Clinical Decision Support for Traumatic Brain Injury: Identifying a Framework for Practical Model-Based Intracranial Pressure Estimation at Multihour Timescales

Background The clinical mitigation of intracranial hypertension due to traumatic brain injury requires timely knowledge of intracranial pressure to avoid secondary injury or death. Noninvasive intracranial pressure (nICP) estimation that operates sufficiently fast at multihour timescales and requires only common patient measurements is a desirable tool for clinical decision support and improving traumatic brain injury patient outcomes. However, existing model-based nICP estimation methods may be too slow or require data that are not easily obtained. Objective This work considers short- and real-time nICP estimation at multihour timescales based on arterial blood pressure (ABP) to better inform the ongoing development of practical models with commonly available data. Methods We assess and analyze the effects of two distinct pathways of model development, either by increasing physiological integration using a simple pressure estimation model, or by increasing physiological fidelity using a more complex model. Comparison of the model approaches is performed using a set of quantitative model validation criteria over hour-scale times applied to model nICP estimates in relation to observed ICP. Results The simple fully coupled estimation scheme based on windowed regression outperforms a more complex nICP model with prescribed intracranial inflow when pulsatile ABP inflow conditions are provided. We also show that the simple estimation data requirements can be reduced to 1-minute averaged ABP summary data under generic waveform representation. Conclusions Stronger performance of the simple bidirectional model indicates that feedback between the systemic vascular network and nICP estimation scheme is crucial for modeling over long intervals. However, simple model reduction to ABP-only dependence limits its utility in cases involving other brain injuries such as ischemic stroke and subarachnoid hemorrhage. Additional methodologies and considerations needed to overcome these limitations are illustrated and discussed.

The AN-CoW model is comprised of a subcranial arterial network and the CoW vessels, which are modeled using 3-element electrical analogs in MatLab SimuLink. Within them, vessel state variables pressure P and flow Q evolve (as voltage and current, respectively) under the influence of local vessel parameters (R, C, L) and states of adjoining vessels. Base values for all vessel-level parameters and boundary conditions were adopted from previous studies (viz. [?] and references therein).
Vessel-level parametrization in the AN-CoW Physical parametrization of vessel-level hemodynamics in the AN-CoW involves vessel dimensions (crosssectional area A 0 and length l), material properties (vessel linear compliance ∂P/∂A, vessel elasticity constant β, and blood density ρ), and a friction scaling term (χ, which depends on vessel mechanical properties and flow profile [?]). A local elastic pressure model P = P (A; β, A 0 ) is adopted from [?], where is the change in internal pressure with respect to transmural vessel pressure. Parameters defining the passive electrical components of each vessels are resistance R, capacitance C, and inductance L. These may be define approximated [?] from the physical parameters according to respectively. The relationship between A and vessel radius r is elementary.
Boundary conditions: Boundary conditions representing unresolved downstream vasculature are 3-element Windkessel (i.e. RCR-circuit) models. Outflow boundaries at the cerebral arteries are by defined current ICM pressure and a resistances. These resistances are set as in [?] so that bilateral arterial flows intially target 1.3 ml/s, 2.2 ml/s, and 1.15 ml/s across anterior, middle, and posterior cerebral arteries, respectively, under initial ICP of 15 mm Hg.
In bi-directionally coupled models, CoW terminal vessels connect directly with the necessary IC vessels and require ICM pressure and resistance to coordinate with AN-CoW outflow. Specifically, the currently known estimates of pressure and resistance within the ICM are applied to the bi-directionally coupled middle cerebral artery. Remaining uncoupled CoW termini are set as in the uni-directionally coupled case.
Parameter Reduction: We assumed that vessel length and radius dimensions (l, r) scale uniformly within the AN and globally parametrized LRC values according to proportionalities (θ l , θ r ) in relation to the base values. This defines a nonlinear transformation of the electrical parameters via (R, C, L) ← θ l · θ −4 r R, θ 3 r C, θ −2 r L . The three remaining parameters -those for 3-element Windkessel boundaries and CoW outflow resistance -are handled analogously with proportions (ω l , ω r ) and R term , respectively. Because CoW and adjacent vessel radii are approximately adult-sized by about 5 years of age [?], we did not scale vessels within the CoW model component.
Scaling the reference values en masse is effective within a realistic range of parameter values, as shown in Fig 3 of the main text. This figure summarizes the relative effect of scaling parameters on properties of ICM inflow signals, determined by 500 simulations of parameters uniformly sampled from 0.5-1.5 for lengths and resistance and 0.9-1.1 for radii. Properties of ICM inflow signals are most sensitive to scaling of AN vessel dimensions and are less sensitive to scaling of the terminal resistance and AN boundary Windkessel values. Scaling of AN vessel dimensions is more influential on the ICM than those related to CoW terminal resistance and AN boundary Windkessel values. This re-parametrization reduces the AN-CoW component identification to five proportionalities (θ l , θ r , ω l , ω r , R term ). It establishes a simple systemwide control over the vascular properties, improves parameter sensitivity, and provides a meaningful path to accurate model identification. . Random joint variations of scale parameters (and terminal resistance scaling, not shown) are sampled and assigned to 500 simulations via Latin hypercube sampling. Uniform sampling distribution ranges were [0.5, 1.1] for lengths, [0.9, 1.1] for radii, and [0.5, 2] for resistance, with weak and positive covariances (0.5) assumed between lengths (and radii) in an attempt to preserve anatomical fidelity.