A Method for Evaluating Brain Deformation Under Sagittal Blunt Impacts Using a Half-Skull Human-Scale Surrogate

Traumatic brain injury (TBI) affects more than 2.8 × 10⁶ patients in the USA per year and rates of TBI emergency visits increased nearly 54% between 2006 and 2014 [1]. TBI commonly occurs from blunt impact to the head such as unintentional falls, sport collisions and motor vehicle accidents [2]. Select populations can be at higher risk of blunt TBI due to the nature of their work such as military personnel and athletes [3–5]. For instance, sports-related impacts are problematic because of their repetitive nature and the wide range of impact locations.

Trauma to the brain is a biomechanical problem where the initiating event is a dynamic loading (blunt, inertial, blast) to the head [6–11]. Dynamic loads induce damaging head motions causing injury to neurons and their fibers called axons because of rapid deformation of the brain tissue [8–13]. The biomechanical impact parameters of any blunt TBI can be significantly different in terms of speed of impact, magnitude of force, duration of the impact as well as the direction and placement of the impact on the head [14–16]. To study the biomechanics of blunt TBI many approaches have been used. Measuring real-time rigid body kinematics of the head using wearable devices on human subjects has greatly improved and is used to explore how various blunt impact scenarios can lead to concussion in sports [17–20]. In the laboratory, surrogate head models are often instrumented with accelerometers, strain gages and pressure transducers to measure skull deformation, intercranial pressure, and head kinematics [21–23]. The biofidelity in these models can be improved with the limited use of postmortem human subjects to evaluate skull deformation and fracture [24–26]. To evaluate intracranial motions within brain tissue and simulants, high speed X-ray imaging of neutral density markers has been used to achieve high-speed measurements in a closed head [27,28].

To date, there are only few approaches that directly measure intracranial motions that can be used to calculate deformations. There is a deep history of translating head kinematics to resulting motion and damage of the brain using matched computational models to determine stresses and strains within brain structures that can be related to animal models of TBI. Finite element simulations have broadly been used to bridge the gap between the mechanical input, response of the brain tissues and structures, and clinical outcomes [29–31]. For these simulations, the heterogeneous distribution of stresses and strains, which may injure the brain, are estimated based on experimental animal and cadaveric data, mechanical testing of tissue samples, and reconstructions of real-life injury scenarios. While finite element models provide excellent spatial and temporal resolution with anatomic accuracy, they need to be validated against experimental data [32,33]. Surrogates of the human head can help provide experimental data [24,34].

To study the relationship between the mechanical parameters of the primary injury and the spatial and temporal deformation patterns in the brain, there is a need to develop an experimental TBI model that can be readily altered to study varying anatomical, material property and loading parameters and rapidly collect and analyze changes in deformation patterns. In this effort, we aim at directly measuring brain deformation (strain and strain rates) in different brain regions of interest (e.g., cortex, hippocampus and brain stem) in a full-scale human head model using a drop tower and by varying the impactor speed and direction of blunt impact. Inspired by earlier work [35,36], we created a full-scale physical model of half human head and neck from which brain deformation is measured using visual markers on a brain surrogate material to capture spatial and temporal deformation during blunt trauma. These deformation time series present an opportunity to understand the relationship between the mechanical trauma event and the biomechanical event occurring to the brain tissue.

For the purposes of model development, economical and anatomically accurate human PVC skull models (Anatomy Warehouse) were used to produce the surrogates. Reported tensile modulus for PVC is between 2.5 and 5 GPa and remains constant under dynamic loads. PVC has an elongation at tensile strength of 0.04-0.1 and fracture elongation 0.030 [37,38]. Reported values for human cranial bone are between 0.45 and 10 GPa and elongation at tensile strength 0.05–0.1, fracture elongation 0.030–0.15 [39–43], suggesting that PVC is a reasonable surrogate material. To create the surrogate skull, the mandible and maxilla bones were removed and a cut was made approximately 2 cm lateral to the midsagittal line, exposing the inside surface of the calvarium, Fig. 1. The foramen magnum, foramen ovale, jugular foramen and foramen spinosem were manually sealed with hot glue and epoxy.

For the brain surrogate, a synthetic ballistics gel 20% (Clear Ballistics) was used. Organic ballistics gelatin has been used since 1960 to simulate the density and viscosity of human tissue and has an elastic modulus within 25 to 300 kPa based on formulation and storage conditions [44,45]. Organic ballistics gel must be stored at 10 °C and breakdown of the gelatin begins after just a few day [46]. Synthetic gels are composed of polystyrene, polyisoprene, and mineral oil (formulations are typically proprietary). They can be left at room temperature without contamination issues and melted for reuse [46]. Organic and synthetic gels have been previously used to simulate brain tissue by many groups [47–53] with reported tensile modulus between 15 and 125 kPa varying with composition and manufacturer [46,53,54]. Clear Ballistics gel used in this study has a reported range between 43 and 125 kPa [53]. Dynamic testing of brain tissue has a reported tensile modulus between 8 and 60 kPa which varies based on the testing method and brain region tested [55,56]. The Clear Ballistics gel was chosen since it is in the range of brain stiffness in the literature and provided the storage, reuse and optical properties needed for this model development.

To mold the brain simulants, the gel as supplied was melted at 121 °C (250 °F) in accordance with the manufacturer's instructions and poured into the half skull to midsagittal line. A custom-made skull-holder was made that allowed for a level pour into the skull (not shown). The gel was qualitatively observed to shrink after cooling.

On the gel surface, a grid of markers was applied midsagittal plane using a stencil and an ink marker (Fig. 1(b)). The stencil was prepared on a three-dimensional printer with a grid of holes 7 mm apart. Working within the camera resolution, markers ranged 12-18 pixels in diameter and spaced at 30 pixel intervals. Accurate visual tracking also required high contrast at the marker edges. We found using dark dots on the Clear Ballistics gel produced more accurate marker tracking than the opaque and yellow colored gelatin based ballistics gel. Several ink types for the markers were tested and the best results were achieved with heat resistant Sharpie industrial marker. After the ink dried, an approximately 15 mm thick layer of gel was poured on top of the markers, filling the space created from gel cooling.

For this model, we assume symmetry about the human skull's midsagittal plane, therefore deformation experienced by our “half skull” is mirrored by the opposite side of the brain. To prevent motion out of the plane of symmetry, a ¼″ thick sheet of polycarbonate was cut to fit onto the surface of the skull to constrain the brain while allowing visualization of the marker motion. Initial tests have shown that ballistic gels are tacky on the surface and can stick and release from the window causing the markers to distort. A lubricant, WD40, was placed on the gel and polycarbonate surfaces to reduce friction between interfaces. The head model and window were pressed together with C clamps and then fused to a rigid epoxy base. WD40 had no observable effects on the oil based synthetic gels.

To complete a head-skull-brain surrogate for blunt impact testing, the skull-brain model was mounted to a Hybrid III Anthropomorphic neck (Humanetics, Fig. 1(b)). The mounting fixture consisted of two plastic plates. The top plate was glued using epoxy to the base of the skull and had a hole pattern matching the bottom the plate. The bottom plate had a hole pattern that matches both the hybrid III neck and the top plate. The bottom plate was mounted first into the hybrid III neck then bolted to the top plate.

The skull-brain-neck assembly was adapted to a Uni-axial Impact Monorail Machine (Cadex Inc.). For practicality of high-speed imaging we chose an experimental setup with the surrogate head stationary at the base of the drop tower and the impactor as a dropping anvil striking the surrogate head at the bottom, Fig. 1. The surrogate head was secured with custom-made bases: (1) a flat mount to simulate crown impacts (Fig. 1(e)) and (2) a 45-degree angle mount to simulating forehead impacts (Fig. 1(f)). For the crown impact, the skull and neck were mounted upright and aligned so that the drop tower headform stuck the skull at coronal suture. For the frontal impact, the skull and neck were mounted at a 45 deg and aligned so that the drop tower headform struck the skull at the frontal bone. All impacts were aligned as close as possible to the midsagittal plane and we ensured the impactor struck the skull and not the polycarbonate window.

The EN960 Magnesium headform (assembled weight of 4.54 kg or 10lbs) provided with the monorail system was used as an impactor. The impact machine is equipped with a time gate to allow for impact velocity of the headform to be measured. The drop height is the input variable for the drop tower, with increased drop heights corresponding to increased impact velocities. Actual impact velocity and impactor acceleration are recorded by the drop tower controller and saved in an output file.

The full-scale human surrogate was tested under two configurations: crown and frontal impact using 3 drop tower heights of 9, 26, and 49 cm. Measured velocities were 1.34 m/s (3 mph) for the 9 cm height and 2.23 m/s (5 mph) for the 26 cm height. These velocities are comparable to head impacts in bicycle accidents [57–60] and low speed pedestrian accidents [61,62]. Preliminary tests at 3.12 m/s (49 cm drop) caused the PVC skulls to occasionally crack under the crown orientation, and the remaining validation experiments were limited to the 1.34 m/s (3 mph) and 2.23 m/s (5 mph) drops.

Impacts and the resulting motion of the surrogate head and brain were recorded with a high-speed camera (Photron FASTCAM SA3 model 60 K), Fig. 1(d). To maintain the camera's maximum resolution of 1024 p × 1024 p, videos were recorded with 8 bit grayscale at 1,000 frames/s, Fig. 1(c). During impact, as the head model moves, its position relative to the lighting will cause the surrogate brain surface to change brightness and cause reflections. Appropriate lighting was essential. We found the use of two LED lamps (Generay SP-E-360D) positioned on each side, at approximately a 30 deg angle to the midsagittal plane of the model rather than the front minimized glare and reduced changes in light intensity. LED lamps also increased brightness and contrast for optimal video quality for tracking and resolution. After recording, the pixel coordinates of the black markers were determined for each video frame in time using the two-dimensional tracking feature in Pro-Analyst Software (Xcitex, Woburn, MA). Using the first video frame, markers were assigned numbers row by row from left to right, Fig. 2(a). Consistent numbering across videos allowed the same markers in different impact scenarios to be compared. After the software finished automated tracking, each video frame was visually inspected for tracking errors. The most prevalent error was the software losing track of the black marker and deviating to track another feature. When errors were encountered, brightness and contrast of the video was changed followed by retracking the marker with error. If still tracking remained unsatisfactory, a larger tracking area (consisting of more pixels) was selected to facilitate retracking of the marker. Selecting a larger area decreases the probability of the software wrongly identifying the location of one marker with another similar marker.

Tracked marker positions from each video were exported from Pro-analyst as individual excel spreadsheets and organized as follows: the first two columns contained the video frame number and time in seconds. Then, each consecutive pair of columns listed each point's xy positions for each consecutive video frame. The data were saved in Excel format and imported into matlab using the “xlsread” function.

To calculate surrogate skull kinematics, two undeformed points on the skull were used to calculate the linear and rotational acceleration of the surrogate head. We first calculated the displacement of each point using matlab diff function then divided by sampling frequency to calculate velocity. Then, we differentiated again using the same approach to calculate linear acceleration in x and y directions. Resultant acceleration was calculated by doing the square root of the sum of squares. Same approach was used to calculate rotational acceleration using the point angle with respect to the origin.

where ε_xx is the strain in the x direction

• ε_yy is the strain in the y direction

• ε_xy and ε_yx are the shear strain

Because this calculation was repeated for each video frame, each spatial location accumulated a strain-time history, Fig. 2(c). The maximum magnitude of the strain in each time histories was identified using the max function in matlab.

where $ε˙$ is the strain rate, ε₁₀ is 10% of maximum strain at time point t₁₀ and ε₉₀ is 90% of maximum strain at time point t₉₀.

The time window (t₁ to t₂) for impulse calculation was set to 15 ms. To find the maximum strain impulse a moving time window, centered about each temporal data point in the strain-time history, was used to iteratively calculate the impulse value until the maximum value was found.

To visualize the spatial distribution of the results, we plotted heat maps of strain magnitude, strain rates and strain impulse on the coronal section of the head model. The heat maps were generated in matlab using its “countourf” function. To examine strains that occur in brain structure regions of interest, the spatial deformation map was divided into 6 sections corresponding to the frontal lobe, parietal lobe, hippocampus, occipital lobe, brainstem, and cerebellum, Fig. 3(a).

Maximum principal strain, strain impulse and strain rate data were presented as means and standard deviations. To compare the different impact scenarios in terms of maximum principal strains, strain impulse and strain rate, four different statistical approaches were used. First, an ANOVA (anova1 matlab function) was performed to reject the null hypothesis that all group means are equal. Second, we plotted the histograms of each injury scenario and calculated skewness (skewness matlab function) and kurtosis (kurtosis matlab function) to analyze the data distribution. Third, we plotted quantile quantile (QQ) plots (qqplot matlab function) and cumulative distribution function (CDF) plots (cdfplot matlab function) for each injury scenario to compare the data to a standard normal distribution. Fourth, the Bajgier–Aggarwal test was used to identify mixed Gaussian distributions and fitting a mixed Gaussian distribution was done using fitgmdist matlab function. Fitting a linear regression to the data and calculating p values was done using the fitlm matlab function.

A full-scale model of the human skull, brain and neck was tested under 4 impact scenarios: 1.34 m/s (3 mph) crown impacts (n = 4), 2.23 m/s (5 mph) crown impacts (n = 4), 1.34 m/s (3 mph) forehead impacts (n = 6), and 2.23 m/s (5 mph) forehead impacts (n = 6). The resulting motion of the surrogate skull-brain-neck was captured with high-speed video for spatial and temporal analysis of rigid body kinematics and resulting intracranial deformations. The kinematics of the surrogate head is summarized in Table 1.

For each impact scenario, motions of the brain markers were used to calculate deformations from consecutive video frames representing 1 ms in time, Fig. 2. The maximum principal strains, strain rates, and strain impulses were identified temporally and averaged at each spatial location across trials.

An advantage of this model is the ability to examine strains that occur in brain structure regions of interest under various head injury loading conditions, Fig. 3(a). We found that the principal strain-time histories varied considerably from region to region, depending on the impact speed as well as impact direction, Fig. 3(b). The statistical distribution of the principal strains within each brain region is shown in Fig. 3(c). Crown impacts were characterized by high strains distributed across the parietal, frontal and hippocampal regions with longer durations whereas frontal impacts were characterized by sharply rising and falling strains primarily found in the parietal, frontal, hippocampal and occipital regions. Note that the principal strain ε₁ represents maximum tensile strains, ε₂ represents maximum compressive strains and the shear is determined from ε₁ and ε₂, Eq. (5). For simplicity and consistency with the literature, shear strains will be reported in the remaining results.

For crown impacts, the angle of the striking headform was close to the alignment of the Hybrid III neck and there was little neck motion, Fig. 1(e), see Supplemental Video 1 available in the Supplemental Materials on the ASME Digital Collection. Accordingly, deformation was largest in the area focal to the impact site (frontal lobe, parietal lobe and hippocampus) and driven in part by large flexions of the thin skull near the impact site, Fig. 4(a). The spatial distribution colormaps show high levels of maximum shear strain (γ_max) concentrated to the frontal, parietal and hippocampal regions, Fig. 4(b). The spatial distribution of strain rates and strain impulses were in the same focal area to the region of impact; however, the distributions are different, Figs. 4(c) and 4(d). Higher rates of strain are found near the skull-brain interface in the parietal lobe while larger strain impulses are developed in the hippocampus and parietal lobe. The statistical distribution of maximum strain, rate and impulse at both the 1.34 m/s (3 mph) and 2.23 m/s (5 mph) impact speeds are presented in Fig. 5. For crown impact mean maximum principal strains were 0.082 ± 0.056 (1.34 m/s (3 mph)) and 0.144 ± 0.097 (2.23 m/s (5 mph)). Strain rates had a mean of 17.90 ± 9.86 s⁻¹ (1.34 m/s (3 mph)) and 35.51 ± 20.96 s⁻¹ (2.23 m/s (5 mph)). Strain impulse had a mean of 0.904 ± 0.41 ms (1.34 m/s (3 mph)) and 1.347 ± 0.53 ms (2.23 m/s (5 mph)).

For frontal impacts, impact energy transferred into a large motion of the skull from neck flexion as compared to the crown impact, Fig. 1(f), Supplemental Video 2 available in the Supplemental Materials. In addition, the skull was thicker at the point of impact and no skull flexion was observed, Fig. 5(a). The spatial distribution colormaps show a different distribution of maximum shear strains (γ_max) that are away from the impact site and along the crown brain-skull interface in the parietal lobe, Fig. 6(b). Maximum strain rates were also found away from the site impact in the parietal lobe, Fig. 6(c). Strain impulses were largest in the parietal lobe, Fig. 6(d). The statistical distribution of strain, rate and impulse are presented in Fig. 5. For frontal impact mean maximum principal strains were 0.060 ± 0.047 (1.34 m/s (3 mph)) and 0.118 ± 0.082 (2.23 m/s (5 mph)). Strain rates had a mean of 14.06 ± 11.46 s⁻¹ (1.34 m/s (3 mph)) and 30.22 ± 21.50 s⁻¹ (2.23 m/s (5 mph)). Strain impulse had a mean of 0.510 ± 0.15 ms (1.34 m/s (3 mph)) and 0.997 ± 0.26 ms (2.23 m/s (5 mph)).

Overall, the direction and velocity of impact lead to significantly different shear strains, strain rates and impulses, p < 0.01 by ANOVA F (3,408) = 61.24, Fig. 5. To describe the statistical distribution of data, we plotted the maximum principal strain histograms (see Supplemental Figures S1A and S1B available in the Supplemental Materials on the ASME Digital Collection). Analysis revealed that frontal impact histograms are skewed left (skewness > 0.5) toward lower strains and crown impact histograms are skewed right (skewness < 0.5) toward higher strains. Also, in frontal impact histograms data are more concentrated about the mean (leptokurtic with kurtosis > 3) while crown impacts data was more dispersed (platykurtic with kurtosis < 3).

The strain rate and strain impulse histograms for crown impact showed the same characteristic dispersed platykurtic distribution as the strains (kurtosis < 3, Supplemental Figures S1C–S1F available in the Supplemental Materials). Examination of the shape of the QQ plot for crown impact showed 3 distinct curves indicative of multimodality, Supplemental Figure S2A available in the Supplemental Materials. Further, the cumulative frequency plot indicated 3 S-shapes staked on top of each other, Supplemental Figure S2C available in the Supplemental Materials [65]. A multimodal distribution in the case of crown impacts was confirmed using the Bajgier–Aggarwal test (kurtosis < 2.2). Consequently, the crown impact principal strains histograms were fit with a mixed Gaussian distribution that correlate with 3 distinct brain regions, Supplemental Figure S3 available in the Supplemental Materials. The first region incorporates 44% of the brain consisting of the frontal lobe, most of the hippocampus and most of the parietal lobe with an average strain of 0.25 ± 0.035. The second region represents 29% of the brain consisting of the occipital lobe and small part of the parietal lobe with an average strain of 0.16 ± 0.016. The third region represents 27% of the brain consisting of the cerebellum with average strain of 0.078 ± 0.03.

The strain rate histogram for frontal impact was platykurtic which indicated the possibility of multimodal distribution, Supplemental Figure S1F available in the Supplemental Materials. In contrast, maximum principal strain and strain impulse showed no multimodality in frontal impact, Supplemental Figures S1B and S1D available in the Supplemental Materials. Multimodality for strain rates was confirmed using the Bajgier–Aggarwal test (kurtosis < 2.2) [65]. Fitting a mixed Gaussian distribution to the data showed that strain rates can be grouped into two regions, Supplemental Figure S4 available in the Supplemental Materials. The first region consists of 60% of the brain including the parietal lobe, occipital lobe and half of the frontal lobe with an average of 42 s⁻¹±22.4. The second region consists of 40% of the brain including the hippocampus, brain stem, and cerebellum and half of the frontal lobe with much lower strain rates with an average of 12.4 s⁻¹±6.7.

To analyze how strains develop spatially across the brain, we examined when each location reached maximum strain (t_max) and the time point when strain begins (t₁₀). The time at which all strain values reached their peak (t_max at each strain location) occurred approximately at the same time over a narrow 5 ms range (10–15 ms). To visualize the temporal development of strains, t₁₀ (the time at which shear strain is at 10% of the maximum shear strain, Fig. 2) was plotted as a heat map over the brain regions, Figs. 7(a) and 7(b). Crown impacts occur quickly across the brain and over a shorter time window than frontal impacts where strains are initiated over a much longer time window. Comparing Figs. 7(a) and 7(b) with Figs. 4 and 6, spatial locations where t₁₀ occurred at earlier time points coincided with high shear strain regions.

To confirm there was a correlation between the time deformation begins and the peak value of strain, a linear regression with ANOVA showed significance for frontal impact (F(3,101) = 18.9, p < 0.001) and for crown impact (F(3,101) = 5.62, p < 0.02), Supplemental Figures S5A and S5B available in the Supplemental Materials on the ASME Digital Collection. The negative slope for frontal and crown impact linear regression indicates where deformation begins first, higher strains were reached. Similar trends were found for strain rate and impulse where higher strain rates and impulses were reached in regions where deformation begins first, Supplemental Figures S5C–S5F available in the Supplemental Materials.

The duration over which injurious strains occur is an important aspect of the biomechanical motion that can contribute to injury [66–68]. The strain-time histories at each spatial location were used to consider the time period over which the maximum strains occurred. To calculate injury duration, we used the strain time history to find the two time points at which strain valued 10% of maximum (t₁ prior to the peak value and t₂ after the peak value). Injury duration was calculated by finding the time difference between these two points.

Fitting a linear regression showed a negative correlation between injury duration and maximum shear strain for frontal impact (F (3,101) = 28.8, p < 0.001) and for crown impact (F (3,101) = 10.7, p < 0.02). This trend indicates that strains with lower duration correlate with the development of maximum shear strains, Figs. 7(c) and 7(d). The negative correlation was also seen with strain impulse and strain rate, Supplemental Figure S6 available in the Supplemental Materials on the ASME Digital Collection.

The rate at which injury occurs, which is distinct from the duration of the injury, is also an important mechanical parameter due to the viscoelastic properties of the brain [69,70]. The rate of injury can be represented by the rate at which strains are developed (strain rate) in the brain. A scatter plot between maximum shear strains and strain rates were higher. Strains were associated with higher strain rates (Figs. 7(e) and 7(f), (F(3,101) = 252, p < 0.001)). It is also important to note that high strain rates were associated with short durations and impulses indicating that injury from blunt impact leads to fast but short lived strains [71].

Injury to the brain has been well linked to injurious levels of strain in preclinical in vitro models of TBI. Strains in closed head animal and human models, however, rely on computational models of the head and brain to estimate stresses and strains that can develop in the brain from head injury scenarios. These computational models have correlated well with estimated levels of strain, particularly for diffuse axonal injury (DAI) [20]. Within this literature, a proposed head injury risk threshold of 15% strain correlated well with preclinical models associated with a 50% risk of developing DAI [19,72]. Using this approach, the percentage area of brain with shear strains higher than 0.15 for each injury scenario was calculated, Fig. 8(a). Crown impact had larger areas with shear strain above the 0.15 threshold; 53.17% ± 0.7 for 2.23 m/s (5 mph) and 12.9% ± 0.8 for 1.34 m/s (3 mph) compared with 32.9% ± 3.2 and 2.5% ± 0.5 for frontal impact. The spatial distribution of strains exceeding injury thresholds is important to determine brain region of vulnerability, Figs. 8(b) and 8(c). Areas above threshold in the 2.23 m/s (5 mph) crown impact occurred in the frontal, parietal, occipital lobes and hippocampus. For 2.23 m/s (5 mph) frontal impact area above threshold was mainly parietal lobe and part of the frontal lobe.

Analogous to the spatial distribution of shear strains exceeding injury thresholds is the Cumulative Strain Damage Measure (CSDM 15) which quantifies the volume of the brain that exceeds a threshold value of 15% tensile strain and a 50% risk of developing DAI [73]. To consider this approach, areas of brain with tensile strains higher than 0.15 were calculated. Frontal impact had higher areas with tensile strain above the threshold 5.69% ± 1.3 for 2.23 m/s (5 mph) compared with 3.571% ± 1.05 for crown impact, Fig. 8(d). Areas above threshold were different than for shear strains. Frontal impact was mainly parietal lobe and part of the frontal lobe whereas crown impact areas above threshold were frontal lobe (Figs. 8(e) and 8(f)).

Trauma to the head is first and foremost a biomechanical problem. The type and degree of head trauma is directly related to the kinematics of the head, the boundary conditions of the skull and neck, and the type of loading being applied. For instance, skull fracture is related to direct impacts and linear motions whereas subdural hematoma and diffuse axonal injury are related to nonimpact rotational motions and the resultant inertial motion of the brain [74–80]. For closed head injuries, it is generally accepted that rapid deformation of the brain is the mechanical initiator of TBI [81–84]. Accordingly, in vitro models of TBI use the application of strain to study the real-time initiation and progression of damage to neurons [85–87].

Assessment of risk of head injury also relies on the quantification of strains that occur in the brain associated with various types (blunt, blast, inertial) and severities of TBI. This is currently done by measuring head kinematics in real world scenarios, using the head kinematics in computational models to estimate resulting strains within the brain, and then compare predicted strains to injury thresholds established in animal and human studies [19,20,88]. State of the art sensors have been applied to measuring the kinematics of the whole head [89,90]. To measure the spatial and temporal response of the brain tissue is technically more challenging due to the closed skull and rates associate with head injury. High speed X-ray imaging of neutral density markers have been used to visualize motion [27,28]. In addition to measuring kinematics instrumented surrogate heads have measured extensively intercranial pressure [21,22].

Due to the broad ability to collect data from human subjects, head kinematics are primarily used to predict the likelihood of sustaining a TBI in a given event, but they offer limited insights into the strain induced mechanism of injury. Currently the best direct method to measure the resulting deformations within the closed cranium of human scale models is the use of radio opaque markers and high speed X-ray [81]. While this method offers the best three-dimensional data to validate computational models, it is a difficult procedure, requires expensive resources and provides low resolution deformation data. Here, we developed a new method for the direct measurement of deformation and sagittal strain calculation within the surrogate brain of a surrogate skull, brain, and neck physical model subjected to blunt impacts. This work was inspired by previous studies [77,91–95].

The degree and location of strains within the brain can differ with each head injury scenario, which is believed to contribute to the variability in TBI clinical outcome and risk prediction [7,76,96]. Indeed, some studies have shown that outcome from a head injury does not simply scale with head kinematic magnitudes such as linear or rotational acceleration but are a result of varying boundary and impact conditions [96–98]. Well-controlled animal models have also been known to have variations in outcome measures and are likely related to changes or variations in boundary and impact conditions [99]. In this study, location and speed of impact were experimentally varied and the differences in the spatial and temporal development of strains in the human scale physical model were analyzed.

Higher impact velocities corresponded to higher strain values across all experimental situations. However, there were large differences in the spatial and temporal strain responses between crown and forehead impacts. Overall, the experimental results in this study suggest that for the same speed, crown impact leads to more damaging strain patterns than a frontal impact. Data show that crown impact had an average maximum principal strain (MPS) 22% higher than frontal impact for the same impact speed (average MPS for frontal impact 0.118 ± 0.082 and for crown impact 0.144 ± 0.097 at 2.23 m/s (5 mph)). Likewise, the average strain rate was 17% higher under crown impact (average strain rate for frontal impact 30.22 ± 21.50 s⁻¹ and for crown impact 35.51 ± 20.96 s⁻¹ at 2.23 m/s (5 mph)). Lastly strain impulse was also 35% higher under crown impact (average strain impulse for frontal impact 0.997 ± 0.26 ms and for crown impact 1.347 ± 0.53 ms at 2.23 m/s (5 mph)).

Our data are consistent with several reports in the literature. Using half human skull physical models under pure rotation in the sagittal plane, maximum shear strains of 0.2 at a strain rate of 35 s⁻¹ over a duration of 12-13 ms were obtained [77]. In another study using a half skull model of the miniature pig commonly used in TBI research, maximum shear strain of 0.32 at a strain rate of 53 s⁻¹ over a duration of 12–13 ms was produced. These results from pure rotation of the skull are directly comparable to the strains produced in this study. Importantly, however, head impacts used in this study produced much higher strain rates; well-over 60 s⁻¹ in many locations, Figs. 7(e) and 7(f). In terms of brain-skull relative displacement it has been reported that crown impact produces higher displacement of the skull (5.9 ± 2.8 mm) compared to frontal impact (2.75 ± 2.3 mm) and is similar to our observations with the model used in this study. In another study under helmeted conditions, higher strains were produced under frontal impact versus crown in contrast to our model. The presence of a helmet, however, likely protects against skull flexion at the site of impact. Our results also indicate the strains in the brain are due primarily to the deflection of the skull in comparison to frontal impact.

Many computational studies of head impacts have predicted values for strains in the brain from head impacts and are comparable to the strains measured in this study. For instance, in a finite element model of frontal impact a maximum principal strain of 0.2 and an average strain of 0.08 ± 0.012 was reported [100]. In another finite element model for frontal impact, a maximum principal strain range between 0.17 and 0.36 was reported depending on the impact severity [101]. Using kinematic data from human subject in high school sports a finite element model found average maximum principal strains of 0.280 ± 0.089 and maximum principal strain rates of 54.3 s⁻¹±33.9 [102]. In a helmeted study, a maximum principal strain of 0.254 in frontal impact and 0.161 in crown impact [103].

The deformation data from the model was analyzed to describe differences in spatial patters across experiments. First, we found that the strain distribution under crown impact was skewed toward higher strain while frontal impact was skewed toward lower strains. Second, under crown impact 53% of the brain had shear strains higher than a threshold of 0.15 verses 32% under frontal impact, Fig. 8. Third, brain regions with strains higher than 0.15 were the parietal lobe and small parts of the frontal and occipital lobes in frontal impact and the frontal, parietal, occipital lobes and hippocampus under crown impact, Fig. 8.

The deformations pattern produced with this model are consistent with published finite element models results. From frontal impacts, some models have implicated the parietal, frontal, and occipital lobes [104,105]. Other models have reported only frontal and parietal lobes as areas of vulnerability [100,101] or just the frontal lobe [106]. Variability in reporting regional vulnerability could be accounted to differences in the loading and boundary conditions as well as different impact speeds. In a helmeted study of frontal impact, both parietal and occipital lobes were reported as areas of vulnerability [103]. Interestingly, all models, including our results, agreed on cerebellum as an area of least vulnerability.

We could not find published data on unhelmeted crown impacts. In one study of crown impact with a helmet, areas of vulnerability correlated with our results [103]. Comparison of strain distribution heatmaps indicate higher strains in cerebrum compared with cerebellum and brain stem which matches our results being the frontal, parietal, and occipital lobes as well as the hippocampus are areas of vulnerability.

A main distinction between frontal and crown impact was the multimodality of spatial strain distribution. Crown impact showed a clear multimodality in maximum principal strain distribution as well as strain impulse and strain rate, Supplemental Figures S1–S3 available in the Supplemental Materials on the ASME Digital Collection. Alternatively, frontal impact showed multimodality only in strain rate while maximum principal strains and strain impulse showed a single population distribution skewed to the left Supplemental Figure S1 available in the Supplemental Materials. The multimodality of strain distribution provides a glimpse of the variability of strains, rates, and impulse spatially, given each impact direction leading to dramatically different patterns.

We evaluated the temporal development of strain spatially across the simulated brain in three ways: rise times of the strains, duration of the strain impulses, and the temporal development of strains (t₁₀) to illustrate how the brain deformations progresses through the brain from the time of impact. We found a significant correlation between short rise times and peak strains. The same correlation was evident for injury duration, small injury durations significantly correlated with higher strains. This finding is important due to the viscoelastic property of brain tissues were faster development of strains would be associated with the generation of higher damaging stresses in the brain tissues [56,107,108]. In an animal model of TBI, we have found that high rate, short duration injuries can lead to outcomes that are different but significant from the broad TBI literature illustrating the importance of controlling these mechanical parameters on injury.

To visualize how strains develop and propagate with time spatially through the brain, we plotted a heat map of the time at which strains begin (t₁₀). For crown impact, strains travel from top to bottom creating three areas of strain populations. For frontal impact, strains develop from front to back splitting brain into two distinct areas of strain populations. The temporal heatmaps also indicate that peak strains begin first followed by lower strains in both crown and frontal impact.

The model developed in this study represents a complementary method to investigate and analyze the spatial and temporal variations in strains that can occur in the brain under sagittal blunt impact scenario. There are, however, model limitations that should be considered including geometry, boundary conditions, and material properties. The intracranial geometry of the replica skull is assumed to be accurate; however, it did not include intracerebral structures such as the falx cerebri as well meninges, veins, and Cerebrospinal fluid. The ballistics gel used for the surrogate brain was poured directly into the skull and only bears the general shape of human brain. Furthermore, the heterogeneity of the brain from the gray matter and white matter distribution is missing. In future studies, features such as major vessels, the ventricles, the tentorium, falx, and meninges can be added to increase the complexity of this model. Mechanical characterization of selected materials becomes more important with increasing the surrogate's geometric complexity.

There are two boundary conditions that likely affect the model performance. First, the parasagittal cut to produce a half skull to allow visualization of the brain motion weakens the skull in terms of flexural strength. While our data demonstrates the importance of skull flexion in brain deformation under crown impact, the deformations in this study are likely larger compared to a full skull. A future model will need to address the flexural stiffness under crown impacts. Skull flexion under frontal impact was not measurable from our video data. The second important boundary condition is the no-slip condition between the gel and the interior wall of the skull. Future work will need to include a more realistic brain-skull interface.

The replication of material properties for the skull and brain are common limitations in surrogate modeling. Similar to geometry, the most accurate material model of the skull would be to use a fresh human skull and beyond to scope of an adaptable and reusable experimental model. Even a dried human skull would not be a completely accurate model as the properties change dramatically postmortem [41–43]. The more complex material property limitation is replicating the heterogeneous and anisotropic brain. While brain is not homogeneous like the ballistic gel used here, this model will allow the testing of gel stiffness and anatomical features on the strain response under blunt impacts. While the reported tensile modulus for the ballistics gel used in this study overlaps with measured modulus for brain (see Methods), some studies suggest that actual human brain could be considerably less stiff than many materials that have been used as brain surrogates [56,107,108].

This paper presents a new method for studying blunt intracranial injuries with visual markers that preserves spatial and temporal data. Building upon similar studies in the past, the model performed as expected under the experimental protocol. This model can provide very useful data on how the brain will respond under any mechanical loading scenario. Indeed, existing strain thresholds used in the TBI field are based on results from similar models used many years ago [77]. With targeted improvements, this model can be used to experimentally explore many anatomical features or relate head kinematics to patterns of brain deformation.

• The U.S. Army Research Laboratory (Funder ID: 10.13039/100006754).

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.