Tomographic reconstruction with a generative adversarial network

This paper presents a deep learning algorithm for tomographic reconstruction (GANrec). The algorithm uses a generative adversarial network (GAN) to solve the inverse of the Radon transform directly. It works for independent sinograms without additional training steps. The GAN has been developed to fit the input sinogram with the model sinogram generated from the predicted reconstruction. Good quality reconstructions can be obtained during the minimization of the fitting errors. The reconstruction is a self-training procedure based on the physics model, instead of on training data. The algorithm showed significant improvements in the reconstruction accuracy, especially for missing-wedge tomography acquired at less than 180° rotational range. It was also validated by reconstructing a missing-wedge X-ray ptychographic tomography (PXCT) data set of a macroporous zeolite particle, for which only 51 projections over 70° could be collected. The GANrec recovered the 3D pore structure with reasonable quality for further analysis. This reconstruction concept can work universally for most of the ill-posed inverse problems if the forward model is well defined, such as phase retrieval of in-line phase-contrast imaging

Single-exposure X-ray phase imaging microscopy with a grating interferometer

The advent of hard X-ray free-electron lasers enables nanoscopic X-ray imaging with sub-picosecond temporal resolution. X-ray grating interferometry offers a phase-sensitive full-field imaging technique where the phase retrieval can be carried out from a single exposure alone. Thus, the method is attractive for imaging applications at X-ray free-electron lasers where intrinsic pulse-to-pulse fluctuations pose a major challenge. In this work, the single-exposure phase imaging capabilities of grating interferometry are characterized by an implementation at the I13-1 beamline of Diamond Light Source (Oxfordshire, UK). For comparison purposes, propagation-based phase contrast imaging was also performed at the same instrument. The characterization is carried out in terms of the quantitativeness and the contrast-to-noise ratio of the phase reconstructions as well as via the achievable spatial resolution. By using a statistical image reconstruction scheme, previous limitations of grating interferometry regarding the spatial resolution can be mitigated as well as the experimental applicability of the technique

Clinically practical pharmacometrics computer model to evaluate and personalize pharmacotherapy in pediatric rare diseases: application to Graves' disease

ObjectivesGraves' disease (GD) with onset in childhood or adolescence is a rare disease (ORPHA:525731). Current pharmacotherapeutic approaches use antithyroid drugs, such as carbimazole, as monotherapy or in combination with thyroxine hormone substitutes, such as levothyroxine, as block-and-replace therapy to normalize thyroid function and improve patients' quality of life. However, in the context of fluctuating disease activity, especially during puberty, a considerable proportion of pediatric patients with GD is suffering from thyroid hormone concentrations outside the therapeutic reference ranges. Our main goal was to develop a clinically practical pharmacometrics computer model that characterizes and predicts individual disease activity in children with various severity of GD under pharmacotherapy.MethodsRetrospectively collected clinical data from children and adolescents with GD under up to two years of treatment at four different pediatric hospitals in Switzerland were analyzed. Development of the pharmacometrics computer model is based on the non-linear mixed effects approach accounting for inter-individual variability and incorporating individual patient characteristics. Disease severity groups were defined based on free thyroxine (FT4) measurements at diagnosis.ResultsData from 44 children with GD (75% female, median age 11 years, 62% receiving monotherapy) were analyzed. FT4 measurements were collected in 13, 15, and 16 pediatric patients with mild, moderate, or severe GD, with a median FT4 at diagnosis of 59.9 pmol/l (IQR 48.4, 76.8), and a total of 494 FT4 measurements during a median follow-up of 1.89 years (IQR 1.69, 1.97). We observed no notable difference between severity groups in terms of patient characteristics, daily carbimazole starting doses, and patient years. The final pharmacometrics computer model was developed based on FT4 measurements and on carbimazole or on carbimazole and levothyroxine doses involving two clinically relevant covariate effects: age at diagnosis and disease severity.DiscussionWe present a tailored pharmacometrics computer model that is able to describe individual FT4 dynamics under both, carbimazole monotherapy and carbimazole/levothyroxine block-and-replace therapy accounting for inter-individual disease progression and treatment response in children and adolescents with GD. Such clinically practical and predictive computer model has the potential to facilitate and enhance personalized pharmacotherapy in pediatric GD, reducing over- and underdosing and avoiding negative short- and long-term consequences. Prospective randomized validation trials are warranted to further validate and fine-tune computer-supported personalized dosing in pediatric GD and other rare pediatric diseases

Behavior of Runge-Kutta Discretizations near equlibria of Index 2 Differential Algebraic Systems

We analyze Runge-Kutta discretizations applied to index 2 differential algebraic equations (DAE's) near equilibria. We compare the geometric properties of the numerical and the exact solutions. It is shown that projected and half-explicit Runge-Kutta methods reproduce the qualitative features of the continuous system correctly. The proof combines scaling techniques for index 2 differential algebraic equations with some invariant manifold results of Schropp and classical results for discretized ordinary differential equations of Garay

A Dynamical Systems Approach to Constrained Minimization

We present an ordinary differential equations approach to solve general smooth minimization problems including a convergence analysis. Generically often the procedure ends up at a point which fulfills sufficient conditions for a local minimum. This procedure will then be rewritten in the concept of differential algebraic equations which opens the route to an efficient implementation. Furthermore, we link this approach with the classical SQP-approach and apply both techniques onto two examples relevant in applications

Attracting sets in index 2 Differential Algebraic Equations and in their Runge-Kutta Discretizations

We analyze Runge-Kutta discretizations applied to index 2 differential algebraic equations (DAE's) in the vicinity of attracting sets. We compare the geometric properties of the numerical and the exact solutions and show that projected and half-explicit RungeKutta methods reproduce the qualitative features of the continuous system correctly. The proof combines invariant manifold results of Schropp [13] and classical results for discretized ordinary differential equations of Kloeden, Lorenz [10]

One and Multistep Discretizations of Index 2 Differential Algebraic Systems and their use in Optimization

An approach to solve constrained minimization problems is to integrate a corresponding index 2 differential algebraic equation (DAE). Here corresponding means that the!-limit sets of the DAE dynamics are local solutions of the minimization problem. In order to obtain an efficient optimization code we analyse the behavior of certain Runge-Kutta and linear multistep discretizations applied to these DAEs. It is shown that the discrete dynamics reproduces the geometric properties and the long time behavior of the continuous system correctly. Finally, we compare the DAE approach with a classical SQP-method

Invariant manifolds in differential algebraic equations of index 3 and in their Runge-Kutta discretizations

In the present paper we analyze the geometric properties of projected Runge-Kutta methods when applied to index 3 differential algebraic equations in Hessenberg form. These methods admit the integration of index 3 DAEs without any drift effects. We show that the phase portrait is well reproduced in its relationship between space and control variables