From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses

The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses. We outline possible steps toward translating this computational approach to the bedside, to supplement today's evidence-based medicine with a quantitatively founded model-based medicine that integrates mechanistic knowledge with patient-specific information

Advanced signal processing methods in dynamic contrast enhanced magnetic resonance imaging

Tato dizertační práce představuje metodu zobrazování perfúze magnetickou rezonancí, jež je výkonným nástrojem v diagnostice, především v onkologii. Po ukončení sběru časové sekvence T1-váhovaných obrazů zaznamenávajících distribuci kontrastní látky v těle začíná fáze zpracování dat, která je předmětem této dizertace. Je zde představen teoretický základ fyziologických modelů a modelů akvizice pomocí magnetické rezonance a celý řetězec potřebný k vytvoření obrazů odhadu parametrů perfúze a mikrocirkulace v tkáni. Tato dizertační práce je souborem uveřejněných prací autora přispívajícím k rozvoji metodologie perfúzního zobrazování a zmíněného potřebného teoretického rozboru.This dissertation describes quantitative dynamic contrast enhanced magnetic resonance imaging (DCE-MRI), which is a powerful tool in diagnostics, mainly in oncology. After a time series of T1-weighted images recording contrast-agent distribution in the body has been acquired, data processing phase follows. It is presented step by step in this dissertation. The theoretical background in physiological and MRI-acquisition modeling is described together with the estimation process leading to parametric maps describing perfusion and microcirculation properties of the investigated tissue on a voxel-by-voxel basis. The dissertation is divided into this theoretical analysis and a set of publications representing particular contributions of the author to DCE-MRI.

Mechanistic machine learning: how data assimilation leverages physiologic knowledge using Bayesian inference to forecast the future, infer the present, and phenotype

We introduce data assimilation as a computational method that uses machine learning to combine data with human knowledge in the form of mechanistic models in order to forecast future states, to impute missing data from the past by smoothing, and to infer measurable and unmeasurable quantities that represent clinically and scientifically important phenotypes. We demonstrate the advantages it affords in the context of type 2 diabetes by showing how data assimilation can be used to forecast future glucose values, to impute previously missing glucose values, and to infer type 2 diabetes phenotypes. At the heart of data assimilation is the mechanistic model, here an endocrine model. Such models can vary in complexity, contain testable hypotheses about important mechanics that govern the system (eg, nutrition’s effect on glucose), and, as such, constrain the model space, allowing for accurate estimation using very little data

Mathematical and Statistical Modeling in Cancer Systems Biology

Cancer is a major health problem with high mortality rates. In the post-genome era, investigators have access to massive amounts of rapidly accumulating high-throughput data in publicly available databases, some of which are exclusively devoted to housing Cancer data. However, data interpretation efforts have not kept pace with data collection, and gained knowledge is not necessarily translating into better diagnoses and treatments. A fundamental problem is to integrate and interpret data to further our understanding in Cancer Systems Biology. Viewing cancer as a network provides insights into the complex mechanisms underlying the disease. Mathematical and statistical models provide an avenue for cancer network modeling. In this article, we review two widely used modeling paradigms: deterministic metabolic models and statistical graphical models. The strength of these approaches lies in their flexibility and predictive power. Once a model has been validated, it can be used to make predictions and generate hypotheses. We describe a number of diverse applications to Cancer Biology, including, the system-wide effects of drug-treatments, disease prognosis, tumor classification, forecasting treatment outcomes, and survival predictions

Inverse problems from biomedicine: Inference of putative disease mechanisms and robust therapeutic strategies

Many complex diseases that are difficult to treat cannot be mapped onto a single cause, but arise from the interplay of multiple contributing factors. In the study of such diseases, it is becoming apparent that therapeutic strategies targeting a single protein or metabolite are often not efficacious. Rather, a systems perspective describing the interaction of physiological components is needed. In this paper, we demonstrate via examples of disease models the kind of inverse problems that arise from the need to infer disease mechanisms and/or therapeutic strategies. We identify the challenges that arise, in particular the need to devise strategies that are robust against variable physiological states and parametric uncertaintie

Computational neuroimaging strategies for single patient predictions

AbstractNeuroimaging increasingly exploits machine learning techniques in an attempt to achieve clinically relevant single-subject predictions. An alternative to machine learning, which tries to establish predictive links between features of the observed data and clinical variables, is the deployment of computational models for inferring on the (patho)physiological and cognitive mechanisms that generate behavioural and neuroimaging responses. This paper discusses the rationale behind a computational approach to neuroimaging-based single-subject inference, focusing on its potential for characterising disease mechanisms in individual subjects and mapping these characterisations to clinical predictions. Following an overview of two main approaches – Bayesian model selection and generative embedding – which can link computational models to individual predictions, we review how these methods accommodate heterogeneity in psychiatric and neurological spectrum disorders, help avoid erroneous interpretations of neuroimaging data, and establish a link between a mechanistic, model-based approach and the statistical perspectives afforded by machine learning