2.1

Iterative polychromatic reconstruction

At the core of the iterative polychromatic reconstruction implementation is a polychromatic forward projection, adapted from Mason et al.:⁴

where p_α is simulated projection under angle α, r₀(E_j) is spectral air norm, A is forward-projection operator, and is a polychromatic attenuation model transforming the relative electron density volume ρ_e into attenuation coefficients μ. The polychromatic forward projection combines thus prior spectral knowledge about the imaging system (spectral air norm) and material characteristics (polychromatic attenuation model).

The spectral air norm r₀(E_j) resolves the (energy-integrated) air norm after bowtie filtration r_BT according to spectral characteristics of the imaging system:

where ο denotes element-wise product, S(E_j) is the system sensitivity. It combines source and detector properties:

where I_s(E_j) is the spectrum flux at the source, F_s(E_j) is inherent filtration at the source, μ_Ti; and l_Ti are respectively attenuation coefficient and thickness of the titanium filter, μ_A1 and I_A1 are respectively attenuation coefficient and thickness profile of the aluminium bowtie filter, and η_d(E_j) is the detector efficiency.

The polychromatic attenuation model takes the form of a piecewise linear fit:⁴

where f_i(ρ_e) is a material class identification function, ο denotes element-wise product, α_i(E_j) and α_i(E_j) are energy-dependent fit coefficients. The material class identification function maps relative electron density values to corresponding fit segments:⁴

where k_i marks a break point between the i and i + 1 fit segments, with k₀ =0 and k_Nf = ∞. As described in Mason et al.,⁴ model parameters α_i(E_j), β_i(E_j) and k_i are obtained via a fit to human tissue materials from ICRP Publication,¹⁰ albeit in extended energy range from 15keV to 140 keV.

Similarly to our established iCBCT reconstruction,⁷ for RED volume ρ_e optimization, we use a penalized likelihood cost function with total variation (TV) regularization¹¹ with a modified expression for the data-fidelity gradient:

where A^T is the back-projection operator acting on the difference between measured projection q_α and the polychromatic forward projection p_α defined in (1). To accelerate the polychromatic reconstruction, we utilize separable quadratic surrogate cost function,¹² ordered subsets,¹³ and Nesterov momentum method.¹⁴

2.2

Reconstruction pipeline

The polychromatic reconstruction pipeline is a natural extension of our iCBCT reconstruction pipeline, which is a two-pass approach.⁷ In the first pass of the iCBCT pipeline, the initial HU volume is reconstructed with algebraic reconstruction technique (ART) from fASKS¹⁵ scatter-corrected projections. In the second pass, the initial volume is further refined with statistical reconstruction based on penalized maximum likelihood (PL) using projection images scatter-corrected with Acuros® CTS.

The iterative polychromatic reconstruction (IPR) requires pre-processed projection images. The pre-processing step comprises object and hardware scatter corrections. In our two-pass polychromatic reconstruction pipeline, depicted in Fig. 1, scatter correction is done at two stages. The first pass fASKS scatter correction is carried out identically as in the iCBCT pipeline, and provides input for initial ART reconstruction. In the second pass, scatter correction is done by Acuros® CTS, which consumes the initially reconstructed HU volume to solve the linear Boltzmann transport equation. The scatter-corrected projection images are then fed into IPR to reconstruct the final RED volume.

Figure 1:

Diagram showing a two-pass polychromatic reconstruction pipeline. In the first pass, algebraic reconstruction technique (ART) consumes projections corrected for scatter with a kernel-based approach (fASKS). HU volume from first-pass provides input for Acuros® CTS scatter correction for subsequent second-pass iterative polychromatic reconstruction (IPR).

3.1

Direct RED reconstruction

To demonstrate the use of the polychromatic model for direct RED reconstruction, we scanned the head insert of a CBCT electron density phantom (Model 062MA, Computerized Imaging Reference Systems, Inc., Norfolk, VA, USA) on a Varian Halcyon machine (Varian Medical Systems, Palo Alto, CA, USA). The scan was acquired in full-fan geometry at 125 kVp and with kV blades in the longitudinal direction collimated to the height of the phantom electron density plugs. RED volume was reconstructed with 5 initial iCBCT ART iterations, followed by 50 IPR iterations on projections scatter-corrected with Acuros® CTS. Number of iterations was determined empirically for better RED accuracy and image quality.

Central slice through reconstructed RED volume is depicted in Fig. 2a and the resulting difference to ground truth (GT) values relative to water is shown in Fig. 2b. As GT, we assigned nominal RED values from the phantom specification. Mean reconstructed RED values within each plug (areas indicated by dashed circles in Fig. 2a) are listed in Table 1. Except for ‘Lung inhale’ and ‘Dense bone 800’ plugs, tissue materials were reconstructed with relative RED error below 3%, thus enabling accurate treatment dose calculation.

Figure 2:

Central slice of reconstructed RED volume (left; W/L = 0.6/1.0) compared to ground truth (GT) RED (right; W/L = 15/0 %). Positive difference (red) values in right panel denote lower reconstructed values w.r.t. GT. Dashed circles indicate regions for mean RED value calculations.

Table 1:

Mean reconstructed RED values for inserts at central slice and their differences to the ground truth (GT) relative to water

3.2

Beam hardening artifact reduction

To illustrate the benefit of polychromatic reconstruction for beam hardening artifact reduction, we scanned the CIRS CBCT electron density phantom with bone inserts (from left to right: solid dense bone 800, solid dense bone 1750, solid trabecular bone 200, solid dense bone 800, solid dense bone 1250) aligned in one row. The phantom was scanned on a Varian Halcyon™ machine in full-fan beam geometry at 125 kVp with kV blades in the longitudinal direction collimated to the insert height for scatter reduction. We compared two reconstructions shown in Fig. 3: a standard iCBCT reconstruction (5 ART iterations, followed by Acuros® CTS scatter correction and 10 PL iterations) and a polychromatic reconstruction (5 iCBCT ART iterations, followed by Acuros® CTS scatter correction and subsequent 50 IPR iterations; with number of iterations determined empirically for better RED accuracy and image quality. To compare HU values for both reconstructions, we transformed the RED volume from the polychromatic reconstruction to a VMI using (4) at Ej = 66.5 keV, corresponding to the mean beam energy at 125 kVp.

Figure 3:

Beam hardening artifact near bone plugs is reduced in the VMI from polychromatic reconstruction (right) as compared to an iCBCT reconstruction (left). W/L = 500/75 HU

The shading near bone plugs present in the iCBCT reconstruction (Fig. 3a) caused by beam hardening is reduced in the polychromatic reconstruction (Fig. 3b).

3.3

Metal artifact mitigation

We also tested the ability of polychromatic reconstruction to reduce metal artifacts. For that purpose, we selected a scan of a patient with bilateral metal hip implants (data courtesy of Queen’s Hospital in Romford). The scan was acquired on a Varian Halcyon™ machine in half-fan beam configuration at 125 kVp. We compared three reconstructions shown in Fig. 4: a standard iCBCT reconstruction (5 ART iterations, followed by Acuros® CTS scatter correction and 5 PL iterations), an iCBCT reconstruction with metal artifact reduction (MAR) and a polychromatic reconstruction (5 iCBCT ART iterations, followed by Acuros® CTS object scatter correction and subsequent 25 IPR iterations). To compare HU values for both reconstructions, we transformed the RED volume from the polychromatic reconstruction to a VMI at E_j = 74.5 keV. The polychromatic model used for this reconstruction was extended by a fit to common hip replacement alloys¹⁶ in addition to typical human tissues¹⁰ and comprised of N_f =4 segments.

Figure 4:

Metal artifact within bladder region is reduced in the VMI from polychromatic reconstruction (middle) as compared to a standard iCBCT reconstruction (left). As a reference, an iCBCT reconstruction with heuristic metal artifact reduction (MAR) is shown on the right. W/L = 500/75 HU. Patient data courtesy of Queen’s Hospital in Romford

The shading between hip joints caused by metal implants visible in the iCBCT reconstruction (Fig. 4a) is reduced in the VMI from the polychromatic reconstruction (Fig. 4b), improving the visibility of the bladder. Some level of metal artifacts still remains, however, we point out that, unlike in the iCBCT MAR reconstruction (Fig. 4c) the result of the polychromatic reconstruction is based solely on the underlying polychromatic model without metal inpainting in projections.