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.: Although quantitative physiology has developed numerous mathematical descriptions of components of the human body, their application in clinical medicine has been limited to a few mostly primitive and physiologically inaccurate models. One reason for this is that the inverse problem of identifying unknown model parameters and states from prior knowledge and clinical observations does not usually have a unique solution. Hypothesizing that this non-uniqueness might actually convey clinically useful information, we used a simplified mathematical model of the cardiovascular system and its control, in combination with Bayesian inference techniques, to simulate the diagnosis of low blood pressure in an acute care setting. The inference procedure yielded a distribution of physiologically interpretable model parameters and states that exhibited multiple peaks. The key observation was that these peaks corresponded directly to clinically relevant differential diagnoses, enabling a quantitative, probabilistic assessment of the simulated patient's condition. We conclude that the proposed probabilistic approach to the inverse problem in quantitative physiology may not only be useful for quantitative interpretation of clinical data, and eventually allow model-based prediction and therapy optimization, but also provides a novel link between mathematically described physiological mechanisms and the clinical concept of differential diagnoses based on patient-specific information.