# Rapidly and accurately estimating brain strain and strain rate across head
impact types with transfer learning and data fusion

Xianghao Zhan, Yuzhe Liu, Nicholas J. Cecchi, Olivier Gevaert, Michael M.
Zeineh, Gerald A. Grant, and David B. Camarillo This work was supported by the
Department of Bioengineering, Stanford University and the Office of Naval
Research Young Investigator Program (N00014-16-1-2949).X. Zhan, Y. Liu, N.
Cecchi, and D. Camarillo are with the Department of Bioengineering, Stanford
University, Stanford, 94305, USA. (Corresponding Author: Y. Liu e-mail:
yuzheliu@stanford.edu)O. Gevaert is with the Department of Biomedical Data
Science and Stanford Center for Biomedical Informatics Research, Stanford
University, Stanford, 94305, USAM. Zeineh is with the Department of Radiology,
Stanford University, Stanford, 94305, USAG. Grant is with the Department of
Neurosurgery, Stanford University, Stanford, 94305, USA

###### Abstract

Brain strain and strain rate are effective in predicting traumatic brain
injury (TBI) caused by head impacts. However, state-of-the-art finite element
modeling (FEM) demands considerable computational time in the computation,
limiting its application in real-time TBI risk monitoring. To accelerate,
machine learning head models (MLHMs) were developed, and the model accuracy
was found to decrease when the training/test datasets were from different head
impacts types. However, the size of dataset for specific impact types may not
be enough for model training. To address the computational cost of FEM, the
limited strain rate prediction, and the generalizability of MLHMs to on-field
datasets, we propose data fusion and transfer learning to develop a series of
MLHMs to predict the maximum principal strain (MPS) and maximum principal
strain rate (MPSR). We trained and tested the MLHMs on 13,623 head impacts
from simulations, American football, mixed martial arts, car crash, and
compared against the models trained on only simulations or only on-field
impacts. The MLHMs developed with transfer learning are significantly more
accurate in estimating MPS and MPSR than other models, with a mean absolute
error (MAE) smaller than $0.03$ in predicting MPS and smaller than $7s^{-1}$
in predicting MPSR on all impact datasets. The MLHMs can be applied to various
head impact types for rapidly and accurately calculating brain strain and
strain rate. Besides the clinical applications in real-time brain strain and
strain rate monitoring, this model helps researchers estimate the brain strain
and strain rate caused by head impacts more efficiently than FEM.

###### Index Terms:

traumatic brain injury, brain strain, transfer learning, head impact,
kinematics

##  I Introduction

Traumatic brain injury (TBI) is a global health hazard that affects more than
55 million people worldwide and contributes to more than 2.2 million emergency
department visits and more than 200 thousand hospitalizations in the United
States [1]. TBI can be caused by head impacts from various sources including
traffic accidents, blasts, various contact sports and domestic abuse [2, 3, 4,
5, 6, 7, 8]. Additionally, mild TBI, instead of directly causing death or
disabilities, can be harder to detect and the detection is important because
TBI may lead to accumulation of brain damage over time, which can progress to
long-term cognitive deficits and even neurodegeneration [9]. The prevalence
and the severe consequences of TBI patients highlight the need for better
monitoring of brain injury risks because early detection and intervention are
essential for recovery and prevention of further brain damage [10].

Brain strain, particularly maximum principal strain (MPS), has been regarded
as an effective predictor of TBI [6, 11, 12]. Although a comprehensive
understanding of the biological consequences resulting from mechanical
loadings of the head to the resultant brain injury are not fully understood,
strain-based metrics correlate well with brain injury [13, 14, 15, 16, 17]. In
addition to brain strain, the maximum principal strain rate (MPSR) correlates
well with traumatic axonal injury (TAI) [18, 19], which suggests that TBI is
dependent on not only the brain strain but also the strain rate. To compute
the brain strain and strain rate, the head kinematics, which can be measured
by various wearable devices, are used as the input [5, 20, 21]. Finite element
modeling (FEM) is the state-of-the-art method for the computation of brain
strain and strain rate [22, 23, 24]. The major limitations of FEM are lengthy
computational time and complicated computational software, which may not be
easily accessible to researchers, clinicians and sport teams [25]. These
limitations prevent the brain strain and strain rate from becoming widely used
as the metrics in quantifying TBI risks in real-world applications because
there may be hours passed after an American football players got impacted when
the TBI risks are finally available. To complement the FEM, brain injury
criteria have been developed by researchers with reduced-order mechanical
models and statistical data fitting [26, 27, 28, 29, 7]. These brain injury
criteria can be calculated quickly based on the head kinematics. However, most
brain injury criteria only output a single value, which limits the region-
specificity of the risk information and makes it hard to directly interpret
the TBI risks from the perspective of brain biomechanics. Furthermore, the
effectiveness of brain injury criteria is generally tested on the prediction
of brain strain rather than the strain rate [26, 27, 29], and those brain
injury criteria highly correlated with MPS are regarded as more accurate TBI
risk estimators.

Newly developed machine learning head models (MLHMs), which can be regarded as
function approximators of FEM, start to address the issues of computational
cost of FEM and the information-dimensionality limitation intrinsic to brain
injury criteria [25, 30]. Once the MLHMs are trained, the brain strain can be
computed within a second, which may be helpful for near real-time TBI risk
monitoring. However, the previously developed MLHMs are limited in several
ways. First, they only model brain strain rather than brain strain and strain
rate. To get strain rate, one still needs to resort to the complicated and
time-consuming FEM. Second, the generalizability of these MLHMs is an issue
significantly impacting its real-world applications: the model accuracy is not
guaranteed across different types of head impacts, which is also a typical
problem for the conventional risk estimation models like brain injury criteria
[29]. This second limitation is more evident on small on-field impact datasets
(not simulated impacts but real-world impacts recorded with sensors), because
there are data distribution drifts from the simulated data (on which the MLHMs
are trained) to the specific types of on-field data. However, there may not be
enough on-field impacts collected to fully manifest the on-field data
distributions to enable accurate predictions. For instance, our MLHMs showed
higher accuracy on the head model simulated impacts and the college football
(CF) impacts, but significantly lower accuracy on the mixed martial arts (MMA)
impacts [25]. These two limitations leave the MLHMs as neither robust nor
comprehensive enough to guarantee accurate estimation of TBI risks caused by
various on-field head impacts.

To improve the generalizability across different types of head impacts,
particularly the TBI risk estimation accuracy on small on-field impact
datasets, and further optimize the MLHMs to be both fast and accurate to
predict the strain rate from the perspective of model optimization, we
developed two strategies for more powerful MLHMs: data fusion and transfer
learning. With these two strategies, we developed a series of MLHMs on the
impact datasets from simulation, CF, MMA, and car crashes to be able to
predict both MPS and MPSR rapidly and accurately for specific types of head
impacts. The abbreviations used in this study are shown in Table 1.

TABLE I: The major abbreviations used in this study. Abbreviation | Meaning
---|---
TBI | traumatic brain injury
FEM | finite element modeling
MLHM | machine learning head model
MPS | maximum principal strain
MPSR | maximum principal strain rate
MAE | mean absolute error
TAI | traumatic axonal injury
CF | college football
MMA | mixed martial arts
HM | head model
NFL | National Football League
NHTSA | National Highway Traffic Safety Administration
BBB | blood-brain-barrier

##  II Methods

###  II-A Data description

To prepare a dataset consisting of a variety of head impacts from different
sources, we collected the head kinematics from a total of 13,623 head impacts
from various sources: 1) 12,780 laboratory-reconstructed head impacts (labeled
as HM for head model) simulated from a validated finite element (FE) model of
the Hybrid III anthropomorphic test device (ATD) headform [31]; 2) 302 college
football (labeled as CF) head impacts which were recorded by the Stanford
instrumented mouthguard [20, 32]; 3) 457 MMA head impacts (labeled as MMA)
which were recorded by the Stanford instrumented mouthguard [33, 6]; 4) 36
selected reconstructed helmeted head impacts from the National Football League
(labeled as NFL) [34]; 5) 48 head impacts from automobile crashworthiness
tests conducted by the National Highway Traffic Safety Administration (labeled
as NHTSA). The distributions of the MPS, MPSR, peak resultant angular
acceleration and peak resultant angular velocity are shown in Fig. 1.

Figure 1: The distribution of the example kinematics features, MPS, and MPSR
across various datasets. The distribution of the peak angular velocity (Ang.
Vel.) magnitude (A), the peak angular acceleration (Ang. Acc.) magnitude (B),
the 95th percentile MPS (C) and the 95th percentile MPSR (D).

The head model simulated impacts were regarded as the basis dataset for model
development before we performed data fusion between the on-field data and the
basis dataset, or before we transferred the basis models trained on the
simulated impacts to different on-field datasets. To improve the model
accuracy, we simulated 12,780 impacts. First, the bare headform was impacted
at different locations with velocities from 2 m/s to 8 m/s, which resulted in
a total of 1,065 impacts [25]. The impact kinematics were processed via a
second-order Butterworth low-pass filter (cut-off frequency: 150Hz). Then,
considering the symmetry of the FE head model of the Hybrid III ATD, we
performed the data augmentation by switching the kinematics along different
axes (X: posterior-to-anterior, Y: left-to-right, Z: superior-to-inferior).
This method was used to enlarge the impact datasets with 12 sets of impact
with 1,065 impacts in each set. If XYZ is used to denote the kinematics of the
1,065 original impacts, we further enlarged the impact datasets with XNYZ,
XZY, XZNY, YXZ, YZX, ZXY, NYZX, ZYX, ZXNY, ZNYX, NYXZ (the N before each axis
denotes the negative kinematics along that axis). For example, the XZY denotes
switching the original 1,065 impacts’ kinematics between the Y axis and the Z
axis. The on-field head impacts were published in previous studies, and the
details of the post-processing can be found in [25, 20, 32, 33, 6, 34]

The KTH FE model (Stockholm, Sweden) [23], which is a validated FE head model,
was used to model the brain strain and strain rate caused by impacts. The
model was developed in LS-DYNA (Livermore, CA, USA). The KTH FE model takes
the brain, skull, scalp, meninges, falx, tentorium, subarachnoid cerebrospinal
fluid (CSF), ventricles, and 11 pairs of the largest bridging veins in the
modeling. Responses of the head model correlate well with experimental data of
brain-skull relative motion [35], intracranial pressure [35], and brain strain
[36]. In this study, to output more diverse and comprehensive risk information
[19, 18] without losing the high-dimensional spatial information of the strain
and the strain rate for each brain element, the MPS and MPSR for all 4,124
brain elements were extracted from the KTH model as the reference output
values to be modeled by two series of deep learning head models (for MPS and
MPSR, respectively). As for the computational cost, it usually takes 7 hours
to model one impact with a computer (16GB RAM, Intel Core i7-6800K CPU).

###  II-B Head impact kinematics features

Features, such as the peak value of angular acceleration magnitude, are
important for brain strain prediction based on head impact kinematics, which
have been shown in our previous study [25]. In this study, to get more
accurate and generalizable brain strain and strain rate estimators, we
extracted both temporal features and spectral features from the head
kinematics by taking a union of the features extracted in two of our previous
studies [25, 37]. The features were based on four different types of
kinematics: 1) the linear acceleration at the head center of gravity $a(t)$,
2) the angular velocity $\omega(t)$, 3) the angular acceleration $\alpha(t)$,
and 4) the angular jerk $j(t)$. The angular acceleration and the angular jerk
were derived from the angular velocity via a five-point stencil numerical
difference equation. For each type of kinematics, four channels were involved:
three directions (X, Y, and Z) and the magnitude.

First, we extracted the 160 temporal features (based on angular velocity and
angular acceleration) that were used in our previously developed MLHMs [25],
which included 20 features for each channel of signal: the maximum values, the
minimum values, the integral values, the integral of absolute values, three
sets of maximum and minimum values of the exponential moving average of the
signal derivatives with different smoothing factors [38, 39], and the extrema
information (the numbers of all positive extrema and of all negative extrema
and the second to the fifth positive/negative extrema values). These features
were extracted because they took both the signal intensities and time
histories into consideration and proved to be effective in accurately
predicting whole-brain strain, with specific details and reasons shown in our
previous study [25].

Second, to better improve the predictive power of the features and the
generalizability of the models, we added another 350 temporal and spectral
features that were used in another study [37]. The temporal features included
the peaks of the absolute values of four channels for $a(t)$, $\omega(t)$,
$\alpha(t)$, $j(t)$, which aggregated to 16 features. Furthermore, the square-
root and squared features based on the 16 temporal features were included to
account for the non-linearity in the relationship between kinematics and brain
strain/strain rate. We have shown in our previous feature analysis study that
the first-power, squared-root and second-power features were the most
predictive for strain modeling (i.e., significantly more predictive than
higher powers) [40]. Then, 304 spectral features were extracted [37]: we
partitioned the frequency domain into 19 frequency windows with a width of
20Hz from 0Hz to 300Hz, and with a width of 50Hz from 300Hz to 500Hz (the
Nyquist frequency). The windows were set to better reflect the low-frequency
details. Within each frequency window, the mean spectral density was
extracted. The spectral features were extracted because they proved to be
effective in classifying different types of head impacts (e.g., CF, MMA, car
crashes) [38], which manifested that they contained the information related to
the impact types. Therefore, to get more accurate models for different types
of head impacts, we included these spectral features in the modeling. It
should be noted that our previous study [37] reported 352 temporal and
spectral features but only 350 were extracted in this study, because there
were two overlapped features with the previous 160-feature set (i.e., the
maximum values of the magnitudes of $\omega(t)$, $\alpha(t)$).

To sum up, there were 510 temporal and spectral features extracted from four
types of kinematics ($a(t)$, $\omega(t)$, $\alpha(t)$, $j(t)$) which were used
in the modeling of MPS and MPSR for the entire brain. Feature standardization
was performed according to the following formula to avoid imbalanced weights
for different features caused by feature range mismatches:

$\tilde{X}(i,j)=\frac{X(i,j)-\mathrm{mean}_{i}(X(i,j))}{\mathrm{std}_{i}(X(i,j))}$
(1)

$\tilde{X}(i,j)$ denotes the standardized $j^{\text{th}}$ feature of the
$i^{\text{th}}$ impact. $\mathrm{mean}_{i}()$ and $\mathrm{std}_{i}()$ denotes
the mean and standard deviation over the variable $i$ based on the raw feature
$X$. The parameters used in this study were calculated based on the training
data in the hyperparameter tuning process and on the union of the training
data and validation data in the model evaluation process (Please refer to
details in Section 2E).

The feature extraction and signal processing were done in MATLAB R2020a
(Austin, TX, USA). The data standardization was done in Python 3.7 with
scikit-learn packages [41].

###  II-C Development of the basis deep learning model

Based on the dataset HM, two separate basis MLHMs were developed to model the
mapping from the kinematic features to the MPS and MPSR given by the FE
simulations. To develop the models, the entire dataset HM (12,780 impacts) was
randomly partitioned into 70% training data for model training, 15% validation
data for hyperparameter tuning and 15% test data for model performance
evaluation, which is illustrated in Fig. 2A.

Figure 2: The illustration of the model development and assessment processes.
The processes to develop the basis models developed for the dataset HM (A),
and for the on-field datasets (B). The two proposed strategies in adapting for
different on-field impacts and the baseline models we compared against (B).
The datasets and models related to the on-field impacts are in dotted gray
boxes, while those related to the simulated impacts (dataset HM and basis
models) are in solid white boxes. The models are represented with oval boxes
and the datasets are represented with rectangular boxes.

The models shared the same network structure, which consisted of five layers
(excluding the input layer (510 neurons) and the output layer (4124 neurons)):
1) hidden layer 1: 500 neurons coupled with the rectified linear unit (ReLU)
as the activation function; 2) dropout layer 1 with 0.5 as the dropout rate;
3) hidden layer 2: 300 neurons coupled with the ReLU as the activation
function; 4) dropout layer 2 with 0.5 as the dropout rate; 5) hidden layer 3:
100 neurons coupled with the ReLU as the activation function. The design of
this structure followed the guidance of firstly condensing kinematics
information from the 510 features and then predicting the output variable. The
connection weights of the MLHMs were randomly initialized to break the model
symmetry at the start of model training. To improve the model
generalizability, the dropout and L2 penalty were used as forms of
regularization. To drive the gradient descent and model training, the mean
squared error (MSE) was used as the loss function. To boost the training
efficiency and get faster convergence, the adaptive moment estimation (Adam)
[42] optimizer was used as the optimizer with 128 set as the batch size.

The hyperparameters in the development of the basis model included: the
specific numbers of hidden neurons, the training epochs, the strength of L2
penalty, and the learning rate. They were tuned based on the prediction
performance on 15% validation data (prediction performance metrics shown in
Section 2E).

Before training the models, we adopted the same data augmentation strategies
of adding moderate Gaussian noise into the features which were used in our
previous studies [25, 43, 44] and proved to effectively improve model
accuracy:

$Noise=c\times\mathrm{std}_{i}(X(i,j))\times\delta,\quad\delta\sim N(0,1)$ (2)

where $j$ denotes the $j$-th feature and $c$ is the coefficient of noise level
taking one of the values in ($0.01,0.02$). Upon completing the data
augmentation, the total number of training impacts was tripled.

Additionally, to further optimize the accuracy, we applied the logarithmic
transform on the labels (MPS, MPSR) in the development of the basis deep
learning model to stabilize the residual variance and avoid negative MPS and
MPSR predictions. To use this transform, in the training stage, the MPS and
MPSR values were transformed by taking its logarithm. In the prediction stage,
the predicted values were inverse-transformed as MPS and MPSR by
exponentiation.

The data augmentation and deep learning were performed in Python 3.7, using
the Keras package with the TensorFlow 2.0 backend [45].

###  II-D Data fusion and transfer learning strategies

As shown in our previous studies [25, 29], many brain injury risk estimation
models show that accuracy is not guaranteed across different types of head
impacts, which may be caused by 1) that the limited on-field impacts cannot
properly determine the model parameters and 2) the distribution shifts from
the model training data (source domain) to the test data (target domain).
Although we can develop the basis model on the simulated dataset, researchers
typically attach more significance to the model performance on the on-field
impacts than that on the simulated data for potential real-world applications.
Therefore, to improve the accuracy of MLHMs on different types of on-field
head impacts, we developed two strategies to adapt the basis models trained on
dataset HM to better adapt to the on-field impacts, which are illustrated in
Fig. 2B:

Data fusion strategy: the on-field impacts (CF/MMA/NHTSA/NFL) were firstly
partitioned into the training data, validation data, and test data (Fig. 2B).
The training data from the on-field dataset were fused with the larger dataset
HM in the development of MPS and MPSR models. In this way, the model can
benefit from the large number of impacts from the dataset HM and learn the
general relationship between kinematics features and the MPS and MPSR. To
account for the potential feature distribution variation from dataset HM to
the on-field data, we recalculated the mean and standard deviation for feature
data standardization based on the union of dataset HM and the on-field
training data. We refer to this approach as data fusion because we combine the
computer-simulated impacts and on-field impacts measured by sensors for model
development.

Furthermore, to account for the potentially different MPS and MPSR
distributions, for this strategy, in addition to the logarithmic transform, we
adopted the data whitening approach according to the following formula:

$\tilde{Y}(i,j)=\frac{Y(i,j)-\mathrm{mean}_{i}(Y(i,j))}{\mathrm{std}_{i}(Y(i,j))}$
(3)

$Y(i,j)$ denotes the logarithmic-transformed MPS and MPSR of the
$j^{\text{th}}$ brain element for the $i^{\text{th}}$ impact. The
$\mathrm{mean}_{i}(Y(i,j))$ and $\mathrm{std}_{i}(Y(i,j))$ for each of the
4124 brain elements were calculated on the combination of dataset HM and
training set of on-field impacts in hyperparameter tuning process, and on
dataset HM, the training and validation sets of on-field impacts in model
evaluation. $\mathrm{mean}_{i}(Y(i,j))$ and $\mathrm{std}_{i}(Y(i,j))$ were
recorded to inverse-transform the prediction of the logarithmic-transformed
MPS and MPSR. The assumption was that the dataset used to calculate
$\mathrm{mean}_{i}(Y(i,j))$ and $\mathrm{std}_{i}(Y(i,j))$ represented a
general distribution and in this way, the prediction model can also benefit
from the overall distribution information. The logarithmic-transform was
performed before the data whitening. In the prediction stage, the inverse-
transformed MPS and MPSR need exponentiation to get the MPS and MPSR
predictions.

Transfer learning strategy: upon partitioning the on-field impacts into
training, validation, and test sets, we used the training set to fine-tune the
connection weights of the basis models pre-trained on the dataset HM (Fig.
2B). The fine-tuning process was done by freezing the connection weights of
the first 0/1/2 hidden layers and using the weights of the basis model as the
new initialization before another around of training was performed on the on-
field training impacts. The number of frozen layers, the number of training
epochs, the learning rate were set as the hyperparameters, which were tuned on
the on-field validation impacts. As the adapted models were derived from the
basis models, we fine-tuned the models with fewer epochs and/or lower learning
rate which led to model convergence without overfitting to the limited on-
field training impacts. To address the potential different feature
distribution, data standardization was performed based on the union of dataset
HM and the on-field training impacts. Data augmentation mentioned in the
previous section was also used on the on-field training impacts before the
second round of training (fine-tuning) was performed.

###  II-E Model evaluation

To quantify the model accuracy of the series of MLHMs we developed on various
datasets (HM/CF/MMA/NHTSA/NFL), the following metrics were used:

1) Mean absolute error (MAE): the MAE between the predicted MPS/MPSR and the
reference MPS/MPSR given by the KTH model, firstly averaged over 4,124 brain
elements and then averaged over all test impacts (calculation details shown in
[25]). Finally, the summary statistics (mean, median, STD) were calculated
over 20 parallel experiments with random dataset partitions. This metric was
used because it has the same unit as the MPS/MPSR for researchers to easily
perceive the model accuracy and compare the error with the injury threshold.

2) Root mean squared error (RMSE): the RMSE between the predicted MPS/MPSR and
the reference values given by the KTH model, which was calculated in a similar
manner as the MAE [25]. This metric was used in addition to the MAE because it
emphasizes the large errors more. It is also in the same unit as the MPS/MPSR
for easy comprehension.

3) Coefficient of determination ($R^{2}$): the $R^{2}$ was firstly calculated
between the predicted MPS/MPSR and the reference values on 4,124 brain
elements and then averaged across the test impacts. The details have been
shown in [25]. This metric was used because the majority of previous
publications related to brain strain estimation models demonstrate model
accuracy in this metric. In addition to the MAE and RMSE which directly
reflect the accuracy in the same units as MPS/MPSR, the $R^{2}$ values further
reflect the goodness of fit and how much variance in the reference values can
be explained by the predicted values.

To evaluate the performance improvement of the data fusion strategy and the
transfer learning strategy on the on-field datasets (CF/MMA/NHTSA/NFL), we
compared them with the following four baselines, which were also described in
Fig. 2B and Table 2:

1) The pre-trained model: the basis MLHMs trained on the dataset HM and then
directly used to predict the MPS/MPSR of the on-field test impacts. This
baseline model was used to show the effect of the fine-tuning (the second
round of MLHM weight training) on the on-field training data.

2-3) The models trained on the on-field training set: the MLHMs were trained
on the training set partitioned from the on-field datasets (CF/MMA/NHTSA/NFL)
either with both the logarithmic transform and the data whitening on the
labels, or with the logarithmic transform only. These two baseline models were
used to directly show the effect of the transfer learning strategy and data
fusion strategy: whether these two strategies enabled accurate predictions
that may not be achieved by merely training on the limited quantity of the on-
field data. These models were labeled in the format of CF 1 (with both
logarithmic transform and data whitening) and CF 2 (with only logarithmic
transform) in the result sections.

4) The data fusion model without data whitening: the MLHMs were trained on the
union of the dataset HM and the training set partitioned from the on-field
datasets (CF/MMA/NHTSA/NFL). This baseline model was used to show the effect
of the data whitening used in the data fusion strategy. This baseline model
was labeled as ”Fusion 2” in the results to be distinct from the proposed data
fusion strategy (”Fusion 1”).

Furthermore, to evaluate the effect of the quantity of on-field training data
on the model accuracy, we gradually varied the ratio of the on-field training,
validation, and test data on two large on-field datasets (CF, MMA), which is
referred to as ”1-2X” (percentage of training data) and ”X” (percentage of
validation data and test data) in Fig. 2B. Then, under various scenarios with
different quantities of on-field training data, the model accuracy with the
data fusion strategy and the transfer learning strategy was compared with that
from the baseline models. With this varying ratio of training, validation, and
test data, we simulated the real-world application scenarios where users may
not have large quantities of on-field data to train and fine-tune a MLHM to
accurately predict MPS and MPSR. This experiment setting tested whether the
proposed two strategies can achieve high accuracy with different extents of
training data inadequacy.

It is important to note that the varying ratio experiment simulated different
levels of on-field training data inadequacy. Besides, two smaller on-field
datasets were also used as the validation of the model performances in real-
world application scenarios when there is not a large quantity of on-field
data for model training and fine-tuning. We included these two datasets
because the performance of the two proposed modeling strategies could manifest
whether the hardship of accurately predicting brain strain and strain rate can
be solved with the two proposed strategies. Due to the limited quantity of
data in these two datasets, we partitioned the datasets into 50% training
data, 25% validation data and 25% test data so that there were more than 10
validation and test impacts in each experiment to give reasonable and robust
results.

###  II-F Statistical tests

To ensure robust results and test statistical significance, we did 20 parallel
experiments for each prediction task and used the Wilcoxon signed-rank test to
compare the accuracy (in MAE) of the models developed on the two proposed
strategies and that of the baseline models. The paired t-test was not used
because the Shapiro-Wilk test rejected the normal distribution assumption on
some of the results; the Wilcoxon signed-rank test do not rely on the
normality. The most conservative p-values were reported in the result
sections, which held true for all the pairwise comparisons (e.g., between the
transfer learning model and each of any other model), unless reported
otherwise in more details.

##  III Results

###  III-A Model performance on dataset HM

The abbreviations for model reference used in the result sections are shown in
Table 2.

TABLE II: The abbreviations for model reference. Abbreviation | Model
---|---
Transfer | The MLHM with transfer learning strategy (pre-trained on dataset HM and fine-tuned on on-field training set)
Pre-train | The baseline MLHM trained on the dataset HM and directly used to predict the test impacts
CF/MMA/NFL/NHTSA 1 | The baseline MLHM trained on the on-field training data with logarithmic transform and data whitening
CF/MMA/NFL/NHTSA 2 | The baseline MLHM trained on the on-field training data with logarithmic transform only
Fusion 1 | The MLHM developed with the data fusion strategy with logarithmic transform and data whitening
Fusion 2 | The baseline MLHM developed with the data fusion strategy with logarithmic transform only

According to the process of developing the basis MPS/MPSR models introduced in
Section 2C and the metrics introduced in Section 2E, the basis models were
built and evaluated on the dataset HM. The results are shown in Table 3. The
model trained on 70% of the dataset HM (8,946 training impacts in each
experiment) showed the ability to accurately predict MPS and MPSR of the
entire brain for the test impacts (1,917 test impacts in each experiment),
with an averaged MAE of 0.015 for MPS prediction and 2.818 $s^{-1}$ for MPSR
prediction (averaged over twenty paralleled experiments with random dataset
partitions). The accuracy for MPS and MPSR prediction can also be reflected by
the mean $R^{2}$ values: 0.860 and 0.786, respectively, which indicates that
the basis MLHMs are accurate in predicting whole-brain MPS and MPSR. The MAE
for the MPS prediction was much smaller than the differences of brain strain
seen in injury and non-injury cases (between 0.3 and 0.4) [46, 23]. The MAE
for the MPSR prediction was also much smaller than the concussion threshold
(around 25$s^{-1}$) [47], the threshold for accurate axonal injury prediction
in large animal models (120$s^{-1}$) [19] and the threshold for accurate brain
contusion volume prediction in small animal models (2500$s^{-1}$ [15]).

TABLE III: The hyperparameters and the model performance metrics of the basis MPS and MPSR models developed on dataset HM. Output | Learning Rate | Training Epochs | L2 Regularization | MAE (Mean $\pm$ STD) | RMSE (Mean $\pm$ STD) |  $R^{2}$ (Mean $\pm$ STD)
---|---|---|---|---|---|---
MPS | 0.0003 | 3000 | 0.01 | 0.015 $\pm$ 0.001 | 0.024 $\pm$ 0.001 | 0.860 $\pm$ 0.009
MPSR | 0.0005 | 3000 | 0.05 | 2.818 $\pm$ 0.080 | 7.145 $\pm$ 1.294 | 0.786 $\pm$ 0.038

###  III-B Model performance on large on-field datasets

Although high accuracy is achieved on the dataset HM, we attach significance
to the model performance on the on-field datasets for sake of TBI risk
monitoring. Therefore, two strategies, data fusion and transfer learning, were
proposed and compared with the baseline models. The model accuracy (in MAE) on
the two larger on-field datasets (CF and MMA) with varying ratios of training,
validation, and test data were shown in Fig. 3 (RMSE and $R^{2}$ results shown
in Fig. S1 and S2).

According to the results on dataset CF for the whole-brain MPS prediction, the
transfer learning models were the most accurate ($p<0.01$), with MAE smaller
than 0.015, except that with 30% on-field training impacts (91 impacts), there
was no statistically significant difference in MAE between the transfer
learning model and the data fusion model (Fusion 1) ($p>0.05$). The data
fusion models with both logarithmic transform and data whitening (Fusion 1)
did not show significantly better performance when compared with the model
trained merely on the CF training data ($p>0.05$), except that with 30% on-
field training impacts, the Fusion 1 model was significantly more accurate
than this baseline model ($p<0.001$). For the whole-brain MPSR prediction, the
transfer learning models were also the most accurate models ($p<0.01$), with
MAE smaller than 3 $s^{-1}$ under all training set ratios, while the data
fusion models (Fusion 1) were the second most accurate and significantly
better than the baseline models ($p<0.001$).

On dataset MMA, for the MPS prediction, the transfer learning models were the
most accurate under five different ratios of training data ($p<0.001$), with
the MAE smaller than 0.015. The data fusion models (Fusion 1) did not
significantly improve the MPS prediction accuracy when compared with the
models trained only on the MMA training data ($p>0.05$). For the MPSR
prediction, the transfer learning models were the most accurate models under
varying training set ratios ($p<0.01$). The data fusion models (Fusion 1) were
generally the second most accurate models, but did not show significant
improvement over the baseline model (MMA 1) on every training set ratio. These
results indicate that the pre-training based on the dataset HM and fine-tuning
based on the dataset CF/MMA can adapt the models to be more accurate for the
MPS and MPSR estimation of these two specific types of on-field data. On the
contrary, though using the dataset HM as well, the data-fusion-based MLHMs
(Fusion 1) generally lag behind the transfer learning strategy in accuracy.
The models may also improve the model accuracy to a limited extent, but the
improvement is not guaranteed. Compared with the MPS MLHMs we previously
developed [25] with 70% MMA training data, the transfer learning MLHMs reached
a mean MAE around 0.013 and a mean $R^{2}$ around 0.7, which is evidently more
accurate than the previously developed MLHMs (mean MAE around 0.025, mean
$R^{2}$ around 0.6).

As for the comparison between the transfer learning models and the pre-trained
models, the former models were significantly more accurate than the latter
models ($p<0.01$). This indicates that the additional model fine-tuning (the
second round of MLHM connection weight training on the on-field training data)
improved the model for specific on-field prediction tasks. When the two data
fusion models (Fusion 1/2) were compared, it is shown that the data whitening
process contributes to the model accuracy improvement, as the Fusion 1 models
were significantly more accurate than the Fusion 2 models. Furthermore, the
MPS model trained only on the on-field training data tended to be more
accurate with more training data, which indicates that one limitation of the
accuracy of models merely based on the on-field data is the quantity of the
training impacts.

Figure 3: The model accuracy of predicting MPS and MPSR on the dataset CF and
dataset MMA with different ratios of training data. The mean absolute error
(MAE) of the MPS prediction models on dataset CF (A) and dataset MMA (B). The
MAE of the MPSR prediction models on dataset CF (C) and dataset MMA (D). Due
to the huge variation among different models, the MAE ranges were selected to
clearly show the most accurate models. Note that the training set ratio refer
to the percentage of on-field data used for training purposes, which is the
”1-2X” in Fig. 2 and in Section 2E.

In addition to showing the accuracy of the transfer-learning-based models over
all brain elements, we have also calculated the MAE on the brain elements
based on different brain regions and the results are shown in Fig. 4 and Table
S2. The results show that overall, the MPS/MPSR models based on transfer
learning manifest high accuracy on various brain regions, with a mean MAE
smaller than 0.025 for MPS prediction and a mean MAE smaller than 5.2 $s^{-1}$
for MPSR prediction across different brain regions. The MLHMs tended to be
slightly more accurate on some regions (brainstem, cerebellum, thalamus) but
slightly less accurate on other regions (corpus callosum, midbrain), in terms
of MAE. The error was well below the injury thresholds in MPS and MPSR which
are mentioned previously [46, 23, 19, 47, 15].

Figure 4: The region-specific mean absolute error of the transfer learning
models on dataset HM, dataset CF and dataset MMA with 70% training data and
15% test data (mean and STD over 20 parallel experiments). BS: brainstem, CC:
corpus callosum, CL: cerebellum, GM: gray matter, MB: midbrain, TH: thalamus,
WM: white matter.

###  III-C Model performance on small on-field datasets

The results of the model accuracy were further validated on the two real-world
on-field datasets (NFL: 36 impacts, NHTSA: 48 impacts) with far fewer impacts.
On these two small datasets, the percentage of training, validation, and test
data were set to be 50%, 25% and 25%, to ensure enough test impacts in each
experiment for robust accurate estimates. The MPS and MPSR model accuracy in
MAE is shown in Fig. 4 (RMSE and $R^{2}$ results shown in Fig. S3 and S4). On
dataset NFL, the median MAE based on the transfer learning MPS model was
smaller than 0.025 and the median MAE based on the transfer learning MPSR
prediction was smaller than 4 $s^{-1}$. For the MPS prediction, the transfer
learning model was the most accurate ($p<0.001$). For MPSR prediction, the
transfer learning model was more accurate than the data fusion models
($p<0.001$) but did not show statistical significance with the pre-trained
model ($p>0.05$). On dataset NHTSA, the transfer learning models were the most
accurate models for both MPS prediction and MPSR prediction ($p<0.001$), with
a median MPS prediction MAE smaller than 0.028 and a median MPSR prediction
MAE smaller than 7 $s^{-1}$. The two models trained on NFL training data (18
impacts) failed to predict the MPS and MPSR due to the fact that some
predictions caused numerical overflow on 32-bit floating point, and therefore
we deemed these two models unable to predict MPS and MPSR on dataset NFL (Fig.
5). In addition, the data fusion strategies were also effective in accurately
predicting the MPS and MPSR, but generally, the models directly trained on the
limited NFL/NHTSA data failed to accurately predict the MPS and MPSR. These
results indicate that both of the proposed strategies were effective in
achieving accurate MPS and MPSR predictions which otherwise may not be
achieved by directly training on the limited on-field data, while the transfer
learning models were still the best performing models on all cases.

Figure 5: The model accuracy of predicting MPS and MPSR on the dataset NFL and
dataset NHTSA with 50% training data and 25% test data for each dataset. The
mean absolute error (MAE) of the MPS prediction models on dataset NFL (A) and
dataset NHTSA (B). The prediction MAE of the MPSR prediction models on dataset
NFL (C) and dataset NHTSA (D). Due to the large variation among different
models, the MAE ranges were selected to clearly show the most accurate models.
Note that the models trained on NFL dataset only failed to predict the MPS and
MPSR for the test impacts due to numerical errors.

###  III-D Visualization of MPS and MPSR predictions

To visually examine the model accuracy in predicting MPS and MPSR. We selected
the example test impacts from dataset HM, CF, MMA, NFL and NHTSA, by firstly
ranking the predictions with 95th percentile MPS and MPSR and taking the the
median, and plotted the 3D brain MPS and MPSR maps given by the model
predictions (Fig. 6 A). Note that 95th percentile rather than the 100th
percentile was selected to avoid potential computational artifacts from
analysis [48]. Here the predictions given by transfer-learning-based MLHMs and
the reference KTH model (FEM) output were compared with 3D point clouds. It
can be shown from the results that, for each type of on-field impacts, the
high-strain and high-strain-rate regions predicted by the MLHMs were similar
to those output by the FEM. Besides the accuracy shown in the example 3D
visualizations, we plotted the overall distributions of the predicted MPS/MPSR
on the on-field datasets and compared them against the reference values given
by the KTH model (Fig. 6 B and C). It can be seen that the transfer-learning-
based MLHMs predict the overall distribution of the MPS and MPSR accurately.
Particularly, on the two small on-field datasets (NFL and NHTSA), with limited
impacts for fine-tuning, the transfer-learning MLHMs can reproduce the
distribution well, which indicates that the MLHMs can be applied to monitoring
MPS and MPSR caused by head impacts..

Figure 6: The visualization of the accuracy of MPS/MPSR prediction with
example point clouds and overall distribution violin plots. The point clouds
predicted and reference MPS/MPSR of the example impacts based on the transfer
learning models (A), and the violin plot of the overall distribution of
predicted and reference MPS/MPSR for the on-field datasets (B,C). The example
impacts were selected based on the median 95th percentile MPS/MPSR for each
dataset. The high-strain and high-strain-rate regions were colored to
visualize the accuracy of the predictions given by the transfer-learning
models.

##  IV Discussion

In this study, we proposed two strategies, data fusion and transfer learning,
to optimize the machine learning head models (MLHMs) to more accurately
predict the brain strain (MPS) and strain rate (MPSR) for different types of
on-field impacts. This study aims to address the problem of the large
computational cost associated with calculation of brain strain and strain rate
with FEM. Further, this study sought to address the limitations of previously
developed MLHMs: 1) they are only able to predict brain strain and 2) their
accuracy are limited by the quantity of the training data. As a result, for
the on-field impacts collected from college football, MMA, car crashes, and
NFL, the series of MPS/MPSR models developed with the transfer learning
strategy (when we pre-train the MPS/MPSR models on the large dataset of head
model simulated impacts and fine-tune them with small quantities of on-field
impacts), generally turn out to be the most accurate models when compared with
the models merely trained on the on-field data and the models trained by
fusing the large dataset of head model simulated impacts and the on-field
impacts. The results indicate that the transfer learning strategy enables the
learned general brain dynamics, i.e., the relationship between head kinematics
and MPS/MPSR, to be transferred to on-field impacts for more accurate MPS/MPSR
estimation.

This study provides two significant contributions to the field of brain injury
research. First, the developed series of MLHMs significantly reduce the
computational time cost resulting from conventional FEM. The series of MLHMs,
once trained, can estimate the MPS and MPSR of an impact within 1 ms with a
personal computer (8GB RAM, Intel Core i5-6300U CPU). On the contrary, it
takes hours for the KTH model to model an impact and output its MPS and MPSR
with a more powerful computer (16GB RAM, Intel Core i7-6800K CPU), which makes
it almost impossible to output real-time warnings for early intervention
approaches to protect contact sport athletes soon after they sustain an
impact. This significant reduction of computational time, without loss of
accuracy in MPS and MPSR estimation, enables researchers and clinicians to
efficiently perform TBI risk estimation in real-time. Therefore, this series
of MLHMs can be applied by sport team managers and clinicians to quickly
monitor the brain MPS and MPSR for athletes, on the premise that the impact
kinematics are measured by wearable devices [21, 20]. Previous evidence
suggests that high brain MPS and MPSR correlate with pathological changes
related to TBI, including traumatic axonal injury (TAI) and blood-brain-
barrier (BBB) disruption [6, 18, 19]. Further, previous studies have also
shown that early detection and intervention improve patient recovery from TBI
[10]. Therefore, by combining wearable sensor technology with the series of
MLHMs developed in this study, better precautionary and protective decisions
for contact sport athletes can be made in a timely manner, such as resting and
substitution suggestions, better protective gear suggestions, and even medical
imaging instructions.

The second major contribution of this study is that the MLHMs developed in
this study provide the users with the region-specific and high-dimensional
brain strain and strain rate information for TBI diagnosis. Although various
brain injury criteria have been developed in previous studies to address the
time consumption of FEM [22, 27, 12, 11, 29], these brain injury criteria only
output one value to summarize the overall brain injury risks and are hard to
directly interpret for users without an injury biomechanics background. They
cannot output region-specific detailed brain strain/strain rate information.
In contrast, the MLHMs are able to predict the brain strain and strain rate
for every brain element and visualize them in a 3D map, which makes it easier
for users to compute region-specific risk information and visually evaluate
the TBI risks caused by head impacts without the need to fully understand the
underlying biomechanics.

Furthermore, when compared with the MLHMs previously developed by our group
and other researchers [30, 25], this study bears unique innovations. First,
this study provides the users with novel MPSR prediction models which have not
been developed by previous studies. Although the brain strain, particularly
MPS, has been shown to correlate well with concussion and BBB disruption [13,
14, 15, 16, 17, 6], the predictive power of strain rate, particularly MPSR, is
a very important complement to MPS. Researchers have manifested that MPSR
correlates well with TAI and therefore, TBI is not only dependent on the brain
strain but also on the strain rate [19, 18]. In addition to the MPS prediction
models, this study further enables fast diagnosis using MPSR.

More importantly, this study leverages transfer learning and data fusion
strategies to address inferior model performance on small on-field datasets.
In our previous studies, the generalizability of TBI risk estimation models
(including brain injury criteria and MLHMs) has been limited [25, 29]. Even
though the models may perform well on the datasets where they are trained and
developed, their accuracy may deteriorate when applied to specific types of
on-field impacts. Particularly, this often occurs when they are applied to
estimate the risks for impact types with inadequate training data [25]. Due to
the limited on-field training data, MLHMs developed mainly based on simulated
head impacts cannot accurately estimate both the general brain dynamics and
the dataset-specific characteristics intrinsic in certain on-field impacts.
Therefore, the MLHMs may overfit to the simulated head impacts, which leads to
their inferior accuracy when applied to certain on-field impact types where
the on-field data distribution is far different from that of the simulated
impacts. With the transfer learning strategy and data fusion strategy, the
MLHMs are more accurate on the smaller on-field datasets. Because researchers
usually attach more significance to the model performance on on-field impacts,
this study achieves the goal of further optimizing the on-field impact risk
estimation accuracy for real-world applications.

In this study, the two proposed strategies for better on-field impact MPS/MPSR
predictions generally work well in reducing the prediction MAE and increasing
prediction $R^{2}$. Although both strategies attempt to leverage the
information gained from the large dataset of simulated head impacts, the
transfer learning strategy generally outperformed the data fusion strategy on
almost all the experiments in this study. This can be due to 1) the different
information processing protocols of these two different strategies, and 2) how
these two strategies leverage the prior knowledge unique to their methods for
estimating MPS/MPSR. The data fusion strategy processes the information in
parallel by directly combining the simulated impacts and the on-field data,
while the transfer learning strategy processes the information in series by
first modeling on the simulated impacts and then on the on-field impacts. The
parallel structure generally weighs the simulated impacts and on-field impacts
equally, while the series structure attend more to the on-field data because
although the model parameters in the fine-tuning process are initialized based
on the simulated data, the ultimate parameters of the MLHMs are determined by
the on-field data. As a result, the transfer-learning-based models can better
adapt to the on-field data distribution.

These two different strategies leverage different prior knowledge learned from
the training data. The data fusion strategy adopts the data whitening of the
labels (MPS, MPSR), which incorporates the distribution information of the
simulated data and on-field data. The distribution of MPS and MPSR of the
training data (i.e., the label distribution) can be regarded as the prior
knowledge that is leveraged in the prediction. Therefore, the predictions are
influenced by the MPS and MPSR distributions in the training data via the data
whitening process. On the contrary, the transfer learning strategy leverages
the prior knowledge stored in the model parameters (MLHM connection weights),
which reflects the predictor-label relationship, rather than the label
distribution. With the transfer learning strategy, the MLHMs learns the brain
dynamics, which are the intrinsic characteristics of brain, in the pre-
training process. Then, the fine-tuning process enables the MLHMs to adapt the
dataset-specific characteristics intrinsic to the on-field impacts. In other
words, the relationship between the kinematics features and the brain
strain/strain rate is transferred, while what is fine-tuned is the dataset-
specific characteristics. To sum up, in addition to the common part of
learning the mapping from predictors (kinematics) to the labels (MPS and
MPSR), which are shared by both strategies, the data fusion strategy further
leveraged the prior knowledge in the label distributions via data whitening,
while the transfer learning strategy further leveraged the prior knowledge in
the predictor-label relationship via model parameter fine-tuning.

The variations in model performance across types of on-field impacts indicate
the difference between on-field data and the head model simulated impacts. For
instance, the pre-trained models without fine-tuning show high accuracy on the
dataset CF and dataset NFL in both MPS and MPSR predictions. There were even
no statistically significant differences between the transfer learning model
and the pre-trained model in MPSR prediction on dataset NFL. These results
indicate that the dataset HM, dataset CF, and dataset NFL are generally
similar in their data distributions. On the contrary, the pre-trained models
show significantly inferior accuracy on dataset MMA in predicting MPS and
MPSR, which are even less accurate than the models trained merely on the on-
field MMA impacts. This observation indicates that the models trained on
dataset HM do not generalize well onto MMA impacts and the differences between
these two datasets are more evident than those among the HM, CF, and NFL
datasets. This observation may be explained by the fact that the head model
simulated impacts are generally simulated for the research of American
football impacts, and therefore, the simulated impacts may better represent
the characteristics shown in college football or NFL impacts [29].
Additionally, the MMA head impacts are measured without protective helmets
while the football impacts are measured with protective helmets, which may
effectively change the impact responses of the head [49]. The distribution
drifts reflect the different characteristics of various types of head impacts
[50] and according to the results, the transfer learning is effective in
capturing the distribution drifts across head impact types and enables more
accurate MPS and MPSR estimation. Furthermore, for the models trained only on
the on-field training data, the accuracy generally increases with more
training data. It is possible that with adequate on-field data, these models
can approximate the best performing transfer-learning models.

Additionally, previous publications have focused on region-specific brain
injuries caused by head impacts and region-specific injury management, where
emphasis has been placed on brain regions such as the brainstem [51], corpus
callosum [52, 53], and cerebellum [54, 55]. As we investigated the model
accuracy across different brain regions, the models turned out to be generally
accurate across different brain regions, with slightly higher accuracy on the
brainstem, cerebellum, and thalamus than the corpus callosum in terms of MAE.
Because one of the major advantages of MLHMs over brain injury criteria is the
whole-brain strain and strain rate predictability, with the MLHMs, researchers
can extract the region-specific brain strain and strain rate information to
evaluate TBI risk information for different brain regions. With prior
knowledge of human physiology and the region-specific strain and strain rate
information, researchers and clinicians can focus more on the potential
outcomes that may be related to region-specific pathology including BBB
disruption and TAI.

Although this study shows the effectiveness of data fusion and transfer
learning in optimizing TBI risk estimation, there are several limitations that
need to be pointed out. First, we used the KTH model as the reference method
to determine the accuracy of the MLHMs. The KTH model is limited when we
compare it with the state-of-the-art finite element head models (FEHM) [56,
57]. For instance, the gyri and sulci can have significant influences on the
behavior of FEHM. However, they are not included in the KTH model. Future
studies can focus on the development of MLHMs based on more advanced FEHM.

Second, the brain difference and head shape variation among different
individuals are not considered in this study. There have been previous studies
showing that individual differences can bear significant influence on brain
strain [56]. Therefore, to make the MLHMs even more accurate across different
people, future studies can take other personal predictors into the models.

Furthermore, the series of MLHMs developed in this study are based on the
features extracted from the kinematics (the linear acceleration, the angular
velocity, the angular acceleration, and the angular jerk). Therefore, the
quality of the engineered features set an upper threshold of model
performances. We adopted this feature engineering approach because: 1) these
features have been shown to be very effective in aggregating the temporal and
spectral information from the signals and predicting brain strain [25, 40]; 2)
there are limited quantities of on-field data to train the end-to-end MLHMs
out of the raw signals; and 3) due to the different triggering patterns,
sampling rates, method of attachment to the head, recording time window
lengths of various measurement devices to collect the on-field data and the
different patterns of impact kinematics across various impact types, there may
be issues such as the time mismatch of the start/peaks of the impacts
collected from different devices. Therefore, with limited training data,
directly feeding the signals into MLHMs may not lead to effective feature
extraction. In contrast, the feature engineering approaches shown in this
study can be effective to summarize the information stored in the signals
which we thought could contribute to brain strain and strain rate without
misleading the MLHMs with temporal details. However, as more data are
available, more data-driven feature extraction approaches such as the
convolutional neural network (CNN), variational autoendocer (VAE), and
recurrent neural network (RNN) with long short term memory (LSTM) can be
tested and applied to get more accurate models without the feature engineering
step. These types of complex neural network structures are effective in
extracting information with large quantities of training data without human
knowledge and feature designs, and therefore may be able to further optimize
the MLHMs.

##  V Conclusion

This study proposes data fusion and transfer learning strategies to develop a
series of optimized machine learning head models (MLHMs) to more accurately
predict the brain strain (MPS) and strain rate (MPSR) for different types of
on-field impacts. The results show that the MLHMs developed with the transfer
learning strategy are generally the most accurate to estimate the MPS and MPSR
for on-field impacts collected from college football, MMA, car crashes, and
NFL, when compared with models trained on the on-field data only and models
trained on the union of the head model simulated impacts and the on-field
impacts. The results indicate that the transfer learning strategy enables the
MLHMs to learn the general brain dynamics from large quantities of simulated
head impacts and then adapt to specific types of on-field impacts via fine-
tuning. The MLHMs developed in this study enables fast and accurate
computation of brain strain and strain rate resulting from various on-field
impacts for real-time risk estimation of traumatic brain injury, which cannot
be achieved with the conventional finite element modeling and previous MLHMs
developed by researchers.

##  VI Acknowledgement

The authors express their gratitude for the suggestions and assistance in
transfer learning given by Mr. Fanjin Wang from University College London.

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