Residency · Residency · Diagnostic Radiology

MRI Physics I: Magnetism, Precession, and Signal Generation

Fundamental Concepts of Nuclear Magnetism

Nuclear Spin and Magnetic Moment

Magnetic resonance imaging exploits a fundamental property of certain atomic nuclei: intrinsic angular momentum, or spin. Nuclei with an odd number of protons and/or neutrons possess this property, and the nucleus most relevant to clinical MRI is hydrogen-1, which consists of a single proton. Hydrogen is by far the most abundant MRI-relevant nucleus in the body, present in enormous quantities in both water and fat. A spinning charged particle creates a small magnetic dipole moment, effectively making each proton behave like a tiny bar magnet. In the absence of an external magnetic field, these nuclear spins are randomly oriented and produce no net magnetization.

Behavior in an External Magnetic Field (B0)

When placed in a strong external magnetic field (called B0), protons adopt one of two orientations: parallel to the field (a lower-energy state, sometimes called spin-up) or antiparallel (a higher-energy state, spin-down). A slight excess of protons settle into the parallel state, creating a net longitudinal magnetization vector (M0) aligned with the external field. The population difference is described by the Boltzmann distribution and is remarkably small, only about 3 extra protons per million at 1.5 Tesla. However, because the number of hydrogen protons in even a small volume of tissue is astronomically large, this tiny fractional excess produces a detectable net magnetization. Importantly, higher field strengths increase this population difference linearly, which is why 3T scanners produce more signal than 1.5T scanners.

Precession and the Larmor Equation

Protons in an external magnetic field do not simply snap into alignment with B0. Instead, they precess, wobbling around the B0 axis in much the same way a spinning top wobbles under the influence of gravity. The frequency of this precession, called the Larmor frequency, is governed by the single most important equation in MRI: omega0 = gamma x B0, where omega0 is the Larmor frequency in MHz, gamma is the gyromagnetic ratio (42.58 MHz/T for hydrogen), and B0 is the external magnetic field strength in Tesla. At 1.5T, protons precess at approximately 63.87 MHz; at 3.0T, at approximately 127.74 MHz. The Larmor equation is foundational because it governs resonance, spatial encoding through gradients, and chemical shift phenomena.

Excitation and Signal Generation

Radiofrequency (RF) Excitation

To generate an MRI signal, the system applies a brief radiofrequency (RF) pulse at exactly the Larmor frequency, delivered perpendicular to B0 through a transmit coil. This is the resonance condition: the RF frequency must precisely match the precessional frequency of the protons for energy transfer to occur. The RF pulse tips the net magnetization vector away from its equilibrium position along the longitudinal (z) axis and into the transverse (xy) plane. The angle through which the magnetization is tipped, called the flip angle, is determined by the amplitude and duration of the RF pulse. A 90-degree pulse tips all longitudinal magnetization into the transverse plane, while a 180-degree pulse inverts the magnetization from parallel to antiparallel, or can be used to refocus dephased spins.

Transverse Magnetization and the MR Signal

Once tipped into the transverse plane, the magnetization vector precesses at the Larmor frequency. This precessing magnetization induces an oscillating voltage in the receiver coil, following Faraday's law of electromagnetic induction. This induced voltage is the MR signal, and its amplitude is proportional to the amount of transverse magnetization present.

Free Induction Decay (FID)

The signal that appears immediately after an RF pulse is called the free induction decay (FID). It decays rapidly because individual protons within the tissue dephase, meaning they lose the phase coherence that was established by the RF pulse. Dephasing occurs for two reasons: intrinsic spin-spin interactions between neighboring protons (which cause irreversible signal loss characterized by the time constant T2) and inhomogeneities in the B0 field (which cause additional, reversible dephasing). The observed signal decay rate, which combines both effects, is characterized by T2 (T2-star), which is always shorter than T2. The relationship is expressed as 1/T2 = 1/T2 + 1/T2', where T2' represents the dephasing contribution from field inhomogeneity alone.

Relaxation Mechanisms

T1 Relaxation (Longitudinal/Spin-Lattice Relaxation)

After the RF pulse tips the magnetization into the transverse plane, the longitudinal component (Mz) gradually recovers back to its equilibrium value (M0). This recovery process is called T1 relaxation or spin-lattice relaxation because the protons release the absorbed RF energy to the surrounding molecular environment (the "lattice"). Recovery follows an exponential curve: Mz(t) = M0(1 - e^(-t/T1)), where the T1 time constant is defined as the time required for Mz to recover to 63% of M0.

T1 depends on molecular motion, specifically how closely the tumbling frequency of molecules matches the Larmor frequency. Water molecules are small and tumble very quickly, producing a poor match and therefore a long T1 (roughly 2,000 to 4,000 ms). Fat molecules are intermediate in size and happen to tumble at frequencies close to the Larmor frequency, enabling very efficient energy transfer and producing a short T1 (approximately 250 ms at 1.5T). Solids tumble very slowly and also have long T1 values. An important practical consequence is that T1 increases with field strength, because the Larmor frequency increases and fewer molecular motions match it. Gadolinium-based contrast agents work by shortening the T1 of nearby water molecules, causing them to produce increased signal on T1-weighted images.

T2 Relaxation (Transverse/Spin-Spin Relaxation)

While longitudinal magnetization is recovering, transverse magnetization (Mxy) is simultaneously decaying through T2 relaxation. This process reflects the loss of phase coherence among precessing spins as each proton experiences slightly different local magnetic fields due to the influence of neighboring spins. Some protons precess a little faster and others a little slower, and the resulting dephasing causes net signal loss. This decay is exponential: Mxy(t) = Mxy(0) x e^(-t/T2), where the T2 time constant is the time for Mxy to decay to 37% of its initial value.

T2 depends on molecular interactions. Water, with its high molecular mobility and fewer spin-spin interactions, has a long T2 (roughly 1,000 to 2,000 ms). Fat has an intermediate T2 (about 80 ms). Solids, with restricted motion and strong spin-spin interactions, have very short T2 values. Unlike T1, T2 is relatively independent of field strength. In biological tissues, T2 is always much shorter than T1. A clinically important rule is that most pathologic processes (edema, inflammation, tumor) increase both T1 and T2, because they increase the water content of the tissue.

T2* Relaxation

T2 is the observed transverse relaxation rate in the presence of real-world B0 inhomogeneities. Because these inhomogeneities add an extra source of dephasing on top of intrinsic T2 effects, T2 is always shorter than T2. Gradient-echo sequences are sensitive to T2* effects, which is why susceptibility-weighted imaging (SWI) based on gradient-echo techniques can detect blood products, calcification, and iron deposition.

The Spin-Echo Sequence

90-180 Degree Pulse Combination

The spin-echo sequence is a foundational MRI technique that elegantly separates true T2 decay from the reversible dephasing caused by field inhomogeneities. It begins with a 90-degree excitation pulse that tips magnetization into the transverse plane. Spins immediately begin to dephase (the FID). At a time equal to TE/2 (half the echo time), a 180-degree refocusing pulse is applied. This pulse effectively reverses the direction of the dephasing caused by static field inhomogeneities: the faster-precessing spins are flipped behind the slower ones, so they "catch up." At time TE, the spins rephase to form a spin echo. The signal at this echo is reduced from the original FID only by irreversible T2 decay, not by the reversible T2* dephasing. Multiple 180-degree pulses can be applied to generate a train of echoes, with each successive echo showing progressively more T2 decay.

Timing Parameters

Two timing parameters control the contrast in a spin-echo image. TR (repetition time) is the interval between successive 90-degree excitation pulses and controls how much T1 relaxation occurs between excitations. A short TR (less than 500 ms) emphasizes T1 differences between tissues, while a long TR (greater than 2,000 ms) allows near-complete T1 recovery, minimizing T1 weighting. TE (echo time) is the time from the 90-degree pulse to the center of the spin echo, and it controls how much T2 decay is captured. A short TE (less than 20 ms) minimizes T2 weighting, while a long TE (greater than 80 ms) emphasizes T2 differences.

Image Weighting

Combining these parameters produces different types of contrast. T1-weighted images (short TR, short TE) show fat as bright and fluid as dark. T2-weighted images (long TR, long TE) show fluid as bright and fat as intermediate in signal. Proton density-weighted images (long TR, short TE) minimize both T1 and T2 contrast, and the signal intensity primarily reflects the concentration of hydrogen protons in each tissue.

Tissue Signal Characteristics

Signal Intensities of Common Tissues

<image>A vector diagram showing the physics of MRI signal generation in four sequential steps. Step 1: net magnetization (M0) aligned along the B0 axis (z-axis) at equilibrium. Step 2: a 90-degree RF pulse tips the magnetization vector into the transverse (xy) plane, shown with a curved arrow indicating the rotation. Step 3: the magnetization vector precessing in the transverse plane, with individual spin vectors beginning to fan out (dephase), representing the FID. Step 4: the signal decay curve (FID envelope) plotted as signal amplitude versus time, showing exponential decay with T2 rate. Labels include B0 direction, Mz (longitudinal), Mxy (transverse), precession direction, and T2 decay.</image>

<image>A diagram illustrating T1 and T2 relaxation curves side by side. Left panel: T1 recovery curve showing exponential recovery of longitudinal magnetization (Mz) from zero back to M0, with three curves for fat (short T1, rapid recovery), gray matter (intermediate), and CSF (long T1, slow recovery). The 63% recovery point is marked for each tissue as its T1 value. Right panel: T2 decay curve showing exponential decay of transverse magnetization (Mxy) from its initial maximum, with curves for CSF (long T2, slow decay), gray matter (intermediate), and muscle (shorter T2, faster decay). The 37% remaining point is marked for each tissue. Below each panel, a simulated MR image shows the resulting tissue contrast: T1-weighted (fat bright, CSF dark) and T2-weighted (CSF bright, fat intermediate).</image>

<image>A step-by-step diagram of the spin-echo sequence showing the formation of an echo. Timeline from left to right: (1) 90-degree RF pulse at time 0 tips magnetization into transverse plane; (2) spins dephase during free precession (shown as fan of vectors spreading apart); (3) 180-degree refocusing pulse at TE/2 flips the spin vectors; (4) spins rephase as faster-precessing spins catch up with slower ones; (5) spin echo forms at time TE with maximum rephasing. Below the vector diagrams, the signal amplitude versus time shows the FID after the 90-degree pulse, signal decay, then echo reformation. The T2 decay envelope connecting the echo peaks is shown as a dashed line, demonstrating that irreversible T2 decay still causes net signal loss with each successive echo.</image>

Clinical Pearls

The Larmor equation (omega = gamma x B0) is the foundation of MRI: it determines the resonance frequency, enables spatial encoding through the application of gradient fields, and explains chemical shift artifacts. T1 and T2 are independent tissue properties, but pathology such as edema, inflammation, and tumor generally increases both, making lesions appear dark on T1-weighted and bright on T2-weighted images. Fat appears bright on T1-weighted images because its molecular tumbling frequency closely matches the Larmor frequency, enabling efficient energy transfer and producing a short T1; this is one of the most commonly tested MRI concepts. T2 decay is irreversible (caused by molecular interactions), while T2' decay (from field inhomogeneity) is reversible with a 180-degree refocusing pulse, which is precisely why spin-echo sequences produce T2-weighted images while gradient-echo sequences are T2*-weighted. Moving from 1.5T to 3T approximately doubles the SNR, but T1 values lengthen and certain artifacts (susceptibility, chemical shift, SAR) are amplified. CSF serves as a reliable internal reference standard: it should appear dark on T1-weighted images (long T1) and bright on T2-weighted images (long T2). If the CSF signal does not match the expected weighting, the pulse sequence parameters should be reconsidered.

References

• Bushberg JT, et al. The Essential Physics of Medical Imaging, 4th edition
• McRobbie DW, et al. MRI From Picture to Proton, 3rd edition, Cambridge University Press
• Hashemi RH, et al. MRI: The Basics, 4th edition, Lippincott Williams & Wilkins
• Pooley RA. "AAPM/RSNA Physics Tutorial for Residents: Fundamental Physics of MR Imaging." RadioGraphics, 2005

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