In physics and chemistry, specifically in nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), and electron spin resonance (ESR), the Bloch equations are a set of macroscopic equations that are used to calculate the nuclear magnetization M = (M x, M y, M z) as a function of time when relaxation times T 1 and T 2 are present.

The Bloch Equation, named after physicist Felix Bloch who won the Nobel Prize for discovery of magnetic resonance phenomena, describes almost all behavior seen in MRI. Here, we will describe this equation and derive key results to use for explaining the behavior of the net magnetization and its interaction with magnetic fields.

In 1946 Felix Bloch published a mathematical analysis of the "Nuclear Induction" phenomenon including a set of equations explaining the origin and properties of the NMR signal. This paper is very readable and does not require a high level of mathematics or physics background.

The Bloch equations are a set of coupled differential equations that describe the behavior of the net magnetization in a sample under the influence of B0. The following description is taken out of Chapter 4 in Haacke et al., Magnetic Resonance Imaging: …

Jan 23, 2023 · Bloch Equations - Lab Frame • Precession – Magnitude of M unchanged – Phase (rotation) of M changes due to B • Relaxation – T1 changes are slow O(100ms) – T2 changes are fast O(10ms) – Magnitude of M can be ZERO • Diffusion – Spins are thermodynamically driven to exchange positions. – Bloch-Torrey Equations {Precession ...

The simulator is used to explore fundamental aspects of MRI such as precession, resonance, excitation, inhomogeneity and relaxation. Important concepts such as rotating frames, weightings, spoilers, spin-echoes, stimulated echoes and driven equilibrium can also be …

Imagine a sequence with 2 gradients of area GT, with a 180 refocusing pulse between. What is the expected value of the spin echo signal as a function of D, Δt, GT, ignoring T2?

We first provide a brief background section of the idealized MR imaging process and concepts, including Larmor precession, the phenomenological Bloch equations and the pulse sequence diagram.

May 26, 2020 · Magnetic resonance imaging (MRI) is able to resolve the response of a system to a magnetic field in space, thereby creating images. This blog introduces a simplified description of magnetic resonance, the vector model using the Bloch equations.

The Bloch Simulator requires the browser functionality WebGL to work (graphics accelleration). Advice for checking and enabling it is here: