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.8.S1.S16001.].

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

Purpose: 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. Approach: 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. The mathematical tool we use for images is the characteristic function, which can be calculated if the multivariate probability density function for the image data is known. For objects, which are functions of continuous variables rather than discrete pixels or voxels, the characteristic function becomes infinite dimensional, and we refer to it as the characteristic functional. Results: Several innovative mathematical results are derived, in particular for simultaneous imaging of multiple PRPs. Then the application of these methods to cancers that disrupt the mammalian target of rapamycin signaling pathway and to COVID-19 are discussed qualitatively. One reason for choosing these two problems is that they both involve lipid rafts. Conclusions: We found that it was necessary to employ a new algorithm for energy estimation to do simultaneous single-photon emission computerized tomography imaging of a large number of different tracers. With this caveat, however, we expect to be able to acquire and analyze an unprecedented amount of molecular imaging data for an individual COVID patient.

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. We demonstrate the application of this tool with pancreatic stereotactic body radiation therapy (SBRT) clinical data and explore the origin of motion sensitivity. METHODS: The technique is described as follows. (a) Use tumor-motion data measured from patients to calculate the motion-convolved dose of the gross tumor volume (GTV) and the organs at risk (OARs). (b) Calculate tumor control probability (TCP) and normal tissue complication probability (NTCP) from the motion-convolved dose-volume histograms. (c) Construct TOC curves from TCP and NTCP models. (d) Calculate the area under the TOC curve (AUTOC) and use it as a figure of merit for treatment efficacy. We used tumor motion data measured from patients to calculate the relation between AUTOC and motion magnitude for 25 pancreatic SBRT treatment plans. Furthermore, to explore the driving factor of motion sensitivity of a given plan, we compared the dose distribution of motion-sensitive plans and motion-robust plans and studied the dependence of motion sensitivity to motion directions. RESULTS: Our technique is able to recognize treatment plans that are sensitive to motion. Under the presence of motion, the treatment efficacy of some plans changes from providing high tumor control and low risks of complications to providing no tumor control and high risks of side effects. Several treatment plans experience falloffs in AUTOC at a smaller magnitude of motion than other plans. In our dataset, a potential indicator of a motion-sensitive treatment plan is that the duodenum is in proximity to the tumor in the SI direction. CONCLUSIONS: The TOC framework can serve as a tool to quantify the effects of internal organ motion in radiation therapy. With pancreatic SBRT clinical data, we applied this tool to study the change in treatment efficacy induced by motion for individual treatment plans. This framework could potentially be used clinically to understand the effects of motion in an individual patient and to design a patient-specific motion management plan. This framework could also be used in research to evaluate different components of the treatment process, such as motion-management techniques, treatment-planning algorithms, and treatment margins.

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. We treat each physiological process as a random function of position and time within a tumor, defining the joint statistics of such functions via the infinite-dimensional characteristic functional. The theory is illustrated by analyzing several models of drug delivery and response of a tumor to therapy. To apply the methodology to precision cancer therapy, we use maximum-likelihood estimation with Emission Computed Tomography (ECT) data to estimate unknown patient-specific physiological parameters, ultimately demonstrating how to predict the probability of tumor control for an individual patient undergoing a proposed therapeutic regimen.

Determinants of Cervical Cancer Screening among Jamaican Women / Determinantes del cribado de cáncer cervical entre mujeres jamaiquinas

ABSTRACT Objective: To assess the extent to which six sociodemographic variables and three lifestyle practices of women are associated with Pap smear testing, given that cervical cancer is the second leading cause of women 's cancer mortality in Jamaica and that this cancer is preventable with the use of screening methods such as the Pap smear. Methods: Secondary data from Jamaica 's 2008 Reproductive Health Survey were utilized in the study. The sample consisted of 6123 women aged between 21 and 49 years who were sexually experienced. Logistic regression analysis was used to determine whether age, educational attainment, union status, area of residence, wealth quintile, parity, age of sexual initiation, number of lifetime sexual partners and smoking status could predict the likelihood of Pap smear screening among Jamaican women. Results: Of the 6123 women, 79.1% had participated in Pap smear screening. It was found that those who were younger, less educated, single, in visiting relationships, of lower wealth quintiles, had fewer children, an early age of sexual initiation, fewer lifetime sexual partners and who formerly smoked were less likely to undergo Pap smear screening. Conclusion: Policies to increase cervical cancer screening should target women with the characteristics that make them less likely to be screened. Special attention should be directed to poor and uneducated women who are already burdened by their economic and social status. Invitation to screening and periodic small group educational sessions on cervical cancer at public health facilities should also be considered.

RESUMEN Objetivo: Evaluar hasta qué punto seis variables sociodemográficas y tres prácticas de estilo de vida de las mujeres, se asocian con las pruebas de Papanicolau, dado que el cáncer cervical es la segunda causa principal de mortalidad por cáncer entre las mujeres en Jamaica, a pesar de que este tipo de cáncer es prevenible con el uso de métodos de cribado como la citología vaginal. Métodos: En el estudio se utilizaron datos secundarios de la Encuesta de Salud Reproductiva de Jamaica en 2008. La muestra estuvo formada por 6123 mujeres de entre 21 y 49 años de edad, que tuvieron experiencia sexual. Se utilizó un análisis de regresión logística para determinar si la edad, el nivel de educación, el estado de la unión, el área de residencia, el quintil de riqueza, la paridad, la edad de iniciación sexual, el número de parejas sexuales en su vida, y el estatus del hábito de fumar podrían predecir la probabilidad del cribado de la prueba de Papanicolau entre las mujeres jamaicanas. Resultados: De las 6123 mujeres, el 79.1% había participado en el cribado de la prueba citológica vaginal. Se encontró que las mujeres más jóvenes, menos educadas, solteras, con relaciones de visita, con quintiles de riqueza más bajos, menos hijos, temprana edad de iniciación sexual, menos parejas sexuales en su vida, y menos dadas a fumar, presentaban menor probabilidad de someterse a las pruebas de Papanicolau. Conclusión: Las políticas encaminadas a aumentar el cribado del cáncer cervical, deben dirigirse a las mujeres con características que las hacen menos propensas a ser examinadas. Debe prestarse especial atención a las mujeres pobres e incultas, que ya están agobiadas por su estatus económico y social. También debe tenerse en cuenta la invitación a participar tanto en el cribado como en las sesiones educativas periódicas sobre el cáncer cervical, realizadas por grupos pequeños en los centros de salud pública.

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. However, the emergence of detectors that measure continuous data, e.g. particle-processing (PP) detectors, has the potential to eliminate null functions. PP detectors process signals produced by each particle and estimate particle attributes, which include two position coordinates and three components of momentum, as continuous variables. We consider Charged-Particle Emission Tomography (CPET), which relies on data collected by a PP detector to reconstruct the 3D distribution of a radioisotope that emits alpha or beta particles, and show empirically that the null functions are significantly reduced for alpha particles if ≥3 attributes are measured or for beta particles with five attributes measured.

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. We propose a direct three-dimensional (3D) autoradiography technique, which we call charged-particle emission tomography (CPET). This 3D imaging technique enables imaging of thick tissue sections, thus increasing laboratory throughput and eliminating distortions due to registration. CPET also has the potential to enable in vivo charged-particle imaging with a window chamber or an endoscope. METHODS: Our approach to charged-particle emission tomography uses particle-processing detectors (PPDs) to estimate attributes of each detected particle. The attributes we estimate include location, direction of propagation, and/or the energy deposited in the detector. Estimated attributes are then fed into a reconstruction algorithm to reconstruct the 3D distribution of charged-particle-emitting radionuclides. Several setups to realize PPDs are designed. Reconstruction algorithms for CPET are developed. RESULTS: Reconstruction results from simulated data showed that a PPD enables CPET if the PPD measures more attributes than just the position from each detected particle. Experiments showed that a two-foil charged-particle detector is able to measure the position and direction of incident alpha particles. CONCLUSIONS: We proposed a new volumetric imaging technique for charged-particle-emitting radionuclides, which we have called charged-particle emission tomography (CPET). We also proposed a new class of charged-particle detectors, which we have called particle-processing detectors (PPDs). When a PPD is used to measure the direction and/or energy attributes along with the position attributes, CPET is feasible.

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. After a brief introduction to the general theory of characteristic functionals, many examples relevant to imaging applications are presented. The propagation of characteristic functionals through both a binned and list-mode imaging system is also discussed. Methods for using characteristic functionals and image data to estimate population parameters and classify populations of objects are given. These methods are based on maximum likelihood and maximum a posteriori techniques in spaces generated by sampling the relevant characteristic functionals through the imaging operator. It is also shown how to calculate a Fisher information matrix in this space. These estimators and classifiers, and the Fisher information matrix, can then be used for image quality assessment of imaging systems.

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. This paper shows how TOC can be applied to chemotherapy with the administered drug dosage as the variable. The area under a TOC curve (AUTOC) can be used as a figure of merit for therapeutic efficacy, analogous to the area under an ROC curve (AUROC), which is a figure of merit for diagnostic efficacy. In radiation therapy, AUTOC can be computed for a single patient by using image data along with radiobiological models for tumor response and adverse side effects. The mathematical analogy between response of observers to images and the response of tumors to distributions of a chemotherapy drug is exploited to obtain linear discriminant functions from which AUTOC can be calculated. Methods for using mathematical models of drug delivery and tumor response with imaging data to estimate patient-specific parameters that are needed for calculation of AUTOC are outlined. The implications of this viewpoint for clinical trials are discussed.

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, SrI2:Eu and CsI:Na scintillator crystals. At 662 keV, SrI2:Eu was found to be sub-Poisson, while CsI:Na and YAP:Ce were found to be super-Poisson. An experiment setup inspired from the Hanbury Brown and Twiss experiment was used to measure the correlations as a function of time between the outputs of two photomultiplier tubes looking at the same scintillation event. A model of the scintillation and the detection processes was used to generate simulated detector outputs as a function of time for different values of Fano factor. The simulated outputs from the model for different Fano factors was compared to the experimentally measured detector outputs to estimate the Fano factor of the scintillation photons for YAP:Ce, LaBr3:Ce scintillator crystals. At 662 keV, LaBr3:Ce was found to be sub-Poisson, while YAP:Ce was found to be close to Poisson.

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. The propagation and conservation laws for radiance in each of these domains are reviewed. Building upon these concepts, we distinguish four categories of imaging detectors that all respond in some way to the incident radiance, including the new category of photon-processing detectors (capable of measuring radiance on a photon-by-photon basis). This allows us to rigorously show how the concept of radiance is related to the statistical properties of detector outputs and to the information content of a single detected photon. A Monte-Carlo technique, which is derived from the Boltzmann transport equation, is presented as a way to estimate probability density functions to be used in reconstruction from photon-processing data.

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. We investigated if lower noise in the scintillation light will result in better spatial and energy resolutions. The impact of Fano factor on the estimation of position of interaction and energy deposited in simple gamma-camera geometries is estimated by two methods - calculating the Cramér-Rao bound and estimating the variance of a maximum likelihood estimator. The methods are consistent with each other and indicate that when estimating the position of interaction and energy deposited by a gamma-ray photon, the Fano factor of a scintillator does not affect the spatial resolution. A smaller Fano factor results in a better energy resolution.

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.

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 therapy operating characteristic (TOC) curve, developed in the context of radiation therapy, is a plot of the probability of tumor control vs. 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. The TOC can be applied to chemotherapy with the administered drug dosage as the variable. The area under a TOC curve (AUTOC) can be used as a figure of merit for therapeutic efficacy, analogous to the area under an ROC curve (AUROC), which is a figure of merit for diagnostic efficacy. In radiation therapy AUTOC can be computed for a single patient by using image data along with radiobiological models for tumor response and adverse side effects. In this paper we discuss the potential of using mathematical models of drug delivery and tumor response with imaging data to estimate AUTOC for chemotherapy, again for a single patient. This approach provides a basis for truly personalized therapy and for rigorously assessing and optimizing the therapy regimen for the particular patient. A key role is played by Emission Computed Tomography (PET or SPECT) of radiolabeled chemotherapy drugs.

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.

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.

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. The system also possesses an adaptive pinhole aperture with multiple collimator diameters and pinhole sizes, as well as the possibility to switch between multiplexed and non-multiplexed imaging configurations. In this paper, we describe the fabrication of the AdaptiSPECT pinhole aperture and its controllers.

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 µm. The flexible nature of this system allows the application of adaptive imaging techniques. We present system details; calibration, acquisition, and reconstruction methods; and imaging results.