To better understand the underlying secondary injury parameters affecting the positive silver stained regions, we stained with specific antibody markers for cells commonly altered following injury Fig. APP is a commonly used marker for axonal injury. There was no change in APP immunoreactivity in the optic tract Fig. Myelin content was examined via MBP immunoreactivity. Axonal integrity was further examined using a pan-NF antibody. All positive silver stained regions showed these same histologic features, however, to varying degrees depending on the severity of the injury in that region.
Regions with altered DTI metrics exhibit histologic abnormalities consistent with injury. Representative photomicrographs of sham A—E and 0. Retraction bulbs and axonal varicosities are prominent in magnified photomicrographs of the 0. Figure 5 depicts group analyses results for the bilateral brachium of the superior colliculus, hippocampus, and optic tract.
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Neuroinflammation is significantly increased in white matter regions exhibiting altered DTI metrics. After multiple comparisons correction, changes within the brachium of the superior colliculus and optic tract exhibited significant differences between sham and CHIMERA-injured brains. A , IBA-1 immunoreactivity is significantly elevated in the left and right brachium of the superior colliculus.
B , GFAP immunoreactivity is significantly elevated in the left and right brachium of the superior colliculus and optic tract. C , MBP immunoreactivity is elevated in multiple regions but not significantly elevated in the brachium of the superior colliculus, hippocampus, and optic tract. The brachium of the superior colliculus and optic tract exhibit increased neuroinflammation as well as reduced FA on the difference maps.
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MBP showed a slight increase in the majority of regions analyzed including the bilateral brachium of the superior colliculus and optic tract Fig. APP immunoreactivity was increased in the right brachium of the superior colliculus and left hippocampus Fig. Statistics for all 19 ROIs are presented in Table 3.
Visualization of direct relationships between DTI metrics and histopathology in a region known to be injured by several metrics, the left optic tract, is shown by the scatterplots in Figure 6. Mean FA and immunohistochemistry values are shown for the left optic tract of each brain sample included in this study. In this region, sharp distinctions between groups can be seen based on both FA and quantitative histology values.
Lines are shown that separate the data points associated with injured from uninjured samples. Using even a single metric for classification of injury status is fairly successful at distinguishing injured samples from uninjured samples as only a single point would be misclassified using FA alone. For all four immunohistological measures in the left optic tract, it is possible to classify all samples into injured and noninjured samples based on a single threshold value. FA changes in relation to immunohistochemical alterations within the left optic tract.
The optic tract is a region that exhibited very clear reductions in FA. In the left optic tract, sharp distinctions between groups can be seen based on both FA and quantitative histology values, as indicated by the dotted line. The analysis was performed based on two sets of features.
Table 4 shows two combinations of parameters: 1 DTI metrics and 2 histology markers. Classification error was determined by number of incorrect classifications made by random forests Table 4. When all ROIs were considered for both DTI metrics alone and histology metrics alone, 1 out of 5 sham samples was misclassified making the classification error for sham animals equal to 0. A , B , To identify metrics that contribute the most to classification accuracy for sham and injured samples, the left optic tract and left brachium of the superior colliculus were investigated.
Mean decrease accuracy values and standard error were graphed for each of these regions from the random forests analysis of all DTI parameters A and all histology markers B. A , Classification using all DTI parameters revealed most in the left brachium of the superior colliculus and left optic tract have similar levels of importance for classification.
WL and WP of the optic tract were the most informative metric; however, WP of left brachium was the least informative metric. T was not informative for classification in either region. B , All histology measures of the left optic tract had high importance for the classification. The random forests measure of mean decrease accuracy characterizes the relative importance of parameters and regions for classification. The random forests analysis feature results were ranked based on this measure and several ROIs were consistently at the top of the list.
The top three ROIs for injury classification are listed alongside the DTI and histology metrics that contributed to their classification ability in Table 5. To provide a comprehensive visual representation of the random forests analysis results, the mean decrease in accuracy is shown in Figure 7 for the two ROIs that were selected by random forests as top classifiers for each model: the left optic tract DTI parameters and left brachium of the superior colliculus Table 5 , histology markers.
It is important to note that the mean decrease accuracy value depends on the particular parameters chosen to build the random forests. Therefore, this value may be different for a given feature depending on the parameter set of the full model and should be considered to describe the importance of a variable within the context of the chosen combination of features Fig. Classification using all DTI parameters revealed most DTI metrics of left optic tract and brachium of the superior colliculus have similar levels of importance for classification with the exception of WP of left brachium being less informative and WP of optic tract being more informative Fig.
TR was a poor predictor for both regions investigated. When all histology markers were investigated, all histology measures of the left optic tract had high importance for the classification. Changes in T and reductions in FA were apparent in the optic tract, brachium of the superior colliculus, corpus callosum, and cingulum bundle.
Group difference maps also revealed FA decreases in the hippocampus. When careful histologic studies were done on the same tissue, silver staining confirmed the presence of neurodegeneration in the optic tract, brachium of the superior colliculus, corpus callosum, and cingulum bundle. This pattern of silver stain reproduces the findings of Namjoshi et al. The colocalization of decreased FA in white matter tracts with positive silver staining suggests that FA is sensitive to the identification of DAI following closed head injury.
Beyond the identification of injured brain regions using DTI, a primary goal of this work was to better understand the cellular alterations that underlie changes in DTI metrics. To accomplish this, the regions demonstrating the greatest level of abnormality across several metrics, the optic tract, brachium and hippocampus, were carefully examined by their qualitative and quantitative ROI values for DTI and histology metrics within the same sample.
The optic tract was carefully examined in this study as it demonstrated an abundance of silver stain, as well as having the methodological advantage of high coherence and simple geometry, making it well suited for investigation by DTI. There were no gross abnormalities of the optic tract in the T2 image.
Injury to the optic tract was confirmed via immunohistochemistry. On the other hand, IBA-1 and GFAP were elevated and disruption of axonal integrity was found by pan-NF antibody, which demonstrated the presence of retraction bulbs and axonal varicosities throughout the optic tract. Taken together these findings are in agreement with other studies of DAI in the observation that reduced FA and AD are consistent with axonal damage, beading, infiltrating microglia and reactive glial cells. Notably, these pathophysiological mechanisms were found to be overlapping and concurrent with one another.
This extends a general caveat about DTI metrics. DTI metrics are known to be sensitive to pathophysiological alterations; however, they are not specific to a particular pathophysiological mechanism. The correlation of a particular DTI metric with a specific pathophysiological mechanism does not preclude the presence of other concurrent pathology that may contribute as much or more to abnormal water diffusion. These metrics are less commonly used than other DTI metrics, but provide increased information about the shape of the diffusion ellipsoid in tissue with similar FA Westin et al.
In the current study, the combination of decreased linear and increased planar anisotropy in damaged white matter tracts may arise for several reasons, including axonal morphology changes, cell infiltration, and more complicated architectural changes observed following injury in the network of inflammatory cells surrounding particular parts of injured tissue such as the astrocytic network Roth et al. While the brachium of the superior colliculus demonstrated many of the same histologic features as the optic tract including ample neuroinflammation and axonal disruption, DTI metrics were not as similarly altered as for the optic tract.
AD in this region was not altered, but WL anisotropy was decreased, which may suggest greater sensitivity of the linear anisotropy measure compared with AD. Another explanation for the difference in DTI metrics in this region is that partial volume effects of this very thin structure reduce the sensitivity of the imaging metrics. Histology in this region showed an increase in APP immunoreactivity, which is indicative of potentially subtle axonal damage to the hippocampus.
While this is intuitively attractive, several aspects of this type of analysis precluded the use of such an approach in this study. The study would require a much larger sample of controls and injured brains, to accurately investigate how neurophysiology correlates with DTI metrics in healthy tissue, and then to investigate how TBI neuropathology potentially alters these relationships. Correlation analysis could be useful if enough data were available to determine with high statistical certainty the correlation of metrics in each group and compare correlates in injured tissue to correlates in healthy tissue.
Due to our experimental design, i. Instead of correlation analysis, the random forests analysis approach was implemented to determine the classification potential of each type of parameter collected in this study along with the importance of each ROI selected to successfully predict TBI status. Perhaps the greatest remaining challenge for the effective use of DTI tools in brain research is the gap in understanding of the neurobiological correlates of DTI measures.
For example, a decrease in FA may arise from demyelination, axonal loss, crossing fibers, or infiltrating cells, each having a clearly different impact on the brain despite an identical FA value. Complete characterization of the multiple cellular and molecular components contributing to DTI metrics would require a very large battery of histology markers. Additionally, neuropathology will affect the way a DTI metric behaves in a particular region, especially in a complex neuropathology with multiple secondary injury mechanisms, as is the case in TBI. A study like the one described would require a large sample size and the measurement of multiple parameters.
This type of analysis is beyond the scope of the current study; however, within the current study, we propose using a machine-learning algorithm that can handle a multiparametric dataset and show that it can easily extract important parameters for classification free of user bias. The question of which metrics are most affected by TBI and therefore most informative of TBI neuropathology was investigated.
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When all histology markers were considered together, the same sham sample was misclassified by the histology yet the one CHIMERA-injured sample was correctly classified. DTI metrics were equivalent to histology markers in classifying sham samples. Histology markers, however, more accurately classified injured samples when compared to DTI metric classification. Each of these trials had similar classification accuracy as when using all DTI parameters, which suggests that the selection of particular DTI metrics does not greatly change the information about injury that is conveyed by DTI in this model.
While this misclassification may arise for several reasons, it is likely related to the specimen preparation. When looking at the top three best regions for classification, the algorithm primarily selected data from the ROIs identified as injured by group analyses of DTI metrics and histology markers optic tract, brachium, hippocampus. The two regions selected as most important for classification in the models, the optic tract and brachium of the superior colliculus, were abundant in silver staining and showed reduced FA on the difference maps.
Random forests has shown that it is capable of selecting injured ROIs in a manner unaffected by potential operator-induced bias. This tool could prove clinically useful given that the TBI diagnosis results in a heterogeneous population consisting of several injury severities with no useful prognostic tools for separating the population. Other studies have shown the utility of random forests in identifying ROIs with DTI abnormalities in temporal lobe epilepsy Chiang et al.
This study highlights how machine-learning algorithms may assist in the hunt for neuroimaging as well as other biomarkers of TBI in future studies. This study was intentionally designed to obtain and compare comprehensive information within the same biological specimen including high-quality imaging and multiple histologic stains.
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This also limits the generalizability of the study results. The data presented are intended to introduce a classification approach that is novel to this type of study as well as a comprehensive understanding of the types of neurobiological changes that underlie diffusion metric. The question regarding neurobiological correlates of DTI metrics is a very important point of discussion Budde et al.
DTI is quickly proving to be a useful neuroimaging technique for a variety of neuropathologies Chen et al. However, the neurobiology underlying DTI abnormalities is still poorly understood. Other studies have addressed this question by correlating a particular histologic measure to a DTI metric, which can be an informative approach, but must acknowledge the contribution of other overlapping changes in brain tissue and be careful to not associate changes in a DTI metric with a singular cellular alteration. Rather, damage to brain tissue causes a number of different but often simultaneous cellular processes including microglia infiltration and proliferation, astrocyte swelling, Na-K pump breakdown inducing disruption of concentration gradients, excitotoxic neuronal death, and breakdown of myelin sheath compaction.
Likewise, the current study only investigated a single time point after injury 7 d , which would not capture the complex array of cellular and molecular alterations that are changing over time. These dynamic alterations would affect DTI metric values to different extents, changing the relationship between histopathology and diffusion imaging at different times. All these cellular and molecular mechanisms contribute to changes in the water diffusion within a voxel, making it unlikely that a one-to-one correspondence will explain the relationship between histologic features and DTI metric changes.
Instead of explaining DTI changes with neurohistology, DTI metrics should be viewed as an additional tool to help explain neuropathology, potentially with its own biological relevance. DTI has the added benefit of being a clinically available tool. Using a more accurate neuropathological TBI injury model and a translatable tool to study that model, may improve understanding of the neurobiology of clinical TBI and may lead to more effective therapeutics.
TBI is a highly prevalent neurologic condition yet lacks predictive diagnostics and effective therapeutics. Using TBI animal models that accurately replicate human TBI and focus on clinically translatable outcomes may aid in the search for biomarkers and therapeutics.
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The same regions showing DTI abnormalities also showed changes in histologic markers of injury. Remarkably, DTI metric abnormalities were colocalized with abnormalities in various histology markers indicating that multiple cellular mechanisms initiated by TBI may be responsible for the observed changes in DTI metrics. A machine-learning algorithm, random forests, was able to accurately detect regions identified as injured and classify injured samples using only DTI metrics. Further studies using carefully acquired radiologic-histopathological measurements in experimental TBI animal models, over multiple time points would elucidate translational methods with neurobiological meaning for TBI.
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The Lyran Alliance later requested to take part, with Lyran engineers quickly beginning to dominate the entire project after Katherine Steiner-Davion took over the Regency of the Federated Commonwealth. By the time that came to pass, however, such a large amount of time and money had been invested into the project that three states had no choice but to proceed with production. When Katherine restricted production earmarked for the FedCom to units loyal to her, Theodore Kurita licensed production to Kressly Warworks to ensure more pro-Victor elements in the Armed Forces of the Federated Commonwealth could also access the design.
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MechWarrior 4: Mercenaries version of the Chimera. To test if chimera states represent a universal behavior in SPP models, we also investigated an extended version of the modified Vicsek model 1 of the form. Compared to the minimal model 1 , the first term on the right hand side of 8 replaces the piece-wise constant coupling function of 1.
The second term on the right hand side of Eq. Note that Eq. In particular, the self-propelled chimera region yellow in Fig. Typical examples of the system behavior in this case are illustrated by videos S6, S7 sup. In conclusion, we have shown the existence of chimera states in a modified version of the Vicsek model. There are two types of chimera states: a localized directional state, where some number of particles assemble in a flock and move coherently together, and a scattered directional state, where the majority of particles synchronizes in phase but yet do not gather into a localized group.
These states exist for a wide range of coupling parameters. The transitions between different states occur through chaotic itinerancy when the system is captured by different attractors from the neighboring regions. We have described the behavior of the system in the case of the most striking one-headed self-propelled chimera state. We have derived the continuum limit for the proposed model, and shown that the joint condition for both types of chimera states, e. We have found similar chimera-like regimes for a general SPP model including a cohesion term with both attractive and repulsive parts and assuming more realistic smooth phase alignment functions.
This indicates a common, probably universal phenomenon, in SPP models of a new kind, due to the non-local phase lag interaction. Abstract We report the appearance of chimera states in a minimal extension of the classical Vicsek model for collective motion of self-propelled particle systems. Ks, Xt, Vicsek, A. Ben-Jacob, I. Xie, H. Larger, B. Maistrenko, O. Sudakov, O. Omelchenko, A. Provata, J. Hizanidis, E. Olmi, E.