# Specific absorption rate

```{admonition} TL;DR
:class: tldr

- {func}`~pypulseqpp.safety.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. {func}`~pypulseqpp.safety.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.
{func}`~pypulseqpp.safety.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.[^eichfelder]

{class}`~pypulseqpp.safety.VopModel` holds the $(N, N_c, N_c)$ VOP stack, in
W/kg per unit channel drive squared, and an optional global matrix;
{func}`~pypulseqpp.safety.read_vops` reads it from a `.mat` or `.npz` file.
{func}`~pypulseqpp.safety.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 {func}`~pypulseqpp.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
{meth}`~pypulseqpp.Sequence.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

* {func}`~pypulseqpp.safety.check_sar`,
  {func}`~pypulseqpp.safety.read_vops` and
  {func}`~pypulseqpp.safety.example_vops` — the calls.
* {func}`~pypulseqpp.calc_rf_power` and
  {meth}`~pypulseqpp.Sequence.calc_rf_power` — RF power in Pulseq's Hz units.
* {doc}`../../examples/checks` — running the check over a
  sequence and reading its report.

## References

[^eichfelder]: Eichfelder G, Gebhardt M. Local specific absorption rate control for parallel transmission by virtual observation points. *Magnetic Resonance in Medicine*. 2011;66(5):1468–1476. [doi:10.1002/mrm.22927](https://doi.org/10.1002/mrm.22927).