Association Between Resistance to Cerebrospinal Fluid Flow Near the Foramen Magnum and Cough-Associated Headache in Adult Chiari Malformation Type I

Abstract

Cough-associated headaches (CAHs) are thought to be distinctive for Chiari malformation type I (CMI) patients and have been shown to be related to the motion of cerebrospinal fluid (CSF) near the foramen magnum (FM). We used computational fluid dynamics (CFD) to compute patient-specific resistance to CSF motion in the spinal canal for CMI patients to determine its accuracy in predicting CAH. Fifty-one symptomatic CMI patients with cerebellar tonsillar position (CTP) ≥ 5 mm were included in this study. The patients were divided into two groups based on their symptoms (CAH and non-CAH) by review of the neurosurgical records. CFD was utilized to simulate CSF motion, and the integrated longitudinal impedance (ILI) was calculated for all patients. A receiver operating characteristic (ROC) curve was evaluated for its accuracy in predicting CAH. The ILI for CMI patients with CAH (776 dyn/cm⁵, 288—1444 dyn/cm⁵; median, interquartile range) was significantly larger compared to non-CAH (285 dyn/cm⁵, 187–450 dyn/cm⁵; p = 0.001). The ILI was more accurate in predicting CAH in CMI patients than the CTP when the comparison was made using the area under the ROC curve (AUC) (0.77 and 0.70, for ILI and CTP, respectively). ILI ≥ 750 dyn/cm⁵ had a sensitivity of 50% and a specificity of 95% in predicting CAH. ILI is a parameter that is used to assess CSF blockage in the spinal canal and can predict patients with and without CAH with greater accuracy than CTP.

Introduction

Chiari malformation type I (CMI) is a structural abnormality of the cerebellum at the craniovertebral junction, and it is radiologically defined by a ≥ 5 mm caudal displacement in the cerebellar tonsillar position (CTP) below the foramen magnum (FM) [1–3]. It is estimated that between 1/1000 and 1/1500 individuals have CMI [4]. In addition, several other researchers have approximated the CMI prevalence as 0.1% [5–9]. However, the estimates vary as a result of variable diagnostic criteria. Headache is the most common symptom for adult CMI patients, followed by neck pain [10,11]; in one study, 98% of 265 CMI patients reported that they suffer from headaches [12]. In addition, CMI patients may also experience a variety of other symptoms such as cognitive effects, muscle weakness or numbness, vertigo, sensory changes, tinnitus, fatigue, difficulty swallowing, insomnia, depression, hypertension, and vomiting [13–18].

The applicability of the 5 mm definition in diagnosing CMI patients is being questioned, as some individuals who meet the magnetic resonance (MR) imaging criteria are asymptomatic, while some individuals with less than 5 mm CTP show symptoms of CMI [13]. Researchers are examining other anatomical features [19–23] in addition to physiological factors such as cerebrospinal fluid (CSF) velocity at the base of the skull [24–28] in an effort to find parameters that better reflect CMI severity. In 2019, Bolognese et al. [29] collected opinions of 63 internationally recognized CMI experts from four continents with a collective surgical experience,  >15,000 CMI cases through a detailed questionnaire. More than 85% of the respondents agreed in rejecting the 5 mm definition as a basis for diagnosing CMI [29]. Thus, there is an expert consensus of the need to determine additional parameters to aid clinicians in the diagnosis of CMI.

Using phase contrast MR imaging, researchers have shown that peak CSF velocity below the tonsillar tips for asymptomatic and symptomatic CMI patients ranges between 2 and 20 cm/s [26]. In a study by McGirt et al. [25], patients with occipital headache were shown to have higher CSF velocity, indicating a greater obstruction of flow as compared to patients with frontal and generalized headache. In another study by Bhadelia et al. [30], in which MRI pencil beam imaging was used, a significant decrease in the stroke volume near the FM was observed immediately after coughing for CMI patients as compared to healthy controls. In addition to phase contrast MR imaging measurements, researchers have been using computational fluid dynamics (CFD) to better understand the patterns of CSF flow as well as to quantify several hydrodynamic properties of that flow in CMI patients in a noninvasive manner [31–38].

Another hydrodynamic property that has been used in quantifying CSF flow dynamics is longitudinal impedance (LI) [36,39,40]. LI is defined as the ratio of pressure harmonic to the flow harmonic at the same frequency [41]. LI has been used by many researchers to obtain the resistance within a conduit (such as vein grafts, aorta, and spinal canal) to unsteady fluid motion at a given frequency [42–45]. In addition, LI is solely dependent on the geometry of the conduit as described by Milnor and Nichols et al., shown experimentally by Skelly et al., Schwartz et al., and Curi et al., and shown numerically by Shaffer [40,42,46–49]. As such, the LI characterizes the relation between the pressure gradient and the CSF flow rate. Shaffer et al. [40] showed elevated resistance to CSF flow in CMI subjects as compared to healthy volunteers. In their study, the mean LI for the CMI group (551 ± 66 dyn/cm⁵) was found to be more than twice that of healthy controls (220 ± 17 dyn/cm⁵) [40]; however, the symptomatology for the CMI patients was not available for correlation.

Only a few studies have found correlation between engineering parameters and CMI symptomatology [18,24,50,51]. Houston et al. [18] showed that a higher CTP is correlated with disability, increased pain, and delayed memory performance. In addition, fourth ventricular fastigium height and posterior cranial fossa osseous area were found to be correlated with disability and cognitive effects, respectively. Bhadelia et al. [24] showed that CMI patients with cough-associated headache (CAH) have significantly shorter CSF systole as compared to non-CAH patients. In another study, Bezuidenhout et al. [51] observed a negative correlation between the percentage change in CSF stroke volume (from a resting state to postcoughing) and disease severity in CMI patients. It is important to note that, in this study, no significant relationships were observed between disease severity and anatomical measurements [51]. However, in a 2020 study, Huang et al. [50] showed that CTP was the only morphological parameter identified from two-dimensional (2D) anatomical images that could be used to identify CMI patients with CAH. They found that a larger CTP value (CTP ≥ 14) was able to accurately differentiate between patients with and without CAH.

It is generally thought that a reduction in the CSF spaces and motion of the CSF between the cranium and the spinal canal is related to CMI symptomatology. In addition, CAH is a symptom that is specific to CMI patients. Hence, in this study, the goal was to determine if LI is capable of predicting CAH in CMI patients. Since LI serves as a measure of CSF flow obstruction, we hypothesize that LI will be elevated for CMI patients with CAH as compared to patients without CAH.

Materials and Methods

Ethics and Patients.

Institutional review board's approval was obtained for this retrospective study with a waiver of informed consent. We reviewed the electronic database for consecutive CMI patients evaluated by neurosurgeons at Beth Israel Deaconess Medical Center (Boston, MA) from 2011 through 2018. Only CMI patients having an MRI examination that included high-resolution three-dimensional (3D) T2-weighted images (slice thickness = 0.5–2 mm, pixel spacing = 0.45/0.45–0.97/0.97 mm) and the availability of neurosurgical notes with detailed information about the patient's symptomatology were included. Patients with a history of posterior fossa decompression surgery—which would alter the CSF flow and, thus, may change the patient's symptoms—were excluded. MRI scans were acquired using 1.5 T or 3 T GE Signa HDx scanners (GE Healthcare, Milwaukee, WI) or a 1.5 T Magnetom Espree scanner (Siemens, Erlangen, Germany). All MRI images were obtained while patients were in supine position in the MR scanner, were breathing quietly, and were not coughing.

Cerebellar tonsillar position values were measured from sagittal T1-weighted images by two neuroradiologists; the average of the two measurements is reported, and the inter-rater agreement between the readers was assessed with a correlation coefficient of 0.92 [50,51]. For this study, a total of 51 CMI patients with CTP ≥ 5 mm (the current radiological definition for CMI) were included; seven patients had associated syringomyelia. Neurosurgery notes were reviewed (blinded to the MRI findings) to determine the presence or absence of CAH.

In this study, CAH was considered to be present when neurosurgeon made a specific note of its presence in a patient. The patients were divided into two groups based on the presence or absence of CAH: a total of 30 patients (four with syringomyelia) were assigned to the CAH group (mean age of 37.6 ± 11.9), and 21 patients (three with syringomyelia) were assigned to the non-CAH group (mean age of 34.5 ± 8.4 years). There was no significant age difference between the two groups (p = 0.47).

Model Construction.

In order to construct a model of the CSF space, semi-automatic active contour (snake) segmentation was used to complete the segmentation process on the 3D MRI images in standard DICOM format using itk-snap open-source software (developed by the University of Pennsylvania in collaboration with the University of Utah) [52]. Segmentation was performed for the CSF spaces located in the thecal sac surrounding the spinal cord in the axial plane from the FM to a location 60 mm in the caudal direction (approximate to the C3 and C4 vertebrae), and a 3D model of CSF was exported (Fig. 1(a)). Smoothing was applied to remove pixilation artifacts using meshlab open-source software (developed at the Alessandro Faedo Institute of Information Science and Technologies, Pisa, Italy) by the default Laplacian smoothing algorithm (Fig. 1(b)). Inlet and outlet extensions were added (40 mm at each end) to have near fully developed flow in the smoothed model geometry using Autodesk Maya (Autodesk, San Rafael, CA), as shown in Fig. 1(c).

Fig. 1.

Flow domain generation steps: (a) segmented CSF space, (b) CSF space after smoothing, and (c) CSF space with added extensions

Mesh Generation and Cerebrospinal Fluid Flow Simulation.

To create the mesh for the CSF space model, the commercial software ansys icem cfd (Ansys, Inc., Canonsburg, PA) was used. First, the model was imported in stereolithography format. Surfaces of the modeled CSF space were modified, and three parts were created: INLET (caudal end of the CSF space), OUTLET (cranial end of the space), and WALL (the dura and spinal cord surfaces). An unstructured tetrahedral mesh was created using two different Tetra/Mixed mesh methods: the Robust (Octree) method and the Quick (Delaunay) method. In addition, six linearly increasing prismatic layers were generated near the wall to capture the high-velocity gradient in the boundary layer. The resulting mesh ranged between 0.7 and 1.3 × 10⁶ tetrahedral elements, depending on the shape and size of the flow geometry (Fig. 2). The following boundary conditions were imposed for each part: velocity inlet for the INLET, pressure outlet for the OUTLET, and wall for the WALL. It has been shown previously that LI depends only on the geometry and not on the CSF waveform frequency or amplitude [40,42,46–49,53]. Hence, the same CSF flow waveform (volume flow rate shown in Fig. 3) was imposed at the inlet for all cases as a velocity boundary condition.

Fig. 2.

Example of a mesh generated for CSF space with enlarged views of the linearly increasing prismatic layers (lower left) and mesh structure near cerebellar tonsils (lower right)

Fig. 3.

CFD simulation results for patient CAH-31: Pressure drop between the FM and a location that is 25 mm below the FM plane (top), volume flow rate (bottom), and LI result (center), with the corresponding ILI value (area under the curve from 1 to 8 Hz)

An assessment of the instantaneous Reynolds number (Re) was performed to determine the appropriateness of a laminar flow assumption. The Reynolds number in the form of flow rate is given by

$$\mathrm{Re}=\hspace{0.17em}\frac{4\mathrm{*}\rho \mathrm{*}Q}{\pi \mathrm{*}\mu \mathrm{*}{D}_H}$$ (1)

with the hydraulic diameter defined as

$$D_H=\frac{4\mathrm{*}A}{P}$$ (2)

Of the 51 patients included in this study, three showed severe reductions in area, with hydraulic diameters ${(D}_H)$ of 2.4, 2.6, and 3.4 mm. Since CSF has been shown to have physical properties that are similar to water at body temperature [54], CSF was modeled as water at 37 °C with a density $(\rho )$ of 1.0 g/cm³ and a viscosity $(\mu )$ of 0.001 P. The peak flow rate $\left(Q\right)$ was approximately 3.0 cm³/s. Thus, the largest Reynolds number (1590) was calculated for the patient with D_H = 2.4 mm. Given the time required for turbulence to develop during the cardiac cycle, the flow field will not reach turbulent or transitional flow conditions and, thus, the assumption of laminar flow is reasonable.

The commercial finite volume solver ansys fluent (Ansys, Inc.) was utilized to conduct the CFD simulations. The Navier–Stokes equation was discretized using a second-order upwind scheme in space and a second-order implicit scheme in time along with Green–Gauss node-based spatial discretization, and the SIMPLE pressure velocity coupling was chosen. The minimum residuals for continuity and the x, y, and z velocities were set to 10⁻⁵. A maximum of 80 iterations were permitted for each step so as to achieve convergence. Simulations were run for 100 time steps per cardiac cycle (where each time-step was equal to 6.953 ms, heart rate = 86.3 bpm) over two cycles. Only the second cycle was used for calculating the LI in order to reduce the impact of startup effects. Velocity and pressure values were exported in EnSight file format for postprocessing. These values were examined at two slice locations: at the FM and at a location 25 mm caudal to the FM. This distance was selected to be consistent with previous studies [36,39,40] such to capture the spinal canal region that is most impacted by the low-lying cerebellar tonsils. For each time-step, the spatially averaged pressure at each slice location was evaluated. The LI (Z_L), which is a measure of the unsteady resistance to pulsatile motion of CSF flow for a given harmonic, was calculated by dividing the Fourier transfer coefficients of the pressure drop time trace between the two slices by the Fourier transfer coefficients of the volume flow rate time trace as shown in the following equation:

$$Z_L=\hspace{0.17em}\frac{\mathcal{F}(\Delta P(t\left)\right)}{\mathcal{F}\left(Q\right(t\left)\right)}$$ (3)

In the aforementioned equation, $\mathrm{\Delta }P\left(t\right)$ is the spatially averaged pressure drop between the FM plane and the plane 25 mm caudal to the FM as a function of time. Each time point pressure values at the two different planes were computed through CFD simulations, and the pressure drop for one patient (patient CAH-31) is shown in Fig. 3. The parameter $Q\left(t\right)$ is the CSF volume flow rate as a function of time, which was imposed at the inlet boundary condition (Fig. 3). The resulting Z_L was integrated from 1 to 8 Hz to obtain the integrated longitudinal impedance (ILI), which is a characteristic value that represents the overall resistance to CSF flow in the upper spinal canal. It should be noted that the selection of frequency range is somewhat arbitrary but is designed to provide an estimate of the overall impedance [47]. Several different frequency and harmonic ranges were used by researchers depending on the application of impedance calculation [42,49,55,56]. Hence, the frequency range from 1 to 8 Hz was selected since most of the CSF volume displaced occurs at 1 Hz frequency and less than one percent of the CSF volume displaced occurs above 8 Hz. CFD simulations of the CSF spaces in each of the 51 CMI patients were conducted, and the ILI for each patient was calculated (see the Z_L and the resulting ILI for one of the CMI patients in this study, as shown in Fig. 3).

A Mann–Whitney test was used to compare the CTP measurements and the calculated ILI values for patients with and without CAH. A p-value of  <0.05 was considered statistically significant. Since the ILI varies in a nonlinear fashion between patients, the natural logarithm of ILI was used for the correlation analysis between ILI and CTP [57]. Receiver operating characteristic (ROC) curves were plotted for both CTP and ILI to evaluate their accuracy in predicting CAH in CMI patients. In addition, patients were divided into two groups based on their CTP value (patients with CTP ≤ 7 mm and patients with CTP > 7 mm, respectively) to assess ILI and CTP performance in predicting CAH at different CTP [25].

Results

Figure 4 shows the ILI and CTP results for the 51 CMI patients in our study. The CTP value was significantly larger (median 1.5×) for patients with CAH (12 mm, 8–16 mm; median, interquartile range) than for those without CAH (8 mm, 6.8–11 mm; p = 0.009). In addition, the ILI for CMI patients with CAH (776 dyn/cm⁵, 288–1444 dyn/cm⁵) was significantly larger (median 2.7×) as compared to the CMI patients without CAH (285 dyn/cm⁵, 187–450 dyn/cm⁵; p = 0.001). Moreover, it can be noticed from Fig. 4 that while the range of ILI values was much larger for CAH patients as compared to the range for non-CAH patients (140 to 200,000 dyn/cm⁵ in CAH patients versus 144 to 1218 dyn/cm⁵ in non-CAH patients), the ranges of the CTP values were similar for both groups (5 to 27 for the CAH group versus 5 to 24 mm for the non-CAH group).

Fig. 4.

ILI and CTP values for all CMI patients: ILI distribution (top) and corresponding CTP values (bottom). Black rectangular boxes in the plots on the left represent the median and interquartile range for ILI and CTP values.

We found no significant correlation between the natural logarithm of ILI and CTP values for the CAH group (r = 0.27, p = 0.15) or non-CAH patients (r = 0.36, p = 0.11) as can be noticed from Fig. 5. However, a significant but not strong correlation was seen between the natural logarithm of ILI and CTP values for all patients (r = 0.37, p = 0.008).

Fig. 5.

ILI versus CTP for patients in both groups

The area under the ROC curve (AUC) is used to assess the accuracy of a given model's predictions [58]. ROC models typically include measures of both sensitivity (the true positive probability divided by the sum of the true positive probability plus the true false negative probability) and specificity (the true correct rejection probability divided by the true correct rejection rate plus the true false alarm probability). In this study, we wished to apply this methodology to assess whether ILI differed in precision when categorizing CMI patients with and without CAH relative to tonsillar position.

Based on the ROC curve, the ILI value showed better accuracy in predicting CAH in CMI patients than the CTP value, as shown in Fig. 6 and Table 1. The AUC values for CTP, ILI, and the multivariate model (the combination of CTP and ILI) were 0.70, 0.77, and 0.77, respectively (Fig. 6). When using a CTP ≥ 14 mm as the criterion to identify CMI patients with CAH, only a small percentage of the CAH patients were identified correctly (sensitivity = 33%), and one non-CAH patient was incorrectly identified (specificity = 95%). This criterion had a positive predictive value (PPV) of 91% and a negative predictive value (NPV) of 50%. When ILI ≥ 750 dyn/cm⁵ was used as the criterion to identify CMI patients with CAH, half of the patients in the CAH group were identified correctly (sensitivity = 50%), and one non-CAH patient was identified incorrectly (specificity = 95%), which resulted in a PPV of 94% and an NPV of 57%. The AUC values for the CTP and ILI in the patient group with CTP ≤ 7 mm were 0.49 and 0.73 and in the patient group with CTP > 7 mm were 0.68 and 0.77, respectively (Fig. 7).

Fig. 6.

ROC curves for all 44 CMI patients in this study

Table 1.

Accuracy of CTP and ILI criteria in predicting CAH in a group of 51 CMI patients

Criterion	Sensitivity (%)	Specificity (%)	PPV (%)	NPV (%)
CTP ≥ 8 mm	73	52	69	58
CTP ≥ 10 mm	57	62	68	50
CTP ≥ 12 mm	47	90	87	54
CTP ≥ 14 mm	33	95	91	50
ILI ≥ 500 dyn/cm5	60	81	82	59
ILI ≥ 600 dyn/cm5	53	86	84	56
ILI ≥ 700 dyn/cm5	53	90	89	57
ILI ≥ 750 dyn/cm5	50	95	94	57

Fig. 7.

ROC curve for two groups of patients: Patients with CTP ≤ 7 mm (ILI = solid line with circles, CTP = solid line with triangles) and patients with CTP > 7 mm (ILI = dashed line, CTP = dotted line)

Discussion

As headaches are the most common symptom reported by adult CMI patients [12–14], it would be clinically advantageous to be able to differentiate CMI-related headaches from generalized headaches that are not related to CMI. In a study by McGirt et al. [25], patients with generalized and frontal headaches were shown to be one-tenth as likely to have a CSF obstruction as compared to patients with occipital headaches. In that study, CSF flow was classified as hindbrain CSF flow obstruction if biphasic flow was absent various structures near the FM. Biphasic flow is caudally and cranially CSF motion during the cardiac cycle. It was also shown that CMI patients with obstructed CSF flow did better after posterior fossa decompression surgery as compared to CMI patients with normal CSF flow [25].

The International Headache Society defined CAH as an occipital or suboccipital headache of short duration (i.e., less than 5 min) that is provoked by a precipitating factor such as coughing or other Valsalva maneuver-like activities and is associated with other symptoms and/or clinical signs of brainstem, cerebellar, lower cranial nerve, and/or cervical spinal cord dysfunction [59]. CAH is the most distinctive of all the headaches associated with CMI and is reported as a symptom by one-third to half of CMI patients [60,61]. CAH may also be useful as a clinical indicator of CSF blockage severity. Bhadelia et al. [30] and Bezuidenhout et al. [62] have previously shown a decrease in CSF motion for 10 to 15 s postcoughing for CMI patients with CAH, which implies a temporary increase in the obstruction to CSF flow after coughing. In this study, we used CFD to compute the resistance to CSF motion in the spinal canal near the FM, and we used ILI as a measure of CSF flow obstruction in symptomatic CMI patients with and without CAH. We found that the median ILI for CMI patients with CAH was almost three times larger than those for the non-CAH group. Thus, ILI could potentially be a clinically significant parameter to determine the severity of CSF obstruction.

While CTP is often associated with CSF obstruction, it is a length measurement of tonsillar herniation below the FM that does not capture the three-dimensionality of the spinal canal obstruction near the FM [40]. The calculation of the ILI incorporates the full three-dimensional geometry of the spinal cord and, thus, is more indicative of resistance to CSF motion in the spinal canal. As shown in Figs. 4 and 5, a high CTP value did not necessarily result in a large ILI value (patient non-CAH-7) or vice versa (patients CAH-50 and CAH-51). For example, one of the highest ILI values (27,000 dyn/cm⁵) was measured for a patient with a CTP of 7 mm (patient CAH-50), whereas a different patient (patient non-CAH-7) having a much higher CTP value (24 mm) had a much smaller ILI value (423 dyn/cm⁵). Examination of the MRI scan in the axial plane near the FM for the subject with the 7 mm CTP (patient CAH-50) revealed substantial crowding in the spinal canal as compared to the subject with the 24 mm CTP that showed minimal crowding (patient non-CAH-7), as can be seen in Fig. 8. Thus, CSF obstruction cannot be reliably assessed using CTP.

Fig. 8.

MR images for two CMI patients that show the sagittal and axial planes near the FM. The MR image demonstrates greater foraminal crowding in patient CAH-50, who has a CTP = 7 mm and an ILI = 27,000 dyn/cm⁵ (left) as compared to a patient non-CAH-7, who has a CTP = 24 mm and an ILI = 423 dyn/cm⁵ (right).

Numerous studies have reported differences in 2D morphology in the brain between CMI patients and healthy subjects [20,22,23], but only a few studies found a significant relationship between CMI symptom severity and morphometric differences [18,50]. Huang et al. [50] showed the extent of tonsillar herniation as the only 2D morphology to be different between CMI patients with and without CAH; however, they found the sensitivity of the CTP value to be low (AUC = 0.65) when predicting CAH, and this prediction was 100% specific for a criterion of CTP ≥ 14 mm. In our study, we found the average tonsillar position for patients in the CAH group, with an AUC = 0.70, to be 50% higher than in the non-CAH group. In contrast, the performance of the ILI value in predicting which patients had CAH was better, with an AUC = 0.77. In general, an AUC of 0.5 suggests no discrimination (i.e., ability to diagnose patients with and without the disease or a certain condition based on the test), while an AUC of 0.7 to 0.8 is considered to have acceptable performance, an AUC of 0.8 to 0.9 is considered excellent, and an AUC above 0.9 is considered outstanding [63]. ROC analysis of CMI patients without syringomyelia (n = 44) showed similar AUC values for CTP, ILI, and the multivariate model of 0.71, 0.79, and 0.76, respectively.

McGirt et al. [25] found that patients with occipital headaches were eight times more likely to have tonsillar herniation greater than 7 mm as compared to patients with frontal or generalized headache. Hence, we divided our patients into two groups based on tonsillar position—one group of patients had CTP ≤ 7 mm (n = 13) and the other group had CTP > 7 mm (n = 38)—to evaluate the performance of the ILI value and the CTP value in identifying the CAH patients; the results are shown in Fig. 7. The performance of the CTP value in predicting CAH in CMI patients was not acceptable for the patients either with CTP ≤ 7 mm (AUC = 0.49) or with CTP > 7 mm (AUC = 0.68). However, the performance of the ILI value in predicting CAH in CMI patients was within the acceptable range for both groups: the AUC was 0.73 for patients with CTP ≤ 7 mm and 0.77 for those with CTP > 7 mm. Thus, ILI may have a higher correlation with other symptomatology as compared to CTP. Further studies need to be conducted to examine this aspect.

Several limitations were present in our study. These limitations included the following:

• Our study is retrospective. As such, it may have more potential sources of bias and confounding effects than a prospective study.

• We had to depend on electronic records of the medical histories provided by CMI patients as interpreted by different neurosurgeons regarding the presence or absence of CAH. It was unclear how strictly the neurosurgeons followed the International Headache Society definition for CAH [59].

• The ILI value is dependent on the manual process used for segmenting the CSF space in the patients' MR images as well as subject variability. Thus, the quality of the MR images and the operator's evaluation of each image will impact the final geometry that represents the CSF space for a given patient—which, in turn, will impact the computed value for the ILI, since the ILI is highly dependent on the geometry of the CSF space.

• The ILI value is calculated based on static anatomical MRI scans that do not capture brain tissue motion. Previous research has shown that during the cardiac cycle, CMI patients exhibit a brain tissue motion of magnitude ∼500 μm in the caudocranial direction [64–66]. Pahlavian et al. [36] modeled the cerebellar tonsils and spinal cord as rigid bodies moving in the caudocranial direction (∼300 μm) and found the ILI values to be 19% larger for the model with motion as compared to the static model. However, there is no previous study to show the brain motion during coughing.

• Examination of the assumption that ILI is independent of the CSF waveform was conducted using a waveform with half the flow amplitude of the original waveform. The results from the analysis showed ILI to be different by as much as 40% for three cases with extremely severe blockage (40%, 35%, and 27%) and <1% for other cases. This is likely due to the large Reynolds number for these extremely crowded geometries (Re at maximum flow during cycle based on hydraulic diameters of 1590, 1470, and 1120) where the flow may be near the transition to turbulence compared to the other cases (in which the Reynolds number was always less than ∼750). Our CFD analysis made the assumption of laminar conditions for all cases, which may have introduced error in the ILI calculation for the three cases with extremely severe blockage. However, since these cases had ILI values that were tenfold greater than the typical ILI values, the prediction results for CAH are similar even with the large error for those three cases. It should be noted that ILI still produced a better prediction of CAH compared to the CTP when excluding those three extreme blockage cases, albeit less of a difference than when they were included.

• In the calculation of the ILI, the brain morphology above the FM is ignored, as the methodology requires a conduit in order to compute the ILI. Thus, an ILI value only represents the resistance to CSF motion below the FM plane. Any obstruction above the FM is not represented by the ILI.

In conclusion, our study showed that ILI appears to be a useful parameter for predicting CMI headaches and it performed better than CTP in identifying patients with CAH. Hence, the ILI value provides a useful parameter for quantifying the extent of CSF obstruction, whereas CTP does not necessarily provide an accurate representation of the extent of CSF flow blockage. A more controlled, specific, prospective study where patients record the frequency, duration, and severity of their CAH is needed to fully understand the clinical relevance ILI.

Funding Data

• National Institutes of Health, NINDS R15 (Grant No. 1R15NS109957-01A1; Funder ID: 10.13039/100000002).

• Conquer Chiari.