Theory for a non-invasive diagnostic biomarker for craniospinal diseases

Abstract

Monitoring intracranial pressure (ICP) and craniospinal compliance (CC) is frequently required in the treatment of patients suffering from craniospinal diseases. However, current approaches are invasive and cannot provide continuous monitoring of CC. Dynamic exchange of blood and cerebrospinal fluid (CSF) between cranial and spinal compartments due to cardiac action transiently modulates the geometry and dielectric properties of the brain. The resulting impedance changes can be measured and might be usable as a non-invasive CC surrogate. A numerically robust and computationally efficient approach based on the reciprocity theorem was developed to compute dynamic impedance changes resulting from small geometry and material property changes. The approach was successfully verified against semi-analytical benchmarks, before being combined with experimental brain pulsation data to study the information content of the impedance variation. The results indicate that the measurable signal is dominated by the pulsatile displacement of the cortical brain surface, with minor contributions from the ventricular surfaces and from changes in brain perfusion. Different electrode setups result in complementary information. The information content from the investigated three electrode pairs was employed to successfully infer subject-specific brain pulsation and motion features. This suggests that non-invasive CC surrogates based on impedance monitoring could be established.

Keywords: Computational electrostatics; Continuous monitoring; Craniospinal compliance; Craniospinal disease screening; Intracranial pressure; Non-invasive diagnostics.

Graphical abstract

Fig. 1

Developed computational pipeline based on the reciprocity theorem for dynamic EM problems. A closed-form equation for determining effective charge layer distributions is derived and used to compute the associated impedance changes (via the electric charge variation dQ) as well as sensitivity maps ($S(r)$, functional derivative of dQ to local brain pulsation). A sensitivity map provides insight into the spatial distribution of pulsation-contributions to the measurable impedance signal.

Fig. 2

Sketch illustrating a dynamic EM problem with a shifting interface. The impedance computation due to the dynamic geometry changes is mathematically recast (using the reciprocity theorem) into the task of determining equivalent dipolar charge-density distributions residing at the shifting interface. Numerical methods are then developed to efficiently estimate those distributions.

Fig. 3

Geometries of the (a) 1D, (b) 2D symmetric, (c) 2D asymmetric, and (d) 3D benchmarks; (e) geometry changes in the 2D asymmetric benchmark.

Fig. 4

Simulation post-processing pipeline used for EM simulations with the MIDA model.

Fig. 5

Schematic description of the pipeline used to process the imaging-based deformation data in preparation for their combination with the computationally determined sensitivity maps.

Fig. 6

(Top) Illustrative KNN-smoothed deformation data from one subject at one time point during the cardiac cycle; (a) right-left, (b) anterior-posterior, and (c) cranial-caudal component. (Middle) Illustration of the brain deformation over one cardiac cycle (the coloring denotes the motion magnitude); (left) streamlines and principal motion trajectories, (middle) vector field views, (right) schematic representation of the overall brain deformation pattern; see Section 3 for extended explanation and interpretation and Fig. S9 for an animated 3D visualization of the streamlines of sub-interval (II). (Bottom) Time-intervals of the pulsation period corresponding to the motion visualizations in the Middle.

Fig. 7

Coupling MIDA-based EM simulations and MRI deformation data to compute dC and dR. The displacement and, therefore, the signal contribution maps are time dependent and only a snapshot is shown (see Fig. S10 for an animated, transient version).

Fig. 8

The (a) 1^st, (b) 2^nd, and (c) 3^rd electrode configuration and the corresponding sensitivity magnitude ($|S|$) on the cortex ((d)-(f): total sensitivity combining geometry pulsation and dielectric property change contributions – the latter is uniform, as a result of the homogeneous blood distribution assumption, and much smaller than the former).

Fig. 9

Simulated capacitance (left) and resistance (right) variations associated with the cortical CSF-brain interface, shown over the cardiac cycle for the 2^nd electrode configuration. (Top) dC and dR from data of all eight subjects, using the KNN extrapolation method; (Bottom) comparison between predictions obtained using KNN and FFT reconstruction for the average of all subjects.

Fig. 10

Simulated capacitance (left) and resistance (right) variations associated with the ventricular CSF-brain interface, shown over the cardiac cycle for the 2^nd electrode configuration. (Top) dC and dR from data of all eight subjects, using the KNN extrapolation method; (Bottom) comparison between predictions obtained using KNN and FFT reconstruction for the average of all subjects.

Fig. 11

Comparison of the geometry-pulsation- and the blood-perfusion-contributions to the capacitance (left) and resistance (right) variations (average over all subjects, two cardiac cycles, 2^nd electrode configuration, FFT-reconstructed deformation data). The contributions from the cortical and ventricular CSF-brain interfaces are distinguished. Note the difference in scaling for ventricular vs. cortical CSF-brain interfaces.

Fig. 12

Comparison across the three electrode configurations from Fig. 8 of the simulated total (cortical and ventricular) capacitance and resistance variations over the cardiac cycle obtained using FFT extrapolation.

Fig. 13

Correlation between the subject-averaged measurable signals and subject-averaged deformation data features using FFT-reconstructed data. ${\mathit{dC}}_{1,2,3}$ and ${\mathit{dR}}_{1,2,3}$: capacitance and resistance variation for 1^st, 2^nd, and 3^rd electrode configurations, ${\mathit{dV}}_{\mathit{CSF}}$: brain volume change, $T_S$: brain translation, and $R_S$: brain rotation. Each dot in the scatter plots corresponds to one time-point.

Fig. 14

(Top) simulated measurable signals for the 2^nd electrode configuration using FFT reconstruction; (Bottom) ${\mathit{dV}}_{\mathit{CSF}}$: brain volume change, $T_S$: brain translation (surface averaged), and $R_S$: brain rotation (surface averaged).

Fig. 15

Correlation between the measurable signals and deformation data features using FFT reconstruction. ${\mathit{dC}}_{1,2,3}$ and ${\mathit{dR}}_{1,2,3}$: capacitance and resistance variation for 1^st, 2^nd and 3^rd electrode configurations, ${\mathit{dV}}_{\mathit{CSF}}$: CSF volume change, $T_S$: total translation of the cortex, and $R_S$: total rotation of the cortex. Each dot in the scatter plots corresponds to one subject and one time-point. The nonlinear relationships (‘loops’; bold: mean over all subjects, dashed: illustrative individual subjects) between ${\mathit{dC}}_2$ and $R_S$ are shown on the top right. In view of the multiple electrode pairs and the different deformation features, the loops should be viewed as being higher-dimensional (i.e., a vector of size $n_t·(n_f+n_s)\text{; }{n}_t$: number of time-points, $n_f$: number of features, $n_s$: number of signals).

Fig. 16

Box-plot of the deviations for all subjects of the measurement-signal-based volume change, translation, and rotation predictions from their real values. Those deviations are much smaller than the deviations of the different subjects from the mean, or than their variability (significance assessed using the Wilcoxon signed-rank test; $\star :p$-value$<5\%,\star \star :p$-value$<1\%$); ${\mathit{dV}}_{\mathit{CSF}}$: CSF volume change, $T_S$: brain translation (surface averaged), and $R_S$: brain rotation.