Hydrogen and the MR signal: fMRI from zero, lesson 2

Part 2 of 32 · Beginner · fMRI from zero: the series

Every fMRI picture starts as a faint radio signal from the hydrogen in your brain's water. This lesson explains where that signal comes from, in four steps: protons, a magnet, a radio pulse and a coil.

The one-sentence idea

In a strong magnet, hydrogen protons line up a little, and a radio pulse makes them send a signal back.

Explain it simply

The brain is about three quarters water. Each water molecule has two hydrogen atoms, and the centre of each one is a single proton. A proton spins, and that makes it a tiny magnet.

Outside a scanner, these tiny magnets point every way. They cancel out, so there is nothing to measure.

Step 1: the magnet. The scanner's main field, B0, is strong: 3 tesla is about 60,000 times the Earth's field.

In it, the protons wobble around the field direction, like spinning tops. This wobble is called precession.

Step 2: a tiny excess. Slightly more protons point along the field than against it. Their sum is one small magnet, the net magnetisation, written M.

Step 3: the radio pulse. The scanner sends a short radio pulse. It only works at one frequency, the speed of the wobble.

Think of pushing a child on a swing: you must push in time with the swing. The pulse tips M over on its side.

Step 4: the signal. Tipped M keeps turning, like a magnet spinning near a wire.

A receive coil around the head picks this up as a faint radio wave. That wave is the raw MR signal.

For a data engineer, it is like a huge sensor array:

MRI word	Data engineering view
Proton	One tiny sensor with a random reading
Net magnetisation	The average of billions of readings: random noise cancels, a small bias remains
RF pulse	A broadcast on one exact channel; only listeners on that channel react
Receive coil	The antenna that records the reply as a time series

Go one level deeper

The Larmor frequency. The wobble has a fixed speed, set by the field: 42.58 MHz per tesla for hydrogen.

Field	Turns per second
1.5 T	about 64 million (63.9 MHz)
3 T	about 128 million (127.7 MHz)
7 T	about 298 million (298 MHz)

These are radio frequencies, which is why the pulse is called an RF pulse.

How tiny is the excess? At 3 T and body temperature, only about 10 in every million protons make it.

But a 2 mm cube of brain holds about 400 billion billion protons. So the tiny excess still adds up to a magnet the coil can hear.

Why tip it over? M along the field doesn't change, so it makes no signal. Once it turns sideways, its field sweeps past the coil and makes a small voltage.

What happens next. The signal fades within tens of milliseconds, and M slowly grows back along the field.

These two clocks, T2* and T1, are the next lesson. BOLD fMRI reads the signal during that fast fade.

Visual: four steps to a signal

Try it yourself: switch the magnet on, change the field strength and fire the pulse.

Why it matters for data analysis

• The scanner records radio waves, not pictures. Each coil records a time series, and lesson 8 shows how these become images. Most datasets share only the final images (DICOM or NIfTI files).
• Field strength is key metadata. It is stored in the DICOM header and in BIDS as MagneticFieldStrength. Data from 1.5 T and 3 T scanners differ, so record it and use it when you combine datasets.
• Stronger magnets give more signal. The signal grows roughly in step with the field. That is why research uses 3 T and 7 T, but stronger fields also bring more distortion.
• Anything with hydrogen shows up. Water in tissue, blood and the fluid around the brain all give signal. How fast each one fades makes the contrast between them.

Key terms

Term	Meaning
Proton	The centre of a hydrogen atom; it acts like a tiny magnet
B0	The scanner's main magnetic field, measured in tesla (T)
Precession	The wobble of a proton around the field direction
Larmor frequency	The speed of that wobble: 42.58 MHz per tesla for hydrogen
Net magnetisation (M)	The sum of all the tiny magnets in a voxel
RF pulse	A short radio pulse at the Larmor frequency that tips M over
Receive coil	The antenna around the head that picks up the signal

Check yourself

1. Why does MRI use hydrogen? It is the most common atom in the body, mostly in water and fat. Each hydrogen proton acts as a small magnet, so it gives a strong signal.
2. What is the Larmor frequency at 1.5 T? 42.58 × 1.5 = about 63.9 MHz.
3. Why must the radio pulse be at exactly the Larmor frequency? Only a pulse in time with the protons' wobble can tip them, like pushing a swing at the right moment. Other frequencies have almost no effect.

Go further

• Hydrogen and the MR signal, the interactive page for this lesson.
• Elster A. D. Questions and Answers in MRI. Short, clear answers on every part of MRI physics.
• McRobbie D. W. et al. (2017). MRI from Picture to Proton, 3rd ed. Cambridge University Press. A friendly book on how MRI works.

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For learning only, not medical advice.

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