Model Czochralski single-crystal growth at 2,150°C in Iridium crucibles, 511 keV positron annihilation stopping physics, Time-of-Flight (TOF) picosecond timing, and 20-year cleanroom fab economics for cancer imaging PET/CT gantries.
| Year | Ramp | Revenue | OpEx | EBITDA | Deprec. | Taxes | FCF | Cumul. NPV |
|---|
Where c is the speed of light (3×10¹⁰ cm/s) and Δt_CTR is coincidence timing resolution. For 200 ps CTR, the spatial position uncertainty along the chord shrinks from 35 cm down to 3.0 cm.
Where D_torso is the average patient diameter (~35 cm). TOF PET provides a >3.4× SNR gain, which corresponds to a >11-fold increase in Noise-Equivalent Count Rate (NECR).
Where μ is linear attenuation coefficient (0.86 cm⁻¹ for LYSO due to Z_eff = 66 and density 7.1 g/cm³) and L is pixel length (2.0 cm). High stopping power eliminates inter-crystal scatter.
The parity-allowed 5d-to-4f dipole transition in Ce³⁺ activator ions produces 32,000 blue photons/MeV with a 40 ns decay time and no slow afterglow component, matching SiPM spectral sensitivity.
Model pure Lu₂SiO₅:Ce,Ca growth at 2,150°C, zero Y-segregation, 32 ns decay, and clinical TOF-PET arrays.
Model Gd₂SiO₅:Ce Czochralski growth at 1,900°C, 200°C borehole MWD gamma logging, and fast PET imaging.
Model Lu₃Al₅O₁₂:Ce Czochralski growth at 2,010°C, 0.8 µm synchrotron micro-CT screens, and high-Z stopping.
Model Bi₄Ge₃O₁₂ Bridgman crystal growth, GeO₂ feedstocks, high-Z gamma stopping, and PET/calorimeter arrays.
Model Bridgman growth at 783°C, sub-3% FWHM gamma resolution, and drybox hermetic canning for RIID detectors.