Compartmental analysis of dynamic nuclear medicine data: models and identifiability

Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the first of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework. Specifically, here we discuss the identifiability problem for a general n-dimension compartmental system and provide uniqueness results in the case of two-compartment and three-compartment compartmental models. The second paper will utilize this framework in order to show how non-linear regularization schemes can be applied to obtain numerical estimates of the tracer coefficients in the case of nuclear medicine data corresponding to brain, liver and kidney physiology

Iterative algorithms for a non-linear inverse problem in atmospheric lidar

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms outperform standard methods in terms of sensitivity to noise and reliability of the estimated profile.Comment: 19 pages, 6 figure

Modeling and inference of spatio-temporal protein dynamics across brain networks

Models of misfolded proteins (MP) aim at discovering the bio-mechanical propagation properties of neurological diseases (ND) by identifying plausible associated dynamical systems. Solving these systems along the full disease trajectory is usually challenging, due to the lack of a well defined time axis for the pathology. This issue is addressed by disease progression models (DPM) where long-term progression trajectories are estimated via time reparametrization of individual observations. However, due to their loose assumptions on the dynamics, DPM do not provide insights on the bio-mechanical properties of MP propagation. Here we propose a unified model of spatio-temporal protein dynamics based on the joint estimation of long-term MP dynamics and time reparameterization of individuals observations. The model is expressed within a Gaussian Process (GP) regression setting, where constraints on the MP dynamics are imposed through non--linear dynamical systems. We use stochastic variational inference on both GP and dynamical system parameters for scalable inference and uncertainty quantification of the trajectories. Experiments on simulated data show that our model accurately recovers prescribed rates along graph dynamics and precisely reconstructs the underlying progression. When applied to brain imaging data our model allows the bio-mechanical interpretation of amyloid deposition in Alzheimer's disease, leading to plausible simulations of MP propagation, and achieving accurate predictions of individual MP deposition in unseen data

Reference Tissue Models for FDG-PET Data: Identifiability and Solvability

A reference tissue model (RTM) is a compartmental approach to the estimation of the kinetic parameters of the tracer flow in a given two-compartment target tissue (TT) without explicit knowledge of the time activity curve (TAC) of tracer concentration in the arterial blood. An \u201cindirect\u201d measure of arterial concentration is provided by the TAC of a suitably chosen one-compartment reference tissue (RT). The RTM is formed by the RT and the TT. In this paper, it is shown that the RTM is identifiable, i.e., the rate constants are uniquely retrievable, provided that a selection criterion for one of the coefficients, which is based on the Logan plot of the RT, is introduced. The exchange coefficients are then evaluated by the application of a Gauss-Newton method, with a regularizing term, accounting for the ill-posedness of the problem. The reliability of the method is validated against synthetic data generated according to realistic conditions, and compared with the full two-compartment model for the TT, here used as \u201cgold standard.\u201d Finally, the RTM is applied to the estimate of the rate constants in the case of animal models with murine cancer cell lines CT26 inoculated

Para um desenvolvimento de competências interculturais

El grupo de Galapro “Intercomprensión e interculturalidad”, está compuesto por participantes de lenguas romances, en su mayoría formadores, que han decidido relacionar de alguna manera la intercomprensión entre las lenguas de una misma familia con cuestiones relacionadas con la diversidad de culturas y costumbres. El objetivo marcado es la realización de un artículo o trabajo que analice un aspecto concreto de la interculturalidad en una sesión del Chat de una plataforma anterior, denominada Galanet, donde se investigaba y ponía en práctica la intercomprensión. Concretamente, hemos decidido tratar las formas de la cortesía en este lugar y entre lenguas/culturas distintas. Pero para ello, presentaremos primero una serie de características que nos sitúen en esa nueva forma de comunicación que es el Chat. Tras los análisis concretos de distintos aspectos de la cortesía (traducción e interculturalidad, otros aspectos y las negaciones y sus respuestas) propondremos algunas aplicaciones didácticas posibles en base a todo lo estudiado. En concreto, ofrecemos un cuestionario para los participantes en chats de diversas lenguas para conocer las representaciones sobre la interculuralidad y la cortesía que manejan. Algunos de los objetivos de estas propuestas didácticas podrían ser: encontrar modos de potenciar la interculturalidad, conocer las costumbres y modos lingüísticos corteses y descorteses de otras culturas para evitar el conflicto, deconstruir mitos y anular estereotipos, etc. Los materiales utilizados para componer este artículo han sido en primer lugar, ejemplos de Chats extraídos de Galanet que trataban diferencias culturales y/o lingüísticas. Entre ellos tenemos, una sesión que se ocupaba de lo no verbal y lo gestual entre extranjeros, otra que trataba sobre los falsos amigos, un Chat denominado “Agua”, pero que se dedicaba a las interferencias entre lenguas romances y experiencias en el extranjero de los participantes y finalmente, el Chat “Comida” que es el que hemos elegido para realizar nuestro análisis y que incluye varios temas “interculturales” como el orden de las comidas o la forma de leer la hora. Además de esta base de datos que recopila ejemplos empíricos se han incluido en los foros otros artículos de carácter teórico, como aquel que trata las formas de gestionar el conflicto en los chats y foros , varias fichas de lectura tomadas de Galanet y Galapro y se nos ha animado a visitar los ficheros específicos de esta segunda plataforma que trataban sobre la intercomprensión

Data-driven modelling of neurodegenerative disease progression: thinking outside the black box

Data-driven disease progression models are an emerging set of computational tools that reconstruct disease timelines for long-term chronic diseases, providing unique insights into disease processes and their underlying mechanisms. Such methods combine a priori human knowledge and assumptions with large-scale data processing and parameter estimation to infer long-term disease trajectories from short-term data. In contrast to 'black box' machine learning tools, data-driven disease progression models typically require fewer data and are inherently interpretable, thereby aiding disease understanding in addition to enabling classification, prediction and stratification. In this Review, we place the current landscape of data-driven disease progression models in a general framework and discuss their enhanced utility for constructing a disease timeline compared with wider machine learning tools that construct static disease profiles. We review the insights they have enabled across multiple neurodegenerative diseases, notably Alzheimer disease, for applications such as determining temporal trajectories of disease biomarkers, testing hypotheses about disease mechanisms and uncovering disease subtypes. We outline key areas for technological development and translation to a broader range of neuroscience and non-neuroscience applications. Finally, we discuss potential pathways and barriers to integrating disease progression models into clinical practice and trial settings