Specific absorption rate

Specific absorption rate#

TL;DR

  • check_sar() computes time-averaged local and global SAR in W/kg from a virtual-observation-point model and compares them with local_limit and global_limit, by default 10 W/kg and 3.2 W/kg, the IEC 60601-2-33 normal-mode head values. The check does not use the gradient system limits.

  • Channel \(c\) is driven with \(v_c(t) = d_c\,s_c\,b_c(t)\), the RF waveform in Hz scaled by drive_per_hz and the block’s RF shim. Local SAR in a window \(W\) is the largest time-averaged quadratic form over the VOPs, \(\max_k \mathrm{SAR}_k(W)\).

  • The averaging windows are the repetitions detected from the block definitions, reported as tr_size blocks, or the whole sequence when its blocks do not divide into repetitions. The check does not aggregate the per-window values over a regulatory averaging interval such as the 6-minute interval of IEC 60601-2-33.

  • With reference, the report adds sar_ratio and energy_ratio. The scale of drive_per_hz and of the VOPs cancels in both ratios; relative channel gains do not.

  • A True result states only that the computed window-averaged SAR values do not exceed the supplied limits under the stated VOP model and drive calibration. example_vops() is a synthetic model for demonstration only.

RF transmission deposits energy in tissue. The specific absorption rate (SAR, W/kg) is regulated as a global value over the exposed mass and a local value over 10 g of tissue, each averaged over a stated time and bounded by IEC 60601-2-33 according to the operating mode. check_sar() computes time-averaged local and global SAR from a virtual-observation-point model and compares them with the local_limit and global_limit arguments. The check does not use the gradient system limits.

Virtual observation points#

For a transmit array with \(N_c\) channels driven by a phasor vector \(\mathbf{v}\), local SAR at position \(\mathbf{r}\) is a Hermitian quadratic form,

\[ \mathrm{SAR}(\mathbf{r}) = \mathbf{v}^{\mathsf H} \, Q(\mathbf{r}) \, \mathbf{v}, \]

with one matrix \(Q\) per position from an electromagnetic simulation on a body model. Virtual observation points (VOPs) compress these matrices into a small set \(\{Q_k\}\) whose largest value bounds the largest value over the body model.[1]

VopModel holds the \((N, N_c, N_c)\) VOP stack, in W/kg per unit channel drive squared, and an optional global matrix; read_vops() reads it from a .mat or .npz file. example_vops() returns a synthetic eight-channel model of a loop array around a uniform cylinder, with no tissue, coil coupling or conservative field, for demonstration only.

Channel drive and time average#

An RF event states its amplitude in Hz of \(B_1^+\). The conversion to channel drive is a property of the transmit chain and loading, and is supplied as drive_per_hz, one value or one per channel, in the drive unit of the VOPs. Channel \(c\) is driven with

\[ v_c(t) = d_c \, s_c \, b_c(t), \]

where \(d_c\) is drive_per_hz, \(b_c\) the RF waveform in Hz resampled every microsecond as calc_rf_power() does, and \(s_c\) the block’s RF shim, or default_shim for a single-channel pulse without one. A single-channel pulse is played as the same waveform on every channel. For each averaging window \(W\) of duration \(T_W\),

\[ \mathrm{SAR}_k(W) = \frac{1}{T_W} \int_W \mathbf{v}(t)^{\mathsf H} Q_k \, \mathbf{v}(t)\,\mathrm{d}t, \qquad \mathrm{SAR}_{\mathrm{local}}(W) = \max_k \mathrm{SAR}_k(W), \]

and global SAR is the same integral with the global matrix.

Averaging windows#

check_sar evaluates RF energy over the repetitions repetition() detects from the sequence’s block definitions, reported as tr_size blocks: consecutive windows of tr_size blocks from the first block, or the whole sequence as one window when its blocks do not divide into repetitions. A TRsize definition the sequence records is used when the blocks repeat with it. The result is True when every window’s local SAR is at most local_limit and, with a global matrix, every window’s global SAR is at most global_limit. The defaults, 10 W/kg and 3.2 W/kg, are the IEC 60601-2-33 normal-mode head values.

The report states every window’s first and last block, duration, local SAR, VOP index and global SAR. These per-window quantities may subsequently be aggregated over a regulatory averaging interval, such as the 6-minute interval of IEC 60601-2-33; the check itself does not perform that aggregation.

Comparison with a reference sequence#

With reference, a second sequence evaluated under the same model, drive and default shim, or the report of an earlier call, the report adds

\[ r_{\mathrm{SAR}} = \max_{W,k} \frac{\mathrm{SAR}_k(W)}{\mathrm{SAR}_k^{\mathrm{ref}}}, \qquad r_{\mathrm{E}} = \max_{W} \left[ \max_k \frac{\mathrm{SAR}_k(W)}{\mathrm{SAR}_k^{\mathrm{ref}}} \right] \frac{T_W}{T^{\mathrm{ref}}}, \]

as sar_ratio and energy_ratio, with the reference values taken from the reference’s window of largest local SAR. The scale of drive_per_hz and of the VOPs cancels in both ratios; relative channel gains do not. For a reference lasting its minimum repetition time, \(r_{\mathrm{E}}\) scales that repetition time to the energy per repetition of the checked sequence.

Limitations#

The estimate covers the RF energy of the sequence’s own waveforms in a stated VOP model and drive calibration. It does not cover RF coil heating, gradient heating, the scanner’s predownload assessment or transmit monitoring, and it makes no statement about a particular subject. A True result states only that the computed window-averaged SAR values do not exceed the supplied limits under that model and calibration.

See also#

References#