Lawrence L. Wald
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Lawrence L. Wald has a total of 974 co-authors. Here are the top co-authors by number of shared publications:
- Jonathan R. Polimeni
Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, United States
38 shared publications Elfar Adalsteinsson
Harvard‐MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology Cambridge Massachusetts USA
32 shared publicationsKawin Setsompop
Department of Radiology, Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital and Harvard Medical School, Building 149, Room 2301, 13th Street, Charlestown, Boston, MA, 02129, USA
24 shared publicationsBruce R. Rosen
Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, USA
18 shared publicationsThomas Witzel
Q Bio Inc., San Carlos, USA
18 shared publications- Bastien Guerin
Martinos Center, MGH, Harvard Medical school
17 shared publications
Latest Publications
- 6 October 2026
- Published by Wiley in NMR in Biomedicine
- Vol. 39 (11)
Low‐Cost, Computer‐Free Spin Echo Generator Board
A Spin Echo Generator Board has been designed as an affordable tool for MR system quality assurance, demonstration, and education. Inspired by earlier work on inexpensive spin echo generator circuit boards, the board uses low‐cost digital timing circuits for pulse generation and mixers for RF pulse gating, without requiring a computer. It produces a simple rectangular excitation pulse followed by a refocusing pulse, with user‐adjustable pulse widths, TE, and TR delays. The board features an integrated T/R switch, pre‐amplifier, and an onboard 9‐V battery holder for standalone operation. External requirements include only a synthesizer, RF power amplifier, oscilloscope for display, and a tuned RF coil placed within a magnet. The hands‐on platform and real‐time feedback support practical applications, such as verifying signal generation and coil performance. In an educational setting, the board enables students to explore how variations in timing parameters influence MR signal behavior. It provides a transparent learning environment in which students can investigate fundamental MRI concepts, including flip angle, resonance, and T 2 relaxation, through direct experimentation. Functionality is demonstrated on a 0.5‐T tabletop magnet and 0.1‐T whole‐body MRI scanner.
- 6 October 2026
- Published by Wiley in NMR in Biomedicine
- Vol. 39 (11)
Low‐Cost, Computer‐Free Spin Echo Generator Board
A Spin Echo Generator Board has been designed as an affordable tool for MR system quality assurance, demonstration, and education. Inspired by earlier work on inexpensive spin echo generator circuit boards, the board uses low‐cost digital timing circuits for pulse generation and mixers for RF pulse gating, without requiring a computer. It produces a simple rectangular excitation pulse followed by a refocusing pulse, with user‐adjustable pulse widths, TE, and TR delays. The board features an integrated T/R switch, pre‐amplifier, and an onboard 9‐V battery holder for standalone operation. External requirements include only a synthesizer, RF power amplifier, oscilloscope for display, and a tuned RF coil placed within a magnet. The hands‐on platform and real‐time feedback support practical applications, such as verifying signal generation and coil performance. In an educational setting, the board enables students to explore how variations in timing parameters influence MR signal behavior. It provides a transparent learning environment in which students can investigate fundamental MRI concepts, including flip angle, resonance, and T 2 relaxation, through direct experimentation. Functionality is demonstrated on a 0.5‐T tabletop magnet and 0.1‐T whole‐body MRI scanner.
- 1 September 2026
- Published by Wolters Kluwer Health in Stroke
- Vol. 57 (9) , 2577-2589
Ultra-Low-Field Brain MRI for Point-of-Care Applications: A Technology Review
Magnetic resonance imaging (MRI) is a cornerstone of neurological care, serving as the gold standard for diagnosing pathologies, such as brain tumors and, together with computed tomography, stroke. However, the high capital costs, specialized infrastructure requirements such as expensive and bulky radiofrequency-shielding cages, and the operational complexity of conventional high-field scanners (1.5T and 3T) largely confine MRI to centralized imaging facilities. This scenario often leads to reliance on brain computed tomography or ultrasound in point-of-care settings, despite MRI’s superior soft-tissue contrast for diagnosis and prognosis. In the past decade, there has been renewed interest in compact and simplified ultra-low-field (under 0.1T) MRI scanners, fueled by advances in engineering and computing. Here, we review the recent developments in ultra-low-field brain MRI, which enable imaging in open environments and demonstrate initial clinical applicability in point-of-care settings. We also envision future developments along 3 focus areas (ie, hardware, imaging protocols, and data-driven image formation and analysis) to address the current limitations of image quality and contrast in ultra-low-field brain MRI systems.
- 1 September 2026
- Published by Wolters Kluwer Health in Stroke
- Vol. 57 (9) , 2577-2589
Ultra-Low-Field Brain MRI for Point-of-Care Applications: A Technology Review
Magnetic resonance imaging (MRI) is a cornerstone of neurological care, serving as the gold standard for diagnosing pathologies, such as brain tumors and, together with computed tomography, stroke. However, the high capital costs, specialized infrastructure requirements such as expensive and bulky radiofrequency-shielding cages, and the operational complexity of conventional high-field scanners (1.5T and 3T) largely confine MRI to centralized imaging facilities. This scenario often leads to reliance on brain computed tomography or ultrasound in point-of-care settings, despite MRI’s superior soft-tissue contrast for diagnosis and prognosis. In the past decade, there has been renewed interest in compact and simplified ultra-low-field (under 0.1T) MRI scanners, fueled by advances in engineering and computing. Here, we review the recent developments in ultra-low-field brain MRI, which enable imaging in open environments and demonstrate initial clinical applicability in point-of-care settings. We also envision future developments along 3 focus areas (ie, hardware, imaging protocols, and data-driven image formation and analysis) to address the current limitations of image quality and contrast in ultra-low-field brain MRI systems.
- Open Access
Peripheral Nerve Stimulation Optimized Pulses for EPI (POPE) allows high-resolution fMRI
Purpose: Recent improvements in MRI gradient design and amplifiers, advanced MRI scanners are now routinely utilizing slew rates of several hundred T/m/s. However, full gradient performance cannot be exploited in high-resolution EPI due to peripheral nerve stimulation (PNS) limits. We aim to characterize and mitigate these PNS constraints using a simple sequence modification: PNS-optimized EPI gradient pulse shapes. Methods: PNS-Optimized Pulses for EPI (POPE): we selectively reduce the slew rate of gradient pulses at periods of high predicted PNS spikes, while leaving the rest of the waveform unchanged. Results: POPE allows 7%-35% faster imaging of EPI protocols resolutions of 1mm-0.3mm resolutions without exceeding predicted PNS. With such improvements, POPE allows robust 0.3 mm isotropic fMRI protocols that would have exceeded safety limits without it. Conclusion: POPE facilitates locally precise fMRI activation mapping on clinical 7T scanners at spatial resolution that were previously unattainable due to PNS limitations.
Open AccessPeripheral Nerve Stimulation Optimized Pulses for EPI (POPE) allows high-resolution fMRI
Purpose: Recent improvements in MRI gradient design and amplifiers, advanced MRI scanners are now routinely utilizing slew rates of several hundred T/m/s. However, full gradient performance cannot be exploited in high-resolution EPI due to peripheral nerve stimulation (PNS) limits. We aim to characterize and mitigate these PNS constraints using a simple sequence modification: PNS-optimized EPI gradient pulse shapes. Methods: PNS-Optimized Pulses for EPI (POPE): we selectively reduce the slew rate of gradient pulses at periods of high predicted PNS spikes, while leaving the rest of the waveform unchanged. Results: POPE allows 7%-35% faster imaging of EPI protocols resolutions of 1mm-0.3mm resolutions without exceeding predicted PNS. With such improvements, POPE allows robust 0.3 mm isotropic fMRI protocols that would have exceeded safety limits without it. Conclusion: POPE facilitates locally precise fMRI activation mapping on clinical 7T scanners at spatial resolution that were previously unattainable due to PNS limitations.
- Open Access
- 23 April 2026
- Published by Elsevier in Journal of Magnetic Resonance
- Vol. 388, 108074
Theory of magnetic resonance in non-uniform, non-static, and non-unidirectional fields: From bending frames to kappa spaces
- 23 April 2026
- Published by Elsevier in Journal of Magnetic Resonance
- Vol. 388, 108074
Open AccessTheory of magnetic resonance in non-uniform, non-static, and non-unidirectional fields: From bending frames to kappa spaces
- Open Access
- 1 January 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Medical Imaging
- Vol. 45 (9) , 1
The Ritz Adjoint Method for MRI Pulse Design
High-field magnetic resonance imaging (MRI) suffers from pronounced magnetic field inhomogeneities and subject-specific field variations, motivating the inscanner design of individually tailored excitation pulses to exploit the full capabilities of high-field MRI. Contemporary methods may employ piecewise-constant (PWC) waveform parameterizations to design excitation pulses, which require many optimization variables and hinder rapid, inscanner customization. We represent the radiofrequency (RF) and gradient waveforms in a global waveform basis, demonstrated using a Chebyshev polynomial basis, to reduce problem dimensionality and accelerate convergence, while ensuring waveform smoothness. The adjoint method efficiently computes derivatives of the excitation objective function with respect to the basis coefficients, which each influence an entire waveform. GPU acceleration of derivative computation further reduces computation time, while system and safety constraints are enforced throughout the optimization. Using this global waveform basis yields an approximate five- to ten-fold speedup in subject-specific (tailored) pulse optimization for non-selective excitations and, in the best case, comparable gains for slice-selective designs, making real-time, subject-specific pulse optimization feasible even for advanced pulse types.
- 1 January 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Medical Imaging
- Vol. 45 (9) , 1
Open AccessThe Ritz Adjoint Method for MRI Pulse Design
High-field magnetic resonance imaging (MRI) suffers from pronounced magnetic field inhomogeneities and subject-specific field variations, motivating the inscanner design of individually tailored excitation pulses to exploit the full capabilities of high-field MRI. Contemporary methods may employ piecewise-constant (PWC) waveform parameterizations to design excitation pulses, which require many optimization variables and hinder rapid, inscanner customization. We represent the radiofrequency (RF) and gradient waveforms in a global waveform basis, demonstrated using a Chebyshev polynomial basis, to reduce problem dimensionality and accelerate convergence, while ensuring waveform smoothness. The adjoint method efficiently computes derivatives of the excitation objective function with respect to the basis coefficients, which each influence an entire waveform. GPU acceleration of derivative computation further reduces computation time, while system and safety constraints are enforced throughout the optimization. Using this global waveform basis yields an approximate five- to ten-fold speedup in subject-specific (tailored) pulse optimization for non-selective excitations and, in the best case, comparable gains for slice-selective designs, making real-time, subject-specific pulse optimization feasible even for advanced pulse types.
- Top Cited PapersOpen Access
- 23 October 2025
- Published by Springer Nature in Nature Neuroscience
- Vol. 28 (11) , 2380-2391
Cortical and subcortical mapping of the human allostatic–interoceptive system using 7 Tesla fMRI
The brain continuously anticipates the body’s energetic needs and prepares to meet them before they arise—a process called allostasis. To support allostasis, the brain continually models the body’s sensory state, a process known as interoception. Here we replicate and extend a large-scale system that supports allostasis and interoception in the human brain using ultrahigh precision 7 Tesla functional magnetic resonance imaging ( n = 90), improving precision in subgenual and pregenual anterior cingulate topography and expanding brainstem nuclei mapping. Our functional connectivity analyses provide corroborating evidence for more than 96% of the anatomical connections documented in nonhuman animal tract-tracing studies. This system also includes regions of dense intrinsic connectivity throughout the system, some of which were identified previously as part of the backbone of neural communication across the brain. These results reinforce the existing evidence for a whole-brain system that supports the modeling and regulation of the body’s internal milieu.
- 23 October 2025
- Published by Springer Nature in Nature Neuroscience
- Vol. 28 (11) , 2380-2391
Top Cited PapersOpen AccessCortical and subcortical mapping of the human allostatic–interoceptive system using 7 Tesla fMRI
The brain continuously anticipates the body’s energetic needs and prepares to meet them before they arise—a process called allostasis. To support allostasis, the brain continually models the body’s sensory state, a process known as interoception. Here we replicate and extend a large-scale system that supports allostasis and interoception in the human brain using ultrahigh precision 7 Tesla functional magnetic resonance imaging ( n = 90), improving precision in subgenual and pregenual anterior cingulate topography and expanding brainstem nuclei mapping. Our functional connectivity analyses provide corroborating evidence for more than 96% of the anatomical connections documented in nonhuman animal tract-tracing studies. This system also includes regions of dense intrinsic connectivity throughout the system, some of which were identified previously as part of the backbone of neural communication across the brain. These results reinforce the existing evidence for a whole-brain system that supports the modeling and regulation of the body’s internal milieu.
- Open Access
- 22 July 2025
- Published by Springer Nature in Nature Biomedical Engineering
- Vol. 10 (2) , 406
Publisher Correction: Ultra-high gradient connectomics and microstructure MRI scanner for imaging of human brain circuits across scales
- 22 July 2025
- Published by Springer Nature in Nature Biomedical Engineering
- Vol. 10 (2) , 406
Open AccessPublisher Correction: Ultra-high gradient connectomics and microstructure MRI scanner for imaging of human brain circuits across scales
- Top Cited PapersOpen Access
- 16 July 2025
- Published by Springer Nature in Nature Biomedical Engineering
- Vol. 10 (2) , 309-324
Ultra-high gradient connectomics and microstructure MRI scanner for imaging of human brain circuits across scales
Defining the connectome, the complete matrix of structural connections between the nervous system nodes, is a challenge for human systems neuroscience due to the range of scales that must be bridged. Here we report the design of the Connectome 2.0 human magnetic resonance imaging (MRI) scanner to perform connectomics at the mesoscopic and microscopic scales with strong gradients for in vivo human imaging. We construct a 3-layer head-only gradient coil optimized to minimize peripheral nerve stimulation while achieving a gradient strength of 500 mT m −1 and a slew rate of 600 T m −1 s −1 , corresponding to a 5-fold greater gradient performance than state-of-the-art research gradient systems, including the original Connectome (Connectome 1.0) scanner. We find that gains in sensitivity of up to two times were achieved by integrating a 72-channel in vivo head coil and a 64-channel ex vivo whole-brain radiofrequency coil with built-in field monitoring for data fidelity. We demonstrate mapping of fine white matter pathways and inferences of cellular and axonal size and morphology approaching the single-micron level, with at least a 30% sensitivity improvement compared with Connectome 1.0.
- 16 July 2025
- Published by Springer Nature in Nature Biomedical Engineering
- Vol. 10 (2) , 309-324
Top Cited PapersOpen AccessUltra-high gradient connectomics and microstructure MRI scanner for imaging of human brain circuits across scales
Defining the connectome, the complete matrix of structural connections between the nervous system nodes, is a challenge for human systems neuroscience due to the range of scales that must be bridged. Here we report the design of the Connectome 2.0 human magnetic resonance imaging (MRI) scanner to perform connectomics at the mesoscopic and microscopic scales with strong gradients for in vivo human imaging. We construct a 3-layer head-only gradient coil optimized to minimize peripheral nerve stimulation while achieving a gradient strength of 500 mT m −1 and a slew rate of 600 T m −1 s −1 , corresponding to a 5-fold greater gradient performance than state-of-the-art research gradient systems, including the original Connectome (Connectome 1.0) scanner. We find that gains in sensitivity of up to two times were achieved by integrating a 72-channel in vivo head coil and a 64-channel ex vivo whole-brain radiofrequency coil with built-in field monitoring for data fidelity. We demonstrate mapping of fine white matter pathways and inferences of cellular and axonal size and morphology approaching the single-micron level, with at least a 30% sensitivity improvement compared with Connectome 1.0.
- Open Access
- 8 June 2025
- Published by Wiley in Magnetic Resonance in Medicine
- Vol. 94 (5) , 2268-2285
Strong gradients, cool performance: A 64‐channel array coil with concurrent field monitoring and thermal control for ex vivo diffusion‐weighted brain imaging using the 3T connectome 2.0 MRI scanner
Purpose: High‐resolution ex vivo diffusion‐weighted imaging (dMRI) with high ‐values presents significant challenges, including low signal‐to‐noise ratio (SNR), magnetic field perturbations, and temperature‐related measurement shifts. This work introduces a hardware‐based solution to address these limitations in human ex vivo brain imaging.Methods: A customized anatomically conformal 64‐channel receive array coil with a dedicated Tx birdcage coil was developed for 3T diffusion‐weighted imaging of whole human ex vivo brain specimens. Field monitoring capabilities were integrated to correct spatiotemporal field perturbations caused by gradient‐induced eddy currents. Temperature stability throughout extended acquisition periods was achieved through an integrated stabilization system. Coil performance was validated through comprehensive measurement of SNR, g‐factor maps, field camera free induction decays (FIDs), temperature, mean diffusivity, and fractional anisotropy across multiple diffusion‐weighted scans.Results: The system demonstrated 73% higher SNR compared with a 72‐channel in vivo head coil. Integration of the field camera maintained its FID quality without SNR penalties or significant receive coil coupling effects. Temperature stabilization improved the reliability of quantitative diffusion‐weighted measurements by eliminating measurement drift during a 13‐hour acquisition, where mean diffusivity and mean kurtosis would have increased by 22% and decreased by 19%, respectively.Conclusion: We describe an integrated hardware approach for addressing higher order field perturbations, thermal instability, and SNR challenges in human ex vivo whole brain dMRI under high‐diffusion sensitizing gradient conditions. This approach combines an anatomically optimized multichannel receive array, concurrent field monitoring, and active temperature stabilization. Enhanced image quality and improved reliability of quantitative MR imaging were demonstrated with this comprehensive hardware solution.
- 8 June 2025
- Published by Wiley in Magnetic Resonance in Medicine
- Vol. 94 (5) , 2268-2285
Open AccessStrong gradients, cool performance: A 64‐channel array coil with concurrent field monitoring and thermal control for ex vivo diffusion‐weighted brain imaging using the 3T connectome 2.0 MRI scanner
Purpose: High‐resolution ex vivo diffusion‐weighted imaging (dMRI) with high ‐values presents significant challenges, including low signal‐to‐noise ratio (SNR), magnetic field perturbations, and temperature‐related measurement shifts. This work introduces a hardware‐based solution to address these limitations in human ex vivo brain imaging.Methods: A customized anatomically conformal 64‐channel receive array coil with a dedicated Tx birdcage coil was developed for 3T diffusion‐weighted imaging of whole human ex vivo brain specimens. Field monitoring capabilities were integrated to correct spatiotemporal field perturbations caused by gradient‐induced eddy currents. Temperature stability throughout extended acquisition periods was achieved through an integrated stabilization system. Coil performance was validated through comprehensive measurement of SNR, g‐factor maps, field camera free induction decays (FIDs), temperature, mean diffusivity, and fractional anisotropy across multiple diffusion‐weighted scans.Results: The system demonstrated 73% higher SNR compared with a 72‐channel in vivo head coil. Integration of the field camera maintained its FID quality without SNR penalties or significant receive coil coupling effects. Temperature stabilization improved the reliability of quantitative diffusion‐weighted measurements by eliminating measurement drift during a 13‐hour acquisition, where mean diffusivity and mean kurtosis would have increased by 22% and decreased by 19%, respectively.Conclusion: We describe an integrated hardware approach for addressing higher order field perturbations, thermal instability, and SNR challenges in human ex vivo whole brain dMRI under high‐diffusion sensitizing gradient conditions. This approach combines an anatomically optimized multichannel receive array, concurrent field monitoring, and active temperature stabilization. Enhanced image quality and improved reliability of quantitative MR imaging were demonstrated with this comprehensive hardware solution.
- Open Access
- 15 May 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Translational Engineering in Health and Medicine
- Vol. 13, 275-285
Measurement of Peripheral Nerve Magnetostimulation Thresholds of a Head Solenoid Coil Between 200 Hz and 88.1 kHz
Objective: Magnetic fields switching at kilohertz frequencies induce electric fields in the body, which can cause peripheral nerve stimulation (PNS). Although magnetostimulation has been extensively studied below 10 kHz, the behavior of PNS at higher frequencies remains poorly understood. This study aims to investigate PNS thresholds at frequencies up to 88.1 kHz and to explore deviations from the widely accepted hyperbolic strength-duration curve (SDC). Methods and procedures: PNS thresholds were measured in the head of 8 human volunteers using a solenoidal coil at 16 distinct frequencies, ranging from 200 Hz to 88.1 kHz. A hyperbolic SDC was used as a reference to compare the frequency-dependent behavior of PNS thresholds. Results: Contrary to the predictions of the hyperbolic SDC, PNS thresholds did not decrease monotonically with frequency. Instead, thresholds reached a minimum near 25 kHz, after which they increased by an average of 39% from 25 kHz to 88.1 kHz across subjects. This pattern indicates a significant deviation from previously observed behavior at lower frequencies. Conclusion: Our results suggest that PNS thresholds exhibit a non-monotonic frequency dependence at higher frequencies, diverging from the traditional hyperbolic SDC. These findings offer critical data for refining neurodynamic models and provide insights for setting PNS safety limits in applications like MRI gradient coils and magnetic particle imaging (MPI). Further investigation is needed to understand the biological mechanisms driving these deviations beyond 25 kHz. Clinical impact: These findings call for further basic research into biological mechanisms underlying high frequency PNS threshold trends, and supports refinement of safety guidelines for MRI and MPI systems for clinical implementation.
- 15 May 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Translational Engineering in Health and Medicine
- Vol. 13, 275-285
Open AccessMeasurement of Peripheral Nerve Magnetostimulation Thresholds of a Head Solenoid Coil Between 200 Hz and 88.1 kHz
Objective: Magnetic fields switching at kilohertz frequencies induce electric fields in the body, which can cause peripheral nerve stimulation (PNS). Although magnetostimulation has been extensively studied below 10 kHz, the behavior of PNS at higher frequencies remains poorly understood. This study aims to investigate PNS thresholds at frequencies up to 88.1 kHz and to explore deviations from the widely accepted hyperbolic strength-duration curve (SDC). Methods and procedures: PNS thresholds were measured in the head of 8 human volunteers using a solenoidal coil at 16 distinct frequencies, ranging from 200 Hz to 88.1 kHz. A hyperbolic SDC was used as a reference to compare the frequency-dependent behavior of PNS thresholds. Results: Contrary to the predictions of the hyperbolic SDC, PNS thresholds did not decrease monotonically with frequency. Instead, thresholds reached a minimum near 25 kHz, after which they increased by an average of 39% from 25 kHz to 88.1 kHz across subjects. This pattern indicates a significant deviation from previously observed behavior at lower frequencies. Conclusion: Our results suggest that PNS thresholds exhibit a non-monotonic frequency dependence at higher frequencies, diverging from the traditional hyperbolic SDC. These findings offer critical data for refining neurodynamic models and provide insights for setting PNS safety limits in applications like MRI gradient coils and magnetic particle imaging (MPI). Further investigation is needed to understand the biological mechanisms driving these deviations beyond 25 kHz. Clinical impact: These findings call for further basic research into biological mechanisms underlying high frequency PNS threshold trends, and supports refinement of safety guidelines for MRI and MPI systems for clinical implementation.