Stroke classification using Virtual Hybrid Edge Detection from in silico electrical impedance tomography data

TL;DR

This paper tackles rapid differentiation of ischemic versus hemorrhagic stroke using noninvasive electrical impedance tomography (EIT) data from realistically detailed 2D head phantoms. It introduces Virtual Hybrid Edge Detection (VHED) functions derived from boundary measurements via complex geometrical optics with the Beltrami coefficient $\mu=(1-\sigma)/(1+\sigma)$, and then feeds a simple fully connected neural network (FCNN) with either raw voltages or VHED features. The results show that VHED inputs are notably more robust to realistic measurement noise than raw voltages, maintaining high accuracy across multiple stroke shapes, while in the noise-free case raw data can perform slightly better. This work demonstrates the viability of VHED-based preprocessing for ambulance-ready stroke triage and provides a clear path toward extending the approach to three dimensions and clinical translation.

Abstract

Electrical impedance tomography (EIT) is a non-invasive imaging method for recovering the internal conductivity of a physical body from electric boundary measurements. EIT combined with machine learning has shown promise for the classification of strokes. However, most previous works have used raw EIT voltage data as network inputs. We build upon a recent development which suggested the use of special noise-robust Virtual Hybrid Edge Detection (VHED) functions as network inputs, although that work used only highly simplified and mathematically ideal models. In this work we strengthen the case for the use of EIT, and VHED functions especially, for stroke classification. We design models with high detail and mathematical realism to test the use of VHED functions as inputs. Virtual patients are created using a physically detailed 2D head model which includes features known to create challenges in real-world imaging scenarios. Conductivity values are drawn from statistically realistic distributions, and phantoms are afflicted with either hemorrhagic or ischemic strokes of various shapes and sizes. Simulated noisy EIT electrode data, generated using the realistic Complete Electrode Model (CEM) as opposed to the mathematically ideal continuum model, is processed to obtain VHED functions. We compare the use of VHED functions as inputs against the alternative paradigm of using raw EIT voltages. Our results show that (i) stroke classification can be performed with high accuracy using 2D EIT data from physically detailed and mathematically realistic models, and (ii) in the presence of noise, VHED functions outperform raw data as network inputs.

Figures (5)

• Figure 1: Parallel VHED X-rays and virtual detector geometry.
• Figure 2: VHED functions revealing geometric information about the conductivity. Jump singularities in the conductivity are reflected in the VHED profiles in a similar manner to parallel beam X-ray tomography. The angle $\varphi=0$ indicates the direction perpendicular to the virtual X-rays (dashed lines). (a) Function $\widehat{\omega}^{+}(1,t,0)$ propagates singularities from the interior of the domain to its boundary. Note that an artifact is visible at $t=0$ (indicated by an arrow). (b) Function $\widehat{\omega}_{\hbox{\tiny odd}}^{+} := \left( \widehat{\omega}^+ - \widehat{\omega}^- \right) / 2$. Subtracting $\widehat{\omega}^{-}$ from $\widehat{\omega}^{+}$ eliminates the even terms and suppresses the artifact at $t=0$. Nevertheless, because of the election $z=1$, singularities closer to the right edge have a larger amplitude than the singularities closer to the left edge. (c) After applying the averaging operator, the VHED profile $T_{\hbox{\tiny odd}}^{+}\mu$ shows equal-size (but opposite sign) singularities at the leftmost and rightmost vertical lines.
• Figure 3: Effect of the Fourier windowing process applied to the VHED functions. The blue curve shows $T_{\hbox{\tiny odd}}\mu(t,0)$ corresponding to conductivity in Fig. \ref{['fig:VHED_functions']} where the small disc inclusion has a conductivity value higher than background, while the red curve shows $T_{\hbox{\tiny odd}}\mu(t,0)$ corresponding to the same conductivity but with the small disc inclusion having lower conductivity than background. (a) Unrealistic VHED profiles with cutoff frequency $\tau_{m} =50$, which would only be possible in a noise-free scenario. (b) Realistic VHED profiles considering a cutoff frequency $\tau_{m}=5$, as would be appropriate in a real-world scenario with noise.
• Figure 4: Two-dimensional model resembling a slice of a human head. (a) Reference model containing five different compartments of importance for electrophysiology of the human head: grey matter, white matter, cerebrospinal fluid, skull and other soft tissues representing the scalp. (b) Reference model included in a elliptic shape. The dark blue region can be interpreted as a fixed helmet of constant conductivity with electrodes attached to its exterior. (c) The head anatomy inside the helmet of one simulated patient.
• Figure 5: Samples of the training and test datasets. (a) The stroke is represented by circular inclusion. This type of inclusion is considered for the training dataset and for the first set of the test dataset. (b) A conductivity sample from the second test dataset where the stroke is modeled as an elliptic inclusion. (c) A conductivity sample from the third test dataset where the stroke is modeled as multiple inclusions containing one disc and one elliptic inclusion.