KEYWORDS: Sensors, Silicon, Gallium arsenide, Monte Carlo methods, Data modeling, Calcium, Distortion, X-ray detectors, Medical imaging, Photon counting
Purpose: In-Depth photon counting detectors (PCXD) use an edge-on configuration and have multi-layer segmentations. The benefit of this configuration for additional spectral information depends on the energy response. Also, inter-layer cross-talk introduces correlation to the signal collected from each layer, which makes the independent Poisson model no longer valid for estimating the Cramér-Rao lower bound (CRLB) of the material decomposition variance. We proposed to use a multivariate Gaussian model as the substitute address the data correlation. Methods: A 120 kVp incident spectrum was simulated and transmitted through 25cm of water and 1cm of calcium. 5- layer In-Depth and 1-layer Edge-On PCXDs with full energy resolution were simulated using Monte Carlo methods. We selected Si, GaAs and CdTe as detector materials. The detectors were defined to have 1mm wide pixels and thickness of 70mm (Si), 10.5mm (GaAs) and 3mm (CdTe). Geant4 was used and energy response functions (ERF) capturing secondary events were obtained, together with the Gaussian parameter estimates. We evaluated the CRLBs of the In-Depth and Edge-On detectors for each material and the systematic variance bounds were compared. Results: For uncorrelated data, the CRLB can assume Poisson statistics. As the data becomes more correlated, the Poisson CRLB fails to capture the cross-talk effect, but a Gaussian model can, and is accurate if the number of photons is not small. The CRLB analysis shows that the effects of the ERF and the noise correlation are significant. If cross-talk can be corrected, the depth information proves to be beneficial and can reduce the variance lower bound by 3% to 10% depending on the detector material. Conclusions: The multivariate Gaussian model was validated to be a good substitute to the Poisson model for PCXD CRLB estimation. It can avoid the errors that would otherwise be caused by correlated measurements.
Purpose: Photon counting x-ray detectors (PCXD) may improve dose-efficiency but are hampered by limited count rate. They generally have imperfect energy response. Multi-layer ("in-depth") detectors have been proposed to enable higher count rates but the potential benefit of the depth information has not been explored. We conducted a simulation study to compare in-depth detectors against single layer detectors composed of common materials. Both photon counting and energy integrating modes were studied. Methods: Polyenergetic transmissions were simulated through 25cm of water and 1cm of calcium. For PCXD composed of Si, GaAs or CdTe a 120kVp spectrum was used. For energy integrating x-ray detectors (EIXD) made from GaAs, CdTe or CsI, spectral imaging was done using 80 and 140kVp and matched dose. Semi-ideal and phenomenological energy response models were used. To compare these detectors, we computed the Cramér-Rao lower bound (CRLB) of the variance of basis material estimates. Results: For PCXDs with perfect energy response, depth data provides no additional information. For PCXDs with imperfect energy response and for EIXDs the improvement can be significant. E.g., for a CdTe PCXD with realistic energy response, depth information can reduce the variance by ~50%. The improvement depends on the x-ray spectrum. For a semi-ideal Si detector and a narrow x-ray spectrum the depth information has minimal advantage. For EIXD, the in-depth detector has consistent variance reduction (15% and 17%~19% for water and calcium, respectively). Conclusions: Depth information is beneficial to spectral imaging for both PCXD and EIXD. The improvement depends critically on the detector energy response.
Purpose: Some qualitative studies report a preference for blended dual-energy (DE) CT images over single energy (SE)
images for liver CT imaging at the same dose. This is counter to theoretical expectations for simple tasks. We
hypothesized that perhaps the broad spectrum of DE might be beneficial for a combination of tasks. We compare the
CNR of SE and blended DE images for single and composite tasks, in part to see if they explain the preference.
Methods: We simulated pre- and post-contrast SE abdominal CT imaging at various kVp but at constant average dose.
Next, 80kVp and 140kVp scans with different dose allocations, dose matched to the SE images, were simulated. DE
images were blended linearly with optimized blending ratios. The CNRs of liver against other soft tissues were used as a
composite image quality metric for evaluation and comparison between the SE and DE protocols. In addition, the
combination of the CNR of many tissue pairs pre- and post-contrast.
Results: The CNR of pre-contrast single kVp imaging mostly increases with increasing tube voltage while 90kVp or
lower energy yields higher CNR for post-contrast images, depending on the differential iodine concentration of each
tissue. Similar trends are seen in the DE blended CNR curves. Results from the composite multi-CNR metric
demonstrate that the SE protocol has better performance.
Conclusions: Our study showed that an optimized SE protocol produces higher CNR, even for a range of tasks. This
suggests that the reason for the radiologist preference must be something other than a fundamental advantage of DE.
The dose efficiency of dual energy imaging can be improved if the spectra are filtered to increase spectral separation.
Our preliminary simulations showed that a fixed Gd filter can be efficacious in rapid kVp-switching systems. We
conducted physical experiments on a table top x-ray system to verify the performance improvement before moving
forward to a real CT scanner. We chose a commercial
Gd2O2S screen as our filter and used an acrylic-copper step wedge
phantom. Data were collected at 70 and 125 kVp, with and without the filter. The tube current was adjusted to make the
exposure rate with and without the filter to be roughly the same. The data were decomposed into basis material images
and the variance of the decomposition was measured for each
acrylic-copper thickness pair. Simulations were done with
the same experimental settings for comparison and validation.
The experiments verified that a Gd filter can reduce the variance at fixed dose. The variance reduction is monotonically
stronger as the object becomes more attenuating. This study demonstrates the potential of fixed Gd filtration to improve
the dose efficiency and material decomposition precision for rapid kVp-switching dual energy systems.
For the first time, we summarized previous work, representing the mechanism of photodynamic therapy (PDT) and
ordering a set of mathematical models. Valid models were devoted to the simulation of PDT process, which involved
two major parts, the photodynamic reaction and photothermal effect. The model covered four common lighting modes,
which were point light source, collimated light beam, planar light source and linear light source (in vivo optical fiber) of
50mW~400mW various light intensity and energy of 50J~200J. A homogeneous sphere was used as a tissue phantom
and different exposure situations were simulated to study the relationship between the light fluence and PDT. The result
turned out that low power light with long treatment time was preferred for photodynamic reaction while photothermal
effect required high power. In addition, comparison between the results of the continuous light and intermittent light of a
point light source was carried out, which validated the experimental results and drew some conclusions of light
modulation optimization. Also, by increasing light intensity to the range of 700mW~3W, the photothermal effect of
high-intensity light was simulated. The same effect of uniformly distributed gold particles in the tissue was analyzed and
discussed.
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