Eric C. Frey

An analytical model of the effects of pulse pileup on the energy spectrum recorded by energy resolved photon counting x-ray detectors.

Purpose: Recently, novel CdTe photon counting x-ray detectors (PCXDs) with energy discrimination capabilities have been developed. When such detectors are operated under a high x-ray flux, however, coincident pulses distort the recorded energy spectrum. These distortions are called pulse pileup effects. It is essential to compensate for these effects on the recorded energy spectrum in order to take full advantage of spectral information PCXDs provide. Such compensation can be achieved by incorporating a pileup model into the image reconstruction process for computed tomography, that is, as a part of the forward imaging process, and iteratively estimating either the imaged object or the line integrals using, e.g., a maximum likelihood approach. The aim of this study was to develop a new analytical pulse pileup model for both peak and tail pileup effects for nonparalyzable detectors. n nMethods: The model takes into account the following factors: The bipolar shape of the pulse, the distribution function of time intervals between random events, and the input probability density function of photon energies. The authors used Monte Carlo simulations to evaluate the model. n nResults: The recorded spectra estimated by the model were in an excellent agreement with those obtained by Monte Carlo simulations for various levels of pulse pileup effects. The coefficients of variation (i.e., the root mean square difference divided by the mean of measurements) were 5.3%–10.0% for deadtime losses of 1%–50% with a polychromatic incident x-ray spectrum. n nConclusions: The proposed pulse pileup model can predict recorded spectrum with relatively good accuracy.

Modeling the performance of a photon counting x-ray detector for CT: Energy response and pulse pileup effects

PURPOSEnRecently, photon counting x-ray detectors (PCXDs) with energy discrimination capabilities have been developed for potential use in clinical computed tomography (CT) scanners. These PCXDs have great potential to improve the quality of CT images due to the absence of electronic noise and weights applied to the counts and the additional spectral information. With high count rates encountered in clinical CT, however, coincident photons are recorded as one event with a higher or lower energy due to the finite speed of the PCXD. This phenomenon is called a pulse pileup event and results in both a loss of counts (called deadtime losses) and distortion of the recorded energy spectrum. Even though the performance of PCXDs is being improved, it is essential to develop algorithmic methods based on accurate models of the properties of detectors to compensate for these effects. To date, only one PCXD (model DXMCT-1, DxRay, Inc., Northridge, CA) has been used for clinical CT studies. The aim of that study was to evaluate the agreement between data measured by DXMCT-1 and those predicted by analytical models for the energy response, the deadtime losses, and the distorted recorded spectrum caused by pulse pileup effects.nnnMETHODSnAn energy calibration was performed using 99mTc (140 keV), 57Co (122 keV), and an x-ray beam obtained with four x-ray tube voltages (35, 50, 65, and 80 kVp). The DXMCT-1 was placed 150 mm from the x-ray focal spot; the count rates and the spectra were recorded at various tube current values from 10 to 500 microA for a tube voltage of 80 kVp. Using these measurements, for each pulse height comparator we estimated three parameters describing the photon energy-pulse height curve, the detector deadtime tau, a coefficient k that relates the x-ray tube current I to an incident count rate a by a = k x I, and the incident spectrum. The mean pulse shape of all comparators was acquired in a separate study and was used in the model to estimate the distorted recorded spectrum. The agreement between data measured by the DXMCT-1 and those predicted by the models was quantified by the coefficient of variation (COV), i.e., the root mean square difference divided by the mean of the measurement.nnnRESULTSnPhoton energy versus pulse height curves calculated with an analytical model and those measured using the DXMCT-1 were in agreement within 0.2% in terms of the COV. The COV between the output count rates measured and those predicted by analytical models was 2.5% for deadtime losses of up to 60%. The COVs between spectra measured and those predicted by the detector model were within 3.7%-7.2% with deadtime losses of 19%-46%.nnnCONCLUSIONSnIt has been demonstrated that the performance of the DXMCT-1 agreed exceptionally well with the analytical models regarding the energy response, the count rate, and the recorded spectrum with pulse pileup effects. These models will be useful in developing methods to compensate for these effects in PCXD-based clinical CT systems.

Three-dimensional imaging-based radiobiological dosimetry.

Targeted radionuclide therapy holds promise as a new treatment for cancer. Advances in imaging are making it possible for researchers to evaluate the spatial distribution of radioactivity in tumors and normal organs over time. Matched anatomical imaging, such as combined single-photon emission computed tomography/computed tomography and positron emission tomography/computed tomography, has also made it possible to obtain tissue density information in conjunction with the radioactivity distribution. Coupled with sophisticated iterative reconstruction algorithms, these advances have made it possible to perform highly patient-specific dosimetry that also incorporates radiobiological modeling. Such sophisticated dosimetry techniques are still in the research investigation phase. Given the attendant logistical and financial costs, a demonstrated improvement in patient care will be a prerequisite for the adoption of such highly-patient specific internal dosimetry methods.

Comparison of Residence Time Estimation Methods for Radioimmunotherapy Dosimetry and Treatment Planning—Monte Carlo Simulation Studies

Estimating the residence times in tumor and normal organs is an essential part of treatment planning for radioimmunotherapy (RIT). This estimation is usually done using a conjugate view whole body scan time series and planar processing. This method has logistical and cost advantages compared to 3-D imaging methods such as Single photon emission computed tomography (SPECT), but, because it does not provide information about the 3-D distribution of activity, it is difficult to fully compensate for effects such as attenuation and background and overlapping activity. Incomplete compensation for these effects reduces the accuracy of the residence time estimates. In this work we compare residence times estimates obtained using planar methods to those from methods based on quantitative SPECT (QSPECT) reconstructions. We have previously developed QSPECT methods that provide compensation for attenuation, scatter, collimator-detector response, and partial volume effects. In this study we compared the use of residence time estimation methods using QSPECT to planar methods. The evaluation was done using the realistic NCAT phantom with organ time activities that model 111In ibritumomab tiuxetan. Projection data were obtained using Monte Carlo simulations (MCS) that realistically model the image formation process including penetration and scatter in the collimator-detector system. These projection data were used to evaluate the accuracy of residence time estimation using a time series of QSPECT studies, a single QSPECT study combined with planar scans and the planar scans alone. The errors in the residence time estimates were 3.8%, 15%, and 2%-107% for the QSPECT, hybrid planar/QSPECT, and planar methods, respectively. The quantitative accuracy was worst for pure planar processing and best for pure QSPECT processing. Hybrid planar/QSPECT methods, where a single QSPECT study was combined with a series of planar scans, provided a large and statistically significant improvement in quantitative accuracy for most organs compared to the planar scans alone, even without sophisticated attention to background subtraction or thickness corrections in planar processing. These results indicate that hybrid planar/QSPECT methods are generally superior to pure planar methods and may be an acceptable alternative to performing a time series of QSPECT studies.

Three‐dimensional radiobiological dosimetry of kidneys for treatment planning in peptide receptor radionuclide therapy

PURPOSEnPeptide receptor radionuclide therapy (PRRT) delivers high absorbed doses to kidneys and may lead to permanent nephropathy. Reliable dosimetry of kidneys is thus critical for safe and effective PRRT. The aim of this work was to assess the feasibility of planning PRRT based on 3D radiobiological dosimetry (3D-RD) in order to optimize both the amount of activity to administer and the fractionation scheme, while limiting the absorbed dose and the biological effective dose (BED) to the renal cortex.nnnMETHODSnPlanar and SPECT data were available for a patient examined with (111)In-DTPA-octreotide at 0.5 (planar only), 4, 24, and 48 h post-injection. Absorbed dose and BED distributions were calculated for common therapeutic radionuclides, i.e., (111)In, (90)Y and (177)Lu, using the 3D-RD methodology. Dose-volume histograms were computed and mean absorbed doses to kidneys, renal cortices, and medullae were compared with results obtained using the MIRD schema (S-values) with the multiregion kidney dosimetry model. Two different treatment planning approaches based on (1) the fixed absorbed dose to the cortex and (2) the fixed BED to the cortex were then considered to optimize the activity to administer by varying the number of fractions.nnnRESULTSnMean absorbed doses calculated with 3D-RD were in good agreement with those obtained with S-value-based SPECT dosimetry for (90)Y and (177)Lu. Nevertheless, for (111)In, differences of 14% and 22% were found for the whole kidneys and the cortex, respectively. Moreover, the authors found that planar-based dosimetry systematically underestimates the absorbed dose in comparison with SPECT-based methods, up to 32%. Regarding the 3D-RD-based treatment planning using a fixed BED constraint to the renal cortex, the optimal number of fractions was found to be 3 or 4, depending on the radionuclide administered and the value of the fixed BED. Cumulative activities obtained using the proposed simulated treatment planning are compatible with real activities administered to patients in PRRT.nnnCONCLUSIONSnThe 3D-RD treatment planning approach based on the fixed BED was found to be the method of choice for clinical implementation in PRRT by providing realistic activity to administer and number of cycles. While dividing the activity in several cycles is important to reduce renal toxicity, the clinical outcome of fractionated PRRT should be investigated in the future.

Improved dose?volume histogram estimates for radiopharmaceutical therapy by optimizing quantitative SPECT reconstruction parameters

In radiopharmaceutical therapy, an understanding of the dose distribution in normal and target tissues is important for optimizing treatment. Three-dimensional (3D) dosimetry takes into account patient anatomy and the nonuniform uptake of radiopharmaceuticals in tissues. Dose-volume histograms (DVHs) provide a useful summary representation of the 3D dose distribution and have been widely used for external beam treatment planning. Reliable 3D dosimetry requires an accurate 3D radioactivity distribution as the input. However, activity distribution estimates from SPECT are corrupted by noise and partial volume effects (PVEs). In this work, we systematically investigated OS-EM based quantitative SPECT (QSPECT) image reconstruction in terms of its effect on DVHs estimates. A modified 3D NURBS-based Cardiac-Torso (NCAT) phantom that incorporated a non-uniform kidney model and clinically realistic organ activities and biokinetics was used. Projections were generated using a Monte Carlo (MC) simulation; noise effects were studied using 50 noise realizations with clinical count levels. Activity images were reconstructed using QSPECT with compensation for attenuation, scatter and collimator-detector response (CDR). Dose rate distributions were estimated by convolution of the activity image with a voxel S kernel. Cumulative DVHs were calculated from the phantom and QSPECT images and compared both qualitatively and quantitatively. We found that noise, PVEs, and ringing artifacts due to CDR compensation all degraded histogram estimates. Low-pass filtering and early termination of the iterative process were needed to reduce the effects of noise and ringing artifacts on DVHs, but resulted in increased degradations due to PVEs. Large objects with few features, such as the liver, had more accurate histogram estimates and required fewer iterations and more smoothing for optimal results. Smaller objects with fine details, such as the kidneys, required more iterations and less smoothing at early time points post-radiopharmaceutical administration but more smoothing and fewer iterations at later time points when the total organ activity was lower. The results of this study demonstrate the importance of using optimal reconstruction and regularization parameters. Optimal results were obtained with different parameters at each time point, but using a single set of parameters for all time points produced near-optimal dose-volume histograms.

Effects of shortened acquisition time on accuracy and precision of quantitative estimates of organ activity.

PURPOSEnQuantitative estimation of in vivo organ uptake is an essential part of treatment planning for targeted radionuclide therapy. This usually involves the use of planar or SPECT scans with acquisition times chosen based more on image quality considerations rather than the minimum needed for precise quantification. In previous simulation studies at clinical count levels (185 MBq 111In), the authors observed larger variations in accuracy of organ activity estimates resulting from anatomical and uptake differences than statistical noise. This suggests that it is possible to reduce the acquisition time without substantially increasing the variation in accuracy.nnnMETHODSnTo test this hypothesis, the authors compared the accuracy and variation in accuracy of organ activity estimates obtained from planar and SPECT scans at various count levels. A simulated phantom population with realistic variations in anatomy and biodistribution was used to model variability in a patient population. Planar and SPECT projections were simulated using previously validated Monte Carlo simulation tools. The authors simulated the projections at count levels approximately corresponding to 1.5-30 min of total acquisition time. The projections were processed using previously described quantitative SPECT (QSPECT) and planar (QPlanar) methods. The QSPECT method was based on the OS-EM algorithm with compensations for attenuation, scatter, and collimator-detector response. The QPlanar method is based on the ML-EM algorithm using the same model-based compensation for all the image degrading effects as the QSPECT method. The volumes of interests (VOIs) were defined based on the true organ configuration in the phantoms. The errors in organ activity estimates from different count levels and processing methods were compared in terms of mean and standard deviation over the simulated phantom population.nnnRESULTSnThere was little degradation in quantitative reliability when the acquisition time was reduced by half for the QSPECT method (the mean error changed by < 1%, e.g., 0.9%-0.3% = 0.6% for the spleen). The magnitude of the errors and variations in errors for large organ with high uptake were still acceptable for 1.5 min scans, even though the errors were slightly larger than those for the 30 min scans (i.e., < 2% for liver, < 3% for heart). The errors over the ranges of scan times studied for the QPlanar method were all within 0.3% for all organs.nnnCONCLUSIONSnThese data indicate that, for the purposes of organ activity estimation, acquisition times could be reduced at least by a factor of 2 for the QSPECT and QPlanar methods with little effect on the errors in organ activity estimates. The acquisition time can be further reduced for the QPlanar method, assuming well-registered VOIs are available and the activity distribution in organs can be treated as uniform. Although the differences in accuracy and precision were statistically significant for all the acquisition times shorter than 30 min, the magnitude of the changes in accuracy and precision were small and likely not clinically important. The reduction in SPECT acquisition time justified by this study makes the use of SPECT a more clinically practical alternative to conventional planar scanning for targeted radiotherapy treatment planning.

Arterial Wall Dosimetry for Non-Hodgkin Lymphoma Patients Treated with Radioimmunotherapy

Tumors in non-Hodgkin lymphoma (NHL) patients are often proximal to the major blood vessels in the abdomen or neck. In external-beam radiotherapy, these tumors present a challenge because imaging resolution prevents the beam from being targeted to the tumor lesion without also irradiating the artery wall. This problem has led to potentially life-threatening delayed toxicity. Because radioimmunotherapy has resulted in long-term survival of NHL patients, we investigated whether the absorbed dose (AD) to the artery wall in radioimmunotherapy of NHL is of potential concern for delayed toxicity. SPECT resolution is not sufficient to enable dosimetric analysis of anatomic features of the thickness of the aortic wall. Therefore, we present a model of aortic wall toxicity based on data from 4 patients treated with 131I-tositumomab. Methods: Four NHL patients with periaortic tumors were administered pretherapeutic 131I-tositumomab. Abdominal SPECT and whole-body planar images were obtained at 48, 72, and 144 h after tracer administration. Blood-pool activity concentrations were obtained from regions of interest drawn on the heart on the planar images. Tumor and blood activity concentrations, scaled to therapeutic administered activities—both standard and myeloablative—were input into a geometry and tracking model (GEANT, version 4) of the aorta. The simulated energy deposited in the arterial walls was collected and fitted, and the AD and biologic effective dose values to the aortic wall and tumors were obtained for standard therapeutic and hypothetical myeloablative administered activities. Results: Arterial wall ADs from standard therapy were lower (0.6–3.7 Gy) than those typical from external-beam therapy, as were the tumor ADs (1.4–10.5 Gy). The ratios of tumor AD to arterial wall AD were greater for radioimmunotherapy by a factor of 1.9–4.0. For myeloablative therapy, artery wall ADs were in general less than those typical for external-beam therapy (9.4–11.4 Gy for 3 of 4 patients) but comparable for 1 patient (32.6 Gy). Conclusion: Blood vessel radiation dose can be estimated using the software package 3D-RD combined with GEANT modeling. The dosimetry analysis suggested that arterial wall toxicity is highly unlikely in standard dose radioimmunotherapy but should be considered a potential concern and limiting factor in myeloablative therapy.

Toward Time Resolved Cardiac CT Images with Patient Dose Reduction: Image-based Motion Estimation

Two major problems with the current electrocardiogram-gated cardiac CT imaging technique are a large patient radiation dose and insufficient temporal resolution. Our long-term goal is to develop new time resolved and low dose cardiac CT imaging techniques that consist of image reconstruction algorithms and estimation methods of the time-dependent motion vector field of the heart from the acquired CT data. Toward this goal, we developed a method that estimates the 2D components of the motion vector field from a sequence of cardiac CT images.

The effect of volume-of-interest misregistration on quantitative planar activity and dose estimation

In targeted radionuclide therapy (TRT), dose estimation is essential for treatment planning and tumor dose response studies. Dose estimates are typically based on a time series of whole-body conjugate view planar or SPECT scans of the patient acquired after administration of a planning dose. Quantifying the activity in the organs from these studies is an essential part of dose estimation. The quantitative planar (QPlanar) processing method involves accurate compensation for image degrading factors and correction for organ and background overlap via the combination of computational models of the image formation process and 3D volumes of interest defining the organs to be quantified. When the organ VOIs are accurately defined, the method intrinsically compensates for attenuation, scatter and partial volume effects, as well as overlap with other organs and the background. However, alignment between the 3D organ volume of interest (VOIs) used in QPlanar processing and the true organ projections in the planar images is required. The aim of this research was to study the effects of VOI misregistration on the accuracy and precision of organ activity estimates obtained using the QPlanar method. In this work, we modeled the degree of residual misregistration that would be expected after an automated registration procedure by randomly misaligning 3D SPECT/CT images, from which the VOI information was derived, and planar images. Mutual information-based image registration was used to align the realistic simulated 3D SPECT images with the 2D planar images. The residual image misregistration was used to simulate realistic levels of misregistration and allow investigation of the effects of misregistration on the accuracy and precision of the QPlanar method. We observed that accurate registration is especially important for small organs or ones with low activity concentrations compared to neighboring organs. In addition, residual misregistration gave rise to a loss of precision in the activity estimates that was on the order of the loss of precision due to Poisson noise in the projection data. These results serve as a lower bound on the effects of misregistration on the accuracy and precision of QPlanar activity estimate and demonstrate that misregistration errors must be taken into account when assessing the overall precision of organ dose estimates.