Scanning linear estimation: improvements over region of interest (ROI) methods

Future trends for patient-specific dosimetry methodology in molecular radiotherapy

Molecular radiotherapy is rapidly expanding, and new radiotherapeutics are emerging. The majority of treatments is still performed using empirical fixed activities and not tailored for individual patients. Molecular radiotherapy dosimetry is often seen as a promising candidate that would allow personalisation of treatments as outcome should ultimately depend on the absorbed doses delivered and not the activities administered. The field of molecular radiotherapy dosimetry has made considerable progress towards the feasibility of routine clinical dosimetry with reasonably accurate absorbed-dose estimates for a range of molecular radiotherapy dosimetry applications. A range of challenges remain with respect to the accurate quantification, assessment of time-integrated activity and absorbed dose estimation. In this review, we summarise a range of technological and methodological advancements, mainly focussed on beta-emitting molecular radiotherapeutics, that aim to improve molecular radiotherapy dosimetry to achieve accurate, reproducible, and streamlined dosimetry. We describe how these new technologies can potentially improve the often time-consuming considered process of dosimetry and provide suggestions as to what further developments might be required.

A Projection-Domain Low-Count Quantitative SPECT Method for α-Particle-Emitting Radiopharmaceutical Therapy

Single-photon emission-computed tomography (SPECT) provides a mechanism to estimate regional isotope uptake in lesions and at-risk organs after administration of α-particle-emitting radiopharmaceutical therapies (α-RPTs). However, this estimation task is challenging due to the complex emission spectra, the very low number of detected counts (~20 times lower than in conventional SPECT), the impact of stray-radiation-related noise at these low counts, and the multiple image-degrading processes in SPECT. The conventional reconstruction-based quantification methods are observed to be erroneous for α-RPT SPECT. To address these challenges, we developed a low-count quantitative SPECT (LC-QSPECT) method that directly estimates the regional activity uptake from the projection data (obviating the reconstruction step), compensates for stray-radiation-related noise, and accounts for the radioisotope and SPECT physics, including the isotope spectra, scatter, attenuation, and collimator-detector response, using a Monte Carlo-based approach. The method was validated in the context of 3-D SPECT with 223Ra, a commonly used radionuclide for α-RPT. Validation was performed using both realistic simulation studies, including a virtual clinical trial, and synthetic and 3-D-printed anthropomorphic physical-phantom studies. Across all studies, the LC-QSPECT method yielded reliable regional-uptake estimates and outperformed the conventional ordered subset expectation-maximization (OSEM)-based reconstruction and geometric transfer matrix (GTM)-based post-reconstruction partial-volume compensation methods. Furthermore, the method yielded reliable uptake across different lesion sizes, contrasts, and different levels of intralesion heterogeneity. Additionally, the variance of the estimated uptake approached the Cramér-Rao bound-defined theoretical limit. In conclusion, the proposed LC-QSPECT method demonstrated the ability to perform reliable quantification for α-RPT SPECT.

Preclinical SPECT and SPECT-CT in Oncology

Molecular imaging enables both spatial and temporal understanding of the complex biologic systems underlying carcinogenesis and malignant spread. Single-photon emission tomography (SPECT) is a versatile nuclear imaging-based technique with ideal properties to study these processes in vivo in small animal models, as well as to identify potential drug candidates and characterize their antitumor action and potential adverse effects. Small animal SPECT and SPECT-CT (single-photon emission tomography combined with computer tomography) systems continue to evolve, as do the numerous SPECT radiopharmaceutical agents, allowing unprecedented sensitivity and quantitative molecular imaging capabilities. Several of these advances, their specific applications in oncology as well as new areas of exploration are highlighted in this chapter.

Optimization of an Adaptive SPECT System with the Scanning Linear Estimator

A method for optimization of an adaptive Single Photon Emission Computed Tomography (SPECT) system is presented. Adaptive imaging systems can quickly change their hardware configuration in response to data being generated in order to improve image quality for a specific task. In this work we simulate an adaptive SPECT system and propose a method for finding the adaptation that maximizes the performance on a signal estimation task. To start with, a simulated object model containing a spherical signal is imaged with a scout configuration. A Markov-Chain Monte Carlo (MCMC) technique utilizes the scout data to generate an ensemble of possible objects consistent with the scout data. This object ensemble is imaged by numerous simulated hardware configurations and for each system estimates of signal activity, size and location are calculated via the Scanning Linear Estimator (SLE). A figure of merit, based on a Modified Dice Index (MDI), quantifies the performance of each imaging configuration and it allows for optimization of the adaptive SPECT. This figure of merit is calculated by multiplying two terms: the first term uses the definition of the Dice similarity index to determine the percent of overlap between the actual and the estimated spherical signal, the second term utilizes an exponential function that measures the squared error for the activity estimate. The MDI combines the error in estimates of activity, size, and location, in one convenient metric and it allows for simultaneous optimization of the SPECT system with respect to all the estimated signal parameters. The results of our optimizations indicate that the adaptive system performs better than a non-adaptive one in conditions where the diagnostic scan has a low photon count - on the order of thousand photons per projection. In a statistical study, we optimized the SPECT system for one hundred unique objects and demonstrated that the average MDI on an estimation task is 0.84 for the adaptive system and 0.65 for the non-adaptive system.

Optimal channels for channelized quadratic estimators

We present a new method for computing optimized channels for estimation tasks that is feasible for high-dimensional image data. Maximum-likelihood (ML) parameter estimates are challenging to compute from high-dimensional likelihoods. The dimensionality reduction from M measurements to L channels is a critical advantage of channelized quadratic estimators (CQEs), since estimating likelihood moments from channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier. The channelized likelihood is then used to form ML estimates of the parameter(s). In this work we choose an imaging example in which the second-order statistics of the image data depend upon the parameter of interest: the correlation length. Correlation lengths are used to approximate background textures in many imaging applications, and in these cases an estimate of the correlation length is useful for pre-whitening. In a simulation study we compare the estimation performance, as measured by the root-mean-squared error (RMSE), of correlation length estimates from CQE and power spectral density (PSD) distribution fitting. To abide by the assumptions of the PSD method we simulate an ergodic, isotropic, stationary, and zero-mean random process. These assumptions are not part of the CQE formalism. The CQE method assumes a Gaussian channelized likelihood that can be a valid for non-Gaussian image data, since the channel outputs are formed from weighted sums of the image elements. We have shown that, for three or more channels, the RMSE of CQE estimates of correlation length is lower than conventional PSD estimates. We also show that computing CQE by using a standard nonlinear optimization method produces channels that yield RMSE within 2% of the analytic optimum. CQE estimates of anisotropic correlation length estimation are reported to demonstrate this technique on a two-parameter estimation problem.

Singular value decomposition for photon-processing nuclear imaging systems and applications for reconstruction and computing null functions

Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and implemented for graphics processing units (GPUs). Further, this approach leverages another important advantage of PP systems, namely the possibility to perform photon-by-photon real-time reconstruction. We demonstrate the application of the approach to perform reconstruction in a simulated 2D SPECT system. The results help to validate and demonstrate the utility of the proposed method and show that PP systems can help overcome the aliasing artifacts that are otherwise intrinsically present in PC systems.

Comparison of the scanning linear estimator (SLE) and ROI methods for quantitative SPECT imaging

In quantitative emission tomography, tumor activity is typically estimated from calculations on a region of interest (ROI) identified in the reconstructed slices. In these calculations, unpredictable bias arising from the null functions of the imaging system affects ROI estimates. The magnitude of this bias depends upon the tumor size and location. In prior work it has been shown that the scanning linear estimator (SLE), which operates on the raw projection data, is an unbiased estimator of activity when the size and location of the tumor are known. In this work, we performed analytic simulation of SPECT imaging with a parallel-hole medium-energy collimator. Distance-dependent system spatial resolution and non-uniform attenuation were included in the imaging simulation. We compared the task of activity estimation by the ROI and SLE methods for a range of tumor sizes (diameter: 1-3 cm) and activities (contrast ratio: 1-10) added to uniform and non-uniform liver backgrounds. Using the correct value for the tumor shape and location is an idealized approximation to how task estimation would occur clinically. Thus we determined how perturbing this idealized prior knowledge impacted the performance of both techniques. To implement the SLE for the non-uniform background, we used a novel iterative algorithm for pre-whitening stationary noise within a compact region. Estimation task performance was compared using the ensemble mean-squared error (EMSE) as the criterion. The SLE method performed substantially better than the ROI method (i.e. EMSE(SLE) was 23-174 times lower) when the background is uniform and tumor location and size are known accurately. The variance of the SLE increased when a non-uniform liver texture was introduced but the EMSE(SLE) continued to be 5-20 times lower than the ROI method. In summary, SLE outperformed ROI under almost all conditions that we tested.

Task-based measures of image quality and their relation to radiation dose and patient risk

The theory of task-based assessment of image quality is reviewed in the context of imaging with ionizing radiation, and objective figures of merit (FOMs) for image quality are summarized. The variation of the FOMs with the task, the observer and especially with the mean number of photons recorded in the image is discussed. Then various standard methods for specifying radiation dose are reviewed and related to the mean number of photons in the image and hence to image quality. Current knowledge of the relation between local radiation dose and the risk of various adverse effects is summarized, and some graphical depictions of the tradeoffs between image quality and risk are introduced. Then various dose-reduction strategies are discussed in terms of their effect on task-based measures of image quality.