Developing Brain-Strain-Based Scaling to Inform the Clinical Relevance of Mouse Models of Concussion Induced by Rotation

Laboratory animal experiments are an invaluable tool for studying mild traumatic brain injury (mTBI)/concussion. Among them, rodent neurotrauma experiments have been most widely used, as transgenic and gene targeting technologies in mice allow us to test the roles of different genes in recovery from brain injury. Furthermore, the clinical relevance of rodent concussion studies can be improved by using these technologies to study concussions in animals that carry the human versions of genes known to play a role in neurological disease. However, delivering concussion injuries to the mice that are relevant to real-world human head impacts is challenging, as the mouse and human heads are dramatically different in shape and size. In the vast majority of mouse concussion experiments, the pathological and behavioral consequences of the injuries are evaluated without considering whether the injury model produces brain stretches (maximum principal strains) of the same magnitude as those experienced by human brains undergoing similar impacts. We conducted a total of 201 computational simulations to understand both human and mouse brain strains that are directly linked to neuronal damage during closed-head concussive impacts. To represent real-world human head impacts we simulated mouse head impacts with durations of 1.5 ms (Type 1 scaling), followed by simulations with durations between 1 and 2 ms (Type 2), and finally, simulations with durations from 0.75 to 4.5 ms (Type 3) to develop scaling between human and mouse, as well as to reveal the predicted effects of small and large changes in impact durations on brain strain. Guided by these simulations we calculated that peak rotational velocities in mice could be achieved by scaling human peak rotational velocities with factors of 5.8, 4.6, and 6.8, for flexion/extension, lateral bending, and axial rotation, respectively, to reach equal brain strains between human and mouse. The effects of impact durations on scaling were also calculated and longer-duration mouse head impacts needed larger scaling factors to reach equal strain. The scaling method will help us to create brain injury in the mouse with brain strain loading equivalent to those experienced in real-world human head impacts.


Background
Traumatic brain injury (TBI) is one of the leading causes of death and disability around the world, and occurs in more than 2.87 million people in America every year (1). Patients of TBI may suffer from physical, cognitive, social, emotional, and behavioral symptoms, and serious TBI can cause permanent disability and death (2). While symptoms in mild TBI (mTBI) patients typically resolve within 7 to 10 days post-injury (3), 15% of mTBI patients go on to develop post-concussion syndrome and long-term cognitive impairment (4). Animal studies of mTBI are actively being pursued to understand the pathophysiological underpinnings of concussion and post-concussion syndrome.
There are various types of animal TBI experiments reported in the literature, partially because of the variability in human TBI that is being modeled. Researchers have focused on three models including open-skull cortical impact injury (CCI), open-skull fluid percussion injury (FPI) and closed-head weight drop-impact acceleration injury (5). Openskull TBI using the cortical impactor has been popular as it allows direct loading to the brain tissue and induces high brain strain above 0.30 to the underlying cortical layers (6). Open-skull TBI using the FPI also induces high strain up to ~ 0.1 and high pressure of approximately 180 kPa (7). Despite the greater convenience of open skull TBI, closed-head TBI is considered more clinically relevant because it does not require a craniotomy (8) and real-world mTBI/concussions happen with closed-skull conditions. Hence, closed-head models have been prioritized in mTBI/concussion investigation with a majority of studies using rodents (9)(10)(11). The challenge is to ensure the mechanical loadings that rodent brains experienced in the laboratory setting are relevant to those experienced by human beings during real-world impacts.
It is well established that brain sizes are connected with mammalian physiology (12,13). Thus, one method that has been used to scale brain injuries between species has focused on the effects of mass (14). Primates that have similar brain shape to human and Ommaya et al (14) reported that the risk of producing concussion in humans and primates is related to brain mass, which is determined by brain size. In studying blast injuries, Bowen et al (15) scaled the duration of the positive phase and the maximum reflected overpressure of air blast to get the same biological response among 13 species, by using scaling factors including body mass and ambient pressure. Wood et al (16) re-examined the allometric relationship between physiological manifestation and body mass across species, and came up with a new law that scales the duration of air blast using a ratio of reference mass to target animal mass using apnea data as injury evaluations.
There are also methods for scaling TBI between species that focus on parameters beyond brain mass. Takhounts et al (17) adopted a scaling law which scaled the amplitude and time of the loading condition to generate equal stress/velocity in two models of injury. Jean et al (18) focused on blast-induced TBI and emphasized that the human brain was more sensitive to blast than other mammalian species and proposed a scaling law taking relative acoustic impedance and surrounding protective structures into consideration. Saunders et al. developed a scaling rule based on the comparison between responses of two finite element (FE) models to fifteen available injury metrics (19). A recent study conducted by Wu et al. compared four scaling laws, including one self-developed, frequency-based method, by comparing the calculated brain strains using human, macaque, and baboon brain FE models (20).
Given the lack of scaling laws between human and mouse for mTBI studies, our goal was to devise a scaling factor to translate the kinematics of human head impacts to the kinematics in laboratory mouse impacts producing similar or equivalent degrees of brain strain. We first evaluated traditional mass-based scaling and equal stress/velocity scaling methods and found that they were not accurate in scaling human to mouse mTBI. We then compared strain-based injury metrics, including cumulative strain damage measure (CSDM)10 and average strain, to identify pairs of different rotational loading conditions predicted to result in similar brain strains in human and mouse (difference < 3%). These analyses have led us to propose scaling laws in three rotational axes that will provide a useful and efficient reference when evaluating the clinical relevance of mouse mTBI experiments and when comparing the results of mouse mTBI experiments across laboratories (21).

The Finite Element Human Brain and Mouse Brain Models and Simulations
The human FE brain model was developed from detailed computed tomography (CT) and MRI scans of an average adult male (21), using feature-based multi-block technology (22) to efficiently create high-quality hexahedral elements for the cerebrum, cerebellum, brainstem, corpus callosum, ventricles, and thalamus. The model was validated and exercised based on the experimental data of thirty-five cases and currently serves as one of the most used human head models to study brain responses (21). The mouse FE brain model includes the olfactory bulb, cerebral gray matter, corpus callosum, brainstem (midbrain, pons and medulla oblongata), cerebellum, lateral ventricle, 3rd ventricle, 4th ventricle, internal capsule, external capsule and part of spinal cord. Hexahedral meshes were used to ensure the accuracy of simulation. The mouse brain FE model has been used previously to successfully predict brain damage after experimental TBI (23,24). All the simulations were processed in HyperMesh (Altair Engineering, Troy, MI) and LS-PREPOST, and computed in LS-DYNA (Livermore Software Technology Corporation, Livermore, CA). Acceleration loading curves were adjusted based on the unit used by the models and applied to the center of gravity of each model using *BOUNDARY_PRESCRIBED_MOTION keyword to induce flexion, lateral bending, and axial rotation.
Brain model materials, rational of kinematic loading condition to the model, and postprocessing were consistent among the human and mouse. A linear viscoelastic (LVE) constitutive model for brain material properties was used in human and mouse finite element models. Although the human skull structures were modeled, these bony structures were treated as rigid for prescribed rotational loading, which is consistent with the loading condition to the mouse brain model for which a rigid skull layer was used to prescribe head rotations. The maximum principal (tensile) strain (MPS) was calculated for both the human and mouse brain, as brain tensile strains were found to be related to neuronal damage (25,26)

Real-World-Relevant mTBI Loading Condition
Extensive measurements of human head kinematics are available. Specifically, Rowson et al (27) created a large data set of human head six degrees of freedom acceleration of 1712 impacts by mean of installing accelerometers into the helmets of collegiate football players in 2007 and reported an average injury duration of 14 ms from 1712 cases. In 2012, Rowson et al (28) applied the same method to a study of 335 football players. In this study 300,977 sub-concussive and 57 concussive head impacts were detected and recorded. For concussive impacts, the average rotational acceleration was 5,022 rad/s 2 . Based on the rotational head kinematics observed in these two experiments, and on the rotational acceleration versus time graph of National Football League (NFL) reconstructed impacts obtained using the six degrees of freedom (6 DOF) device (29) and Head Impact Telemetry (HIT) System (30), the acceleration loading condition for human mTBI is set to be half sinusoidal curve with the peak acceleration of 5,000 rad/s 2 and duration of 10 ms and 15 ms. Based on previous simulations, a theoretical sinusoidal curve could be used to produce similar brain strains compared to the complex kinematics curves (31). Meanwhile, although head impacts induced both linear and rotational kinematics, it's found that rotational kinematics was responsible for generating over 95% of brain strain (31) and hence was the focus of this study.

Evaluating Traditional Mass-Based and Equal Stress/Velocity Scaling Laws
The human head kinematics was scaled to mouse head kinematics based on traditional laws, and then applied to the mouse FE brain model to quantify predicted strain responses.
Mass-based scaling law (14,32) Brain mass-based scaling law focuses on the ratio of brain mass across species. Firstly, the mass of human brain model is 1256 grams (21), while the mouse brain model mass is 0.410 grams (24). According to the scaling law, the duration and the peak acceleration scaling factors were calculated based on the brain mass ratio between human and mouse as equations (1) (2) and (3) shown below After this, the scaling factors were applied to human loading condition, the results are shown below Peak acceleration for mouse = 5000 (ℎ ) = 5000 0.00474 = 1055 Krad/s 2 (4) Duration for mouse = 10 (ℎ ) = 10 14.5 = 0.6897 ≈ 0.69 (5) Equal stress/velocity scaling law (17,33) This scaling law focuses on the ratio of brain geometry. The length ratio of brain equals cube root of mass ratio. Peak rot acceleration for mouse = 5000 (ℎ ) * * = 5000 * 14.5 * 14.5 = 1055 krad/s 2 (7) Duration for mouse = 10 (ℎ ) = 10 14.5 = 0.69 (8) In brief, despite different calculation procedures, the mass-based and equal-stress/equalvelocity-based models predicted the same kinematic parameters (peak acceleration and duration) would produce TBIs in the mouse equivalent to the average human TBI with a peak acceleration of ~5000Krad/s 2 as reported by Rowson [29].

Developing Scaling Law Based on Brain Strain: Calculation of CSDM and Average Values (Type 1 with Fixed Time Duration)
In mTBI, one of the most common and vital pathologic mechanisms is axonal damage (34). Cater et al (25) calculated the cell loss of hippocampal slice cultures which experienced 30 different loading conditions expressed by the combinations of strain and strain rate and proved that the long-term responses of brain tissue to mechanical loading are correlated with strain instead of strain rate. Hence, we used the CSDM metric to calculate the loading to the whole brain. Equation (1) shows the formula for calculating the CSDM value.
In an in vivo experiment, Bain et al (26) generated electrophysiological impairments by stretching guinea pig optical nerves with a final threshold strain of 18%. Three days later the guinea pigs were euthanized, and their optic nerves evaluated for the presence of axonal bulbs. At an 18% strain threshold morphological and functional axonal damage was observed. In this study, a CSDM of 10 was chosen when comparing mechanical response of brain tissue between mouse and human to be certain of setting a lower threshold for a strain that likely produces pathology significant enough to be clinically relevant. Besides CSDM10, the average strain which roughly represents the loading to the entire brain was also used. The CSDM-predicted values for all cases are calculated through an in-house program previously described (35).
The goal of mouse experiments was to yield kinematic curves generating the same CSDM values between the human and mouse. The entire process is described in Figure 1. The angular acceleration curves from real-world situations were simplified as sine curves and these curves were prescribed to human brain model to analyze brain tissue stretches ( Figure  1). We then used the duration of mTBI in the mouse as 1.5 milliseconds (Type 1 scaling) as has been reported in mouse mTBI kinematic studies (36,37) and started with an initial guess of mouse head rotational accelerations at 190 krad/s 2 . Then we predicted mouse model brain strain severity to the targeted human brain loadings, and adjusted rotational acceleration up or down based on the comparison, and solved the updated loading condition on mouse brain ( Figure 1). Finally, scaling laws were evaluated and developed when equivalent strains of the human and mouse brains were reached ( Figure 1).

Figure 1
Workflow diagram represents methods in step how brain-strain-based scaling law was developed. Finite human brain and mouse brain finite element (FE) models were used to transfer head kinematics to brain strains. Three types of scaling with Type 1 indicating fixed 1.5 ms duration, Type 2 indicalting slightly changed duration, and Type 3 indicating larger changed duration.

Developing Scaling Law While Considering the Effect of Varying Durations (Type 2&3)
In general, the same process ( Figure 1) was adopted while in Type 2 scaling, time durations were slightly varied from 1 to 2 ms, and in Type 3 scaling, time durations were largely varied from 0.75 to 4.5 ms.

Slightly Changed Time Duration (Type 2):
Kinematic studies of head injury have shown that peak rotational velocity has a much stronger correlation with brain strain metrics such as CSDM, than either rotational acceleration or linear kinematics (31,(38)(39)(40)(41). Hence, rotational velocity was chosen as the primary factor for scaling. A scaling law for rotational velocity will have a range of applications because an infinite combination of amplitudes and durations can produce the same velocity. As a result, the duration of an injury is also a significant factor when devising scaling laws. In order to make the scaling law practical and universal, to allow experimentalists to realize these kinematics parameters, a new group of simulations were conducted to explore applicable duration ranges. The acceptable tolerance was set to be less than a 3% difference between human and mouse in terms of brain strain measured using CSDM10.
Mouse model with human brain material: Since brain material properties are agerelated (42) and brain material properties reported in the literature vary among researchers (43,44), an independence test for brain materials was further conducted by applying human brain material properties to the mouse head model. This method can help understand the effect of shape and size without being affected by material diversity.

Largely Changed Time Durations (Type 3):
Given the fact that there are laboratory mouse experiments performed with time durations that do not fall between 1 and 2 milliseconds (9,45,46), the Type 3 study was conducted with an objective to understand how large changes in injury duration might affect the brain-strain-based scaling law. To minimize computational cost only 3 impact durations of 0.75, 3, and 4.5 milliseconds were simulated.

RESULTS
In total, 201 simulations were computed (Table 1): 3 for typical human mTBI-relevant head impacts, 2 for evaluating the current mass-based and equal stress/velocity scaling laws, 77 for developing scaling factors based on brain strain at an injury duration of 1.5 ms (Type 1), 75 for identifying the effect of small changes in injury duration (Type 2), and 22 for evaluating the effect of large changes injury duration (Type 3). A typical human or mouse head injury simulation took 2 CPUs approximately 8 hours to complete. All simulations terminated normally.

Evaluation of Traditional Scaling Laws
The typical loading condition for mTBI and the corresponding loading condition scaled from it were applied to the human and mouse brain FE models. The CSDM10 metric, which quantified the volume of brain elements experiencing principal strain above 0.10, was used to determine the severity of brain injury. After simulations, using the mass-based or the equal stress/velocity-based laws the CSDM10 in the human brain FE model was found to be 0.740, while the CSDM10 in the mouse brain FE model and human-material mouse brain model of 0.954 and 0.947 respectively. Accordingly, mouse brain showed much larger high strain areas and model materials did not affect the observation that applying traditional scaling laws to develop mouse head impacts would have significantly increased injury severity (Figure 2).

Figure 2
Evaluation of current scaling law. Applying traditional scaling induced larger strains in the mosue brain.

Scaled Mouse Brain Strain Data
Simulations were made of 78 mouse head rotations which were then used to calculate the relations between peak rotational acceleration and duration that defined rotational acceleration curves applied to drive FE brain models, peak rotational velocity that was calculated by integrating rotational acceleration over time, and mouse brain strain. First, our simulations demonstrated that the CSDM10-based brain injury severity had a strong positive correlation with peak rotational velocity (R-squared = 0.98, Figure 3a). Constrained to the same-rotational-velocity data group, the CSDM10 value has a negative correlation with impact duration (R-squared = 0.99, Figure 3c) while the peak velocity remained the same. Both rules indicated that longer durations and smaller peak rotational accelerations induced less damage. The same trends were also found in a modified mouse model with human brain material properties (21)   The scaling factor shows the ratio of peak velocity between loading conditions of mouse and human brain model. The scaling factors are different for different rotation directions as predicted. The largest scaling factor is 6.8 for axial rotation, followed by 5.8 for flexion and 4.6 for lateral bending (Table 2). The unit is rad/s; c M = Mouse (Peak rotational velocity), H = Human (Peak rotational velocity), Scaling factor is the ratio between mouse head peak rotational velocity and human head peak rotational velocity.

Effect of Mouse Brain Material
As for mouse brain FE model with human brain materials, the scaling factors become larger to 7.5, 6.3 and 7.1 for flexion, lateral bending, and axial rotation respectively (Table 3). The unit is rad/s; c M = Mouse (Peak rotational velocity), H = Human (Peak rotational velocity), Scaling factor is the ratio between mouse head peak rotational velocity and human head peak rotational velocity.
Meanwhile, the average strain showed a similar trend as CSDM did (R-squared > 0.99, Figure 3). The comparison of average strain results from human brain FE model, mouse brain FE model, and mouse brain FE model using human brain material materials are compared in Figure 4. In general, the differences were less than 10% during flexion and lateral bending modes.

Figure 4
The comparison of predicted average strain between human, mouse and modified mouse models. The average strain around 0.15 indicates the injury severity is mild.

Strain distribution predicted by the human brain FE model
In simulations for head impacts around the Y axis (causing flexion), the area that experienced MPS greater than 0.10 was the cortex with a maximum strain of 0.54. Additional scattered strains were also seen around the surface of corpus callosum (0.23) and brainstem (0.31), with the cerebellum being less stretched (0.19) (Figure 5a and d). In simulations for lateral bending, the corpus callosum, thalamus, basal ganglia, cortex and cerebellum all experienced MPS larger than 0.1. The corpus callosum and cortex reached a maximum strain of 0.48 and 0.44 respectively (Figure 5b). Lastly in simulations of injuries causing axial rotation, the most severe injury of all three cases, nearly all parts of the brain were affected. The cortex suffered the largest strain (0.74) at its surface. The corpus callosum had a strain of 0.37 and the hippocampus stood out in this loading condition with a strain of 0.46. The highest stretch always took place at the cortex except in lateral bending for which the corpus callosum experienced the highest strain (Figure 5c).

Strain distribution predicted by the mouse brain FE model
Unlike the human brain FE model, MPS distributed in the mouse FE model showed a figure-eight pattern for simulations of injuries causing flexion (Figure 5a and d). The highest MPS (0.47) can be found in the cerebral cortex. The second highest strain was in cerebellum (0.36). Brain stem, olfactory and pons experienced relatively small strains. In simulations of injuries causing lateral bending, the cortex had the highest strain of 0.38, while there were lower strains in the cerebellum (0.33) and thalamus (0.32) (Figure 5b). The worst damage among all mouse cases was predicted in simulations of injuries causing axial rotations, where the cortex and cerebellum had MPS of 0.8 and 0.75, respectively, but only a few portions of thalamus and brain stem experiencing MPS over 0.10. Distributions of strain for simulations of injury were not significantly different between the mouse brain FE model and the mouse brain FE model using human brain material with the exception that strains were lower in injury simulations with axial rotation (Figure 5c).

The Effect of Varying Durations
In reaching less than 3% difference of brain strain (CSDM10) between human and mouse brain, a duration of 1.37 to 1.62 ms was found for flexion loading, a duration of 1.34 to 1.62 ms was found for lateral bending, and a duration of 0.97 to 1.82 ms for axial rotation. With the same rotational velocity, the longer the duration, which corresponded to lesser peak acceleration, the smaller area in the brain would experience high-level strain ( Figure  3 c and d).
Results from simulations using flexion loading and durations of 0.75 ms, 1.5 ms, 3 ms, and 4.5 ms demonstrated a linear correlation between duration and scaling factors with a scope of 0.82 (R-squared = 0.99, Figure 6a). Under lateral bending, a similar linear relation was shown with a slope of 0.66 (R-squared = 0.99) while under axial rotation, scaling factors were similar for durations 1.5, 3.0 and 4.5 ms but smaller for a duration of 0.75 ms, forming a nonlinear relationship between duration and scaling factor. In general, larger scaling factors were calculated for loadings with a longer impact duration (Figure 6b).

DISCUSSION
Mouse experiments are needed to study the pathophysiology of mTBI, but such studies are hampered by a lack of understanding of how laboratory impacts to the outside of the head translate into brain strain inside the head. This lack of understanding makes it difficult to draw consistent correlations between laboratory mouse head impacts causing mTBI and the observed pathological and behavioral consequences from human head impacts. It also makes it difficult to evaluate the clinical relevance of the mouse mTBI models in use. Meanwhile, traditional scaling laws that did not take account the shape differences between mouse and human brains were found invalid based on our data. To fill this gap, we simulated head impacts using human and mouse brain FE models to understand the internal brain strains, which are the direct cause of neuronal and functional damage and have been quantified in vitro (47,48). These analyses have led to 3 findings. First, we found that peak rotational velocity could serve as an efficient metric for scaling. Second, we developed direction-specific scaling laws, as the same rotational kinematics could result in various degrees of brain injury when applied to different rotational directions (49,50). Moreover, the geometry difference between human and mouse brain complicated the process of finding human-to-mouse scaling parameters. Our data supported measuring and scaling mouse head rotational velocities, which allow us to generate strain (CSDM10) in the mouse brain similar to that in the human brain with differences less than 3%. We calculated scaling factors 5.8 for scaling up human-head rotational velocities during flexion/extension loading, 4.6 for lateral bending, and 6.8 for axial rotation. Lastly, we investigated the applicable time duration range of developed laws and reported potential changes for shorter or longer mouse head impact durations. For example, the scaling factor changed from 5.8 for 1.5-ms impact to 8.3 for 4.5-ms impact. To the best of our knowledge, this study serves as a unique investigation correlating laboratory mouse brain strain to human brain strain, and provides a useful reference for mouse mTBI experiments.
We focused on simulating rotational kinematics of the closed-head impacts in this study, as our previous data supported that rotation was responsible for more than 95% of strains developed in the brain (31). Doing so, we were able to capture the most important strainrelated kinematics. In laboratory closed-head impact tests, no matter where the animal heads were hit, the induced linear and rotational kinematics were the culprits that induced brain responses and led to brain damage, especially for mild TBI impacts for which skull deformation is limited. Meanwhile, open-skull laboratory neurotrauma loadings such as CCI and FPI are still widely used, for which part of the skull was removed and mouse cortical brain could experience strains up to 0.3 and higher in CCI (6) and around 0.10 in FPI (7). The focus on rotational kinematics in this study was consistent with mouse model such as CHIMERA (9) and swine models, both focusing on inducing head rotations (51,52). Also, our scaling method was based on brain MPS and a limitation of this study needs to be acknowledged as the lack of investigation into damage related to the axon and vascular directions, which remain to be further investigated in the future.
Scaling studies have been conducted with the understanding of various degrees of brain injury (49,50) and the acknowledgement of the geometry difference between human and animal brain. One example is to use natural frequency of the brain through a single-degreeof-freedom mechanical model (40). One of the challenges is in such a method is to understand the frequency values which have diverse features (53). On the other hand, the widely used mass-based scaling or same-stress-same-velocity approaches (14,17) were found to generate different strains between the mouse and human brains, partially due to the huge geometrical differences between human and mouse brains, and hence found not fit for scaling mTBI mouse experiments. The brain strain or peak overpressure as a metric to evaluate the severity of blunt and blast-induced impact was used in the field (16,20), as these brain internal responses directly cause injuries. In our work, the MPS-based CSDM was used to develop the unique mouse-to-human scaling laws.
The fixed impact duration of around 1.5 ms used in this study for Type 1 scaling has been used in models of rat TBI (37). In addition, several rotational injury devices have been developed to induce mTBI in brain by exerting rotation (54)(55)(56). In these studies, mouse post-injury behavior was examined through various methods such as elevated plus maze and rotarod performance test. As various injury devices deliver different impact durations, we have expanded our scaling laws to accommodate both slightly changed durations (Type 2) and largely changed durations (Type 3). In all these Type 1, 2, and 3 scaling laws, the agreements between human and mouse brain strains were reached. Table 4   Note. a The unit is rad/sms; b The unit is krad/s 2msrad/s.

CONCLUSIONS
To facilitate developing and understanding laboratory closed-head mouse mTBI experiments, which are designed to study human mTBI, we conducted a total of 201 simulations to investigate mouse and human brain strains during various impacts. Our data supported scaling human rotational velocity by 5.8, 4.6, and 6.8 under flexion/extension, lateral bending, and axial rotation, respectively, for mouse laboraotry experiments. We also found that traditionally used mass-based or same-stress-same-velocity scaling laws did not apply to human-to-mouse brain injury scaling. Meanwhile, it should be noted that the application of above scaling parameters best fit for mouse head impact durations of 1 to 2 ms, while with longer impact durations, larger scaling numbers are needed.