CASRAI Dictionary

Tag: measurement

  • MRI: The Physics of the Measurement Explained

    Magnetic resonance imaging (MRI) is a measurement technique that produces spatial maps of nuclear magnetic resonance signals, most often from the hydrogen nuclei (protons) abundant in water and fat. An MRI scanner places a sample in a strong static magnetic field, excites the nuclei with radiofrequency pulses, and records the faint signal the nuclei emit as they return to equilibrium. This article describes the physics of how that signal is produced, localised and reconstructed. It is a methods explainer about the instrument and the measurement, not an account of how any individual image should be interpreted.

    The starting point: nuclear spin in a magnetic field

    Certain atomic nuclei, including the single proton of hydrogen-1, possess an intrinsic quantum property called spin, which gives them a small magnetic moment. In the absence of an external field these moments point in random directions and there is no net magnetisation. When the sample is placed inside the scanner’s strong static field, conventionally labelled B0 and measured in tesla, the moments adopt a slight preferential alignment with the field. The result is a small bulk magnetisation along the field direction.

    Within that field the nuclei precess, wobbling like a spinning top, at a characteristic frequency. This is the Larmor frequency, and it is proportional to the field strength: stronger fields produce higher precession frequencies and, all else being equal, a larger signal. The proportionality constant is the gyromagnetic ratio, a fixed property of each nucleus. For hydrogen at clinical and research field strengths the Larmor frequency falls in the radiofrequency band, which is why radio waves are the natural tool for manipulating the spins.

    Excitation: the radiofrequency pulse

    To generate a measurable signal, the scanner transmits a radiofrequency (RF) pulse tuned precisely to the Larmor frequency. Because the pulse matches the precession frequency, energy is transferred efficiently to the spin system, a condition known as resonance. The pulse tips the bulk magnetisation away from the static-field axis and into the transverse plane, where its rotation induces a small oscillating voltage in a nearby receiver coil. That induced voltage is the raw MRI signal.

    Once the pulse is switched off, the magnetisation begins to return to its equilibrium alignment. The way it returns carries information about the local molecular environment, and this is the basis of MRI contrast.

    Relaxation: T1 and T2

    Two largely independent relaxation processes govern the recovery. T1, the longitudinal or spin-lattice relaxation time, describes how quickly the magnetisation re-grows along the static-field axis as the spins release energy to their surroundings. T2, the transverse or spin-spin relaxation time, describes how quickly the rotating magnetisation loses coherence as individual spins drift out of phase with one another. A related quantity, T2*, includes additional dephasing caused by small imperfections in the field.

    Parameter What it describes Physical cause
    T1 Recovery of magnetisation along B0 Energy exchange with the molecular lattice
    T2 Loss of phase coherence in the transverse plane Spin-spin interactions
    T2* Faster transverse decay including field inhomogeneity Local field variations plus spin-spin effects

    Different materials have different T1 and T2 values, so by choosing when to excite and when to measure, an experimenter weights the signal towards one relaxation property or another. This is what produces the visible distinction between tissues in a reconstructed image, and it is a property of the measurement parameters rather than an interpretation of the sample.

    Spatial encoding: turning signal into an image

    A plain RF excitation tells you the total resonance signal but nothing about where in the sample it came from. MRI solves this with gradient coils that superimpose small, controlled, spatially varying magnetic fields on top of B0. Because the Larmor frequency depends on field strength, a gradient makes the precession frequency vary with position. The scanner uses three orthogonal gradients in a carefully timed sequence: a slice-selection gradient applied during the RF pulse so that only one plane is excited, a frequency-encoding gradient that makes frequency map onto one in-plane axis, and a phase-encoding gradient that imprints position onto the signal phase along the other axis.

    The signals collected under these gradients fill a raw data matrix known as k-space, which represents the spatial frequencies of the object rather than the picture itself. Applying an inverse Fourier transform to k-space converts those spatial frequencies into the familiar image. The reconstruction is a mathematical operation on measured data, and understanding it is essential to reporting a study reproducibly; our guide on reporting analytical methods reproducibly covers how acquisition parameters should be documented.

    Why MRI sits alongside other measurement techniques

    MRI is one of several physical techniques researchers use to probe matter without contact. It shares the pulse-and-detect logic of ultrasound, and like time-domain spectroscopy it relies on a Fourier transform to move between a measured signal and an interpretable representation. Standard vocabulary for describing such methods in the research record is maintained in the CASRAI dictionary, and the broader context of where measurement sits in a project appears across our research lifecycle coverage.

    Frequently asked questions

    Why does MRI use hydrogen nuclei?

    Hydrogen is overwhelmingly the most abundant magnetically active nucleus in water- and fat-containing samples, and it has a relatively large gyromagnetic ratio, which together give the strongest signal. Other nuclei such as phosphorus-31 or carbon-13 can be imaged in specialised research spectroscopy, but they produce much weaker signals.

    What does field strength change in the measurement?

    A higher static field raises the Larmor frequency and increases the equilibrium magnetisation, which generally improves signal-to-noise ratio and allows finer spatial detail or faster acquisition. It also changes relaxation behaviour and engineering demands, so field strength is a key parameter to record when reporting a method.

    What is k-space?

    K-space is the raw data domain in which MRI signals are collected. Each point encodes a spatial frequency of the object, and the full image is obtained by an inverse Fourier transform of the completed k-space matrix. It is a representation of the measurement, not the picture itself.

    Is MRI quantitative?

    The underlying parameters, including T1, T2 and proton density, are physical quantities that can in principle be measured numerically. Quantitative MRI sequences aim to recover these values rather than weighted contrasts, which is why precise reporting of acquisition settings is essential for reproducibility, as discussed in our reproducibility coverage and the guidance for authors.

  • Ultrasound: How the Technique Works

    Ultrasound is a measurement technique that probes a material by transmitting high-frequency sound pulses and timing the echoes that bounce back from internal boundaries. Because the speed of sound in a medium is approximately known, the time an echo takes to return can be converted into a depth, and the strength of the echo into a brightness value. Repeating this across many directions builds a map of acoustic boundaries. This article explains the physics of how the technique produces a measurement; it is not a guide to interpreting any particular image.

    What ultrasound actually is

    Sound is a mechanical pressure wave that travels through a medium by compressing and rarefying the material. Audible sound spans roughly twenty hertz to twenty kilohertz; ultrasound is simply sound above the upper limit of human hearing. Research and imaging systems typically use frequencies of a few megahertz, far higher than audible sound. Frequency matters because it sets the wavelength, and the wavelength sets the finest detail the wave can resolve: higher frequencies give finer resolution but are absorbed more strongly and therefore penetrate less deeply. Choosing a frequency is a trade-off between resolution and penetration, and it is a parameter worth recording in any methods description.

    The piezoelectric transducer

    The heart of an ultrasound system is the transducer, which both transmits and receives sound. It relies on the piezoelectric effect: certain crystals and ceramics change shape when a voltage is applied across them, and conversely generate a voltage when mechanically deformed. To transmit, the system applies a short electrical pulse, the element flexes and pushes on the medium, launching a brief pressure wave. To receive, the same element is left to vibrate when an echo arrives, and its deformation generates a small voltage that the electronics amplify and record. A single transducer therefore acts as both loudspeaker and microphone, switching rapidly between the two roles.

    Modern systems use arrays of many small elements. By firing the elements with carefully staggered timing, the system can steer and focus the beam electronically, sweeping it across the field of view without moving the device. This beam-forming is purely a matter of controlled timing and interference of the emitted waves.

    Pulse-echo and time-of-flight

    The core measurement is pulse-echo. The transducer emits a short pulse, then listens. Whenever the pulse crosses a boundary between materials with different acoustic properties, part of it reflects back. The system measures the time-of-flight, the interval between emission and the return of each echo, and converts it to a distance using the relationship that depth equals the speed of sound multiplied by the round-trip time, divided by two. The division by two accounts for the wave travelling to the boundary and back.

    Quantity measured Derived information Physical basis
    Echo arrival time Depth of the boundary Speed of sound times time, halved
    Echo amplitude Strength of the reflection Acoustic mismatch at the boundary
    Frequency shift of echo Velocity of a moving reflector Doppler effect

    By assigning each echo a position from its timing and a brightness from its amplitude, and repeating across many beam directions, the system assembles a cross-sectional image of acoustic boundaries. The picture is a direct consequence of measured timings and amplitudes, much as an MRI image is a consequence of measured resonance signals.

    The Doppler principle

    Ultrasound can also measure motion. When a sound wave reflects from a moving boundary, the frequency of the returning echo shifts: it rises if the reflector approaches the transducer and falls if it recedes. This is the Doppler effect, the same phenomenon that changes the pitch of a passing siren. By comparing the transmitted and received frequencies, the system calculates the component of the reflector’s velocity along the beam. Doppler ultrasound thus turns a frequency measurement into a velocity measurement, and the geometry between beam and motion must be accounted for in the calculation.

    Reporting an ultrasound measurement

    Because the technique is governed by physical parameters, reproducibility depends on documenting them: transmit frequency, the assumed speed of sound, focal settings and the processing applied to the raw echoes. Our guide on reporting analytical methods reproducibly sets out how such parameters belong in a methods section, and the CASRAI dictionary standardises the vocabulary. The broader place of measurement in a study is covered across our research lifecycle articles.

    Frequently asked questions

    Why does higher frequency give finer detail?

    Higher frequency means shorter wavelength, and a wave can resolve features only down to roughly its own wavelength. Shorter wavelengths therefore distinguish closer boundaries, at the cost of being absorbed more quickly and so penetrating less deeply into the material.

    What makes an echo strong or weak?

    An echo arises wherever the acoustic impedance, a product of density and sound speed, changes between two materials. A large mismatch reflects more of the wave and produces a strong echo; a small mismatch reflects little. The amplitude recorded is a property of the boundary, reported as brightness.

    How does Doppler measure velocity?

    It compares the frequency of the emitted pulse with the frequency of the returning echo. Motion of the reflector shifts the echo frequency, and the size of that shift is proportional to the reflector’s velocity component along the beam, a relationship that follows directly from the Doppler equation.

    Is ultrasound the same idea as radar or sonar?

    The pulse-echo timing logic is shared: emit a pulse, time the return, convert to distance. Sonar uses sound in water, radar uses radio waves, and ultrasound uses high-frequency sound in solids or soft media. The contrasts and reproducibility considerations are discussed further in our reproducibility coverage and the author guidance.