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Robotic Brain Universe

How MRI sees the brain

Nuclear magnetic resonance, relaxation and k-space; structural, diffusion and functional MRI; their pitfalls; and AI, portable and 11.7 T scanners.

Intermediate · about 11 min · updated 2026-10-02 · awaiting clinical review

Illustrative simulation excitatory inhibitory

How protons in a magnetic field produce the signal; T1, T2 and image contrast; gradients, k-space and echo-planar imaging; BOLD fMRI and what it really measures; diffusion imaging in stroke; templates and automated segmentation used in this atlas; statistical and safety pitfalls; compressed sensing, learned reconstruction, portable low-field scanners, 11.7 T imaging and language decoding.

Contents
  1. Listening to the body's protons
  2. What MRI measures
  3. Why MRI transformed neuroscience
  4. How an image is made
  5. When signals change
  6. When MRI misleads or harms
  7. The mathematics of MRI
  8. Technology: AI, portable scanners and ultra-high fields
  9. Milestones
  10. Frontiers
  11. Check yourself

Listening to the body's protons

An MRI scanner makes pictures from the faint radio signals of atomic nuclei. In a magnetic field, hydrogen nuclei (protons) resonate at a frequency set by the field: 42.58 MHz for every tesla. Tune a radio to that frequency, tip the nuclei and listen as they relax, and the body becomes visible without a single incision.[1,2,3]

The physics earned a Nobel Prize in 1952; turning it into images earned another in 2003. Since then MRI has learned to see blood oxygen, the diffusion of water, and the activity of the working brain.[4,5,6,7]

The grey-scale sections you can cut through this atlas are a real MRI volume, the MNI ICBM 2009a T1 template, and the cortical surfaces come from FreeSurfer, software that builds models of the brain from T1-weighted scans. This reading explains how such images are made, what they can and cannot show, and where MRI is heading.[8,9]

What MRI measures

Resonance. In 1946 Purcell, Torrey and Pound reported resonance absorption by nuclear magnetic moments in a solid, and Bloch described nuclear induction: nuclei in a magnetic field absorb and emit radio waves at their resonant frequency. Bloch and Purcell shared the 1952 Nobel Prize in Physics for these methods of nuclear magnetic precision measurement.[2,3,4]

Relaxation. After a radio pulse tips them, the nuclei return to equilibrium in two ways, with two time constants: T1 (recovery along the field) and T2 (loss of the signal across it). Tissues differ in T1 and T2; in 1971 Damadian showed that malignant tumours in rats had relaxation times outside the range of the normal tissues studied.[2,10,11]

Contrast. Scans can be weighted towards T1, T2 or the density of protons. Templates such as those built by Fonov and colleagues come as T1-weighted, T2-weighted and proton density-weighted volumes of the same average anatomy.[12,13]

Key numbers

Proton resonance frequency per tesla
42.577 MHz[1]
Field strength of conventional clinical scanners
1.5–3 T[14]
Field of the portable bedside scanner studied at Yale
0.064 T[15]
Field of the Iseult human scanner
11.7 T[16]
Labels assigned to each voxel by FreeSurfer's whole-brain segmentation
37[17]

Why MRI transformed neuroscience

Structure in living people. MRI shows the brain's anatomy in detail in living people. Automated methods now label each voxel of a scan, distinguishing structures such as the caudate, putamen, thalamus and hippocampus with accuracy comparable to manual labelling, sensitive enough to detect volume changes that precede probable Alzheimer's disease.[9,17]

Activity without injection. Deoxyhaemoglobin is paramagnetic, so venous blood is a natural contrast agent. Ogawa and colleagues showed in 1990 that this blood-oxygenation-level-dependent (BOLD) contrast tracks blood oxygen in the brain; in 1992 Kwong and colleagues used it to make completely non-invasive maps of human brain activity.[6,18]

A common space. Templates define a common coordinate system so that scans from different people can be registered, segmented and compared; age-appropriate templates reduce bias when the anatomy differs from the adult average, as in children.[8,12]

How an image is made

Encoding position. In 1973 Lauterbur showed that adding magnetic field gradients, so that the field and hence the resonant frequency vary with position, lets nuclear magnetic resonance form images; the same year Mansfield and Grannell described the signal in terms of diffraction. The 2003 Nobel Prize in Physiology or Medicine went to Lauterbur and Mansfield 'for their discoveries concerning magnetic resonance imaging'.[5,19,20]

k-space. For many imaging methods, the scanner samples the object in the Fourier spatial-frequency domain, called k-space; the gradients steer which points are sampled when, and a Fourier transform turns the samples into an image. Echo-planar imaging, which grew from Mansfield's 1977 work on multi-planar imaging with spin echoes, is fast: Kwong and colleagues used it to map human brain activity with a temporal resolution of seconds.[18,21,22]

Echoes. A second radio pulse can refocus spins that have drifted out of phase, producing a spin echo; Hahn described spin echoes in 1950, and diffusion measurements are built on them.[7,13,23]

From protons to a pictureStrong static fieldprotons resonate at 42.58 MHzper teslaRadio-frequency pulsetips the magnetisationGradients encode positionthe resonant frequency variesacross the headEcho recordedthe signal is weighted by T1, T2or diffusionk-space filledsamples of the image's spatialfrequenciesImage reconstructedFourier transform, or learnedand sparse reconstruction
From protons to a picture. The basic chain shared by most MRI sequences. Reconstruction is classically a Fourier transform; compressed sensing and neural networks can recover images from fewer samples.[1,13,19,21,24,25]
Text version of the diagram
  1. Strong static field: protons resonate at 42.58 MHz per tesla. Leads to Radio-frequency pulse.
  2. Radio-frequency pulse: tips the magnetisation. Leads to Gradients encode position.
  3. Gradients encode position: the resonant frequency varies across the head. Leads to Echo recorded.
  4. Echo recorded: the signal is weighted by T1, T2 or diffusion. Leads to k-space filled.
  5. k-space filled: samples of the image's spatial frequencies. Leads to Image reconstructed.
  6. Image reconstructed: Fourier transform, or learned and sparse reconstruction.

When signals change

Seconds: the BOLD response. In Kwong and colleagues' 1992 study, flashing lights at 8 Hz raised the signal in primary visual cortex by about 1.8%, with a mean rise-time constant of 4.4 seconds for the BOLD-sensitive images: brain activity is seen through a slow blood response.[18]

Minutes: stroke. In cats, diffusion-weighted images showed ischaemic regions as early as 45 minutes after an artery was blocked, whereas T2-weighted images failed to show clear injury for 2–3 hours. Diffusion imaging measures an apparent diffusion coefficient that differs between normal and diseased tissue.[7,26]

Years: development. Because the brain changes as children grow, Fonov and colleagues built templates for specific age ranges between 4.5 and 18.5 years, from a large, carefully screened sample of healthy children.[12]

When MRI misleads or harms

What BOLD really shows. Recording neurons and fMRI at the same time in monkeys, Logothetis and colleagues found that local field potentials predicted the BOLD response better than spiking; BOLD seems to reflect an area's input and local processing more than its output.[27]

Statistics. Using real resting-state data and 3 million random group analyses, Eklund and colleagues showed that the parametric methods in the widely used packages SPM, FSL and AFNI were invalid for cluster-wise inference, inflating false positives, while a non-parametric permutation test gave nominal results.[28]

High-field artefacts. At 7 T and above, scanners face non-uniform radio-frequency fields, stronger susceptibility artefacts and greater radio-frequency energy deposition in tissue.[29]

Contrast agents. In a study of 381 patients, high signal in the dentate nucleus and globus pallidus on unenhanced T1-weighted images was related to the number of previous doses of gadolinium-based contrast.[30]

The mathematics of MRI

MRI rests on a resonance condition, two relaxation laws and the Fourier transform.[2,21]

Larmor frequency[1,16,29]
f0=γ2πB0,γ2π≈42.577 MHz T−1f_0 = \frac{\gamma}{2\pi} B_0, \qquad \frac{\gamma}{2\pi} \approx 42.577\ \mathrm{MHz\,T^{-1}}

Protons resonate at a frequency proportional to the magnetic field: about 63.9 MHz at 1.5 T, 127.7 MHz at 3 T, 298 MHz at 7 T and 498 MHz at 11.7 T.

Symbols in Larmor frequency
SymbolMeaningUnit
f0f_0resonant (Larmor) frequencyMHz
γ\gammagyromagnetic ratio of the protonrad s⁻¹ T⁻¹
B0B_0static magnetic fieldT
Relaxation[2,10,11]
Mz(t)=M0(1−e−t/T1),Mxy(t)=Mxy(0) e−t/T2M_z(t) = M_0\left(1 - e^{-t/T_1}\right), \qquad M_{xy}(t) = M_{xy}(0)\, e^{-t/T_2}

After a 90° pulse, magnetisation along the field recovers with time constant T1, while the measurable signal across the field decays with time constant T2. Tissues with different T1 and T2 give different signals at the same moment, which is the origin of image contrast.

Symbols in Relaxation
SymbolMeaningUnit
MzM_zmagnetisation along the static field—
MxyM_{xy}magnetisation across the field, which induces the signal—
M0M_0equilibrium magnetisation—
T1,T2T_1, T_2longitudinal and transverse relaxation timesms
The signal is a Fourier transform[19,20,21]
s(t)=∫ρ(r) e−i2π k(t)⋅r dr,k(t)=γ2π∫0tG(τ) dτs(t) = \int \rho(\mathbf{r})\, e^{-i 2\pi\, \mathbf{k}(t)\cdot\mathbf{r}}\, d\mathbf{r}, \qquad \mathbf{k}(t) = \frac{\gamma}{2\pi}\int_0^t \mathbf{G}(\tau)\, d\tau

With gradients switched on, the recorded signal at each moment is one sample of the Fourier transform of the image, at the point k reached by integrating the gradient over time. Filling k-space and inverting the transform gives the image.

Symbols in The signal is a Fourier transform
SymbolMeaningUnit
s(t)s(t)recorded signal—
ρ(r)\rho(\mathbf{r})weighted proton density at position r (the image)—
k(t)\mathbf{k}(t)position in k-space (spatial frequency)m⁻¹
G\mathbf{G}magnetic field gradientT/m
Apparent diffusion coefficient[7,23,26]
S=S0 e−b ADC  ⇒  ADC=1bln⁡S0SS = S_0\, e^{-b\,\mathrm{ADC}} \;\Rightarrow\; \mathrm{ADC} = \frac{1}{b}\ln\frac{S_0}{S}

Diffusion weighting makes the signal fall with the diffusion of water; measuring with and without it gives the apparent diffusion coefficient, which reflects all incoherent motions within a voxel. The early stroke study used b values of 1,413 s/mm².

Symbols in Apparent diffusion coefficient
SymbolMeaningUnit
S,S0S, S_0signal with and without diffusion weighting—
bbdiffusion weighting (b value)s/mm²
ADCADCapparent diffusion coefficientmm²/s
Compressed sensing[24]
m^=arg⁡min⁡m∥Ψm∥1subject to∥Fum−y∥2<ϵ\hat{m} = \arg\min_m \|\Psi m\|_1 \quad \text{subject to} \quad \|F_u m - y\|_2 < \epsilon

If an image is sparse in some transform (for example wavelets), it can be recovered from randomly undersampled k-space by finding the sparsest image consistent with the measured data. This lets scans run faster.

Symbols in Compressed sensing
SymbolMeaningUnit
mmthe image to reconstruct—
Ψ\Psisparsifying transform, such as wavelets or finite differences—
FuF_uundersampled Fourier transform (the scanner's measurement)—
yymeasured k-space data—
ϵ\epsilonallowed data mismatch, set by noise—

Technology: AI, portable scanners and ultra-high fields

AI reconstruction. AUTOMAP recast reconstruction as supervised learning: a deep neural network learns the mapping from raw sensor data to the image, and showed better noise immunity and fewer artefacts than hand-crafted reconstruction. The fastMRI project released a public dataset of raw k-space data from knee scans for developing machine-learning reconstruction.[25,32]

Raw k-space samplesLearned transformHidden featuresRefinementImage pixels
Learned reconstruction (schematic). A schematic of reconstruction as learning: a network trained on pairs of sensor data and images learns the transform between them, instead of a hand-designed chain of steps.[25]

Portable MRI. A portable low-field scanner imaged 50 critically ill patients at the bedside in intensive care with no adverse events, finding abnormalities in 29 of 30 patients without COVID-19. In a second study, with a 0.064 T scanner, neuroradiologists reading 144 examinations detected intracerebral haemorrhage with 80.4% sensitivity and 96.6% specificity.[14,15]

Ultra-high fields. Scanners at 7 T and above gain signal and contrast, allowing finer structures and smaller physiological effects to be seen. In 2024 the Iseult team reported in vivo human brain images at 11.7 T, with safety assessed using physiological, vestibular, behavioural and genotoxicity measurements.[16,29]

Field strength and frequency[1,14,15,16,29]
FieldProton frequencyExample
0.064 T2.7 MHzPortable bedside scanner
1.5–3 T63.9–127.7 MHzConventional clinical scanners
7 T298 MHzUltra-high-field human scanners
11.7 T498 MHzIseult human scanner

Milestones

From nuclear induction to 11.7 tesla

  1. 1946Purcell, Torrey and Pound report nuclear resonance absorption; Bloch describes nuclear induction.[2,3]
  2. 1952Bloch and Purcell share the Nobel Prize in Physics.[4]
  3. 1971Relaxation times distinguish tumours from normal tissue in rats.[11]
  4. 1973Lauterbur forms images with gradients; Mansfield and Grannell describe NMR 'diffraction'.[19,20]
  5. 1977Mansfield describes multi-planar imaging with spin echoes.[22]
  6. 1986Diffusion imaging in neurological disorders.[7]
  7. 1990BOLD contrast; diffusion imaging detects early ischaemia.[6,26]
  8. 1992Non-invasive maps of human brain activity with fMRI.[18]
  9. 2003Lauterbur and Mansfield receive the Nobel Prize in Physiology or Medicine.[5]
  10. 2016'Cluster failure' exposes inflated false positives in fMRI statistics.[28]
  11. 2018Deep learning reconstructs images directly from sensor data.[25]
  12. 2021Portable low-field MRI at the bedside.[14,15]
  13. 2023Continuous language decoded from fMRI.[33]
  14. 2024Human brain images at 11.7 T.[16]

Frontiers

Decoding language. A decoder trained on fMRI generated intelligible word sequences that recovered the meaning of speech a person heard or imagined, and even of silent videos. Testing mental privacy, the authors found that the person's cooperation was needed both to train and to apply the decoder.[33]

MRI everywhere. Low-field portable scanners could bring MRI to intensive care units and to resource-limited settings where conventional, access-controlled scanners are unavailable.[14,15]

Mesoscale imaging. At 11.7 T, T2- and T2*-weighted images approach mesoscale resolution within short acquisition times, with high signal and contrast-to-noise ratio.[16]

Check yourself

Check yourself

  1. At what frequency do protons resonate in a 3 T scanner?
    Show answer

    About 127.7 MHz (42.577 MHz per tesla × 3).

  2. What do T1 and T2 describe?
    Show answer

    T1 is the recovery of magnetisation along the field; T2 is the decay of the signal across it.

  3. What do magnetic field gradients do in MRI?
    Show answer

    They make the resonant frequency vary with position, encoding where the signal comes from (sampling k-space).

  4. What is BOLD contrast based on?
    Show answer

    Deoxyhaemoglobin is paramagnetic, so the MRI signal depends on blood oxygenation.

  5. Which neural signal best predicted the BOLD response in Logothetis's experiments?
    Show answer

    Local field potentials, rather than spiking output.

  6. Why did diffusion imaging matter for stroke?
    Show answer

    In cats it showed ischaemia within 45 minutes, while T2-weighted images showed no clear injury for 2–3 hours.

  7. What did 'Cluster failure' show?
    Show answer

    That common parametric methods for cluster-wise fMRI inference had inflated false-positive rates.

  8. What did the fMRI language decoder need from the person being decoded?
    Show answer

    Their cooperation, both to train and to apply the decoder.

Glossary[2,6,7,10,12,13,18,21,24]

Larmor frequency
The resonant frequency of nuclei in a magnetic field, proportional to the field.
T1
Time constant for magnetisation to recover along the main field.
T2
Time constant for the signal across the field to decay.
Gradient
A magnetic field that varies with position, used to encode location.
k-space
The spatial-frequency domain in which MRI data are sampled.
Spin echo
A signal regained by refocusing spins with a second pulse.
Echo-planar imaging
A fast imaging method that samples k-space rapidly, used for fMRI.
BOLD
Blood-oxygenation-level-dependent contrast, the basis of most fMRI.
Apparent diffusion coefficient
A measure of water diffusion within a voxel from diffusion-weighted images.
Template
An average brain image defining a common space for comparing scans.
Compressed sensing
Recovering a sparse image from undersampled measurements.

References

  1. National Institute of Standards and Technology. CODATA value: proton gyromagnetic ratio in MHz/T. The NIST Reference on Constants, Units, and Uncertainty. https://physics.nist.gov/cgi-bin/cuu/Value?gammapbar
  2. Bloch F. Nuclear induction. Physical Review 1946;70(7-8):460-474. doi:10.1103/PhysRev.70.460
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  4. Nobel Prize Outreach. The Nobel Prize in Physics 1952. NobelPrize.org 1952. https://www.nobelprize.org/prizes/physics/1952/summary/
  5. Nobel Prize Outreach. The Nobel Prize in Physiology or Medicine 2003. NobelPrize.org 2003. https://www.nobelprize.org/prizes/medicine/2003/summary/
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  16. Boulant N, Mauconduit F, Gras V, Amadon A, Le Ster C, Luong M, et al.. In vivo imaging of the human brain with the Iseult 11.7-T MRI scanner. Nature Methods 2024;21(11):2013-2016. doi:10.1038/s41592-024-02472-7
  17. Fischl B, Salat DH, Busa E, Albert M, Dieterich M, Haselgrove C, et al.. Whole Brain Segmentation. Neuron 2002;33(3):341-355. doi:10.1016/S0896-6273(02)00569-X
  18. Kwong KK, Belliveau JW, Chesler DA, Goldberg IE, Weisskoff RM, Poncelet BP, et al.. Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation. Proceedings of the National Academy of Sciences 1992;89(12):5675-5679. doi:10.1073/pnas.89.12.5675
  19. Lauterbur PC. Image formation by induced local interactions: examples employing nuclear magnetic resonance. Nature 1973;242(5394):190-191. doi:10.1038/242190a0
  20. Mansfield P, Grannell PK. NMR 'diffraction' in solids?. Journal of Physics C: Solid State Physics 1973;6(22):L422-L426. doi:10.1088/0022-3719/6/22/007
  21. Twieg DB. The k-trajectory formulation of the NMR imaging process with applications in analysis and synthesis of imaging methods. Medical Physics 1983;10(5):610-621. doi:10.1118/1.595331
  22. Mansfield P. Multi-planar image formation using NMR spin echoes. Journal of Physics C: Solid State Physics 1977;10(3):L55-L58. doi:10.1088/0022-3719/10/3/004
  23. Stejskal EO, Tanner JE. Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. The Journal of Chemical Physics 1965;42(1):288-292. doi:10.1063/1.1695690
  24. Lustig M, Donoho D, Pauly JM. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine 2007;58(6):1182-1195. doi:10.1002/mrm.21391
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Template anatomy for education. Not patient-specific. Not for clinical decision-making.