Erratum: Publisher's Note: Stochastic models for objects and images in oncology and virology: application to PI3K-Akt-mTOR signaling and COVID-19 disease.

[This corrects the article DOI: 10.1117/1.JMI.

Stochastic models for objects and images in oncology and virology: application to PI3K-Akt-mTOR signaling and COVID-19 disease.

The goal of this research is to develop innovative methods of acquiring simultaneous multidimensional molecular images of several different physiological random processes (PRPs) that might all be active in a particular disease such as COVID-19. Our study is part of an ongoing effort at the University of Arizona to derive biologically accurate yet mathematically tractable models of the objects of interest in molecular imaging and of the images they produce. In both cases, the models are fully stochastic, in the sense that they provide ways to estimate any estimable property of the object or image.

Is there a role for image science in the brave new world of artificial intelligence?

Knowledge of the principles of image science is essential to the successful application of artificial intelligence in medical imaging.

Objective assessment of the effects of tumor motion in radiation therapy.

Purpose: Internal organ motion reduces the accuracy and efficacy of radiation therapy. However, there is a lack of tools to objectively (based on a medical or scientific task) assess the dosimetric consequences of motion, especially on an individual basis. We propose to use therapy operating characteristic (TOC) analysis to quantify the effects of motion on treatment efficacy for individual patients.

Physiological random processes in precision cancer therapy.

Many different physiological processes affect the growth of malignant lesions and their response to therapy. Each of these processes is spatially and genetically heterogeneous; dynamically evolving in time; controlled by many other physiological processes, and intrinsically random and unpredictable. The objective of this paper is to show that all of these properties of cancer physiology can be treated in a unified, mathematically rigorous way via the theory of random processes.

Null functions in three-dimensional imaging of alpha and beta particles.

Null functions of an imaging system are functions in the object space that give exactly zero data. Hence, they represent the intrinsic limitations of the imaging system. Null functions exist in all digital imaging systems, because these systems map continuous objects to discrete data.

Charged-particle emission tomography.

Purpose: Conventional charged-particle imaging techniques - such as autoradiography - provide only two-dimensional (2D) black ex vivo images of thin tissue slices. In order to get volumetric information, images of multiple thin slices are stacked. This process is time consuming and prone to distortions, as registration of 2D images is required.

Characteristic functionals in imaging and image-quality assessment: tutorial.

Characteristic functionals are one of the main analytical tools used to quantify the statistical properties of random fields and generalized random fields. The viewpoint taken here is that a random field is the correct model for the ensemble of objects being imaged by a given imaging system. In modern digital imaging systems, random fields are not used to model the reconstructed images themselves since these are necessarily finite dimensional.

Therapy operating characteristic curves: tools for precision chemotherapy.

The therapy operating characteristic (TOC) curve, developed in the context of radiation therapy, is a plot of the probability of tumor control versus the probability of normal-tissue complications as the overall radiation dose level is varied, e.g., by varying the beam current in external-beam radiotherapy or the total injected activity in radionuclide therapy.

Radiance and photon noise: imaging in geometrical optics, physical optics, quantum optics and radiology.

The statistics of detector outputs produced by an imaging system are derived from basic radiometric concepts and definitions. We show that a fundamental way of describing a photon-limited imaging system is in terms of a Poisson random process in spatial, angular, and wavelength variables. We begin the paper by recalling the concept of radiance in geometrical optics, radiology, physical optics, and quantum optics.

Estimation of Fano factor in inorganic scintillators.

The Fano factor of an integer-valued random variable is defined as the ratio of its variance to its mean. Correlation between the outputs of two photomultiplier tubes on opposite faces of a scintillation crystal was used to estimate the Fano factor of photoelectrons and scintillation photons. Correlations between the integrals of the detector outputs were used to estimate the photoelectron and photon Fano factor for YAP:Ce, SrI:Eu and CsI:Na scintillator crystals.

Impact of the Fano Factor on Position and Energy Estimation in Scintillation Detectors.

The Fano factor for an integer-valued random variable is defined as the ratio of its variance to its mean. Light from various scintillation crystals have been reported to have Fano factors from sub-Poisson (Fano factor < 1) to super-Poisson (Fano factor > 1). For a given mean, a smaller Fano factor implies a smaller variance and thus less noise.

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.

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.

Molecular Imaging in the College of Optical Sciences - An Overview of Two Decades of Instrumentation Development.

During the past two decades, researchers at the University of Arizona's Center for Gamma-Ray Imaging (CGRI) have explored a variety of approaches to gamma-ray detection, including scintillation cameras, solid-state detectors, and hybrids such as the intensified Quantum Imaging Device (iQID) configuration where a scintillator is followed by optical gain and a fast CCD or CMOS camera. We have combined these detectors with a variety of collimation schemes, including single and multiple pinholes, parallel-hole collimators, synthetic apertures, and anamorphic crossed slits, to build a large number of preclinical molecular-imaging systems that perform Single-Photon Emission Computed Tomography (SPECT), Positron Emission Tomography (PET), and X-Ray Computed Tomography (CT). In this paper, we discuss the themes and methods we have developed over the years to record and fully use the information content carried by every detected gamma-ray photon.

Quantifying and Reducing Uncertainties in Cancer Therapy.

There are two basic sources of uncertainty in cancer chemotherapy: how much of the therapeutic agent reaches the cancer cells, and how effective it is in reducing or controlling the tumor when it gets there. There is also a concern about adverse effects of the therapy drug. Similarly in external-beam radiation therapy or radionuclide therapy, there are two sources of uncertainty: delivery and efficacy of the radiation absorbed dose, and again there is a concern about radiation damage to normal tissues.

The iQID camera: An ionizing-radiation quantum imaging detector.

We have developed and tested a novel, ionizing-radiation Quantum Imaging Detector (iQID). This scintillation-based detector was originally developed as a high-resolution gamma-ray imager, called BazookaSPECT, for use in single-photon emission computed tomography (SPECT). Recently, we have investigated the detector's response and imaging potential with other forms of ionizing radiation including alpha, neutron, beta, and fission fragment particles.

Fisher Information Analysis of Depth-of-Interaction Estimation in Double-Sided Strip Detectors.

In very-high-spatial-resolution gamma-ray imaging applications, such as preclinical PET and SPECT, estimation of 3D interaction location inside the detector crystal can be used to minimize parallax error in the imaging system. In this work, we investigate the effect of bias voltage setting on depth-of-interaction (DOI) estimates for a semiconductor detector with a double-sided strip geometry. We first examine the statistical properties of the signals and develop expressions for likelihoods for given gamma-ray interaction positions.

High-Resolution Anamorphic SPECT Imaging.

We have developed a gamma-ray imaging system that combines a high-resolution silicon detector with two sets of movable, half-keel-edged copper-tungsten blades configured as crossed slits. These apertures can be positioned independently between the object and detector, producing an anamorphic image in which the axial and transaxial magnifications are not constrained to be equal. The detector is a 60 mm × 60 mm, one-millimeter-thick, one-megapixel silicon double-sided strip detector with a strip pitch of 59 m.

Fabrication of the pinhole aperture for AdaptiSPECT.

AdaptiSPECT is a pre-clinical pinhole SPECT imaging system under final construction at the Center for Gamma-Ray Imaging. The system is designed to be able to autonomously change its imaging configuration. The system comprises 16 detectors mounted on translational stages to move radially away and towards the center of the field-of-view.

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.

RADIANCE AND PHOTON NOISE: Imaging in geometrical optics, physical optics, quantum optics and radiology.

A fundamental way of describing a photon-limited imaging system is in terms of a Poisson random process in spatial, angular and wavelength variables. The mean of this random process is the spectral radiance. The principle of conservation of radiance then allows a full characterization of the noise in the image (conditional on viewing a specified object).

Synthetic phase-shifting for optical testing: point-diffraction interferometry without null optics or phase shifters.

An innovative iterative search method called the synthetic phase-shifting (SPS) algorithm is proposed. This search algorithm is used for maximum-likelihood (ML) estimation of a wavefront that is described by a finite set of Zernike Fringe polynomials. In this paper, we estimate the coefficient, or parameter, values of the wavefront using a single interferogram obtained from a point-diffraction interferometer (PDI).

Objective assessment of image quality VI: imaging in radiation therapy.

Earlier work on objective assessment of image quality (OAIQ) focused largely on estimation or classification tasks in which the desired outcome of imaging is accurate diagnosis. This paper develops a general framework for assessing imaging quality on the basis of therapeutic outcomes rather than diagnostic performance. By analogy to receiver operating characteristic (ROC) curves and their variants as used in diagnostic OAIQ, the method proposed here utilizes the therapy operating characteristic or TOC curves, which are plots of the probability of tumor control versus the probability of normal-tissue complications as the overall dose level of a radiotherapy treatment is varied.

Skeletal muscle satellite cell migration to injured tissue measured with 111In-oxine and high-resolution SPECT imaging.

The delivery of adult skeletal muscle stem cells, called satellite cells, to several injured muscles via the circulation would be useful, however, an improved understanding of cell fate and biodistribution following their delivery is important for this goal to be achieved. The objective of this study was to evaluate the ability of systemically delivered satellite cells to home to injured skeletal muscle using single-photon emission computed tomography (SPECT) imaging of (111)In-labeled satellite cells. Satellite cells labeled with (111)In-oxine and green fluorescent protein (GFP) were injected intravenously after bupivicaine-induced injury to the tibialis anterior muscle.