Spatial distribution of human arachnoid trabeculae

Abstract

Traumatic brain injury (TBI) is a common injury modality affecting a diverse patient population. Axonal injury occurs when the brain experiences excessive deformation as a result of head impact. Previous studies have shown that the arachnoid trabeculae (AT) in the subarachnoid space significantly influence the magnitude and distribution of brain deformation during impact. However, the quantity and spatial distribution of cranial AT in humans is unknown. Quantification of these microstructural features will improve understanding of force transfer during TBI, and may be a valuable dataset for microneurosurgical procedures. In this study, we quantify the spatial distribution of cranial AT in seven post‐mortem human subjects. Optical coherence tomography (OCT) was used to conduct in situ imaging of AT microstructure across the surface of the human brain. OCT images were segmented to quantify the relative amounts of trabecular structures through a volume fraction (VF) measurement. The average VF for each brain ranged from 22.0% to 29.2%. Across all brains, there was a positive spatial correlation, with VF significantly greater by 12% near the superior aspect of the brain (p < .005), and significantly greater by 5%−10% in the frontal lobes (p < .005). These findings suggest that the distribution of AT between the brain and skull is heterogeneous, region‐dependent, and likely contributes to brain deformation patterns. This study is the first to image and quantify human AT across the cerebrum and identify region‐dependencies. Incorporation of this spatial heterogeneity may improve the accuracy of computational models of human TBI and enhance understanding of brain dynamics.

This study is the first to image human arachnoid trabeculae in situ and quantify the spatial distribution across the cerebrum. Incorporation of this spatial heterogeneity may improve the accuracy of computational models of human TBI, and enhance understanding of brain injury dynamics.

1. INTRODUCTION

Traumatic brain injury (TBI) is an increasingly common occurrence across the USA (Coronado et al. 2012). Diffuse axonal injury is a major subset of TBI in which large brain deformations damage white matter axons and result in a broad array of neurological symptoms. The magnitude of brain deformation is mediated, in part, by the mechanical connection between the brain and the skull (Talbert, 2016). This mechanical connection is composed of cerebral spinal fluid, subarachnoid vasculature, and arachnoid trabeculae (AT) sandwiched between the arachnoid and pia mater membranes on the deep side of the cranial dura mater. Cranial AT are predominantly made of type I collagen and help tether the brain to the skull (Haines, 1991; Haines and Ard, 2002; Talbert, 2016). Under rapid head acceleration, these collagen tethers limit the amount of displacement between the brain and skull, maintain the positioning of vasculature, and affect the overall deformation of the brain (Scott et al. 2016).

Light microscopy, transmission electron microscopy, and scanning electron microscopy have been used to investigate the composition and morphology of small sections of the subarachnoid space (Alcolado et al. 1988; Nicholas and Weller, 1988; Killer et al. 2003; Petroni et al. 2003; Weller, 2005; Saboori and Sadegh, 2015). From this work, much is known about the specific cellular and extracellular content of the pia‐arachnoid complex (PAC). A study of optic nerve cross sections by Killer et al. (2003) revealed that the structure and density of AT vary widely along the length of the optic nerve. Similar heterogeneities have been reported in the spinal column as well (Parkinson, 1991). Saboori and Sadegh (2015) qualitatively observed variations in the structure of cranial AT, but there has been no systematic study of the quantity and distribution of AT across the human cranial PAC.

The width of a typical trabecular column structure is well below the resolution of traditional brain imaging techniques such as magnetic resonance imaging or computed tomography (Killer et al. 2003). Microscopic imaging methods, such as scanning electron microscopy and transmission electron microscopy, require specimen preprocessing that may distort morphology, limiting quantitative assessment across brain regions. To address these shortcomings, Scott and Coats (2015) used optical coherence tomography (OCT) to image the PAC of the juvenile porcine brain. OCT uses backscatter interferometry with a near‐infrared light source that enables three‐dimensional (3D) imaging of collagen structures at the surface of the PAC without physical or chemical disruption. Volumetric images can be acquired with a resolution up to 1.5 μm and to a depth of 1.64 mm. In order to image subdural layers of the meninges via OCT, removal of the skull is necessary. This limits in vivo characterization of the human brain to small regions exposed during surgical procedures (Hartmann et al. 2019). To characterize the PAC across the entire brain, post‐mortem subjects must be used. Delamination of the arachnoid membrane from the meningeal dura has been observed post mortem (Mortazavi et al. 2018). This delamination, combined with a loss of cerebrospinal fluid, causes the PAC to deflate from its in vivo configuration. For the smaller porcine brains imaged by Scott and Coats, this did not present a significant difficulty as structures could still be visualized in the sulci. However, human sulci are much deeper and post‐mortem depressurization lowers the AT structures out of the focal range of the OCT.

The objective of the present study was to measure AT volume fraction (VF) across the surface of the human brain and quantify regional variability. To overcome challenges associated with depressurization in post‐mortem human subjects, a feedback‐controlled saline injection system was used to reinflate the subarachnoid space to physiological pressure. We employed semi‐automatic segmentation of OCT images to compare AT VF across regions. Understanding and quantifying the variability of these microstructures at the brain–skull interface may lead to improved predictions of axonal injury and TBI, and contribute valuable information for preoperative planning of microneurosurgeries. Further, regional variations in AT VF may be an indicator of a heterogeneous brain–skull interface and contribute to unique patterns of brain deformation during impact.

2. METHODS

2.1. Post‐mortem human subject head preparation

The studies were reviewed by the University of Utah Institutional Review Board and determined to be exempt from human study regulation. Fresh‐frozen human cadaver heads [ages 32–86 years, n = 9 (Table 1), purchased from Science Care Inc., Pheonix, AZ, USA] were thawed in a refrigerator over 2 days, brought to room temperature over 8 h, and dissected. No chemical pre‐processing was performed prior to freezing. Average time between death and head isolation and freezing was 8.1 ± 2.8 days. Heads were frozen for an average of 36.3 ± 14.2 days before thawing. Heads were thawed in an upright position to promote symmetry between right and left sides. Skin above the base of the temple was removed, followed by the aponeurosis and periosteum. Two large cranial windows, approximately 15 cm in the anterior–posterior direction and 7 cm in the inferior–superior direction, were cut using an autopsy saw (model Shandon 10 000; Thermo Fisher Scientific, Waltham, MA, USA), one for each hemisphere, leaving the sagittal sinus intact. Care was taken not to disrupt the dura during the craniotomy. Once the bone was removed, the dura mater was resected to expose the PAC. The dissected heads were placed within a custom stereotactic frame, which allowed precise positioning of the OCT lens (Figure 1). Tissues were regularly hydrated by spraying a 0.9% saline solution onto exposed brain surfaces.

Table 1.

Donor information

Subject	Sex	Age, years	Height, cm	Weight,  kg	Cause of death
1	Male	82	175	64.4	Respiratory failure
2	Male	54	191	135.2	Cardiopulmonary arrest
3	Male	78	188	82.1	Respiratory failure
4	Male	56	178	54.4	Lung cancer
5	Male	81	180	90.7	Acute interstitial pneumonitis
6	Male	70	178	79.4	Cardiopulmonary arrest
7	Male	50	168	39.5	Prostate cancer
8	Female	32	168	47.6	Gastric cancer
9	Female	67	170	101.6	Cardiovascular disease

Figure 1.

(A) Post‐mortem human subject heads were placed in a stereotactic frame. (B) The optical coherence tomography (OCT) lens and saline injection system were positioned such that saline injection occurred immediately adjacent to the imaged sulcus

2.2. Imaging protocol

The OCT imaging was conducted using a Bioptigen R2200 OCT scanner (Leica Microsystems Inc.) with an ultra‐high‐resolution light source with a full‐width half maximum bandwidth of 120 nm and scanning frequency of 32,000 lines per second. A 12‐mm telecentric lens was used. The scanner was operated using Bioptigen InVivoVue software. Scan resolution was controlled by two main parameters, A‐scan per B‐scan and number of B‐scans. The A‐scan per B‐scan setting controls the in‐plane resolution in the x‐direction (Figure 2) while the number of B‐scans controls the out‐of‐plane resolution in the z‐direction. Optimal settings were determined by preliminary test scans performed on three fixed human cadaver brains. Subsequent imaging of fresh tissue exhibited deeper light penetration and the ability to resolve trabecular structures to a greater depth compared to imaging of fixed tissues. A scan volume of 5 mm × 5 mm × 1.64 mm was large enough to capture the full width of larger sulci while achieving suitable resolution for image processing. Based on measurements of a small subset of images (n = 36), the width of trabecular fibers ranged from 19.2 µm to 45.5 µm, with an average of 30.5 µm. A total of 800 A‐scans per B‐scan were chosen to give a lateral resolution (x‐direction) of 6.25 µm. Axial resolution (y‐direction) of the system was 1.6 µm and 400 B‐scans were taken for an out‐of‐plane resolution of 12.5 µm (z‐direction; Figure 2). Using anatomical features of gyri and sulci as guides, the imaging location was manually recorded by marking a two‐dimensional (2D) brain template. This marked template was used to determine the 2D coordinates of each image location for spatial analyses.

Figure 2.

Example three‐dimensional volume of human pia‐arachnoid complex obtained from optical coherence tomography (OCT). OCT Settings were 800 A‐scans per B‐scan, 400 B‐scans per C‐scan, and one C‐scan. This resulted in a voxel resolution of 6.25 µm (x) × 1.61 µm (y) × 12.5 µm (z)

Each hemisphere of the brain was subdivided into six regions using a 2 × 3 grid to classify regions as frontal, parietal or occipital, and as inferior or superior (Figure 3). At least two scan volumes were captured within each region for each brain. The starting side for imaging of each subject was alternated between right and left to avoid bias. Superior regions were often imaged prior to inferior regions (n = 29) to prevent injected saline from leaking into the workspace during subsequent imaging; however, many inferior regions (n = 24) were imaged without imaging superior regions above them, eliminating any potential time‐dependent effects. The starting region (frontal, parietal or occipital) was chosen at random for each side and each subject.

Figure 3.

Representative scan locations (black boxes) for pia‐arachnoid complex imaging

At each image location, the stereotactic frame was adjusted to first bring the arachnoid membrane in focus. A 27‐gauge injection needle was then inserted through the arachnoid membrane near the junction of two or more sulci. In these locations, the depressurized arachnoid membrane spanned the gyrus and left a defined subarachnoid space. The needle was placed into this space. A custom feedback‐controlled pressure system locally inflated the subarachnoid space with 0.9% saline to 10 mmHg, within the physiological range of intracranial pressure (7–15 mmHg). The inflation system consisted of a pressure monitor (model 1‐06‐64‐04‐2; Pendotech Princeton, NJ, USA) and syringe pump (NE300 New Era Pump Systems Farmingdale). Feedback control was provided by an Arduino Uno (Arduino, Turin, Italy) and a MATLAB program (Mathworks Natick, MA, USA). Pressure was held at 10 ± 1.5 mmHg. The inflation radius was approximately 1 cm from the needle insertion site. The OCT focus was readjusted to compensate for membrane movement, and a volumetric OCT scan was collected. Volumetric OCT scan times were approximately 12 s. Total time to inflate and image a single subject was approximately 6 h. Locations where the subarachnoid space was not able to maintain pressure or inflate were not imaged.

2.3. Image processing and analysis

Three 2D B‐scan slices were selected from each volume stack. These images were denoised using a non‐local means filter (Darbon et al. 2008; Buades et al. 2011) and segmented using a semi‐automated algorithm in MATLAB. The algorithm used an adaptive threshold to segment the arachnoid membrane and AT from surrounding fluid and cortical tissue. Adaptive thresholding was chosen over global thresholding because the pixel intensity of the arachnoid structures decreased with increased imaging depth. A user‐generated mask was applied to limit the region of interest to areas below the arachnoid membrane and between cortical tissue. Region of interest was limited to depths of 750 μm below the bottom of the arachnoid membrane to avoid regions where light attenuation becomes problematic. A connected component analysis and denoising routine were used to remove foreground components of ≤40 pixels, which were representative of salt and pepper noise, typical of OCT imaging. Background holes in the segmentation < 10 pixels in size were filled.

The segmented 2D images were used to estimate the area fraction of AT by taking the ratio of pixels representing AT to the total number of pixels within a user‐selected region of interest below the arachnoid membrane (Figure 4). To focus the analysis on AT rather than subarachnoid vasculature, vessels were manually removed from the area of interest. The method of using multiple 2D area fraction measurements to estimate the 3D VF has been validated previously by our group (Scott and Coats, 2015), and we therefore refer to the average area fraction as the VF for the remainder of this study. The mean VF across the three B‐scans was used to represent the entire imaging volume. To quantify error in the semi‐automated segmentation program, a subset of images (n = 68) were manually segmented. VF from the manual segmentation was compared to VF calculated from the semi‐automated program.

Figure 4.

(A) Filtered two‐dimensional optical coherence tomography image of Subject 1. (B) Selected region of interest. (C) Segmented arachnoid trabeculae in the region of interest. Volume fraction was calculated by dividing the segmented arachnoid trabeculae pixels (red) by the region of interest (blue)

2.4. Statistical analysis

Correlations between VF and subject age, weight, and height were evaluated using a bivariate correlation test in JMP (SAS Institute Inc.). To test for the prevalence of tissue decay that might affect VF measurements, we performed a correlation analysis between VF and the number of days between death and image acquisition. A correlation analysis was also performed between VF and the imaging order, which serves as an estimate of the relative amount of time into an imaging session the scan was taken. These correlations were performed for each anatomical subregion. A series of one‐way analyses of variance (ANOVAs) with matched pairs were used to determine the effect of brain region on trabecular VF. An ANOVA was used to evaluate differences in VF between subjects. A Tukey's honest significant difference test was used to further explore subject‐to‐subject differences.

2.5. Spatial maps

Spatial maps of subject VF were created using a Voronoi tessellation method (Aurenhammer, 1991). This method creates a collection of polygon cells by constructing perpendicular bisectors between each of the provided seed points. An initial Voronoi diagram was created using the scan location coordinates as seed points. The diagram was then constrained by the boundaries of a digital image of a generic reference brain. A grayscale value between 0 and 1 was assigned to each Voronoi cell based on the average VF measured at each scan location. A color map was assigned to map grayscale values to an RGB color triplet.

2.6. Spatial statistics

Moran's I and Geary's C spatial analyses were performed to identify continuous trends in VF with imaging location. Moran's I and Geary's C are two spatial autocorrelation metrics to evaluate the similarity of data measured at nearby sampling points. Moran's I uses variance from the mean, while Geary's C, a close variant, uses point‐to‐point comparisons. Both metrics were evaluated to establish whether or not methodological choices would affect conclusions. These definitions are illustrated mathematically in Equations(1) and (2).

$$I=\frac{N\sum _i\sum _j{w}_{\mathit{ij}}(x_i-\overline{x})(x_j-\overline{x})}{W\sum _i{(x_i-\overline{x})}^2}$$ (1)

$$C=\frac{(N-1)\sum _i\sum _j{w}_{\mathit{ij}}{\left(x_i-x_j\right)}^2}{2W\sum _i{\left(x_i-\overline{x}\right)}^2}$$ (2)

In the above equations $w_{\mathit{ij}}$ is a spatial weight matrix, N is the number of scans, $x_i$ and $x_j$ are measurements of VF, $\overline{x}$ is the mean VF for a given subject, and W is the sum of all $w_{\mathit{ij}}$. Moran's I ranges from −1 to 1. Values near 0 indicate a random distribution, values near 1 indicate positive spatial correlation, and values near −1 indicate negative correlation. Geary's C ranges from 0 to some value larger than 1. Values significantly larger than 1 indicate negative autocorrelation, while values significantly less than 1 indicate positive correlation (Wrigley et al. 1982; Getis, 1995). The spatial weight matrix w_ij is initially calculated as $w_{\mathit{ij}}=\exp \left(\frac{r_{\mathit{ij}}}{r_c}\right)$ where r_ij is the Euclidean distance between two data points, and r_c is a characteristic radius defined in this study as the average distance between all points within a dataset, as suggested by Chen, 2012. The spatial weight matrix was row normalized so that the sum of each row was equal to 1 (Chen, 2012). Z‐scores were calculated using:

$$Z_I=\frac{I-\frac{I}{N-1}}{{\sigma }_I}$$ (3)

$$Z_C=\frac{C-1}{{\sigma }_C}$$ (4)

With the following definitions as derived in Wrigley et al. (1982):

$${\sigma }_I^2=\frac{N{S}_4-S_3{S}_5}{(N-1)(N-2)(N-3)W^2}-{\left(\frac{-1}{N-1}\right)}^2$$ (5)

$$\begin{array}{c}{\sigma }_C^2=\frac{(N-1)S_1(N^2-3N+3-S_3(N-1))}{W^{2}N(N-2)(N-3)}\\ +\frac{(N^2-3-S_3{(N-1)}^2)}{N(N-2)(N-3)}\\ -\frac{(N-1)S_2(N^2+3N-6-S_3(N^2-N+2))}{4W^{2}N(N-2)(N-3)}\\ \end{array}$$ (6)

$$S_1=\frac{1}{2}\sum _i\sum _j{(w_{\mathit{ij}}+w_{\mathit{ji}})}^2$$ (7)

$$S_2=\sum _i{\left(\sum _j{w}_{\mathit{ij}}+\sum _j{w}_{\mathit{ji}}\right)}^2$$ (8)

$$S_3=\frac{N\sum _i{(x_i-\overline{x})}^4}{{\left(\sum _i{(x_i-\overline{x})}^2\right)}^2}$$ (9)

$$S_4=(N^2-3N+3)S_1-N{S}_2+3W^2$$ (10)

$$S_5=(N^2-N)S_1-2N{S}_2+6W^2$$ (11)

For all statistical analysis, significance was defined as p < .05. Spatial autocorrelation analysis was conducted for each individual hemisphere of each subject. Additionally, data from the left hemisphere were mapped to equivalent locations in the right hemisphere to increase the power of spatial correlation analysis for individual subjects. To create a non‐parameterized combined dataset of all subjects, data were normalized by dividing VF in each brain by the subject mean VF of the brain.

The larger combined dataset allowed a parametric sweep of the characteristic decay parameter r_c. Chen (2012) recommends r_c be set equal to the average distance between all points in a dataset, but there is no unified method. Therefore, to study the effect of the choice of r_c on the results of the autocorrelation analysis, and to provide insight into the natural length scale of AT spatial correlations in the human brain, r_c was varied from 7.5 mm to 150 mm in 20 increments of roughly  7.5 mm. At each increment the weight matrix, I, C, and the corresponding p‐values were recalculated.

3. RESULTS

The average ± SD percent error between the semi‐automated segmentation method and manual segmentation were 0.34% ± 10.4%. There were no overprediction or underprediction trends by the semi‐automated method observed in the study; therefore, the semi‐automated segmentation method was determined to be suitable for the remainder of the analysis.

No significant correlation was found between subject age (r ² = .203, p = .231), weight (r ² = .0334, p = .695) or height (r ² = .492, p = .079). Correlation analyses showed significant negative correlation between VF and the number of days between death and image acquisition in two of the anatomical regions (left superior parietal [r ² = .25, p = .035]) and (left inferior frontal [r ² = .582, p = .046]). On further inspection, a significant negative correlation between VF and imaging sequence order was discovered in Subject 2 (r ² = .692, p = .003). The number of days between death and image acquisition for Subject 4 was nearly double that of any other subject. Subject 2 and Subject 4 also had the longest two times between death and procurement of all subjects. For these reasons, data from Subjects 2 and 4 were omitted from the study.

The average VF measured across the remaining seven brains was 25.56 ± 4.6%. The lowest VF measured at any location was 16.18% and the highest VF measured at any location was 38.75%. Mean VF was significantly higher in Subject 3 (28.71 ± 3.51%) and Subject 5 (29.18 ± 3.66%) compared to the other five subjects (p < .001; Figure 5A). Intra‐brain variance was consistent across all subjects (Figure 5A). Further, whole‐brain variance across subjects was roughly equal to variance within anatomical sub‐regions (Table 2). Specifically, there were no significant differences in VF between hemispheres (Figure 5B). Regional trends were identified using a matched‐paired test that isolated regional effects from subject average VF. These trends were found to persist regardless of hemisphere in almost all subjects. VF in superior regions (26.86 ± 3.95%) was significantly greater than VF in inferior regions by 3.3% [23.57 ± 3.75%; p < .001 (Figure 5C)]. VF was also significantly greater in the frontal lobes (26.83 ± 3.60%) compared to the occipital lobes [24.41 ± 4.71%; p < .001 (Figure 5D)]. Subjects with higher average VF across the entire brain also tended to have higher relative VF within each individual region. VF maps were created for each hemisphere of each subject (Figure 6). In general, spatial maps confirmed the analysis of variance results which showed increased VF in superior and frontal regions. Additionally, measurements of VF tended to resemble closely neighboring measurements, suggesting a positive spatial correlation. Individual spatial autocorrelation statistics for each brain, however, found significant spatial trends with positive correlation in only two individual subjects [Subject 6 and Subject 8 (Table 3)].

Figure 5.

(A) Volume fraction (VF) data for each subject. Subjects 3 and 5 had significantly greater VF than the remaining subjects (p < .001). (B) Hemisphere VF data were not significantly different. (C) VF was significantly greater in superior regions and (D) frontal regions of the brain (** = p < .05 for paired analysis). Error bars denote standard deviations

Table 2.

Volume fraction by regional group and subject

Data grouping	VF values, %
	N *	Mean	SD	p
Frontal	39	26.83	3.6	.0133
Parietal	55	25.56	4.94
Occipital	44	24.41	4.71
Inferior	55	23.57	3.75	<  .0001
Superior	83	26.86	4.64
Left	66	25.23	4.68	.192
Right	72	25.84	4.52
Subject 1	13	24.07	3.71	< .0001
Subject 3	15	28.71	3.51
Subject 5	22	29.18	3.66
Subject 6	23	24.53	4.23
Subject 7	23	24.18	3.63
Subject 8	24	25.84	5.14
Subject 9	18	21.98	3.45

Abbreviation: VF, volume fraction.

^* N is indicative of the number of imaging locations in each grouping. Tests grouped by anatomical region were computed using matched pairs analysis.

Bold font indicates statistical significance.

Figure 6.

Volume fraction (VF) distribution maps across the seven brains. Each region represents the average VF of a single scan location

Table 3.

Moran's I and Geary's C for each brain and for a combined dataset that was composed of volume fraction across all brains, broken up by hemisphere and superimposed onto a single hemisphere map

Subject	IL	p	IR	p	IT	p	CL	p	CR	p	CT	p	, mm
1	−0.52	N/A	−0.05	.285	−0.11	.612	1.02	N/A	0.94	.350	1.01	.951	67
3	−0.23	.376	−0.21	.698	−0.12	.339	1.09	.318	1.06	.515	1.05	.391	54
5	−0.08	.800	−0.10	.948	−0.03	.484	1.00	.938	1.03	.670	1.00	.930	52
6	0.13	<.001	0.03	.022	0.17	<.001	0.77	<.001	0.85	.011	0.80	<.001	53
7	−0.15	.467	−0.03	.197	−0.01	.201	1.02	.757	0.95	.373	0.96	.332	56
8	0.03	.024	−0.03	.272	0.06	<.001	0.93	.173	0.96	.493	0.92	.036	52
9	−0.07	.429	−0.13	.931	−0.06	.921	0.96	.536	1.02	.802	1.01	.801	45
Combined	0.03	<.001	0.06	<.001	0.06	<.001	0.96	.009	0.93	<.001	0.94	<.001	52

I_L, Moran's I statistic for the left hemisphere; I_R, Moran's I statistic for the right hemisphere; C_L, Geary's C statistic for the left hemisphere; C_R, Geary's C statistic for the right hemisphere; r_c, characteristic radius.

N/A indicates the hemisphere had ≤3 data points, so no p‐value was available. Bold font indicates statistical significance.

Bold font indicates statistical significance.

To increase statistical power of spatial autocorrelation statistics, a combined dataset of normalized VF data was created (Figure 7). The combined data exhibited significant positive spatial correlation with both metrics in both hemispheres (Table 3). A parametric sweep of the characteristic radius r_c was performed to evaluate its effect on statistical parameters (Figure 8A). As r_c is the denominator of the exponential weight function w_ij, small values of r_c result in greater exponential decay of spatial weights as distance increases. Larger values of r_c result in a more linear decrease of spatial weight with distance. Spatial correlations were significant in both metrics in both hemispheres for all values of r_c ≥ 20 mm (Figure 8B); however, as r_c increased, Moran's I tended towards 0 and Geary's C tended towards 1, indicating diminishing strength of spatial correlation (Figure 8C,D). These trends indicate that VF measurements were locally clustered and global spatial correlations were weak. These data also suggest small deviations from the r_c values used in this study (45–67 mm) will not alter the statistical conclusions.

Figure 7.

Combined volume fraction (VF) distribution map for all seven brains. Average VF of a single scan location for each brain was normalized by the mean VF of each brain.

Figure 8.

(A) Weight functions for statistical spatial correlations are exponential at low r_c and become linear with larger values of r_c. (B) Spatial statistics become statistically significant at r_c ≥ 20 mm. (C) Moran's I and (D) Geary's C become less positively correlated at larger values of r_c. This indicates the existence of local clustering in arachnoid trabeculae densities

4. DISCUSSION

In this study, we demonstrated the ability to image the human PAC in situ via OCT and quantify the VF of cerebrum AT. We were able to inflate the subarachnoid space with a controlled subarachnoid pressure to mimic in vivo conditions. This allowed visualization of the arachnoid membrane, AT, and subarachnoid vasculature. VF of the AT was quantified using a semi‐automated image segmentation code. Average AT across the entire brain varied between subjects, and the number of subjects included in our study is small due to natural challenges obtaining post‐mortem human subjects. Despite this limitation, however, regional trends occurred throughout most of the seven subjects.

Previous studies of AT in the optic nerve and spinal cord report the density and morphology of trabecular structures change based on anatomical region (Key and Retzius, 1873; Nauta et al. 1983; Rickenbacher et al. 1985; Parkinson, 1991; Liu and Kahn, 1993; Killer et al. 1999, 2003). A detailed review of these studies is provided by Mortazavi et al. (2018). It was not surprising, then, that the VF of AT in this study was also significantly region‐dependent in the cerebrum. We found higher values of VF in superior regions of the brain compared to inferior regions, and higher values of VF in the frontal lobes of the brain compared to the occipital lobes. This trend was consistent regardless of the total average VF in a given subject. While inflation in the superior regions was carried out prior to inferior regions, the order of imaging did not have a significant effect on outcome. Further, left and right hemispheres were imaged sequentially and found not to be significantly different from one another. Therefore, the higher values of VF in the superior regions of the brain are more likely related to increased tethering of the arachnoid membrane to the falx, and increased support for blood vessels within the superior sagittal sinus. Further, increased VF may also act to slow cerebrospinal fluid for improved resorption into the sagittal sinus (Gupta et al. 2010; Saboori and Sadegh, 2011; Ghaffari et al. 2014). The reason for the increased VF of trabeculae in the frontal region compared to the parietal and occipital regions is less clear. Our previous study in piglets found that increased VF of AT reduces brain–skull displacement and cortical strain during traumatic head rotation (Scott and Coats, 2015; Scott et al. 2016). Therefore, one can imagine that the increased tethering in the frontal regions may provide some localized damping of brain motion during activities of daily living and inertial head trauma.

To our knowledge, Hartmann et al. 2019 is the only study to date to report in vivo imaging of the human AT. Imaging of the subarachnoid space in their study was performed intra‐operatively and limited to a single region of interest for each subject in either the frontal or temporal lobes of the brain. They note that the subarachnoid microstructures could still be depicted even after cerebrospinal fluid release. A comparison of a frontal lobe OCT image from their study (Figure 9A) with a frontal lobe OCT image in the present study (Figure 9B) suggests that our approach using in situ imaging in post‐mortem human subjects was successful in capturing high‐resolution images representative of the in vivo subarachnoid microstructures. In order to mimic the in vivo conditions, we inflated the subarachnoid space to physiological pressure levels. Successful inflation of the subarachnoid space required placing the injection needle in a location with existing space between the arachnoid membrane and pia membrane. This restricted our imaging locations to areas near larger sulci or at the intersection of two or more sulci. As a result, most of the AT imaged in our study spanned sulci. However, some imaging locations placed at the terminus of a sulcus allowed for inflation directly above cortical gyri (n = 5). In these locations, the VF of trabeculae were slightly lower than the mean VF of those regions from the same donor. For example, two gyri in Subject 9 had VFs of 18.0% and 19.3%, whereas sulci in the same regions in the same subject had VFs of 19.2% and 19.2%, respectively. However, in Subject 8, a larger reduction in VF was noted in one region. Two gyri measurements were 17.8% and 18.9%. In the same regions for the same subject, the VF measurements in the sulci were 29.2% and 20.6%. This suggests VF along the gyri may be lower than in the sulci, but too few data points were taken in the present study to draw any firm conclusions.

Figure 9.

(A) In situ optical coherence tomography imaging of the human pia‐arachnoid complex from our study shows equal or better resolution of subarachnoid structures when compared to (B) intra‐operative in vivo imaging. Image (B) modified from Hartman et al. 2019. Reprinted by permission of Sage Publications, Ltd

In vivo, the distance between the pia and arachnoid membrane is constrained by the presence of the skull. To image the PAC with OCT, removal of the skull is necessary. This, combined with repressurization of the subarachnoid space may cause the arachnoid membrane to move further from the pia than the in vivo configuration and artificially decrease measures of AT VF; however, in this study, all imaging locations were pressurized to the same conditions so comparisons between locations are still valid. Due to the physical limitations of OCT, image depth was limited to 1.64 mm. Shadowing and light attenuation further reduced imaging to 0.750 mm. While imaging the full depth of sulci was not possible, the width of sulci significantly narrows with depth, resulting in fewer structures at the deeper interfaces. For this reason, we believe the regions of interest used in this study capture trabecular structures representative of the bulk of the connective tissues between the brain and the skull in the sulci. Imaging to greater depths may be possible with advances in OCT technology, but would still be challenging given the limitations of light penetration through the arachnoid mater.

We found significant positive spatial autocorrelation of VF of the AT in two of the seven subjects, and in the overall combined dataset. Spatial autocorrelation findings were similar using both Moran's I and Geary's C, demonstrating that results were not dependent on the precise statistical formulation chosen for analysis. We believe many of the individual brain spatial analyses were not significant because of the limited number of imaging locations we were able to obtain in each brain. Once each cranium was thawed, the time window for imaging before significant tissue degradation was roughly 8 h. The process of positioning the imaging and inflation systems was time‐intensive, thus limiting the number of scans per subject to an average of 18. Observation of the individualized spatial maps of the brains (Figure 6) suggested positive clustering of similar densities. Therefore, we combined the individual brains into a single dataset by normalizing VFs within a brain by the average VF of that brain. Once combined, the significant positive spatial correlation was apparent. This positive spatial clustering results in a heterogeneous distribution of AT across the brain and likely affects the magnitude and distribution of brain deformation during head trauma. Using experimental and computational pig models of TBI, Scott and Coats found increased localization of deformation and force on the surface of the brain when the spatial distribution of AT was incorporated into the predictive models (Scott et al. 2016). In addition, the improved localization increased the sensitivity/specificity of their predictions of extra‐axial hemorrhage from 80%/85% to 94%/100%. The regional dependencies and positive spatial correlations observed in this study of human AT are likely to lead to similar improvements in human computational models of TBI. Further, the spatial clustering may be suggestive of regional vulnerabilities to trauma, both at the cortical surface and in deeper areas of white and gray matter. For example, localized variability in AT VF could lead to stress concentrations at the cortical surface during brain motion, increasing the susceptibility to subarachnoid hemorrhage. An uneven distribution of AT tethers between the brain and skull may also contribute to the directional dependence of TBI severity often reported in human and animal TBI studies (Gennarelli et al. 1982; Eucker et al. 2011; Sullivan et al. 2015). Further investigation into the relationship of AT VF with brain–skull mechanics is necessary to quantify and better understand the influence of the brain–skull interface on TBI severity and variability.

In conclusion, imaging of the human PAC with OCT is an effective tool for characterizing spatial variations of AT VF. Trends of increasing VF from inferior to superior and occipital to frontal have been identified, and significant positive spatial correlations were found when all brains were combined into a single dataset. Based on previous studies by our group, these trends influence brain deformation patterns and locations of injury during traumatic events. Intra‐subject variability suggests that average AT VF does differ from person to person, but the regional trends are persistent across all subjects. To better understand the effect of these microstructures on brain mechanics following head impact, further investigation of the PAC through material characterization is needed. Incorporation of the spatial heterogeneity of these microstructures across the brain may be necessary to improve computational model predictions of TBI and to evaluate the effects of dissection of subarachnoid trabeculae during neurosurgery.

Benko N, Luke E, Alsanea Y, Coats B. Spatial distribution of human arachnoid trabeculae. J. Anat. 2020;237:275–284. 10.1111/joa.13186