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The authors have declared that no competing interests exist.

Conceived and designed the experiments: RHK PJM AMD STG. Performed the experiments: RHK PJM AMD STG. Analyzed the data: RHK PJM AMD STG. Contributed reagents/materials/analysis tools: RHK PJK AMD STG. Wrote the paper: RHK PJM AMD STG.

This article presents the integration of brain injury biomechanics and graph theoretical analysis of neuronal connections, or connectomics, to form a neurocomputational model that captures spatiotemporal characteristics of trauma. We relate localized mechanical brain damage predicted from biofidelic finite element simulations of the human head subjected to impact with degradation in the structural connectome for a single individual. The finite element model incorporates various length scales into the full head simulations by including anisotropic constitutive laws informed by diffusion tensor imaging. Coupling between the finite element analysis and network-based tools is established through experimentally-based cellular injury thresholds for white matter regions. Once edges are degraded, graph theoretical measures are computed on the “damaged” network. For a frontal impact, the simulations predict that the temporal and occipital regions undergo the most axonal strain and strain rate at short times (less than 24 hrs), which leads to cellular death initiation, which results in damage that shows dependence on angle of impact and underlying microstructure of brain tissue. The monotonic cellular death relationships predict a spatiotemporal change of structural damage. Interestingly, at 96 hrs post-impact, computations predict no network nodes were completely disconnected from the network, despite significant damage to network edges. At early times (

According to the Centers for Disease Control and Prevention in the United States, approximately 1.7 million people, on average, sustain a traumatic brain injury annually. During the last few decades, brain neurotrauma biomechanics has been an active area of research involving medical clinicians and a broad range of scientists and engineers. In addition, advances and fast growth of human connectomics continues to reveal new insights into the damaged brain. With recent advances in computational methods and high performance computing, we see the need and the exciting possibility to merge brain neurotrauma biomechanics and human connectomics science to form a new area of investigation - connectome neurotrauma mechanics. For neurotrauma, the idea is simple - inform human structural connectome analysis using physics-based predictions of biomechanical brain injury. If successful, this technique may be further used to inform human functional connectome analysis, thus providing a new tool to help understand the pathophysiology of mild traumatic brain injury.

The finite element method is often used to study neurotrauma

As finite element models advance, experimentally based models of neurotrauma also continue to become more sophisticated, ranging from the macroscopic

As physics-based models become more capable of predicting tissue-level injury mechanisms from improved computational and experimental resources for biomechanics, there remains a need to understand how structural damage in a given location of the brain evolves, and how it may influence functional or cognitive performance over time. Such a goal is complex and difficult. For example, as Kaiser et al. point out

In this study, neurotrauma is investigated by using finite element simulations of a single individual subjected to a simulated head impact. Tissue damage is computed using empirically based damage models that provide a link from macroscopic biomechanical deformation to mesoscopic damage. Axonal bundle tracts are explicitly modeled using a multiscale description of white matter tracts obtained from diffusion tensor imaging. Then, using the physics-based injury predictions for white matter tissue from finite element simulations, the structural brain connectivity or connectome is degraded, and various network measures are computed. This is an important contribution because finite element simulation predictions of tissue damage provide physics-based reasoning for removing nodes or degrading edges to create the “damaged” brain connection matrix. In turn, this approach may provide further insight into mild traumatic brain injury by shedding light on the relationship between mechanical stimulus to the brain and neurobiological processes that result. Furthermore, if successful, the computational framework presented herein could supplement ongoing efforts to evaluate the use of non-invasive medical imaging tools, such as diffusion tensor and spectrum imaging, to detect white matter disruption for neurotrauma diagnostics

A suite of medical imaging and software tools are used to obtain an individual-specific finite element model and structural connectome-based analysis. The overarching process is schematically shown in

(a) The T1 image is (b) segmented into different head materials. The segmented geometry is then used to create (c) a biofidelic three-dimensional finite element volume mesh. The mesh is required for (d) an explicit dynamic finite element simulation that captures the biomechanical response from frontal impact. (e) Diffusion tensor images are used to generate (f) axonal bundle fiber tractography which is used to inform finite element transversely isotropic constitutive descriptions of white matter tissue behavior (c). Tractography is also used to create (g) a network model of the brain that can be (h) degraded over time.

T1 and diffusion tensor magnetic resonance images are taken from a single individual (the corresponding data can be found in

Herein, finite element simulations of the human head are designed to mimic experimental conditions for cadaveric impact tests, which are conducted to understand the dynamics of a frontal impact and the associated compression-tension damage

One limitation of the current finite element model is the exclusion of viscoelasticity in the constitutive description of brain matter. The authors acknowledge that to accurately model the progression of damage, the constitutive model should be extended to account for the time-dependent behavior of brain tissue. The exclusion may have an effect on the outcome of our results, leading to larger shear stresses, but smaller shear strains, thus, less predicted damage. For example, Chafi et al.

In order to model damage using a physics-based approach, either an explicit failure mechanism should be modeled or an empirically based failure threshold is required. For this study, measures of axonal strain and strain rate computed for white matter regions are used as input for empirically based injury threshold predictions that are obtained from cellular culture experiments. Specifically, experimental results for cellular death are described using a mathematical function for tolerance criteria that relates strain to resultant cell death evaluated for up to four days post-injury

where

The reader should understand that we use the local tissue strain and strain rates predicted from finite element simulations of short duration, about

It should be noted that the cellular death estimates that Morrison III et al.

Furthermore, the experiments performed by Morrison III et al.

In order to map the finite element results to network-based analysis tools, output data from each finite element that represents white matter is mapped to a corresponding voxel in the MRI data that is used to create the DTI tractography. This mapping is referred to as the element-to-voxel map. Multiple finite elements within a single voxel are averaged. The element-to-voxel map enables voxels to be assigned additional data, including axonal strain and strain rate from the finite element simulation. Alstott et al.

To understand how the structural network is degraded, consider the schematic shown in

Red voxels indicate that the chosen critical cellular death threshold,

Since Equations 1–3 predict some degree of cell death for non-zero values of axonal strain, strain rate, and time, the additional critical value of cell death,

The deformed configurations of the head, along with contours and response curves for various locations within the brain (frontal, parietal, occipital, temporal, corpus callosum and cerebellum) are shown in

Prediction of the intracranial pressure response is compared to cadaveric experiments

As seen in

Axonal strain at the various brain regions responds slower than the pressure response. The axonal strain begins to substantially grow at 1 ms and shows a gradual rate of change of strain, with a maximum of 33% at

The effective strain rate, also commonly referred to as rate of loading or loading rate, has a maximum value of approximately

The axonal strain and strain rate output from the finite element simulations are used to compute the amount of cellular death, according to Equations 1–3.

Using empirically-based cellular death predictions obtained from in vitro models of neural tissues, local strain and strain rate values computed from finite element simulations are used to specify injury. A computed cellular death of 3% was used as a critical value for defining white matter disruption. Damage is shown in red and the node size represents the percent change of degree. The predicted evolution of damage is shown for the sagittal and corresponding transverse views for 24 (a and b), 48 (c and d), 72 (e and f), and 96 hours (g and h).

Post-Injury (hrs) | % Fully Damaged | % Voxels Above |

Edges | 3% Threshold | |

24 | 0.097 | 0.008 |

48 | 7.19 | 1.1 |

72 | 14.1 | 2.7 |

96 | 19.7 | 4.2 |

Structural changes to the tractography and resulting network arise because of the underlying voxel condition. That is, if a tract goes through a voxel that has reached the critical cellular death value,

This data can be further analyzed by normalizing the number of damaged voxels for a given orientation by the

However, because a monotonic function is used to describe the empirical cellular death prediction, this trend becomes more dilute as time progresses (but should not be extrapolated past 96 hrs since Equations 1–3 are not validated beyond that time). From

Connection strengths were resampled to a Gaussian distribution with a mean of 0.5 and a standard deviation of 0.1. Because of the monotonic cellular death criterion, as long as regions have non-zero axonal strain and strain rate from the finite element simulation, edges in the network eventually become degraded. The connection strength matrices at

In general, a network's global efficiency represents how well-connected the network is compared to a perfectly connected network

The normalized global and mean local efficiencies as a function of time are shown in

Watts and Strogatz

The percent reduction of local efficiencies and the associated betweenness for the top 10 regions affected by impact at 96 hrs are listed in

Brain Region | % Reduction | Betweenness |

Local Eff. at 96 hrs | at 0 hrs | |

Lateral Orbitofrontal (RH) | 45.4 | 0 |

Parahippocampal (RH) | 44.2 | 0 |

Parsorbitalis (RH) | 44.1 | 0 |

Transverse Temporal (RH) | 42.0 | 0 |

Pericalcarine (RH) | 39.4 | 1 |

Parstriangularis (RH) | 39.3 | 2 |

Temporal Pole (RH) | 39.1 | 3 |

Rostral Anterior Cingulate (RH) | 38.4 | 0 |

Frontal Pole (RH) | 38.1 | 12 |

Superior Temporal (RH) | 37.9 | 21 |

RH and LH refer to right and left hemispheres, respectively.

The results reported thus far are based on a critical cell death value of

For the first time, a physics-based model has been linked to a network-based analysis that establishes a coupled computational method to study the effects of localized structural damage or lesions. In the presented work, lesions are simulated by using a state-of-the-art finite element model of the human head, developed for a single individual directly from MRI, impacted on the forehead region. The local finite element variables are coupled to a network-based analysis through an empirically based cellular injury model. The new approach attempts to capture the spatiotemporal structural characteristics of brain trauma. Foundations of this idea stem from previous studies that attempted to establish relationships of lesion sites and the resulting functional impact

The first part of our study involved developing a new three-dimensional human head finite element model for simulating the biomechanical response from frontal impact and comparing it to experimental data obtained from cadavers. The finite element model is unique in that it uses diffusion tensor imaging tractography to inform structural mechanics constitutive laws of the underlying white matter anisotropy in an effort to help elucidate the injury mechanisms of impact neurotrauma. Simulations of frontal impact capture the coup and contrecoup loading profiles, including short duration intracranial pressure gradients with high positive pressures at the coup region, and negative pressures at the contrecoup region (

Empirically based cellular death thresholds were used to predict the time-evolving damage in various brain regions based on finite element-based predictions of local axonal strain and strain rate. The biomechanical simulations predict that the temporal and occipital regions undergo the most axonal strain and strain rate at short times (less than 24 hrs), which leads to cellular death initiation that produces damage which shows dependence on angle of impact and underlying microstructure of brain tissue. The cellular death model that was used in this study is based on experimental observations that cell death was not immediate in response to deformation, but instead increased over four days after insult. Tissue damage becomes more dilute as time progresses (

Interestingly, when using injury criteria proposed in the past, including thresholds of axonal strain

This work has attempted to establish a physics-based methodology to inform structural connectome analysis. In the current model, network edges are degraded by weight rather than simply deleting nodes, in an attempt to include the effects of damage on white matter “fibers of passage” that Alstott et al.

While global efficiency is able to demonstrate widespread effects of damage, local efficiency provided a measure to investigate localized damage within the network related to areas of concentrated axonal strain and strain rate in particular areas of the brain. There was a much larger reduction in local efficiency at areas of high cell damage compared to reduction in the normalized global efficiency, indicating that the brain as a whole is resistant to some degree of localized damage. Brain regions that experienced the largest cellular death showed a larger reduction in local efficiency compared to the global efficiency of the network (

There are exciting possibilities for future work, as well as limitations to the current modeling approach. The current model did not attempt to model the coupled effects to the functional network; instead, we provided an example for a single individual in order to establish a methodology to link physics-based predictions of tissue damage with structural network analysis for frontal impact neurotrauma. It is important to note that the empirical relationships may only be accurate for the rat (not the human), and most likely, there are many more regions that need to be characterized. Our results and conclusions may be altered according to these injury thresholds. Although human injury thresholds are currently limited, as additional brain region injury thresholds are experimentally characterized and improved they can be included in the future. Due to the computational cost of the finite element simulations, the brain was only segmented into 83 different regions. In the future, increased segmentation of regions of interest and improved biofidelity of the finite element model would increase the resolution of the analysis. While this study does not address the resulting functional outcome from structural degradation, coupled structure-function relationships as a result of neurotrauma would be interesting to explore. For example, a coupled analysis may enable functional stimulus that may prohibit or enhance further cell death. For the prediction of tissue damage, additional physics, such as electrochemical reactions, may be useful by incorporating diffusional properties. In addition, increased resolution of the biomechanical response may also be improved by further developing white matter material response descriptions that use multiple fiber tract orientations within a single element, thereby enabling the capability to use diffusion spectrum imaging. There is also an opportunity to use this framework to explore additional injury mechanisms or thresholds from empirical or experimental data, such as intracranial pressure. Note that the current methodology degrades network edges, instead of nodes. In the future, it may be useful to investigate methods for degrading nodes in addition to edges because the all of the nodes represent cortical gray matter, and the gray matter does experience significant strains. This would require a choice of strain measurement other than axonal strain since the gray matter is treated as isotropic. With this type of criteria, it may be possible to degrade a node based on a ratio of damaged voxels within a region of interest compared to the voxel volume of the region as a whole.

Further work should also work to validate this approach in humans. There are at least two distinct areas associated with connectome damage that should be explored in order to validate the approach described herein. The first deals with how well the location of damage within the network description is captured using physics-based predictions. The second validation strategy should address the nature in which edges and nodes in the network are degraded. There are various approaches that may be useful for addressing both areas. For example, in order to validate how well the location of damage is captured, further understanding about how cellular level changes effect fractional anisotropy, that results in altered fiber tractography would be useful to develop. Some of this information may be obtained from various ongoing studies that are examining the ability of DTI to diagnose mTBI, which could also be extended to create degraded structural connectomes. One way to do this may be to use DTI studies pre- and post-injury from typical loading conditions that cause rotation-induced diffuse axonal injury. By providing similar loading profiles within the simulation and comparing computed DTI tractography damage with the clinical data set, maybe results can be compared. Perhaps this may be accomplished using sports-related impact injury, such as American football, where many helmets have sensors built-in to record impact loads.

In conclusion, this work has explored “connectome neurotrauma mechanics” by using physics-based finite element simulations to help elucidate injury mechanisms associated with neurotrauma by using various cellular injury thresholds to define tissue damage, and established a coupled computational framework to inform structural connectome analysis.

The magnitude of peak relative displacement between skull and brain for validation of finite element model.

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Percent reduction in local efficiency at 96 hrs for all brain regions.

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Percent reduction in betweenness at 96 hrs for all brain regions.

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A concise description of the finite element method.

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Material constitutive laws and associated parameters used for the head finite element model.

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Additional finite element validation.

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