Machine learning for cerebral blood vessels' malformations

TL;DR

A linear oscillatory model of blood velocity and pressure for clinical data acquired from neurosurgical operations is developed, providing a robust and interpretable framework for assessing cerebral blood vessel conditions.

Abstract

Cerebral aneurysms and arteriovenous malformations are life-threatening hemodynamic pathologies of the brain. While surgical intervention is often essential to prevent fatal outcomes, it carries significant risks both during the procedure and in the postoperative period, making the management of these conditions highly challenging. Parameters of cerebral blood flow, routinely monitored during medical interventions or with modern noninvasive high-resolution imaging methods, could potentially be utilized in machine learning-assisted protocols for risk assessment and therapeutic prognosis. To this end, we developed a linear oscillatory model of blood velocity and pressure for clinical data acquired from neurosurgical operations. Using the method of Sparse Identification of Nonlinear Dynamics (SINDy), the parameters of our model can be reconstructed online within milliseconds from a short time series of the hemodynamic variables. The identified parameter values enable automated classification of the blood-flow pathologies by means of logistic regression, achieving an accuracy of 73 \%}. Our results demonstrate the potential of this model for both diagnostic and prognostic applications, providing a robust and interpretable framework for assessing cerebral blood vessel conditions.

Figures (11)

• Figure 1: Examples of time series for blood flow velocity (A and B) and pressure (C and D) in clinical data before, during, and after surgery: patient with an arterial aneurysm (A and C), and patient with an arteriovenous malformation (B and D).
• Figure 2: Illustration of the fitting procedure. With larger sparsity threshold $\eta$ the results converge to sparser models. Simulated pressure trajectories from these learned models are compared with the experimental observations. As illustrative examples we select the patients, whose models show the worst match with the experiments by fitting accuracy across all AA (A) and AVM (B) patients. The bars aligned to the threshold values summarize the overall performance of the learned model quantified by RMSE, averaged over all patients with the same pathology (orange bars, standard deviation shown by whiskers), and computational time (blue bars, average over several runs for the patients in A and B). Higher-order models show average RMSE similar to the simplest linear equation \ref{['eq:model']} for AA patients (C). However, on AVM patients (D) the linear model performs strikingly better than the alternatives. For both AA and AVM data, the linear model prevails by the computational cost (blue bars in C and D)
• Figure 3: Examples of pressure-velocity diagrams before (blue), during (orange) and after (green) surgery for time series of a patient with an arterial aneurysm (A--C) and with an arteriovenous malformation (D--F). We simulate equation \ref{['eq:model']} for each patient by using the initial condition of the experimental pressure. The black lines show the simulated trajectory, which is in good agreement with the experimental time series, and display a counterclockwise current---the circulation commonly found in arteries Cherevko2016Parshin2016.
• Figure 4: Reproducibility of AA patients' parameter values. A: example of splitting in half the pressure trajectory taken from an AA patient before surgery. First, we infer parameters from each part (blue and orange trajectories) independently, and then from the whole time series. B: the maximum relative difference of model parameters learned from the two halves shown in A (blue and orange) with respect to the values inferred from the entire series emphasizes the reproducibility of our results.
• Figure 5: Forecasting performance of equation \ref{['eq:model']}. We split the pressure time series into training and test sets. Simulations of the model with parameter values learned from the training sets of various lengths are compared with the time series of the test set. A: an example of splitting an AA patient's pressure time series. The training sets (solid blue line) are delimited by the red vertical lines. The last cardiac cycle (dashed blue line), kept as the test set, is compared with the simulated model (solid black line). Averaged RMSE of the simulated pressure on a test set of a single cardiac cycle across all AA patients indicate insignificant changes in the accuracy with the increasing size of the training set (B), which expectedly offsets the computational cost (C). The orange whiskers in B indicate the standard deviation over all AA patients.