JOURNAL OF NEUROTRAUMAVolume 20, Number 11, 2003© Mary Ann Liebert, Inc.

Age-Dependent Changes in Material Properties of the Brainand Braincase of the Rat

AMIT GEFEN,1 NURIT GEFEN,1 QILIANG ZHU,1

RAMESH RAGHUPATHI,2 and SUSAN S. MARGULIES1

ABSTRACT

Clinical and biomechanical evidence indicates that mechanisms and pathology of head injury in in-fants and young children may be different from those in adults. Biomechanical computer-basedmodeling, which can be used to provide insight into the thresholds for traumatic tissue injury, re-quires data on material properties of the brain, skull, and sutures that are specific for the pediatricpopulation. In this study, brain material properties were determined for rats at postnatal days (PND)13, 17, 43, and 90, and skull/suture composite (braincase) properties were determined at PND 13,17, and 43. Controlled 1 mm indentation of a force probe into the brain was used to measure naive,non-preconditioned (NPC) and preconditioned (PC) instantaneous (Gi) and long-term (G`) shearmoduli of brain tissue both in situ and in vitro. Brains at 13 and 17 PND exhibited statistically in-distinguishable shear moduli, as did brains at 43 and 90 PND. However, the immature (average of13 and 17 PND) rat brain (Gi 5 3336 Pa NPC, 1754 Pa PC; G` 5 786 Pa NPC, 626 Pa PC) was sig-nificantly stiffer (p , 0.05) than the mature (average of 43 and 90 PND) brains (Gi 5 1721 Pa NPC,1232 Pa PC; G` 5 508 Pa NPC, 398 Pa PC). A “reverse engineering” finite element model approach,which simulated the indentation of the force probe into the intact braincase, was used to estimatethe effective elastic moduli of the braincase. Although the skull of older rats was significantly thickerthan that of the younger rats, there was no significant age-dependent change in the effective elasticmodulus of the braincase (average value 5 6.3 MPa). Thus, the increase in structural rigidity of thebraincase with age (up to 43 PND) was due to an increase in skull thickness rather than stiffeningof the tissue. These observations of a stiffer brain and more compliant braincase in the immaturerat compared with the adult rat will aid in the development of age-specific experimental models andin computational head injury simulations. Specifically, these results will assist in the selection offorces to induce comparable mechanical stresses, strains and consequent injury profiles in brain tis-sues of immature and adult animals.

Key words: constitutive properties; finite element analysis; head injury; pediatric animal model; skull;suture

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1Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania.2Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, Pennsylvania.

INTRODUCTION

AN INFANT OR YOUNG CHILD suffering head trauma asa result of a motor vehicle accident, child abuse, or

fall may develop secondary pathologies such as diffusecerebral swelling with an etiology and time course thatare substantially different than those observed in adults(Bruce, 1990; Geddes et al., 2001; Pascussi, 1998;Shapiro, 1985). Biomechanical computer-based modelsare being used with increasing frequency to provide in-sight into the mechanisms of traumatic head injury. Theaccuracy of these simulations in predicting the severityof injury is strongly dependent on an adequate mechan-ical description of material characteristics of the brainand braincase tissues. Until recently, biomechanical mod-els of a pediatric head injury considered the infant andyoung children’s brains and skulls as having the samemechanical properties of adults, such that only the sizewas scaled to fit the simulation (Dejeammes et al., 1984;Duhaime et al., 1987; Kumaresan et al., 2002; Mohn etal., 1979; Stürtz, 1980). However, the human brain andcranium undergo significant alterations over the first 4years of life. Neurons exhibit more extensive dendriticand axonal branching which is accompanied by a rise inlipid content as axonal segments become myelinated(Calder, 1984).

The chemical and structural alterations of the brain mayunderlie the changes in mechanical properties (stiffness)of the brain of the infant/child. Thibault and Margulies(1998) observed that the adult (1-year-old) porcine braintissue was significantly stiffer compared with immature(2–3 day-old) tissue when measured at 1.25% shear strain,but not at 2.5%, over a frequency range of 20–200 Hz.However, at larger strains (up to 50%), which are relevantto clinical head injury, the immature (5-day-old) porcinetissue was about twice as stiff as the adult pig (Prange andMargulies, 2002). The skull of newborns consists of thinflexible plates made of partially calcified bone, which areattached at their margins by the soft connective tissue ofthe sutures, thus constructing a compliant cranial structurecapable of substantial deformation under mechanical loads.Quasi-static (McPherson and Kreiwall, 1980) and dynamic(Margulies and Thibault, 2000; McLaughlin et al., 2000)stress-deformation relationships for cranial bone and su-tures in fetal and newborn humans and animals reveal thatcranial bone and suture stiffness/strength generally in-creases with age. To date, there is a paucity of quantita-tive information regarding the developmental time courseof changes in mechanical properties of brain and skull, andthere are no reports of such age-dependency in speciesother than the pig.

Rodents are the species most often used as experi-mental models of traumatic head injury. Rapid deforma-

tion of the brain as a result of indentation of the intactdura or skull by a pneumatically-driven rigid impactor(controlled cortical impact), or by a fluid bolus on the in-tact dura (fluid-percussion), are currently the most com-monly used and best characterized preclinical models oftraumatic brain injury in adults (Gennarelli, 1994; Lau-rer et al., 2000). Models of closed head injury in the im-mature rat have been established based on physiologicand behavioral parameters typically used to determine in-jury severity in adult rats (Adelson et al., 1996; Prins etal., 1996). Prins et al. (1996) observed that an injury loadof 1.6–2.1 atm with the fluid-percussion device resultedin mild deficits in adults (0% mortality, 7–10 sec of ap-nea), but more severe deficits in the 17-day-old rat pups(30% mortality, 45–60 sec of apnea). Similarly, in mod-ifying the impact-acceleration model of closed head in-jury for immature rats, it was observed that the mortal-ity rate, neurological deficits and tissue damage inimmature rats resulting from a 100-g weight drop wassimilar to those observed after a 450-g weight drop inadult rats (Adelson et al., 1996). When the injury load inimmature rats was adjusted for brain weight, younger(3–7-day-old) rats exhibited apoptotic cell death to agreater extent than adult rats following contusive braininjury (Bittigau et al., 1999). However, these experi-mental model designs utilizing an applied force or pres-sure are not adjusted for the changes in tissue materialproperties of the brain that occur with development, andthese properties may substantially affect the levels of me-chanical strain (and brain injury) in brain tissue in eachinjury paradigm. In contrast, when brain size and tissuestrain were utilized to scale injury parameters in the pig,it was observed that the neonatal pigs were less suscep-tible to histologic and physiologic damage following con-tusive brain injury (Duhaime et al., 2000; Durham et al.,2000).

The goal of this study was, therefore, to measure theelastic properties of brain and skull/suture composite(braincase) in the rat during development from immature(13- and 17-day-old rats) to adult (43- and 90-day-oldrats). At 7–10 postnatal days (PND) of age, the rat is neu-rologically equivalent to a human at birth, and by 12–15postnatal days of age the stage of development in the ratis equivalent to a 2–3-year-old human child (Dobbing,1964; Porterfield and Hendrich, 1993). The neurologicaldevelopment in the rat is complete by ,20 postnatal days,so 43- and 90-day-old rats can be considered neurologi-cally equivalent to human adults. Musculoskeletal de-velopment of the rat, however, continues beyond 43 post-natal days. For example, the mean width of the cranialvault at the postorbital constriction of the rat increasesby 10% between the age of 30 and 58 days (Kvam et al.,1975). Hence, while a 43-day-old rat has completed its

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neurological development, the growth of its skull maynot yet be complete. The elastic characteristics ofskull/sutures at three different ages were estimated bysupplementing the experimental mechanical testing datawith finite element simulations of braincase loading us-ing “reverse engineering.” These mechanical propertydata provide important information for scaling of animalmodel injury parameters and computer simulations of theimmature brain.

MATERIALS AND METHODS

Indentation Testing

Biological tissues are known to display a complexviscoelastic response to mechanical forces that isstrongly dependent on the rate and magnitude of theapplied load. For the purpose of biomechanical analy-sis, however, the brain and braincase are treated as homogenous, isotropic and incompressible materials(Kuijpers et al., 1995; Mendis et al., 1995; Miller etal., 2000; Prange and Margulies, 2002), making it pos-sible to use a rigid indentor to determine the shear mod-ulus. Indentation, a well-characterized method for mea-suring shear and elastic moduli of soft tissues such asbrain (Miller et al., 2000), muscle (Vannah and Chil-dress, 1996), lung parenchyma (Lai-Fook et al., 1976)and the plantar fat pad of the foot (Gefen et al., 2001)allows for the calculation of the shear and elastic mod-uli from the load applied by the indentor and the ex-tent of tissue deflection. In this study, an electro-mechanical computer-controlled indentor, comprisedof a miniature linear stepper motor (minimal displace-ment 0.0032 mm), force transducer (load capacity 1.47N or 150 g) and a linear variable displacement trans-ducer (LVDT), was used to indent the exposed skulland, following removal of the skull and dura, the ex-posed brain tissue, both to a depth of 1 mm. Recentshear measurements showed that gray matter can es-sentially be considered isotropic (properties are inde-pendent of the direction tested), whereas anisotropy ap-pears deeper at the corpus callosum, consistent with theneuroarchitecture (Prange and Margulies, 2002). Thus,for the 1-mm indentation employed in the present studydesign, assumptions of homogeneity and isotropy arereasonable and practical. The tip of the indentor wasmachined to a hemisphere in order to eliminate sharpedges at the indentor-tissue contact surface that maydamage the delicate tissues.

For a hemispherical indentor, the effective shear mod-ulus G (Mega Pascals, MPa) of brain tissue is calculatedusing the Lee and Radok (1960) solution for small dis-placements of a rigid indentor into elastic half-space,

G 5 (1)

where d is the indentation depth (mm) of a smooth rigidsphere with a radius R (mm) into the tissue due to the ac-tion of a load P (Newtons). Subsequently, the elasticmodulus E can be evaluated from

E 5 2G(1 1 v) (2)

where v is Poisson’s ratio (taken as 0.5 for the brain,which is assumed to be an incompressible material).

Based on a report by Zheng et al. (1999), the tip of theindentor was designed such that its radius R was no morethan 25% the thickness of the studied tissue sample. Bythis criterion, small misalignment of the indentor(,12.5°) has a negligible effect on the measured elasticproperties (Zheng et al., 1999). In the current study, thesuperior-inferior extent of the smallest (13-day-old) brainwas 8.2 mm, and therefore, an indentor with radius ofR 5 2 mm was used. To determine the elastic responseof the brain and skull/suture tissues, a constant speed ofindentation (1 mm/sec) was used for all tests. The in-dentor imposed a rapid deformation, which was held for90–160 sec. Theoretically, the rapid “ramp-and-hold” in-dentation of an elastic material produces a load responseof the same wave shape. In practice, for viscoelastic ma-terials such as brain tissue, the load P decreases with timeto a steady state asymptotic value during the “hold” pe-riod. If the time taken to impose the deformation is rel-atively short with respect to the rate of decay in the loadsignal, an instantaneous shear modulus Gi is calculatedfrom Eq. (1) by substituting the peak, or instantaneousload Pi measured immediately after deformation (“ramp”period) was ceased. The long-term shear modulus G` iscalculated using the asymptotic load value, P`.

Experimental Protocol

The protocol was approved by the Institutional Ani-mal Care and Use Committee at the University of Penn-sylvania. Shear moduli of rat brain and skull/suture tis-sues were measured in situ and in vitro for a total of 42animals grouped from nine different litters. Rats were di-vided into four groups according to their age (Table 1):13-day-old (n 5 11), 17-day-old (n 5 10), 43-day-old(n 5 10), and 90-day-old (n 5 11). For each group, 6–7animals were randomly selected for testing the brain andskull/suture composite mechanical properties in situ. Theremaining four to five animals in each age group wereassigned for testing the brain mechanical properties invitro (brain removed from the braincase) in order to ver-ify that tissue properties measured for brain were not af-fected by the confining nature of the braincase.

3P}16dÏRd

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For the purpose of in situ measurements of mechani-cal properties of the brain and braincase, animals wereeuthanized with sodium pentobarbital (postnatal day13–17: 50 mg/kg, postnatal day 43–90: 150 mg/kg, in-traperitoneal). Death was verified by cessation of heart-beat. Post-mortem, the scalp was reflected along a mid-line incision to access the skull. A site for indentationwas randomly assigned over the right or left cerebralhemisphere, and the head was firmly fixed to a rigid sup-port. Prior to measurements, the tip of the indentor waslubricated with surgical gel to prevent adhesion of tissueto the metal probe and to allow free slip of the tissue dur-ing deformation. The indentor was subsequently posi-tioned using its fine system of adjusters until delicate contact was made with the skull surface (Fig. 1) as de-termined by monitoring the force transducer signal on anoscilloscope. Because our primary goal was to quantifyage-related changes in material properties that are inde-pendent of the complex inhomogeneous and anisotropicnature of the brain, a consistent location of the indentorsite was maintained across ages. Force and displacement(LVDT signal) data were continuously measured at asampling rate of 25 scans/sec (25 Hz) using a PC laptopequipped with A/D board and LabView 6i software pack-age (National Instruments, USA).

The brain–braincase composite was preconditioned inorder to stabilize the mechanical response of the tissueby indenting the tissue for 5 cycles to a depth of 1 mm,with the indentor held for 160 sec for each cycle. Theprocess of preconditioning is widely accepted in soft tis-sue mechanical characterization and was shown to pro-duce “standardized” initial conditions and reproducibleload-relaxation measurements for many cardiovascularand orthopaedic soft tissues (Fung, 1993). According toCarew et al. (2000), preconditioning without adequaterest periods between subsequent loading cycles increasespredictive errors, and therefore, a pause of 120 sec wasset between subsequent preconditioning cycles to allowelastic recovery of the tissues. Because skull and brainproperty measurements are often utilized in biomechan-ical analyses of head trauma, where single and suddenlarge loads act, we obtained non-preconditioned (NPC)in addition to preconditioned (PC) Gi and G` data, des-ignating the first preconditioning indentation maneuveras the non-preconditioned indentation run.

Elastic moduli of cranial bone plates may be greaterthan those of sutures by two to three orders of magnitude(Cowin, 2001, Margulies and Thibault, 2000; McLaugh-lin et al., 2000) and therefore, a large share of braincasedeformation under the load of the indentor may be dueto extension or flexion of the sutures. On the other hand,thin cranial bones of the immature rat (13–43 postnataldays of age) were shown to be flexible and bent sub-stantially during our experiments. Therefore, mechanicalproperties calculated in this study for the 13–43-day-oldbraincase reflect an effective structural behavior of acomposite comprised of both cranial bone and suture.Mature 90-day-old animals were not tested for braincaseindentation, since it was observed during preliminary ex-periments that the force required to indent their thick rigidskull with its fused sutures exceeded the operating rangeof the force transducer.

After data were acquired for the brain-braincase com-posite, a cranial window was excised above the right orleft hemisphere and the dura was reflected to expose thebrain. Skull thickness was measured at three different lo-cations on each excised cranial window specimen usinga digital caliper (resolution 0.01 mm). The brain was in-dented in situ to a depth of 1 mm (at 1 mm/sec) and theindentor was held for 90 sec until the response stabilized(Fig. 1). The brain was indented five times to precondi-tion the tissue, allowing 60 sec of rest between subse-quent measurements. For the animals selected for in vitrotesting of brain tissue, the brain was delicately removedfrom the skull using fine surgical scissors after euthana-sia. The harvested brain was then placed on a smoothplastic plate that was pre-lubricated with surgical gel toallow unconstrained deformation of the brain during in-

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FIG. 1. Representative procedure illustrating the contact be-tween the indentor and the brain surface for in situ tests.

TABLE 1. SUBJECT GROUP SIZE

Age [days]

13 17 43 90

Brain/skull tested in situ 7 6 6 6Brain tested in vitro 4 4 4 5Total 11 10 10 11

dentation. Indentation was performed in a manner iden-tical to that used for brain in situ. For all animals testedin vitro, maximal anterior-posterior, superior-inferior andlateral dimensions of the excised brain were obtained us-ing a digital caliper.

Tissues were maintained moist throughout the courseof measurements by intermittently spraying normal salineon the brain surface. At the end of each day of experi-ments, a calibration curve was produced for the forcetransducer by delicately lowering it against the center ofa calibrated, high-precision digital scale (resolution 0.01g) and plotting the force reading versus the correspond-ing voltage output of the transducer. For the nearly lin-ear calibration curves (R2 . 0.999 using linear regres-sion) that were obtained, it was found that the standardcoefficient of variation of the calibration slope was nomore than 0.75% across measurement sessions.

Each load-relaxation curve produced for the intactbraincase and for the exposed brain tissue (both in situand in vitro) was evaluated individually. The long-termindentor-tissue contact loads were averaged over a 10-sec (250 data points) terminal period of the load-relax-ation response. The time-period used for analysis was be-tween 148 and 158 sec for braincase composite andbetween 78 and 88 sec for brain tissue from the time ofinitiation of indentation (as indicated in Fig. 2). For braintissue, instantaneous and long-term shear moduli werecalculated for each load-relaxation curve by respectivelysubstituting the peak and mean long-term contact loadsinto Eq. (1). The long-term contact loads for braincasecomposite were used as input for the finite element sim-ulations, in order to estimate the effective mechanicalproperties of the skull/suture, separate from the brain.

Statistical Analysis of Brain Tissue Properties

Shear moduli G` and Gi calculated for brain in situand in vitro for different animal ages and at precondi-tioning cycles 1–5 were evaluated using a 3-way analy-sis of variance (ANOVA, Systat v10.2). The ANOVAtested the dependence of G` and Gi on the following fac-tors: (i) in situ vs. in vitro results—to determine effectsof the brain’s confinement within the skull on shear mod-uli in situ, (ii) age and (iii) preconditioning of brain tis-sue (loading cycle number 1–5). A value of p less than0.05 was considered statistically significant. A two-wayANOVA test was used to determine the preconditioningcycle for which G` and Gi measurements had been sta-bilized (i.e., statistical similarity between results of sub-sequent loading cycles). Post-hoc Tukey-Kramer tests forG` and Gi values across age groups were carried out forthe NPC (first loading cycle) and PC (fifth cycle) mea-surements. These tests were used to systematically con-duct all the possible pairwise comparisons of means of

each of the 4 mechanical properties (NPC G`, PC G`,NPC Gi, PC Gi) across age groups. Averaged shear mod-uli of brain were quantified for each age group as mean 6standard deviation for n animals.

Finite Element Modeling for Analysis ofBraincase Properties

While indentation measurements of exposed or excisedbrain tissue can be used to determine mechanical prop-erties of the brain, when the intact cranium is indentedall underlying tissues (e.g., dura and brain) also contributeto the measured loads. Hence, after determining long-term brain properties directly, these properties are furtherused to calculate the effective braincase properties usinga “reverse engineering” approach described below.

Three idealized two-dimensional (2D) cross-sectionalfinite element models were constructed (PATRAN,MSC Software; ABAQUS, ABAQUS Inc.) to simulateexperiments of indentation into the intact braincase of13 (Fig. 3a,b), 17- and 43-day-old (Fig. 3d,e) rats. Theskull and its sutures—the braincase—were modeled asa uniform elastic layer that covers a dome-shaped ho-mogenous brain material. Based on previous numericalstudies of motion between the brain and skull, the fric-tion coefficient between the braincase and brain was es-timated to be 0.1 (Miller et al., 1998; Prange and Mar-gulies, 2001). The inferior surface representing thebrain’s anchorage to the skull base was constrained forvertical displacement.

Measurements of skull thickness and brain dimensions(Table 2) were used to define the geometry of the model.After averaging lateral and anterior-posterior brainlengths at each age, the variation across age was less than10%, so the value of 16.8 mm was used as the brain’sbase diameter in all three models. Similarly, superior-in-ferior extent did not vary significantly across age, and8.8 mm was used as apex-to-base brain thickness in allthree models. Thickness of the skull in the models rep-resenting 13- and 17-day-old rats was taken as 0.16 mmaccording to our measurements (Table 2), and 0.40 mmwas used for the 43-day-old rats (Table 2). Long-termpreconditioned elastic moduli E` of exposed and excisedbrain tissue were determined from Eq. (2) to be 2106,1647, and 1263 Pa for the 13-, 17-, and 43-day-old ratbrains, respectively. Poisson’s ratio for brain was definedas 0.5, assuming that the brain is incompressible. Pois-son’s ratio of the braincase was assumed to be 0.4 (Ash-man et al., 1985).

For each of the three model simulations, the rigidhemispherical indentor was displaced 1 mm into thebraincase. Each model was run in an iterative manner todetermine the long-term effective elastic modulus of thebraincase associated with the experimentally measured

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indentor-braincase preconditioned contact-load values of0.025, 0.031, and 0.119 N for the 13, 17, and 43-day-old rats, respectively. The effects of biological variationsin braincase thickness, shear moduli of brain tissue, Pois-son’s ratio of braincase and the braincase-brain frictionwere determined in a sensitivity analysis. Where ap-plicable, the range of parameter values was defined tomatch the standard deviation of measurements acquiredin the present study (skull thickness, brain shear mod-uli). To account for inter-animal variability, Poisson’sratio of the braincase and the braincase-brain interfacefriction coefficient were presumed to be in the range of0.3–0.4 and 0.05–0.15, respectively. Confidence inter-vals were estimated from the sensitivity analysis of pa-rameters.

RESULTS

Tukey-Kramer tests revealed that skull thickness isstatistically indistinguishable ( p 5 0.996) for the twoyounger ages, 13- and 17-day-old, and that at these agesthe skull is significantly thinner (p , 0.0001) comparedwith 43- and 90-day-old rats (Table 2). Superior-inferiorbrain dimensions did not vary significantly with age.Lateral brain width was statistically the same for 13, 17,and 43 days of age, and differed significantly only be-tween the 17- and 90-day-old groups (p 5 0.023). An-terior-posterior brain length was statistically the samefor 13- and 17-day old rats, and between 17- and 43-day-old rats, but significantly differed for all other groupcomparisons.

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FIG. 2. Representative load-relaxation curves obtained for indentation into the (a) braincase of a 43-day-old rat and (b) braintissue of a 13-day-old rat in situ.

(a)Peak Load

Long-TermLoad

Time [Sec]

Fo

rce

[Gra

ms]

Cycle 1

Cycle 2

Cycle 3

Cycle 4

Cycle 5

Cycle 1

Peak Load

Cycle 1

Cycle 2

Cycle 3

Cycle 4

Cycle 5

Time [Sec]

Fo

rce

[Gra

ms]

(b)

Cycle 1 Long-TermLoad

Brain Properties

Both Gi and G` moduli were found to be strongly de-pendent on age (p , 0.001) and loading cycle (p ,0.002) (Figs. 4 and 5). It was further found that in situand in vitro measurements for both G` and Gi were in-

distinguishable (Gi: p 5 0.23; G`: p 5 0.52), indicatingno significant confining effect of the skull for these small,1-mm indentations. Therefore, for subsequent analyses,the in situ and in vitro values for Gi and G` were pooled.It was found that pooled Gi and G` values stabilized af-ter three and four preconditioning cycles, respectively,

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FIG. 3. Simulations of indentation into the braincase for calculation of the effective shear moduli of the skull/suture/dura com-posite: model geometry (a,d), axisymmetric finite element mesh (b,e) and resulting deformed shape and strain distribution afterindentation (c,f) for models representing (a–c) 13-day-old and (d–f) 43-day-old rat braincases. Triangles at the model’s founda-tions indicate constrained vertical displacements.

TABLE 2. RAT SKULL AND BRAIN DIMENSIONS (MEAN 6 STANDARD DEVIATION)

Age [days]

13 17 43 90

Skull thickness [mm]a 0.16 6 0.03b 0.16 6 0.02b 0.40 6 0.03 0.69 6 0.06Anterior-posterior brain length [mm] 17.18 6 0.53b 17.83 6 0.75 19.27 6 0.50 20.70 6 0.61Lateral brain width [mm] 14.93 6 0.56 13.75 6 0.06c 14.43 6 0.21 15.50 6 1.17Superior-inferior brain thickness [mm] 8.53 6 0.41 8.49 6 0.28 8.83 6 0.29 9.34 6 0.93

aSkull thickness was average of measurements at three different locations on each cranial specimen.bp , 0.0001 compared with 43- and 90-day-old rats.cp , 0.05 compared with 90-day-old rats.

and therefore, the fifth loading cycle was considered toproduce fully preconditioned (PC) moduli. Results of theTukey-Kramer tests allowed comparisons of four me-chanical properties—the instantaneous and long-termshear moduli under non-preconditioned or precondi-tioned states—between every possible pair of age groups. The NPC Gi of 13-day-old rat brains was signif-icantly higher (twofold) than that of either 43- or 90-day-old brains (p , 0.002, Fig. 4a), and that of 17-day-oldbrains was significantly higher than the values for either43- or 90-day-old brains (p , 0.002). The NPC G` mod-ulus of 13-day-old rat brains was also shown to be sig-nificantly higher (twofold) than that of 90-day-old brains

(p 5 0.002, Fig. 5a). The PC Gi of 13-day-old rat brainswas significantly higher than that of 43- (p 5 0.029) andthat of 90-day-old brains (1.67-fold, p 5 0.002, Fig. 4b),and PC Gi of 17-day-old rat brains was higher than thatof 90-day-old brains (p 5 0.044, Fig. 4b). For the PCstate, the G` of the 13-day-old rat brain was significantlyhigher than that of the 43-day-old (p 5 0.0011) and 90-day-old (1.85-fold, p 5 0.0001, Fig. 5b) rat brain. Forboth NPC and PC states, the G` and Gi moduli for 13-and 17-day-old brains were similar. Likewise, the G` andGi moduli for NPC and PC states of 43- and 90-day-oldbrains were similar (Table 3). Furthermore, the non-pre-conditioned shear moduli at any given age were signifi-

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FIG. 4. Averaged in situ and in vitro instantaneous shear moduli (Gi) of the brain tissue across age groups in the rat: (a) non-preconditioned (NPC) and (b) fully preconditioned (PC) moduli. Horizontal lines above bars indicate non-significant (NS) dif-ference (p $ 0.05) between results obtained for different age groups.

cantly greater (p , 0.01, Table 3) than preconditionedshear moduli.

In order to conveniently compare the mechanical prop-erties of brains across ages, a score of “0” was given forstatistical similarity (p $ 0.05) and a score of “1” wasgiven for a difference (p , 0.05) between two age groupsin each of the four properties. Accordingly, complete sim-ilarity in mechanical properties between age groups re-sulted in a total score of “0” and complete differenceyielded a score of “4.” From this analysis of scores wefound that 13-day-old (infant-like) and 90-day-old (adult-like) rat brains are distinct in all four mechanical char-acteristics tested (Fig. 6). Brains of the younger animals

(13- and 17-day-old rats) were consistently indistin-guishable in all four mechanical moduli and similarly,the mature brains (43- and 90-day-old) were also com-pletely indistinguishable in all characteristics. In sum-mary, brain moduli significantly decreased between theextremes of the spectrum (13- versus 90-day-old) withno significant difference within young (13- versus 17-day-old) and mature (43- versus 90-day-old) groups.

Braincase Properties

Although the indentation depth was restricted to 1 mmacross all ages, finite element simulations demonstrated

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FIG. 5. Averaged in situ and in vitro long-term shear moduli (G`) of the brain tissue across age groups in the rat: (a) non-pre-conditioned (NPC) and (b) fully-preconditioned (PC) moduli. Horizontal lines above bars indicate non-significant (NS) differ-ence (p $ 0.05) between results obtained for different age groups.

that the deformed profile of the skull in the 13-day-oldrat was sharper than that observed for the 43-day-old ratskull (Fig. 3c,f). Compared to the 43-day-old rat brain(Fig. 3f), the distribution of maximal strains (.15%) inthe 13-day-old rat brain was localized within a smallerarea of the tissue under the indentor (Fig. 3c). Finite el-ement simulations were used to determine the nominalvalues and confidence intervals (CI) for the long-term ef-fective moduli of the braincase for the 13-day-old, 17-day-old (not shown), or the 43-day-old (Fig. 3d,f). Theeffective moduli of the braincase was 5.26 (CI 3.92–7.29)MPa for the 13-day-old, 7.60 (CI 5.61–10.69) MPa for17-day-old, and 6.01 (CI 3.91–10.04) MPa for 43-day-old rat. The sensitivity analysis (Table 4) revealed that

the thickness of the braincase had the greatest influenceon numerical predictions of the braincase’s elastic mod-uli, although the shear modulus of the brain and Pois-son’s ratio of the braincase were also found to be influ-ential. The mean calculated effect for the most influentialfactor—braincase thickness—was 638%, which con-forms to a typical variability in mechanical properties ofbiological tissues (Fung, 1993). It is shown that CI forbraincase elastic moduli estimated for ages of 13, 17, and43 days overlap substantially across ages, and so, we con-clude that effective material properties of the skull/su-ture/dura complex do not change significantly betweenthe ages of 13 and 43 days. We conclude that the appar-ently stiffer structure of a 43-day-old braincase compared

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FIG. 6. Overall summary of scores assigned according to Tukey-Kramer property comparisons between age groups (for pooledin situ and in vitro data). A score of “0” represents statistical similarity between groups and a score of “1” represent a signifi-cant (p , 0.05) difference. It is shown that 13-day-old (infant-like) and 90-day-old (adult-like) rat brains are different in all fourmechanical characteristics. Brains of 13- and 17-day-old rats are similar in all four characteristics and likewise, brains of 43- and90-day-old rats are similar in all characteristics.

TABLE 3. INSTANTANEOUS GI [PA] AND LONG-TERM G` [PA] SHEAR MODULI OF THE RAT BRAIN (MEAN 6 STANDARD DEVIATION)

Young Mature (poolinga data of 13-, 17-day-old rats) (poolinga data of 43-, 90-day-old rats)

NPC PC NPC PC

Gi [Pa] 3336 6 955 1754 6 462 1721 6 680 1232 6 343G` [Pa] 786 6 277 626 6 184 508 6 252 398 6 119

aYoung (13- and 17-day-old) rat brains were statistically similar in all four mechanical characteristics, and likewise mature (43-and 90-day-old) brains were similar in all characteristics.

NPC, non-preconditioned; PC, preconditioned.

with those of 13- and 17-day-old animals may be attrib-uted to an increase in skull thickness, rather than in thematerial’s modulus of elasticity.

DISCUSSION

Maturation in the rat was accompanied by a signifi-cant decrease in the elastic modulus of brain tissue, withno changes in braincase modulus. Specifically, it was ob-served that the mean instantaneous and long-term shearmoduli of the immature (13- and 17-day-old) rat brainbefore preconditioning were 3336 and 786 Pa, respec-tively, and decreased to 1721 and 508 Pa, respectively,in the mature (43- and 90-day-old) rats. Similarly, afterpreconditioning, instantaneous and long-term shear mod-uli of the immature rat brain averaged to 1754 and 626Pa, and decreased to 1232 and 398 Pa, respectively, inthe mature rats. The values for long-term shear moduliof the rat brain obtained in this study are in the samerange (0.1–1 KPa) as that reported for freshly-harvestedporcine, primate and human brain specimens (Table 1 ofThibault and Margulies, 1998; Prange and Margulies,2002). The values obtained in the present study are, how-ever, lower than the range of values (10–40 KPa) reportedfor the shear modulus of human brain specimens obtainedat autopsy (Galford and McElhaney, 1970; Shuck andAdvani, 1972), which may be attributed to post-morteminterval. In support of this hypothesis, it was recentlydemonstrated that properties of porcine brain stiffen sig-nificantly ,5 h after death (Rang et al., 2001). Previousreports have evaluated either preconditioned (Bilston et

al., 2001; Prange and Margulies, 2002) or non-precondi-tioned (Miller et al., 2000, 2002) properties of brain tis-sue. In the present study, both properties were evaluatedand it was observed that non-preconditioned shear mod-uli were significantly greater than the preconditioned val-ues (Table 3), suggesting that peak tissue stress levelsproduced by a single rapid deformation would be higherthan those by multiple deformations of the same magni-tude and duration. Also, these findings imply that a sin-gle application of force or pressure would deform thebrain less than the same force applied multiple times tothe same site. These data underscore the utility of bothnon-preconditioned properties (for a single or first im-pact) and preconditioned properties (for multiple im-pacts) in developing biomechanical (and/or experimen-tal) models of traumatic brain injury. Although thethickness of skull increased significantly with age (Table2), finite element simulations suggested that the effectiveelastic moduli of the rat skull/suture/dura compositestructure did not change significantly (average 6.3 MPa)with age.

Brain Properties

The rise in relative myelin content and the simultane-ous decrease in water content with age may explain thesignificant changes in mechanical characteristics of thebrain reported in this study. Predictions of tissue stiffnessusing biomechanical models have suggested that axons,rather than the surrounding matrix of astrocytes andoligodendrocytes, impart stiffness to the brainstem (Ar-bogast and Margulies, 1999). The mechanical properties

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TABLE 4. SENSITIVITY ANALYSIS OF PARAMETERS: EFFECTS ON THE ELASTIC

MODULUS OF THE BRAINCASE AS PERCENTAGE OF THE NOMINAL VALUE

Effect on predicted effective elastic modulusof the rat skull [%]

Parameter 13-day-old 17-day-old 43-day-old

Variation in braincase thicknessa

120% 225.5 226.2 234.9220% 138.6 140.7 167.1

Variation in shear modulus of braina

120% 210.6 28.0 22.0220% 112.9 110.4 12.3

Poisson’s ratio for the braincase225% 13.4 12.6 14.8

Braincase-brain friction150% 0 0 20.2250% 0 0 0

aRange of variation corresponds to standard deviation of measurements.

of axons have been attributed primarily to neurofilamentproteins, which exhibit a shear modulus of approximately2000 Pa (Leterrier et al., 1996). However, during devel-opment, axons become myelinated, and myelinogenesisoccurs from the last trimester in utero until 12 monthsafter birth in humans, and between PND 10 and 20 in therat (Jacobson, 1963; Norton and Cammer, 1984; Salvatiet al., 2000). On PND 15, about 4 mg of myelin can beisolated from a single rat brain, and this amount increasessixfold by 30 postnatal days (Norton and Cammer, 1984).The modest increase in brain dimensions (approximately10%, Table 2) further suggests that this marked increasein myelin content is associated with increase in volumefraction of lipids with age. Lipids such as myelin exhibita low shear modulus of approximately 100 Pa (Yamadaet al., 2000), suggesting that increases in tissue myelinvolume fraction may reduce the effective modulus ofbrain tissue. In addition, the increase in brain myelin con-tent during development is accompanied by a decrease inwater content. Water content in cerebral cortex of nor-mal rats was observed to decrease from 89% of tissuewet weight on PND 4 to 82% on PND 21 (Johanson etal., 1976; Jones and Andersohn, 1998). This decrease inwater content with age may, by reducing the swellingpressure and the osmotic intracellular pressure (Mizrahiet al., 1986), further lower the stiffness of the brain.

The changes in mechanical properties of brain tissuewith age influence the response of the developing brainto rapid rotational accelerations produced during a trau-matic head injury with or without impact. Many investi-gators use the scaling equation introduced by Ommayaet al. (1967) to transform injury thresholds for rotationalaccelerations, determined experimentally for primates, tothe human. The transformation, assuming the same material properties across species, is up 5 um(Mm/Mp)2/3

where up and um are the rotational accelerations of theprototype and model species, respectively, and Mm, Mp

are the corresponding brain masses. This scaling rela-tionship was subsequently confirmed in experiments us-ing several adult non-human primate species (Ommayaand Hirsch, 1971). More recently, Thibault and Margulies(1998) have also suggested incorporating the ratio inshear moduli between the pediatric and adult brain, sothat Ommaya’s transformation becomes upediatric 5 uadult

(Madult/Mpediatric)2/3 (Gpediatric/Gadult). Averaging acrossall shear moduli types measured herein, a scaling factorof Gpediatric/Gadult 5 1.9 is suggested for the materialproperty portion of the relationship. To account for thedifferences in brain weight, we substitute the values re-ported by Dobbing (1981) for neonate rats (1.25 g for13–17-day-old) and adult rats (1.5 g postnatal day 20and older), yielding that (Madult/Mpediatric)2/3 5 1.13. Ac-cordingly, Ommaya’s transformation between the im-

mature (13–17 PND) and adult (43–90 PND) rat becomesupediatric 5 (2.1)uadult.

Braincase Properties

Although cranial sutures fuse as a function of age, ithas been reported that adult porcine and goat skull suturesare more compliant (Herring and Teng, 2000) and lessstrong (Jaslow, 1990) than surrounding bone. Values ofeffective braincase elastic moduli obtained in this studymay therefore reflect properties of the more compliantlinks of the braincase composite structure—the cranial su-tures, rather than cranial bone. McLaughlin et al. (2000)recently demonstrated that sagittal, coronal and posteriorfrontal sutures in 7-day-old rats have elastic moduli of 13,14, and 2.3 MPa, respectively, values that are in very goodagreement with the results of the present study, where es-timated moduli of the braincase (skull/suture composite)ranged between 3.9 and 10.7 MPa.

It should be noted that the idealized finite elementmodel simulations used herein to calculate effectiveskull/suture/dura material properties were only first ap-proximations to the complex anatomy of the real brain-case and brain structures. The comprehensive sensitivityanalysis compensated for the anatomical simplificationsof the model and was used to determine the influence ofinter-animal variability in skull thickness, brain stiffness,and skull-brain friction on the estimation of skull proper-ties. Our calculations suggested that the effective mater-ial properties of the braincase are indistinguishable be-tween 13 and 43 postnatal days, a result that is consistentwith that reported by Thibault (1997) for cortical bonecomponents of infant and adult porcine skulls. Therefore,the stiffer structural behavior of the braincase of the 43-day-old rat is the outcome of its greater thickness, ratherthan due to an increase in material stiffness. However, in-creases in both effective material stiffness and skull thick-ness may contribute to structural stiffness of the braincasein the human infant (Margulies and Thibault, 2000).

Detecting changes in braincase moduli between 13 and43 postnatal days may be hindered, in part, by a largevariance in the values obtained and sample size. How-ever, the 235% to 167% variability in measured skullelastic moduli (Table 4) is consistent with recently re-ported values of 42% to 68% variability in elastic mod-uli of human skulls (Misch et al., 1999; O’Mahony et al.,2000). Thus, variance in brain and braincase mechanicalproperties with the present sample size is very likely toreflect similar extents of variance in the general popula-tion, attributable to the inherent biological variability.

The idealized simulations depicted in Figure 3c,fdemonstrate the combined effects of skull thickness andbrain stiffness on the distribution of tissue strains under

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the load of the indentor in 13- and 43-day-old rats. Thesharper profile of the deformed shape of the skull and themore focal region of maximal strain in the brain tissue(Fig. 3c) may be attributed to the thinner skull of the 13-day-old rat. The simulations predict that in order to pro-duce similar strain distributions in brains of rats at dif-ferent ages, the braincase of younger rats should beindented to a greater extent. Tissue strain distributionshave been used to identify brain regions that may be sus-ceptible to histologic damage after a traumatic injury(Meaney et al., 1995). Importantly, the present charac-terization of tissue properties and the idealized finite el-ement simulations facilitate future development of moreaccurate three-dimensional finite element models that in-clude both brain and skull anatomies for neonate andadult rats. These future models could be used to predictbrain deformations that could be superimposed over mapsof histologic tissue damage. In this manner, age-specificinjury tolerance values can be determined in terms of lo-cal tissue stress, deformation and strain.

Computational and experimental models designed tosimulate accidental and/or inflicted injury to the brain/braincase are highly dependent on adequate descriptionof tissue material behavior. In addition to the develop-mental changes in brain size and weight reported previ-ously (Dobbing, 1981), our observations indicate that themechanical properties of immature brain tissue signifi-cantly differ from those of the adult brain. Thus, the sameinjury parameters of acceleration and force applied to in-fant and adult rats will produce different stresses andstrains in the brain tissue. Therefore, if the same braintissue stress or strain level is desired for comparativeanalysis of brain injury consequences across ages in therat, the experimental model design should incorporatedata presented in this communication to scale applied ac-celerations and forces between ages.

ACKNOWLEDGMENTS

We are thankful to John Noon for his technical assis-tance in designing and building the indentor and to Brit-tany Coats for her help with the indentation studies. Thestudy was supported by NIH grants R01-NS-39679(S.S.M.) and R01-NS-41562 (R.R.), by a CDC grant R49-CCR-312712 (S.S.M.), and by the Dan David Founda-tion (A.G.).

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Address reprint requests to:Ramesh Raghupathi, Ph.D.

Department of Neurobiology and AnatomyDrexel University College of Medicine

2900 Queen LanePhiladelphia, PA 19129

E-mail: rramesh@drexel.edu

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