Читать книгу Essentials of MRI Safety - Donald W. McRobbie - Страница 101

In some respects, the calculation of induced E from the RF exposure is easier than for the gradients, because to a good first approximation, we can consider B₁ as being uniform in space. The power density P_V, follows from a volumetric version of the Ohm’s law relation “power equals voltage times current”:

(2.27)

Specific absorption rate (SAR) is defined as the power deposited in tissue per unit mass given by

(2.28)

ρ is tissue density. In the simplest case of a uniform sphere, the maximum SAR from a rectangular constant amplitude B₁ pulse repeated N times is [5]

(2.29)

The duty cycle D is the fraction of time for which the B₁ pulse (duration t_p) is active within the MRI sequence TR period:

(2.30)

The average SAR is

(2.31)

For a sphere, the average SAR is 0.4 of the peak SAR. In terms of flip angle α, for a rectangular B₁ pulse

(2.32)

This illustrates the well‐known result that SAR is proportional to the square of the flip angle (for a given pulse shape), increases linearly with the number of RF pulses and is inversely proportional to the pulse duration and sequence repetition time TR.

In general, calculating SAR for arbitrary geometries requires the use of numerical methods [6]. An additional issue arises as a consequence of Ampere’s law (Maxwell’s fourth equation) for frequencies above 10 MHz, in that the induced E, itself, induces an RF magnetic field opposed to B₁ resulting in an overestimation of SAR. Additionally, differing tissue properties, anatomical geometry, and the presence of metallic implants will alter the RF deposition pattern, often resulting in SAR hotspots. The relationship between SAR and heating is non‐linear and heterogeneous and is heavily influenced by the thermal properties of tissue and cooling from perfusion and conduction. These will be considered in Chapter 5.