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Max-b vs min-TE — designing for SNR

There are two dual questions you can ask a waveform designer, and dmipy-design answers both from the same core.

Two modes

Max-b at a fixed TE — design_waveform_now(b_delta, TE=…). You have a TE (fixed by the protocol, a relaxometry requirement, or the readout), and you want the strongest diffusion weighting that fits inside it under the hardware limits.

Min-TE for a target b — min_te_for_b(b_target, b_delta, …). You have a required b-value (the contrast your model needs), and you want the shortest echo time that still reaches it.

Why min-TE is the SNR-optimal design

The measured magnitude decays with echo time as \(\;S \propto e^{-\mathrm{TE}/T_2}\;\) before you ever read it out. Two waveforms that deliver the same b but at different TE therefore give different SNR: the shorter-TE one has lost less signal to transverse relaxation. So for a fixed required b, minimising TE maximises SNR — often the single biggest lever on image quality in a diffusion protocol, larger than the waveform shape itself.

Concretely, at a required \(b\):

\[ \mathrm{SNR}(b) \;\propto\; e^{-\mathrm{TE}(b)/T_2}, \qquad\text{so minimise } \mathrm{TE}(b). \]

It's one primitive, not two solvers

The achievable b is monotonically increasing in TE — a longer TE simply gives more area under \(q(t)\). That monotonicity is what makes the inverse cheap: min_te_for_b bisects TE around the max-b primitive, calling the same NOW design at each candidate TE, with no separate solver and no hand-rolled scan.

from dmipy_design import min_te_for_b, SequenceTiming

timing = SequenceTiming(t_excite=3e-3, t_refocus=6e-3, t_readout_pre_echo=14e-3)
design, te = min_te_for_b(b_target=1e9, b_delta=1.0, timing=timing)   # 1000 s/mm²
print(f"shortest deliverable TE = {te*1e3:.1f} ms")

Which to use

  • Fixed TE (multi-contrast / relaxometry protocols, or a shared TE across shells) → max-b.
  • Fixed b requirement (a model needs a specific diffusion weighting, and you want the best SNR) → min-TE.

Both respect the same deliverability constraints and the derived asymmetric windows, and both hand you a G(t) that dmipy-sim can simulate and dmipy-fit can fit.