Stefan P. Mueller

Development and validation of a Monte Carlo simulation of photon transport in an Anger camera

The geometric component of the point spread function (PSF) of a gamma camera collimator can be determined analytically, and the penetration component can be calculated readily by numerical ray-tracing. A Monte Carlo simulation of photon transport which includes collimator scatter is developed. The simulation was implemented with an array processor which propagates up to 1024 photons in parallel, allowing accurate estimates of the total radial PSF in less than a day. The simulation was tested by imaging monoenergetic point sources of Tc-99m, Cr-51, and Sr-85 (140, 320, and 514 keV, respectively) on a General Electric Star Cam with low-energy, general-purpose, and medium-energy collimators. Comparisons of measured and simulated PSFs demonstrate the validity of the model and the significance of collimator scatter in the degradation of image quality.

Collimator optimization for lesion detection incorporating prior information about lesion size

A Bayesian estimator has been developed as a paradigm for human observer performance in detecting lesions of unknown size in a uniform noisy background. The Bayesian observer used knowledge of the range of possible lesion sizes as a prior; its predictions agreed well with the results of a six-observer perceptual study. The average human response to changes in collimator resolution, as measured by the detectability index, dA, was tracked by the Bayesian detectors signal-to-noise ratio (SNR) somewhat better than by two other estimation models based, respectively, on lesser and greater degrees of lesion size uncertainty. As the range of possible lesion sizes increased, the Bayesian detectors SNR decreased and the optimal collimator resolution shifted towards better resolution. An analytic approximation for the variance of lesion activity estimates (which included the same prior) was shown to predict the variance of the Bayesian estimator over a wide range of collimator resolution values. Because the bias of the Bayesian estimator was small (< 1%), the analytic variance estimate permitted a rapid and convenient prediction of the Bayesian detection SNR. This calculation was then used to optimize the geometric parameters of a two-layer tungsten collimator being constructed from crossed grids for a new imaging detector. A Monte Carlo program was first run to estimate all contributions to the radial point-spread function for collimators of differing tungsten contents and spatial resolution values, imaging 140-keV photons emitted from the center of a 15-cm-diameter, water-filled attenuator. The optimal collimator design for detecting lesions with unknown diameters in the range 2.5-7.5 mm yielded a system resolution of approximately 8.5-mm FWHM, a geometric collimator efficiency of 1.21 x 10(-4), and a single-septum penetration probability of 1%.

Estimation performance at low SNR: predictions of the Barankin bound

Nonlinear quantitation tasks can be viewed as parameter estimation problems, and task performance quantified by the variance of parameter estimates. At high signal-to-noise ratio (SNR), the Cramer-Rao bound (CRB), an absolute lower limit on the variance of any unbiased estimator, is a valid predictor of the variance. At low SNR, however, the CRB may not be achievable, i.e., the realizable parameter variances may exceed the CRB. The determination of this SNR threshold, below which efficient estimation is no longer possible, is of great importance for the optimization of quantitative imaging systems. One approach to this problem is calculating the Barankin bound (BB), which at low SNR predicts larger parameter variances than does the CRB. The computation of the BB, which requires selection of a set of test points in parameter space, presents numerical difficulties. Choosing the test points based on (Chi) 2-confidence regions mitigates the numerical problems and renders the BB calculation practical using very high precision calculations in a computer algebra system. Simulations of a nonlinear two-parameter quantitation task demonstrated that the BB can be used to determine the SNR threshold region were ML-estimation performance no longer achieves the CRB. The BB, however, does not converge at low SNR. Therefore, it cannot be used as an absolute standard of achievable performance, and detailed simulations are necessary to investigate optimized strategies for data acquisition and analysis at very low SNR.

Wavelet compression of noisy tomographic images

3D data acquisition is increasingly used in positron emission tomography (PET) to collect a larger fraction of the emitted radiation. A major practical difficulty with data storage and transmission in 3D-PET is the large size of the data sets. A typical dynamic study contains about 200 Mbyte of data. PET images inherently have a high level of photon noise and therefore usually are evaluated after being processed by a smoothing filter. In this work we examined lossy compression schemes under the postulate not induce image modifications exceeding those resulting from low pass filtering. The standard we will refer to is the Hanning filter. Resolution and inhomogeneity serve as figures of merit for quantification of image quality. The images to be compressed are transformed to a wavelet representation using Daubechies12 wavelets and compressed after filtering by thresholding. We do not include further compression by quantization and coding here. Achievable compression factors at this level of processing are thirty to fifty.

Barankin bound: a model of detection with location uncertainty

We have developed generalized ideal observer models relating human performance in detection tasks to physical properties of medical imaging systems, such as spatial resolution and noise power spectrum. Our approach treats detection as a special case of amplitude estimation, with certain other aspects of the signal, e.g., size or location, considered additional unknown parameters. The models are based on the Barankin lower bound on the precision with which the quantities of interest can be determined. We have found the Barankin bound to be particularly promising in predicting human performance in detection with location uncertainty. Its predictions differ from those of other proposed models in two respects. First, our results suggest that the degradation in performance due to location uncertainty depends on resolution. Second, we have shown analytically that for a given search area, the ratio of ideal observer performance when location is unknown to performance when location is known is nearly independent of signal size. This differs from previously proposed models which predict that the effect of location uncertainty depends on the ratio of signal size to search area, but agrees with the results of reported perceptual experiments testing this question.

X2 isocontours: predictors of performance in nonlinear estimation tasks at low SNR

Maximum-likelihood (ML) estimation is an established paradigm for the assessment of imaging system performance in nonlinear quantitation tasks. At high signal-to-noise ratio (SNR), maximum likelihood estimates are asymptotically normally distributed, unbiased, and efficient, thereby attaining the Cramer-Rao bound (CRB). Therefore, at high SNR the CRB is useful as a predictor of estimation performance. At low SNR, however, the achievable parameter variances are substantially larger than the CRB and the estimates are no longer Gaussian distributed. This implies that intervals derived from the CRB or other tighter symmetric variance bounds do not contain the appropriate fraction of the estimates expected from the normal distribution. We have derived the mathematical relationship between (chi) 2 and the expected probability density of the ML-estimates, and have justified the use of (chi) 2-isocontours to describe the estimates. We validates this approach by simulation of spherical objects imaged with a Gaussian PSF. The parameters, activity concentration and size, were estimated simultaneously by ML, and variances and covariances calculated over 1000 replications per condition. At low SNR, where the CRB is no longer achieved, (chi) 2-isocontours provide a robust predictor of the distribution of the ML- estimates. At high SNR, the (chi) 2-isocontours approach asymptotically the contour derived from the Fisher information matrix.

Impaired lymphocyte function in patients with hepatic malignancies after selective internal radiotherapy

The purpose of our study was to assess the immune function of patients with inoperable hepatic malignancies after treatment with selective internal radiotherapy (SIRT) and to identify possible correlations with clinical parameters. In 25 patients receiving SIRT lymphocyte proliferation and the production of pro- and anti-inflammatory cytokines (interferon-γ and interleukin-10) after stimulation with mitogens and microbial antigens were tested prior to therapy, directly after therapy (day 1) and at day 2, 7 and 28 post therapy using the lymphocyte transformation test and enzyme-linked immunospot assays. Absolute counts and percentages of leukocyte and lymphocyte subsets were determined by flow cytometry. The most prominent finding was an immediate and significant (p < 0.05) decrease of lymphocyte proliferation and interferon-γ production directly after therapy which lasted until day 28 and was stronger upon stimulation with microbial antigens than with mitogens. Moreover, lymphopenia was revealed, affecting all lymphocyte subsets (CD3+, CD4+, CD8+ T cells, CD4+ CD8+ T cells, B cells and NK cells). SIRT led to a reduction in the percentage of activated HLA-DR+ monocytes and of CD45R0+ memory T cells. Higher radiation activity, the presence of liver cirrhosis, chronic kidney disease, diabetes mellitus and metastases were unfavorable factors for immunocompetence, while a better Eastern Cooperative Oncology Group performance status was associated with stronger immunological reactions. In conclusion, SIRT leads to severe impairment of cellular in vitro immune responses. Further studies are needed to assess a potential clinical impact.

The effects of resolution recovery on estimation of binding potential from brain SPECT images

We investigated the effects of resolution recovery and SPECT system sensitivity on performance in estimating binding potential (BP) from dynamic brain SPECT data obtained using I-123-altropane, a dopamine transporter imaging agent. BP is estimated by Fischmans approach, whereby a gamma variate function is fitted to the difference between striatal and occipital time-activity curves (TAC). The TAC were obtained using an approach published by Huesman (1984), who estimated the activity concentration in a ROI directly from the projection dataset without reconstructing the image. We modified this method by incorporating resolution recovery, using a Metz filter. We simulated dynamic projection datasets of a simple striatal phantom and determined the accuracy and precision of estimation of striatal activity concentration and binding potential, both for current system sensitivity and for the higher sensitivity of a new collimator, presently being manufactured. This collimator is expected to increase sensitivity at the center of the brain by a factor of 3, without degrading resolution. The parameter, P, of the Metz filter, which controls the extent of resolution recovery, was varied from 1 to 10/sup 5/. For estimation of striatal activity concentration, increasing the value of P over this range reduced bias and gradually increased variance. For estimation of BP, however, increasing the value of P beyond 2 (for current sensitivity) and beyond 10 (for increased sensitivity) dramatically increased variance. For estimation of striatal activity, there was a broad minimum in RMSE of /spl sim/12% for P between 7 and 100 at current sensitivity, and /spl sim/10% for P between 10 and 300 for improved sensitivity. For estimation of binding potential, the minimum RMSE was 32% (P=2) for current sensitivity, and 17% (p=7) for improved sensitivity. The differences in the effects of resolution recovery on estimation of binding potential and striatal activity concentration are due to the nonlinear nature of the former task.

Effects of nonuniform collimator sensitivity on variance of attenuation-corrected SPECT images

The first step in all intrinsic attenuation-correction algorithms is multiplication of each measured projection by a function which compensates for photon attenuation between a line through the center of rotation, parallel to the detector, and the (convex) external object contour nearest the detector. A nonuniform collimator sensitivity profile which accomplishes this compensation physically rather than computationally would reduce the noise in the projections and, consequently, in the reconstructed images. The authors have compared the variance of reconstructed images of cylindrical phantoms of homogeneous activity concentration and attenuation coefficient for three collimator sensitivity profiles using both the original intrinsic attenuation-correction technique of Tretiak-Metz (1980) and Gullberg-Budinger (1981) and the variant developed by Tanaka (1984). The collimator sensitivity profiles the authors considered were the standard profile, with uniform sensitivity along the projection, and two nonuniform sensitivity profiles which were peaked at the center of the projection. The nonuniform collimator sensitivity profiles led to reduced variances throughout most of the image for both attenuation correction algorithms. These reductions in variance would be expected to lead to improved performance in quantitative imaging tasks.<<ETX>>