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 detected 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, and the detected size is recorded otherwise. 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#