Traumatic brain injury (TBI) is a major public health problem. Intracranial hypertension (ICH) is common after TBI and can cause secondary injury by decreasing local or global cerebral perfusion [1,2]. Cerebral autoregulation governs cerebral blood flow (CBF) by changing local artery diameter [3-5] and usually provides autonomic control of intracranial pressure (ICP). The capacity of this mechanism to adapt to pressure changes may be exhausted by sufficiently acute or prolonged hypertension, which can lead to insufficient perfusion following TBI. Impaired autoregulation also affects a patient’s response to drug therapies to reduce ICP [6]. Therefore, clinical management of ICH after brain injury is crucial for improving patient outcomes.

TBI is often accompanied by elevated systemic arterial blood pressure (ABP) and loss of cranial volume due to cerebral edema. The Monro-Kellie doctrine [7] postulates a constant volume of intracranial (IC) parenchyma (functional brain tissue) and fluids (blood and cerebrospinal fluid [CSF]), so changes in net fluid yield changes in ICP. Consequently, ABP is the primary external ICP driver under this hypothesis, together with changes in volume and fluid [8]. Therefore, clinical protocols seek to control ICP while maintaining cerebral perfusion pressure (CPP, the difference between ABP and ICP) [9] or risk cerebral hypoxia, which may result in death or permanent brain injury.

Important changes in patient ICP occur at minute-to-hour timescales, and clinicians need to know about them quickly. Decisions regarding the escalation of care and intervention for TBI patients are often driven by elevated ICP, typically defined as exceeding 20 mm Hg (1 mm Hg=133.3 Pa approximately) [10]. This underscores the need to monitor the ICP and identify critical changes. An ideal form of clinical decision support would predict ICP many minutes to a few hours in advance, as seconds or minutes might not provide adequate warning for timely intervention.

ICP is measured in situ via an external ventricular drain (gold standard) or a fiberoptic intraparenchymal catheter. Both modalities are invasive and may adversely affect patient outcomes through the risks of infection and hemorrhage [11]. In some patients, the risks associated with monitoring are outweighed by the benefits of ICP- and CPP-guided therapy, but patient selection is critical. Alternatively, noninvasive intracranial pressure (nICP) estimation is less risky and could both inform patient selection and timing for monitor placement (eg, early for those who are predicted to benefit). It may also be paired with invasive ICP monitoring as a powerful clinical decision support tool. Methods of nICP estimation generally involve identifying relationships between ICP and proxies that may be more easily observable in real time. These relationships may be explored empirically or on the basis of explicit models representing underlying physiology; a recent comprehensive survey of nICP estimation modalities is available [12].

Estimation of ICP using models and/or proxy data is highly dependent on the availability of specific data, which limits its use. For example, nICP may be statistically estimated from ABP and concurrent measurements of CBF velocity or cerebral oxygenation via empirical relationships [13,14] or physiological models [15,16]. The collection of such data requires advanced techniques such as transcranial Doppler sonography or near-infrared spectroscopy, which are limited by the availability of instruments and trained technicians. These data must also typically undergo quality control, delaying their availability for nICP estimation. Although nICP may be estimated using various modalities, practical considerations such as clinical logistics and data timeliness render their applications difficult.

An ideal model for clinical decision support of TBI management is one that quickly provides nICP forecasts at multihour timescales from commonly available data and includes IC (as an adjective) process resolution. Such a model does not currently exist. Fast methods based on machine learning and signal processing [17-21] provide empirical nICP forecasts but rely on an abundance of training and/or patient history data that may not be widely available. Real-time models that empirically approximate physiological relationships [15,16] are also fast, but they still require uncommon data and do not provide IC mechanism resolution useful for diagnosis or patient-specific tuning. Mechanistic modeling approaches [22-24] emphasize either broad systemic dynamics or short-time resolution of IC processes and may be too coarse or slow for the purpose of clinical nICP estimation.

Two recent models [15,16,23,24] have been cited extensively in this document. The more anatomically representative model of Ryu et al [23] estimates nICP from ABP without additional data but emphasizes pulse-scale pressure signals rather than hour-scale dynamics. The fast nICP estimation schemes of Kashif et al [15] track ICP at suitable multihour timescales but have stringent requirements for uncommon data, which limits their applicability. Although contrapuntal to one another, both models are foundational to this study, which focuses on the limits and extension of these methodologies for long-time nICP estimation from ABP.

The different methodologies of Kashif et al [15] and Ryu et al [23] present two feasible options for nICP estimation: full systemic integration of the former’s simple model with a systemic hemodynamics model or unintegrated use of the more complex model of the latter. This investigation considers which model development strategy is a better initial step toward an ideal nICP estimation tool in a clinical setting. We present the advantages and disadvantages of each approach: to better inform the development of a tool representative of the ideal model, and to identify the input requirements for each model in relation to clinically available data.

This study has three primary objectives. The first is to extend the simplified nICP estimation framework [15,16] by using a coupled arterial vasculature model to eliminate its dependence on jointly measured CBF. The second is to evaluate the ABP-only simulation of this model and the one developed by Ryu et al [23] for nICP estimation over a duration of hours. The third goal is to clarify the additional model machinery, such as case-specific parameter estimation and inference, needed to implement nICP estimation for complex, clinically important situations. These goals aim to inform the development of a practical tool capable of providing timely support in the clinical decision-making process for TBI patients on a broader timescale than those considered in the literature.

The remainder of this paper is organized as follows: the Methods section presents the models and methods of investigation, describes the model experiments, and establishes the model assessment criterion; the Results section presents the results of the experiments and model comparison and discusses the simulations of cases involving other brain injuries such as ischemic stroke, which are poorly simulated without optimization; and the Discussion section summarizes the analysis and motivates ongoing work toward modeling nICP estimation in a particular direction on the basis of the results and implications.

The comparison of nICP estimation schemes involves three essential parts: model configurations, aortic inflow data that drive the system, and metrics used to compare models on the basis of various aspects of performance, which are presented in the following subsections.

The CHARIS v1.0.0 collection (Charis hereafter [32]), publicly available from PhysioNet [33], comprises 50 Hz joint radial ABP and ICP time series of 13 patients. These data satisfy the model requirements, including documentation of diagnosed IC injuries, and suffice for model input and evaluation. Using radial ABP data as aortic introduces biases against systolic pressure more than diastolic [34,35], and these errors are consistent among our experiments. Sophisticated transformations exist [36] for reconstructing aortic pressure from radial ABP, but the simple approach taken here avoids uncertainties associated with additional algorithmic processing.

For model comparison, this study focuses on Charis patient #6, a 20-year-old male with TBI, based on the simplicity of his injury, cleanliness of joint ABP-ICP signal, and representativeness of base parameters (eg, optimal scaling parameters for the AN-CoW were approximately 1). In addition, large-scale noise or corrupt signals are common in the records of the patients (Multimedia Appendix 4); most of their ABP and/or ICP data could not be used contiguously for 4- to 6-hour periods without extensive and uncertain preprocessing of the available data.

Figure 4 identifies the possible sampling frequencies for the aortic model inflow. Models #1 and #2 have stricter aortic inflow requirements than models #3 and #4, as their simpler ICMs require ABP sample frequency in the rightmost portion of the scale (<10 Hz) for waveform feature identification. For example, previous studies [15,16] validated the regressive method of the simple ICM using data sampled at 20-70 Hz and 125 Hz. Such data are obtainable but are not commonly available and typically require quality control.

Lower-frequency ABP time series, which are more accessible and cleaner, are assumed to comprise nonoverlapping 1-minute (quaque 1-minute [q1m]) averages of systolic and diastolic pressures and heart rate. A waveform model (defined by a superposition of beta distribution probability density functions; Multimedia Appendix 5) projects these discrete q1m data into continuous time using patient-specific waveform parameters 𝛾, which are then sampled for convenience at 60 Hz. In relation to Figure 4, this process maps q1m data (identified by the red mark) into the scale usable by the simpler models to test the robustness of their data requirements.

Each experiment was evaluated using three scores: rating error, classification accuracy, and speed for simulations over time interval [0,T] in N 1-minute intervals, which quantify the desirable properties of the nICP estimates [37,38] for the purposes of relative comparison. The symbol nICP^* herein indicates nICP debiased against the observed ICP during the first hour of the simulation. The justification for this correction is that skill scores evaluate the model’s ability to track variability in recorded ICP data rather than estimate the absolute pressure. It also accounts for some of the bias introduced through the misuse of radial blood pressure as aortic inflow pressure. Each evaluation is applied to an nICP estimate, the score of which is then associated with the model that produces it.

The first score is the time-averaged standard error between the ICP and the debiased model estimate:

Assessment of nICP and model efficiency for the first hours of patient #6 indicates that model #2 has a lower error than model #1 and is more practical than model #3. Figure 5 shows the observed ICP signal along with the estimates from models #1 to #3. Patient ICP was initially stable near 20 mm Hg for approximately an hour and gradually increased to approximately 24 mm Hg during the final 2.5 hours. Temporary pressure drops near 10, 75, 105, and 142 minutes likely reflect interventions (eg, mannitol or hyperventilation treatments) [32]. The observed ICP signal used in the model evaluation is shown in solid red. This reference ICP is decreased by approximately 2.5 mm Hg after 243.5 minutes to compensate for the sharp 5+ mm Hg record discontinuity, which may be due to transducer recalibration. The original unaltered 1-minute average ICP observations (dashed light red) are shown for reference over the interval 244 to 360 minutes.

Model comparison is organized into three subtopics: qualitative differences, quantitative differences, and observations about resolvable timescales and fidelity.

Models can use commonly available ABP summary records under appropriate representation without additional waveform data. The use of models #1 and #2 is limited by pulse-resolving ABP inflow, but this requirement may be weakened using waveform transformation of q1m ABP summary time series of phase pressures and heart rate (Multimedia Appendix 5). Figure 7 shows that the original nICP estimate of model #2 (blue dashed) and one using q1m inflow (γ₆, solid blue) are largely indistinguishable, although smoother inflow data of the latter avoids the instability around 175 minutes. The estimate from q1m ABP has a 3% larger error (r₁=3.7 mm Hg), although there is no qualitative difference in clinical accuracy or speed compared with the original estimate. Furthermore, the lack of patient-specific waveform parameters has little effect on simulated nICP in this model: all model scores are roughly preserved in 2 additional runs (cyan and magenta) using waveform parameters of Charis patients #8 and #9 (γ₈ and γ₉, respectively), which differ in postsystole shape (inset). However, model #2 nICP estimates based on q1m ABP without heart rate data (not shown) were highly inaccurate due to errors in the numerical calculation of the ICM inflow pressure derivative.

This study compared multicomponent modeling approaches to nICP estimation using commonly available data over multihour timescales to produce actionable clinical information. The purpose was to better inform the direction of estimation development by identifying the advantages, limits, and additional requirements of the 2 options. The choices were to integrate a simple ICM into a systemic hemodynamic model or to unidirectionally couple a more complex ICM to the hemodynamic model component. We assessed these methods based on error (r₁), clinical accuracy (r₂), and speed (r₃) of their estimates as well as on their dependence on data and parameter identification. The first key result is that the bidirectional coupling of the simple model is sufficiently fast and potentially accurate and can be implemented using commonly available q1m ABP data without patient-specific waveforms. Specifically, analysis of model performance during a slow ICH event revealed that inclusion of bidirectional coupling improved the low-frequency model resolution of ICP, improving estimation quality while remaining an order of magnitude faster than real time. The second main result is that the complex model approach is too slow for use in the targeted applications. In particular, model #3 required nearly 6 hours to perform a 1-hour simulation along with ad hoc changes to both input parameters and output solution, which can only be eliminated by parameter estimation from additional input data at additional computation time. Limited by publicly available data, the three model approaches considered here represent practical implementations of existing methods; therefore, this study is a comparison of existing models implemented in a typical, sparse data environment.

The stronger-performing simple model approach may use ABP summary data without patient specificity of the inflow waveform and is able to resolve minute-scale nICP variations at additional costs. Its ICM, originally designed to run on high-frequency joint ABP-CBF samples, was coupled to a hemodynamic model of upstream vasculature derived from the complex model to establish ABP-only data dependence. Our experiments show that simple model data dependence can be further reduced to coarse clinical summary data of phase pressures and heart rate, which is independent of the patient-specific postsystole waveform shape. The use of q1m summary data also serves to filter the aortic forcing, which is an important consideration given that the bidirectional setup is more prone to feedback instabilities originating from inflow noise. Furthermore, summary ABPs are less noisy and therefore reduce spurious feedback instabilities in fully coupled simple models (Figure 7 near 175 minutes).

Slow model speed and the need for ICM parameter identification limit the utility of the complex model. The estimation of nICP under model #3 is an order of magnitude slower than the clock time under pulsatile aortic inflow and is only slightly faster than real time under mean ABP. In both cases, strong parameter dependence renders model initialization difficult, and nICP estimates are inaccurate without posterior modification. Some ICM parameters may not be stationary over multihour timescales and may explain the difficulty in maintaining nondivergent behavior beyond the first hour of simulation. The inference necessary to identify these parameters results in additional computational overhead, making near real-time estimation an unrealistic expectation. However, these parameters provide extremely useful diagnostic information and make complex model estimations more suitable for retrospective analysis rather than operational support.

The main results of this work are summarized below:

Bidirectional model #2 provides a basis for analyzing latent empirical relationships among patient signals and model parameters, including trends and covariances, which may be used to predict patient ICP changes. Such a system would greatly benefit both clinical decision support and care-level logistics by indicating possible changes in patient status with sufficient lead time to adjust room, equipment, and staff. This may also give practitioners advance warning with a timeframe for planning treatments, permitting earlier and lower-risk interventions to combat IC hypertension. Recent works [46-49] include machine learning approaches to ABP prediction and could be used in conjunction with the presented methods for short-term prediction of nICP. The application of these algorithms to low-sample-rate q1m ABP records has not been reported in the literature.

The speed of model #2 indicates that it is a plausible candidate for use within a statistical estimation and forecast scheme that requires many forward model integrations. The accurately identified parameters, together with acceptable simulation speed, add the possibility of practical forecast capabilities based on trends in diagnostically computed model parameters. For the applications discussed in this work, distributional trends and higher-order moments in ICM resistance and compliance may be inferred from robustly optimized model #2 simulations of a patient’s relevant history. This statistical information may then be used to predict possible future ICP outcomes under current ABP measurements or ABP forecasts, potentially providing valuable and timely clinical decision support for caretakers and facility management.

This study identified the distinct advantages and disadvantages of the 2 paths within a modeling framework and clarified the applicability of each. Although model #2 was more successfully validated at multihour timescales, it required uninterpretable control parameters (G) in more complex cases. In contrast, the ICM of model #3 is highly parameter dependent and difficult to identify from accessible data, even for simple cases. These results ultimately motivate the development of a hybrid approach that strategically combines simplifications of the mechanistically resolved processes of model #3 with the speed advantages of locally stationary parameters in model #2. The desire to have an appropriate number of physiologically interpretable parameters for data-optimized modeling contextualizes the problem as one of mechanistic machine learning [50-52].

Our preliminary hypothesis of this work was that the high degree of anatomical fidelity offered by the complex multicompartment model would provide the most diagnostic information from available data. It also had numerous model parameters that could be inferred from patient data in the longer view of the research program, which is to aid in patient-specific clinical support. We pursued an implementation of model #4 using the spatially-resolved vascular system and complex ICM [23], which had recently been used within a data assimilation system [24]. Concern for speed motivated the elimination of the spatial resolution of vessels within the hemodynamic model by adopting the 0D electrical framework, but this approach could not be easily bidirectionally coupled to the analytical ICM. It remained unidirectionally coupled and became model #3. In contrast, the simple model (#1, [15]) was easily integrated bidirectionally into the AN-CoW system, becoming model #2, and this eliminated its dependence on localized CBF data. This fully incorporated model had better tracking of lower-frequency trends in ICP and could resolve higher-frequency ICP waves with additional computational cost, and importantly, it did not require the additional parameter identification of the offline complex ICM for simple cases. However, the lack of sophistication and parametrization in models #1 and #2 is the reason why external parameters for additional control are required for more complex patient cases.

Although the need for additional inference is clear for the application of models #2 and #3, there are substantive differences in methodology and potential benefits. Namely, simple model #2 is easily identified but is limited to applications where a strong correlation between systemic ABP and ICP response is present. This lack of internal parameters necessitates the use of nonstationary external controls for application in complex cases. Although these parameters may plausibly be estimated via ensemble filtering, they are not interpretable, and the necessary mapping between clinical data and the control parameters is unknown and requires further development. In contrast, model #3 has numerous highly interpretable and diagnostically informative parameters that must be properly inferred for meaningful simulations. These are likely estimable from historic patient data using traditional methods (eg, MCMC estimation or optimization), but the value of this investment may be limited if parameters are dynamic and/or only nICP estimation is sought. Given that the estimation of nICP, rather than clinical interpretability, is the primary objective of this project, the continued development of inference machinery for model #2 is the best choice.

The long-term vision of this project remains the development of a bidirectionally coupled model with anatomical fidelity (ie, model #4) fast enough for pre-emptive diagnostic uses such as nICP forecast and the identification of pathophysiology. One path toward this goal is the hybridization of methodologies that integrate an ICM of intermediate complexity under piecewise stationarity assumptions akin to those of simple models. Possible ICMs include those mentioned previously and a simplified (eg, linearized) counterpart of model #3. This should reduce the computational burden of the complex model and allow it to be more easily coupled interactively with the upstream vascular component. Such a model would further benefit from highly interpretable inference based on data available when administering care, with the additional advantage of supporting summary ABP inflow. A remaining question is whether a model formulated in this way can be made fast enough to provide timely and clinically actionable information.