Extending bioelectric navigation for displacement and direction detection

Bioelectric navigation [1] is a recently proposed modality for endovascular navigation of catheters. Here, a set of electrodes is placed along the tip of the catheter. A constant amplitude AC current of low frequency (730 Hz) is generated between an electrode at the catheter tip and a ground electrode further down the catheter body. This current generates an electric field which depends on the shape of the blood vessel. Using the same or a different pair of electrodes, the electric field can be probed. Recording the voltage difference between this pair of electrodes over time produces a signal waveform which can be used to detect the current branch of the vasculature the catheter is in. This voltage difference mostly depends on the local diameter of the blood vessel. Thus, when the catheter passes by local geometric vascular features, such as bifurcations, stenosis or aneurysms, or when it moves into a smaller side branch, this produces detectable changes in the waveform. The current vascular branch of the catheter is determined by matching the voltage difference waveform to a set of reference signals simulated from a 3D CT of the anatomy of interest.

So far, the concept has been shown to be able to identify the branch the catheter is currently in, but not the exact location of the tip inside this branch [1]. The approach also assumed that the catheter was monotonously moving forward, while in realistic surgical scenarios, the surgeon might also pull the catheter back and then readvance it (e.g., in order to enter side branches). These are the challenges we aim to tackle within this work.

There is a plethora of approaches for non-fluoroscopic tracking of catheters. (For an extensive discussion, see [2].) Conceptually closest to bioelectric navigation are some systems used for cardiac ablation and thus navigation inside the cardiac chambers. Some examples include CARTO 3 [3], EnSite NavX [4] and Kodex EPD [5]. These all differ from bioelectric navigation in different aspects. They either use external field generators for generating a magnetic field, in which the catheter is tracked. Alternatively, electrode patches attached to the patient’s skin (usually 3 pairs which each send electric currents in the x, y or z axis) are used to generate an electric field that is then passively sensed by electrodes on the catheter. The closest to bioelectric navigation is Kodex EPD, in which electric fields are generated between pairs of surface electrodes, but also between catheter electrodes and surface electrodes, meaning that the catheter electrodes do not only act as passive field sensors. Still, Kodex EPD has been only reported for navigation inside the cardiac chambers. In comparison, bioelectric navigation aims at navigating the vasculature (e.g., abdominal aorta or coronary arteries). Also, bioelectric navigation does not use any external surface electrodes, but relies solely on electrodes attached to and moving with the catheter. For our proposed concept, we draw inspiration from the above-mentioned systems using external (stationary) skin electrodes and propose to extend bioelectric navigation by a stationary electrode, placed inside a blood vessel, for estimating catheter displacement and movement direction.

We aim to tackle the problem that a catheter tracked by bioelectric navigation misses information on movement direction and displacement between anatomical features. We want a solution that we can fit onto a catheter together with the electrodes needed for bioelectric navigation. Then one could detect the current vascular branch, movement direction and exact position along the branch. Thus, we propose an electric sensing concept for direction and displacement, in order to be able to use the same electrodes on the catheter that bioelectric navigation already needs. Ideally, we could use the same electrodes for both tasks to evade adding further hardware complexity to the catheter.

For bioelectric navigation, we assume a tetrapolar electrode configuration is used. This consists of two current injection and two voltage sensing (detection) electrodes (see Fig. 1, left).

We choose this configuration as it is robust to radial shifts of the catheter inside the vessel (i.e., displacements perpendicular to the centerline) [6]. Here, we propose to extend this setup with an additional electrode that is not attached to the catheter, and is stationary (see Fig. 1, middle). In clinical practice, this electrode could, for example, be attached to the vascular access sheath which stays in place at the site where the surgeon cut the patient’s skin and blood vessel in order to access the vasculature. In this work, we investigate how to estimate catheter displacement (along the centerline) and movement direction using measurements obtained by means of this stationary electrode.

Our approach is based on the idea of estimating the electric field locally between the detection electrodes. We take inspiration from the ideas introduced by the LocaLisa system [7] where the authors used six external electrodes attached to the patient skin for tracking the catheter inside the cardiac chamber. We aim to transfer this idea from 3D movement inside the cardiac chamber, using a field generated by electrodes outside of the body, to 1D movement along the centerline of the blood vessel, using electrodes inside the blood stream. In contrast to the LocaLisa approach, in our case one of the field-generating electrodes is moving, i.e., non-stationary, which will have implications discussed later.

We propose to generate an electric current between catheter tip electrode and stationary electrode. This current flow causes continuous voltage drops along its path. Given our two detection electrodes, we can measure the voltage drop between them. We also know the distance between these electrodes \(\Delta d_{det}\) by catheter design. We can thus estimate the mean voltage drop per spatial unit between these two electrodes (e.g., 1V per millimeter). If we assume that the catheter body at the detection electrodes is aligned with the centerline of the blood vessel, we thereby obtain an estimate of the mean voltage drop per spatial displacement along the centerline. This is equivalent to estimating the component of the electric field vector along the centerline segment between the detection electrodes:with \(V_{det,A}\) being the voltage between detection electrode A and the stationary electrode, and \(V_{det,B}\) being the voltage between detection electrode B and the stationary electrode. This estimated electric field component contains the information of how much the voltage will change if we move a small step along the centerline. If we measure the voltage at detection electrode A at times t and \(t+\Delta t\), we can then estimate the movement along the centerline within this time frame byCumulatively summing up these displacements \(\Delta d_{cath}\) then gives our estimate of total catheter displacement. Using Eqs. 1 and 2 to obtain these estimates is referred to as approach I from now on.

For now, we implicitly made the assumption that the electric field at the detection electrodes is static, i.e., it does not change while the catheter moves. However, the tip electrode of our catheter, which generates the field, moves together with the rest of the catheter. Our simulations (see ”Simulation results” Section) indicate that as long as the blood vessel is assumed to be surrounded by electrically non-conducting tissue, the assumption of a static field holds true, as all electric current is constrained into the vessel lumen. Under the more realistic assumption that the vessel is surrounded by tissue that can also conduct electric current, though, we observe that the electric field changes while the catheter moves. In this case, the voltage change at detection electrode A is not only influenced by the movement of the electrode inside the electric field. It is also influenced by the movement of the tip electrode which changes the electric field itself, and thus, Eq. 2 does not hold true anymore. We propose to compensate for this by adding one more electrode to the catheter. It is placed slightly behind the tip electrode. We refer to this electrode as \(tip^*\) from now on. The distance between tip and tip* is the same as the distance between the detection electrodes, \(\Delta d_{det}\) (see Fig. 1, right). We then generate a second electric current between this electrode and the stationary electrode, with a slightly different frequency (e.g., 900 Hz). Given the known distance between the tip and \(tip^*\) electrodes, we can now try to estimate the change in voltage at detection electrode A caused by the movement of the tip electrode by a distance \(\Delta d_{tip}\):Here, \(V_{det,A}\) is the voltage at detection electrode A generated by the field of the tip electrode, and \(V^*_{det,A}\) is the voltage at detection electrode A generated by the field of the \(tip^*\) electrode. We assume that the total voltage change at electrode A is the sum of changes caused by tip motion (Eq. 3) and the movement of the detection electrodes (Eq. 2). If we further assume that tip and detection electrodes move by the same distance (\(\Delta d_{cath} = \Delta d_{tip}\)), we can obtain the compensated formula for estimating catheter displacement asUsing Eq. 4 (together with Eqs. 1 and 3) to obtain displacement estimates is referred to as approach II from now on.

To investigate the effects of surrounding tissue on the electric field, we set up an FEM simulation pipeline. As vascular model, we chose the abdominal vasculature of a subject with abdominal aortic aneurysm (AAA), shown in Fig. 2 on the outer left. To speed up the simulations, we cropped one large vessel from the model using 3D Slicer [8], as shown in the inner left and inner right panels of Fig. 2. We also extract the centerline along this vessel using 3D Slicer’s Vascular Modeling Toolkit. We use FreeCAD¹ to decimate the resulting mesh and convert it to brep format. Gmsh [9] is used for meshing. We model the catheter as a disk extruded along a spline fitted to the centerline. Tissue surrounding the blood vessels is modeled as a cube. The stationary electrode is placed close to the beginning of the vessel (centerline index 10 of 209). For each location on the centerline (starting from index 70), we build a gmsh model by importing the vascular model. Then, we place the catheter with detection electrodes centered around the current centerline location inside the vascular model, and create the surrounding tissue cube. Elmer Solver [10] is used to simulate static current flow using the Static Current Conduction model of Elmer. An exemplary simulation result in one catheter location, color-mapped by the voltage at each point in space, is shown in Fig. 2 on the outer right.

We wanted to validate our displacement estimation in a real setup. A simple vascular phantom (see Fig. 3) was downloaded from a public repository of data associated with [1]. We cut a few branches, rescaled and 3D printed the model. As plastic is not conducting, this phantom corresponds to the case of non-conducting tissue, and we use approach I to estimate displacement. We generated an AC current with a frequency of 1 kHz and a constant amplitude of 100\(\mu A\) between tip electrode and a stationary electrode fixed to the vascular tree root. The voltages of detection electrodes and between detection and stationary electrodes were measured using two PicoScope Oscilloscopes (2203 and 3204D). We used a synchronization procedure to synchronize the measurements of the two oscilloscopes and account for slight deviations in their sampling frequencies. This procedure is detailed in the Supplementary Material (Online Resource 1). We used a Webster decapolar catheter (Fig. 3 right) with 5 pairs of electrodes. Each pair is 3mm center-to-center apart (= \(\Delta d_{det})\).

As we know the length of each vascular centerline from the 3D model, we use this as ground truth to validate our displacement estimation approach. For each of the lower 3 branches, we moved the catheter until the most proximal electrode was exactly at the end of the branch. We then pulled back the catheter until the most proximal electrode was exactly at the root of the phantom. The distance traveled by the catheter is thus exactly the length of the centerline of the branch, which we obtained with 3D Slicer. This pullback was recorded 10 times. We then also recorded 10 runs where the catheter was moved until the tip electrode was at the end of the branch, and pulled back until the most proximal electrode was at the root. The distance traveled by the catheter in this case was the length of the centerline minus 4.0 cm (the distance between the centers of tip and proximal electrodes on the catheter).

First, we investigated the effect of surrounding conductive tissue on the electric field during catheter motion. We found that if the surrounding tissue is not conducting, the tip motion of the catheter causes no change in the electric field inside the blood vessel (as assumed in approach I). In case of the surrounding tissue being electrically conductive, the electric field in the vessel changes when the catheter moves (see Fig. 4). This justifies the use of approach II in such scenarios.

Next, we simulated the catheter moving by 100 steps (8.90 cm) along the vessel. We ran simulations for zero tissue conductivity, a conductivity ratio of 0.2 (\(=\frac{tissue\;conductivity}{blood\;conductivity}\)) and 0.32, the latter one following [11]. We simulated with a distance between tip electrode and first sensing electrode of 2.82 cm and a distance between the sensing electrodes \(\Delta d_{det}\) of 0.36 cm and one time with the sensing electrode being closer to the tip (distance of 1.62 cm). We compare the results to ground truth displacements. We tested the performance with the catheter moving at different speeds, with catheter displacement \(\Delta d_{cath}\) between subsequent steps varying from 0.885mm (= \(\frac{1}{4}\) of \(\Delta d_{det}\)) to 3.54mm (=\(\Delta d_{det}\)). The results are depicted in Fig. 5 for \(\Delta d_{cath}\) of 0.885mm and Table 1 for all \(\Delta d_{cath}\). From the results, it can be seen that approach I estimates catheter displacement accurately when the surrounding tissue is non-conductive, with absolute errors below 0.89 mm for a ground truth displacement of 89 mm (Table 1, column 1). Nonetheless, estimates from approach I strongly deviate from the ground truth displacement if surrounding tissue with nonzero conductivity is present. Using approach II to correct for these effects improves the estimated displacement in all cases with conductive surrounding tissue (Table 1, columns 2 and 3). Approach II still underestimates the displacement, with absolute cumulative errors up to 34 mm. This indicates that effects of surrounding tissue cannot be fully compensated for by this approach, although it mitigates the impact on the estimated displacement. For two different values of surrounding tissue conductivity (column 2 and 3), the estimated displacements are comparable. The results in column 4 further indicate that moving the detection electrodes too close to the tip electrode deteriorates the results. This might be because closer to the tip, the field changes more strongly with tip motion (see Fig. 4). Looking at the errors along the full path of the catheter (Fig. 5), it can be seen that the above-mentioned errors originate from a systematic underestimation of displacements in each time step. These add up along the path, leading to absolute errors that increase with the length of the traveled path.

The results of the experiments in the 3D printed phantom are given in Table 2 and visualized in the lower right image of Fig. 5. Our displacement estimates show a good overall agreement with the ground truth branch lengths. Nonetheless, it can be seen that they differ from the near-perfect results of the simulation of approach I with non-conducting tissue. While the mean of the 10 runs per setting correlates with the ground truth branch lengths, the estimated length still differs from the ground truth. The mean error varies for different branches between 0.2 and 1.2 cm. The standard deviation of the estimated branch lengths from repeated pullbacks is low, with a maximum of 0.11 cm for Branch 3, indicating good reproducibility. To set these values into clinical perspective, an accuracy of < 5mm is considered sufficient for EVAR interventions, although higher accuracy is needed for fenestrated procedures [12]. Our system cannot meet these accuracy requirements yet.

The results indicate that the approach works not only in simulation, but also in a physical setup. Still, further investigations are needed to determine the source of estimation errors and deviations between repeated runs. There are multiple effects that have not been modeled in the simulations, such as interface effects on the contact surface between electrodes and blood, or the catheter moving off centerline. Potentially one of these effects is the cause for the mismatch between simulated and physical experimentation results.