Predicting the effects of epidural stimulation to improve hand function in patients with spinal cord injury: An active learning-based solution using dynamic sample weighting

In patients with chronic spinal cord injury (SCI), few therapies are available to improve neurological function. Neuromodulation of the spinal cord with epidural stimulation (EDS) has shown promise enabling the voluntary activation of motor pools caudal to the level of the injury. EDS is performed with multiple electrode arrays in which several stimulation variables such as the frequency, amplitude, and location of the stimulation significantly affect the type and amplitude of motor responses. This paper presents a novel technique to predict the final functionality of a patient with SCI after cervical EDS within a deep learning framework. Additionally, we suggest a committee-based active learning method to reduce the number of clinical experiments required to optimize EDS stimulation variables by exploring the stimulation configuration space more efficiently. We also developed a novel method to dynamically weight the results of different experiments using neural networks to create an optimal estimate of the quantity of interest. The essence of our approach was to use machine learning methods to predict the hand contraction force in a patient with chronic SCI based on different EDS parameters. The accuracy of the prediction of stimulation outcomes was evaluated based on three measurements: mean absolute error, standard deviation, and correlation coefficient. The results show that the proposed method can be used to reliably predict the outcome of cervical EDS on maximum voluntary contraction force of the hand with a prediction error of approximately 15%. This model could allow scientists to establish stimulation parameters more efficiently for SCI patients to produce enhanced motor responses in this novel application. Author Summary Spinal cord injury (SCI) can lead to permanent sensorimotor deficits that have a major impact on quality of life. In patients with a motor complete injury, there is no therapy available to reliably improve motor function. Recently, neuromodulation of the spinal cord with epidural stimulation (EDS) has allowed patients with motor-complete SCI regain voluntary movement below the level of injury in the cervical and thoracic spine. EDS is performed using multi-electrode arrays placed in the dorsal epidural space spanning several spinal segments. There are numerous stimulation parameters that can be modified to produce different effects on motor function. Previously, defining these parameters was based on observation and empiric testing, which are time-consuming and inefficient processes. There is a need for an automated method to predict motor and sensory function based on a given combination of EDS settings. We developed a novel method to predict the gripping function of a patient with SCI undergoing cervical EDS based on a set of stimulation parameters within a deep learning framework. We also addressed a limiting factor in machine learning methods in EDS, which is a general lack of training measurements for the learning model. We proposed a novel active learning method to minimize the number of training measurements required. The model for predicting responses to EDS could be used by scientists and clinicians to efficiently determine a set of stimulation parameters that produce a desired effect on motor function.


96
Given the extensive input and output information associated with modifying stimuli and 97 characterizing motor responses, respectively, there is a need for efficient machine learning 98 algorithms to explore the wide range of stimulation properties and locations available with EDS. 106 We refer to this process in the following sections as the "dynamic weighting method."

107
Results Our dataset consisted of 237 samples taken from a single patient with chronic SCI in 109 which each sample was a combination of stimulation parameters (i.e., frequency, intensity, and 110 location) and a target outcome score. In order to evaluate the proposed method, a 10-fold cross-111 validation of test and training data was used (i.e., training on 9 folds, and testing on the 112 remaining 1 fold while cycling the test fold and averaging all test performance results). Using 113 this strategy, the following results were obtained from all 237 samples.
114 Outcome prediction performance 115 122 for the mean and median estimates, and the correlation coefficient is greater. In addition, Table 1 123 compares the results using i) a neural network predictor trained alongside the dynamic weight 124 predictor, and ii) a support vector regression (SVR) predictor trained on the dynamically 125 weighted targets. From this comparison, training a new SVR predictor instead of using the 126 existing neural predictor yielded more accurate predictions.
127   169 different EDS parameters. The accurate prediction of hand contraction force will reduce the 170 lengthy testing sessions needed to obtain stimulation settings empirically. This is the first study 171 to use such an approach in a patient with cervical SCI so far was we know.

172
In this study, the proposed dynamic weighting method was used to derive a target value 174 EDS. Dynamic weighting proved to be more accurate than using equally weighted averages. In 175 general, the dynamic weighting method can be applied to derive a single quantity when there are 176 several measurement samples available, which is useful when the traditional filtering and 177 averaging methods are not sufficient. We limited the active learning queries to a pool of samples 178 that were generated during subject testing before -this was not an exhaustive set of all possible 179 stimulation combinations, but did represent the available dataset from this patient. However, the 180 algorithm could be allowed in future applications to query the entire space of stimulation 181 variables that is reasonable to obtain based on hardware limitations and patient comfort. The 182 committee-based active learning method that we described increased learning efficiency, which 183 can reduce the number of clinical experiments necessary to identify optimal stimulation 184 configurations.

185
The SVR model produced more accurate predictions of motor function than a neural 186 network. However, it should be mentioned that in other possible applications of the proposed 187 dynamic weighting method, using the jointly trained neural predictor with enough training data 188 might be a reasonable option. In order to limit the number of experiments required to obtain 189 training data, an active learning method similar to the one that we described can be used. This 190 approach used 30% less data than the random sampling method and yielded similar accuracy, 191 which may translate into a genuine saving of time and discomfort for each patient.

192
The current study has some limitations. 200 Our approach can likely be applied in a similar manner to the lumbosacral spine as well in order 201 to predict walking ability in response to EDS.

Materials and methods
203 Ethics statement

204
The study and the experimental protocols were approved by the UCLA Institutional

212
A 32-contact paddle (Coverage X32, Boston Scientific Corporation) was implanted in the 213 dorsal aspect of the cervical spine (Fig 3). In this study, the paddle contacts in each row were 214 stimulated together. We explored stimulation frequencies of 5, 30, 60 and 90 Hz and intensities 215 between 1 mA to 6 mA. 246 The markers show that it is unreliable simply to use the peak value, and the results are improved 247 using the proposed method. 257 corresponding to the EMG signal during a single trial (Fig 6). For each portion, the median 258 amplitude among the 5% of maximum amplitudes was calculated as the score of that trial. The 259 logic behind selecting the median amplitude among the 5% of maximum amplitudes, instead of 260 simply using the peak value, is that the median value significantly increases the robustness of

268
After calculating the scores associated with each experiment within a session, the final 269 scores for each stimulation experiment were calculated using the following formula.

270
(1) = -271 Where Score baseline is the score before applying any stimulation, and Score stim is the score during 272 stimulation. The final score is the percentage of variation between the stimulation score and the 273 baseline score obtained during each test session.

275
Three scores were available for each experiment corresponding to each trial. We 282 values. The problem becomes more complicated considering that, within each experiment, the 283 subject was less fatigued in the first trial compared to the following two. Therefore, we used a 284 weighted average to calculate the target values, and the weights were determined using a 285 predictor model that dynamically predicted the appropriate weights for each trial score. We 286 created two neural networks in which one network was used as an outcome predictor, and the 287 other one was used as a weight predictor, and we trained them jointly. The first neural network 288 was responsible for predicting the stimulation outcome, and the second one was responsible for 289 predicting the weights that were applied to each trial score in the calculation of the target value.

299
In order to direct the network to learn from relative sample values rather than absolute 300 values, the score values normalized by their median values (NS1, NS2, and NS3 in Fig 7) were 301 used as inputs for the weight predictor. The last layer of the weight predictor is a softmax layer, 302 which guarantees that the predicted weights are always positive and sum to one.

303
After multiplying the score values (the median of the top 5% of the highest EMG 304 amplitudes) with these predicted weights, we estimated the target value, which is the weighted 305 average of the scores (see the dotted part (c) of Fig 7). The softmax layer played a significant