International Journal of Bioelectromagnetism Vol. 21, No. 1, pp. 7-20, 2019.

www.ijbem.org

FEM Simulation of Bioimpedance-Based Monitoring of Ventricular Dilation and Intracranial Pulsation Carlos Castelara, Fabian Flürenbrocka, Leonie Korna, Anne Benninghausb, Berno

Misgelda, Sergey Shchukinc, Klaus Radermacherb, and Steffen Leonhardta aChair for Medical Information Technology, RWTH Aachen University, Aachen, Germany

bChair of Medical Engineering, RWTH Aachen University, Aachen, Germany cBauman Moscow State Technical University, Moscow, Russia

Correspondence: Carlos Castelar, Chair for Medical Information Technology, RWTH Aachen University, Pauwelsstraße 20, 52074 Aachen, Germany

E-mail: castelar@hia.rwth-aachen.de Website: www.medit.hia.rwth-aachen.de Phone: +49 241 80 23203

Abstract. Intracranial dynamics play an important role in ventricular enlargement and are the focus of ongoing research. In this Finite Element (FE) study, a bioimpedance drainage catheter has been investigated as a volume monitoring device for the treatment of hydrocephalus. For this, six platinum ring electrodes are integrated on the surface of a drainage catheter. Three different FE brain models have been generated: a geometric model, a complete anatomical model, and a simplified anatomical model. The latter is a compromise between anatomical detail and geometric simplification, reducing computational cost. This model simplification is supported by sensitivity distribution analysis, which indicates that the region of higher sensitivity for the proposed measurement setup is concentrated around the impedance catheter. A silicon-carbon mixture brain phantom that replicates the intracranial electrical properties is proposed to validate the measurement principle in vitro. Ventricular volumes ranging from 20 ml to 199 ml have been simulated. It has been observed that the measured impedance decreases exponentially with increasing ventricular volume, i.e. volume estimation accuracy is higher for small ventricular volumes (20 ml) but is reduced for larger volumes. Additionally, the feasibility of bioimpedance monitoring of the pulsatile ventricular volume fluctuations has been successfully simulated. Keywords: Hydrocephalus; bioimpedance; ventricular volumetry; intracranial pulsation; FEM; brain phantom

1. Introduction Cerebrospinal fluid (CSF) is produced in the choroid plexus as a secretion from arterial blood and

circulates through the intracranial ventricular space, the spinal canal, and the subarachnoid spaces (SAS). It has been widely accepted that CSF is reabsorbed into the blood circulation at the sagittal sinus through the arachnoidal granulations, although new theories indicate other possible absorption sites in addition [Hladky and Barrand, 2014]. CSF volume in the ventricular space and SAS comprises approximately 150 ml. With an average production of 20 ml/h, around 500 ml are produced and reabsorbed each day [Schünke et al., 2018].

Hydrocephalus is a congenital or acquired pathological enlargement of the intracranial ventricular space which is often accompanied by an increase in intracranial pressure (ICP). It usually manifests as the consequence of a disruption in the production-circulation-absorption CSF cycle [Misgeld et al., 2015]. Hydrocephalus may be classified into hydrocephalus occlusus (obstructive hydrocephalus) or hydrocephalus communicans (communicating hydrocephalus). In the case of the former, as the term indicates, an obstruction blocks the normal CSF pathway either partially or completely, causing CSF accumulation upstream of the obstruction. The latter, on the other hand, occurs even though no apparent obstruction is detected. Some theories indicate that this may be due to increased resistance to outflow (ROF) [Albeck et al., 1998]. This, however, does not explain why CSF accumulation and ventricular enlargement occur primarily in the lateral and third ventricles. It is hypothesized that abnormal changes in the viscoelastic properties of intracranial and/or spinal structures might cause a significant decrease in

8

the overall craniospinal compliance which in turn causes a gradual expansion of the ventricular volume [Greitz, 2004].

Idiopathic Normal Pressure Hydrocephalus (iNPH) falls under the communicating type of hydrocephalus and is characterized by an ICP which remains, most of the time, within physiological ranges, although the ventricles still dilate. The ventricular volume for iNPH patients is approximately 138 ml in average and therefore about 100 ml larger than in healthy subjects [Matsumae et al., 1996; Ringstad et al., 2015]. Normally, iNPH is accompanied by the Hakim Triad of symptoms: urinary incontinence, gait ataxia, and dementia. The incidence of iNPH in Germany increased from zero to 1.36/100.000/year in the last fifteen years, and it is currently considered to be the only curable form of dementia [Lemcke et al., 2016]. It is also estimated that iNPH accounts for at least 10 % of the new dementia diagnoses every year [Hakim et al., 2001]. The exact pathophysiology of iNPH is still unclear, although it is well accepted that a reduction in craniospinal compliance plays an important role in its development stage [Bateman, 2000; Greitz, 2004].

1.1 Hydrocephalus treatment Hydrocephalus is usually treated by draining excess CSF with a temporary or a permanent shunt

through a passive pressure valve. If the ICP overcomes a pre-set opening pressure, the valve opens and drains fluid from the ventricle into another body compartment (e.g., the peritoneal cavity, where it can be readily reabsorbed). However, the pre-set opening pressure is fixed in many designs and cannot adapt to the patient’s specific requirements. It may vary considerably, leading to either overdrainage which, if not detected timely, may cause the collapse of the ventricles (slit ventricles), tissue damage and the reoccurrence of the original symptoms; or underdrainage which implies no or minor improvement of the symptoms. In the case of iNPH, this proves even more problematic, since a low opening pressure threshold is needed and the risk of overdrainage is higher. Therefore, the development of a feedback-controlled shunt, which adapts and optimizes the opening and closing of the valve to the patient’s requirements, might result in a significant reduction of shunt complications and failures. First intelligent shunt prototypes have been developed and tested [Elixmann et al., 2014]. The focus of this paper is to study in silico the feasibility of bioimpedance-based volumetric measurements, which might in future be integrated into smart-shunt prototypes to serve as an appropriate control parameter in addition to ICP measurements [Elixmann et al., 2013].

1.2 Bioimpedance-based volumetry Currently, and to the best of the authors’ knowledge, no commercial implant design allows the

continuous monitoring of ventricular volume. For research, a bioimpedance-based solution has been previously proposed [Elixmann et al., 2013; Linninger, Basati, et al., 2009] The bioimpedance technique allows the determination of static and dynamic tissue properties in relation to their passive electrical properties. In this respect, the Cole-Cole model is well established to describe the frequency-dependent characteristics of tissue [Gabriel et al., 1996]. The technique has been tested for the volume determination of hollow organs such as the left and right ventricular volume for the heart [McKay et al., 1984], and the estimation of the urinary bladder volume [Schlebusch et al., 2014]. Since the conductivity of CSF (σCSF = 2.01 S/m) is relatively much larger than the conductivity of brain parenchyma (σparenchyma = 0.17 S/m), the intraventricular bioimpedance measurement may provide volumetric information [Basati et al., 2011]. For this, a drainage catheter with integrated electrodes on its surface is proposed (see Materials and Methods). Baan et al. introduced the impedance-based monitoring of cardiac ventricular volume monitoring using the impedance catheter concept, in which a constant current is injected between the outer ring electrodes and the resulting voltage drop is measured between the inner electrodes. With geometrical assumptions, the total volume may then be derived from the multiple volume segments [Baan et al., 1984].

1.3 Intracranial pulsation An impedance sensor catheter for hydrocephalus might be able to monitor the dynamic volume

change caused by the pulsatile ventricular wall expansion continuously and thus may provide an insight into the dynamic compliance properties of the brain. The relevance of intracranial pulsations in overall craniospinal hydrodynamics has been addressed in the literature [Wagshul et al., 2011]. The Monro-Kellie doctrine describes intracranial volume as the sum of the brain, blood, and CSF volumes, as incompressible, and therefore constant. Intracranial arterial pulsation is responsible for the compression of cerebral veins and/or caudal displacement of CSF into the spinal canal, which is possible due to the elasticity of the compliant dural sac. This observation is supported by phase-contrast magnetic resonance imaging (PC-MRI) [Balédent et al., 2001; El Sankari et al., 2011]. A ventricular volume variation of 10 – 20 % during the cardiac cycle (CC) has been reported, whereby the pattern is similar to the ICP

9

waveform [Lee et al., 1989], with the choroid plexus motion driving CSF and ventricular oscillation [Egnor et al., 2002; Wagshul et al., 2011]. Furthermore, it has been proposed that an increased pulsatility of the intracranial arterial branches may be transferred to the CSF volume and might contribute to ventricular dilation in iNPH [Bateman et al., 2005; Qvarlander et al., 2017].

2. Materials and Methods

2.1 Finite Element Model In literature, different approaches have been explored to model the onset of hydrocephalus [Goffin

et al., 2017]. These range from e.g. lumped parameter models of intracranial dynamics to explore the role of cardiovascular coupling in ICP pulsatility [Ambarki et al., 2007; Misgeld et al., 2015], 2D structural mechanics finite element (FE) models [Nagashima et al., 1987], to 2D and 3D computational fluid dynamics (CFD) models that simulate CSF flow and determine stress distribution [Linninger, Xenos et al., 2009] and patient-specific FE models [Lefever et al., 2013]. In the present study, FE simulations were performed with COMSOL Multiphysics (Comsol Inc., Burlington, VM, USA) with the AC/DC and Structural Mechanics modules. Multiple 3D FE models of varying complexity, including simplified geometries and anatomical models, have been generated. The geometric models were created using COMSOL geometry tools. The magnetic resonance images (MRI) used for the anatomical model were obtained from the dataset made available by the Surgical Planning Laboratory [Halle et al., 2017].

Simplified geometrical models Figure 1 shows the simplified geometric models of the brain (Model 1). It consists of a cylindrical-

shaped brain containing a single ellipsoidal ventricle in its interior. An ellipsoidal shape was selected since it is closer to the anatomical shape of the anterior ventricular horn in comparison to spherical or cylindrical shapes. Five different discrete volumes were meshed (20, 40, 60, 80, and 100 ml) in the FE model. Silicone-based brain phantoms with the same geometrical parameters have been produced in order to perform in vitro bioimpedance measurements with a precision LCR Meter E4980A (Agilent Technologies Inc., Santa Clara, CA, USA) and compare them to the static volume estimation FE simulation results.

Figure 1 Left: Geometrical model (Model 1) of a cylindrical brain with a single ellipsoidal ventricle and concentric positioned impedance catheter. Middle: Silicone-carbon brain phantom with impedance catheter. The sample is cut in half for visualization purposes. Right: Silicone phantoms with different inner ventricular volume.

10

Anatomical models A complete segmentation of the intracranial structures was performed based on the procedure

presented by [Teichmann et al., 2017], for which segmentation software ITK-SNAP 3.6.0 [Paul A. Yushkevich et al., 2006] and Blender 2.79a were used. The final model (Model 2, shown in Figure 2, middle and right) includes a detailed ventricular space, brain parenchyma, fat, connective tissue, skin, and skull.

Simplified anatomical models As a compromise between less computationally

intensive geometrical models and anatomically accurate meshes, a simplified anatomical model has been proposed, consisting of a cylindrical head shape with skin, skull, brain parenchyma, and lateral ventricles. This simplification is based on the results obtained for the sensitivity maps and current density profiles (see Results). The ventricular volume meshes were imported from the anatomical mesh as described in the previous section and reduced to include only the lateral ventricles (Figure 3) since it is here where normally most of the dilation occurs in hydrocephalus [Damasceno, 2015]. The simplified anatomical model of the ventricle includes the anterior, posterior and lateral horn structures. Figure 4 shows three different meshes with varying lateral ventricular volume for Model 3.

Figure 3 Simplified anatomical geometry (Model 3) of the lateral ventricles.

Figure 2 Left: Segmentation of the human brain and ventricle. Middle: Mesh grid of the complete head (Model 2). Right: Mesh model of the complete intracranial ventricular structures including lateral ventricles, third, fourth ventricles, and aqueduct.

Figure 4 Simplified anatomical model (Model 3) with lateral ventricles of 24.95ml (left), 84.2 ml (middle), and 199.6 ml (right).

11

Impedance catheter The electrode catheter (IMTEK, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany) is

depicted in Figure 5 with the corresponding dimensions. The electrodes consist of 12.5 µm thick platinum metal, MP35N wiring and an insulating silicone rubber coating around the catheter tip. The placement of the catheter for the impedance measurement is concentric to the cylinder and ellipsoid in the case of Model 1. For Model 2 and Model 3, the catheter is placed horizontally, aligned within the right anterior horn (see Figure 5, right).

Study physics COMSOL is material-oriented, i.e. each model must have one or more domains with the

corresponding material properties assigned to them. Two electrical parameters are of interest: Electrical conductivity (σ) and relative permittivity (εr). For these, a tissue parameter library can be obtained from [Pettersen and Høgetveit, 2011] which is based on data from [Gabriel et al., 1996]. The electrodes were modeled as steel conductors with parameters obtained from the COMSOL library (σ = 4.03x106 S/m and εr = 1). The simulated injected current was 250 µA at 50 kHz.

To simulate the dynamic pulsatile volume, a ventricular wall displacement was applied, considering a 15 % ventricular volume change per CC [Lee et al., 1989] for an equivalent 20 ml spherical ventricle, which results in approximately 1 mm maximum amplitude of radial ventricular wall displacement. The ventricular displacement (d(t)) applied in the simulation is described by Eq. (1), as presented in [Linninger, Xenos, et al., 2009] for the cyclic motion of the choroid plexus, with the assumption that the interior of the ventricle is compressed and follows this motion.

푑(푡) = 퐴(1.3 + sin 휔푡 − − cos(2휔푡 − )) , (1)

where A = amplitude of ventricular wall displacement (1 mm), 휔 = heart rate frequency (2휋 rad/s)

and t = time [sec]. One cardiac cycle was simulated, with one complete mesh generation and computation per time frame.

Mesh sensitivity analysis has been performed on all models to guarantee mesh refinement independence in the results. Mesh quality has also been assessed with the element aspect ratio and skewness criteria.

Post-processing Impedance sensitivity (S) [퐴 푚⁄ ] as described in [Kauppinen et al., 2006; Malmivuo, 2010] was

computed in COMSOL and used to visualize the impact of a conductivity change at each voxel (v) (see Eq. (2)). The local volume impedance density (LVID) [ 표ℎ푚 ∙ 퐴 푚⁄ ], which characterizes the contribution of each local voxel on the total measured impedance has also been implemented [Pettersen and Høgetveit, 2011]. The transfer impedance for a tetrapolar bioimpedance measurement is described by

Figure 5 Left: Drainage catheter with six integrated platinum electrodes (e1-e6). Middle: Spacing dimensions of the ring electrodes on the drainage catheter. Right: Positioning of the catheter in Model 2 and 3.

12

푍 = 퐿푉퐼퐷 푑푉 = 휌 ∙ 푆푑푉 = 휌 ∙ 퐽⃗ ∙ 퐽⃗푑푉

(2)

where 휌 is the local electrical resistivity [표ℎ푚 ∙ 푚], 퐽⃗ and 퐽⃗ are the local current density fields

[ 퐴 푚⁄ ] which correspond to the current injection electrodes and the measurement electrodes, respectively.

2.2 Silicone-based brain phantom prototyping To validate the FEM simulation results for the static

volume estimation, a novel silicone-based brain phantom is proposed, with the goal to mimic the electrical and mechanical properties of the brain. Table 1 shows a literature survey on the electrical properties of the human brain. To replicate the electrical properties of brain parenchyma, a mixture of silicone and carbon particles is used. Silicone-carbon phantom probes of Model 1 (see Fig. 1, right) and Model 2 (Figure 6) have been cast and tested for electrical conductivity. Two types of silicone were tested, SF00 – RTV2 (Silikonfabrik, Ahrensburg, Germany) and Sylgard 527 Silicone gel (Dow Corning, Midland, Michigan, USA) which have been reported to approximate the brain’s mechanical properties [Basati et al., 2011]. To provide silicone with electrical conductivity, two different types of carbon particles were chosen: Vulcan XC 72R carbon black (Cabot, Boston, Massachusetts, USA) with a particle size of 30 nm and which has already been reported as a filler for the production of conductive polydimethylsiloxanes (PDMS) [Sethi et al., 2017], and carbon fibers with an average length of 3 mm (R&G Faserverbundwerkstoffe GmbH, Waldenbuch, Germany). Figure 7 shows the results for the electrical properties of the silicone-carbon phantoms. The mixture samples seem to be highly homogenous since the electrical resistance varies linearly with the height of cylindrical samples (Figure 7, left). As expected, the electrical conductivity of the sample increases exponentially with the carbon concentration of the mixture (Figure 7, right). It was observed that the conductivity of brain parenchyma is approximated by a 0.3 % carbon mixture. To mimic CSF, a saline solution with a conductivity of σCSF = 2.01 S/m was used.

Table 1 Literature survey on the electrical properties of human brain tissue

Tissue Conductivity [S/m] Observations Source

Grey matter 0.26 f = 50 kHz, living human brain [Koessler et al., 2017] Grey matter 0.285 f = 50 kHz, living human brain [Latikka et al., 2001]

Grey matter 0.03-0.4 f = 1 Hz – 10 kHz [Grimnes and Martinsen, 2014] Grey matter 1.13 f = 800 MHz, less than 10h

postmortem [Schmid et al., 2003]

White matter 0.19 f = 50 kHz, living human brain [Koessler et al., 2017]

White matter 0.256 f = 50 kHz, living human brain [Latikka et al., 2001]

White matter 0.03-0.3 f = 1 Hz – 10 kHz [Grimnes and Martinsen, 2014]

CSF 1.25 f = 50 kHz, living human brain [Latikka et al., 2001]

CSF 1.72-1.85 High-resolution EEG [Ferre, 1999] CSF 1.79-1.80 f = 10 Hz – 10 kHz, body

temperature [Baumann et al., 1997]

Figure 6 Silicone-carbon (left) and silicone (right) anatomical brain phantoms

13

2.3 Volume estimation Baan and co-workers estimated the ventricular volume by assuming that the volume segment

between two measuring electrodes may be approximated as a cylinder [Baan et al., 1984]. Therefore, the resistance [ohm] of a ventricle segment can be estimated as

where (푙)is electrode distance, σfluid is the conductivity of the fluid in the hollow organ, and Aseg the

cylindrical cross-section area. If Vseg is the volume of the ventricular segment, then

Figure 8 Ellipsoid approximation of the ventricular volume. a, b, and c correspond to the height of different

ellipsoidal segments. Current is applied between the outer electrodes to perform bioimpedance volumetry with tetrapolar measurements.

The total volume of the hollow organ may be then obtained by summing all the volume segments. Alternatively, the shape of a prolate ellipsoid may be assumed to describe the ventricular volume

(see Figure 8). A prolate ellipsoid is described by

푅 = 푙

휎 ∙ 퐴 (3)

푉 = 퐴 ∙ 푙 = 푙

휎 ∙ 푅 (4)

Figure 7 Silicone-carbon phantom electrical properties. Left: Sample resistance [ohm] vs Sample height [cm] for three different carbon particle concentrations (0.79 %, 0.66 % and 0.33 % mixtures). Right: Sample conductivity[S/m] vs. carbon particle concentration [%]. The conductivity of brain parenchyma is achieved with a 0.3 % mixture.

14

푟 = 푥 + 푦 = 푤 (1−푧ℎ ) (5)

where x, y, and z are cartesian coordinates, r is the radius, w the width of the ellipsoid and h the height, here taken as the distance between the two outer electrodes (c). By assuming that the equipotential surfaces of the electric field may be approximated as planes, the ellipsoidal ventricle may now be divided into infinitesimal cylindrical slices with resistance δR

훿푅 = 휌 ∙ 훿푧

휋 ∙ 푟 (푧) = 휌 ∙ 훿푧

휋 ∙ 푤 (1 − 푧ℎ )

(6)

where ρ is the fluid resistivity [표ℎ푚 ∙ 푚]. By integrating from the lower to the upper voltage electrodes, an expression for the measured resistance R may be obtained as follows:

푅 = 훿푅 훿푧 =휌

휋 ∙ 푤1

1− 푧ℎ

훿푧

푅 = 휌

휋 ∙ 푤 ∙푐2 푡푎푛ℎ

푏 − 푐2

푐2

− 푡푎푛ℎ푎 − 푐

2푐2

푅 = 휌 ∙ 푙휋 ∙ 푤 (7)

where parameter le is defined as a function of heights a, b, and c (see Figure 8) as follows:

푙 = 푐2 푡푎푛ℎ

푏 − 푐2

푐2

− 푡푎푛ℎ푎 − 푐

2푐2

(8)

Since the volume of an ellipsoid may be calculated as 푉 = 43 휋푤 ℎ, inserting this equation to

Eq. (5) gives an expression for the estimated ventricular volume from the measured resistance:

푉 _ =4 ∙ 푙

3 ∙ 휎 ∙ 푅 (9)

3. Results

3.1 Current paths and Sensitivity maps The sensitivity maps of Model 1 and Model 2 (Figure 9 and Figure 10) show that the measurement

is highly sensitive to the immediate surroundings of the catheter, as expected. Since CSF has a relatively much higher conductivity than the surrounding brain parenchyma, the outer tissue groups (e.g., skull and skin impedance) have negligible contributions to the measured signal. A compromise between anatomical precision and low computational cost is therefore suggested and implemented with Model 3.

Furthermore, the sensitivity distribution plots show that for Model 1, a higher sensitivity is achieved for a 20 ml ellipsoid. A considerable decrease in sensitivity is observed for 40 ml volumes and, although for larger volumes the decrease continues, this decrease is barely observable. For Model 2 (Figure 10) a similar behavior is observed since the highest sensitivity is achieved for volumes 24 ml and 43 ml with a considerable drop for the higher values.

15

Figure 9 Sensitivity distribution for Model 1. Ventricular volumes (rows) are 20, 40, 60, 80, and 100 ml. Current is injected t through e1 and e6. Please refer to Fig. 5 for electrode configuration. Left column: Sensitivity for measurement electrodes e2 and e5, middle column: measurement electrodes e2 and e3, and right column: electrodes e4 and e5. The plots show an observable change in sensitivity distribution from 20 ml to 40 ml. For volumes above 40 ml, the sensitivity plots for each measurement arrangement remain relatively constant.

16

Figure 10 Sensitivity distribution for Model 2. Only the ventricular domain is shown for better visualization. The surrounding tissue shows negligible sensitivity as compared to Model 1, higher sensitivity for the ventricular wall is achieved at lower volumes. Ventricular volumes (rows) are 24, 43, 61, 84, and 111 ml. Left column: Sensitivity for measurement electrodes e2 and e5. middle column: measurement electrodes e2 and e3, and right column: electrodes e4 and e5. Please refer to Fig. 5 for electrode positions.

17

3.2 Static volume estimation

Simulation results indicate that, as the ventricular volume increases, the measured impedance decreases exponentially (Figure 11, left). Since the sensitivity of the measurement is highest around the impedance catheter, (Figure 9 and Figure 10), this behavior is expected. Phantom measurements on silicone and silicone-carbon probes replicate a similar trend, although with a higher measured resistance than the resistance obtained by the FE simulation results. Comparing the volume estimations for FE results and phantom measurements for both the cylindrical and the ellipsoidal approach, both methods show low accuracy, although the ellipsoidal method shows slightly better performance (Figure 11, right). This is confirmed by FE results for Model 2 (Figure 12). In fact, the estimated value for the 24 ml ventricular volume for FE model 3 shows only a small error (5.7 % deviation). The error increases for higher volumes up to 80 % for the maximal simulated volume of 199 ml. The higher accuracy for volume estimation with Model 3 as compared to Model 1 might be explained by the more realistic geometry. The anatomical ventricle has walls which are closer together than those from the geometrical ellipsoid, allowing the sensor to detect impedance changes over a wider range of volumetric changes.

3.3 Dynamic impedance monitoring To test whether it may be feasible to record impedance changes of a pulsatile ventricular wall for 24

ml-sized lateral ventricles, a dynamic wall displacement was applied in Model 3 for one CC. By applying Eq. (1) with a 1 mm ventricular wall expansion amplitude (A), the resulting maximum ventricular volume change is approximately 4 ml for Model 3, which agrees with literature data. The impedance curve obtained by the FE simulation shows pulsatile behavior, see Figure 13, which is pulsatile, with the expected inverse behavior.

Figure 11 Electrical resistance of Model 1 for different ventricular volumes for silicone probes and FEM simulations. Right: Volume estimation results for Model 1 with cylindrical and elliptic estimation for phantom and FEM simulations.

Figure 12 Volume estimation for Model 2 FEM simulations. The ellipsoidal approach provides a better approximation than the cylindrical approach. however, for volumes higher than 40 ml, both methods seem to be inaccurate.

18

4. Discussion The results for the current densities and sensitivity distribution plots (Figure 9 and Figure 10) indicate

that, since the measurement is highly sensitive to the immediate surroundings of the impedance catheter, a simplified anatomical model may be sufficiently detailed to adequately perform simulative studies of ventricular bioimpedance measurements, reducing the computational cost. Furthermore, this also explains the exponential decay trend between the measured voltage and ventricular volume as observed by the static volume simulations and phantom measurements (Figure 11, left). At lower volumes, the current flows through more brain parenchyma as compared to higher volumes where it primarily flows through CSF. The contrast in conductivity between these two primary tissues of interest explains the higher sensitivity of the impedance sensor at lower ventricular volumes (Figure 9 and Figure 10), which results in an increasing error for higher volumes in both estimation methods (Figure 11 and Figure 12). For the lower volumes (around 20 and 40 ml), the error is reduced and estimated at 5.7 % for the 24 ml-sized FE Model 3. This may signify that, in a practical scenario, the impedance sensor may perform with quite reduced accuracy at higher ventricular volumes. However, it is envisioned that the sensor be used for a feedback-controlled shunt system with which it is aimed to keep ventricular volumes at physiologically normal sizes, i.e., in the range of high sensitivity. Additionally, since better results are obtained for lower volumes, i.e., when the impedance catheter is closer to the ventricular wall, other setups need to be considered, including the possibility of catheter fixation and/or placing the catheter partially within the brain parenchyma.

Intracranial blood pulsatility has been observed to play a significant role in cerebral hydrodynamics.

During systole, intracranial volume increases approximately 1 ml, displacing the brain inwards a contracting the ventricles, which in turn causes a ventricular outflow through the aqueduct of around 35 µL per cardiac cycle. A cervical stroke volume of cranial CSF into the compliant spinal canal is also observed [Benninghaus et al., 2017; El Sankari et al., 2011]. The role of intracranial cardiovascular pulsation in ventricular dilation is a topic of current research, and an impedance sensor which proves to be capable of monitoring the pulsatility of the ventricular wall may provide valuable insight in this topic. This has been tested with FE Model 3 (Figure 13) showing that this may be feasible.

5. Conclusion In this in silico study, the feasibility of bioimpedance-based monitoring of intracranial ventricular

volume has been tested. Different FEM models of increasing complexity have been used to analyze ventricular volumetry and monitoring of ventricular pulsation with the bioimpedance technique. Current and future work is focused on further FE simulations to test for possible noise sources which have not been considered in this study such as the effect of movement and impedance catheter displacement, as well as the role of the complex anatomy of the ventricles in the volume estimation, in the search for more accurate volumetric models. For validation, a hydrocephalus test-bench that reproduces the intracranial mechanical and electrical properties of the human brain for both the static volume determination as well as the dynamic volume change monitoring is envisioned. The proposed silicone-carbon brain phantom seems to provide a valid in vitro model to be implemented in the bioimpedance hydrocephalus test-bench

Figure 13 Impedance signal (red, solid line) resulting from a pulsatile ventricular volume (blue, dashed). The impedance signal follows the ventricular volume change inversely.

19

Acknowledgments The present work was financially supported by the German Research Fund (DFG) Grant Numbers:

LE 817/24-1 and RA 548/12-1. We thank Prof. Stieglitz, IMTEK Freiburg, and his team for the impedance catheter production.

References Albeck, M. J., Skak, C., Nielsen, P. R., Olsen, K. S., Børgesen, S. E., & Gjerris, F. (1998). Age dependency of resistance to

cerebrospinal fluid outflow. Journal of Neurosurgery, 89, (2, 275–278). doi:10.3171/jns.1998.89.2.0275 Ambarki, K., Baledent, O., Kongolo, G., Bouzerar, R., Fall, S., & Meyer, M.-E. (2007). A new lumped-parameter model of

cerebrospinal hydrodynamics during the cardiac cycle in healthy volunteers. IEEE transactions on bio-medical engineering, 54, (3, 483–491). doi:10.1109/TBME.2006.890492

Baan, J., van der Velde, E. T., Bruin, H. G. de, Smeenk, G. J., Koops, J., van Dijk, A. D., et al. (1984). Continuous measurement of left ventricular volume in animals and humans by conductance catheter. Circulation, 70, (5, 812–823).

Balédent, O., Henry-Feugeas, M. C., & Idy-Peretti, I. (2001). Cerebrospinal Fluid Dynamics and Relation with Blood Flow. Investigative Radiology, 36, (7, 368–377). doi:10.1097/00004424-200107000-00003

Basati, S. S., Harris, T. J., & Linninger, A. A. (2011). Dynamic brain phantom for intracranial volume measurements. IEEE transactions on bio-medical engineering, 58, (5, 1450–1455). doi:10.1109/TBME.2010.2050065

Bateman, G. A. (2000). Vascular compliance in normal pressure hydrocephalus. AJNR. American journal of neuroradiology, 21, (9, 1574–1585).

Bateman, G. A., Levi, C. R., Schofield, P., Wang, Y., & Lovett, E. C. (2005). The pathophysiology of the aqueduct stroke volume in normal pressure hydrocephalus: can co-morbidity with other forms of dementia be excluded? Neuroradiology, 47, (10, 741–748). doi:10.1007/s00234-005-1418-0

Baumann, S. B., Wozny, D. R., Kelly, S. K., & Meno, F. M. (1997). The electrical conductivity of human cerebrospinal fluid at body temperature. IEEE transactions on bio-medical engineering, 44, (3, 220–223). doi:10.1109/10.554770

Benninghaus, A., Goffin, C., Leonhardt, S., & Radermacher, K. (2017). Functional modeling of the craniospinal system for in-vitro parameter studies on the pathogenesis of NPH. Current Directions in Biomedical Engineering, 3, (2). doi:10.1515/cdbme-2017-0173

Damasceno, B. P. (2015). Neuroimaging in normal pressure hydrocephalus. Dementia & Neuropsychologia, 9, (4, 350–355). doi:10.1590/1980-57642015DN94000350

Egnor, M., Zheng, L., Rosiello, A., Gutman, F., & Davis, R. (2002). A model of pulsations in communicating hydrocephalus. Pediatric neurosurgery, 36, (6, 281–303). doi:10.1159/000063533

El Sankari, S., Gondry-Jouet, C., Fichten, A., Godefroy, O., Serot, J. M., Deramond, H., et al. (2011). Cerebrospinal fluid and blood flow in mild cognitive impairment and Alzheimer's disease: a differential diagnosis from idiopathic normal pressure hydrocephalus. Fluids and barriers of the CNS, 8, (1, 12). doi:10.1186/2045-8118-8-12

Elixmann, I. M., Kwiecien, M., Goffin, C., Walter, M., Misgeld, B., Kiefer, M., et al. (2014). Control of an electromechanical hydrocephalus shunt--a new approach. IEEE transactions on bio-medical engineering, 61, (9, 2379–2388). doi:10.1109/TBME.2014.2308927

Elixmann, I. M., Ordonez, J., Stieglitz, T., & Leonhardt, S. (2013). In-Vitro Evaluation of a Drainage Catheter with Integrated Bioimpedance Electrodes to Determine Ventricular Size. Biomedizinische Technik. Biomedical engineering. doi:10.1515/bmt-2013-4042

Ferre, T. C. (1999). Development of High-Resolution EEG Devices. Int. J. Bioelectromagnetism, 1, (1, 4–10). https://ci.nii.ac.jp/naid/10024889250/en/.

Gabriel, S., Lau, R. W., & Gabriel, C. (1996). The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Physics in Medicine and Biology, 41, (11, 2251).

Goffin, C., Leonhardt, S., & Radermacher, K. (2017). The Role of a Dynamic Craniospinal Compliance in NPH-A Review and Future Challenges. IEEE reviews in biomedical engineering, 10, (310–322). doi:10.1109/RBME.2016.2620493

Greitz, D. (2004). Radiological assessment of hydrocephalus: new theories and implications for therapy. Neurosurgical review, 27, (3, 145-65; discussion 166-7). doi:10.1007/s10143-004-0326-9

Grimnes, S., & Martinsen, O. G. (2014). Bioimpedance and Bioelectricity Basics (3rd ed.). Burlington: Elsevier Science. Hakim, C., Hakim, R., & Hakim, S. (2001). Normal-Pressure Hydrocephalus. Neurosurgery Clinics of North America, 12, (4,

761–773). doi:10.1016/S1042-3680(18)30033-0 Halle, M., Talos, I.-F., Jakab, M., Makris, N., Meier, D., Wald, L. L., et al. (2017). Multi-modality MRI-based Atlas of the Brain,

Surgical Planning Laboratory, Department of Radiology, Brigham and Women\textquoterights Hospital, Harvard Medical School, Boston, MA, USA. http://www.spl.harvard.edu/publications/item/view/2037.

Hladky, S. B., & Barrand, M. A. (2014). Mechanisms of fluid movement into, through and out of the brain: evaluation of the evidence. Fluids and barriers of the CNS, 11, (1, 26). doi:10.1186/2045-8118-11-26

Kauppinen, P., Hyttinen, J., & Malmivuo, J. (2006). Sensitivity distribution visualizations of impedance tomography measurement strategies. International Journal of Bioelectromagnetism, 8, (1, 1–9).

Koessler, L., Colnat-Coulbois, S., Cecchin, T., Hofmanis, J., Dmochowski, J. P., Norcia, A. M., et al. (2017). In-vivo measurements of human brain tissue conductivity using focal electrical current injection through intracerebral multicontact electrodes. Human Brain Mapping, 38, (2, 974–986). doi:10.1002/hbm.23431

Latikka, J., Kuurne, T., & Eskola, H. (2001). Conductivity of living intracranial tissues. Physics in Medicine and Biology, 46, (6, 1611–1616). doi:10.1088/0031-9155/46/6/302

Lee, E., Wang, J. Z., & Mezrich, R. (1989). Variation of lateral ventricular volume during the cardiac cycle observed by MR imaging. American Journal of Neuroradiology, 10, (6, 1145–1149). http://www.ajnr.org/content/10/6/1145.

Lefever, J. A., Jaime García, J., & Smith, J. H. (2013). A patient-specific, finite element model for noncommunicating hydrocephalus capable of large deformation. Journal of Biomechanics, 46, (8, 1447–1453). doi:10.1016/j.jbiomech.2013.03.008

Lemcke, J., Stengel, D., Stockhammer, F., Güthoff, C., Rohde, V., & Meier, U. (2016). Nationwide Incidence of Normal Pressure Hydrocephalus (NPH) Assessed by Insurance Claim Data in Germany. The open neurology journal, 10, (15–24). doi:10.2174/1874205X01610010015

20

Linninger, A., Xenos, M., Sweetman, B., Ponkshe, S., Guo, X., & Penn, R. (2009). A mathematical model of blood, cerebrospinal fluid and brain dynamics (no. 6). Journal of mathematical biology (pp. 729–759).

Linninger, A., Basati, S., Dawe, R., & Penn, R. (2009). An impedance sensor to monitor and control cerebral ventricular volume. Medical engineering & physics, 31, (7, 838–845). doi:10.1016/j.medengphy.2009.03.011

Malmivuo, J. (2010). Principle of reciprocity solves the most important problems in bioimpedance and in general in bioelectromagnetism. Journal of Physics: Conference Series, 224, (12001). doi:10.1088/1742-6596/224/1/012001

Matsumae, M., Kikinis, R., Mórocz, I. A., Lorenzo, A. V., Sándor, T., Albert, M. S., et al. (1996). Age-related changes in intracranial compartment volumes in normal adults assessed by magnetic resonance imaging. Journal of Neurosurgery, 84, (6, 982–991). doi:10.3171/jns.1996.84.6.0982

McKay, R. G., Spears, J. R., Aroesty, J. M., Baim, D. S., Royal, H. D., Heller, G. V., et al. (1984). Instantaneous measurement of left and right ventricular stroke volume and pressure-volume relationships with an impedance catheter. Circulation, 69, (4, 703–710). doi:10.1161/01.CIR.69.4.703

Misgeld, B. J.E., Mondal, R., & Leonhardt, S. (2015). Pulsatile cerebrospinal model with cardio-vascular coupling. IFAC-PapersOnLine, 48, (20, 183–188). doi:10.1016/j.ifacol.2015.10.136

Nagashima, T., Tamaki, N., Matsumoto, S., Horwitz, B., & Seguchi, Y. (1987). Biomechanics of Hydrocephalus: A New Theoretical Model. Neurosurgery, 21, (6, 898–904). doi:10.1227/00006123-198712000-00019

Paul A. Yushkevich, Joseph Piven, Cody Hazlett, H., Gimpel Smith, R., Sean Ho, James C. Gee, et al. (2006). User-Guided 3D Active Contour Segmentation of Anatomical Structures: Significantly Improved Efficiency and Reliability. Neuroimage, 31, (3, 1116–1128).

Pettersen, F.-J., & Høgetveit, J. O. (2011). From 3D tissue data to impedance using Simpleware ScanFE+IP and COMSOL Multiphysics – a tutorial. Journal of Electrical Bioimpedance, 2, (1). doi:10.5617/jeb.173

Qvarlander, S., Ambarki, K., Wåhlin, A., Jacobsson, J., Birgander, R., Malm, J., et al. (2017). Cerebrospinal fluid and blood flow patterns in idiopathic normal pressure hydrocephalus. Acta neurologica Scandinavica, 135, (5, 576–584). doi:10.1111/ane.12636

Ringstad, G., Emblem, K. E., Geier, O., Alperin, N., & Eide, P. K. (2015). Aqueductal Stroke Volume: Comparisons with Intracranial Pressure Scores in Idiopathic Normal Pressure Hydrocephalus. AJNR. American journal of neuroradiology, 36, (9, 1623–1630). doi:10.3174/ajnr.A4340

Schlebusch, T., Nienke, S., Leonhardt, S., & Walter, M. (2014). Bladder volume estimation from electrical impedance tomography. Physiological measurement, 35, (9, 1813–1823). doi:10.1088/0967-3334/35/9/1813

Schmid, G., Neubauer, G., & Mazal, P. R. (2003). Dielectric properties of human brain tissue measured less than 10 h postmortem at frequencies from 800 to 2450 MHz. Bioelectromagnetics, 24, (6, 423–430). doi:10.1002/bem.10123

Schünke, M., Schulte, E., & Schumacher, U. (2018). Kopf, Hals und Neuroanatomie (Prometheus, LernAtlas der Anatomie / Michael Schünke, Erik Schulte, Udo Schumacher; Illustrationen von Markus Voll, Karl Wesker, 5., vollständig überarbeitete Auflage). Stuttgart: Georg Thieme Verlag.

Sethi, D., Ram, R., & Khastgir, D. (2017). Electrical conductivity and dynamic mechanical properties of silicon rubber-based conducting composites: effect of cyclic deformation, pressure, and temperature. Polymer International, 66, (9, 1295–1305). doi:10.1002/pi.5385

Teichmann, D., Rohe, L., Niesche, A., Mueller, M., Radermacher, K., & Leonhardt, S. (2017). Estimation of Penetrated Bone Layers During Craniotomy via Bioimpedance Measurement. IEEE transactions on bio-medical engineering, 64, (4, 765–774). doi:10.1109/TBME.2016.2577892

Wagshul, M. E., Eide, P. K., & Madsen, J. R. (2011). The pulsating brain: A review of experimental and clinical studies of intracranial pulsatility. Fluids and barriers of the CNS, 8, (5). doi:10.1186/2045-8118-8-5