JOURNAL OF NEUROTRAUMA Volume 20, Number 11, 2003 © Mary Ann Liebert, Inc.
Age-Dependent Changes in Material Properties of the Brain and 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 infants and young children may be different from those in adults. Biomechanical computer-based modeling, which can be used to provide insight into the thresholds for traumatic tissue injury, requires data on material properties of the brain, skull, and sutures that are specific for the pediatric population. 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`) shear moduli of brain tissue both in situ and in vitro. Brains at 13 and 17 PND exhibited statistically indistinguishable shear moduli, as did brains at 43 and 90 PND. However, the immature (average of 13 and 17 PND) rat brain (Gi 5 3336 Pa NPC, 1754 Pa PC; G` 5 786 Pa NPC, 626 Pa PC) was significantly 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 estimate the effective elastic moduli of the braincase. Although the skull of older rats was significantly thicker than that of the younger rats, there was no significant age-dependent change in the effective elastic modulus of the braincase (average value 5 6.3 MPa). Thus, the increase in structural rigidity of the braincase with age (up to 43 PND) was due to an increase in skull thickness rather than stiffening of the tissue. These observations of a stiffer brain and more compliant braincase in the immature rat compared with the adult rat will aid in the development of age-specific experimental models and in computational head injury simulations. Specifically, these results will assist in the selection of forces to induce comparable mechanical stresses, strains and consequent injury profiles in brain tissues of immature and adult animals. Key words: constitutive properties; finite element analysis; head injury; pediatric animal model; skull; suture
1 Department 2 Department
of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania. of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, Pennsylvania.
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GEFEN ET AL.
INTRODUCTION
A
suffering head trauma as a result of a motor vehicle accident, child abuse, or fall may develop secondary pathologies such as diffuse cerebral swelling with an etiology and time course that are substantially different than those observed in adults (Bruce, 1990; Geddes et al., 2001; Pascussi, 1998; Shapiro, 1985). Biomechanical computer-based models are being used with increasing frequency to provide insight into the mechanisms of traumatic head injury. The accuracy of these simulations in predicting the severity of injury is strongly dependent on an adequate mechanical description of material characteristics of the brain and braincase tissues. Until recently, biomechanical models of a pediatric head injury considered the infant and young children’s brains and skulls as having the same mechanical properties of adults, such that only the size was scaled to fit the simulation (Dejeammes et al., 1984; Duhaime et al., 1987; Kumaresan et al., 2002; Mohn et al., 1979; Stürtz, 1980). However, the human brain and cranium undergo significant alterations over the first 4 years of life. Neurons exhibit more extensive dendritic and axonal branching which is accompanied by a rise in lipid content as axonal segments become myelinated (Calder, 1984). The chemical and structural alterations of the brain may underlie 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 brain tissue 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 relevant to clinical head injury, the immature (5-day-old) porcine tissue was about twice as stiff as the adult pig (Prange and Margulies, 2002). The skull of newborns consists of thin flexible plates made of partially calcified bone, which are attached at their margins by the soft connective tissue of the sutures, thus constructing a compliant cranial structure capable 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 sutures in fetal and newborn humans and animals reveal that cranial bone and suture stiffness/strength generally increases with age. To date, there is a paucity of quantitative information regarding the developmental time course of changes in mechanical properties of brain and skull, and there are no reports of such age-dependency in species other than the pig. Rodents are the species most often used as experimental models of traumatic head injury. Rapid deformaN INFANT OR YOUNG CHILD
tion of the brain as a result of indentation of the intact dura or skull by a pneumatically-driven rigid impactor (controlled cortical impact), or by a fluid bolus on the intact dura (fluid-percussion), are currently the most commonly used and best characterized preclinical models of traumatic brain injury in adults (Gennarelli, 1994; Laurer et al., 2000). Models of closed head injury in the immature rat have been established based on physiologic and behavioral parameters typically used to determine injury severity in adult rats (Adelson et al., 1996; Prins et al., 1996). Prins et al. (1996) observed that an injury load of 1.6–2.1 atm with the fluid-percussion device resulted in mild deficits in adults (0% mortality, 7–10 sec of apnea), but more severe deficits in the 17-day-old rat pups (30% mortality, 45–60 sec of apnea). Similarly, in modifying the impact-acceleration model of closed head injury for immature rats, it was observed that the mortality rate, neurological deficits and tissue damage in immature rats resulting from a 100-g weight drop was similar to those observed after a 450-g weight drop in adult rats (Adelson et al., 1996). When the injury load in immature rats was adjusted for brain weight, younger (3–7-day-old) rats exhibited apoptotic cell death to a greater extent than adult rats following contusive brain injury (Bittigau et al., 1999). However, these experimental model designs utilizing an applied force or pressure are not adjusted for the changes in tissue material properties of the brain that occur with development, and these properties may substantially affect the levels of mechanical strain (and brain injury) in brain tissue in each injury paradigm. In contrast, when brain size and tissue strain were utilized to scale injury parameters in the pig, it was observed that the neonatal pigs were less susceptible to histologic and physiologic damage following contusive brain injury (Duhaime et al., 2000; Durham et al., 2000). The goal of this study was, therefore, to measure the elastic 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-old rats). At 7–10 postnatal days (PND) of age, the rat is neurologically equivalent to a human at birth, and by 12–15 postnatal days of age the stage of development in the rat is equivalent to a 2–3-year-old human child (Dobbing, 1964; Porterfield and Hendrich, 1993). The neurological development in the rat is complete by ,20 postnatal days, so 43- and 90-day-old rats can be considered neurologically equivalent to human adults. Musculoskeletal development of the rat, however, continues beyond 43 postnatal days. For example, the mean width of the cranial vault at the postorbital constriction of the rat increases by 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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AGE-DEPENDENT CHANGES IN MATERIAL PROPERTIES OF THE BRAIN neurological development, the growth of its skull may not yet be complete. The elastic characteristics of skull/sutures at three different ages were estimated by supplementing the experimental mechanical testing data with finite element simulations of braincase loading using “reverse engineering.” These mechanical property data provide important information for scaling of animal model injury parameters and computer simulations of the immature brain.
MATERIALS AND METHODS Indentation Testing Biological tissues are known to display a complex viscoelastic response to mechanical forces that is strongly dependent on the rate and magnitude of the applied load. For the purpose of biomechanical analysis, however, the brain and braincase are treated as homogenous, isotropic and incompressible materials (Kuijpers et al., 1995; Mendis et al., 1995; Miller et al., 2000; Prange and Margulies, 2002), making it possible to use a rigid indentor to determine the shear modulus. Indentation, a well-characterized method for measuring shear and elastic moduli of soft tissues such as brain (Miller et al., 2000), muscle (Vannah and Childress, 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 moduli from the load applied by the indentor and the extent of tissue deflection. In this study, an electromechanical computer-controlled indentor, comprised of a miniature linear stepper motor (minimal displacement 0.0032 mm), force transducer (load capacity 1.47 N or 150 g) and a linear variable displacement transducer (LVDT), was used to indent the exposed skull and, following removal of the skull and dura, the exposed brain tissue, both to a depth of 1 mm. Recent shear measurements showed that gray matter can essentially be considered isotropic (properties are independent of the direction tested), whereas anisotropy appears deeper at the corpus callosum, consistent with the neuroarchitecture (Prange and Margulies, 2002). Thus, for the 1-mm indentation employed in the present study design, assumptions of homogeneity and isotropy are reasonable and practical. The tip of the indentor was machined to a hemisphere in order to eliminate sharp edges at the indentor-tissue contact surface that may damage the delicate tissues. For a hemispherical indentor, the effective shear modulus G (Mega Pascals, MPa) of brain tissue is calculated using the Lee and Radok (1960) solution for small displacements of a rigid indentor into elastic half-space,
3P G5 } 16dÏRd
(1)
where d is the indentation depth (mm) of a smooth rigid sphere with a radius R (mm) into the tissue due to the action of a load P (Newtons). Subsequently, the elastic modulus 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 the indentor was designed such that its radius R was no more than 25% the thickness of the studied tissue sample. By this criterion, small misalignment of the indentor (,12.5°) has a negligible effect on the measured elastic properties (Zheng et al., 1999). In the current study, the superior-inferior extent of the smallest (13-day-old) brain was 8.2 mm, and therefore, an indentor with radius of R 5 2 mm was used. To determine the elastic response of the brain and skull/suture tissues, a constant speed of indentation (1 mm/sec) was used for all tests. The indentor imposed a rapid deformation, which was held for 90–160 sec. Theoretically, the rapid “ramp-and-hold” indentation of an elastic material produces a load response of the same wave shape. In practice, for viscoelastic materials such as brain tissue, the load P decreases with time to a steady state asymptotic value during the “hold” period. If the time taken to impose the deformation is relatively short with respect to the rate of decay in the load signal, an instantaneous shear modulus Gi is calculated from Eq. (1) by substituting the peak, or instantaneous load Pi measured immediately after deformation (“ramp” period) was ceased. The long-term shear modulus G ` is calculated using the asymptotic load value, P`.
Experimental Protocol The protocol was approved by the Institutional Animal Care and Use Committee at the University of Pennsylvania. Shear moduli of rat brain and skull/suture tissues were measured in situ and in vitro for a total of 42 animals grouped from nine different litters. Rats were divided 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, 6–7 animals were randomly selected for testing the brain and skull/suture composite mechanical properties in situ. The remaining four to five animals in each age group were assigned for testing the brain mechanical properties in vitro (brain removed from the braincase) in order to verify that tissue properties measured for brain were not affected by the confining nature of the braincase.
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GEFEN ET AL. TABLE 1. SUBJECT G ROUP SIZE Age [days]
Brain/skull tested in situ Brain tested in vitro Total
13
17
43
90
7 4 11
6 4 10
6 4 10
6 5 11
For the purpose of in situ measurements of mechanical properties of the brain and braincase, animals were euthanized with sodium pentobarbital (postnatal day 13–17: 50 mg/kg, postnatal day 43–90: 150 mg/kg, intraperitoneal). Death was verified by cessation of heartbeat. Post-mortem, the scalp was reflected along a midline incision to access the skull. A site for indentation was randomly assigned over the right or left cerebral hemisphere, and the head was firmly fixed to a rigid support. Prior to measurements, the tip of the indentor was lubricated with surgical gel to prevent adhesion of tissue to the metal probe and to allow free slip of the tissue during deformation. The indentor was subsequently positioned using its fine system of adjusters until delicate contact was made with the skull surface (Fig. 1) as determined by monitoring the force transducer signal on an oscilloscope. Because our primary goal was to quantify age-related changes in material properties that are independent of the complex inhomogeneous and anisotropic nature of the brain, a consistent location of the indentor site was maintained across ages. Force and displacement (LVDT signal) data were continuously measured at a sampling rate of 25 scans/sec (25 Hz) using a PC laptop equipped with A/D board and LabView 6i software package (National Instruments, USA).
FIG. 1. Representative procedure illustrating the contact between the indentor and the brain surface for in situ tests.
The brain–braincase composite was preconditioned in order to stabilize the mechanical response of the tissue by indenting the tissue for 5 cycles to a depth of 1 mm, with the indentor held for 160 sec for each cycle. The process of preconditioning is widely accepted in soft tissue mechanical characterization and was shown to produce “standardized” initial conditions and reproducible load-relaxation measurements for many cardiovascular and orthopaedic soft tissues (Fung, 1993). According to Carew et al. (2000), preconditioning without adequate rest periods between subsequent loading cycles increases predictive errors, and therefore, a pause of 120 sec was set between subsequent preconditioning cycles to allow elastic recovery of the tissues. Because skull and brain property measurements are often utilized in biomechanical analyses of head trauma, where single and sudden large loads act, we obtained non-preconditioned (NPC) in addition to preconditioned (PC) Gi and G` data, designating the first preconditioning indentation maneuver as the non-preconditioned indentation run. Elastic moduli of cranial bone plates may be greater than those of sutures by two to three orders of magnitude (Cowin, 2001, Margulies and Thibault, 2000; McLaughlin et al., 2000) and therefore, a large share of braincase deformation under the load of the indentor may be due to extension or flexion of the sutures. On the other hand, thin cranial bones of the immature rat (13–43 postnatal days of age) were shown to be flexible and bent substantially during our experiments. Therefore, mechanical properties calculated in this study for the 13–43-day-old braincase reflect an effective structural behavior of a composite comprised of both cranial bone and suture. Mature 90-day-old animals were not tested for braincase indentation, since it was observed during preliminary experiments that the force required to indent their thick rigid skull with its fused sutures exceeded the operating range of the force transducer. After data were acquired for the brain-braincase composite, a cranial window was excised above the right or left hemisphere and the dura was reflected to expose the brain. Skull thickness was measured at three different locations on each excised cranial window specimen using a digital caliper (resolution 0.01 mm). The brain was indented in situ to a depth of 1 mm (at 1 mm/sec) and the indentor was held for 90 sec until the response stabilized (Fig. 1). The brain was indented five times to precondition the tissue, allowing 60 sec of rest between subsequent measurements. For the animals selected for in vitro testing of brain tissue, the brain was delicately removed from the skull using fine surgical scissors after euthanasia. The harvested brain was then placed on a smooth plastic plate that was pre-lubricated with surgical gel to allow unconstrained deformation of the brain during in-
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AGE-DEPENDENT CHANGES IN MATERIAL PROPERTIES OF THE BRAIN dentation. Indentation was performed in a manner identical to that used for brain in situ. For all animals tested in vitro, maximal anterior-posterior, superior-inferior and lateral dimensions of the excised brain were obtained using a digital caliper. Tissues were maintained moist throughout the course of measurements by intermittently spraying normal saline on the brain surface. At the end of each day of experiments, a calibration curve was produced for the force transducer by delicately lowering it against the center of a calibrated, high-precision digital scale (resolution 0.01 g) and plotting the force reading versus the corresponding voltage output of the transducer. For the nearly linear calibration curves (R2 . 0.999 using linear regression) that were obtained, it was found that the standard coefficient of variation of the calibration slope was no more than 0.75% across measurement sessions. Each load-relaxation curve produced for the intact braincase and for the exposed brain tissue (both in situ and in vitro) was evaluated individually. The long-term indentor-tissue contact loads were averaged over a 10sec (250 data points) terminal period of the load-relaxation response. The time-period used for analysis was between 148 and 158 sec for braincase composite and between 78 and 88 sec for brain tissue from the time of initiation of indentation (as indicated in Fig. 2). For brain tissue, instantaneous and long-term shear moduli were calculated for each load-relaxation curve by respectively substituting the peak and mean long-term contact loads into Eq. (1). The long-term contact loads for braincase composite were used as input for the finite element simulations, in order to estimate the effective mechanical properties of the skull/suture, separate from the brain.
Statistical Analysis of Brain Tissue Properties Shear moduli G` and Gi calculated for brain in situ and in vitro for different animal ages and at preconditioning cycles 1–5 were evaluated using a 3-way analysis of variance (ANOVA, Systat v10.2). The ANOVA tested the dependence of G` and G i on the following factors: (i) in situ vs. in vitro results—to determine effects of the brain’s confinement within the skull on shear moduli in situ, (ii) age and (iii) preconditioning of brain tissue (loading cycle number 1–5). A value of p less than 0.05 was considered statistically significant. A two-way ANOVA test was used to determine the preconditioning cycle for which G` and Gi measurements had been stabilized (i.e., statistical similarity between results of subsequent loading cycles). Post-hoc Tukey-Kramer tests for G` and Gi values across age groups were carried out for the NPC (first loading cycle) and PC (fifth cycle) measurements. These tests were used to systematically conduct 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 moduli of brain were quantified for each age group as mean 6 standard deviation for n animals.
Finite Element Modeling for Analysis of Braincase Properties While indentation measurements of exposed or excised brain tissue can be used to determine mechanical properties of the brain, when the intact cranium is indented all underlying tissues (e.g., dura and brain) also contribute to the measured loads. Hence, after determining longterm brain properties directly, these properties are further used to calculate the effective braincase properties using a “reverse engineering” approach described below. Three idealized two-dimensional (2D) cross-sectional finite element models were constructed (PATRAN, MSC Software; ABAQUS, ABAQUS Inc.) to simulate experiments of indentation into the intact braincase of 13 (Fig. 3a,b), 17- and 43-day-old (Fig. 3d,e) rats. The skull and its sutures—the braincase—were modeled as a uniform elastic layer that covers a dome-shaped homogenous brain material. Based on previous numerical studies of motion between the brain and skull, the friction coefficient between the braincase and brain was estimated to be 0.1 (Miller et al., 1998; Prange and Margulies, 2001). The inferior surface representing the brain’s anchorage to the skull base was constrained for vertical 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 brain lengths at each age, the variation across age was less than 10%, so the value of 16.8 mm was used as the brain’s base diameter in all three models. Similarly, superior-inferior extent did not vary significantly across age, and 8.8 mm was used as apex-to-base brain thickness in all three models. Thickness of the skull in the models representing 13- and 17-day-old rats was taken as 0.16 mm according to our measurements (Table 2), and 0.40 mm was used for the 43-day-old rats (Table 2). Long-term preconditioned elastic moduli E` of exposed and excised brain tissue were determined from Eq. (2) to be 2106, 1647, and 1263 Pa for the 13-, 17-, and 43-day-old rat brains, respectively. Poisson’s ratio for brain was defined as 0.5, assuming that the brain is incompressible. Poisson’s ratio of the braincase was assumed to be 0.4 (Ashman et al., 1985). For each of the three model simulations, the rigid hemispherical indentor was displaced 1 mm into the braincase. Each model was run in an iterative manner to determine the long-term effective elastic modulus of the braincase associated with the experimentally measured
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GEFEN ET AL.
(a)
Peak Load Cycle 1 Cycle 2 Cycle 3 Cycle 4
Force [Grams]
Cycle 5
Long-Term Load
Cycle 1
Time [Sec]
(b)
Cycle 1 Cycle 2
Peak Load
Cycle 3 Cycle 4
Force [Grams]
Cycle 5
Long-Term Load
Cycle 1
Time [Sec]
FIG. 2. Representative load-relaxation curves obtained for indentation into the (a) braincase of a 43-day-old rat and (b) brain tissue of a 13-day-old rat in situ.
indentor-braincase preconditioned contact-load values of 0.025, 0.031, and 0.119 N for the 13, 17, and 43-dayold rats, respectively. The effects of biological variations in braincase thickness, shear moduli of brain tissue, Poisson’s ratio of braincase and the braincase-brain friction were determined in a sensitivity analysis. Where applicable, the range of parameter values was defined to match the standard deviation of measurements acquired in the present study (skull thickness, brain shear moduli). To account for inter-animal variability, Poisson’s ratio of the braincase and the braincase-brain interface friction coefficient were presumed to be in the range of 0.3–0.4 and 0.05–0.15, respectively. Confidence intervals were estimated from the sensitivity analysis of parameters.
RESULTS Tukey-Kramer tests revealed that skull thickness is statistically indistinguishable ( p 5 0.996) for the two younger ages, 13- and 17-day-old, and that at these ages the skull is significantly thinner (p , 0.0001) compared with 43- and 90-day-old rats (Table 2). Superior-inferior brain 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 between the 17- and 90-day-old groups (p 5 0.023). Anterior-posterior brain length was statistically the same for 13- and 17-day old rats, and between 17- and 43day-old rats, but significantly differed for all other group comparisons.
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AGE-DEPENDENT CHANGES IN MATERIAL PROPERTIES OF THE BRAIN
FIG. 3. Simulations of indentation into the braincase for calculation of the effective shear moduli of the skull/suture/dura composite: model geometry (a,d), axisymmetric finite element mesh (b,e) and resulting deformed shape and strain distribution after indentation (c,f) for models representing (a–c) 13-day-old and (d–f) 43-day-old rat braincases. Triangles at the model’s foundations indicate constrained vertical displacements.
Brain Properties Both Gi and G` moduli were found to be strongly dependent on age (p , 0.001) and loading cycle (p , 0.002) (Figs. 4 and 5). It was further found that in situ and in vitro measurements for both G` and Gi were inTABLE 2. RAT SKULL
AND
distinguishable (Gi: p 5 0.23; G `: p 5 0.52), indicating no 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 after three and four preconditioning cycles, respectively,
BRAIN DIMENSIONS (MEAN 6
STANDARD DEVIATION )
Age [days] 13 Skull thickness [mm]a Anterior-posterior brain length [mm] Lateral brain width [mm] Superior-inferior brain thickness [mm] a Skull
0.16 6 17.18 6 14.93 6 8.53 6
17 0.03b 0.53b 0.56 0.41
0.16 17.83 13.75 8.49
6 0.02b 6 0.75 6 0.06c 6 0.28
43 0.40 19.27 14.43 8.83
6 0.03 6 0.50 6 0.21 6 0.29
thickness was average of measurements at three different locations on each cranial specimen.
bp
, 0.0001 compared with 43- and 90-day-old rats. c p , 0.05 compared with 90-day-old rats.
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90 0.69 20.70 15.50 9.34
6 0.06 6 0.61 6 1.17 6 0.93
GEFEN ET AL.
FIG. 4. Averaged in situ and in vitro instantaneous shear moduli (Gi) of the brain tissue across age groups in the rat: (a) nonpreconditioned (NPC) and (b) fully preconditioned (PC) moduli. Horizontal lines above bars indicate non-significant (NS) difference (p $ 0.05) between results obtained for different age groups.
and therefore, the fifth loading cycle was considered to produce fully preconditioned (PC) moduli. Results of the Tukey-Kramer tests allowed comparisons of four mechanical properties—the instantaneous and long-term shear moduli under non-preconditioned or preconditioned states—between every possible pair of age groups. The NPC G i of 13-day-old rat brains was significantly higher (twofold) than that of either 43- or 90-dayold brains (p , 0.002, Fig. 4a), and that of 17-day-old brains was significantly higher than the values for either 43- or 90-day-old brains (p , 0.002). The NPC G` modulus of 13-day-old rat brains was also shown to be significantly higher (twofold) than that of 90-day-old brains
(p 5 0.002, Fig. 5a). The PC Gi of 13-day-old rat brains was significantly higher than that of 43- (p 5 0.029) and that 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 that of 90-day-old brains (p 5 0.044, Fig. 4b). For the PC state, the G` of the 13-day-old rat brain was significantly higher than that of the 43-day-old (p 5 0.0011) and 90day-old (1.85-fold, p 5 0.0001, Fig. 5b) rat brain. For both NPC and PC states, the G` and Gi moduli for 13and 17-day-old brains were similar. Likewise, the G` and Gi moduli for NPC and PC states of 43- and 90-day-old brains were similar (Table 3). Furthermore, the non-preconditioned shear moduli at any given age were signifi-
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AGE-DEPENDENT CHANGES IN MATERIAL PROPERTIES OF THE BRAIN
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-preconditioned (NPC) and (b) fully-preconditioned (PC) moduli. Horizontal lines above bars indicate non-significant (NS) difference (p $ 0.05) between results obtained for different age groups.
cantly greater (p , 0.01, Table 3) than preconditioned shear moduli. In order to conveniently compare the mechanical properties of brains across ages, a score of “0” was given for statistical similarity (p $ 0.05) and a score of “1” was given for a difference (p , 0.05) between two age groups in each of the four properties. Accordingly, complete similarity in mechanical properties between age groups resulted in a total score of “0” and complete difference yielded a score of “4.” From this analysis of scores we found that 13-day-old (infant-like) and 90-day-old (adultlike) rat brains are distinct in all four mechanical characteristics tested (Fig. 6). Brains of the younger animals
(13- and 17-day-old rats) were consistently indistinguishable in all four mechanical moduli and similarly, the mature brains (43- and 90-day-old) were also completely indistinguishable in all characteristics. In summary, brain moduli significantly decreased between the extremes of the spectrum (13- versus 90-day-old) with no significant difference within young (13- versus 17day-old) and mature (43- versus 90-day-old) groups.
Braincase Properties Although the indentation depth was restricted to 1 mm across all ages, finite element simulations demonstrated
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GEFEN ET AL. TABLE 3. INSTANTANEOUS GI [PA ] AND LONG -TERM G` [PA ] SHEAR MODULI OF THE RAT BRAIN (MEAN 6 STANDARD DEVIATION ) Young (poolinga data of 13-, 17-day-old rats)
Gi [Pa] G` [Pa]
Mature (poolinga data of 43-, 90-day-old rats)
NPC
PC
NPC
PC
3336 6 955 786 6 277
1754 6 462 626 6 184
1721 6 680 508 6 252
1232 6 343 398 6 119
a Young (13- and 17-day-old) rat brains were statistically similar in all four mechanical characteristics, and likewise mature (43and 90-day-old) brains were similar in all characteristics. NPC, non-preconditioned; PC, preconditioned.
that the deformed profile of the skull in the 13-day-old rat was sharper than that observed for the 43-day-old rat skull (Fig. 3c,f). Compared to the 43-day-old rat brain (Fig. 3f), the distribution of maximal strains (.15%) in the 13-day-old rat brain was localized within a smaller area of the tissue under the indentor (Fig. 3c). Finite element simulations were used to determine the nominal values and confidence intervals (CI) for the long-term effective moduli of the braincase for the 13-day-old, 17day-old (not shown), or the 43-day-old (Fig. 3d,f). The effective 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 for 17-day-old, and 6.01 (CI 3.91–10.04) MPa for 43-dayold rat. The sensitivity analysis (Table 4) revealed that
the thickness of the braincase had the greatest influence on numerical predictions of the braincase’s elastic moduli, although the shear modulus of the brain and Poisson’s ratio of the braincase were also found to be influential. The mean calculated effect for the most influential factor—braincase thickness—was 638%, which conforms to a typical variability in mechanical properties of biological tissues (Fung, 1993). It is shown that CI for braincase elastic moduli estimated for ages of 13, 17, and 43 days overlap substantially across ages, and so, we conclude that effective material properties of the skull/suture/dura complex do not change significantly between the ages of 13 and 43 days. We conclude that the apparently stiffer structure of a 43-day-old braincase compared
FIG. 6. Overall summary of scores assigned according to Tukey-Kramer property comparisons between age groups (for pooled in situ and in vitro data). A score of “0” represents statistical similarity between groups and a score of “1” represent a significant (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 four mechanical characteristics. Brains of 13- and 17-day-old rats are similar in all four characteristics and likewise, brains of 43- and 90-day-old rats are similar in all characteristics.
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AGE-DEPENDENT CHANGES IN MATERIAL PROPERTIES OF THE BRAIN 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 modulus of the rat skull [%] Parameter Variation in braincase thicknessa 120% 220% Variation in shear modulus of braina 120% 220% Poisson’s ratio for the braincase 225% Braincase-brain friction 150% 250% aRange of
13-day-old
17-day-old
43-day-old
225.5 138.6
226.2 140.7
234.9 167.1
210.6 112.9
28.0 110.4
22.0 12.3
13.4
12.6
14.8
0 0
0 0
20.2 0
variation corresponds to standard deviation of measurements.
with those of 13- and 17-day-old animals may be attributed to an increase in skull thickness, rather than in the material’s modulus of elasticity.
DISCUSSION Maturation in the rat was accompanied by a significant decrease in the elastic modulus of brain tissue, with no changes in braincase modulus. Specifically, it was observed that the mean instantaneous and long-term shear moduli of the immature (13- and 17-day-old) rat brain before preconditioning were 3336 and 786 Pa, respectively, and decreased to 1721 and 508 Pa, respectively, in the mature (43- and 90-day-old) rats. Similarly, after preconditioning, instantaneous and long-term shear moduli of the immature rat brain averaged to 1754 and 626 Pa, and decreased to 1232 and 398 Pa, respectively, in the mature rats. The values for long-term shear moduli of the rat brain obtained in this study are in the same range (0.1–1 KPa) as that reported for freshly-harvested porcine, primate and human brain specimens (Table 1 of Thibault and Margulies, 1998; Prange and Margulies, 2002). The values obtained in the present study are, however, lower than the range of values (10–40 KPa) reported for the shear modulus of human brain specimens obtained at autopsy (Galford and McElhaney, 1970; Shuck and Advani, 1972), which may be attributed to post-mortem interval. In support of this hypothesis, it was recently demonstrated that properties of porcine brain stiffen significantly ,5 h after death (Rang et al., 2001). Previous reports have evaluated either preconditioned (Bilston et
al., 2001; Prange and Margulies, 2002) or non-preconditioned (Miller et al., 2000, 2002) properties of brain tissue. In the present study, both properties were evaluated and it was observed that non-preconditioned shear moduli were significantly greater than the preconditioned values (Table 3), suggesting that peak tissue stress levels produced by a single rapid deformation would be higher than those by multiple deformations of the same magnitude and duration. Also, these findings imply that a single application of force or pressure would deform the brain less than the same force applied multiple times to the same site. These data underscore the utility of both non-preconditioned properties (for a single or first impact) and preconditioned properties (for multiple impacts) in developing biomechanical (and/or experimental) models of traumatic brain injury. Although the thickness of skull increased significantly with age (Table 2), finite element simulations suggested that the effective elastic moduli of the rat skull/suture/dura composite structure did not change significantly (average 6.3 MPa) with age.
Brain Properties The rise in relative myelin content and the simultaneous decrease in water content with age may explain the significant changes in mechanical characteristics of the brain reported in this study. Predictions of tissue stiffness using biomechanical models have suggested that axons, rather than the surrounding matrix of astrocytes and oligodendrocytes, impart stiffness to the brainstem (Arbogast and Margulies, 1999). The mechanical properties
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GEFEN ET AL. of axons have been attributed primarily to neurofilament proteins, which exhibit a shear modulus of approximately 2000 Pa (Leterrier et al., 1996). However, during development, axons become myelinated, and myelinogenesis occurs from the last trimester in utero until 12 months after birth in humans, and between PND 10 and 20 in the rat (Jacobson, 1963; Norton and Cammer, 1984; Salvati et al., 2000). On PND 15, about 4 mg of myelin can be isolated from a single rat brain, and this amount increases sixfold by 30 postnatal days (Norton and Cammer, 1984). The modest increase in brain dimensions (approximately 10%, Table 2) further suggests that this marked increase in myelin content is associated with increase in volume fraction of lipids with age. Lipids such as myelin exhibit a low shear modulus of approximately 100 Pa (Yamada et al., 2000), suggesting that increases in tissue myelin volume fraction may reduce the effective modulus of brain tissue. In addition, the increase in brain myelin content during development is accompanied by a decrease in water content. Water content in cerebral cortex of normal rats was observed to decrease from 89% of tissue wet weight on PND 4 to 82% on PND 21 (Johanson et al., 1976; Jones and Andersohn, 1998). This decrease in water content with age may, by reducing the swelling pressure and the osmotic intracellular pressure (Mizrahi et al., 1986), further lower the stiffness of the brain. The changes in mechanical properties of brain tissue with age influence the response of the developing brain to rapid rotational accelerations produced during a traumatic head injury with or without impact. Many investigators use the scaling equation introduced by Ommaya et al. (1967) to transform injury thresholds for rotational accelerations, determined experimentally for primates, to the human. The transformation, assuming the same material properties across species, is u¨p 5 u¨m (Mm/Mp )2/3 where u¨p and u¨m are the rotational accelerations of the prototype and model species, respectively, and Mm, Mp are the corresponding brain masses. This scaling relationship was subsequently confirmed in experiments using several adult non-human primate species (Ommaya and Hirsch, 1971). More recently, Thibault and Margulies (1998) have also suggested incorporating the ratio in shear moduli between the pediatric and adult brain, so that Ommaya’s transformation becomes u¨pediatric 5 u¨adult (Madult/Mpediatric)2/3 (Gpediatric/Gadult). Averaging across all shear moduli types measured herein, a scaling factor of Gpediatric/Gadult 5 1.9 is suggested for the material property portion of the relationship. To account for the differences in brain weight, we substitute the values reported by Dobbing (1981) for neonate rats (1.25 g for 13–17-day-old) and adult rats (1.5 g postnatal day 20 and older), yielding that (Madult/Mpediatric)2/3 5 1.13. Accordingly, Ommaya’s transformation between the im-
mature (13–17 PND) and adult (43–90 PND) rat becomes u¨pediatric 5 (2.1)u¨adult.
Braincase Properties Although cranial sutures fuse as a function of age, it has been reported that adult porcine and goat skull sutures are more compliant (Herring and Teng, 2000) and less strong (Jaslow, 1990) than surrounding bone. Values of effective braincase elastic moduli obtained in this study may therefore reflect properties of the more compliant links of the braincase composite structure—the cranial sutures, rather than cranial bone. McLaughlin et al. (2000) recently demonstrated that sagittal, coronal and posterior frontal sutures in 7-day-old rats have elastic moduli of 13, 14, and 2.3 MPa, respectively, values that are in very good agreement with the results of the present study, where estimated moduli of the braincase (skull/suture composite) ranged between 3.9 and 10.7 MPa. It should be noted that the idealized finite element model simulations used herein to calculate effective skull/suture/dura material properties were only first approximations to the complex anatomy of the real braincase and brain structures. The comprehensive sensitivity analysis compensated for the anatomical simplifications of the model and was used to determine the influence of inter-animal variability in skull thickness, brain stiffness, and skull-brain friction on the estimation of skull properties. Our calculations suggested that the effective material properties of the braincase are indistinguishable between 13 and 43 postnatal days, a result that is consistent with that reported by Thibault (1997) for cortical bone components of infant and adult porcine skulls. Therefore, the stiffer structural behavior of the braincase of the 43day-old rat is the outcome of its greater thickness, rather than due to an increase in material stiffness. However, increases in both effective material stiffness and skull thickness may contribute to structural stiffness of the braincase in the human infant (Margulies and Thibault, 2000). Detecting changes in braincase moduli between 13 and 43 postnatal days may be hindered, in part, by a large variance in the values obtained and sample size. However, the 235% to 167% variability in measured skull elastic moduli (Table 4) is consistent with recently reported values of 42% to 68% variability in elastic moduli of human skulls (Misch et al., 1999; O’Mahony et al., 2000). Thus, variance in brain and braincase mechanical properties with the present sample size is very likely to reflect similar extents of variance in the general population, attributable to the inherent biological variability. The idealized simulations depicted in Figure 3c,f demonstrate the combined effects of skull thickness and brain stiffness on the distribution of tissue strains under
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AGE-DEPENDENT CHANGES IN MATERIAL PROPERTIES OF THE BRAIN the load of the indentor in 13- and 43-day-old rats. The sharper profile of the deformed shape of the skull and the more focal region of maximal strain in the brain tissue (Fig. 3c) may be attributed to the thinner skull of the 13day-old rat. The simulations predict that in order to produce similar strain distributions in brains of rats at different ages, the braincase of younger rats should be indented to a greater extent. Tissue strain distributions have been used to identify brain regions that may be susceptible to histologic damage after a traumatic injury (Meaney et al., 1995). Importantly, the present characterization of tissue properties and the idealized finite element simulations facilitate future development of more accurate three-dimensional finite element models that include both brain and skull anatomies for neonate and adult rats. These future models could be used to predict brain deformations that could be superimposed over maps of histologic tissue damage. In this manner, age-specific injury tolerance values can be determined in terms of local tissue stress, deformation and strain. Computational and experimental models designed to simulate accidental and/or inflicted injury to the brain/ braincase are highly dependent on adequate description of tissue material behavior. In addition to the developmental changes in brain size and weight reported previously (Dobbing, 1981), our observations indicate that the mechanical properties of immature brain tissue significantly differ from those of the adult brain. Thus, the same injury parameters of acceleration and force applied to infant and adult rats will produce different stresses and strains in the brain tissue. Therefore, if the same brain tissue stress or strain level is desired for comparative analysis of brain injury consequences across ages in the rat, the experimental model design should incorporate data presented in this communication to scale applied accelerations and forces between ages.
ACKNOWLEDGMENTS We are thankful to John Noon for his technical assistance in designing and building the indentor and to Brittany Coats for her help with the indentation studies. The study was supported by NIH grants R01-NS-39679 (S.S.M.) and R01-NS-41562 (R.R.), by a CDC grant R49CCR-312712 (S.S.M.), and by the Dan David Foundation (A.G.).
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