[Paper Review] Input-Output Non-Linear Dynamical Systems applied to Physiological Condition Monitoring

Konstantinos Georgatzis, Christopher K. I. Williams+1 more|arXiv (Cornell University)|Jul 31, 2016

Hemodynamic Monitoring and Therapy25 references3 citations

TL;DR

This paper proposes a data-driven input-output non-linear dynamical system (IO-NLDS) to model the effects of Propofol infusion on ICU patients' vital signs, outperforming traditional pharmacokinetic/pharmacodynamic (PK/PD) models without requiring physiological priors. The IO-NLDS achieves significantly lower SMSE (up to 60% reduction) and better BIC scores across all prediction horizons, demonstrating superior predictive performance on real patient data.

ABSTRACT

We present a non-linear dynamical system for modelling the effect of drug infusions on the vital signs of patients admitted in Intensive Care Units (ICUs). More specifically we are interested in modelling the effect of a widely used anaesthetic drug (Propofol) on a patient's monitored depth of anaesthesia and haemodynamics. We compare our approach with one from the Pharmacokinetics/Pharmacodynamics (PK/PD) literature and show that we can provide significant improvements in performance without requiring the incorporation of expert physiological knowledge in our system.

Motivation & Objective

• To develop a data-driven alternative to expert-knowledge-based PK/PD models for predicting patient responses to drug infusions in ICUs.
• To evaluate whether a non-linear dynamical system can outperform conventional compartmental PK/PD models in predicting vital signs like blood pressure and BIS.
• To demonstrate that a model free of physiological constraints can achieve better predictive performance using only observed infusion and response data.
• To explore the feasibility of learning complex, patient-specific drug-response dynamics without prior assumptions about underlying physiological states.

Proposed method

• The IO-NLDS models the latent physiological state as a non-linear dynamical system driven by drug infusion rates, with a non-linear output mapping to observed vital signs.
• The model is trained using an unscented Kalman filter for state estimation and the expectation-maximization (EM) algorithm for parameter learning.
• The latent state evolution is governed by a non-linear state transition function, while the output is modeled via a non-linear function mapping latent states to observed vital signs.
• The model is trained per patient using 40 ICU patient datasets with Propofol infusion and corresponding BPsystolic, BPsystolic, and BIS measurements.
• Model comparison uses SMSE and BIC to evaluate predictive performance across 1-step to 20-step prediction horizons.
• The IO-NLDS does not assume any physiological interpretation of the latent states, allowing it to learn arbitrary representations that best fit the data.

Experimental results

Research questions

• RQ1 Can a purely data-driven non-linear dynamical system outperform expert-constructed PK/PD models in predicting patient vital signs after drug infusion?
• RQ2 Does the absence of physiological constraints in the latent state space improve predictive accuracy on real ICU data?
• RQ3 To what extent does the IO-NLDS reduce prediction error compared to the PK/PD model across different prediction horizons?
• RQ4 Is the performance gain of the IO-NLDS statistically significant across multiple patients and vital signs?

Key findings

• The IO-NLDS achieved significantly lower SMSE than the PK/PD model across all prediction horizons, with mean SMSE reductions of up to 60% on BIS and 50% on BPdiastolic at 20-step prediction.
• The IO-NLDS achieved a lower BIC score than the PK/PD model in all cases, indicating better model fit after penalizing for complexity.
• In 92% of all evaluated cases, the IO-NLDS prediction accuracy exceeded that of the PK/PD model, with the majority of improvements being statistically significant.
• Paired t-tests showed statistical significance (p < 0.05) in 10 out of 12 comparisons, with p-values ranging from 1.6×10⁻² to 4.8×10⁻¹⁷.
• The only non-significant results were for 1-step predictions on BPdiastolic (p=0.14) and BIS (p=0.37), suggesting marginal differences in these specific cases.
• The IO-NLDS demonstrated consistent performance gains across all three vital signs (BPsys, BPdia, BIS) and all prediction horizons, with the largest improvements observed at longer horizons.