Robust Medical Monitor Design

With recent advances in low-power low-cost communication, sensing, and actuation technologies, Medical Cyber Physical Systems (MCPS) have revolutionized automated medical diagnostics and care. With this revolution, dawns a new era of medical monitoring where fusing measurements from multiple devices provides unprecedented early detection of critical conditions. However, often explicit models and/or rich training data relating available measurements to the critical conditions are unavailable or impractical. Under these troublesome scenarios, this tutorial presents a parameter invariant approach to medical monitor design which has been successful in developing monitors for conditions related to hypoxia, diabetes, and hypovolemia. Owing its mathematical origin to the robust radar signal processing literature, the parameter-invariant approach to medical monitor design is presented as consisting of three parts: (1) foundations of parameter-invariant design, (2) modeling physiological processes for monitoring, and (3) constant false alarm rate (CFAR) testing. To illustrate each component, the tutorial makes extensive use of case study monitors related to medical alarms for hypoxia, hypovolemia, and hypoglycemia. The foundations of parameter-invariant design consists of a design philosophy aimed at providing a monitor robust to nuisance artifacts/parameters in the data. This ultimately requires the co-design of physiological models and test statistics such that maximal invariance is achieved with respect to the nuisances. In this component, we first introduce the high-level mathematical foundations for parameter-invariant design, then provide examples of three parameter-induced transformations and their respective invariant tests common in real-world medical monitoring applications, namely: translation, scale, and rotation. Case study monitors related to hypoxia, hypovolemia, and hypoglycemia are introduced and employed throughout the rest of the tutorial. While there are many approaches to physiological modeling, the parameter-invariant approaches utilizes a compartment-modeling approach to develop low-order models which accurately describe physiological trends, subject to noise uncertainty. Examples illustrating how to identify these trends from published medical studies and patient physiological data are provided. The aforementioned case studies are employed to reinforce the usefulness of this approach, including the modeling of uncertainty of the general trend using a noise of unknown variance. Through model manipulation and extensive use of null space projections, a CFAR test for the critical event is designed providing near-constant performance across the population. This is achievable by first generating a statistic constrained to a class of parameter-invariant statistics, then designing a test that simultaneously monitors the patient condition while ensuring the model accuracy and testing power is sufficient. Consistent with the model development, all concepts related to CFAR testing are demonstrated (and evaluated) through the case studies. Novice participants with an undergraduate-level understanding of linear algebra will be introduced to a new and powerful monitor design technique never before applied in the medical domain. Those familiar with signal processing will enjoy the elegance and rigor of the CFAR test design and gain invaluable insight into medical monitoring problem design and physiological modelings. Complementary, those familiar with physiology will gain insight into how high order physiological models can be reduced to useful models for the purposes of medical monitoring.