Full-Field Brain Strain Reconstruction from Sparse Displacement Data using Machine Learning

Introduction: : Traumatic Brain Injury (TBI) poses a substantial public health challenge, with millions affected annually (Peterson et al., 2019). Quantifying brain deformation, or strain, during head impacts is crucial for developing effective injury prevention strategies and advancing computational TBI models. Current experimental methods that measure brain deformation face a few limitations. Tagged Magnetic Resonance Imaging (tMRI) offers high-resolution, full-field strain maps but is restricted to non-injurious conditions. Conversely, sonomicrometry uses ultrasonic pulses between piezoelectric crystals embedded in the brain tissue to track displacements during concussive impacts. While sonomicrometry provides displacement data during injurious impacts in cadaveric subjects, it suffers from sparse measurement density, capturing only discrete points rather than the full-field information needed for comprehensive strain analysis.
Computational models, vital for simulating brain impact and guiding protective device design, require robust calibration and validation with real-world data (Madhukar et al,. 2019). However, a gap exists in current methodologies to accurately measure full-field brain deformation under injurious loading conditions with sufficient detail. This study aims to bridge this critical gap by leveraging machine learning (ML) to develop sparse interpolation algorithms capable of reconstructing high-resolution, full-field brain strain maps from spatially sparse displacement data, simulating sonomicrometry inputs. By training these algorithms with down-sampled tMRI data, we seek to enhance our ability to predict brain strain, ultimately improving TBI risk assessment and informing the development of better protective strategies.

Materials and

Methods: : This study utilized a publicly available dataset of 3D tagged MRI (tMRI) scans from 21 volunteer human subjects (https://www.nitrc.org/projects/bbir). For each subject, 25 two-dimensional (2D) axial slices were extracted from the central portion of the 3D volume to serve as ground truth full-field displacement data. To simulate the sparse data characteristic of discrete sonomicrometry sensors, these high-resolution tMRI slices were systematically down-sampled. Markers of varying number and location were sampled (e.g., 1, 25, 150, 500 markers), and sensitivity analyses were planned to assess prediction accuracy based on varying spatial distribution and density of these input markers.
A custom image super-resolution machine learning approach was employed. This model consists of a 5-layer multi-layer perceptron followed by 5 convolutional blocks designed to upscale the sparse input to a full-resolution strain map. The network was trained using data from 18 subjects, with 3 random subjects reserved for testing to ensure generalization and prevent data leakage. The AdamW optimizer was used to minimize the mean squared error (MSE) loss between the ML-predicted strain maps and the ground-truth tMRI-derived strain fields during training (Loshchilov et al., 2019). Performance evaluation metrics included root mean square error (RMSE), and importantly, the structural similarity index measure (SSIM), which assesses the perceptual similarity beyond pixel-wise differences (Zhou et al,. 2004).

Results, Conclusions, and Discussions::

Results:
Initial training of our model using down-sampled tMRI data demonstrated that the network could learn a mapping to predict full-field strain from discrete sensor data. Training with 25 marker points yielded SSIM values up to 0.81 against original tMRI data. However, qualitative assessment revealed a significant loss of structural detail and anatomical specificity as seen in Figure 1. Further analysis showed the model, when trained solely on sparse data, converged towards an "average brain" strain pattern, irrespective of individual subject input. SSIM values were consistently higher (average 0.21 increase) against an average brain slice than subject-specific ground truth strains. Varying input marker numbers (1 to 500) did not substantially improve subject-specific anatomical detail reconstruction as demonstrated in subject 1 (Figure 2). Training loss typically plateaued by 10 epochs.

Discussion:
While the image super-resolution ML approach achieved numerically plausible results (e.g., high SSIM), training on sparse displacement data alone is insufficient for reconstructing high-fidelity, subject-specific brain strain maps. Our model's tendency to predict an "average brain" highlights a critical loss of anatomical specificity, problematic for TBI risk assessment where individual structural deformation is paramount. The limited spatial information in down-sampled inputs did not enable the current model to infer detailed, individualized strain patterns. As a result, the current approach does not adequately bridge sparse sonomicrometry data and dense tMRI-like strain fields with subject-specific accuracy.

Conclusion:
This study demonstrates challenges in using conventional image super-resolution ML, trained only on sparse data, for detailed brain strain map reconstruction. While generating reasonable strain outputs, the model failed to preserve crucial subject-specific anatomical details, defaulting to an average representation. This indicates sparse displacement data alone is insufficient for accurate, individualized full-field strain prediction with this architecture. Future work will explore alternative ML architectures, such as U-Net, incorporate structural MRI data for anatomical context, and investigate physics-informed neural networks. This research underscores the complexity of bridging data modalities in TBI research, highlighting the need for more sophisticated approaches for clinically relevant strain predictions during injurious head impact.

Acknowledgements and/or References (Optional):: Acknowledgements:
Research reported in this study was supported by the National Institute of Neurological Disorders and Stroke of the National Institutes of Health under Award Number R01NS136056.

References:
1. Peterson AB, Xu L, Daugherty J, Breiding MJ. Surveillance report of traumatic brain injury-related emergency department visits, hospitalizations, and deaths, United States, 2014. 2019.
2. Madhukar A, Ostoja-Starzewski M. (2019). Finite element methods in human head impact simulations: a review. Ann Biomed Eng.
3. https://www.nitrc.org/projects/bbir
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