ARL-TR- 7962 ● MAR 2017

US Army Research Laboratory

Morphological Characterization of the Frontal 

and Parietal Bones of the Human Skull

by Stephen L Alexander

SURVICE Engineering Company, Belcamp, MD

Karin Rafaels 

Survivability/Lethality Analysis Directorate, ARL

C Allan Gunnarsson and Tusit Weerasooriya

Weapons and Materials Research Directorate, ARL

Approved for public release; distribution unlimited.
NOTICES

Disclaimers

The findings in this report are not to be construed as an official Department of the 

Army position unless so designated by other authorized documents.

Citation of manufacturer’s or trade names does not constitute an official 

endorsement or approval of the use thereof.

Destroy this report when it is no longer needed. Do not return it to the originator.
ARL-TR- 7962 ● MAR 2017

US Army Research Laboratory

Morphological Characterization of the Frontal 

and Parietal Bones of the Human Skull

by Stephen L Alexander

SURVICE Engineering Company, Belcamp, MD

Karin Rafaels 

Survivability/Lethality Analysis Directorate, ARL

C Allan Gunnarsson and Tusit Weerasooriya

Weapons and Materials Research Directorate, ARL

Approved for public release; distribution unlimited.
ii

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid 

OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

March 2017

2. REPORT TYPE

Technical Report

3. DATES COVERED (From - To)

October 2015–December 2016

4. TITLE AND SUBTITLE

Morphological Characterization of the Frontal and Parietal Bones of the Human Skull

5a. CONTRACT NUMBER

W911QX-16-D-0014

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Stephen L Alexander, Karin Rafaels, C Allen Gunnarsson, Tusit Weerasooriya

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

US Army Research Laboratory

ATTN: RDRL-WMP-B

Aberdeen Proving Ground, MD 21005-5066

8. PERFORMING ORGANIZATION REPORT NUMBER

ARL-TR-7962

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)

11. SPONSOR/MONITOR'S REPORT NUMBER(S)

12. DISTRIBUTION/AVAILABILITY STATEMENT

Approved for public release; distribution unlimited.

13. SUPPLEMENTARY NOTES

14. ABSTRACT

Bone specimens were collected from the frontal and parietal bones of 4 adult, human skulls. The microstructure was characterized using 

micro-tomography (CT) at about 6-μm resolution to map the change of porosity as a function of the depth, P(d), from the inner surface 

nearest to the brain to the outer surface nearest to the skin. A quantifiable method was developed using the measured P(d) to objectively 

distinguish between the 3 layers of the skull: the outer table, diploë, and inner table. The thickness and average porosity of each of the 

layers were then calculated from the measured porosity distributions. A Gaussian function was used to represent the P(d) curves. The 

Gaussian parameters were identified through least squares, and the values indicated the peak porosity and the relative thickness of the 

diploë. The results for total thickness, the thickness and average porosity of each of the layers, and the Gaussian parameters were compared 

between the 2 bone types (frontal and parietal), while accounting for skull-to-skull variability. The primary differences were that parietal 

bones generally had a larger diploë accompanied by a thinner inner table. The arrangement of the porous vesicular structure within the outer 

table was also obtained with micro-CT scans with longer scan times, using enhanced parameters for higher resolution and lower noise in the 

images. From these scans, the porous structure of the bone appeared to be randomly arranged in the transverse plane, compared to the 

porous structure of the human femur, which is aligned in the loading direction. 

15. SUBJECT TERMS

human skull, skull morphology, micro-CT, skull mechanics, micro-tomography 

16. SECURITY CLASSIFICATION OF:

17. LIMITATION

 OF

 ABSTRACT

Unclassified

18. NUMBER

 OF 

 PAGES

78

19a. NAME OF RESPONSIBLE PERSON

Carey Gunnarsson

a. REPORT

Unclassified

b. ABSTRACT

Unclassified

c. THIS PAGE

Unclassified

19b. TELEPHONE NUMBER (Include area code)

410.306.0990

Standard Form 298 (Rev. 8/98)

Prescribed by ANSI Std. Z39.18
Approved for public release; distribution unlimited.

iii

Contents

List of Figures v

List of Tables viii

Preface ix

Acknowledgments x

1. Introduction 1

2. Methods 3

2.1 Specimen Extraction 3

2.2 Microcomputed Tomography 7

2.3 Summary of Terminology Used 9

2.4 Statistical Analysis 10

3. Results 10

3.1 Representative Images from Each Extraction Grid 10

3.2 Outer Table, Diploë, and Inner Table Layer Identification and 

Thickness Measurements 14

3.3 Porosity of Each Layer 20

3.4 Fitting Gaussian Functions to the Measured Porosity-Depth Profiles 22

3.5 Pore Orientation 27

4. Discussion 30

4.1 Frontal-Parietal Comparison in the Context of Skull-to-Skull 

Variability 32

4.2 Porous Space in the Outer Table 34

4.3 Assumptions, Limitations, and Sources of Error Associated with 

Quantitative Porosity Assessment 35

4.3.1 Measurement Error: Scanning Parameters and Image 

Postprocessing 35
Approved for public release; distribution unlimited.

iv

4.3.2 Approximating the Porosity Variation with a Gaussian 

Function 36

4.3.3 Method for Layer Identification 37

5. Conclusions 38

6. References 39

Appendix A. Analysis of Error Associated with Scanning Parameters and 

Postprocessing Steps 43

Appendix B. Box Plots of Results for the Gaussian Coefficients 

(A, B, and C) 47

Appendix C. Summary Data for the Thickness Parameters 51

Appendix D. Sufficiency of Cross-Sectional Dimensions to Provide 

Representative Results 58

List of Symbols, Acronyms, and Abbreviations 64

Distribution List 65
Approved for public release; distribution unlimited.

v

List of Figures

Fig. 1 Schematic of the human skull, viewed from above. The locations of 

the specimen grids are shown on the frontal and parietal bones. 

Distances from the grid centers to the coronal suture and midline 

(sagittal suture) are depicted by C and S, respectively. Note: the 

parietal grid is shown on the right parietal bone only as an example. 

For some skulls, the parietal grid originated from the left parietal bone, 

as listed in Table 1. ................................................................................4

Fig. 2 BB numbering scheme for each specimen extraction grid from each 

skull. Markings outside the grid indicate in-situ orientation: superior 

(S, toward the top of the skull), inferior (I, toward the base of the 

skull), anterior (A, toward the front of the skull), posterior (P, toward 

the rear of the skull), right (R), and left (L). ..........................................6

Fig. 3 Example of the rotation applied to the image stack in DataViewer such 

that the normal at the center of the outer table was in the vertical 

direction. Images shown are through-thickness and are from Specimen 

04-03. .....................................................................................................9

Fig. 4 Through-thickness image of Specimen 04-02 (a), and cross-sectional 

images of the outer table (b), diploë (c), and inner table (d) ...............11

Fig. 5 Representative images from each bone section. Through-thickness 

images are on the left and cross-sectional images of the diploë are on 

the right. The bones are (a) 04-14, (b) 06-06, and (c) 06-26. .............12

Fig. 6 Representative images from each bone section. Through-thickness 

images are on the left and cross-sectional images of the diploë are on 

the right. The bones are (d) 07-10, (e) 10-04, and (f) 10-17...............13

Fig. 7 Porosity as a function of depth, P(d), for Specimen 04-03..................14

Fig. 8 Procedure to determine the outer table, diploë, and inner table 

thicknesses from the porosity-depth profile. This example uses the 

porosity-depth profile of Specimen 04-03 (Fig. 7). .............................15

Fig. 9 Average values of the overall skull thickness, t...................................16

Fig. 10 Average values of the thickness percentage of the outer table, tttt ......16

Fig. 11 Average values of the thickness percentage of the diploë, tttt.............17

Fig. 12 Average values of the thickness percentage of the inner table, tttt.......18

Fig. 13 Layer thickness percentages averaged over each skull (left) and bone 

type (right). Standard deviations are shown in Fig. 14.......................19

Fig. 14 Layer thickness percentages (shown in Fig. 13) with standard 

deviations. Absolute values in millimeters are shown in Appendix C, 

Figure C-1. ...........................................................................................19

Fig. 15 Porosity of each layer, averaged by skull of origin (left) and by bone 

type (right) ...........................................................................................22

Fig. 16 Porosity of each layer, averaged by extraction grid.............................22
Approved for public release; distribution unlimited.

vi

Fig. 17 Porosity profile of Specimen 04-03 (Fig. 7) with the Gaussian fit, 

PPPP . The 3 Gaussian parameters are shown schematically. For this 

example, results were A = 82%, B = 47%, C = 28%, and R2 = 0.96. .23

Fig. 18 Average Gaussian fits of the porosity profiles. The solid line shows 

the Gaussian function (Eq. 1) derived using the mean parameters. The 

shaded area represents corridors of ±σ of the Gaussian function........24

Fig. 19 Average values of the Gaussian coefficient A, related to the peak 

porosity (Fig. 17) .................................................................................25

Fig. 20 Average values of the Gaussian coefficient B, which is the thickness 

percentage at which the porosity peaks (Fig. 17) ................................26

Fig. 21 Average values of the Gaussian coefficient C, related to the spread of 

the porosity distribution (Fig. 17)........................................................27

Fig. 22 Digitally coloring the pores in the outer table of Specimen 10-02 (from 

frontal bone). (a) The entire specimen. (b) The outer table selection, 

with thickness tt00 ∗ = 1.42 mm. (c) The pores in the outer table. (d) 

The pores in the outer table, with digital color added. (e) A top-down 

view of the pores, looking down on the outer surface of the specimen. 

Average pore diameter = 90 μm. .........................................................29

Fig. 23 Pores within the outer table of Specimen 04-12 (from parietal bone). 

The side view (a) and top-down view (b), are analogous to Fig. 22 (d) 

and (e). Outer table thickness, tt ∗ = 1.11 mm. Average pore 

diameter = 86 μm. ................................................................................30

Fig. 24 Porous space within the outer cortical region of a human femoral bone 

specimen, visualized with micro-CT. The pores are shown as grey 

objects. .................................................................................................35

Fig. 25 Through-thickness image of Specimen 06-07. For this specimen, the 

porosity-depth profile could not be described by the Gaussian fit. A 

secondary porous region, in addition to the diploë, is evident near the 

inner surface (bottom of the figure). ....................................................37

Fig. A-1 Porosity-depth profile from each scan (top) and the Gaussian fits 

(bottom)................................................................................................45

Fig. B-1 Box plots of the Gaussian coefficient A...............................................48

Fig. B-2 Box plots of the Gaussian coefficient B...............................................49

Fig. B-3 Box plots of the Gaussian coefficient C ..............................................50

Fig. C-1 Absolute thickness measurements (mm) of each of the layers for the 

frontal bone (left) and parietal bone (right) .........................................53

Fig. C-2 Box plots of the total skull thickness (t) in mm...................................54

Fig. C-3 Box plots of the thickness percentage of the outer table (tttt)..............55

Fig. C-4 Box plots of the thickness percentage of the diploë (tttt).....................56

Fig. C-5 Box plots of the thickness percentage of the inner table (tttt)...............57
Approved for public release; distribution unlimited.

vii

Fig. D-1 Porosity convergence (left) for a cross-sectional image (right) from the 

diploë of Specimen 04-14 ....................................................................61

Fig. D-2 Porosity convergence (left) for a cross-sectional image (right) from the 

diploë of Specimen 04-16 ....................................................................61

Fig. D-3 Porosity convergence (left) for a cross-sectional image (right) from the 

diploë of Specimen 04-17 ....................................................................61

Fig. D-4 Porosity convergence (left) for a cross-sectional image (right) from the 

diploë of Specimen 10-14 ....................................................................62

Fig. D-5 Porosity convergence (left) for a cross-sectional image (right) from the 

diploë of Specimen 10-16 ....................................................................62

Fig. D-6 Porosity convergence (left) for a cross-sectional image (right) from the 

diploë of Specimen 10-17 ....................................................................62

Fig. D-7 Porosity convergence (left) for a cross-sectional image (right) from the 

diploë of Specimen 06-05 ....................................................................63
Approved for public release; distribution unlimited.

viii

List of Tables

Table 1 PMHS sample information ....................................................................5

Table 2 Scanning parameters..............................................................................7

Table 3 Terminologies........................................................................................9

Table 4 Total skull thickness, t .........................................................................16

Table 5 Relative outer table thickness percentage, tttt......................................17

Table 6 Relative diploë thickness percentage, tttt.............................................18

Table 7 Relative inner table thickness percentage, tttt.......................................19

Table 8 Porosity percentage in the outer table..................................................20

Table 9 Porosity percentage in the diploë.........................................................21

Table 10 Porosity percentage in the inner table..................................................21

Table 11 Effects of bone type and skull origin on porosity percentage..............21

Table 12 Gaussian coefficient A.........................................................................25

Table 13 Gaussian coefficient B.........................................................................26

Table 14 Gaussian coefficient C.........................................................................27

Table 15 Scanning parameters for high-resolution, low-noise scans..................28

Table 16 Skulls with significant differences between frontal and parietal 

bones....................................................................................................32

Table A-1 Micro-CT scanning parameters for error analysis...............................44

Table A-2 Parameter results..................................................................................45

Table A-3 Coefficient of Reliability (R) for each parameter ................................46

Table C-1 Relative layer thicknesses (% of total thickness).................................52

Table C-2 Absolute layer thicknesses (mm).........................................................52
Approved for public release; distribution unlimited.

ix

Preface

The research reported in this document was performed in connection with contract 

W911-QX-14-C0016 and W911QX-16-D-0014 with the US Army Research 

Laboratory. The views and conclusions contained in this document are those of 

TKC Global Inc., SURVICE Engineering Company, and the US Army Research 

Laboratory. Citation of manufacturer’s or trade names does not constitute an 

official endorsement or approval of the use thereof. The US Government is 

authorized to reproduce and distribute reprints for Government purposes 

notwithstanding any copyright notation hereon.
Approved for public release; distribution unlimited.

x

Acknowledgments

The authors would like to acknowledge the contributions of Gajanan Deshmukh 

(US Army Aberdeen Test Center), who assisted in postprocessing the specimen 

micrographs, and Ann Mae DiLeonardi (US Army Research Laboratory) for help 

with specimen extraction.
Approved for public release; distribution unlimited.

1

1. Introduction

One of the primary functions of the skull is to protect the brain from mechanical 

insults. In the human case, the brain is protected by the calvarium, which consists 

of 4 bones joined together by sutures: the frontal bone, the 2 parietal bones on the 

sides, and the occipital bone toward the rear. The cross-sectional profile of these 

cranial bones is organized in a sandwich structure of 3 layers. The outer and inner 

tables are made of dense cortical bone, and the middle layer, also known as the 

diploë, is porous trabecular bone. 

Understanding the mechanical response of these bones with sandwich structure to 

externally applied mechanical loading aids the design and evaluation of head 

protection equipment and strategies. The mechanical properties of bone are 

strongly correlated to bone-volume-fraction (fbv), or its complement, porosity 

(1 - fbv). A power-law relationship between the apparent modulus of bone and the 

fbv has been extensively developed in the literature, as reviewed by Helgason et al. 

(2008). This apparent modulus describes the far-field response of the overall 

structure of bone, and it has been shown to depend on the fbv raised to an 

exponential factor falling in the range between 2 and 3 (Carter and Hayes 1977;

Goulet et al. 1994; Alexander et al. 2016). However, these results have been almost 

exclusively developed for bones without the sandwich structure of the skull, such 

as the femur, vertebra, and tibia (Helgason et al. 2008). The subdivision of the 

cranial thickness (or depth) into 3 distinct layers with a rapidly changing porosity 

profile challenges the use of a single modulus-porosity relationship to describe the 

mechanical response of the skull. 

An early study on modulus-density relationships in the skull was by McElhaney et 

al. (1970). In this pioneering work, the compression modulus of human skull 

loaded normal to the outer surface was approximated by a function of the third 

power of the porosity (porosity to the power of 3). More recently, the authors of 

the present report used the concept of the power-law relationship between modulus 

and bone volume fraction to describe localized, depth-dependent mechanical 

properties of animal cranial bone (Alexander et al. 2016). In this work, the 

deformation response of the various sections of the cranial bone in response to 

loading was visualized and quantified (quantitative-visualization), and shown to 

vary through the thickness of the skull from the inner to outer surface. In addition, 

the variation of the fbv along the thickness was also measured. Finally, the change 

of apparent modulus through the thickness was calculated by relating the gradient 

in deformation (strain) to the fbv gradient. 
Approved for public release; distribution unlimited.

2

However, the ability of a similar power-law relationship to account for the localized 

properties of the human skull would depend on the structure of human cranial bone, 

which is not well known. Several aspects of the skull morphology must be 

investigated before relating the modulus with the depth. First, the change of 

porosity through the thickness of the human cranial bone must be quantified. Then, 

any differences in these porosity changes between the various bones of the 

calvarium must be identified. Moreover, aligned microstructures within the skull 

(structural anisotropy) could imply directional dependence in the mechanical 

response (mechanical anisotropy). Mechanical anisotropy would need to be 

accounted for if a directional dependence is present, since approximating the 

modulus from only the porosity assumes that the relevant microstructure is 

randomly arranged (structural isotropy), without preferential alignment. As far as 

we know, these details of the human skull morphology have not been fully 

addressed in the existing literature.

Several authors have quantified the thickness of the 3 layers of the human skull 

(McElhaney et al. 1970; Fry and Barger 1978; Peterson and Dechow 2002, 2003;

Lynnerup et al. 2005; Sabanciogullari et al. 2013; Huang et al. 2015). However, 

previous reports of layer thicknesses have generally relied on qualitative methods 

of layer identification and segregation, which are not ideal. For example, the 

inconsistency of the porosity in the diploë has challenged the use of qualitative 

methods for delineation between layers, making layer identification either difficult 

or impossible in some regions of the skull (Lynnerup et al. 2005; Huang et al. 2015;

Lillie et al. 2016). Furthermore, these methods have also led to subjectivity in the 

identification of the layer boundaries, which is likely responsible for the large 

amount of variations that are reported in literature (Boruah et al. 2015). Only a few 

recent studies have presented quantitative methods for layer segregation, resulting 

in repeatable results (Boruah et al. 2013; Boruah et al. 2015; Lillie et al. 2015). One 

method identified the diploë by the onset of pixels corresponding to porous space 

within specified regions of the image stack (Boruah et al. 2013; Boruah et al. 2015)

while another used a full-width-half-max analysis of the X-ray attenuation through 

the thickness of the specimen (Lillie et al. 2015).

The porosity (porous-volume-fraction) of human cranial bone has only been 

reported as an average over the entire thickness of the skull that includes all 3 layers 

(Rahmoun et al. 2014), or for each layer as an average within that layer (Boruah et 

al. 2013; Boruah et al. 2015). McElhaney et al. (1970) was an exception in 

considering the depth-dependence of the porosity. This study suggested that the 

through-thickness variation of porosity could be described by a 1-term Gaussian 

function: a bell-shaped curve with the porosities lowest in the tables and peaking in 

the diploë. However, this use of the Gaussian function to approximate the through-
Approved for public release; distribution unlimited.

3

thickness porosity variation was motivated only by observation of the porosity 

distribution from serial sections, using a technique that was not detailed in the paper 

(McElhaney et al. 1970).

Finally, the extent of structural anisotropy in the transverse plane of the skull, 

parallel to the outer surface, is unclear. In the extensively studied load-bearing 

cortical part of long bones, such as the femur, microstructure is aligned in the 

direction of anatomical loading along the long axis (Peyrin et al. 2000) and 

mechanical properties are transversely isotropic at mesoscale. These 

microstructural subelements are called osteons, and consist of a cylindrical pore in 

the center, called the Haversian canal, which is encircled by lamella reinforced with 

collagen-mineral fibrils. While the outer and inner tables of cranial bone are known 

to contain osteons (Trammell 2012), the alignment of these osteons and other 

microstructural details have not been conclusively determined or reported in 

literature. Some degree of directional dependence in the transverse plane has been 

found from mechanical characterization of the outer table, thereby indicating the 

presence of anisotropy (Peterson and Dechow 2003). However, evidence of 

consistent directional dependencies in human skulls is not present in literature.

The preset study used high-resolution microcomputed tomography (micro-CT) to 

quantify the change of porosity through the thickness from the outer to the inner 

surface, through the diploë. Gaussian functions were optimized to describe the 

high-resolution porosity measurements, and a systematic method for differentiating 

between the 3 microstructural layers was developed. The porosity and thickness 

ratios of the 3 layers were then calculated. The results were compared between 

skulls and bone types to determine any systematic variation between the different 

bones of the skulls, while accounting for the random skull-to-skull variation. 

Finally, the 3-dimensional arrangement of the vesicular structure within the outer 

table was visualized using higher resolution micro-CT. The visual results were 

used to identify the extent of structural alignment within the dense part of the skull 

bone structure.

2. Methods

2.1 Specimen Extraction

Bone specimens originated from the skulls of 4 fresh (nontreated) and frozen, male 

postmortem human subject (PMHS) donors aged 76–86 yrs. The skulls did not 

have a history of musculoskeletal diseases nor did they demonstrate any 

macroscopic pathological changes near the specimen extraction sites. 
Approved for public release; distribution unlimited.

4

Sections of the frontal and parietal bones were retrieved from the skulls using a 

handheld bone saw after all soft tissues had been removed. 

Nine specimens were then collected from each section of the skull. The sets of 9

specimens formed a square grid, as depicted in the example given in Fig. 1. The 

location of the grid on the skull was recorded prior to each extraction with 2

measurements, which localized the center of the grid. The measurement marked as 

C in Fig. 1 was from the center of the grid to the coronal suture. The coronal suture 

separates the frontal bone, which is anterior to (in front of) the suture, from the 2

parietal bones, posterior to (behind) the suture. The measurement marked as S in 

Fig. 1 was from the center of the grid to the anteroposterior midline, which divides 

the skull into left and right sides. This midline was identified by the sagittal suture, 

which lies posterior to the coronal suture. The sagittal suture was also manually 

extrapolated to the frontal bone to measure S for extraction grids from frontal 

bones.

Fig. 1 Schematic of the human skull, viewed from above. The locations of the specimen 

grids are shown on the frontal and parietal bones. Distances from the grid centers to the 

coronal suture and midline (sagittal suture) are depicted by C and S, respectively. Note: the 

parietal grid is shown on the right parietal bone only as an example. For some skulls, the 

parietal grid originated from the left parietal bone, as listed in Table 1.
Approved for public release; distribution unlimited.

5

Table 1 PMHS sample information

Skull 

no.

(AA)

Age 

(yrs)

Weight

(kg)

Stature

(cm) Bone

Specimen 

no. range

(BB)

Distance 

from midline 

(cm)

Distance 

from 

coronal 

suture (cm)

04 79 72 177 Frontal

Parietal (R)

01 to 09

10 to 18

0

6.4

–3.6

3.8

06 83 63 175 Frontal 01 to 09 0 6.5

. . . . . . . . . . . . Parietal (L) 19 to 27 –5.9 –5.2

07 86 66 172 Frontal 10 to 18 –2 6.6

10 76 54 182 Frontal 01 to 09 0 6.1

. . . . . . . . . . . . Parietal (R) 10 to 18 5.6 –3.4

Note: Parietal bones on the left (L) and right (R) side of the skull are separately identified. Distances are 

listed from the center of the grid. Negative distances from the coronal sutures indicate that the grid was 

posterior to (behind) the suture. Negative distances from the midline indicate the grid was to the left of the 

midline.

Each of the specimens was catalogued with an AA-BB label, in which AA was the 

skull number (04, 06, 07, or 10) and BB was the unique number of the specimen 

within each skull (ranging from 01 to 27). The BB numbering scheme is shown for 

each bone in Fig. 2. For the purposes of this report, the term superior refers to the 

top of the head (farthest from the shoulders) and inferior refers to the bottom of the 

head (toward the shoulders).

The specimens were cut from the bone sections using a diamond-coated bone 

pathology saw (Exact 312, Exact Technologies, Inc.) with continual irrigation to 

reduce any damage due to heating. Extracted specimens were approximately 

rectangular parallelepipeds, with dimensions on the outer surfaces of 8 × 8 mm. 

The specimens included the entire thickness of the skull, with both outer and inner 

surfaces left intact. The thickness of the specimen was the distance measured from 

the inner surface, closest to the brain, to the outer surface, closest to the skin. The 

thickness will also be referred to as the depth dimension in this report. The term 

specimen(s) will be used throughout this report to refer to these individual 

specimens extracted from the skull.

After extraction, each specimen was immersed in Hanks Buffered Saline Solution 

(HBSS) and stored in an individual vial. Vials were kept at 4 °C when the specimen 

was not actively used for morphological characterization.
Approved for public release; distribution unlimited.

6

Fig. 2 BB numbering scheme for each specimen extraction grid from each skull. Markings 

outside the grid indicate in-situ orientation: superior (S, toward the top of the skull), inferior 

(I, toward the base of the skull), anterior (A, toward the front of the skull), posterior (P, toward 

the rear of the skull), right (R), and left (L).
Approved for public release; distribution unlimited.

7

2.2 Microcomputed Tomography

Prior to imaging, specimens were removed from storage, wrapped in HBSS-soaked 

gauze, and placed in a small vial to be mounted in the scanner. The vial was also 

filled with HBSS. 

The specimens were imaged using a micro-CT scanner (Skyscan 1172, Bruker

micro-CT), with scanning parameters designated by 1 of the 4 different sets listed 

in Table 2. For all 4 sets, micro-CT scans were performed at

62 kV and 161 mA while using a 0.5-mm aluminum filter. The use of different 

scanning parameters was necessitated by external circumstances related to the 

scanner. Parameters were chosen to balance the competing needs to minimize the 

electrical and image noise, while also minimizing the time required to scan each 

specimen. The effect of the different scanning parameters on the quantitative data 

was further investigated in Appendix A. The results indicated that the variability 

in measured parameters from micro-CT images were relatively small for the range 

and combinations of parameters given in Table 2.

Table 2 Scanning parameters

Parameter 

set (no.)

Resolution/voxel 

size (μm)

Frame avg. 

(no. of 

frames)

Rotation 

step (°)

Random 

movement

Approx. scan 

time (h)

1 6.7 10 0.2 5 12

2 6.1 10 0.2 20 13

3 5.3 12 0.1 20 18

4 5.3 10 0.15 20 10.5

An image stack was reconstructed from the initial micro-CT scan. It was rotated 

using DataViewer software (Bruker micro-CT) so that the normal at the center of 

the outer table was aligned in the vertical direction, as shown in Fig. 3. After 

rotation, each image of the stack represented a 1-voxel-thick horizontal slice of the 

specimen. In this report, the image plane will also be referred to as the transverse 

plane. The error associated with stack rotation was quantified in Appendix A and 

shown to be negligible.

After rotation, the voxels corresponding to the specimen were selected by creating 

the volume of interest (VOI) within CTAn Software (Bruker micro-CT). The VOI 

of individual specimens were independently identified, as each specimen had 

different overall dimensions. The first step in creating the VOI was to select the 

images corresponding to the top and bottom of the specimen, which bounded the 

VOI. These bounds were selected in the following manner. The operator started 
Approved for public release; distribution unlimited.

8

at the top of the image stack, above the specimen. The images in this region did 

not contain any bone. Then, the image stack was traversed down toward the center 

of the specimen until reaching an image containing the full perimeter of the 

specimen. This image was well below the outer surface. The full specimen 

perimeter was noted. The image stack was then traversed upward, toward the outer 

surface, until the area corresponding to bone was 50% of the specimen area 

identified from the image with the full perimeter. This image with the 50% bone 

area was selected as the “top” of the specimen. The “bottom” of the specimen was 

selected in a similar manner. The operator started from an image slice far below 

the specimen. The image stack was traversed up toward the center until reaching 

an image with the full specimen perimeter. Finally, the image stack was again 

traversed down toward the inner surface, and the last image for which the specimen 

area was occupied by at least 50% bone was selected as the “bottom” of the 

specimen.

Each of the transverse images within the stack contained both the specimen area 

and voxels corresponding to the media encompassing the specimen. Therefore, 

after identifying the top and bottom VOI bounds, the operator then demarcated the 

boundary of the specimen within the transverse images. The boundary was 

manually traced using the polygonal region of interest (ROI) tool. These polygonal 

ROIs were created on several image slices within the top and bottom VOI bounds. 

The ROIs for the remaining images were automatically created from the manually

traced polygons using interpolation (CTAn software). Finally, the operator 

inspected visually all of the VOI images to ensure that the combination of ROIs 

over all of the slices encapsulated the specimen. The process was iterated to correct 

the ROIs as needed. 
Approved for public release; distribution unlimited.

9

Fig. 3 Example of the rotation applied to the image stack in DataViewer such that the 

normal at the center of the outer table was in the vertical direction. Images shown are 

through-thickness and are from Specimen 04-03.

After VOI creation, images were filtered using a Gaussian blur (σ = 1.5) to reduce 

noise. Images were then binarized using the 3-D Otsu algorithm (Otsu 1975), 

constrained to the VOI.

2.3 Summary of Terminology Used

Table 3 provides a summary of terms introduced in the preceding sections, which 

are relevant to the image analysis procedures and specimen identification.

Table 3 Terminologies

Term Description

Extraction

Specimen The individual coupons collected from the skulls for analysis and 

catalogued with an AA-BB label.

Skull layers/sections Refers to the 3 layers that comprise the sandwich structure of the adult 

human skull: outer table, diploë, and inner table.

Extraction grid The grid of 9 specimens extracted from each bone. The arrangement 

of each grid within a rectangular section of the skull was shown in 

Fig. 2

Bone type Frontal or parietal (Fig. 1)

Imaging and Analysis

Thickness/depth The dimension that spans from the inner surface to the outer surface of 

the specimens

Transverse plane The plane corresponding to the images, perpendicular to the normal of 

the outer surface of the specimen

ROI The region of interest of each image in the micro-CT stack, selected so 

as to contain the transverse planes of the specimen

VOI The 3-D volume of interest of the micro-CT stack, selected so as to 

separate the specimen from the surrounding media
Approved for public release; distribution unlimited.

10

2.4 Statistical Analysis

Three different pooling methods were used to average the various parameters that 

were calculated from each individual specimen. First, the parameters were 

averaged only over each extraction grid. This produced 7 averages: for different 

bone types (parietal and frontal) of each skull (04, 06, 07, and 10). Then, results 

were pooled for each bone type, regardless of its skull origin. This gave 2 averages, 

one for frontal and the other for parietal. Finally, results were pooled by skull of 

origin, regardless of bone type. This procedure gave 3 averages, for Skulls 04, 06,

and 10. No such pooling by skull origin was needed for Skull 07 because only one 

bone type (frontal) was scanned from this skull. 

Two-way analysis of variance (ANOVA) and posthoc tests were used to further 

quantify the relative effect of 2 sources of variation: bone type (frontal, parietal) 

and skull origin (Skull 04, Skull 06, or Skull 10). These tests did not include results 

from Skull 07, since only the frontal bone was studied from this skull. Statistical 

analysis was carried out using JMP software (JMP 12.0.1, SAS Institute). 

Statistical difference was determined at a 95% confidence level (p < 0.05). 

Differences between the results pooled by bone type (parietal and frontal) were 

calculated with Student’s t-test. For all other groups, differences were calculated 

using Tukey’s Honestly Significant Difference (HSD) test. 

3. Results

3.1 Representative Images from Each Extraction Grid

Representative specimens from the 2 types of bone (parietal and frontal) were 

selected for each skull. Figures 4–6 show 2 different types of images for each of 

these specimens. The through-thickness image shows the whole depth dimension, 

from the inner, brain-most, surface of the bone to the outer, skin-most, surface of 

the bone. Various cross-sectional images are also included at various depths. The 

cross-sectional images correspond to image slices roughly perpendicular to the 

normal at the center of the outer surface of the skull. 

Figure 4 shows a through-thickness image of Specimen 04-02 with cross-sectional 

images of each of the 3 sections: outer table, diploë, and inner table. 

Figures 5 and 6 show through-thickness images from the remaining bones, 

accompanied by a cross-sectional image of the diploë.
Approved for public release; distribution unlimited.

11

Fig. 4 Through-thickness image of Specimen 04-02 (a), and cross-sectional images of the 

outer table (b), diploë (c), and inner table (d)
Approved for public release; distribution unlimited.

12

Fig. 5 Representative images from each bone section. Through-thickness images are on 

the left and cross-sectional images of the diploë are on the right. The bones are (a) 04-14, (b) 

06-06, and (c) 06-26.
Approved for public release; distribution unlimited.

13

Fig. 6 Representative images from each bone section. Through-thickness images are on 

the left and cross-sectional images of the diploë are on the right. The bones are (d) 07-10, (e) 

10-04, and (f) 10-17.
Approved for public release; distribution unlimited.

14

3.2 Outer Table, Diploë, and Inner Table Layer Identification 

and Thickness Measurements

The porosity of each binarized image within a given stack was calculated as the 

fraction of the porous area to the total area of the image. The result described the 

porosity as a function of depth, P(d), from the inner surface to the outer surface of 

the specimen. An example is given in Fig. 7.

Fig. 7 Porosity as a function of depth, P(d), for Specimen 04-03

The overall thickness of the entire specimen, tt, was measured from the size of the 

micro-CT image stack (VOI, as described in Section 2.2). The size in pixels was 

converted to millimeters based on the isotropic voxel size (Table 2). Next, the 

thicknesses of the outer table, diploë, and inner table were calculated as ttoo, ttdd, and 

ttii, respectively. Section thicknesses were calculated directly from the porositydepth profile derived from the micro-CT measurements, P(d). The procedure 

started at the outer surface, d = 100%, where the porosity was always less than 

30%. The depth d was then decreased until P(d) > 30%. The first depth, d, for 

which P(d) > 30%, was taken as the transition from the outer table to the diploë. 

Then, the depth was further decreased toward d = 0% (the inner surface). The next 

depth, d, for which P(d) again fell below 30% was taken as the transition boundary 

from the diploë to the inner table. 

Figure 8 shows a schematic of this process of identifying the 3 sections. The 

process was based on a cutoff threshold of the porosity percentage to have 

repeatable results. This method offered an improvement over the subjective 

analysis used in literature. 
Approved for public release; distribution unlimited.

15

Fig. 8 Procedure to determine the outer table, diploë, and inner table thicknesses from the 

porosity-depth profile. This example uses the porosity-depth profile of Specimen 04-03 

(Fig. 7).

The cutoff porosity percentage of 30% was chosen because the outer and inner 

tables are consistently considered as cortical bone, while the diploë is considered 

trabecular bone. Secondly, cortical bone has been described as bone with porosity 

of less than 30%, while trabecular bone has porosity greater than 30% (Mow and 

Huiskes 2005). 

Figures 9–12 show the mean and standard deviation of the 4 parameters: t, ttoo, ttdd, 

and ttii averaged over each extraction grid. Tables 4–7 list the extraction grid

averages. The tables also list the average over each skull (Skull 4, Skull 6, and 

Skull 10) and the average over each bone type (frontal, parietal). The tables indicate 

which groups are statistically different (p < 0.05, Section 2.4). Appendix C contains 

box plots of the 4 thickness parameters: t, ttoo, ttdd, and ttii. 

Two-way ANOVA (Section 2.4) indicated that both skull origin and bone type had 

a significant effect for all 4 of these parameters (p < 0.05). The interaction effect 

between skull origin and bone type was only significant for t and ttii. Appendix C 

contains results for the thickness in millimeters of each of the 3 layers of the skull 

(outer table, diploë, and inner table), calculated for each extraction grid and 

grouping.
Approved for public release; distribution unlimited.

16

Fig. 9 Average values of the overall skull thickness, t

Table 4 Total skull thickness, t

Grouping mean ± std Connecting symbols

Skull 04, frontal 9.6 ± 0.5 *

Skull 06, frontal 8.5 ± 1.1 #

Skull 06, parietal 8.3 ± 0.5 #

Skull 10, frontal 7.0 ± 0.8 @

Skull 10, parietal 6.1 ± 0.7 @ &

Skull 04, parietal 5.5 ± 0.3 &

Skull 06, pooled 8.4 ± 0.9 ¶

Skull 04, pooled 7.6 ± 2.1 ◄

Skull 10, pooled 6.6 ± 0.8 ∆

Frontal, pooled 8.4 ± 1.4 ^

Parietal, pooled 6.7 ± 1.3 $

Note: Results are reported in units of millimeters. Groups that do not share the same symbol in the 

Connecting symbols column are significantly different.

Fig. 10 Average values of the thickness percentage of the outer table, tt
Approved for public release; distribution unlimited.

17

Table 5 Relative outer table thickness percentage, tt

Grouping mean ± std Connecting symbols

Skull 10, parietal 24.1 ± 6.4 *

Skull 04, frontal 23.5 ± 3.2 *

Skull 10, frontal 23.3 ± 2.6 *

Skull 06, frontal 21.2 ± 1.6 * #

Skull 04, parietal 18.6 ± 5.3 * #

Skull 06, parietal 15.7 ± 4.2 #

Skull 10, pooled 23.7 ± 4.8 ¶

Skull 04, pooled 21.0 ± 5.0 ¶ ◄

Skull 06, pooled 18.5 ± 4.2 ◄

Frontal, pooled 22.7 ± 2.7 ^

Parietal, pooled 19.4 ± 6.3 $

Note: Results are reported in units of thickness percentage (%). Groups that do not share the same symbol in 

the Connecting symbols column are significantly different.

Fig. 11 Average values of the thickness percentage of the diploë, tt
Approved for public release; distribution unlimited.

18

Table 6 Relative diploë thickness percentage, tt

Grouping mean ± std Connecting symbols

Skull 06, parietal 71.3 ± 5.4 *

Skull 04, parietal 68.1 ± 7.9 * #

Skull 10, parietal 58.6 ± 11.2 # @

Skull 04, frontal 53.1 ± 5.0 @ &

Skull 06, frontal 42.9 ± 12.4 & §

Skull 10, frontal 33.5 ± 8.3 §

Skull 04, pooled 60.6 ± 10.0 ¶

Skull 06, pooled 57.1 ± 17.3 ¶

Skull 10, pooled 46.1 ± 16.1 ◄

Parietal, pooled 66.0 ± 9.8 ^

Frontal, pooled 43.2 ± 11.9 $

Note: Results are in units of thickness percentage (%). Groups that do not share the same symbol in the 

Connecting symbols column are significantly different.

Fig. 12 Average values of the thickness percentage of the inner table, tt
Approved for public release; distribution unlimited.

19

Table 7 Relative inner table thickness percentage, tt

Grouping mean ± std Connecting symbols

Skull 10, frontal 43.1 ± 8.6 *

Skull 06, frontal 35.8 ± 12.0 *

Skull 04, frontal 23.5 ± 5.3 #

Skull 10, parietal 17.4 ± 6.3 # @

Skull 04, parietal 13.3 ± 3.5 @

Skull 06, parietal 13.0 ± 2.9 @

Skull 10, pooled 30.3 ± 15.1 ¶

Skull 06, pooled 24.4 ± 14.5 ◄

Skull 04, pooled 18.4 ± 6.8 ∆

Frontal, pooled 34.1 ± 12.0 ^

Parietal, pooled 14.6 ± 4.7 $

Note: Results are in units of thickness percentage (%). Groups that do not share the same symbol in the 

Connecting symbols column are significantly different.

Fig. 13 Layer thickness percentages averaged over each skull (left) and bone type (right). 

Standard deviations are shown in Fig. 14.

Fig. 14 Layer thickness percentages (shown in Fig. 13) with standard deviations. Absolute 

values in millimeters are shown in Appendix C, Figure C-1.
Approved for public release; distribution unlimited.

20

3.3 Porosity of Each Layer

The average porosity of each of the 3 layers was calculated from the change of 

porosity with depth, P(d). The porosity profile was averaged along the depth 

corresponding to each of the layers. The method for identifying these layers was 

described in Section 3.2. The average porosity of each layer is reported in 

Tables 8–10. Figure 15 shows the layer porosities averaged by skull of origin (Skull 

4, Skull 6, Skull 10) and by bone type (frontal, parietal). Figure 16 provides more 

detail, showing the average of each extraction grid.

Two-way ANOVA (Section 2.4) was conducted to determine the significance of 

the skull origin and bone type on the porosity of each layer. The results are listed 

in Table 11.

Table 8 Porosity percentage in the outer table

Grouping mean ± std Connecting symbols

Skull 04, parietal 12.6 ± 2.6 *

Skull 06, parietal 9.5 ± 3.5 #

Skull 04, frontal 6.9 ± 1.3 # @

Skull 10, parietal 6.7 ± 2.2 # @

Skull 06, frontal 5.3 ± 0.9 @

Skull 10, frontal 4.1 ± 0.6 @

Skull 04, pooled 9.7 ± 3.5 ¶

Skull 06, pooled 7.4 ± 3.3 ◄

Skull 10, pooled 5.4 ± 2.1 ∆

Parietal, pooled 9.6 ± 3.6 ^

Frontal, pooled 5.4 ± 1.5 $

Note: Groups that do not share the same symbol in the Connecting symbols column are significantly different.
Approved for public release; distribution unlimited.

21

Table 9 Porosity percentage in the diploë

Grouping mean ± std Connecting symbols

Skull 10, Parietal 64.5 ± 10.4 *

Skull 04, Parietal 62.8 ± 2.4 *

Skull 04, Frontal 61.9 ± 2.2 *

Skull 06, Parietal 61.4 ± 1.3 *

Skull 10, Frontal 59.9 ± 6.2 *

Skull 06, Frontal 48.4 ± 3.9 #

Skull 04, pooled 62.3 ± 2.3 ¶

Skull 10, pooled 62.2 ± 8.6 ¶

Skull 06, pooled 54.9 ± 7.2 ◄

Parietal, pooled 62.9 ± 6.1 ^

Frontal, pooled 56.7 ± 7.4 $

Note: Groups that do not share the same symbol in the Connecting symbols column are significantly different.

Table 10 Porosity percentage in the inner table

Grouping mean ± std Connecting symbols

Skull 06, Parietal 20.0 ± 5.4 *

Skull 06, Frontal 19.8 ± 6.2 *

Skull 04, Frontal 19.1 ± 3.4 * #

Skull 04, Parietal 14.2 ± 2.6 * # @

Skull 10, Parietal 13.6 ± 3.8 # @

Skull 10, Frontal 12.1 ± 2.6 @

Skull 06, pooled 19.9 ± 5.6 ¶

Skull 04, pooled 16.6 ± 3.9 ¶

Skull 10, pooled 12.8 ± 3.2 ◄

Frontal, pooled 17.0 ± 5.5 ^

Parietal, pooled 15.9 ± 4.9 ^

Note: Groups that do not share the same symbol in the Connecting symbols column are significantly different.

Table 11 Effects of bone type and skull origin on porosity percentage

Layer Bone type Skull of origin Interaction

Outer table X X . . .

Diploë X X X

Inner table . . . X . . .

Note: Factors that were significant in the 2-way ANOVA analysis (p < 0.05) are listed with an “X”.
Approved for public release; distribution unlimited.

22

Fig. 15 Porosity of each layer, averaged by skull of origin (left) and by bone type (right)

Fig. 16 Porosity of each layer, averaged by extraction grid

3.4 Fitting Gaussian Functions to the Measured Porosity-Depth 

Profiles

To further study the change of porosity with depth, a one-term Gaussian function 

was fitted and optimized to P(d), as measured using micro-CT. The Gaussian 

function was given by

PPGG(dd) = AAee−[(dd−BB)⁄CC]2

. (1)

Equation 1 was fit to the P(d) measurements for each specimen, using the fit 

function of MATLAB. Three parameters A, B, and C represented the Gaussian 

function as shown in Fig. 17. In Eq. 1, A describes the peak porosity reached in the 

diploë and will be referred to as the amplitude. The parameter B describes the 

depth, d, at which the porosity peaks. The parameter C is related to the spread of 

the porosity distribution along the depth, and is the percent width when the porosity 

is equal to AAee−1⁄4, or roughly 78% of A.
Approved for public release; distribution unlimited.

23

Fig. 17 Porosity profile of Specimen 04-03 (Fig. 7) with the Gaussian fit, PP ( ). The 3

Gaussian parameters are shown schematically. For this example, results were A = 82%, 

B = 47%, C = 28%, and R2 = 0.96.

The correlation coefficient, R2, was also calculated for each Gaussian fit. Low 

correlation coefficients were observed for specimens exhibiting unusual 

phenomena, which could not be adequately modeled with a Gaussian function. 

R2 = 0.65 was selected as the threshold and specimens with RR2 < 0.65 were not 

used in calculation of summary statistics. Three specimens fell into this category: 

06-01, 06-04, and 06-07. These cases are presented in the discussion (Section 4.3).

The mean and standard deviation (std or σ) of the parameters A, B, and C were 

calculated for each of the statistical groups as described in Section 2.4. Figure 18

shows plots of the resulting Gaussian function with the mean ± σ. 
Approved for public release; distribution unlimited.

24

Fig. 18 Average Gaussian fits of the porosity profiles. The solid line shows the Gaussian

function (Eq. 1) derived using the mean parameters. The shaded area represents corridors of 

±σ of the Gaussian function.
Approved for public release; distribution unlimited.

25

Two-way ANOVA (Section 2.4) indicated that both skull origin and bone type were 

significant effects for all 3 parameters A, B, and C (p < 0.05). The interaction effect 

between these 2 sources of variation was only significant for parameters A and B.

Figures 19–21 show the mean and standard deviation for the parameters A, B, and 

C, respectively. These statistics are also reported in Tables 12–14, while also

indicating which groups are statistically different. Appendix B contains box plots 

(based on quartiles) of the parameters A, B, and C. 

Fig. 19 Average values of the Gaussian coefficient A, related to the peak porosity (Fig. 17)

Table 12 Gaussian coefficient A

Grouping mean ± std Connecting symbols

Skull 10, parietal 82.1 ± 12.4 *

Skull 04, parietal 80.5 ± 3.4 *

Skull 04, frontal 78.1 ± 2.9 *

Skull 06, parietal 77.6 ± 1.3 *

Skull 10, frontal 74.9 ± 8.4 *

Skull 06, frontal 59.5 ± 9.3 #

Skull 04, pooled 79.3 ± 3.3 ¶

Skull 10, pooled 78.5 ± 10.9 ¶

Skull 06, pooled 70.4 ± 10.8 ◄

Parietal, pooled 80.1 ± 7.4 ^

Frontal, pooled 72.2 ± 10.2 $

Note: Results are in units of porosity percent (%). Groups that do not share the same symbol in the Connecting 

symbols column are significantly different.
Approved for public release; distribution unlimited.

26

Fig. 20 Average values of the Gaussian coefficient B, which is the thickness percentage at 

which the porosity peaks (Fig. 17)

Table 13 Gaussian coefficient B

Grouping mean ± std Connecting symbols

Skull 10, frontal 60.0 ± 4.8 *

Skull 06, frontal 53.6 ± 4.6 #

Skull 04, frontal 50.9 ± 3.2 # @

Skull 06, parietal 50.1 ± 1.6 # @

Skull 04, parietal 49.5 ± 2.3 # @

Skull 10, parietal 46.9 ± 3.9 @

Skull 10, pooled 53.5 ± 8.0 ¶

Skull 06, pooled 51.5 ± 3.5 ¶ ◄

Skull 04, pooled 50.2 ± 2.8 ◄

Frontal, pooled 55.0 ± 5.8 ^

Parietal, pooled 48.8 ± 3.0 $

Note: Results are in units of thickness percentage (%). Groups that do not share the same symbol in the 

Connecting symbols column are significantly different.
Approved for public release; distribution unlimited.

27

Fig. 21 Average values of the Gaussian coefficient C, related to the spread of the porosity 

distribution (Fig. 17)

Table 14 Gaussian coefficient C

Grouping mean ± std Connecting symbols

Skull 06, parietal 37.5 ± 4.0 *

Skull 04, parietal 35.1 ± 4.1 * #

Skull 10, parietal 30.1 ± 5.9 # @

Skull 04, frontal 28.6 ± 2.6 @

Skull 06, frontal 28.2 ± 4.8 @

Skull 10, frontal 17.9 ± 3.6 &

Skull 06, pooled 33.8 ± 6.3 ¶

Skull 04, pooled 31.9 ± 4.7 ¶

Skull 10, pooled 24.0 ± 7.9 ◄

Parietal, pooled 34.2 ± 5.5 ^

Frontal, pooled 24.5 ± 6.3 $

Note: Results are in units of thickness percentage (%). Groups that do not share the same symbol in the 

Connecting symbols column are significantly different.

3.5 Pore Orientation

Additional micro-CT scans were performed to visualize the much finer details of 

orientation of the porous structure in the outer table of 2 of the specimens. 

Specimens 10-02 and 04-12 were used to include results from both frontal bone 

(10-02) and parietal bone (04-12). Scanning parameters for these scans are listed 

in Table 15. These parameters were carefully selected to maximize resolution while 

minimizing image noise, with the result that scanning time for each specimen 

exceeded 50 h. After completion of the scan, the image stack was then rotated as 

previously described (Section 2.2). The VOI was created to only include the images 

of the outer table. The top-most image and the ROIs in the transverse planes were 
Approved for public release; distribution unlimited.

28

selected using the same procedures as described in Section 2.2. The bottom of the 

VOI corresponded to the bottom-most image of the outer table. Selection of this 

bottom-most image was based on visual inspection, excluding images from the 

transition zone between the outer table and the diploë. To identify this bottommost image, the operator started from the outer surface and traversed toward the 

diploë region. The first image that showed a marked increase in porosity was 

selected as the bottom of the VOI. The resulting thickness of the outer table for 

these procedures, tt0

∗

, was necessarily smaller than the thickness of the outer table 

as calculated by the method for layer identification previously presented (ttoo, 

Section 3.2). The thickness of the outer tables selected by this method were tt0

∗ = 

1.42 mm and tt0

∗ = 1.11 mm for Specimens 10-02 and 04-12, respectively.

Table 15 Scanning parameters for high-resolution, low-noise scans

Resolution/voxel 

size (μm)

Frame avg. (no.

of frames)

Rotation 

step (°)

Random 

movement

Approx. scan 

time (h)

3.7 20 0.05 20 55.5

After VOI selection, the images were filtered (Gaussian, σ = 1) and then binarized

so that the pores were displayed as white objects and the bone as black background. 

Thresholds were determined manually to satisfy the competing interests of 

preserving small porous features (increasing the threshold value) while avoiding 

image noise (decreasing the value). First, the threshold values corresponding to the 

automated binarization of several unfiltered images in the image stack were 

obtained using CTAn. This binarizing feature of CTAn is based on the unfiltered 

image and uses the Otsu method (Otsu 1975). However, in the current study, 

images were first filtered prior to final binarization. Therefore, threshold values 

were able to be used which were higher than those that were automatically 

generated by CTAn. Using higher values on the filtered image maximized the 

porous space that was preserved during binarization while still avoiding image 

noise. Starting with the automated values produced by CTAn, a trial-and-error 

method was used to increase the thresholds to the maximum possible value before 

image noise was seen in the resulting filtered-binarized image.

After binarization, CTVox (Bruker micro-CT) was used for 3-D visualization of 

the images. Figure 22 provides an overview of the process to visualize the 

arrangement of the pore structure in the outer table of Specimen 10-02. Figure 23

shows pores in the outer table of Specimen 04-12. The micro-CT software CTAn 

(Bruker micro-CT) was used to calculate the average thickness (diameter) of the 

pores within the outer table region of the 2 specimens. The average diameters were 

90 and 86 μm for Specimens 10-02 and 04-12, respectively.
Approved for public release; distribution unlimited.

29

Fig. 22 Digitally coloring the pores in the outer table of Specimen 10-02 (from frontal bone). 

(a) The entire specimen. (b) The outer table selection, with thickness tt00

∗ = 1.42 mm. (c) The 

pores in the outer table. (d) The pores in the outer table, with digital color added. (e) A topdown view of the pores, looking down on the outer surface of the specimen. Average pore 

diameter = 90 μm.
Approved for public release; distribution unlimited.

30

Fig. 23 Pores within the outer table of Specimen 04-12 (from parietal bone). The side view 

(a) and top-down view (b), are analogous to Fig. 22 (d) and (e). Outer table thickness, tt00

∗ = 

1.11 mm. Average pore diameter = 86 μm. 

4. Discussion

The change of porosity through the thickness of the skull measured in this report 

provided more insight than previous studies reported in literature. The method that 

was presented was analogous to examining serial sections separated by less than 

10 μ and which were perpendicular to the normal at the center of the outer surface. 

This method provided the porosity variation in the skull at a much higher resolution, 

compared to previously reported porosities averaged over the entire thickness 

(Motherway et al. 2009; Rahmoun et al. 2014) or averaged over each of the 3 layers 
Approved for public release; distribution unlimited.

31

(Boruah et al. 2013). The most striking feature of the high-resolution porosity 

profile was the peak porosity observed in the diploë (e.g., Fig. 7). This porosity 

peak has implications for the mechanical response of the skull because mechanical 

properties of porous bone have been reported to weaken with increasing porosity, 

to an exponential factor.

Porosity variation, P(d), was described using a Gaussian function to systematically 

compare porosity profiles between samples. The 3 parameters that were calculated 

from the Gaussian fit (Eq. 1) defined the porosity of the diploë layer in the bone: 

the peak porosity of the diploë (A) in units of porosity percentage (%), the location 

of the peak porosity (B) in units of thickness percentage (%), and the relative spread 

in width (C) of the peak porosity in units of thickness percentage (%). Defining a 

standardized shape for the porosity profiles enabled interbone comparisons of the 

porosity distributions in the diploë, as measured by the peak (A) and width (C) of 

the Gaussian fit (discussed in the following paragraphs).

A method to objectively distinguish between the 3 layers of the skull based on P(d) 

was also presented in this report. Previously, layers were mostly identified using 

subjective methods, such as visualization with or without a microscope (e.g.,

McElhaney et al. 1970; Hubbard 1971; Peterson and Dechow 2002, 2003). Others 

have used digital images, without, however, specifying a systematic, repeatable 

approach (Ruan and Prasad 2001). The proposed method offered several possible 

improvements. First, the repeatability of layer identification was aided by relying 

on a quantitative threshold to distinguish the layers, based on the porosity. The 

only point of operator subjectivity was in the preliminary rotation of the image stack 

(discussed in Section 4.3.1). The few recent studies that used quantitative, rather 

than qualitative, methods to identify layers were not based on the change of porosity 

through the thickness (Boruah et al. 2013; Boruah et al. 2015; Lillie et al. 2015). 

Using the porosity variation for layer identification may provide a clearer link 

between morphology and mechanics due to the strong relationship that has been 

reported between the modulus and the porosity (Helgason et al. 2008).

Secondly, the present method, using a step size of less than 10 μ, was also based on 

much higher-resolution data compared to previous methods using only the unaided 

eye or an optical microscope (McElhaney et al. 1970; Hubbard 1971; Peterson and 

Dechow 2002, 2003). Finally, the present method also accounted for variations in 

the transverse plane. Observation of a bone segment using a light microscope only 

presents a surface view of the specimen. On the other hand, the porosity-depth 

profile underlying the present method was created by averaging across the sectional 

images of the specimen in the transverse plane. The limitations of the method are

discussed in Section 4.3.3. 
Approved for public release; distribution unlimited.

32

4.1 Frontal-Parietal Comparison in the Context of Skull-to-Skull 

Variability

The micrographs from frontal and parietal bones were clearly different by simple 

observation, even prior to resorting to quantitative analysis (e.g., Figs. 5 and 6). 

However, a large skull-to-skull difference was also visible at the same time. The 

analytical methods of this report helped to distinguish these 2 sources of variation. 

A total of 10 parameters were calculated for each specimen: 4 measures of relative 

layer thickness (as described in Section 3.2), the average porosity of each of the 3 

layers (Section 3.3), and the 3 parameters of the Gaussian fit (Section 3.4). Twoway ANOVA indicated that both interbone and interskull effects were significant 

sources of variation for all parameters except for the porosity of the inner table.

However, further analysis indicated that the most pronounced differences between 

frontal and parietal bones may be in the relative thickness of the diploë and the 

inner table. Table 16 summarizes the results reported in Sections 3.2, 3.3, and 3.4, 

indicating which skulls had significant differences between their frontal and 

parietal bones in each of the 10 parameters.

Table 16 Skulls with significant differences between frontal and parietal bones

Parameter Skulls Bone type with 

greater mean value Reference table

Overall thickness (t, mm) Skull 4 Frontal Table 4

Outer table thickness (ttoo, %) (none) . . . Table 5

Diploë thickness (ttdd, %) Skulls 4, 6, and 10 Parietal Table 6

Inner table thickness (ttii, %) Skulls 4, 6 and 10 Frontal Table 7

Porosity of outer table Skulls 4 and 6 Parietal Table 8

Porosity of diploë Skull 6 Parietal Table 9

Porosity of inner table (none) . . . Table 10

Peak porosity (A) Skull 6 Parietal Table 12

Depth of peak porosity (B) Skull 10 Frontal Table 13

Width of peak porosity (C) Skulls 4, 6, and 10 Parietal Table 14

Note: Summarized from the tables listed in the “Reference table” column.

Significant differences between the frontal and parietal bones in each of the 3 skulls 

was only seen for 3 parameters: ttdd, ttii, and C. Both ttdd and C are measures of the 

relative thickness of the diploë, and both were significantly higher in the parietal 

bones than in the frontal bones of the 3 skulls. This difference indicates that the 

parietal bones had a larger diploë region. The parameter ttii is the relative thickness 

of the inner table, and it was larger in the frontal bones than in the parietal bones. 

Taken together, the frontal-parietal differences of these 3 parameters indicate that 

the parietal bones have larger diploë layers than frontal bones, and that the parietal 
Approved for public release; distribution unlimited.

33

bones compensate with correspondingly smaller inner tables. These differences 

were clearly visible in Figs. 13 and 14.

We are not aware of any other literature reporting this observed tradeoff in 

thickness between the diploë and the inner table. For example, Boruah et al. (2015)

reported that the inner table was significantly larger in the parietal bone than in the 

frontal bone for 5 out of 10 tested skulls. However, the same report also found the 

outer table to be larger in the parietal bone than in the frontal bone for 5 out of 10 

skulls; whereas, this difference in outer table thickness was not seen in the present 

study. The study of Boruah et al. (2015) also did not find the diploë to be 

consistently thicker in a particular bone type. The differences in results are likely 

due to different methods for layer identification (discussed below). Differences 

could also be due to the smaller number of samples in the current study, which used 

only 3 skulls to draw frontal-parietal comparisons.

The tradeoff seen in the parietal bone, between an increased diploë thickness and 

decreased inner table thickness, could also explain a primary point of divergence 

between the present results and previous reports. Many authors have reported that, 

on average, the outer table is thicker than the inner table (Hubbard 1971; Peterson 

and Dechow 2002; Boruah et al. 2013; 2015). However, the present study found 

this to only occur in extraction grids from the parietal bones and not from frontal 

bones (see Appendix C, Table C-1). This finding could be a result of the thinner 

inner table in parietal bones, which compensate for a thicker diploë.

In this study, the relative thickness of the outer table was not significantly different 

between the frontal and parietal bones. The lack of a consistent frontal-parietal 

difference in outer table thickness has also been reported in previous studies. 

(Peterson and Dechow 2003; Boruah et al. 2015)

The observations of the overall thickness (Table 4) showed that any difference in 

thickness between the frontal and parietal bones may be inconsistent and may be 

overruled by skull-to-skull variability. For example, in only 1 skull was the overall 

thickness significantly different between the 2 bone types. Moreover, the overall 

thicknesses of the frontal bones of each of the 3 skulls were significantly different 

(Table 4), and this was the only occurrence when a parameter was significantly 

different between each of the 3 skulls within a given bone type. 

The difference in the peak porosity of the diploë, parameter A, between the 2 bone

types may not be as pronounced or repeatable as the difference in relative diploë 

thickness. In only 1 of the 3 skulls was the parameter A significantly different 

between the frontal and parietal bones; whereas, the difference in diploë thickness 

percentage was significant for all 3 skulls. Boruah et al. (2015) also found 
Approved for public release; distribution unlimited.

34

inconsistent trends between skulls when comparing the bone volume fraction (the 

complement of porosity) of the diploë between the frontal and parietal bones.

4.2 Porous Space in the Outer Table

The structure of load-bearing bones is highly anisotropic, with osteons aligned in 

the direction of physiological loading to reinforce the bone. However, the human 

skull is not generally considered a load-bearing bone. Therefore, preferential 

alignment of the osteons in the tables of the skull cannot be assumed a priori, and 

their arrangement has not been fully characterized or reported in literature. 

We characterized the microstructure of the small pores in the outer table using highresolution micro-CT to observe if the pores were preferentially aligned along a 

given direction. The pores within the tables included the Haversian canals, which 

are the central cylindrical pores of osteons. Therefore, the alignment of the pores 

provides an indication of osteonal alignment, implying the degree of structural and 

mechanical anisotropy.

The long axis of the porous canals were generally oriented in the transverse plane, 

and no predominant orientation within this plane was visible in the high-resolution 

micro-CT scans of the upper table of the skull (Figs. 22 and 23). These figures 

originated from 2 different bone types (frontal and parietal) from 2 different skulls 

(04 and 10). They provide high-resolution confirmation of the observation reported 

by McElhaney et al. (1970), which was based on observation of serial sections of 

cranial bone using unspecified methods.

The random arrangement in the transverse plane is in sharp contrast to the 

preferential alignment of osteons along the loading direction in load-bearing bones 

such as the femur. As a means of comparison, Fig. 24 provides a 3-D representation 

of the porous space within the outer cortical region of a human femur specimen 

used by our group as part of a different set of experiments (Sanborn et al. 2016).
Approved for public release; distribution unlimited.

35

Fig. 24 Porous space within the outer cortical region of a human femoral bone specimen, 

visualized with micro-CT. The pores are shown as grey objects.

4.3 Assumptions, Limitations, and Sources of Error Associated 

with Quantitative Porosity Assessment

The goal of the quantitative analysis of skull structure was to maximize the 

repeatability of measurements to draw comparisons between extraction grids, bone

types, and skulls. Nevertheless, several factors may introduce error into these 

comparisons.

Error could have arisen in the comparison of bone types (frontal, parietal) across 

different skulls. These comparisons implicitly assumed that the extracted 

specimens were comparable across skulls. Care was taken to extract bone sections 

from the skull that appeared similar in external features. However, variations were 

inevitable due to the variability associated with human skulls. An example is 

provided by the 3 specimens with failed Gaussian fits. In addition, each extraction 

grid of specimens was from a different distance away from the sutures (Table 1). 

The variability in distance from the sutures could introduce an additional variable 

if cranial structure changes as a function of these distances, which has been 

previously observed (McElhaney et al. 1970).

4.3.1 Measurement Error: Scanning Parameters and Image 

Postprocessing

Scanning parameter variations and subsequent postprocessing of the images could 

have introduced error into the porosity analysis. Four different sets of scanning 

parameters were used (Table 2) due to external circumstances. In addition, several 

postprocessing steps were necessary to calculate the porosity profile from the 

images. First, the outer surface of the specimen was rotated so that the surface 

normal at the center of the outer table was aligned in the vertical direction (Fig. 3). 
Approved for public release; distribution unlimited.

36

However, this realignment could have introduced subjectivity due to the 

irregularity of the outer surface. After rotation, the pixels corresponding to the 

specimen, or ROI, were then separated from pixels representing the surrounding 

media on the top and the bottom of the specimen. Any uncertainty associated with 

the ROI selection could have a direct impact on the measurement of overall 

thickness, t, considering it is calculated from the overall height of the image stack. 

Finally, the images were converted from gray scale to a binary format for the 

quantitative image analysis. An automated algorithm was used to eliminate 

operator subjectivity in the threshold identification for the grayscale images.

Appendix A presents a quantification of measurement error arising from scanning 

parameter differences and postprocessing procedures. Specimen 06-25 was 

scanned under different parameters, and the resulting images from each scan were 

also independently postprocessed. The variation between results indicated the total 

error associated with scanning parameter variation, image stack rotation, and 

specimen ROI selection. It was concluded that the total measurement error for each 

parameter was much lower than the amount of specimen-to-specimen deviation 

within an extraction grid, generally accounting for less than 10% of the total 

interspecimen variability.

4.3.2 Approximating the Porosity Variation with a Gaussian Function

In this study, the porosity-depth profile was assumed to be adequately described by 

a Gaussian distribution. The porosity-depth profiles of 60 from a total of 63 

specimens were well described by the Gaussian function (R2 > 0.65). The Gaussian 

curve was considered an inappropriate fit for only 3 specimens: 06-01, 06-04, and 

06-07. These specimens did not have distinguishable inner tables with dense 

cortical bone. Instead, the region normally composed of the dense inner table was 

filled with large pores, creating a second porous region in addition to the diploë. 

As an example, Fig. 25 shows a through-thickness image of one of these specimens, 

06-07. The in-situ arrangement of these 3 specimens was roughly along a vertical, 

superior-inferior line on the frontal bone (Fig. 2). Therefore, these porous regions 

in the inner table could be evidence of a persistent network of cavities oriented in 

the superior-inferior direction and near the inner surface. The skull contains veins 

in the diploë, and the inner surface had several foramina that allowed for passage 

of vessels into the cranial bone. The cavities near the inner surface of the specimens 

with low R2 values were likely components of the vesicular passages from the 

meninges into the cranium. Indeed, various deviations from the canonical 3-layered 

morphology have also been reported elsewhere, accompanied by an inability to 

discretize the thickness into 3 separate layers (Ruan and Prasad 2001).
Approved for public release; distribution unlimited.

37

Fig. 25 Through-thickness image of Specimen 06-07. For this specimen, the porosity-depth 

profile could not be described by the Gaussian fit. A secondary porous region, in addition to 

the diploë, is evident near the inner surface (bottom of the figure).

4.3.3 Method for Layer Identification

A new, more repeatable method to distinguish between the layers was identified 

using the porosity-depth profile together with a cutoff percentage. This procedure 

was based on several assumptions. First, the outer and inner tables were assumed 

to consist entirely of cortical bone with a porosity less than 30%, and the diploë 

was assumed to be only trabecular bone with a porosity of greater than 30%. 

However, the porosity-depth profiles indicated a porosity gradient, and 

identification of a single cutoff value remained somewhat arbitrary. Moreover, the 

results indicated that the threshold of 30% may have been high, leading to inflated 

values for table thicknesses. For example, the inner table of many specimens, as 

identified by the present method, included regions where the porosity spiked above 

30%. This could indicate that a lower threshold may be used in the future.

Secondly, the method assumed that the porosity only varied in the depth dimension, 

from the outer to inner surfaces, and that the porosity was constant in the transverse 

dimension. This assumption appeared to be valid based on the visual inspection of 

the micro-CT images (e.g., Fig. 5), and is further analyzed in Appendix D.
Approved for public release; distribution unlimited.

38

5. Conclusions

The change in porosity was measured across the thickness of the skull, from the 

outer to inner surfaces, using micro-CT with a resolution of less than 10 μ. The 

resulting porosity-depth profiles were used to calculate the thicknesses of the 3 

layers of the skull: the outer and inner tables and the diploë. Each of the porositydepth profiles were fit to a Gaussian function, from which the peak diploë porosity 

was calculated together with the spread of porosity across the depth. The measured 

parameters enabled a comparison between frontal and parietal bones while 

accounting for skull-to-skull variation, allowing us to reach the following 

conclusions:

• The diploë occupies relatively more thickness in the parietal bone than in 

the frontal bone. The increased thickness percentage of the diploë in the 

parietal bone appears to be compensated by a relatively thinner inner table. 

Given the porosity-modulus relationship, these differences would suggest 

that parietal bone is weaker than frontal bone.

• On the other hand, measurements of the total specimen thickness did not 

consistently show significant differences between the frontal and parietal 

bone. At the same time, there were significant differences between donors. 

For example, the thicknesses of frontal bone specimens were significantly 

different between all 3 skulls.

• The peak porosity reached in the diploë was not consistently different 

between the frontal and parietal bones. 

Finally, the porous space within the outer tables of the frontal and parietal bones 

was imaged with micro-CT using a resolution less than 5 μm. The microstructural 

subunits of the outer table of the skull bone appeared randomly oriented in the 

transverse plane.
Approved for public release; distribution unlimited.

39

6. References

Alexander SL, Gunnarsson CA, Weerasooriya T. Structural influence on the 

mechanical response of adolescent Göttingen porcine cranial bone. Aberdeen 

Proving Ground (MD): Army Research Laboratory (US); 2016 Oct. Report 

No.: ARL-TR-7845.

Boruah S, Henderson K, Subit D, Salzar R, Shender B, Paskoff G. Response of 

human skull bone to dynamic compressive loading. In: Proceedings of the 

International Research Council on Biomechanics of Injury (IRCOBI) 

Conference; 2013 Sep 11–13; Gothenburg, Sweden: IRCOBI Vol. 13. p. 497.

Boruah S, Paskoff GR, Shender BS, Subit DL, Salzar RS, Crandall JR. Variation 

of bone layer thicknesses and trabecular volume fraction in the adult male 

human calvarium. Bone. 2015;(77):120–134.

Carter DR, Hayes WC. The compressive behavior of bone as a two-phase porous

structure. The J of Bone and Joint Surgery. 1977;59(7):954–962.

Fry, FJ, Barger, JE. Acoustical properties of the human skull. The J of the 

Acoustical Soc of America. 1978;(63):1576–1590.

Goulet RW, Goldstein SA, Ciarelli MJ, Kuhn JL, Brown MB, Feldkamp LA. The 

relationship between the structural and orthogonal compressive properties of 

trabecular bone. J of Biomechanics. 1994;27(4):375–389.

Helgason B, Perilli E, Schileo E, Taddei F, Brynjólfsson S, Viceconti M. 

Mathematical relationships between bone density and mechanical properties:

a literature review. Clinical Biomechanics. 2008;23(2):135–146.

Huang AH, Sun HH, Skolnick GB, Woo AS. Thickness of calvarium and diploic 

space in children ages 0 to 17 as assessed by computed tomography. European 

J of Plastic Surgery. 2015;38(3):193–198.

Hubbard RP. Flexure of layered cranial bone. J of Biomechanics. 1971;4(4):

251–263.

Lillie EM, Urban JE, Weaver AA, Powers AK, Stitzel JD. Estimation of skull table 

thickness with clinical CT and validation with micro-CT. J of Anatomy. 

2015;226(1):73–80.

Lillie EM, Urban JE, Lynch SK, Weaver AA, Stitzel JD. Evaluation of skull 

cortical thickness changes with age and sex from computed tomography scans. 

J of Bone and Mineral Research. 2016;31(2):299–307.
Approved for public release; distribution unlimited.

40

Lynnerup N, Astrup JG, Sejrsen B. Thickness of the human cranial diploë in 

relation to age, sex and general body build. Head and Face Medicine. 

2005;1(13):1–7.

McElhaney JH, Fogle JL, Melvin JW, Haynes RR, Roberts VL, Alem NM. 

Mechanical properties of cranial bone. J of Biomechanics. 1970;3(5):495–511.

Motherway JA, Verschueren P, Van der Perre G, Vander Sloten J, Gilchrist MD. 

The mechanical properties of cranial bone: the effect of loading rate and cranial 

sampling position. J of Biomechanics. 2009;42(13):2129–2135.

Mow VC, Huiskes R. Basic orthopaedic biomechanics and mechano-biology.

Alphen aan den Rijn (Netherlands): Lippincott Williams and Wilkins; 2005.

Otsu, Nobuyuki. A threshold selection method from gray-level histograms. 

Automatica. 1975;11.285(296):23–27.

Peterson J, Dechow PC. Material properties of the inner and outer cortical tables of 

the human parietal bone. The Anatomical Record. 2002;268(1):7–15.

Peterson J, Dechow PC Material properties of the human cranial vault and zygoma. 

The Anatomical Record Part A: Discoveries in Molecular, Cellular, and 

Evolutionary Biology. 2003;274(1):785–797. 

Peyrin F, Salome M, Nuzzo S, Cloetens P, Laval-Jeantet AM, Baruchel J. 

Perspectives in three-dimensional analysis of bone samples using synchrotron 

radiation microtomography. Cell Mol Biol. 2000; 46:1089–1102.

Cited in: Cooper DML, Turinsky AL, Sensen CW, Hallgrimsson B. 

Quantitative 3D analysis of the canal network in cortical bone by micro‐

computed tomography. The Anatomical Record Part B: The New Anatomist.

2003.274(1):169–179.

Rahmoun J, Auperrin A, Delille R, Naceur H, Drazetic P. Characterization and

micromechanical modeling of the human cranial bone elastic properties. 

Mech Research Comm. 2014;60:7–14.

Ruan J, Prasad P. The effects of skull thickness variations on human head dynamic 

impact responses. Stapp Car Crash J. 2001;45:395–414.

Sabanciogullari V, Salk I, Cimen M. The relationship between total calvarial 

thickness and diploë in the elderly. International J of Morphology. 

2013;31(1):38–44.
Approved for public release; distribution unlimited.

41

Sanborn B, Gunnarsson CA, Foster M, Weerasooriya T. Quantitative visualization 

of human cortical bone mechanical response: studies on the anisotropic 

compressive response and fracture behavior as a function of loading rate. 

Experimental Mechanics. 2016;56(1)81–95.

Trammell LH. Neurocranial histomorphometrics [dissertation]. [Knoxville (TN)]: 

University of Tennessee; 2012.
Approved for public release; distribution unlimited.

42

INTENTIONALLY LEFT BLANK.
Approved for public release; distribution unlimited.

43

Appendix A. Analysis of Error Associated with Scanning 

Parameters and Postprocessing Steps
Approved for public release; distribution unlimited.

44

Specimen 06-25 was scanned 4 different times using the parameters described 

below in Table A-1. These scans were taken for the purpose of protocol 

determination and were not explicitly executed for error analysis. Nevertheless, the 

quantitative results can provide insight into the total error arising from the variation 

of scanning parameters used in the report (Table 2) and from the error involved in 

postprocessing. For example, the resolution of these scans ranged from 6.7 to 

5.3 μm, which covered the full range of resolutions used in the report.

Table A-1 Micro-CT scanning parameters for error analysis

Scan no.

Resolution/voxel 

size (μm)

Frame avg. 

(no. of frames)

Rotation 

step (°)

Random 

movement Filter

Scan 1 6.7 10 0.2 20 Al, 0.5 mm

Scan 2 6.1 10 0.2 20 none

Scan 3 6.1 10 0.2 20 Al, 0.5 mm

Scan 4 5.3 10 0.15 20 Al, 0.5 mm

Each dataset from each scan was postprocessed independently. The same methods 

as described in the report were used after each scan for image stack rotation, region 

of interest (ROI) selection, image binarization, the calculation of the porosity-depth 

profile P(d), and the calculation of the Gaussian fit (Eq. 1). Similarly, the 4

parameters calculated in Section 3.2 from the porosity-depth profile (t, ttoo, ttdd, ttii) 

and the 3 parameters calculated in Section 3.4 from the Gaussian fit (A, B, and C) 

were also calculated for these scans. Figure A-1 shows the porosity-depth profiles 

from each scan and the Gaussian fits. Table A-2 reports the results for each of the 

7 parameters.
Approved for public release; distribution unlimited.

45

Fig. A-1 Porosity-depth profile from each scan (top) and the Gaussian fits (bottom)

Table A-2 Parameter results

Scan no.

tt

(μm)

tt

(%)

tt

(%)

tt

(%)

A

(porosity %)

B

(%)

C

(%)

Scan 1 8122 19.4 63.8 16.8 76.3 49.0 32.5

Scan 2 8161 19.1 65.2 15.7 76.0 48.9 32.7

Scan 3 8259 20.2 63.0 16.8 76.6 48.4 32.1

Scan 4 8118 18.9 66.3 14.8 76.2 49.0 32.8

σσMM 65.5 0.6 1.5 0.9 0.3 0.3 0.3

Note: Units are in depth percentage points, except for parameters t and A, which are in units of μm and percent porosity, 

respectively. Also shown is the standard deviation due to measurement (σσMM) for each parameter.

The Coefficient of Reliability, R, has been used by others to relate the amount of 

variation due to measurement error to the total amount of inter-specimen variation.1

Adapted to the present case, the Coefficient of Reliability for a given parameter can 

be defined by Eq. A-1:

 1

Ulijaszek SJ, Kerr DA. Anthropometric measurement error and the assessment of nutritional status. British J 

of Nutrition. 1999;82(03):165–177.
Approved for public release; distribution unlimited.

46

RR = 1 − (σσMM)2

(σσoo)2 . (A-1)

In Eq. A-1, the standard deviation due to measurement of the parameter is given by 

σσMM and the total, interspecimen standard deviation observed in the results is given 

by σσoo. The results for R are shown in Table A-3. R was calculated for each 

parameter using the σσMM from the error study of Spec 06-25 (Table A-2) together 

with the standard deviation values reported from each extraction grid (Sections 3.2 

and 3.4).

Table A-3 Coefficient of Reliability (R) for each parameter

Extraction grid tt tt tt tt A B C

Skull 4, frontal 98.2 96.9 91.4 96.8 99.3 99.1 98.4

Skull 4, parietal 95.8 98.8 96.6 92.6 99.4 98.2 99.4

Skull 6, frontal 99.7 87.4 98.6 99.4 99.9 99.5 99.5

Skull 6, parietal 98.5 98.1 92.7 89.3 96.5 96.1 99.3

Skull 10, frontal 99.3 95.0 96.9 98.8 99.9 99.6 99.2

Skull 10, parietal 99.1 99.2 98.3 97.7 100.0 99.4 99.7

Mean 98.4 95.9 95.8 95.8 99.2 98.6 99.2

Note: R is calculated for each parameter using Eq. A-1, and is reported in percentage (%).

The Coefficient of Reliability quantifies the amount of the variation observed in 

each extraction grid that was not due to measurement error.2,3 In Table A-3, R was

reported as greater than 90%, with only 2 exceptions. This indicates that 

measurement error associated with scanning parameter variation and 

postprocessing is generally accountable for less than 10% of the total amount of 

observed variation in each grid. Furthermore, even the lowest R value (87.4%) 

indicated that the total measurement error accounted for less than 13% of the 

interspecimen error. 

 2

Ulijaszek SJ, Kerr DA. Anthropometric measurement error and the assessment of nutritional status. British

Journal of Nutrition. 1999;82(03):165–177.

3

Lewis SJ. Quantifying measurement error. In: S. Anderson, editor. Current and recent research in 

osteoarchaeology 2: 1999; Proceedings of the 4th, 5th and 6th meetings of the Osteoarchaeological 

Research Group. Barnsley (England): Oxbow Books. c1999. p. 54–55.
Approved for public release; distribution unlimited.

47

Appendix B. Box Plots of Results for the Gaussian Coefficients 

(A, B, and C)
Approved for public release; distribution unlimited.

48

Figures B-1 through B-3 present box plots of the results for the Gaussian 

coefficients A, B, and C, respectively. The box plots show the median, first and 

third quartiles, and whiskers extending to 1.5 times the interquartile range. Red 

dots indicate outliers beyond the extent of the whiskers. Each figure shows the 

bone-to-bone variation as well as the skull-to-skull variation. The mean and 

standard deviation of the results were presented in Tables 12–14 in the main report.

Fig. B-1 Box plots of the Gaussian coefficient A
Approved for public release; distribution unlimited.

49

Fig. B-2 Box plots of the Gaussian coefficient B
Approved for public release; distribution unlimited.

50

Fig. B-3 Box plots of the Gaussian coefficient C
Approved for public release; distribution unlimited.

51

Appendix C. Summary Data for the Thickness Parameters
Approved for public release; distribution unlimited.

52

Table C-1 lists the mean and standard deviation for the thickness percentages of the 

outer table (ttoo), diploë (ttdd), and inner table (ttii), as they were reported in 

Section 3.2 (Tables 5–7) of the main report. Table C-2 lists the absolute values (in 

millimeters) of the layer thicknesses, together with the total skull thickness (t). 

These are also shown in Fig. C-1. Figures C-2 through C-5 present box plots of the 

results for total skull thickness (t), as well as for ttoo, ttdd , and ttii. Each figure shows 

the bone-to-bone variation as well as the skull-to-skull variation. 

Table C-1 Relative layer thicknesses (% of total thickness)

Grouping tt tt tt

Skull 04, frontal 23.5 ± 3.2 53.1 ± 5.0 23.5 ± 5.3

Skull 04, parietal 18.6 ± 5.3 68.1 ± 7.9 13.3 ± 3.5

Skull 06, frontal 21.2 ± 1.6 42.9 ± 12.4 35.8 ± 12.0

Skull 06, parietal 15.7 ± 4.2 71.3 ± 5.4 13.0 ± 2.9

Skull 07, frontal 21.7 ± 3.0 52.6 ± 11.1 25.7 ± 8.9

Skull 10, frontal 23.3 ± 2.6 33.5 ± 8.3 43.1 ± 8.6

Skull 10, parietal 24.1 ± 6.4 58.6 ± 11.2 17.4 ± 6.3

Skull 04, pooled 21.0 ± 5.0 60.6 ± 10.0 18.4 ± 6.8

Skull 06, pooled 18.5 ± 4.2 57.1 ± 17.3 24.4 ± 14.5

Skull 10, pooled 23.7 ± 4.8 46.1 ± 16.1 30.3 ± 15.1

Frontal, pooled 22.4 ± 2.7 45.5 ± 12.3 32.0 ± 11.8

Parietal, pooled 19.4 ± 6.3 66.0 ± 9.8 14.6 ± 4.7

Note: Summarized from Tables 5–7 of the main report.

Table C-2 Absolute layer thicknesses (mm)

Grouping tt tt tt tt

Skull 04, frontal 9.6 ± 0.5 2.3 ± 0.3 5.1 ± 0.5 2.3 ± 0.6

Skull 04, parietal 5.5 ± 0.3 1.0 ± 0.3 3.8 ± 0.3 0.7 ± 0.2

Skull 06, frontal 8.5 ± 1.1 1.8 ± 0.1 3.7 ± 1.4 3.0 ± 0.9

Skull 06, parietal 8.3 ± 0.5 1.3 ± 0.3 5.9 ± 0.7 1.1 ± 0.2

Skull 07, frontal 6.5 ± 0.6 1.4 ± 0.2 3.5 ± 0.9 1.7 ± 0.6

Skull 10, frontal 7.0 ± 0.8 1.6 ± 0.9 2.4 ± 0.7 3.0 ± 0.7

Skull 10, parietal 6.1 ± 0.7 1.5 ± 0.4 3.6 ± 0.9 1.0 ± 0.3

Skull 04, pooled 7.6 ± 2.1 1.6 ± 0.7 4.4 ± 0.8 1.5 ± 0.9

Skull 06, pooled 8.4 ± 0.9 1.5 ± 0.4 4.8 ± 1.6 2.1 ± 1.2

Skull 10, pooled 6.6 ± 0.8 1.5 ± 0.3 3.0 ± 1.0 2.0 ± 1.1

Frontal, pooled 7.9 ± 1.5 1.8 ± 0.4 3.7 ± 1.3 2.5 ± 0.9

Parietal, pooled 6.7 ± 1.3 1.3 ± 0.4 4.4 ± 1.3 1.0 ± 0.3
Approved for public release; distribution unlimited.

53

Fig. C-1 Absolute thickness measurements (mm) of each of the layers for the frontal bone 

(left) and parietal bone (right)
Approved for public release; distribution unlimited.

54

Fig. C-2 Box plots of the total skull thickness (t) in mm
Approved for public release; distribution unlimited.

55

Fig. C-3 Box plots of the thickness percentage of the outer table (tt )
Approved for public release; distribution unlimited.

56

Fig. C-4 Box plots of the thickness percentage of the diploë (tt )
Approved for public release; distribution unlimited.

57

Fig. C-5 Box plots of the thickness percentage of the inner table (tt )
Approved for public release; distribution unlimited.

58

INTENTIONALLY LEFT BLANK.
Approved for public release; distribution unlimited.

59

Appendix D. Sufficiency of Cross-Sectional Dimensions to 

Provide Representative Results
Approved for public release; distribution unlimited.

60

In this study, comparison of the porosity-depth profiles across specimens assumed 

that the amount of variation across the transverse plane was negligible. For this 

assumption to be applicable, the cross-sectional area (image plane) had to be 

sufficiently large to provide a true representation of the porosity across the 

transverse plane. If the imaged area of the specimen was too small, the resulting 

porosity measurement would be a measure of local variations and not a 

representative measurement of the bone being studied. This appendix evaluates 

whether the cross-sectional dimensions that were used were sufficiently large to 

provide representative measures.

Images with the least amount of bone were believed to be the biggest cause of 

concern. The extraction grids from the parietal bones of Skulls 10 and 04 had the 

highest values for peak porosity in the diploë, as also indicated with the 

corresponding Gaussian coefficient A (Table 12). Therefore, for the evaluation of 

the present appendix, images were extracted from the diploë of 3 specimens from 

the parietal bone of Skull 10 (10-14, 10-16, and 10-17) and 3 specimens from the 

parietal bone of Skull 04 (04-14, 04-16, and 04-17). An image was also taken from 

the frontal bone of Skull 06 (06-05) for comparison, since this bone had the smallest 

value of peak porosity in the diploë (Table 12).

The image selected from each specimen corresponded to the maximum porosity of 

the porosity-depth profile, P(d). The images were extracted from the binarized data 

set (Section 2.2). For each image, a subset of 3 × 3 pixels was seeded in the center 

of the image. The porosity within the subset was calculated. The subset was then 

enlarged and the porosity was recalculated. This process was iterated until the 

subset included the entire image. 

The range of porosity (max-min) was measured during the final decade of 

increments in subset area. This range was less than 2% for all images. Figures

D-1–D-7 show the porosity plotted as a function of subset size for each of the 

images, together with the binary image. These figures indicated that the porosity 

converged to stable values for all of the images, with the possible exception of 

Specimens 06-05 (Fig. D-7) and 10-14 (Fig. D-4). The result for Specimen 06-05 

was especially surprising. The problem of convergence was expected to be more 

pronounced for images with less bone area, but Specimen 

06-05 had the highest percentage of bone (36.3%).
Approved for public release; distribution unlimited.

61

Fig. D-1 Porosity convergence (left) for a cross-sectional image (right) from the diploë of 

Specimen 04-14

Fig. D-2 Porosity convergence (left) for a cross-sectional image (right) from the diploë of 

Specimen 04-16

Fig. D-3 Porosity convergence (left) for a cross-sectional image (right) from the diploë of 

Specimen 04-17
Approved for public release; distribution unlimited.

62

Fig. D-4 Porosity convergence (left) for a cross-sectional image (right) from the diploë of 

Specimen 10-14

Fig. D-5 Porosity convergence (left) for a cross-sectional image (right) from the diploë of 

Specimen 10-16

Fig. D-6 Porosity convergence (left) for a cross-sectional image (right) from the diploë of 

Specimen 10-17
Approved for public release; distribution unlimited.

63

Fig. D-7 Porosity convergence (left) for a cross-sectional image (right) from the diploë of 

Specimen 06-05
Approved for public release; distribution unlimited.

64

List of Symbols, Acronyms, and Abbreviations

3-D 3-dimensional

ANOVA analysis of variance

HBSS Hanks Buffered Saline Solution

HSD Honestly Significant Difference

fbv bone-volume-fraction

micro-CT microcomputed tomography

PMHS postmortem human subject

ROI region of interest

VOI volume of interest
Approved for public release; distribution unlimited.

65

1 DEFENSE TECHNICAL

(PDF) INFORMATION CTR

DTIC OCA

1 DIRECTOR

(PDF) US ARMY RESEARCH LAB

IMAL HRA

1 DIRECTOR

(PDF) US ARMY RESEARCH LAB

RDRL CIO L

1 GOVT PRINTG OFC

(PDF) A MALHOTRA

3 JOHNS HOPKINS UNIVERSITY 

(PDF) T D NGUYEN

B NOTGHI

S BAILOOR

1 INDIAN INST OF TECH

(PDF) R BHARDWAJ

11 NATICK SOLDIER RSRCH

(PDF) DEV AND ENG CTR

M G CARBONI

D COLANTO

R DILALLA

J FONTECCHIO

B KIMBALL

J KIREJCZYK

J PARKER

M MAFEO

M MARKEY

D PHELPS

J WARD

3 PROG EXECUTIVE OFC 

 (PDF) SOLDIER

A FOURNIER

J MULLENIX

J ZHENG

5 SOUTHWEST RSRCH INST

(PDF) C ANDERSON JR 

S CHOCRON

D NICOLELLA

T HOLMQUIST

G JOHNSON 

1 INST FOR DEFNS ANLYS

(PDF) Y MACHERET

3 MRMC DOD BLAST INJURY

(PDF) RSRCH PROGRAM COOR OFC

R GUPTA

M LEGGIERI

R SHOGE

1 WIAMAN PMO

(PDF) S MARSH

3 MRMC JTAPIC PRGM OFC

(PDF) F LEBEDA

W LEI

J USCILOWICZ

3 US ARMY AEROMEDICAL

(PDF) RSRCH LAB

V CHANCEY

B MCENTYRE

D WISE

1 TARDEC

(PDF) R SCHERER

1 RDECOM HQ

(PDF) AMSRD PE

D RUSIN

44 DIR USARL

(PDF) RDRL SLB W

J GURGANUS

J IVANCIK

W MERMAGEN

K RAFAELS

RDRL WM

S SCHOENFELD

RDRL WMM

M VANLANDINGHAM

RDRL WMM A

D O’BRIEN

T PLAISTED

E WETZEL

RDRL WMM B

T BOGETTI

B LOVE

P MOY

C YEN

RDRL WMM D

S WALSH

 B CHEESEMAN

RDRL WMM E

L VARGAS-GONZALEZ 
Approved for public release; distribution unlimited.

66

RDRL WMP B

A DAGRO

A DILEONARDI

A EIDSMORE

A GUNNARSSON

C HAMPTON

M KLEINBERGER

J MCDONALD

P MCKEE

S SATAPATHY

K THOMPSON

T WEERASOORIYA 

S WOZNIAK

T ZHANG

C HOPPEL

Y HUANG

RDRL WMP C

R BECKER

T BJERKE 

A SOKOLOW

RDRL WMP D

R DONEY

B SCOTT

C RANDOW

RDRL WMP E

S BARTUS

M BURKINS

P GILLICH

M LOVE

P SWOBODA 

RDRL WMP F

N GNIAZDOWSKI

R GUPTA