Novel Electrode Placement in Electrical Bioimpedance–Based Stroke Detection: Effects on Current Penetration and Injury Characterization in a Finite Element Model

Abstract

Objective:

Reducing time-to-treatment and providing acute management in stroke are essential for patient recovery. Electrical bioimpedance (EBI) is an inexpensive and non-invasive tissue measurement approach that has the potential to provide novel continuous intracranial monitoring—something not possible in current standard-of-care. While extensive previous work has evaluated the feasibility of EBI in diagnosing stroke, high-impedance anatomical features in the head have limited clinical translation.

Methods:

The present study introduces novel electrode placements near highly-conductive cerebral spinal fluid (CSF) pathways to enhance electrical current penetration through the skull and increase detection accuracy of neurologic damage. Simulations were conducted on a realistic finite element model (FEM). Novel electrode placements at the tear ducts, soft palate and base of neck were evaluated. Classification accuracy was assessed in the presence of signal noise, patient variability, and electrode positioning.

Results:

Algorithms were developed to successfully determine stroke etiology, location, and size relative to impedance measurements from a baseline scan. Novel electrode placements significantly increased stroke classification accuracy at various levels of signal noise (e.g. p < 0.001 at 40 dB). Novel electrodes also amplified current penetration, with up to 30% increase in current density and 57% increased sensitivity in central intracranial regions (p<0.001).

Conclusion:

These findings support the use of novel electrode placements in EBI to overcome prior limitations, indicating a potential approach to increasing the technology’s clinical utility in stroke identification.

Significance:

A non-invasive EBI monitor for stroke could provide essential timely intervention and care of stroke patients.

I. INTRODUCTION

STROKE is the second leading cause of death globally [1], with ~800,000 strokes occurring each year in the US alone [2]. Following initial incidence, the first 24 hours are of greatest risk to the patient for recurrent stroke [3]. Further, over 25% of admitted patients experience stroke progression in the first 72 hours, which can dramatically worsen outcomes [4]. Ischemic strokes, caused by vessel occlusion or blockage, account for 87% of all strokes while hemorrhagic strokes, caused by vessel rupture or bleed, account for 13% [2]. Both types can be deadly or lead to long-term morbidity, however time-to-treatment and acute management significantly impact patient prognosis [5], [6].

Receiving rapid treatment and acute care for stroke is essential to mitigating long-term disability [7]. Neurologic monitoring is a mainstay in acute care of stroke patients and includes intracranial complication management [8]. Specifically, patients with transient ischemic attacks (TIAs), and those at high risk of recurrent stroke (e.g., ABCD2 scale), hemorrhagic transformations (HT), and large vessel occlusions (LVO) are often monitored as inpatients post initial injury [9]. Of post-acute complications, an autopsy study found HT prevalence to range from 38%-71%, while symptomatic presentation ranged from 0.6%-20%, illuminating a large gap in monitoring capabilities [10]. Given the high prevalence of recurrent stroke, HT and in-clinic stroke progression, a real-time bedside monitor capable of tracking stroke pathology could provide both time and brain saving impacts [4].

Computed tomography (CT) and magnetic resonance imaging (MRI) comprise the current gold standard for acute and subacute stroke detection, but their high costs and limited ability for continuous bedside monitoring demonstrate the need for a more cost-effective and accessible alternative [11].

Electrical bioimpedance (EBI) for intracranial monitoring has presented itself as a potential method for cost-effective, accessible, and continuous monitoring of stroke post-injury [12]. EBI relies on the electrical properties of tissue and measures the surface potentials on a body with contact electrodes to sense the tissue’s electrical impedance [13]. Ischemic and hemorrhagic tissue have respectively low and high conductivities relative to healthy brain tissue [14]; thus, EBI has been used to measure the conductivity changes induced by stroke [12]. EBI computer models have demonstrated conductivity asymmetries between brain hemispheres which arise from unilateral bleeding or clotting, as well as correlated asymmetry directionality (positive or negative) with stroke-type and asymmetry magnitude with stroke size [14], [15]. In vivo studies have provided support for conductivity asymmetry differences detected by EBI [16], [17], however, these studies have not yet produced a method which effectively localizes beyond broad, hemispheric accuracy, nor simultaneously characterizes stroke volume and etiology (ischemic or hemorrhagic).

The primary hurdle in clinical translation of EBI for stroke detection has been the high impedance barrier of the skull [18]–[21]. Because the impedance of the skull is far greater than that of the scalp, current injected by scalp electrodes does not easily penetrate the skull, but rather, circulates the extracranial region. This current-shunting effect has been implicated in the low resolution and accuracy of EBI measurements, discouraging its clinical utility [20]. While some research has been done to optimize electrode placement and quantify the relationship between skull thickness and current penetration [21]–[23], an optimized solution has yet to be realized.

Simulation studies have provided support for detecting impedance changes of stroke [15], [24]–[26] and its ability to localize injured tissue [14], [25], yet face similar barriers in translation to in vivo settings. One postulate of the limited translation is due to an over-simplification of the mesh. Many head models used in computerized simulations lack anatomical detail in capturing the conductivity differences within the intracranial region [19], [27]. Further limitations include the overgeneralization of stroke dynamics. Purely hemispherical models provided foundational support for stroke-induced conductivity asymmetries [14], [15], [24], yet standard ischemic stroke ranges from 10 – 100 mL in size and may occur within any region of the brain [5]. Simulation data considering all regions of the brain and varied stroke type and size remains limited.

Identifying the presence of stroke while simultaneously characterizing its volume and etiology provide essential insight to patient condition and enable rapid response not currently possible. This study presents 1) a novel approach to overcoming the high impedance barrier of the skull through strategic utilization of identified “anatomical windows” for electrode placement, 2) an extensive simulation validating EBI’s ability to detect impedance changes attributed to stroke, both new and progressive, using the proposed novel system in an exhaustive model, and 3) EBI’s sensitivity to identifying stroke type and localizing injury, based on impedance changes from a baseline brain measurement, in the presence of noise for realistic system design and clinical translation. The study was completed using an anatomically precise mesh refined from segmentations of 152 adult human MRIs [28] and encoded with electrodes positioned at various sites on and within the mesh.

In this paper, we outline the mathematical models used to calculate electric potentials (the forward problem) and measure subsequent impedance changes throughout a finite element model (FEM) head mesh. Stroke modelling, analysis of novel electrode placement, and stroke characterization algorithms are then presented. Results are considered in the presence of three kinds of noise and implications for clinical application are discussed.

II. METHODS

A. The Forward Problem

The forward problem computes the electric potential within a domain and the voltage at each electrode given a current injection distribution specified at each electrode. Exterior surface and internal point electrodes are used, where surface electrodes are defined over circular patches of boundary nodes and point electrodes are defined at specific internal nodes of FEM mesh. The forward model is calculated using the complete electrode model (CEM) [29], which has been found to produce the most accurate simulated voltage measurements [30]. The CEM with incorporated internal point electrodes is defined by the following:

$$\nabla \cdot (\sigma \nabla u)={\sum }_{j=1}^{L_P}{\text{I}}_j\delta \left(x-X_{EPj}\right),\text{x}\in \text{Ω},$$ (1)

$$\text{u}+{\text{z}}_{Sl}\sigma \frac{\partial u}{\partial n}=U_{Sl},x\in {\text{E}}_{Sl},l=1,2,\dots L_S$$ (2)

$${\int }_{E_l}\sigma \frac{\partial u}{\partial n}ds=I_{Sl},x\in {\text{E}}_{Sl},l=1,2,\dots L_S$$ (3)

$$\text{u}+{\text{Z}}_{Pl}{\text{I}}_{Pl}=U_{Pl},x\in {\text{E}}_{Pl},l=1,2,\dots L_P$$ (4)

$$\sigma \frac{\partial u}{\partial n}=0,x\in \partial \text{Ω}{\cup }_{l=1}^{L_S}{E}_{Sl},$$ (5)

where σ is the conductivity, u is the electrical potential, n is the inward pointing normal on the boundary of the domain, and x is a point in 3D space. Thus, σ and u are each a function of x. Ω denotes the domain, Ls and Lp are the number of surface and point electrodes, respectively, and U_[]l, I_[]l, z_[]l represent the voltage, current, and contact impedance on the lth surface or point (S or P) electrode (E). Application of (1)–(5) relies on a small modification of the 3D Matlab implementation of the CEM and FEM, using tetrahedral elements and linear basis functions described in [31]. Specifically, the point electrode constructs current patterns by assigning their associated nodes on the right-hand-side of the FEM system to their prescribed source/sink current value. Another usage of this point-electrode/CEM model is given in [32]. The conductivity is specified as a constant across each element.

The linear basis functions of the FEM provide calculations of the current density and Jacobian (sensitivity) matrix, where the calculation of the lead-field formulation [33] of the Jacobian is provided in the Appendix of [34].

B. The Mesh

For this study we utilized the open source NY Head Mesh from the Parra Lab (ICBM-NY), see Figure 1 [28]. The mesh consists of high-resolution (0.5 mm³) segmentations of six primary tissue types (scalp, skull, cerebral spinal fluid, gray matter, white matter, air cavities) from a non-linear average of 152 adult brain MRIs (ICBM152 anatomical template). This FEM captures precise anatomical features, and while computationally costly, was shown to outperform common alternate ‘arbitrary’ head models and an equivalent boundary element model (BEM) [28], [35], [36].

Fig. 1.

Segmentations of head mesh materials. From left: scalp/skin/general tissue, bone, white matter, grey matter, cerebrospinal fluid, eyes. Air cavities not shown.

Tissue properties were modeled to represent a 50 kHz injected current [13]. Gray and white matter segmentations were assigned in vivo conductivities of 0.26 S/m and 0.17 S/m, respectively [37]. Skull and cerebrospinal fluid (CSF) were assigned conductivities of 0.02 S/m and 2.00 S/m, respectively [14], [38]. The singular material defining scalp, skin, and internal extracranial tissue [28], was defined as 0.44 S/m in accordance with scalp conductivity [39]. One refinement was made to include conductivities respective to each eye. This was done by identifying mesh nodes surrounding the eye and throughout the internal region of the eye [40], and defining their conductivities as 1.15 S/m (Figure 1) [39].

C. Model

1). Impedance

Electrical impedance (Z) is defined as the “obstruction to the flow of alternating current”, comprised of Resistance (R) and Reactance (X) [13]:

$$Z=R+jX$$ (6)

$$Z=V/I$$ (7)

Tissue resistance is attributed to its shape, length, and resistivity which largely depends upon the tissue’s water content. In addition to geometry, reactance is primarily attributed to the capacitance of cellular membranes and signal frequency of the injected AC current. Impedance can be generalized to Ohm’s Law where V is the measured electric potential and I is the injected current (Eq. 7).

2). Tetrapolar Impedance Measurement

A tetrapolar impedance measurement system was simulated to inject current from one source electrode (I⁺) to another current carrying sink electrode (I⁻) and measure the induced voltage difference across two separate electrodes (V⁺ & V⁻) (Figure 2A).

Fig. 2.

A) Tetrapolar impedance measurement on scalp. Current is injected from I⁺ to I⁻ and the electric potential difference is calculated between V⁺ and V⁻. B) Electrode positioning at four axial planes and two rotational spacings. Solid lines represent selected positions.

Exhaustive tetrapolar measurements satisfying all electrode patterns (I⁺I⁻V⁺V⁻) across 13 electrodes (E₁ to E₁₃) were simulated (Figure 3). Further combinations allowed the same electrode to be used for two designations (e.g. one electrode as both I⁻V⁻), resulting in 5512 total electrode patterns. An impedance change, ΔZ_IIVV, between a stroke condition (Z_injury) and preinjury baseline (Z_initial) was calculated for each of the electrode patterns:

$$\Delta Z_{IIVV}=Z_{injury}-Z_{initial}$$ (8)

Fig. 3.

Locations of 12 electrodes on scalp (Electrode 13 is on the soft palate and not visible). Head mesh positioning relative to coronal, sagittal, and transverse planes shown at right. Electrodes were categorized by their location relative to the sagittal and coronal planes. Electrodes anterior to the coronal plane were categorized as “frontal”, electrodes posterior to the coronal plane were categorized as “rear”, and electrodes on the coronal plane (top (9), middle left (6), middle right (5)) were categorized as “central”. Electrodes on the left side of the sagittal plane were categorized as “left”, on the right side as “right” and on the sagittal plane itself “medial”.

An average impedance change associated with a specific electrode was defined as the average of all impedance changes computed for which that particular electrode was the current-sinking electrode (i.e. I⁻). Thus, for each modelled stroke, an average impedance was calculated in this manner for each of the 13 electrodes. This approach will be referred to as sink electrode average impedance change (SEAIC), and was selected for the potential localization ability that isolating patterns by sink electrodes might enable. The associated formula is shown below:

$$SEAI{C}_i=\left({\sum }_1^{N\_si}\Delta Z_{{\left(I{I}_{i}VV\right)}_{N\_si}}\right)/N\_si,i=1,\dots 13$$ (9)

where SEAIC_i corresponds to the SEAIC of each electrode (i = 1 – 13) and $\Delta Z_{{\left(I{I}_{i}VV\right)}_{N\_si}}$ corresponds to measured impedance change (8) for each unique electrode pattern in which electrode i is the current-sinking electrode (N_si total patterns).

3). Stroke Model

Ischemic and hemorrhagic stroke lesions were modeled by redefining conductivities within a spherical volume (bolus) in the mesh to 0.05 S/m and 0.7 S/m, respectively [41], [42]. Three primary simulations were explored:

1. Novel electrode placement testing (see II.D.2), which utilized two spherical volumes, 5.58 cm³ and 51.0 cm³ [14], and 26 injury locations distributed evenly throughout the center and periphery of the intracranial region (104 stroke conditions total).

2. Stroke characterization testing (see II.D.4–7), which used the same two stroke volumes, in addition to one hundred new injury locations randomly generated throughout the intracranial region, with each stroke type and size simulated for each location (400 stroke conditions total).

3. Size analysis (see II.D.8), in which a bolus was grown from a volume of 0 mL to 100 mL at 10 mL intervals [43] in four distinct locations (80 stroke conditions total) (Figure 9).

Fig. 9.

Quantified raw impedance measurement (Zbol) corresponding to progressing strokes of varying volumes in four regions. A-D) Zbol of electrode arrangement that measured the highest SEAIC in each injury location. E) A stroke lesion was placed in four locations: contralaterally along coronal plane and in anterior and posterior regions along the sagittal plane (1-4: left, right, frontal, occipital). Stroke size was grown from 0 mL (no injury) to 100 mL in each location. This growth was performed for ischemic (green) and hemorrhagic (red) injuries. Stroke is not shown to size or categorized by conductivity. F) Displays average Zbol across exhaustive electrode arrangements measured at all volumes from 0 mL to 100 mL. P values of significant difference between Zbol of hemorrhagic and ischemic injury are displayed at three volumes.

4). Electrode Placement

a. Scalp Placements

A total of 9 electrodes were assigned as scalp electrodes (Figure 3). Scalp electrodes were defined as mesh surface elements with a 10 mm diameter. Eight of the scalp electrodes were placed circumferentially, parallel to the axial plane, and the 9^th placed on the top of the head at the convergence of the coronal and sagittal planes. All electrode positions on the right and left sides were evenly spaced between front and back electrodes (8 and 7, respectively). The exact location of scalp electrode placement utilized in stroke characterization testing (II.D.3–8) was determined through asymmetry analysis described in II.D.1).

b. Novel Electrode Placement

Key anatomical locations were identified for novel electrode placement as areas proximal to CSF and potentially presenting low impedance “windows” into the intracranial space. Three primary areas were identified: 1) the orbits [39], 2) the soft palate and 3) the base of the skull. Three regions on the orbits were assessed for current injection capability: below the brow ridge, above the cheekbone, and on the tear ducts. Electrodes were placed above the cheekbones and below the brow ridge, respectively, and an electrode was placed on each tear duct. Point electrodes were placed on nodes within the mesh at three positions on the soft palate’s anatomical location [44]. In this phase of testing, the standard mesh from [28] was utilized for optimizing electrode placement. The mesh was later refined to include orbital pathways (as described in, II.B) for subsequent clinical analyses.

D. Analysis and Stroke Identification

This section outlines 1) optimizing scalp and novel electrode placements (II.D.1–2), 2) classification algorithms for identifying stroke type and location based on a baseline measurement (II.D.3–5), 3) practical implementation of these algorithms in varied noise conditions (II.D.6), 4) measures for assessing novel electrode efficacy (II.D.7), and lastly 5) tracking of a progressive stroke sizes with and without requiring a baseline measurement (II.D.8).

1). Hemispheric Asymmetry Analysis

The scalp electrodes (E_1-8) were arranged about an axial plane with minimal conductivity asymmetry between baseline hemispheres. Specifically, a lateral asymmetry index was calculated for the electrodes situated at four different axial planes with two different spacing configurations (30° and 60°) between adjacent electrodes at each plane (eight total scalp placement arrangements, Figure 2B). An Asymmetry Index (AI) between the hemispheres was calculated with (10) and used to select the configuration with the lowest AI:

$$AI=\left(Z_{left}-Z_{right}\right)/\left(Z_{left}+Z_{right}\right)\ast 100$$ (10)

Here Z_left and Z_right represent baseline (non-injured) impedance of the left and right hemispheres, calculated by the mean of the sink electrode average impedance of lateral electrodes on each side (right (E₁,E₅,E₄) and left (E₂,E₆,E₃)) (Figure 3).

2). Novel Electrode Placement Analysis

To determine optimal novel electrode placements (II.C.4.b), an impedance change threshold was used to identify electrodes most sensitive to the simulated injuries. Electrode patterns were deemed “threshold-significant” if they yielded a measured impedance change within the top 5% of all impedance measurements and produced a percent impedance change greater than the median percent change. This was to ensure only patterns which measured large raw and percent changes in impedance were included. Within this subset of patterns, the central soft palate location and the tear ducts proved most sensitive to impedance change (see III.A) given their repeated presence as current-sinking electrodes (I⁻) in “threshold-significant” patterns. These electrodes were thus utilized in the remainder of the analysis (Figure 3).

3). Stroke Detection

Given this study’s emphasis on stroke monitoring relative to baseline impedance measurement (Z_initial), the minimum impedance change for stroke identification was determined using (13). Subsequent stroke characterization assessments (II.D.4–8) were completed with all stroke conditions below threshold (ΔZ_min) deemed “not-detected”, and thus incorrect.

4). Localization

Bolus locations were determined based on the electrode that measured the highest SEAIC. Stroke locations were then assigned relative to the sagittal and coronal planes associated with the location of the highest-SEAIC measuring electrode. For instance, if electrode 3, the left forehead electrode, measured the highest SEAIC the bolus was classified as being in the frontal, left-lateral region (Figure 7). The accuracy of this localization was then tested by identifying the true location of the most proximal electrode using the distance formula (11) to compute the center-to-center distance between the bolus (bol) and each electrode (elec). Actual coordinates of a bolus were derived from the random values generated during bolus creation. Localization accuracy was gauged based on the number of correct location predictions.

Fig. 7.

A-F) Visualizations of correctly classified strokes by location from the exhaustive solve (stroke not shown to size, green = ischemic, red = hemorrhagic). A) Stroke near sagittal plane. B) Stroke in the right hemisphere. C) Stroke in left hemisphere. D) Stroke in frontal lobe. E) Stroke near coronal plane. F) Stroke in occipital lobe / posterior of brain. G) Color map corresponding to percent accuracy of localization of strokes within different sections of the intracranial region. Left image corresponds to localization accuracy in axial plane, right image corresponds to localization accuracy in sagittal plane. Darker shading corresponds to higher localization accuracy.

$$d=\sqrt{{\left(x_{elec}-x_{bol}\right)}^2+{\left(y_{elec}-y_{bol}\right)}^2+{\left(z_{elec}-z_{bol}\right)}^2}$$ (11)

5). Stroke-type Detection

Hemorrhagic injury decreases the impedance of neurologic tissue, while ischemic injury is known to increase impedance [14]. This provides a key pathologic biomarker which we can utilize to anticipate an increase in SEAIC for ischemia and decrease for hemorrhage. Stroke type was thus categorized in accordance with SEAICs (12). Classification accuracy was assessed by comparison to assigned conductivity.

$$\left(\max \left(SEAIC\right)-\min \left(SEAIC\right)\right)=\{\begin{array}{cc}x<0& Hemorrhagic\\ x>0& Ischemic\end{array}$$ (12)

6). Simulated Noise

a. Signal Noise

Randomized Gaussian white noise was added to each impedance measurement, degrading the signal to levels of 100 dB, 85 dB (comparable to current hardware) [45], [46], 64 dB, 40 dB, and 20 dB. Noise was applied to both baseline and stroke conditions prior to calculating ΔZ. Thresholds for detectable signal (ΔZ_min) were calculated in accordance with simulated signal-to-noise ratio (SNR).

$$\Delta Z_{\min }=\raisebox{1ex}{$Z_{initial}$}\!\left/ \!\raisebox{-1ex}{${10}^{\left(\frac{SNR}{20}\right)}$}\right.$$ (13)

Any measurements below this threshold were identified as non-detectable. Accuracy across all stroke characterization measures were assessed as a function of noise introduction.

b. Electrode Placement Noise

Electrode placement noise was simulated by shifting the electrode headband to two different locations. In one placement, the headband was shifted down 30mm and rotated ~17mm (~11°). In the second, the electrode plane was shifted up 30mm and rotated ~17mm (~11°). Effect on accuracy for all stroke characterization methods as a result of placement variability was assessed.

c. Patient-to-patient Variability

Patient-to-patient variability was evaluated by scaling the head mesh size by +/−10% (i.e. scaled by 1.1 and 0.9) to capture smaller and larger head sizes. Accuracy was assessed for all stroke characterization methods as a result of head size variability.

d. Conductivity Variability

The effect of interpatient tissue conductivity differences was analyzed by rerunning the exhaustive stroke simulation (II.C.3.ii) with a second set of conductivities recommended for models that lack patient-specificity as reported in a recent meta-analysis [47]. Stroke characterization accuracy was compared to the accuracy computed with conductivities defined in II.B).

7). Novel Electrode Efficacy

Accuracy of the stroke characterization algorithms was also computed when using only scalp electrodes (E₁-E₉). The accuracy achieved with and without novel electrodes were directly compared. Likewise, current density and sensitivity to conductivity change were assessed in nine locations throughout the intracranial region and compared when novel electrode placements were used (E₁-E₁₃) and when not used (E₁-E₉), where the sensitivity was determined via the Jacobian (see II.A) [48].

8). Tracking Stroke Size

The relationship between measured average impedance and size of injury was recorded for stroke growth simulations from 0 mL to 100 mL. Paired t-tests of average SEAICs across all locations evaluated significance in differentiating stroke type at each size, as well as differentiating each size within each type. F-tests of linear regression quantified the slope response between magnitude impedance and volume of stroke. For all statistics, significance was set to α = 0.05.

9). Current Density Analysis

To determine effect of novel electrodes on intracranial current penetration, average current density across all exhaustive current injection combinations was assessed between electrode systems with novel electrodes (78 unique arrangements of paired I⁺ to I⁻) and without novel electrodes (36 unique arrangements of paired I⁺ to I⁻). Each current injection arrangement (i.e. IIVV pattern) produces a different current density profile, thus averaging across IIVV patterns provides an ensemble metric for assessing current density irrespective of pattern.

Current density was derived from the electric field (E) which is calculated by taking the gradient of the electric potential at each mesh element. The magnitude of the electric field was calculated and multiplied by the conductivity at each element to derive current density (J = σ * E). Average material current density was determined by summing current density across all voxels of a material and dividing by the total volume of the material $\left(\overline{{\text{J}}_{\text{material}}}=\frac{1}{V_{\text{material}}}{\sum }_{\text{n}=1}^{{\text{N}}_{\text{voxel}}}{\text{J}}_{\text{n}}\right)$. Average material current density was then normalized to the material with maximum average current density $\left({\text{J}}_{\text{normalized}}\text{=}\overline{{\text{J}}_{\text{material}}}/\overline{{\text{J}}_{\text{material\_max}}}\right)$. This volume correction was performed to allow for assessment of current penetration by and between material types, irrespective of the relative amount of that material which was present within the mesh, a relevant metric in aiming to assess whether certain anatomical pathways, though small, allow for higher current density.

III. RESULTS

Results are presented in the following order: A) optimal electrode placements, B-C) algorithm accuracy in differentiating stroke-type and localizing injury to an intracranial region, based on change from a baseline measure, D) stroke volume differentiation and progressive stroke tracking, E) impact of noise and novel electrode placement on stroke characterization accuracy, and F) efficacy of novel electrodes based on current penetration and sensitivity analyses.

A. Scalp and Novel Electrode Placement

Conductivity asymmetry (10) was assessed for the eight electrode arrangements (four axial planes, two spacing configurations, see Figure 2B). Scalp electrodes placed approximately 5.5 cm above the brow line with lateral electrode spacing of approximately 6-7 cm correlated to the lowest hemispheric asymmetry: 2.78%.

SEAIC thresholding results demonstrated that the tear duct electrodes were the most commonly occurring electrodes among threshold-significant electrode patterns (see II.D.2). The tear duct electrodes were then included along with the central soft palate point electrode and the electrode at the base of the head, in the complete electrode setup (Figure 3).

B. Stroke Type Differentiation

Hemorrhagic stroke was found to decrease measured impedance from baseline, uninjured measures, whereas ischemic stroke increased measured impedance, matching expected behavior (Figure 4). Conductivity asymmetry between right and left hemispheres after presentation of stroke also demonstrated that the direction of asymmetry (positive or negative) correlated with stroke type (Figure 5), matching prior work [14]. In the simulation consisting of 400 stroke conditions (i.e. type and location), stroke type was correctly categorized (12) in 99.5% of cases from SEAIC measurements (Figure 6).

Fig. 4.

Highest three sink electrode average impedance changes (SEAIC) with maximum ΔZ values for each electrode shown. Stroke volume of 70 mL in Frontal Lobe where A) green bolus = ischemic and B) red bolus = hemorrhagic. The three electrodes highlighted in yellow correspond to electrodes with greatest measured impedance change. These electrodes are most proximal to the center of the bolus as well.

Fig. 5.

A) Table displays the asymmetry indices (AI) for a unilateral bolus in the head mesh plots, B-C). The asymmetry index for two kinds of stroke, ischemic and hemorrhagic, are shown at two respective sizes B) 5.58 mL and C) 51.0 mL. AI was calculated with equation 10, where left and right correspond to hemispheres of the brain.

Fig. 6.

Stroke characterization accuracy vs. signal-to-noise ratio (SNR) across three measures: stroke type classification (ischemic or hemorrhagic); localization relative to sagittal plane (Hemisphere); localization relative to coronal plane (Frontal/Posterior);. A-B) Characterization accuracy across three measures for full electrode system (A) and system with novel electrodes removed (B), at No Noise, 100 dB, 85 dB (current hardware) [45,46], 64 dB (safety factor of 10 with respect to current hardware noise performance), 40 dB, and 20 dB SNRs. In A) ***P < 0.001, **P < 0.01 *P ≤ 0.05. C-E) Display discriminations of each characterization accuracy measure for full electrode system (solid lines) and novel electrodes removed (dashed line). Here Quad refers to combined anterior to posterior quadrant localization within the lateral side discrimination. Error bars correspond ± one standard deviation.

C. Stroke Localization

Simulated stroke caused the greatest measured change in impedance for electrodes proximal to location of a stroke (Figure 4). Hemispheric asymmetry also demonstrated that unilateral stroke induces conductivity asymmetries in accordance with location of stroke (Figure 5). Stroke lateral location was correctly identified to the closest electrode in 99.5% of cases and their location along the sagittal plane was classified correctly in 98.3% of cases (Figure 6). Figure 7 depicts the localization regions by which simulated strokes were classified and the locations of the intracranial region with lower localization resolution; namely, within the central region of the brain and anterior-ventral regions.

D. Stroke Volume

Stroke size positively correlated with the magnitude of hemispheric conductivity asymmetry in unilateral cases (Figure 5). EBI-based stroke detection yielded significant differentiation between small (p < 0.001), medium (p < 0.001), and large (p < 0.001) volumes within both ischemic and hemorrhagic injury with a baseline measurement (Figure 8), while also displaying positive correlation of size and measured impedance across exhaustive cases of injury growth without a baseline measurement (p < 0.001) (Figure 9). In the injury growth paradigm (II.C.3.iii), absolute impedance (Z_bol) increased with volume for ischemic stroke and decreased for hemorrhagic stroke. Mean Z_bol was found to be larger for ischemic injury than hemorrhagic injury: p < 0.05 at 0.137 mL, p < 0.01 at 1.098 mL, and p < 0.001 at 17.16 mL.

Fig. 8.

Box and whisker plots displaying impedance change averaged across all electrode arrangements for A) small (12.8 mL), B) medium (32 mL) and C) large stroke volumes (54 mL). Tails correspond to lower and upper quartile limits. Red crosses correspond to outlying values. Cross sections of small, medium, and large inclusions in central region of brain shown above. Within each size condition, differences between ischemic and hemorrhagic average impedance changes were significant (P < 0.001) and differences in average impedance change between respective stroke types across each size category was significant (P < 0.001).

E. Noise and Electrode System Accuracy

Six levels of randomized Gaussian white noise were introduced to impedance measurements for the full electrode system and no novel electrodes system (Figure 6). Significant increase in accuracy across all metrics was observed with inclusion of the novel electrode placements, varying by noise magnitude (Figure 6). Hemispheric localization accuracy was significantly higher (p < 0.001) for the full electrode system than for the system without novel electrodes at 40 dB and between 64 dB and 100 dB. Likewise, localization accuracy along the sagittal plane was significantly higher for the full electrode system at 85 dB – 100 dB (p < 0.001). Stroke type characterization was significantly higher for the full electrode system at 64 dB (p ≤ 0.05) and 40 dB (p < 0.001).

Changing material type conductivity values to those recommended for studies lacking patient specificity did not have a significant effect on stroke type and localization accuracy. Algorithms correctly classified the location relative to the sagittal plane in 99.5% of cases, the location relative to coronal plane in 97.5% of cases, and the conductivity in 98.25% of cases.

Electrode placement variability was found to decrease accuracy by up to 27.3% (maximum drop). Increasing the head mesh size led to a minor decrease in localization accuracy (0.85%), though stroke type accuracy did not change (Figure 10). Decreasing the size of the head mesh resulted in a slight increase in localization accuracy and did not affect stroke type accuracy.

Fig. 10.

Accuracy dependence on patient-to-patient variability and electrode setup noise. A-B) Rotation and vertical offsetting used in changing electrode placements to assess electrode setup noise. A) Electrode offset down and B) electrode offset up. C) Stroke characterization accuracy across three measures for these offsets and head mesh scaling simulating patient head size variability.

F. Current Density and Sensitivity

Current density and sensitivity to conductivity change within nine regions throughout the head mesh were assessed in full electrode and scalp electrode only systems (Figures 11–12). Both metrics show increased current penetration and sensitivity to the intracranial region with the use of the proposed novel electrode system. Current density was significantly higher in central and inferior regions for the system with novel electrodes (p < 0.01 and p < 0.001). Sensitivity to conductivity change was significantly higher for central, right, and low back and front regions for the novel electrode system (p <0.001).

Fig. 11.

Current density (J) visualization and analysis by tissue type and electrode system. A) Average current density with novel electrodes removed (II.D.9). B) Average current density from full electrode system. A-B) Log₁₀ (J) is plotted across the intracranial region (units = log₁₀(mA/m²)) – note the color bar defines this logarithmic current density ranging from −5 to −1.5. C) Average material current density normalized to the material with maximum average current density by material, ${\text{J}}_{\text{normalized}}\text{=}\overline{{\text{J}}_{\text{material}}}/\overline{{\text{J}}_{\text{material\_max}}}$. D) Total current density in each material (J_material) through the head mesh, across all exhaustive current injection pairs. E) Average current density and percent change between no novel and full electrode systems in nine 20 mm² regions. Regions with P < 0.05 significant increase in current density are highlighted in light green and P < 0.001 significant increase are highlighted in dark green.

Fig. 12.

Sensitivity to conductivity change at each node within the mesh. A) Shows sensitivity for electrode system with novel electrodes removed and B) shows sensitivity of full electrode system. The plot was generated by calculating the maximal Jacobian of the impedance measurement with respect to change in conductivity at each node, compiled across all electrode arrangements [48]. This calculation thereby gives the maximal change in measured impedance due to a small change in conductivity at each node. Log₁₀ scale of this maximal Jacobian was plotted and scale was limited from max −1 to −10. Red corresponds to greater sensitivity to conductivity change (resulting in larger ΔZ) and blue corresponds to less sensitivity to conductivity change at that node. C) Displays average sensitivity values in nine 20 mm² regions for both electrode systems. Percent change in sensitivity from adding novel electrodes to create the full electrode system is shown. Green indicates significant difference in sensitivity within node cluster of P < 0.001.

IV. DISCUSSION

Electrical bioimpedance offers a low-cost, non-invasive augment to help improve current CT and MRI measures for acute stroke patient care [12]. EBI holds the potential for rapid and continuous stroke monitoring, which is paramount for minimizing time-to-treatment and long-term morbidity of stroke [49].

Previous work has demonstrated the ability to detect the onset of intracranial infarction or hemorrhage invasively through EBI in an animal model [50], [51], and computer models have been used to study conductivity asymmetries between hemispheres of the brain after unilateral bleeding or clotting non-invasively [14]. However, the large impedance barrier of the skull has remained an obstacle for adequate current injection to the intracranial region for high accuracy stroke characterization [26]–[28]. In this study, we sought to investigate the clinical utility of a novel electrode setup which bypasses the skull for EBI-based stroke detection.

A. Summary

Successful current penetration of the skull was demonstrated for EBI-based stroke identification through use of novel pathways for current injection to the brain (tear ducts, soft palate and base of skull). An exhaustive simulation of 400 stroke conditions yielded 99.5% accuracy in differentiating ischemic from hemorrhagic stroke, 99.5% accuracy in determining the lateral locale of a stroke, and 98.3% accuracy in localization in the frontal or posterior regions of brain (Figure 6). A second simulation in which stroke volume was increased in four intracranial locations, yielded statistically significant differentiation between the impedance of ischemic and hemorrhagic stroke at volumes as small as 0.137 mL, and identified statistically significant difference between three volume ranges of stroke (Figure 9).

Current density and sensitivity mapping (Figure 11–12) found that novel electrode placements significantly increased sensitivity (p < 0.001) across eight of nine assessed regions and significantly increased current density in four of nine regions (p <0.05); most notably within central and lower regions of the brain that are notoriously difficult for stroke localization and identification [53].

B. Advancements from Prior Work

These findings support previous work which has encouraged the application of EBI for stroke detection [15], [24]–[26], while expanding upon realistic conditions. The use of a refined head mesh [28] addresses the limitation to clinical translation of more coarse meshes utilized in prior research [19], [26], [27].

Previous work in EBI has predominantly addressed stroke localization by hemispheres [14], [54]. This approach neglects frontal to posterior proximity, limiting EBI’s efficacy as a high precision complement to standard imaging procedures. While some research has leveraged Electrical Impedance Tomography (EIT) to image stroke location more precisely, findings from such simulation studies have either not articulated a supported method for such localization [26], or have indicated that such approaches may not be applicable in vivo due to depth of the intracranial region and small sizes of injury [15]. The present study addresses these limitations in localization specificity, offering a method for stroke localization within a 3x3 grid of the intracranial region, supported by an exhaustive set of testing conditions and three kinds of noise analyses. Further, limitations to localization accuracy were included in analysis, identifying locations which may introduce the greatest error (Figure 7).

The influence of noise on EBI measurements has also been considered in stroke characterization. While one study aimed to incorporate Gaussian noise into simulation data [53], the study’s emphasis on EIT and associated computational costs limited the collection of extensive simulation data. Likewise, the majority of studies which have addressed noise have either merely referenced electrode-tissue contact impedance or artefacts of electrical impedance tomography measurement, ultimately discouraging clinical application of EIT for stroke size and type characterization [20], [21]. By utilizing single-frequency impedance sensing in this study, we present algorithms independent from many of the prior limitations induced from the inverse tomography problem. Further, while some significant relationships have been found between conductivity change and stroke type [14], [53] and size [14], [25], the findings of this study expand upon those relationships to an exhaustive set of stroke conditions, including a less explored growing bolus through time, all across three forms of noise: signal noise, electrode placement variation, and head mesh scaling. In turn, the extensiveness of possible stroke scenarios, paired with realistic bounds on signal resolution and resultant high accuracy findings support the translational capacity of this work for stroke size and type identification.

C. Limitations

The New York Head mesh has high anatomical accuracy with respect to locations of tissue, yet uses a relatively simplified, seven material segmentation [37]. These simplifications may have affected the nature in which injected current is distributed throughout the intracranial region. While use of the NY Head mesh exhibited increased performance in measures related to EEG localization and tES targeting over more simplified models, working with more detailed simulations should remain a driving goal in this line of research to promote clinical translation.

The modelled distribution of tissue properties neglects to capture the intricacies of various tissues, bones, and nerves which comprise the novel pathways assessed. A generalized refinement for eyes was implemented to help represent more realistic conductivity distributions for the orbit region, and thus more effectively evaluate the tear duct electrodes. However, by implementing the higher conductivity region we had the potential to favor the tear duct electrode. Thus, the accuracy of stroke characterization was also assessed without reclassification and was found to remain at similar accuracy levels: 99.5% type accuracy, 99.5% side accuracy, 98.25% frontal/posterior accuracy. Thus, reclassification of the eyes did not drastically affect the characterization outcomes. Further mesh refinement or an in vivo model is necessary for further quantification of the potential of these pathways for current injection.

The method in which stroke was modelled also demonstrates limitations of the mesh, as an expanding infarct clinically may be limited in spread by surrounding anatomical barriers (e.g. ventricular walls). As a result, the inflection points evident in the plot of impedance vs. volume stroke (Figure 8) arise when a peripheral stroke crossed into the outer layer of CSF surrounding neurologic tissue. Impedance for ischemic stroke changed more dramatically due to higher contrast between ischemic stroke and conductivity of CSF. In reality, compression of tissue would push into the CSF, but not change its conductivity.

Another limitation of these findings surrounds the low magnitudes of calculated impedance changes across testing conditions. While these measurements were in the range of 1 – 34 Ω for maximal impedance changes, many |ΔZ| measurements were below 1 Ω. Despite the inclusion of signal noise, such low magnitudes may affect signal detection. To account for limitations in measuring small magnitude signals, a detectable signal threshold was implemented at each calculated SNR (13). Every |ΔZ| below the threshold was classified as non-detectable when calculating accuracy, in spite of the fact that the simulation algorithm may otherwise have successfully classified it. Additionally, approximately 10% of all initial impedances measured magnitudes of less than 1 Ω, presenting potential erroneous measurements due to general numerical noise in simulations. To address this, the impedance changes from electrode patterns which measured baseline impedance magnitude of less than 1 Ω were removed from SEAIC calculations. Removing these impedance changes did not significantly affect stroke characterization accuracies across all levels of noise. Lastly, by exploring noise to 20 dB we were able to capture the accuracy drop off, which theoretically should capture the loss of small signals earlier. Primary noise levels to interpret include 85 dB, which is the current lab hardware capabilities [45], and 40 dB, a realistic high noise environment such as an ambulatory setting.

The development of the presented algorithms in a simulation context also pose potential limits to clinical application. While stroke size differences were found relative to raw impedance measurements (Figure 9), stroke etiology and localization measures using the SEAIC metric relied on a baseline, uninjured measure. Such intrapatient algorithms allow for robustness to interpatient variabilities, however in a real-time monitoring context, measurement relative to an injured case would be necessary for monitoring and detection of subsequent or evolving injury. While we assessed the effect that head size variation, electrode placement, and conductivity variability have on stroke characterization, patient conductivity and geometry differences occur on a spectrum and our analyses only assessed each kind of difference in an isolated manner. Nonetheless, findings also demonstrate significant differences in impedance measurements independent of baseline scans, both between stroke volumes and when tracking a growing lesion, emphasizing the translational potential of EBI for use beyond monitoring, including potential ambulatory triage or on-scene stroke type differentiation. Future research should seek to apply these classification algorithms relative to an injured baseline, and quantify a broader spectrum of interpatient variability.

Finally, a single frequency was used for current injection (50 kHz). Using a wider range of current frequencies to interrogate the intracranial space may further increase the localization accuracy and type-classification of stroke lesions.

D. Future Steps

Research on refined head meshes across multi-frequency spectral ranges may uncover additional EBI-based features capable of further improving the accuracy and classification presented in this study. Next a clinical bioimpedance system will be developed to assess EBI’s capacity to monitor stroke passively after injury in vivo. EBI with current injection through low-impedance pathways to the brain may play an important role in providing rapid and accessible diagnosis of stroke in clinical and ambulatory settings, and assist in lowering the long-term morbidity and cost of this public health problem.

V. CONCLUSION

This study identified novel electrode placements for successful intracranial current penetration on the tear ducts, base of skull, and soft palate for EBI in a realistic anatomical model of the head. Custom identification algorithms for stroke etiology, location, and size provided high accuracy for stroke characterization, relative to a baseline measurement, across all measures in the presence of three kinds of noise typical of clinical settings. Novel electrode placements were found to increase characterization accuracy. Current density and sensitivity to conductivity change within the intracranial region was also found to increase with the addition of novel electrodes. The realistic conditions introduced in this simulation study support clinical application of these methods in EBI and provide support for an approach to overcoming the high-impedance barrier of the skull.