in forensic practice , it is difficult to distinguish between accidental and intentionally inflicted head trauma in an injured child . the key question is often whether the head injury was the consequence of a fall or a blow from caretakers suspected of child abuse . computer - based finite element modeling of the head can be used to simulate the events associated with traumatic head injury and quantify biomechanical responses within the brain , but the utility of these models depends upon the accuracy of cranial material property inputs . determining the material properties of pediatric bones and sutures , such as elastic modulus , ultimate stress , and ultimate strain , and elucidating the factors that affect them will not only provide insight into the reaction of the pediatric cranial bones and sutures to loading , but will improve the accuracy of computational and experimental models simulating falls or impacts to a pediatric head [ 47 ] . the dynamic material properties of human adult or animal skull tissues are well documented [ 816 ] , but little information is available about the dynamic properties of human infant cranial bones and sutures . testing speed , strain rate , and cranial sampling position reportedly have significant effects on some or all of the computed mechanical parameters of adult cranial bones . a modest correlation was also found between percent bone volume and the elastic modulus and the maximum bending stress . furthermore , the frontal bone ( fb ) was thicker and less porous and had a higher percent bone volume than the parietal bone ( pb ) ; thus , it fractured under higher forces and absorbed more energy prior to fracturing . coats and margulies were the first to investigate pediatric bone and suture material properties at high rates ( 1.22.8 m / sec ) related to fetal head molding in three - point bending and tension . in addition , pediatric cranial suture deforms 30 times more before failure than pediatric cranial bone . the pb was found to be significantly stiffer and have a higher ultimate stress than occipital bone . mclaughlin et al . reported no significant difference in ultimate stress at failure between the coronal and sagittal sutures of 1-week - old wistar rats . the elastic modulus of coronal and sagittal sutures was 13 mpa and 14 mpa , respectively , while the estimated ultimate strain values were 160% and 120% for the sagittal and coronal sutures , respectively . however , no data currently exist in the literature regarding whether there is a difference in the material properties between coronal and sagittal sutures of human infants . few studies have reported differences in bending properties the purpose of this study was to examine the differences in the material properties of human infants ( 12 years old ) in different bone and suture sampling positions . these results could be used in future computational models simulating the infant head during accidental and intentionally inflicted impact . the cadaver specimens were obtained from deceased infants donated by their families to the southern medical university in china . human infant cranial bones and sutures were obtained from seven fresh - frozen human infant cadavers ( females , three ; males , four ; 1.50.5 years old ) . all materials were thoroughly examined to ensure a lack of skull fractures and malformations and refrigerated at 20c until the preparation and testing , thus minimizing the number of freeze - thaw cycles to prevent bone damage . we then thawed out the subjects in saline no more than 6 hours before the experiment . eight specimens ( 6 cm long , 1 cm wide ) were obtained from each subject : two fb , two pb , two parietal  parietal suture ( sagittal sutures ) samples , and two parietal  frontal suture ( coronal sutures ) samples . the latter two contained suture and bone . we used a vertical band saw and gently filed the cut faces to ensure accurate dimensions . the positions and directions of the samples from the eight skulls were kept as uniform as possible to allow for realistic future comparisons ( figure 1 ) . the width and thickness of each test specimen were measured adjacent to the cross - section where the fracture occurred . the samples ( n=56 ; eight each from seven infant cadavers ) were subjected to a three - point bending test using a bose material testing machine ( elf-3510at ; bose , inc . , chicago , usa ) at 1.5 mm / s after micro - computed tomography measurements . each specimen was thawed at room temperature in saline no more than 4 h prior to testing . prior to testing , each specimen was instrumented with support structures ( figure 2 ) made from a rigid two - part epoxy resin to prevent erroneous slippage during testing and provide a flat surface on which to rest the specimens . this reduced the effective span length for the tests to 4 cm ( the distance between the two epoxy supports ) but still allowed specimen rotation and bending . all data were collected using the computer data acquisition system consisting of the bose material testing machine and a computer . during the mechanical testing , the euler - bernoulli beam theory is applicable only in cases in which the ratio of span length to thickness is at least 8 . in our study , the average span length to thickness ratios of the tested specimens was > 8 . therefore , the euler - bernoulli equation could be used to calculate the elastic modulus ( e ) : where f/ is the force - displacement ratio in the linear elastic region of a three - point bending trace ( figure 3 ) , l is the span of the beam , and i is the moment of inertia of the rectangular cross - section of the beam . the flexural strain ( f ) from three - point bending was calculated from the relationship : where  is the maximum deflection in the center of the beam , t is the thickness of the sample , and l is the span . ultimate strain ( ult ) was selected as the flexural strain corresponding to the ultimate stress . in - plane stress ( xx ) was calculated using timoshenko s corrected version of the beam theory equation , which accounts for radial tensile forces within the beam as the result of an applied concentrated load to the center of the beam : 
 ( 3)xx=3fl8wc3y-0.133fwc where f is the measured force , w is the width of the specimen , l is the span , c is half of the thickness , and y is the location of interest along the y - axis ( outer surfaces at y=c ) in the center of the beam . the ultimate stress ( ult ) the statistical significance of the differences between groups was determined by one - way analysis of variance followed by student - newman - keuls post hoc multiple comparison tests ( two - means comparison ) . correlations were measured using the pearson coefficient and two - tailed p values . the significance level for all analyses was set as p<0.05 and all statistical analyses were performed using spss 21.0 ( spss , inc . , human infant cranial bones and sutures were obtained from seven fresh - frozen human infant cadavers ( females , three ; males , four ; 1.50.5 years old ) . all materials were thoroughly examined to ensure a lack of skull fractures and malformations and refrigerated at 20c until the preparation and testing , thus minimizing the number of freeze - thaw cycles to prevent bone damage . we then thawed out the subjects in saline no more than 6 hours before the experiment . eight specimens ( 6 cm long , 1 cm wide ) were obtained from each subject : two fb , two pb , two parietal  parietal suture ( sagittal sutures ) samples , and two parietal  frontal suture ( coronal sutures ) samples . the latter two contained suture and bone . we used a vertical band saw and gently filed the cut faces to ensure accurate dimensions . the positions and directions of the samples from the eight skulls were kept as uniform as possible to allow for realistic future comparisons ( figure 1 ) . the width and thickness of each test specimen were measured adjacent to the cross - section where the fracture occurred . the samples ( n=56 ; eight each from seven infant cadavers ) were subjected to a three - point bending test using a bose material testing machine ( elf-3510at ; bose , inc . , chicago , usa ) at 1.5 mm / s after micro - computed tomography measurements . each specimen was thawed at room temperature in saline no more than 4 h prior to testing . prior to testing , each specimen was instrumented with support structures ( figure 2 ) made from a rigid two - part epoxy resin to prevent erroneous slippage during testing and provide a flat surface on which to rest the specimens . this reduced the effective span length for the tests to 4 cm ( the distance between the two epoxy supports ) but still allowed specimen rotation and bending . all data were collected using the computer data acquisition system consisting of the bose material testing machine and a computer . during the mechanical testing , the force - displacement curves of the 56 tested specimens were recorded . the euler - bernoulli beam theory is applicable only in cases in which the ratio of span length to thickness is at least 8 . in our study , the average span length to thickness ratios of the tested specimens was > 8 . therefore , the euler - bernoulli equation could be used to calculate the elastic modulus ( e ) : where f/ is the force - displacement ratio in the linear elastic region of a three - point bending trace ( figure 3 ) , l is the span of the beam , and i is the moment of inertia of the rectangular cross - section of the beam . the flexural strain ( f ) from three - point bending was calculated from the relationship : where  is the maximum deflection in the center of the beam , t is the thickness of the sample , and l is the span . ultimate strain ( ult ) was selected as the flexural strain corresponding to the ultimate stress . in - plane stress ( xx ) was calculated using timoshenko s corrected version of the beam theory equation , which accounts for radial tensile forces within the beam as the result of an applied concentrated load to the center of the beam : 
 ( 3)xx=3fl8wc3y-0.133fwc where f is the measured force , w is the width of the specimen , l is the span , c is half of the thickness , and y is the location of interest along the y - axis ( outer surfaces at y=c ) in the center of the beam . the ultimate stress ( ult ) the statistical significance of the differences between groups was determined by one - way analysis of variance followed by student - newman - keuls post hoc multiple comparison tests ( two - means comparison ) . correlations were measured using the pearson coefficient and two - tailed p values . the significance level for all analyses was set as p<0.05 and all statistical analyses were performed using spss 21.0 ( spss , inc . , according to the calculated mechanical properties of pb and fb ( figure 3 ) , both ultimate stress and elastic modulus in fb ( 99.7511.08 mpa and 1265.65120.90 mpa , respectively ) were higher than those in pb ( 87.12  10.58 mpa , p<0.05 and 1103.01112.77 mpa , p<0.01 , respectively ) . no significant difference was found in ultimate strain between pb and fb ( p>0.05 for both ) . the order of ultimate stress and elastic modulus from high to low in different positions of cranial bone was : fb ( 99.7511.08 mpa and 1265.65120.90 mpa , respectively ) > pb ( 87.1210.58 mpa and 1103.01112.77 mpa , respectively ) > coronal suture ( 52.448.71 mpa and 354.8344.86 mpa , respectively ) > sagittal suture ( 44.7510.13 mpa and 408.1259.08 mpa , respectively ) . the order of ultimate strain from high to low was : coronal suture ( 0.20850.0529 mm / mm ) > sagittal suture ( 0.18760.0348 mm / mm ) > fb ( 0.09720.0424 mm / mm ) > pb ( 0.08660.0270 mm / mm ) . significant differences were found in ultimate stress , elastic modulus , and ultimate strain between cranial bones ( pb , fb ) and cranial sutures ( sagittal suture , coronal suture , p<0.01 for elastic modulus between both fb , pb and sagittal suture , coronal suture ; p<0.05 for all others ) . no significant difference was found in ultimate stress , elastic modulus , or ultimate strain between sagittal and coronal sutures ( p>0.05 for all ) . a few human infant finite element models have been constructed to perform a series of virtual experiments [ 6,2429 ] . however , there has been no fe model for infants aged 12 years until now . an important reason for this is that no mechanical properties are documented for 12-year - old infants . the aim of this paper is to study the mechanical properties of the cranial bones and sutures of 12-year - old infants to better understand how the pediatric calvarium differs from that of adults under loading stress . although the mechanical properties of adult cranial bone including ultimate stress and elastic modulus did not differ , it was reported that pediatric cranial bones < 13 months old were significantly stiffer and have a higher ultimate stress than occipital bone . however , no studies have reported the differences in material properties between human infant pb and fb , while few studies have reported the material properties of human pediatric cranial sutures , especially in 12-year - old infants . in our study , the ultimate stress and elastic modulus values of the fb were higher than those of the pb , which was consistent with the findings of coats and margulies in which both ultimate stress and elastic modulus differed between the pb and occipital bone . this result might be related to the fact that the average fb thickness was greater than that of the pb . in addition , the ultimate stress of the pb was higher than those of the sagittal and coronal sutures . the elastic modulus of the pb was also higher than those of the sagittal and coronal sutures , while the ultimate strain of the pb was lower than those of the sagittal and coronal sutures . sutures are more energy absorbent than cranial bone ; thus , they are able to reduce the amount of stress experienced by the surrounding bones . this effect is partially due to the much lower young s modulus of the suture than of the bone , which allows the suture to act as a cushion within the skull . whether there are differences in the material properties of the human pediatric cranial suture remains unknown . these data are also important in the development of an accurate pediatric head injury computational model . as was reported that pediatric pb and occipital bones had different material properties such as ultimate stress and elastic modulus , we wondered whether the material properties would differ from coronal and sagittal sutures . to our surprise , we found no significant difference between coronal and sagittal sutures in ultimate stress , elastic modulus , or ultimate strain . mclaughlin et al . demonstrated that sagittal and coronal sutures in 7-day - old rats had elastic moduli of 13 and 14 mpa , respectively . the difference was not significant , however , which was in very good agreement with the results of the present study . besides , their result was obtained in rats , which differ from humans . since location plays an important role in ultimate stress and elastic modulus , skulls should not be considered homogeneous in the creation of computational models to investigate impact events in pediatric head trauma . however , our study has some limitations . first , the data were obtained from only seven subjects , which is a small sample . second , the assumptions that were made about the geometry of each bending specimen were not large enough to be significant . the analysis method used in this paper assumed that each specimen behaved like a linear beam of a uniform cross - section . although it was observed that the bone samples from different individuals were curved in the same direction , the initial radius of curvature was eight times greater than the thickness of each specimen . despite these limitations , our results provide a valuable reference for relevant research . to the best of our knowledge , the current mechanical data in the literature do not include studies on the differentiating mechanical response of 12-year - old pediatric cranial sagittal and coronal sutures on the mechanical properties of pediatric cranial bones and sutures . the results of our study might extend the scope of our knowledge and aid further studies of the mechanical properties of 12-year - old infant cranial bones and sutures . this study examined the effects of cranial sampling position and bone microstructural parameters on the calculated mechanical properties of pediatric cranial bones and sutures . first , ultimate stress and elastic modulus values of the fb were higher than those of the pb in 12-year - old infants . second , no differences were found between coronal and sagittal sutures in terms of ultimate stress , elastic modulus , or ultimate strain . third , the ultimate stress and elastic modulus values of the fb and pb were higher than those of the sagittal and coronal sutures , while the ultimate strain findings were opposite .
backgroundthe mechanical properties of 12-year - old pediatric cranial bones and sutures and their influential factors were studied to better understand how the pediatric calvarium reacts to loading.material/methodscranial bone and suture specimens were extracted from seven fresh - frozen human infant cadavers ( 1.50.5 years old ) . 
 eight specimens were obtained from each subject : two frontal bones , two parietal bones , two sagittal suture samples , and two coronal suture samples . 
 the specimens were tested in a three - point bend setup at 1.5 mm / s . 
 the mechanical properties , such as ultimate stress , elastic modulus , and ultimate strain , were calculated for each specimen.resultsthe ultimate stress and elastic modulus of the frontal bone were higher than those of the parietal bone ( p<0.05 ) . 
 no differences were found between the coronal and sagittal sutures in ultimate stress , elastic modulus , or ultimate strain ( p>0.05 ) . the ultimate stress and elastic modulus of the frontal and parietal bones were higher than those of the sagittal and coronal sutures ( p<0.05 ) , whereas the opposite ultimate strain findings were revealed ( p<0.05).conclusionsthere was no significant difference in ultimate stress , elastic modulus , or ultimate strain between the sagittal and coronal sutures . 
 however , there were significant differences in ultimate stress , elastic modulus , and ultimate strain between the frontal and parietal bones as well as between the cranial bones and sutures .