Estimation of skull table thickness with clinical CT and validation with microCT

Abstract

Brain injuries resulting from motor vehicle crashes (MVC) are extremely common yet the details of the mechanism of injury remain to be well characterized. Skull deformation is believed to be a contributing factor to some types of traumatic brain injury (TBI). Understanding biomechanical contributors to skull deformation would provide further insight into the mechanism of head injury resulting from blunt trauma. In particular, skull thickness is thought be a very important factor governing deformation of the skull and its propensity for fracture. Current computed tomography (CT) technology is limited in its ability to accurately measure cortical thickness using standard techniques. A method to evaluate cortical thickness using cortical density measured from CT data has been developed previously. This effort validates this technique for measurement of skull table thickness in clinical head CT scans using two postmortem human specimens. Bone samples were harvested from the skulls of two cadavers and scanned with microCT to evaluate the accuracy of the estimated cortical thickness measured from clinical CT. Clinical scans were collected at 0.488 and 0.625 mm in plane resolution with 0.625 mm thickness. The overall cortical thickness error was determined to be 0.078 ± 0.58 mm for cortical samples thinner than 4 mm. It was determined that 91.3% of these differences fell within the scanner resolution. Color maps of clinical CT thickness estimations are comparable to color maps of microCT thickness measurements, indicating good quantitative agreement. These data confirm that the cortical density algorithm successfully estimates skull table thickness from clinical CT scans. The application of this technique to clinical CT scans enables evaluation of cortical thickness in population-based studies.

Introduction

It is estimated there are 1.7 million cases of traumatic brain injuries (TBI) in the USA each year (Coronado et al. 2011). TBI contributed to roughly 5% of all the injuries seen by emergency departments in 2002–2006, but accounted for 30% of all injury-related deaths. Falls and motor vehicle crashes (MVCs) are the number one and two contributors to TBI. The TBIs from MVCs, however, resulted in the largest number of TBI-related deaths (31.8%) (Faul et al. 2010). Although studies have been conducted analyzing TBI from blunt loading conditions, more information is needed to understand the biomechanical contributors to the type and severity of TBI (Yoganandan et al. 2007, 2010; Urban et al. 2012). One important contributor is thought to be skull deformation; therefore characterizing skull thickness is an important step toward understanding skull deformation and its role in TBI. Large-scale skull cortical thickness quantification could also provide further insight into population variability and identify potential covariates for cortical thickness changes within a population.

The skull is a complex component of the skeletal system whose main function is to protect the brain. It is comprised of 22 bones, eight of which form the neurocranium and are connected by synarthrodial joints called sutures. Most of these cranial bones are categorized as flat bones and can be identified by their layered bone structure where a cancellous bone layer, called diploë, is sandwiched between layers of dense cortical bone (cortex). These cortical layers can be identified as the inner and outer tables of the skull (Saladin, 2007). Previous studies have utilized cadavers and primates to evaluate the physical and mechanical properties of the skull (McElhaney et al. 1970; Hubbard, 1971; Hubbard et al. 1971; Jaslow, 1990; Peterson & Dechow, 2003). These studies have found the flexural properties of the skull to be highly dependent on skull thickness. Additionally, Shatsky et al. (1974) and Nusholtz et al. (1984) have reported reversible skull deformations from blunt impacts in the absence of skull fracture, leading to an increased propensity for brain injury (Shatsky et al. 1974; Nusholtz et al. 1984). The physical deformations are believed to contribute to the occurrence and severity of brain injury. Skull flexure is also thought to play a critical role in the mechanical load on the brain from blast impact conditions where the pressure wave generates flexural ripples in the skull (Moss et al. 2009).

The thickness of the layers of the skull, as well as bone mechanical properties, microstructure, and geometry determine the deformation of the skull during an impact (Ruan & Prasad, 2001; Licata, 2009). Through finite element analysis, Ruan & Prasad (2001) demonstrated that increased skull thickness enabled the brain to withstand increased peak accelerations before reaching a known concussive shear stress threshold of 22 kPa. Previous cadaveric work has been performed to quantify the mechanical and physical characteristics of the skull through various loading conditions. These include mechanical characteristics such as ultimate stress, ultimate strain, and modulus of elasticity, as well as physical characteristics such as cortical thickness and bone mineral density (McElhaney et al. 1970; Wood, 1971; Peterson & Dechow, 2003). These data have been collected from both full skull thickness samples containing cortical tables and the diploe, as well as the isolated outer table. Additionally, studies have been performed to characterize flexural stiffness and strength from transverse loading of the cranial bones and the sutures binding them (Hubbard, 1971; Hubbard et al. 1971; Jaslow, 1990). More recently, the effect these physical properties, particularly skull thickness, have on dynamic head response due to blunt loading has been evaluated using finite element analysis. A series of blunt loading simulations applied with a linear impactor to a skull of varied predetermined skull thickness demonstrated a direct correlation between increased full thickness and the peak acceleration the head could withstand before reaching a shear stress threshold (Ruan & Prasad, 2001).

Despite the important role the skull plays in protecting the brain, there is a dearth of information regarding the variability of its physical properties. Previous studies evaluating skull thickness were limited by the need to physically measure samples from cadavers or primates (McElhaney et al. 1970; Hubbard, 1971; Hubbard et al. 1971; Shatsky et al. 1974; Nusholtz et al. 1984; Jaslow, 1990; Saladin, 2007; Yoganandan et al. 2007;). It would be beneficial and more informative to have a method to measure cortical and full skull thickness throughout the skull without the requirement of obtaining physical samples. A method utilizing medical images, particularly clinical computed tomography (CT) head scans, to determine thickness measurements would enable the evaluation of a significantly larger sample size. This would allow the study of population-based variations in skull thickness due to age, sex, and a variety of disease conditions. This expansion is possible due to the ease and ubiquity of clinical CT data collection. Such an approach would also allow for uniform sampling throughout the skull instead of at specified test sites. However, cortical thickness of bone is difficult to quantify due to the resolution limitation of clinical CT scans. Thickness measurements of structures thinner than 2.5 mm are overestimated using the standard full width half max (FWHM) techniques. The FWHM technique calculates the thickness as the distance between the two extreme values of an intensity profile line when the radiodensity (Hounsfield unit) is equal to half the change between the maximum and minimum values. (Newman et al. 1998; Dougherty & Newman, 1999; Prevrhal et al. 2003; Poole et al. 2012). In thin structures, the blur represented by the imaging system's point spread function (PSF) dominates the reconstructed image, resulting in blurry boundaries of the cortical bone. Recently, Treece et al. (2010) presented an algorithm to estimate cortical thickness of thin structures that improves upon this limitation. The algorithm developed by Treece et al. (2010) has been developed and validated for the femur and utilizes cortical density to estimate thickness (Treece et al. 2010, 2012; Poole et al. 2012). Although this method is valuable in estimating cortical thickness of the femur, it has not been validated for other bones, including the skull. The objective of this study is to apply this cortical density method to the skull to validate thickness measurements from clinical CT data of the cranial vault. Application of these methods may be extended to more accurately interpret bone thickness throughout the skull for population-based studies, particularly those which analyze cortical thickness variation from developmental changes in the pediatric population, as well as osteoporosis in the elderly.

Methods

Two male cadavers of ages 49 (skull A) and 56 (skull B) were obtained from the Whole Body Donation Program at the Wake Forest School of Medicine to evaluate the cortical and full thickness of the skull. Clinical head CT scans were collected with an in-plane resolution ranging from 0.488 to 0.625 mm with a slice thickness of 0.625 mm for both cadavers. The scans were visually inspected by a neuroradiologist to confirm normal bone density and geometry. After the clinical CT was obtained, the skulls were removed from the bodies and all soft tissue was removed from the skulls. The skulls were wrapped in gauze and saline, and placed in a freezer. The fresh frozen skulls were thawed to room temperature and kept moist to harvest 3-cm-diameter cylindrical samples using a craniotome. A notch was placed on the posterior or inferior region on each sample to identify sample orientation. Ten samples were taken from the frontal (2), parietal (2), occipital (4), and temporal (2) bones between the two skulls (Fig. 1). The samples from the occipital bones were harvested superior to the occipital protuberance as well as near the foramen magnum. Sampled locations were carefully selected to be contained within the bounds of each bone.

Fig. 1.

(A) Skull samples were collected using a craniotome. (B) Sample locations to be validated from the occipital bone. (C) Sample locations to be validated from the parietal, temporal, and frontal bone.

The bone samples were scanned using a GE CT-120 microCT scanner (Biomedical Research Imaging Center, University of North Carolina at Chapel Hill) to acquire high resolution images. The scans were collected at 25-micron resolution and reconstructed at 50-micron isotropic resolution. The high resolution bone sample scans allowed for highly accurate boundary establishment, differentiating between air, cortical bone, and trabecular bone. The FWHM technique applied to high resolution data is understood to be a good, unbiased estimator of thickness when the actual cortical thickness is sufficiently larger than the scan resolution, as is the case for the tables of the skull (Prevrhal et al. 1999). This enabled the establishment of ‘ground truth’ measurements for later comparison. The contrast between the intensity profile of both a high (microCT) and low (clinical CT) resolution image is shown in Fig. 2. To address the spatial localization differences between the low resolution clinical CT and high resolution microCT, the microCT images were blurred parallel to the cortical tables to match the clinical CT resolution in this dimension (Treece et al. 2012). Blurring the high resolution data parallel to the cortical table created spatially averaged thickness values. These averaged values removed the potential for variability in particular thickness measurements occurring from an irregular skull surface and allowed for a more meaningful comparison with clinical data. This improved the estimation localization of the thickness measurement without compromising the thickness estimation accuracy.

Fig. 2.

(A) An image slice of a parietal bone microCT sample with an intensity profile line drawn from the outer through the inner table. (B) A sample of the intensity profile of the microCT sample. (C) An image slice from the clinical CT of the parietal bone with an intensity profile line drawn from the outer through the inner table. (D) A sample of the intensity profile in a similar location on the skull from the clinical CT image.

The cortical density method developed by Treece et al. (2010) was applied to the clinical head CT scans (Treece et al. 2010, 2012). This method produces thickness measurements by optimizing the cortical density measurement from the scan and factoring this into a piecewise defined Heaviside step function derived from the convolution of both in-plane and out-of-plane PSFs. The in-plane PSF is the spatial resolution blur and is modeled using a Gaussian curve and the out-of-plane PSF is the error associated with the orientation of the cortical bone within each imaging plane (Treece et al. 2010, 2012). The representative cortical density for each CT scan was determined through the collection of hundreds of density measurements of the soft tissue, cortical bone, and trabecular bone throughout the skull and optimized using the Levenberg–Marquardt method, an interpolation method used in non-linear least squares problems (More, 1978). The thickness measurements collected from the blurred microCT images were directly compared with the estimated thickness measurements of the clinical CT. Thickness measurements for both the microCT samples as well as the clinical CT of the skull were associated with point clouds located on the inner and outer skull surfaces. A normal unit vector indicating the normal to the skull surface contour was also established at each landmark in the point cloud.

Three-dimensional (3D) reconstructions of the clinical CT scans for the cadaver skulls and microCT samples were rendered using mimics (v 14.0 Materialise, Leuven, Belgium). The location sampled for microCT was identified on the 3D reconstruction of the skull. Alignment was performed in geomagic studio (v 12.1.0 Geomagic, Research Triangle Park, NC, USA) by manually translating and rotating the microCT sample to the 3D reconstruction of the skull from the clinical CT. The sample locations were identified for alignment through photographs, anatomical landmarks, and surface contours. Alignment was not achieved for three of the 10 samples due to difficulty in precise alignment because of the anatomy. Thus, these three samples were excluded from the validation study (one temporal bone and two occipital bone samples). After alignment, the 3D reconstruction of the skull was converted to a point cloud (Fig. 3A). For each microCT sample, the skull point cloud was reduced to a subsample containing only points in contact with each aligned microCT sample as shown in Fig. 3B. Thickness measurements at these subsampled clinical CT points were compared with the nearest true thickness measurements in the microCT sample. Validation results were evaluated qualitatively from thickness color maps and quantitatively by determining the estimation error as the difference between the microCT measurements and clinical CT thickness measurements. Additionally, clinical CT thickness results were regressed against the microCT thickness and the resulting slopes, R², and the root mean squared error (RMSE) values were compared.

Fig. 3.

(A) 3D point cloud of the skull with aligned parietal bone microCT sample. (B) Sub-selected points from the clinical CT with the aligned microCT.

Results

Each microCT sample was aligned to the clinical CT to observe the thickness results. The high resolution thickness measurements for the seven aligned skull samples were determined using the FWHM technique on the microCT images and are reported in Table 1. The new cortical density method was applied to both the inner and outer tables of the seven aligned samples from the frontal, occipital, parietal, and temporal bones of two cadaver skulls. The accuracy of the cortical density method was compared qualitatively by evaluating the measured thickness values as color maps (Fig. 4).

Table 1.

High resolution thickness values measured with the FWHM technique and estimated thickness values measured with the cortical density method from microCT scans, reported as mean ± standard deviation

	Inner table		Outer table
Bone	High resolution thickness (mm)	Estimated thickness (mm)	High resolution thickness (mm)	Estimated thickness (mm)
Frontal A	1.05 ± 0.362	1.09 ± 0.048	1.76 ± 0.385	1.73 ± 0.089
Parietal A	0.62 ± 0.179	0.64 ± 0.079	1.05 ± 0.342	1.11 ± 0.053
Occipital A1	0.76 ± 0.408	0.77 ± 0.169	0.70 ± 0.305	0.62 ± 0.094
Occipital A2	0.66 ± 0.283	0.55 ± 0.029	1.31 ± 0.378	1.01 ± 0.084
Frontal B	2.58 ± 0.443	2.34 ± 0.081	3.75 ± 0.427	3.79 ± 0.189
Parietal B	1.68 ± 0.678	1.10 ± 0.437	1.42 ± 0.441	1.28 ± 0.143
Temporal B	2.78 ± 0.823	3.02 ± 0.785	2.83 ± 0.770	2.93 ± 0.671

Fig. 4.

Cortical thickness color maps for the outer table of the two cadaveric skulls A and B using the cortical density method with microCT high resolution thickness of samples overlaid.

For each of the seven samples, an average of 400 thickness measurements were taken and compared between the clinical CT and microCT. The estimated thickness measurements from clinical CT were regressed against the high resolution thickness measurements from microCT (Fig. 5). Four measurements were excluded because the microCT thickness was determined to be several millimeters thicker than the average sample thickness and likely included the diploë in the measurement. The line of best fit was constrained to the origin resulting in a slope of 0.916 with an R² value of 0.725.

Fig. 5.

Scatterplot of all cortical thickness measurements. The line of best fit is shown by the solid line and the 95% confidence interval of the data is bounded by the hashed line. The line of best fit is constrained to the origin.

Thickness deviations of the estimated thickness values from the high resolution thickness measurements were used to quantify the accuracy of the cortical density method. The mean and standard deviations of the difference between the high resolution thickness values and the estimated thickness values are shown for each bone in Table 2. Mean estimation error ranged from −0.096 mm (overestimation) to 0.305 mm (underestimation). The right-most column shows the standard deviation of the difference in thickness of the microCT minus clinical CT. The distributions of the differences were all normal based on a goodness of fit test with P < 0.01, narrow, and centered on average at 0.078 mm difference. The inner and outer table color maps of four samples are shown in Fig. 6.

Table 2.

Error in the estimated thickness values with the cortical density method is presented as the mean and standard deviation of the high resolution thickness minus the estimated thickness

Bone	Mean estimation error (mm)	Standard deviation of estimation error (mm)
Frontal A	0.029	0.372
Parietal A	−0.060	0.347
Occipital A1	0.079	0.287
Occipital A2	0.305	0.375
Frontal B	−0.049	0.480
Parietal B	0.141	0.425
Temporal B	−0.096	0.834
All	0.078	0.538

Fig. 6.

Thickness color maps for the inner and outer table of four bone samples for the microCT and clinical CT from left to right.

Discussion

Cortical thickness was evaluated on two cadaver skulls with both a high resolution microCT FWHM measurement and a cortical density-based measurement on the matched clinical CT. Average thickness values of the microCT samples were determined to be below 3 mm with the exception of the outer table of one frontal bone sample and part of the temporal bone. A direct thickness comparison between these results with other literature cannot be made directly due to variability in age, sample location, and other uncontrolled medical factors; however, the results were within one standard deviation of values reported in literature (Table 3) (Hodgson et al. 1970; Ruan & Prasad, 2001; Peterson & Dechow, 2002). Thin cortical layers of the skull require the use of an improved method to overcome the known error associated with FWHM technique on structures thinner than 3 mm (Newman et al. 1998; Dougherty & Newman, 1999; Prevrhal et al. 2003; Poole et al. 2012). Data presented in this study demonstrate that cortical thickness measurements of the main flat bones of the cranial vault can be evaluated more accurately from clinical CT scans using a cortical density-based approach compared with traditional methods (Treece et al. 2010, 2012).

Table 3.

Measured outer table cortical thickness and standard deviation compared with literature values (mm)

Bone	Current microCT data	Peterson & Dechow (2002)	Ruan & Prasad (2001)	Hodgson et al. (1970)
Frontal	2.26 ± 0.41	2.4 ± 0.5	1.53 ± 0.45	1.959 ± 0.46
Parietal	1.24 ± 0.39	2.4 ± 0.7	N/A	N/A
Temporal	2.83 ± 0.77	2.3 ± 0.8	N/A	N/A
Occipital	1.31 ± 0.38	2.9 ± 1.4	N/A	N/A

Differences in measured thickness values may be due to variability in sample location and subject age.

Temporal bone thickness values were collected from the squamous region of this bone, where it is known to contain only cortical bone with no diploic layer. For this reason, table thickness values were similar because each measurement was over the full thickness of the cortical bone, making this bone appear thicker than other samples (Peterson & Dechow, 2003). The results from the thickness deviation analysis between the high (microCT) and low (clinical CT) resolution thickness measurements indicate an overall error of 0.078 mm (± 0.58 mm) where the cortical density-based method slightly underestimates the thickness values measured using microCT. Moreover, 91.3% of the observed error fell within the scanner resolution of the clinical CT. For comparison, a larger sample of 16 cadaveric femurs were evaluated by Treece et al. (2010) and presented an overall error of −0.01 mm (± 0.58 mm) using the cortical density method (Treece et al. 2010). To explain the slightly greater underestimation in the current study, the data were evaluated with respect to the predicted error presented in Treece et al. (2012). The cortical density method was predicted to underestimate sample thickness by less than 10% (‘slight’ underestimation) for structures between 0.9 and 3 mm (Treece et al. 2012). Nearly 60% of the high resolution thickness measurements fell within this ‘slight’ range and could explain the small deviations between this method applied to the skull and the work previously presented from femurs. Additionally, underestimation of the clinical CT data in thinner bones likely stemmed from an overestimation of the optimized cortical density value for each scan used within the cortical density method algorithms. Thicker cortical bone led to a more accurate optimized cortical density which was more favorable to measurements of the femoral shaft than is likely for the thinner tables of the skull (Treece et al. 2012).

To further quantify the validity of the cortical density method on the skull, estimated thickness values were regressed against the high resolution thickness values as shown in Fig. 5. Analysis indicated a slope of 0.916 when constrained to the origin. In a perfect model the slope of such a regression would be 1 and would intersect the origin. The RMSE was compared for the regressions that were constrained to the origin and constrained to the origin with a slope of 1. The resulting errors were 0.525 and 0.682 mm, respectively. The RMSE values can be evaluated as the standard deviation determined through linear regression and therefore are compared with the standard deviations seen in the thickness and difference in thickness results. The RMSE remained lower than some of the standard deviations seen within the thickness and difference in thickness results in this study as well as those reported by Treece et al. (2010). The results of the quantitative comparisons indicated good accuracy with this method. The cortical density method used in this study provides a more accurate thickness estimation than what would be calculated using the FWHM approach. This method enables a reasonable estimation of cortical thickness from clinical CT scans. The ability to determine thickness from such images allows for the analysis of cortical thickness values from a much broader spectrum, beyond cadaveric data. An expanded dataset of thickness values will enable the pursuit of numerous anatomical variation studies to further understand the changes and variability of cortical thickness in the skull.

The validation performed was limited by scanner resolution, sample size, sample alignment, and limitations present in the cortical density method. Higher resolution images from clinical CT scans would further improve the ability to discern cortical thickness and minimize the issue of blur characterized by the PSF (Prevrhal et al. 2003). This, however, would not be a feasible approach because higher resolution CT scans are not permitted for living patient use due to the increased radiation exposure. However, further research could be done using postmortem CT scans routinely gathered as an adjunct to mortuary autopsies. An increased number of cadaveric subjects and samples from each subject would have increased the power associated with this validation. Manual alignment between the microCT and the clinical CT of the samples could also have contributed to some error observed in thickness estimation. Lastly, the cortical density method requires all sampling profile lines to be of a set line length, where this length is selected to be at least three times the expected cortical thickness (Treece et al. 2010). Anticipating cortical thickness values of less than 4 mm, a line length of 12 mm was used. This set length could have an effect on thickness measurements in the few regions where the cortical bone was thicker than 4 mm.

Conclusion

The objective of this work was to validate the cortical density method algorithm for the evaluation of skull cortical thickness. The cortical thickness of two cadaveric skulls was estimated using a cortical density method applied to clinical CT scans. The accuracy of the thickness estimations was compared with those of microCT samples and validated for the cranial vault. This method, when applied to the skull, had results comparable to those previously expressed in literature. An average cortical thickness error of 0.078 ± 0.58 mm was observed with 91.3% of the error contained within the clinical CT scanner resolution, which is a significant improvement from the standard FWHM technique. With this method validated for the skull, there are many more opportunities to evaluate changes in skull cortical thickness including quantifying cortical thickness in adult and pediatric populations. Identifying population-specific variability may help shed light on the biomechanical and anatomical basis for traumatic brain injury.