Peripheral nerve stimulation

Peripheral nerve stimulation#

TL;DR

  • check_pns() estimates the response to the physical-axis slew waveforms, after each block’s rotation and the rotation argument, for a supplied demonstration or scanner-specific coil model. A passing estimate does not establish scanner or patient safety.

  • For a rectangular stimulus of duration \(\tau\), the chronaxie model gives the threshold \(S(\tau) = S_{\mathrm{rh}}(1 + c/\tau)\), with rheobase \(S_{\mathrm{rh}}\) and chronaxie \(c\). Shorter transitions require a larger stimulus.

  • ChronaxieModel shares one chronaxie between the three axes and takes the rheobase and the geometry factor alpha either as one value for every axis or as one per physical axis; a SAFE model, read by read_safe_model(), has coefficients per axis.

  • The axis responses combine as the root-sum-square \(R(t) = \sqrt{R_x(t)^2 + R_y(t)^2 + R_z(t)^2}\), and the estimated threshold is \(R = 1\). The whole sequence is evaluated, because model state depends on preceding slew history.

  • With the same coefficients on every axis, rotation redistributes axis components without changing their root-sum-square. Per-axis rheobase or alpha, and SAFE coefficients, differ by physical axis, so prescription orientation can change the estimate.

Time-varying gradients induce electric fields that can stimulate peripheral nerves. check_pns() estimates the response to the physical-axis slew waveforms, after each block’s rotation and the rotation argument, for a supplied demonstration or scanner-specific coil model. A passing estimate does not establish scanner or patient safety.

Strength-duration relation#

For a rectangular stimulus of duration \(\tau\), the chronaxie model gives the threshold

\[ S(\tau) = S_{\mathrm{rh}}\left(1 + \frac{c}{\tau}\right), \]

where \(S_{\mathrm{rh}}\) is the rheobase and \(c\) is the chronaxie.[1]

../_images/strength_duration.png

Slew rate at unity response for a demonstration chronaxie model and the PyPulseq SAFE example hardware description. Shorter transitions require a larger stimulus.#

Model

Coefficients

Typical source

ChronaxieModel

One chronaxie for the three axes; rheobase and geometry factor alpha for every axis or per physical axis

Explicit demonstration or measured coil parameters

SAFE

Three exponential terms, amplitude scale, and stimulation limit per axis

Scanner hardware description read by read_safe_model()

Sequence response#

Each physical-axis slew waveform drives its corresponding model response. The combined response is the root-sum-square

\[ R(t) = \sqrt{R_x(t)^2 + R_y(t)^2 + R_z(t)^2}, \]

and the estimated threshold is \(R=1\). The trace below is returned directly by check_pns(..., trace=True) for a short-echo-spacing EPI sequence and a clearly synthetic chronaxie model; it does not describe a particular scanner.

../_images/pns_response.png

Axis responses, combined response, threshold, and reported peak for one EPI acquisition. The checker computes every plotted response.#

The check evaluates the whole sequence because model state depends on preceding slew history. With the same coefficients on every axis, rotation redistributes axis components without changing their root-sum-square. Per-axis rheobase or alpha, and SAFE coefficients, differ by physical axis, so prescription orientation can change the estimate.

See also#

References#