11 · Helical Scanning · Narrow Collimation, Long Coverage

One new kwarg — pitch — turns any protocol into a spiral scan.

Helical (spiral) CT solves a geometry problem no detector can: covering a long $z$ range with a narrow beam. Before spiral CT, long coverage meant step-and-shoot: scan a slab, move the table, scan the next slab. Each station is a clean axial scan — but every station has cone-beam edges, and the stitched volume can introduce a discontinuity at a station boundary. A helical scan instead sweeps the collimator past every slice continuously: each $z$ position is, at some moment of the spiral, at the centre of the beam.

This notebook covers a 30 cm reconstructed z-slab both ways, on a wide-cone 256 × 0.625 mm (16 cm) volume scanner, with the tube current chosen so that the two scans deliver the same total beam-width × current × time:

The forward projection is the anti-aliased :dd_fast projector — helical costs it nothing (the projectors consume per-view source/detector arrays; a helix is just a z-ramp in those arrays). Both scans integrate each view over the arc the gantry turns while the detector reads it (view_samples = 5, notebook 01); on the helix each sub-view is also advanced along $z$ by its share of the table feed. Helical reconstruction is rebinned WFBP (Stierstorfer et al. 2004 — the production spiral algorithm family), dispatched automatically whenever the geometry is helical. Both pipelines use the reconstruction chain of notebook 01: detected-spectrum water BHC → reconstruction → HU, with quantum and electronic noise already in the simulated counts. Each simulate! also reports its dose, so the two acquisitions can be compared in CTDIvol and DLP as well as in image quality.

Backend detected: CuArray

Notebook Setup

The shared docs environment, the device from GPUSelect, and a table of contents. Nothing is simulated until section 4.

1. A phantom that changes along $z$ — with no strong hardeners

Two design rules. First, a uniform cylinder would look identical at every slice — useless for judging long-$z$ fidelity — so every slice must be different. Second, no high-Z inserts: beam hardening is its own topic (notebook 10); here it would only confound the geometry comparison.

• a 24 cm water body, 36 cm long (coarse 2.3 mm in-plane / 2 mm z voxels);

• a lung-density rod (≈ −700 HU, radiologically soft) that winds helically around the body axis — one turn per 12 cm of $z$, so its angular position tags every slice;

• an adipose cone (≈ −90 HU) on the axis, radius tapering 4 cm → 0 across the slab — its diameter tags every slice.

2. The helical scan: pitch is the whole API

IEC pitch = table feed per rotation ÷ active collimation. With 20 mm collimation (32 of the scanner's 256 × 0.625 mm rows), pitch 1.0, and 16 rotations, the table travels

$$\text{travel} = \text{pitch} \times \text{collimation} \times n_\text{rot} = 1.0 \times 20\,\text{mm} \times 16 = 32\,\text{cm}.$$

Everything else (Phantom, the scanner, SimOptions, ReconOptions, simulate!, the corrections, the reconstruction call) is the same as in an axial workflow.

3. The reconstruction chain

One BHC model per protocol (calibrated on that acquisition's geometry), then per reconstruction: sinogram-domain water BHC → reconstruction → HU with the BHC's own $\mu_\text{water}$. reconstruct! recognises a helical geometry and runs rebinned WFBP; an axial one runs FDK.

4. Run both acquisitions

Helical: one simulate!, one reconstruction. Volume axial (step-and-shoot): three 10 cm reconstruction stations. For each, the table (here, the phantom window) moves so that the station is centred on the isocentre; the three slabs are then stitched at $z = ±5$ cm. The 16 cm beams of neighbouring stations overlap by 6 cm, so each station's dose is reported with a 10 cm table increment.

Dose of each acquisition (CTDI from a Monte Carlo of the simulated beam in the 32 cm body phantom)

The two DLPs are 414.0 and 414.0 mGy·cm: matching beam width × current × time matches the total exposure. CTDIvol differs because that exposure is spread over different lengths: 32.0 cm of helical travel against three 10.0 cm table increments for the axial stations, whose overlapping 160.0 mm beams are dosed with the IEC wide-beam rule (reference 20.0 mm).

Plan a helical scan

The dose above is the pitch-1.0 scan. At a fixed tube current and rotation time, CTDIvol scales as 1 / pitch, and the table feed per rotation is pitch × collimation, which sets how many rotations (and seconds) a range takes. Move the slider: the numbers below are computed live in your browser from this scan's measured CTDIvol and its 20 mm collimation.

Pitch 1.0: the table moves 20.0 mm per rotation, CTDIvol is 12.94 mGy, and a 30 cm range takes 15.0 rotations, 7.5 s.

5. Slide through $z$: phantom truth vs both scans

Top row: the phantom ground truth as a labelled categorical map. Bottom row: helical (20 mm collimation) and volume axial (the full 16 cm detector, 8× wider). Watch the rod rotate and the cone shrink — and watch what the wide cone does away from each station centre. The axial station boundaries are marked at $z = ±5$ cm for inspection.

Results

1. Water flatness and the coronal view

Mean HU in a fixed water ROI (clear of the rod and the cone), slice by slice, with the axial station boundaries marked, then coronal reformats of both volumes. The table under the plot reduces the profiles to numbers.

"Step" is the change in the ROI mean between the two slices either side of a station boundary; "pixel noise" is the within-ROI standard deviation averaged over the slices.

Verification and Scope

• :dd_fast needed zero changes for helical. The projectors consume per-view geometry arrays (the same representation as ASTRA's cone_vec and CatSim's internal trajectory); the helix lives entirely in those arrays, and so do the sub-views of the view integration, each rotated and advanced along $z$ with the table.

• Helical reconstruction is rebinned WFBP (Stierstorfer et al., Phys Med Biol 49:2209, 2004): row-wise fan→parallel rebinning, parallel ramp filtering, and aperture-weighted (cos², plateau $Q = 0.7$) wedge backprojection with per-half-turn redundancy normalisation. This is the production spiral-CT algorithm family (Siemens WFBP; UCLA FreeCT), and it is dispatched automatically by reconstruct!/fdk_reconstruct whenever is_helical(geom).

• Both scans got identical corrections. Exposure is matched by beam width × current: 16 × 20 mm × 200 mA versus 3 × 160 mm × 133⅓ mA at equal rotation time. That is an acquisition-integral match, not equal CTDIvol or equal noise per slice; the dose table in section 4 gives both scans' CTDIvol and DLP.

• Hybrid IR works on helical unchanged — matched forward/backprojection are geometry-general, subsets are angular-interleaved, and the HIR FDK initialisation routes through WFBP.

• Windmill artifacts around sharp $z$ edges at high pitch are physics (longitudinal sampling), not a defect of the reconstruction.

• Wall-clock (this page was rendered on an NVIDIA RTX PRO 6000, CUDA): helical (5760 views, simulation + corrections + WFBP) 18.7 s; volume axial (3 stations × 360 views) 5.7 s. Both include first-call compilation.

Summary

• pitch and n_rotations are the only additions needed to turn the axial acquisition geometry into a centered helical trajectory.

• :dd_fast consumes the per-view geometry arrays unchanged and remains the default forward projector.

• Helical geometries dispatch automatically to rebinned WFBP; axial stations retain the ordinary FDK path.

• The slice slider, the water-HU profile and the coronal reformats inspect longitudinal coverage, station boundaries and the z-dependent anatomy; the dose table shows what each acquisition costs.