Concepts in Magnetic Resonance Part A最新文献

{"title":"The Discrete Fourier Transform as a Result of Numerically Optimized Magnetic Resonance Image Reconstruction Equations","authors":"Jochen Leupold","doi":"10.1155/cmr/9205245","DOIUrl":"https://doi.org/10.1155/cmr/9205245","url":null,"abstract":"<p>An approach is presented that provides a justification for the use of the discrete Fourier transform in magnetic resonance (MR) image reconstruction. Without a priori knowledge of the Fourier transform, an imaging experiment is described that corresponds to the common spatial encoding process by means of magnetic field gradients. A regular matrix, the so-called encoding matrix, describing a linear system of equations is obtained. The presented approach consists of numerical optimization of the encoding matrix by minimizing its condition number. To accomplish this, the necessary concepts of numerical analysis are thoroughly introduced, which reflects the educational character of the manuscript. As a result, we will see that a numerically optimized encoding matrix is equal to the discrete Fourier transform matrix; thus, an explanation for the use of the discrete Fourier transform in MR image reconstruction is obtained.</p>","PeriodicalId":55216,"journal":{"name":"Concepts in Magnetic Resonance Part A","volume":"2026 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmr/9205245","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148849033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Discrete Fourier Transform as a Result of Numerically Optimized Magnetic Resonance Image Reconstruction Equations","authors":"Jochen Leupold","doi":"10.1155/cmr/9205245","DOIUrl":"https://doi.org/10.1155/cmr/9205245","url":null,"abstract":"<p>An approach is presented that provides a justification for the use of the discrete Fourier transform in magnetic resonance (MR) image reconstruction. Without a priori knowledge of the Fourier transform, an imaging experiment is described that corresponds to the common spatial encoding process by means of magnetic field gradients. A regular matrix, the so-called encoding matrix, describing a linear system of equations is obtained. The presented approach consists of numerical optimization of the encoding matrix by minimizing its condition number. To accomplish this, the necessary concepts of numerical analysis are thoroughly introduced, which reflects the educational character of the manuscript. As a result, we will see that a numerically optimized encoding matrix is equal to the discrete Fourier transform matrix; thus, an explanation for the use of the discrete Fourier transform in MR image reconstruction is obtained.</p>","PeriodicalId":55216,"journal":{"name":"Concepts in Magnetic Resonance Part A","volume":"2026 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmr/9205245","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148849032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":55216,"journal":{"name":"Concepts in Magnetic Resonance Part A","volume":"2026 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148113133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":55216,"journal":{"name":"Concepts in Magnetic Resonance Part A","volume":"2026 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148080745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Erythrocyte Magnetics: Timescale of Alignment in NMR Spectrometers","authors":"Philip W. Kuchel,&nbsp;Stuart J. Elliott,&nbsp;Thomas R. Eykyn","doi":"10.1155/cmr/7473298","DOIUrl":"https://doi.org/10.1155/cmr/7473298","url":null,"abstract":"<p>Discocyte erythrocytes (red blood cells, RBCs) undergo spontaneous alignment in a uniform magnetic field, <b>B</b>₀—a phenomenon initially observed via optical dispersion and light microscopy and later confirmed with nuclear magnetic resonance (NMR) spectroscopy. The phenomenon arises due to the diamagnetic anisotropy of membrane lipids and proteins, which have different energies when oriented parallel or perpendicular to the magnetic field. This behavior is directly relevant to modern NMR experiments performed on cells, in particular multiple quantum filtering of quadrupolar nuclei with nuclear spin quantum number <i>I</i> &gt; ½, which are sensitive to the degree of alignment in intact cells and tissues, forming the basis of our present investigations. Using a quartic equation to represent the surface of a discocyte cell and the boundary element method to integrate over a triangular mesh, we compute the minimum-energy orientation of an RBC in <b>B</b>₀. At a field strength of <b>B</b>₀ = 9.4 T, the energy difference between parallel and orthogonal alignments was calculated to be ∼1200 <i>k</i>_<i>B</i> <i>T</i>, the latter being Boltzmann’s constant <i>k</i>_<i>B</i> times the absolute temperature <i>T</i>, which is the thermal energy of a single particle in solution. Using hydrodynamic theory, we estimate a characteristic realignment time (which has a theoretical 1/||<b>B</b>₀||² dependence) of ∼300 ms at this field strength and extend this to consider the effects of collective behavior in densely packed RBC suspensions. Our findings agree with experimental data showing subsecond reorientational dynamics in strong magnetic fields and provide a physical framework for interpreting magnetic-field-induced structural order in biological tissues, which inform the development of new NMR and magnetic resonance imaging (MRI) methodologies for probing anisotropy, membrane architecture, and cellular organization in vivo.</p>","PeriodicalId":55216,"journal":{"name":"Concepts in Magnetic Resonance Part A","volume":"2026 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmr/7473298","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148080744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":55216,"journal":{"name":"Concepts in Magnetic Resonance Part A","volume":"2026 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148080746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimized Phased Antenna Array for Deep-Targeted Microwave Hyperthermia in Brain Tumor Therapy","authors":"Haode Wang,&nbsp;Tongning Wu,&nbsp;Haoyu Jiang,&nbsp;Congsheng Li","doi":"10.1155/cmr/4206995","DOIUrl":"10.1155/cmr/4206995","url":null,"abstract":"<p>This study develops an optimized personalized microwave hyperthermia framework for glioblastoma treatment, integrating a 19-channel radiofrequency array of geometrically and electromagnetically co-optimized cosine-curved dipole antennas. We initiated the design by optimizing the conductor geometry (amplitude, wavelength, and phase offset) to reshape the current distribution. Concurrently, resonant coupling loops were incorporated to provide additional degrees of freedom for impedance tuning. This combined approach establishes a synergistic mechanism, thereby overcoming the limitations of ultra-high-frequency dipoles and achieving enhanced impedance matching at 2.45 GHz, which is demonstrated by an S₁₁ value of −19.2 dB obtained through particle swarm optimization. The semidefinite relaxation (SDR) algorithm optimizes channel excitations under a 72-W total power constraint to maximize the tumor-specific absorption rate while minimizing exposure to healthy tissue. Multianatomical electromagnetic–thermal validation confirms a treatment planning time of 0.31 min, representing a 50% speed improvement over particle swarm optimization. This delivers a precise 41.69°C mean tumor temperature with superior targeting quantified by a specific absorption rate amplification factor (SAF) of 4.46 and a hotspot-to-target quotient (HTQ) of 0.81. Parametric analysis reveals depth-progressive SAF attenuation from 4.33 at superficial positions to 2.67 at 4 cm depth alongside improved large-tumor targeting achieving SAF 4.63 and HTQ 0.75 at 5 cm diameter. A pediatric model exhibits heightened electromagnetic sensitivity showing SAF 5.02 versus less than 5% variation in adult models, establishing a clinically translatable pathway for precision brain hyperthermia. This work is a computational study validated entirely through in silico simulations, without involving in vivo or clinical experiments.</p>","PeriodicalId":55216,"journal":{"name":"Concepts in Magnetic Resonance Part A","volume":"2026 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmr/4206995","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147288449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rotational Invariance in Resting-State fMRI: A Geometric Framework for Understanding Signal Processing and Connectivity","authors":"Chisondi S. Warioba","doi":"10.1155/cmr/8852818","DOIUrl":"10.1155/cmr/8852818","url":null,"abstract":"<p>Resting-state functional MRI (rsfMRI) analysis relies on complex mathematical operations whose properties and pitfalls are often poorly understood, leading to interpretational errors and suboptimal processing choices. This work presents novel mathematical insights for rsfMRI analysis through three key contributions: (1) a unified geometric framework showing that all common preprocessing and analysis operations can be understood as rotations in time-series vector space, (2) identification of rotationally invariant properties that remain stable across different processing choices, and (3) mathematical equivalences between seemingly different connectivity measures. We demonstrate how the hemodynamic response function acts as a rotation operator in frequency space, derive closed-form expressions for the impact of preprocessing on effective degrees of freedom, and show that correlation and coherence measures can be unified through frequency-weighted integration. Common mathematical errors in the literature are identified and corrected with worked examples. This framework provides practical guidance for choosing connectivity measures, ordering preprocessing steps, and understanding the mathematical constraints imposed by operations such as global signal regression. By connecting abstract mathematical concepts to concrete rsfMRI applications, this work serves as both a theoretical foundation and a practical guide for researchers using functional connectivity methods. Practical applications include detecting network disruption in neuropsychiatric disorders (e.g., schizophrenia) with dramatically improved sensitivity, harmonizing multisite data without complex corrections, optimizing scan protocols for specific effect sizes, and providing robust quality control metrics that outperform traditional approaches.</p>","PeriodicalId":55216,"journal":{"name":"Concepts in Magnetic Resonance Part A","volume":"2026 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmr/8852818","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146130397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparison of Coil Combination Technique Performance for Phase Preservation in bSSFP","authors":"Krithika Balaji,&nbsp;Zimu Huo,&nbsp;Michael Mendoza,&nbsp;Michael Hoff,&nbsp;Anil A. Bharath,&nbsp;Peter J. Lally,&nbsp;Neal K. Bangerter","doi":"10.1155/cmr/8276955","DOIUrl":"https://doi.org/10.1155/cmr/8276955","url":null,"abstract":"<p>MR images are often acquired using a phased array of radiofrequency (RF) channels, with each RF channel being sensitive to only part of the object being scanned. The images collected from each RF channel are combined to generate a single image with higher SNR and more uniform sensitivity than can be obtained with a single channel alone. It is generally desirable to combine the images before performing any analysis in a quantitative imaging (QI) experiment—this way, the voxel-level signals input into the fitting model have high SNR. Computationally, it is often also more efficient than performing a quantitative fitting process on each channel image individually. Although fitting is typically performed on a voxel-level signal magnitude, certain pulse sequences like phase-cycled balanced steady-state free precession (pc-bSSFP) encode important information about tissue properties in the signal phase as well. Therefore, it is desirable to preserve the complex signal during the coil combination process in order for QI analyses to be reliable. While a variety of different coil combination techniques exist, there is little information on which ones best preserve phase for pc-bSSFP. Pc-bSSFP is of particular interest as the complex-valued images are used for relaxometry. This study compared the phase preservation performance of various coil combination techniques: Eigenvalue-based approach for iterative self-consistent parallel imaging reconstruction (ESPIRiT), simple phase robust coil combination (SRCC), full phase robust coil combination (FRCC), adaptive reconstruction (AR), and intrinsic multi-channel phase alignment (IMPA). These techniques were tested on pc-bSSFP data in both a simulated phantom and in vivo knee cartilage. The comparisons were conducted across a range of SNR levels to reflect realistic scenarios. Results showed that ESPIRiT, AR, and IMPA best preserved phase across the range of SNR levels tested.</p>","PeriodicalId":55216,"journal":{"name":"Concepts in Magnetic Resonance Part A","volume":"2025 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmr/8276955","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145686078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parameter Estimation in Two-Dimensional Biexponential Magnetic Resonance Relaxometry: A Case-Study Comparison of Frequentist and Bayesian Approaches","authors":"Tyler Hecht,&nbsp;Griffin S. Hampton,&nbsp;Ryan Neff,&nbsp;Richard G. Spencer,&nbsp;Pak-Wing Fok","doi":"10.1155/cmr/6678358","DOIUrl":"https://doi.org/10.1155/cmr/6678358","url":null,"abstract":"<p>In this paper, we contrast frequentist and Bayesian approaches to parameter estimation for a magnetic resonance (MR) relaxometry signal model which takes the form of a two-dimensional biexponential decay. The signal consists of two terms, each parameterized by an amplitude and a transverse and longitudinal relaxation time constant. There are two user-selected parameters, defining the two-dimensional character of the signal; these are an inversion time <i>T</i><i>I</i> and a set of echo times, <i>T</i><i>E</i>. Of particular interest is the fact that for two values of <i>T</i><i>I</i>, which we call the null points, the signal becomes a monoexponential function in <i>T</i><i>E</i>. Extracting the two parameters—the amplitude and decay constant—from the signal observed at or near a null point is particularly ill-posed since the monoexponential signal is highly overparameterized by the four parameter biexponential models. We seek to estimate these null points, which directly provide values for the longitudinal relaxation time constants, using both frequentist and Bayesian techniques. The frequentist approach uses nonlinear least squares (NLLS), and the Bayesian approach uses the Metropolis–Hastings algorithm. In addition to point estimates, both methods generate point clouds of parameter estimates representing uncertainties. Due to the symmetry of the biexponential model, these point clouds consist of two clusters. The variance of a single cluster and the separation between the two clusters, both of which capture the size of the point clouds, may be used as metrics for ill-posedness. Increasing point cloud size, indicating an undesired greater flexibility in parameter choice, illustrates a greater degree of ill-posedness. We find that both the frequentist and Bayesian approaches can estimate the null points using the extrema of these metrics and yield qualitatively similar and consistent results.</p>","PeriodicalId":55216,"journal":{"name":"Concepts in Magnetic Resonance Part A","volume":"2025 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmr/6678358","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144910452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}