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Felix Bloch's equations underpin MRI

In 1946 Felix Bloch wrote the Bloch equations for nuclear magnetisation, introducing the T1 and T2 relaxation times that later helped make MRI a powerful medical tool.

Felix Bloch
Felix Bloch · 1905–1983
Person
Felix Bloch
Lived
1905–1983
Field
Physics
From
Swiss-American

The story

Within months of returning to Stanford in the autumn of 1945, Felix Bloch and his Stanford colleagues William Hansen and Martin Packard succeeded in detecting radio signals from atomic nuclei, a method Bloch called nuclear induction. Their first sample was ordinary water, and the signal came from the protons in its hydrogen atoms. Detecting the signal was only half the challenge. Physicists also needed a way to describe how the nuclear magnetisation of a sample behaves over time once it is disturbed.

In a theoretical paper that accompanied the experimental demonstration in 1946, Bloch provided that description. His Bloch equations are a set of equations of motion for nuclear magnetisation. They describe how the tiny nuclear magnets precess in a magnetic field and how they relax back toward equilibrium afterwards.

The key to the equations was two parameters that Bloch introduced. The longitudinal relaxation time, T1, describes how quickly the magnetisation realigns with the main magnetic field. The transverse relaxation time, T2, describes how quickly the nuclei fall out of step with each other as they precess. Both depend on how each nucleus interacts with the atoms and molecules around it, so they reflect chemical bonding and biological processes in the material being studied. Between 1950 and 1957 Bloch and R. K. Wangsness worked out a microscopic explanation of why these two parameters behave as they do.

Decades later Paul Lauterbur and others developed a way to turn Bloch's technique into pictures. By applying a magnetic field that varies across space, they linked each resonance frequency to a position, so the signals could be mapped into an image. The result was magnetic resonance imaging, or MRI. Writing in 1994, Robert Hofstadter judged it probably the greatest advance in medical imaging since Röntgen discovered X-rays in 1895.

Bloch's T1 and T2 are much of what gives MRI its power. Because relaxation times differ from one kind of tissue to another, and change with physiological and metabolic processes, scanners can be set to bring out contrasts that X-rays cannot show. Radiologists speak of T1-weighted and T2-weighted images, and the Bloch equations remain the starting point for understanding and designing scanning methods.

Why it matters

MRI lets doctors see soft tissue inside the body in fine detail without ionising radiation, aiding the diagnosis of cancers, strokes, injuries and many other conditions.

About Felix Bloch

Swiss-born physicist who laid the quantum foundations of solid-state physics, discovered nuclear magnetic resonance – the basis of MRI – and became CERN’s first director-general.

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Felix Bloch
1905–1983 · Physics
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