http://www.diva-portal.org

This is the published version of a paper published in Fluids and Barriers of the CNS.

Citation for the original published paper (version of record):

Holmlund, P., Qvarlander, S., Malm, J., Eklund, A. (2019) Can pulsatile CSF flow across the cause ?: A prospective study of patients with communicating . Fluids and Barriers of the CNS, 16(1): 40 https://doi.org/10.1186/s12987-019-0159-0

Access to the published version may require subscription.

N.B. When citing this work, cite the original published paper.

Permanent link to this version: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-157029 Holmlund et al. Fluids Barriers CNS (2019) 16:40 https://doi.org/10.1186/s12987-019-0159-0 Fluids and Barriers of the CNS

RESEARCH Open Access Can pulsatile CSF fow across the cerebral aqueduct cause ventriculomegaly? A prospective study of patients with communicating hydrocephalus P. Holmlund1* , S. Qvarlander1, J. Malm2 and A. Eklund1,3

Abstract Background: Communicating hydrocephalus is a disease where the cerebral ventricles are enlarged. It is charac- terized by the absence of detectable cerebrospinal fuid (CSF) outfow obstructions and often with increased CSF pulsatility measured in the cerebral aqueduct (CA). We hypothesize that the cardiac-related pulsatile fow over the CA, with fast systolic outfow and slow diastolic infow, can generate net pressure efects that could source the ventriculo- megaly in these patients. This would require a non-zero cardiac cycle averaged net pressure diference (ΔPnet) over the CA, with higher average pressure in the lateral and third ventricles.

Methods: We tested the hypothesis by calculating ΔPnet across the CA using computational fuid dynamics based on prospectively collected high-resolution structural (FIESTA-C, resolution 0.39 0.39 0.3 mm3) and velocimetric (2D-PCMRI, in-plane resolution 0.35 0.35 mm2) MRI-data from 30 patients investigated× for communicating× hydrocephalus. × Results: The ΔPnet due to CSF pulsations was non-zero for the study group (p 0.03) with a magnitude of 0.2 0.4 Pa (0.001 0.003 mmHg), with higher pressure in the . The maximum= pressure diference over the car± - diac cycle± ΔP was 20.3 11.8 Pa and occurred during systole. A generalized linear model verifed an association max ± between ΔPnet and CA cross-sectional area (p 0.01) and fow asymmetry, described by the ratio of maximum infow/ outfow (p 0.04), but not for aqueductal stroke= volume (p 0.35). = = Conclusions: The results supported the hypothesis with respect to the direction of ΔPnet, although the magnitude was low. Thus, although the pulsations may generate a pressure diference across the CA it is likely too small to explain the ventriculomegaly in communicating hydrocephalus. Keywords: Communicating hydrocephalus, Computational fuid dynamics, Cerebrospinal fuid pressure, Brain imaging, Cerebral aqueduct

Background Ventriculomegaly in hydrocephalus is thought to be due Tis paper investigates the potential pressure diference to brain tissue deformation as the result of an active over the communicating cerebral aqueduct, a feature distension of the ventricles [1], indicating a pressure that may have a role in cerebral ventricular enlargement gradient between the ventricles and the subarachnoid (or ventriculomegaly) in communicating hydrocephalus. space (i.e. a transmantle pressure gradient). To generate such a pressure gradient, a pressure diference over the

*Correspondence: [email protected] cerebral aqueduct (CA) is expected, since the CA con- 1 Department of Radiation Sciences, Umeå University, Umeå, Sweden nects the ventricles and the subarachnoid space. If the Full list of author information is available at the end of the article CA is obstructed (non-communicating hydrocephalus)

© The Author(s) 2019. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativeco​ ​ mmons.org/licen​ ses/by/4.0/​ . The Creative Commons Public Domain Dedication waiver (http://creativeco​ mmons​ .org/publi​ cdoma​ in/​ zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data. Holmlund et al. Fluids Barriers CNS (2019) 16:40 Page 2 of 10

it is reasonable that the bulk fow generated by the CSF modeling study Dutta-Roy et al. predicted that a trans- production in the could be sufcient to mantle pressure diference of 235.44 Pa (1.764 mmHg) produce a pressure diference and ventriculomegaly. was needed to produce the ventricular expansion and However, in communicating hydrocephalus no apparent brain alterations seen in normal pressure hydrocepha- fow obstruction is shown on radiology [1] leaving the lus, acting over the course of a few days (at most) [16]. question of a pressure diference open. Since ventriculomegaly may develop over a much longer In addition to bulk fow, CSF fows in a to and fro move- time in communicating hydrocephalus (over several ment across the CA, synchronized with the heartbeat [2]. years) the required transmantle pressure diference can A typical characteristic of communicating hydrocephalus be expected to be even lower. A possible way of detect- is high pulsatile CSF fow [3–5], and experimental studies ing and quantifying this pressure diference is by compu- have hinted at a causal link between altered CSF pulsa- tational fuid dynamics (CFD), which provides a useful tions and ventricular enlargement [6–8]. Since the larg- tool for identifying pressure behavior that is impossible est pressure changes in the occur over to assess using in vivo pressure sensors. CFD also allows the CA [9, 10], it is reasonable that altered pulsatile fow us to take the entire CA geometry into account, which is dynamics over the CA could play a part in the develop- problematic to do analytically. Previous CFD studies have ment of ventriculomegaly in these patients. Looking presented data on the pressure diferences over the CA at the fow through the CA, it can be observed that it is in hydrocephalus case studies and in healthy [9, 10, 17, asymmetric, i.e. higher and more rapidly varying dur- 18], but to fully determine its magnitude and potential ing systolic CSF outfow and lower and more gradually role in communicating hydrocephalus a study specifcally varying during diastolic infow [11]. Our hypothesis is designed to investigate the transmantle pressure gradi- that this asymmetry in the pulsatile fow over the open ent in a larger group of communicating hydrocephalus CA can generate a net transmantle pressure gradient, one patients is needed, utilizing the highest quality imaging that, over time, could potentially contribute to the ven- data feasible. triculomegaly in communicating hydrocephalus. In order to evaluate our hypothesis, the aim of this In addition to viscous fow resistance as described by study was to calculate ΔPnet across the CA utilizing CFD the Poiseuille equation, fow through constrictions such based on prospectively collected high-resolution struc- as the CA will result in additional pressure losses. Tese tural and velocimetric magnetic resonance imaging pressure losses occur in places where the geometry is (MRI) data from 30 patients investigated for communi- changing rapidly, resulting in recirculation zones, i.e. vor- cating hydrocephalus. tex formations, where fuid energy is dissipated [12, 13]. In the CA this can occur at the entrance and exit to the Methods third and fourth ventricles due to enlargement/contrac- Bench test of feasibility tion of the fow geometry. Tese contraction and enlarge- Prior to the prospective patient study, bench-tests were ment (or discharge) efects are not only dependent on performed to test the feasibility of the hypothesis. Te geometrical shape but are also non-linearly dependent bench setup consisted of a simplifed aqueduct model, a on the fow rate going into the CA [12, 13]. Tis means diferential pressure (DP) transducer (Druck LPM 8381, that even with zero net fow the asymmetrical pulsations General Electric, US), a programmable syringe pump, through the CA can generate net pressure diferences/ and a container of water representing the third ventri- gradients across the CA over each cardiac cycle. Tis is cle (Fig. 1). Te pressure diference across the model was in contrast to the resistive losses described by Poiseuille, measured while the model was subjected to pulsatile which amount to a net pressure diference of zero if the aqueductal fows produced by the syringe pump. Tese pulsatile fow has a zero net fow. Over time, such a net fows were based on phase contrast MRI data from INPH transmantle pressure gradient could potentially contrib- patients and healthy elderly (from [11]). Te net fow was ute to ventriculomegaly. Tis net pressure gradient and removed to only investigate the efects of the pulsations. thus the net pressure diference (ΔPnet) across the CA Te resulting fow rate was documented by measuring the must be positive (i.e. with higher pressure in the third syringe pump position using a position sensor (F58000136 ventricle) to explain the enlargement of the third and lat- linear position Transducer, LT series, Honeywell, US). eral ventricles. Te system was kept horizontal and the temperature of It should be mentioned that in vivo studies of com- the water was kept close to body temperature (acquired municating hydrocephalus patients have not been able temp: 35°C). Net pressure over the model, ΔPnet bench, was to measure a transmantle pressure gradient (or pressure calculated by averaging the recorded diferential pressure diference) [14, 15], indicating that the corresponding over 30 cardiac cycles. Each measurement was repeated ΔPnet is likely small in magnitude. In a biomechanical six times. Te experiments were recreated by applying the Holmlund et al. Fluids Barriers CNS (2019) 16:40 Page 3 of 10

Table 1 Characteristics of the communicating a hydrocephalus group Fourth Third Parameter Mean ± SD Range 1 mm 30 deg Subjects 30 (total) – 3 mm INPH 15 – Communicating hydrocephalus 9 – Other 6 – 7 mm Sex (female/male) 14/16 – ± 57 mm Age (years) 75 6 60–86 MMSE 24 ± 5 15–30 Evans’ index 0.37 ± 0.04 0.31–0.47 b Hydrostatic DP-sensor Heart rate (bpm) 72 ± 13 47–98 difference: 1.5 kPa †

Q H2O (mainly dementias, but still with enlarged ventricles and (35 deg) a communicating CA). Group characteristics are pre- Aqueduct model sented in Table 1. Syringe pump Fig. 1 Illustration of the CA bench-model (a) and the experimental Magnetic resonance imaging setup (b). The pump was controlled using LabVIEW (National Instruments Corporation, Austin, Texas, US), to recreate aqueductal MRI investigations were carried out on a 3 Tesla scan- pulsatile fows based on CA fows measured in 43 healthy elderly and ner (GE Discovery MR 750, Waukesha, WI) with a 22 idiopathic normal pressure hydrocephalus (INPH) patients [11]. Q 32-channel head coil. Te structural data for the ven- is the pulsatile fow rate, DP is Diferential pressure. †Reference value for intracranial pressure in healthy in the supine position [31] tricular system was acquired by a Fast Imaging Employ- ing Steady-state Acquisition Cycled Phases (FIESTA-C) sequence, a sequence with T2/T1 contrast which allows for excellent distinction between fuid-flled spaces and acquired experimental fow rates and the model geometry surrounding tissues [20, 21]. Te sequence was opti- to CFD simulations to estimate ΔPnet bench CFD. mized to achieve the highest structural resolution pos- sible to avoid partial volume efects and to assess the Study subjects CA geometry as accurately as possible. Te settings Te prospective patient study included thirty-two were: repetition time/echo time 6.5/2.6 ms, fip angle patients referred to the neurological department at Umeå was 55°, acquisition duration roughly 7–8 min, 3 signal 3 University for investigation of communicating hydro- averages, imaging volume 20 × 20 × 3.6 cm , acquisi- cephalus during the time period from October 2016 to tion matrix 512 × 512 × 60. Te FOV included the CA, May 2017. All patients had enlarged cerebral ventricles, the third and the fourth ventricles, but not the entirety ≥ defned as an Evan’s ratio 0.3, and symptoms of normal of the . Te acquisition resolution was pressure hydrocephalus (NPH) (i.e. gait disturbances, thus 0.39 mm × 0.39 mm in-plane, with slice thickness cognitive decline and/or urinary incontinence). Te 0.6 mm. Te slices were interpolated, resulting in a fnal preoperative investigation included case history, neu- resolution of 0.39 mm × 0.39 mm × 0.30 mm. rological examination, blood chemistry, CSF dynamic Te velocity data was acquired by 2D-PCMRI with a investigations and MRI (including sequences specifed plane positioned through the CA (Fig. 2a, b). Te settings below). Patients with obstruction of the CA based on the were: repetition time/echo time 9.8/5.6 ms, fip angle anatomical MRI sequences were excluded (we also veri- 6°, acquisition duration roughly 5–6 min, 3 signal aver- 2 fed that the , i.e. foramen of Magendie, ages, imaging volume 18 × 18 cm , acquisition matrix was open). Two patients were excluded from the analy- 512 × 512, slice thickness 4.0 mm, arrhythmia rejection sis: one with CA obstruction, and one with severely window 20%, 4 views per segment, and velocity encod- increased intracranial pressure (3.8 kPa or 28.5 mmHg), ing was 20 cm/s. Te spatial in-plane acquisition resolu- resulting in a total of n = 30 patients. Out of the thirty tion was thus 0.35 mm × 0.35 mm. Since partial volume patients, 15 were diagnosed as INPH [19], 9 got a difer- efects are known to overestimate CA fow rates [22] we ent hydrocephalus diagnosis (e.g. secondary causes), and aimed for high resolution images for this sequence as 6 were diagnosed with diseases other than hydrocephalus well. Te use of 3 signal averages was used to remedy the Holmlund et al. Fluids Barriers CNS (2019) 16:40 Page 4 of 10

ab

c d

Fig. 2 Illustration of the MRI fow measurements and mesh generation. a The FIESTA acquired data with indications for the PCMRI plane position (red line). b The resulting PCMRI (velocity) image in the plane across the aqueduct. c Segmentation of the ventricular system (red). d The constructed mesh with the defned fow boundaries (red arrows)

potential decrease in the signal to noise ratio that comes the aqueduct was not allowed to change more than 2% for with the increased resolution. A peripheral pulse detec- any subject (group mean: + 1.0 ± 0.8%), while the entire tor allowed for retrospective electrocardiography gating ventricular system did not change more than 4% (group during data reconstruction, and data was reconstructed mean: + 1.5 ± 1.0%). Te foramina of Monro were set as for 32 images over the cardiac cycle. cranial outlet boundaries, while a plane in the fourth ven- tricle located just superior to the lateral and median aper- Reconstruction of patient‑specifc geometries tures was set as the inlet boundary (Fig. 2d). Te volumes Patient-specifc geometries were segmented from the were then exported to the CFD software. FIESTA sequence data (Fig. 2c) using Synopsys’ Sim- pleware™ software (Version M-2017.06; Synopsys Inc., MRI fow velocity analysis Mountain View, USA). PH performed manual segmen- Analyses of the PCMRI measurements were performed tations with guidance from an experienced neuroradi- using Segment (version 2.1 R5960, http://medvi​so.com/ ologist. Smoothing of the segmented volumes was then segme​nt/) [23]. A region of interest (ROI) was drawn performed and a built-in mask statistics function was around the cross-section of the aqueduct in the magni- used to compare the volume of the aqueduct before and tude images, with constant size and position for all 32 after smoothing to minimize potential changes in volume time frames. Segment’s built-in eddy current correction introduced by the smoothing operation. Te volume of was utilized for all measurements. Averaging the velocity Holmlund et al. Fluids Barriers CNS (2019) 16:40 Page 5 of 10

magnitudes of all pixels within the ROI and multiplying Te simulations ran on an iMac (2.93 GHz Intel Core i7) with the cross-sectional area yielded the measured fow and the simulation took roughly 48 h per subject. rate for each time frame. Te same operator performed Since we specifcally aimed to investigate the efects of all PCMRI analyses. However, ffteen subjects were inde- the fow pulsations, the net fow was removed for all sim- pendently analyzed by a second operator to assess the ulations. Omitting the net fow was further motivated by inter-rater variability of the PCMRI analyses. the fact that repeated measurements at diferent points in time have shown high variability in the aqueductal net Computational fuid dynamics fow (intraclass correlation coefcient (ICC) 0.41 [22]). In CFD simulations were performed with COMSOL Mul- contrast, repeated measurements for aqueductal stroke tiphysics utilizing the fnite element method (COMSOL volume (SV) (i.e. pulsatile fow) is high (0.96 for SV [22]). ­Multiphysics®, version 5.3a, www.comso​l.com, COMSOL To verify that our choice of inlet did not signifcantly AB, Stockholm, Sweden). Since CSF is an incompressible alter the velocities in the CA, the maximum velocities Newtonian fuid [24], the CSF fuid and pressure dynam- during the time of maximum outfow from the ventricles ics are described by the non-linear Navier–Stokes equa- were compared between the raw PCMRI-data and the tions for incompressible fow: corresponding plane in the CFD simulations. Te veloc- ∂u ity distribution for a typical case is presented in Fig. 3. ρ + ρ(u ·∇)u −∇· −PI + µ ∇u + (∇u)T = 0 ∂t   Sensitivity analysis for the CFD ∇·u = 0 We performed a mesh sensitivity analysis by testing three meshes of diferent coarseness for 5 randomly selected where u and P represent the CSF velocity and pres- subjects/cases, evaluating the change in the maximum pressure diference ΔPmax (Table 2). Since the relative sure that we want to solve for. Te density was− set3 to ρ = 3 µ = 0.9 × 10 Pa s 1000 kg/m and the viscosity to error between the two fner meshes was only 2 ± 2% [24]. Since fow is expected to be laminar within the ven- (with only one out of fve cases exceeding 2%), the mesh tricular system [17], the built-in laminar fow physics of intermediate coarseness was used throughout as it model was used. To solve the Navier–Stokes equations severely reduced the computational time. For the main we used a non-linear solver based on Newton’s method, analysis (n 30), the average number of mesh elements = 5 5 utilizing a fully coupled approach. Te time stepping was was 5.5 × 10 ± 3.1 × 10 . Te average and minimum handled using COMSOL’s backward diferentiation for- mesh element quality (based on equiangular skew) was mula (BDF) time-solver, an implicit solver based on the 0.67 ± 0.004 and 0.10 ± 0.04, respectively. backward Euler method, with second order accuracy. Te segmented structural volumes were imported to Patient specifc pressure diference COMSOL with the geometry simplifcation factor kept Te ΔPnet was calculated as the time-average of the pres- to a minimum (0.001). Te meshes were constructed sure diference between the and the fora- in COMSOL by using the physics-controlled setting. men of Monro over the cardiac cycle. Te local pressures Boundary conditions were: no-slip on the ventricular and in these two locations were calculated as the average aqueduct walls, open boundary at the two intraventricu- across the inlet boundary (in the fourth ventricle) and lar foramina (i.e. stress normal to the boundary was set to outlet boundaries (the foramina of Monro), respectively. zero), and laminar parabolic infow in the fourth ventri- Since the variations in intracranial pressure over the car- cle (Fig. 2d). All surfaces were modeled as rigid. Te fow diac cycle are a few hundred Pa [25], we expect the ΔPnet rate measured in the CA was applied at the infow bound- to have to be at least of the order of 1 Pa in order to be ary.1 Te 32 points for each fow curve were interpolated meaningful. using cubic splines. Te infow was ramped up from 0 to We also investigated the dependency of ΔPnet on dif- 1 during the simulations’ frst 0.1 s. Te time step was ferent fow and geometrical properties, in order to test t = 10−3 s set to and each simulation ran for 3 cardiac how diferent characteristics contribute to the ΔPnet. Te cycles. Since the results were highly similar for the sec- characteristics investigated were: mid CA cross-sectional ond and third cycles, the third cycle was used for analysis. area, aqueductal SV, and CA fow asymmetry. Te CA fow asymmetry was described in two diferent ways: the maximum outfow/infow ratio (QO/I) and the ratio of time duration of outfow vs. infow (rO/I) (Fig. 4). 1 PCMRI measurements were also performed at the inlet plane in the fourth Finally, we tested two extreme combinations of CA ventricle, but these measurements were discarded due to low signal to noise shape and fow rate in order to estimate the maximum ratios resulting from the large spatial variation in velocities over this plane. achievable ΔPnet using the collected physiological data. Holmlund et al. Fluids Barriers CNS (2019) 16:40 Page 6 of 10

8 8

15 7 15 7

6 6 10 10 5 5 5 5 4 4 elocity [cm/s] elocity [cm/s] V V 0 3 0 3

3 2 3 2 2 3 2 3 1 1 1 2 1 2 1 1 0 0 0 0 0 0 y [mm] -1 -1 y [mm] -1 -1 x [mm] x [mm] Fig. 3 Comparison of PCMRI (left) and CFD velocity profles (right) at maximum CA outfow in an example subject. The maximum spatial velocity for the group was 11.1 ± 5.3 cm/s for the PCMRI measurements and 11.5 ± 6.9 cm/s for the CFD simulations (mean diference: 0.4 ± 4.4 cm/s, − PCMRI-CFD). Generally, the largest diferences were found for small aqueducts or aqueducts with the highest SV. The small diference could be partly attributed to the diference in spatial resolution between the PCMRI data and the CFD meshes (CFD had higher resolution). In this fgure, the CFD data has been down-sampled spatially in order to simplify the visual comparison

Table 2 Mesh sensitivity analysis for the maximum Since we expect the net pressure diference to arise pressure diference ΔPmax across the CA (presented in Pa) mainly due to fow rate asymmetries, the fow rate of Test subject Coarsest mesh Intermediate Finest mesh highest asymmetry (within the investigated group) was mesh applied to the subject geometry with the smallest CA area (Confg. 1). We also applied the fow of largest SV 1 66.0 65.9 66.4 to this geometry (Confg. 2). In separate simulations, 2 18.2 18.6 18.3 the net fow was added to these confgurations to esti- 3 25.2 20.9 19.6 mate its potential contributions, using the group aver- 4 23.2 19.8 19.7 age of 0.77 mL/min. 5 38.9 34.5 35.2

Coarsest, intermediate and fnest corresponded to mesh elements roughly of the order 10­ 5, 4 105 and ­106, respectively. The intermediate mesh was the one × chosen for the main analysis Statistics Statistical calculations were performed using MATLAB (version R2017b, Te Mathworks, Natick, MA). Te existence of a ΔPnet was tested by a two-sided t-test, as 25 were the bench-model comparisons (signifcance level c α 0.05). A positive pressure diference corresponded 20 Qmax-ratio=c/d = to higher pressure in the third ventricle. Te relation rO/I=a/b 15 between ΔPnet and the diferent fow rate and geomet- rical characteristics were analyzed using a generalized 10 linear model (GLM). Te GLM was carried out with

5 b ΔPnet as the dependent variable and CA area, SV and the asymmetry ratio (QO/I or rO/I) as random continu- 0 ous predictor variables. We used only one asymmetry

Flow rate (ml/min) ratio at a time, resulting in two separate GLMs. Values -5 a ± are presented as mean SD unless otherwise specifed. -10 d Results -15 0 0.1 0.2 0.3 0.4 0.50.6 0.7 0.8 0.9 1 Based on aqueductal SV the ICC for the PCMRI anal- % of heart cycle ysis was r = 0.996, with CI = [0.963–0.999] (two-way Fig. 4 A CA fow curve visualizing the asymmetry ratios for CA random efects, absolute agreement, single rater/meas- out- and infow urement), indicating excellent agreement. Holmlund et al. Fluids Barriers CNS (2019) 16:40 Page 7 of 10

1.4

1.2

1

0.8

[Pa] 0.6 net

P 0.4

0.2

0

-0.2

-0.4 0246810121416 Area [mm2]

Fig. 6 The ΔPnet as a function of CA cross-sectional area. Only some of the very smallest aqueducts achieved a pressure diference close to or above 1 Pa

Te maximum pressure diference over the cardiac cycle ΔPmax was 20.3 ± 11.8 Pa (0.15 ± 0.09 mmHg) and occurred during systole. We found no correlation between ΔPnet and ventricular size based on Evan’s index (Pearson’s correlation coefcient r = − 0.01, p = 0.95). Individual results for the ΔPnet are shown in Fig. 6 as a function of CA cross-sectional area. Roughly two- thirds of the subjects had a positive ΔPnet. Looking only at the INPH subgroup the ΔPnet only approached trend Fig. 5 This fgure shows the pressure and velocity distributions for level: ΔPnet = 0.1 ± 0.4 Pa (p = 0.14, n = 15, 10/15 had a a typical subject. Upper: a sagittal slice of the pressure distribution positive ΔPnet) and ΔPmax = 20.1 ± 8.4 Pa. If only the 6 for the point in time of largest pressure diference. The change in subjects not primarily diagnosed with hydrocephalus pressure occurs almost entirely over the CA, with only small changes were removed, the statistical signifcance also vanished in the third and fourth ventricle. Lower: velocity streamlines during ΔPnet 0.1 0.3 Pa (p 0.10, n 24). maximum outfow. The highest velocities were observed in the CA = ± = = Te GLM analysis showed that ΔPnet was signifcantly associated with CA cross-sectional area (p = 0.01) and the maximum fow asymmetry ratio QO/I (p = 0.04), while no association was found for aqueductal SV (p 0.35). The bench‑model test = Replacing QO/I with the time asymmetry ratio rO/I in Te bench-test results verifed a positive ΔPnet bench over the GLM resulted in a non-signifcant association for the cardiac cycle, an efect that was magnifed for the rO/I (p = 0.10), while the results for the CA area and SV CSF fow from INPH compared to healthy (ΔPnet bench: were unchanged. rO/I was, however, strongly correlated 24.0 1.0 vs. 5.0 1.7 Pa, p < 0.01). Te CFD simula- ± ± with QO/I (Pearson’s correlation coefcient r = − 0.88, tions closely recreated the bench-test results (ΔPnet bench p < 0.001). CFD: 25.1 ± 2.3 vs. 6.4 ± 0.2 Pa, p < 0.01). Te results for the extreme cases are presented in Table 3; both of the investigated confgurations yielded Patient‑specifc pressure diference pressure diferences of similar magnitude. Te maximum An example image of the pressure and velocity distri- ΔPnet achieved was 4.9 Pa, corresponding to the geome- butions for a typical simulation is shown in Fig. 5. Te try with smallest CA cross-sectional area combined with ΔPnet due to CSF pulsations was found to be non-zero the largest SV (i.e. Confg. 2). Adding the group average for the study group (p = 0.03) with a positive magnitude net fow to this confguration increased ΔPnet to 9.0 Pa. of 0.2 ± 0.4 Pa (0.001 ± 0.003 mmHg), indicating higher Te diameter of the CA used for the extreme cases was pressure in the third ventricle (range 1.4 to − 0.4 Pa). 1.1 mm. Holmlund et al. Fluids Barriers CNS (2019) 16:40 Page 8 of 10

Table 3 Resulting ΔPnet (presented in Pa) for two extreme are a cause or merely a result of the ventriculomegaly. combinations of CA fow and cross-sectional area Our results indicate that the CSF pulsations over the Confg. 1 Confg. 2 CA work in favor of a transmantle pressure gradient, but only with an average pressure diference of 0.2 Pa. Our ∼ Pulsations only 3.2 4.9 peak-to-peak change in ΔP of 30 Pa was associated Net fow only 0.8 0.8 with a change in ventricular volume of 80 μL (our SV). Pulsations net fow 5.5 9.0 + Using that scaling, a ΔP of 0.2 Pa compared to a ΔP of Confguration 1 corresponds to the CA with the smallest area subjected to the 0 Pa would translate to a change in ventricular volume CA fow with the largest fow asymmetry. Confguration 2 corresponds to the CA −5 with the smallest area subjected to the CA fow of largest SV by 0.5 μL (less than ­10 of the total ventricular volume), which is minute. Te magnitude of 0.2 Pa is also mini- mal when compared to the predicted transmantle pres- Table 4 Results of the PC-MRI and FIESTA measurements sure diference of 235.44 Pa (1.764 mmHg) required to in the CA explain more acute cases of (normal pressure) hydro- cephalus [16]. Furthermore, forty percent of our subjects Parameter Mean ± SD (n 30) = had an estimated net pressure diference in the oppo- SV (μL) 80 51 site direction (i.e. higher pressure in the fourth ventricle ± Evan’s index 0.37 0.04 and subarachnoid space), which would work against an ± Cross-sectional area ­(mm2) 5.6 3.2 enlargement of the third and lateral ventricles in those ± a Net fow (mL/min) 0.74 0.71 subjects. Te lack of a signifcant ΔPnet when removing ± Max fow (caudal) (mL/min) 21.6 11.8a the patients diagnosed with diseases other than hydro- ± a Min fow (cranial) (mL/min) 15.9 9.8 cephalus (n 6) also suggest that the magnitude of ΔPnet − ± = Max fow-min fow (mL/min) 37.5 21.3 may not be relevant in communicating hydrocepha- ± Maximum fow ratio (Q ) 1.32 0.28 lus, as did the results for the INPH subgroup. Te larg- O/I ± Time ratio r 0.85 0.15 est ΔPnet was observed among the smallest CAs (Fig. 6), O/I ± Net fow direction ( / )a 26/4 which could indicate that a narrowed or semi-obstructed + − a Positive sign indicates fow out from the ventricles CA is required to generate any substantial magnitude of this pressure diference. For these reasons, we deem it unlikely that the CA pulsations source ventriculomegaly Te raw MRI data are summarized in Table 4. Te through a pressure diference from fow through the CA. aqueductal SV was positively correlated with the cross- However, since we cannot explicitly determine the long- sectional area of the aqueduct (Pearson’s correlation coef- term efects in this study, we cannot rule out the possibil- ity that the ΔP (even of the magnitude observed) could fcient r = 0.37, p = 0.04). Only four subjects had a CA net net fow in the cranial direction, three of them were diag- afect the ventricular system over very long periods of nosed as INPH. Te Reynolds numbers in the aqueducts time. We should note that this study did not take disease pro- were 108 ± 63 at the time of maximum outfow from the ventricles, supporting the assumption of laminar fow. gression into account, and it is possible that the efects we were looking for had already been compensated for, Discussion e.g. by an increase in CA area, and that the pressure dif- In this study we investigated the hypothesis that aque- ference may have been larger at an earlier stage of the ductal fow pulsations could introduce net pressure disease. Te results from our analysis of the extreme con- efects across the open CA that could source ventricu- fgurations (Table 3) show that with a small CA, a ΔPnet lomegaly in communicating hydrocephalus. Te investi- close to 5 Pa could be achieved by either a severe fow gation consisted of numerically calculating the pressure asymmetry or a small asymmetry and an increased SV. With the additional contribution from the net fow, the diference ΔP across the CA using CFD based on high ∼ resolution MRI data from patients investigated for com- ΔPnet could be as big as 10 Pa. Tis is also supported municating hydrocephalus. We found that the CSF fow by the experimental model results, where a net pressure pulsations over the communicating CA did generate net of 24 Pa was observed across the model CA (the 1 mm pressure efects over the cardiac cycle, but of very low model diameter was slightly smaller than the 1.1 mm magnitude. CA used for the extreme cases). To investigate whether A relationship between high pulsations and a large the pressure efects are diminished over time, and how ventricular volume has been shown previously [26, 27], ΔPnet may change during the development of the dis- but the question has remained whether the pulsations ease, longitudinal studies would be needed. Such studies Holmlund et al. Fluids Barriers CNS (2019) 16:40 Page 9 of 10

would likely demand data from the early stages of the enlargements/contractions. Furthermore, the maximum disease and probably before the symptoms appear, which diference in CA velocity between the CFD and the MRI requires population studies. data (Fig. 6) was generally small, with only a few subjects Te results for the GLM verifed the association showing larger deviations (the fow rates were identical between ΔPnet and CA fow asymmetry, in addition to the by defnition). Finally, the pressure diferences observed cross-sectional area. Tus, the results support the biome- in this study are comparable to that found in previous chanical principles behind the hypothesized ΔP . Te CFD case studies of hydrocephalus [9, 18], with the maxi- net ∼ one exception to this is the lack of association between mum diference (i.e. ΔPmax) being 20–30 Pa. It is inter- the SV and ΔPnet, something we expected to fnd, espe- esting to note that both the net and maximum efects cially due to the strong correlation between CA cross- in the current study are slightly larger compared to that sectional area and SV observed previously [27]. Since the calculated in healthy subjects [10] (roughly fve times correlation between CA area and SV was not as strong larger), which could indicate that the pulsations in hydro- in our study, and the range of the CA area was much cephalus may have an efect on the transmantle pressure smaller, it could mean that this relationship is altered gradient, but one that is still very small in magnitude. with disease progression. It is important to stress that the asymmetrical pressure efects are not only dependent on the asymmetric fow Conclusions but also on the asymmetry in the shape of the CA inlet Tis study confrmed that a transmantle pressure dif- and outlets, i.e. where the CA transitions into the third ference (ΔPnet) due to CSF pulsations is introduced over and fourth ventricle respectively (the locations where the open CA, with higher pressure in the third ventricle, ∼ the discharge efects are expected to be the largest). Tus however the magnitude was low ( 0.2 Pa). While this accurately capturing these efects requires use of the transmantle pressure diference from CA fow is likely entire CA geometry, hence the focus on optimizing the too small to explain the ventriculomegaly in commu- geometrical data. nicating hydrocephalus, long-term cohort or modeling We did not include wall movement of the ventricles, studies must be performed to assess its cumulative efects which may slightly afect the resulting CA pressure dif- on the ventricles. ference [28]. Furthermore, the use of the CA volumetric fow curve as input in the fourth ventricle may intro- Abbreviations duce small changes to the pressure diference. Also, we CA: cerebral aqueduct; CFD: computational fuid dynamics; CSF: cerebrospinal did not include respiratory gating in this study. A recent fuid; FIESTA: fast imaging employing steady state acquisition; GLM: general- ized linear model; ICC: intraclass correlation coefcient; INPH: idiopathic study by Spijkerman et al. [29] has shown that net fow normal pressure hydrocephalus; PCMRI: phase contrast magnetic resonance CA measurements can be confounded by respiratory imaging; ROI: region of interest; SV: aqueductal stroke volume; ΔPnet: net efects, which further indicates that PCMRI CA net fow pressure diference across the cerebral aqueduct over the cardiac cycle; results must be interpreted with caution. However, respi- ΔPmax: maximum pressure diference across the cerebral aqueduct; QO/I: the maximum ventricular outfow/infow ratio through the aqueduct; rO/I: the ratio ration does not seem to afect SV [29], which motivates of time duration of ventricular outfow vs. infow through the aqueduct. the choice in our study of looking at only the contribu- Acknowledgements tion from the pulsations, while removing the efects The authors thank research nurse Kristin Nyman for skilful assistance regard- of net fow. Te measurements were only performed in ing planning, recruitment and correspondence with the study subjects. The the supine posture, even though patients spend most of authors would also like to thank neuroradiologist Jan Zizka for valuable advice their time in an upright position. Tus, the alteration in regarding the segmentations of the ventricular CSF space. ΔPnet with posture was not determined in this study. It is Authors’ contributions also likely that we are pushing the limit for the minimum All authors contributed to the concept and design, data acquisition, data analysis, and interpretation of the results. PH and AE drafted the paper and pressure magnitudes that can be correctly detected using PH and SQ created the fgures. All authors critically edited and revised the input data to CFD from MRI techniques available today. manuscript. All authors read and approved the fnal manuscript. To ascertain the reliability of our CFD approach we put Funding a lot of efort into optimizing the input data to the simu- Open access funding provided by Umeå University. The authors acknowledge lations, achieving a PCMRI resolution that is far above fnancial funding from the Swedish National Space board (Grant 193-17), the the average [30]. In addition, CFD simulations were eval- Swedish Research Council (Grant 2015-05616) and the Swedish Heart and uated against bench tests. Even though the model geom- Lung Foundation (Grant 20140592). etry was highly simplifed in these bench tests, the results Availability of data and materials indicate that our CFD approach can accurately estimate The datasets used and/or analysed during the current study are available from discharge efects for pulsatile fows through aqueduct-like the corresponding author on reasonable request. Holmlund et al. Fluids Barriers CNS (2019) 16:40 Page 10 of 10

Ethics approval and consent to participate 15. Eide PK, Sæhle T. Is ventriculomegaly in idiopathic normal pressure The Regional Ethical Review Board in Umeå approved the study (Approval hydrocephalus associated with a transmantle gradient in pulsatile intrac- number: 2012-396-32M), which was conducted in accordance with the Decla- ranial pressure? Acta Neurochir. 2010;152:989–95. ration of Helsinki, and all participants gave their informed, written consent. 16. Dutta-Roy T, Wittek A, Miller K. Biomechanical modelling of normal pres- sure hydrocephalus. J Biomech. 2008;41:2263–71. Consent for publication 17. Kurtcuoglu V, Soellinger M, Summers P, Boomsma K, Poulikakos D, Not applicable. Boesiger P, et al. Computational investigation of subject-specifc cerebro- spinal fuid fow in the third ventricle and aqueduct of Sylvius. J Biomech. Competing interests 2007;40:1235–45. The authors declare that they have no competing interests. 18. Linninger AA, Xenos M, Zhu DC, Somayaji MR, Kondapalli S, Penn RD. Cerebrospinal fuid fow in the normal and hydrocephalic . Author details IEEE Trans Biomed Eng. 2007;54:291–302. 1 Department of Radiation Sciences, Umeå University, Umeå, Sweden. 19. Relkin N, Marmarou A, Klinge P, Bergsneider M, Black PM. Diagnosing 2 Department of Pharmacology and Clinical Neuroscience, Umeå University, idiopathic normal-pressure hydrocephalus. Neurosurgery. 2005;57:S4–16 Umeå, Sweden. 3 Umeå Centre for Functional Brain Imaging, Umeå University, (discussion ii–v). Umeå, Sweden. 20. Noble DJ, Scofngs D, Ajithkumar T, Williams MV, Jeferies SJ. Fast imaging employing steady-state acquisition (FIESTA) MRI to investigate cerebro- Received: 15 September 2019 Accepted: 5 December 2019 spinal fuid (CSF) within dural refections of posterior fossa cranial nerves. Br J Radiol. 2016;89:20160392. 21. Hingwala D, Chatterjee S, Kesavadas C, Thomas B, Kapilamoorthy TR. Applications of 3D CISS sequence for problem solving in neuroimaging. Indian J Radiol Imaging. 2011;21:90–7. References 22. Wahlin A, Ambarki K, Hauksson J, Birgander R, Malm J, Eklund A. Phase 1. Rekate HL. A contemporary defnition and classifcation of hydrocepha- contrast MRI quantifcation of pulsatile volumes of brain arteries, veins, lus. Semin Pediatr Neurol. 2009;16:9–15. and cerebrospinal fuids compartments: repeatability and physiological 2. Mascalchi M, Ciraolo L, Tanfani G, Taverni N, Inzitari D, Siracusa GF, et al. interactions. J Magn Reson Imaging. 2012;35:1055–62. Cardiac-gated phase MR imaging of aqueductal CSF fow. J Comput 23. Heiberg E, Sjögren J, Ugander M, Carlsson M, Engblom H, Arheden H. Assist Tomogr. 1988;12:923–6. Design and validation of Segment—freely available software for cardio- 3. Abbey P, Singh P, Khandelwal N, Mukherjee KK. Shunt surgery efects on vascular image analysis. BMC Med Imaging. 2010;10:1. cerebrospinal fuid fow across the aqueduct of Sylvius in patients with 24. Bloomfeld IG, Johnston IH, Bilston LE. Efects of proteins, blood cells communicating hydrocephalus. J Clin Neurosci. 2009;16:514–8. and glucose on the viscosity of cerebrospinal fuid. Pediatr Neurosurg. 4. Balédent O, Gondry-Jouet C, Meyer M-E, De Marco G, Le Gars D, Henry- 1998;28:246–51. Feugeas M-C, et al. Relationship between cerebrospinal fuid and blood 25. Behrens A, Lenfeldt N, Qvarlander S, Koskinen LO, Malm J, Eklund A. dynamics in healthy volunteers and patients with communicating Are intracranial pressure wave amplitudes measurable through lumbar hydrocephalus. Invest Radiol. 2004;39:45–55. puncture? Acta Neurol Scand. 2013;127:233–41. 5. Greitz D, Hannerz J, Rahn T, Bolander H, Ericsson A. MR imaging of 26. Ringstad G, Emblem KE, Geier O, Alperin N, Eide PK. Aqueductal stroke cerebrospinal fuid dynamics in health and disease. On the vascular volume: comparisons with intracranial pressure scores in idiopathic pathogenesis of communicating hydrocephalus and benign intracranial normal pressure hydrocephalus. Am J Neuroradiol. 2015;36:1623–30. hypertension. Acta Radiol. 1994;35:204–11. 27. Chiang WW, Takoudis CG, Lee SH, Weis-McNulty A, Glick R, Alperin N. Rela- 6. Di Rocco C, Pettorossi VE, Caldarelli M, Mancinelli R, Velardi F. Communi- tionship between ventricular morphology and aqueductal cerebrospinal cating hydrocephalus induced by mechanically increased amplitude of fuid fow in healthy and communicating hydrocephalus. Invest Radiol. the intraventricular cerebrospinal fuid pressure: experimental studies. 2009;44:192–9. Exp Neurol. 1978;59:40–52. 28. Fin L, Grebe R. Three dimensional modeling of the cerebrospinal fuid 7. Di Rocco C, Di Trapani G, Pettorossi VE, Caldarelli M. On the pathology of dynamics and brain interactions in the aqueduct of sylvius. Comput experimental hydrocephalus induced by artifcial increase in endoven- Methods Biomech Biomed Eng. 2003;6:163–70. tricular CSF pulse pressure. Childs Brain. 1979;5:81–95. 29. Spijkerman JM, Geurts LJ, Siero JCW, Hendrikse J, Luijten PR, Zwanenburg 8. Pettorossi VE, Di Rocco C, Mancinelli R, Caldarelli M, Velardi F. Commu- JJM. Phase contrast MRI measurements of net cerebrospinal fuid fow nicating hydrocephalus induced by mechanically increased amplitude through the cerebral aqueduct are confounded by respiration. J Magn of the intraventricular cerebrospinal fuid pulse pressure: rationale and Reson Imaging. 2019;49:433–44. method. Exp Neurol. 1978;59:30–9. 30. Ragunathan S, Pipe JG. Radiofrequency saturation induced bias in 9. Sweetman B, Xenos M, Zitella L, Linninger AA. Three-dimensional aqueductal cerebrospinal fuid fow quantifcation obtained using two- computational prediction of cerebrospinal fuid fow in the human brain. dimensional cine phase contrast magnetic resonance imaging. Magn Comput Biol Med. 2011;41:67–75. Reson Med. 2018;79:2067–76. 10. Bardan G, Plouraboue F, Zagzoule M, Baledent O. Simple patient-based 31. Malm J, Jacobsson J, Birgander R, Eklund A. Reference values for CSF transmantle pressure and shear estimate from cine phase-contrast MRI in outfow resistance and intracranial pressure in healthy elderly. Neurology. cerebral aqueduct. IEEE Trans Biomed Eng. 2012;59:2874–83. 2011;76:903–9. 11. Qvarlander S, Ambarki K, Wåhlin A, Jacobsson J, Birgander R, Malm J, et al. Cerebrospinal fuid and blood fow patterns in idiopathic normal pressure hydrocephalus. Acta Neurol Scand. 2017;135:576–84. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in pub- 12. Oliveira PJ, Pinho FT, Schulte A. A general correlation for the local loss lished maps and institutional afliations. coefcient in Newtonian axisymmetric sudden expansions. Int J Heat Fluid Flow. 1998;19:655–60. 13. Bullen PR, Cheeseman DJ, Hussain LA, Rufellt AE. The determination of pipe contraction pressure loss coefcients for incompressible turbulent fow. Int J Heat Fluid Flow. 1987;8:111–8. 14. Stephensen H, Tisell M, Wikkelsö C, Hodge CJ, Gjerris F, Børgesen SE, et al. There is no transmantle pressure gradient in communicating or noncom- municating hydrocephalus. Neurosurgery. 2002;50:763–71 (discussion 771-3).