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Medical imaging systems are often evaluated and optimized via objective, or task-specific, measures of image quality (IQ) that quantify the performance of an observer on a specific clinically-relevant task. The performance of the Bayesian Ideal Observer (IO) sets an upper limit among all observers, numerical or human, and has been advocated for use as a figure-of-merit (FOM) for evaluating and optimizing medical imaging systems. However, the IO test statistic corresponds to the likelihood ratio that is intractable to compute in the majority of cases. A sampling-based method that employs Markov-chain Monte Carlo (MCMC) techniques was previously proposed to estimate the IO performance. However, current applications of MCMC methods for IO approximation have been limited to a small number of situations where the considered distribution of to-be-imaged objects can be described by a relatively simple stochastic object model (SOM). As such, there remains an important need to extend the domain of applicability of MCMC methods to address a large variety of scenarios where IO-based assessments are needed but the associated SOMs have not been available. In this study, a novel MCMC method that employs a generative adversarial network (GAN)-based SOM, referred to as MCMC-GAN, is described and evaluated. The MCMC-GAN method was quantitatively validated by use of test-cases for which reference solutions were available. The results demonstrate that the MCMC-GAN method can extend the domain of applicability of MCMC methods for conducting IO analyses of medical imaging systems.

Reliably predicting the future spread of brain tumors using imaging data and on a subject-specific basis requires quantifying uncertainties in data, biophysical models of tumor growth, and spatial heterogeneity of tumor and host tissue. This work introduces a Bayesian framework to calibrate the two-/three-dimensional spatial distribution of the parameters within a tumor growth model to quantitative magnetic resonance imaging (MRI) data and demonstrates its implementation in a pre-clinical model of glioma. The framework leverages an atlas-based brain segmentation of grey and white matter to establish subject-specific priors and tunable spatial dependencies of the model parameters in each region. Using this framework, the tumor-specific parameters are calibrated from quantitative MRI measurements early in the course of tumor development in four rats and used to predict the spatial development of the tumor at later times. The results suggest that the tumor model, calibrated by animal-specific imaging data at one time point, can accurately predict tumor shapes with a Dice coefficient $>$ 0.89. However, the reliability of the predicted volume and shape of tumors strongly relies on the number of earlier imaging time points used for calibrating the model. This study demonstrates, for the first time, the ability to determine the uncertainty in the inferred tissue heterogeneity and the model-predicted tumor shape.

Ultrasound computed tomography (USCT) is an emerging medical imaging modality that holds great promise for improving human health. Full-waveform inversion (FWI)-based image reconstruction methods account for the relevant wave physics to produce high spatial resolution images of the acoustic properties of the breast tissues. A practical USCT design employs a circular ring-array comprised of elevation-focused ultrasonic transducers, and volumetric imaging is achieved by translating the ring-array orthogonally to the imaging plane. In commonly deployed slice-by-slice (SBS) reconstruction approaches, the 3-D volume is reconstructed by stacking together 2-D images reconstructed for each position of the ring-array. A limitation of the SBS reconstruction approach is that it does not account for 3-D wave propagation physics and the focusing properties of the transducers, which can result in significant image artifacts and inaccuracies. To perform 3-D image reconstruction when elevation-focused transducers are employed, a numerical description of the focusing properties of the transducers should be included in the forward model. To address this, a 3-D computational model of an elevation-focused transducer is developed to enable 3-D FWI-based reconstruction methods to be deployed in ring-array-based USCT. The focusing is achieved by applying a spatially varying temporal delay to the ultrasound pulse (emitter mode) and recorded signal (receiver mode). The proposed numerical transducer model is quantitatively validated and employed in computer simulation studies that demonstrate its use in image reconstruction for ring-array USCT.

Many imaging systems can be approximately described by a linear operator that maps an object property to a collection of discrete measurements. However, even in the absence of measurement noise, such operators are generally “blind” to certain components of the object, and hence information is lost in the imaging process. Mathematically, this is explained by the fact that the imaging operator can possess a null space. All objects in the null space, by definition, are mapped to a collection of identically zero measurements and are hence invisible to the imaging system. As such, characterizing the null space of an imaging operator is of fundamental importance when comparing and/or designing imaging systems. A characterization of the null space can also facilitate the design of regularization strategies for image reconstruction methods. Characterizing the null space via an associated projection operator is, in general, a computationally demanding task. In this tutorial, computational procedures for establishing projection operators that map an object to the null space of a discrete-to-discrete imaging operator are surveyed. A new machine-learning-based approach that employs a linear autoencoder is also presented. The procedures are demonstrated by use of biomedical imaging examples, and their computational complexities and memory requirements are compared.

The teachings of the Catholic Church on human sexuality, contraception and the treatment of infertility are well established and clearly explained in many Church documents, including Humanae vitae and Familiaris consortio.In 2022, a book was published in Italian which reported on a seminar organised by an Academy of the Catholic Church about the ethics of life. Titled the Theological Ethics of Life (abbreviated ‘ETV’ in Italian), the conclusion of chapter VII contains statements about contraception and assisted reproductive technologies (ART) which, though somewhat difficult to interpret, appear to be controversial with regard to accepted Church teaching on these subjects.This paper presents a detailed analysis by a group of Australian Catholic doctors and ethicists of an English translation of paragraphs 172 and 173 of ETV and concludes that they contain statements which deviate from and contradict accepted Catholic teaching on contraception and ART.The authors also claim that a thorough up-to-date knowledge and understanding of suitable current alternatives to contraception and ART (eg in-vitro fertilisation, IVF) which are safe, effective, readily accessible and consistent with Catholic ethics appears to be lacking in paragraphs 172 and 173 of ETV.The authors suggest a better understanding of currently available methods to assist with fertility care, aided by input from Catholic medical experts working in the areas of Fertility Awareness Methods (FAMs) and Restorative Reproductive Medicine (RRM) would better inform ongoing debates about contraception and ART within the Church and be of service to the Faithful who should be encouraged to pursue these alternatives which are both effective and consistent with Church teaching on human sexuality and morals.

Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the parameters. Here, we develop a Bayesian inversion framework that uses Interferometric Synthetic Aperture Radar (InSAR) surface deformation data to infer the laterally heterogeneous permeability of a transient linear poroelastic model of a confined GW aquifer. The Bayesian solution of this inverse problem takes the form of a posterior probability density of the permeability. Exploring this posterior using classical Markov chain Monte Carlo (MCMC) methods is computationally prohibitive due to the large dimension of the discretized permeability field and the expense of solving the poroelastic forward problem. However, in many partial differential equation (PDE)‐based Bayesian inversion problems, the data are only informative in a few directions in parameter space. For the poroelasticity problem, we prove this property theoretically for a one‐dimensional problem and demonstrate it numerically for a three‐dimensional aquifer model. We design a generalized preconditioned Crank‐Nicolson (gpCN) MCMC method that exploits this intrinsic low dimensionality by using a low‐rank‐based Laplace approximation of the posterior as a proposal, which we build scalably. The feasibility of our approach is demonstrated through a real GW aquifer test in Nevada. The inherently two‐dimensional nature of InSAR surface deformation data informs a sufficient number of modes of the permeability field to allow detection of major structures within the aquifer, significantly reducing the uncertainty in the pressure and the displacement quantities of interest. Using Interferometric Synthetic Aperture Radar data reduces the uncertainty in selected quantities of interest compared to using prior knowledge onlyThe preconditioned Crank‐Nicolson (pCN) Markov chain Monte Carlo (MCMC) method is extended to exploit posterior curvature and allow better chain mixingWe demonstrate the intrinsic low dimensionality of the poroelastic inverse problem that is, critical for the success of the MCMC method Using Interferometric Synthetic Aperture Radar data reduces the uncertainty in selected quantities of interest compared to using prior knowledge only The preconditioned Crank‐Nicolson (pCN) Markov chain Monte Carlo (MCMC) method is extended to exploit posterior curvature and allow better chain mixing We demonstrate the intrinsic low dimensionality of the poroelastic inverse problem that is, critical for the success of the MCMC method