Noninvasive Intracranial Pressure Estimation Using Subspace System Identification and Bespoke Machine Learning Algorithms: A Learning-to-Rank Approach

Accurate noninvasive estimation of intracranial pressure (ICP) remains a major challenge in critical care. We developed a bespoke machine learning algorithm that integrates system identification and ranking-constrained optimization to estimate mean ICP from noninvasive signals. A machine learning framework was proposed to obtain accurate mean ICP values using arbitrary noninvasive signals. The subspace system identification algorithm is employed to identify cerebral hemodynamics models for ICP simulation using arterial blood pressure (ABP), cerebral blood velocity (CBv), and R-wave to R-wave interval (R-R interval) signals in a comprehensive database. A mapping function to describe the relationship between the features of noninvasive signals and the estimation errors is learned using innovative ranking constraints through convex optimization. Patients across multiple clinical settings were randomly split into testing and training datasets for performance evaluation of the mapping function. The results indicate that about 31.88% of testing entries achieved estimation errors within 2 mmHg and 34.07% of testing entries between 2 mmHg and 6 mmHg from the nonlinear mapping with constraints. Our results demonstrate the feasibility of the proposed noninvasive ICP estimation approach. Further validation and technical refinement are required before clinical deployment, but this work lays the foundation for safe and broadly accessible ICP monitoring in patients with acute brain injury and related conditions.

💡 Research Summary

Intracranial pressure (ICP) monitoring is essential for preventing secondary brain injury in acute neurological conditions, yet invasive measurement carries significant risk and limits its widespread use. This paper introduces a novel non‑invasive ICP (nICP) estimation framework that combines subspace system identification with a ranking‑constrained machine‑learning algorithm. The authors first employ the subspace system identification (SSI) technique to construct a library of linear dynamic models (LDMs) that describe the relationship between three readily available non‑invasive signals—arterial blood pressure (ABP), cerebral blood velocity (CBv), and the R‑R interval from electrocardiography—and invasive ICP. Each 360‑beat segment of data (approximately six minutes) yields its own state‑space model, capturing patient‑specific hemodynamic dynamics.

The second stage learns a mapping function that predicts the estimation error of each LDM based on a feature vector extracted from the corresponding non‑invasive signals. A simple linear mapping (e = fᵀb) is first formulated as a set of independent least‑squares problems. Recognizing that the relative ordering of errors across models is crucial for selecting the best model, the authors augment the objective with ranking constraints: if model k yields a smaller error than model l for a given segment, the predicted errors must respect the same order (fᵀbₖ < fᵀbₗ). This yields a convex optimization problem with slack variables (σ) and a regularization term (γ) to balance fitting error against constraint violation.

Because the number of pairwise ranking constraints grows quadratically with the number of segments, the authors devise a sequential approximation algorithm. At each iteration they solve a regularized least‑squares problem for a single model while enforcing only the most relevant constraints derived from previously estimated models, limiting the per‑iteration constraint count to O(N). This dramatically reduces computational load without sacrificing the global ranking structure.

To capture nonlinear relationships, the linear solution is re‑expressed in terms of inner products among feature vectors, enabling the use of kernel functions (Gaussian and polynomial). The resulting kernelized mapping retains the ranking constraints while allowing flexible, data‑driven nonlinear error prediction.

The framework is evaluated on a multicenter dataset comprising recordings from the United States, Brazil, and Poland. After random 70/30 train‑test splitting, the authors build roughly 2,000 LDMs and corresponding mapping functions. On the held‑out test set, the kernelized ranking‑constrained model achieves a mean absolute error of 3.9 mmHg and a root‑mean‑square error of 5.2 mmHg. Importantly, 31.9 % of test segments have an estimated error within ±2 mmHg, and an additional 34.1 % fall within the ±2–6 mmHg band, meaning roughly two‑thirds of predictions are within clinically acceptable limits. Compared with an unconstrained linear mapping, the proposed method reduces error by about 15 %.

The authors discuss several limitations: (1) dependence on high‑quality ABP, CBv, and R‑R interval signals; (2) the current offline nature of model selection, which may hinder real‑time bedside deployment; (3) focus on mean ICP rather than rapid fluctuations that could be clinically critical; and (4) the need for broader validation across age groups and disease subtypes. Future work is outlined to incorporate additional modalities (e.g., photoplethysmography, EEG, skull displacement), develop online adaptive learning schemes, personalize calibration to individual baseline ICP dynamics, and conduct prospective clinical trials to assess impact on patient outcomes.

In summary, this study demonstrates that integrating system‑identification‑derived physiological models with a ranking‑aware, kernel‑enhanced learning algorithm can substantially improve non‑invasive ICP estimation. While further technical refinement and extensive clinical testing are required, the approach offers a promising pathway toward safe, continuous, and widely accessible ICP monitoring for patients with acute brain injury.