process, in the absence of disability.

Michelangelo buonarroti's code in the frescoes of the sistine chapel - an allusion to gematria of the hebrew/greek alphabet and the Golden Ratio.

According to Giorgio Vasari (1511-1574), the great genius of anatomy, Michelangelo Buonarroti (1475-1564), in painting the frescoes on the ceiling of the Sistine Chapel (1508-1512), demonstrated to the world a new dimension/perspective of painting, especially in the sublime manner with which the artist represented the anatomical details of the characters that made up his frescoes. Since then, the Sistine Chapel has received millions of tourists annually, who marvel at the anatomical beauty of the characters depicted on its ceiling. It has also received many scholars of art and even anatomists, who have often tried to infer theses and explanations regarding Michelangelo's real intentions in elaborating this great work. However, even after five centuries, the Vatican's own official explanations of the true intentions of the artist remain quite uncertain. In an attempt to elucidate Michelangelo's possible intentions in the design of this memorable work, this article presents unpublished evidence that all the frescoes on the ceiling of the Sistine Chapel were organized by the artist according to a code based on the number of characters in each fresco, the gematria of the Hebrew/Greek alphabet, and the Golden Ratio. This decoding process could reveal a key factor influencing the artist's intentions in ordering the elements in this work. Clin. Anat. 31:948-955, 2018. © 2018 Wiley Periodicals, Inc.

Golden-ratio rotated stack-of-stars acquisition for improved volumetric MRI.

PURPOSE: To develop and evaluate an improved stack-of-stars radial sampling strategy for reducing streaking artifacts. METHODS: The conventional stack-of-stars sampling strategy collects the same radial angle for every partition (slice) encoding. In an undersampled acquisition, such an aligned acquisition generates coherent aliasing patterns and introduces strong streaking artifacts. We show that by rotating the radial spokes in a golden-angle manner along the partition-encoding direction, the aliasing pattern is modified, resulting in improved image quality for gridding and more advanced reconstruction methods. Computer simulations were performed and phantom as well as in vivo images for three different applications were acquired. RESULTS: Simulation, phantom, and in vivo experiments confirmed that the proposed method was able to generate images with less streaking artifact and sharper structures based on undersampled acquisitions in comparison with the conventional aligned approach at the same acceleration factors. By combining parallel imaging and compressed sensing in the reconstruction, streaking artifacts were mostly removed with improved delineation of fine structures using the proposed strategy. CONCLUSIONS: We present a simple method to reduce streaking artifacts and improve image quality in 3D stack-of-stars acquisitions by re-arranging the radial spoke angles in the 3D partition direction, which can be used for rapid volumetric imaging. Magn Reson Med 78:2290-2298, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Segmented golden ratio radial reordering with variable temporal resolution for dynamic cardiac MRI.

PURPOSE: Golden ratio (GR) radial reordering allows for retrospective choice of temporal resolution by providing a near-uniform k-space sampling within any reconstruction window. However, when applying GR to electrocardiogram (ECG)-gated cardiac imaging, the k-space coverage may not be as uniform because a single reconstruction window is broken into several temporally isolated ones. The goal of this study was to investigate the image artifacts caused by applying GR to ECG-gated cardiac imaging and to propose a segmented GR method to address this issue. METHODS: Computer simulation and phantom experiments were used to evaluate the image artifacts resulting from three k-space sampling patterns (ie, uniform radial, conventional GR, and segmented GR). Two- and three-dimensional cardiac cine images were acquired in seven healthy subjects. Imaging artifacts due to k-space sampling nonuniformity were graded on a 5-point scale by an experienced cardiac imaging reader. RESULTS: Segmented GR provides more uniform k-space sampling that is independent of heart-rate variation than conventional GR. Cardiac cine images using segmented GR have significantly higher and more reliable image quality than conventional GR. CONCLUSION: Segmented GR successfully addresses the nonuniform sampling that occurs with combining conventional GR with ECG gating. This technique can potentially be applied to any ECG-gated cardiac imaging application to allow for retrospective selection of a reconstruction window. Magn Reson Med 76:94-103, 2016. © 2015 Wiley Periodicals, Inc.