Mental Fatigue Monitoring using Brain Dynamics Preferences

1 INTRODUCTION . As reported by sleep health report ( Adams et al. , 2017 ) , mental fatigue is a major cause in 33 % − 45 % of all road accidents . In general , mental fatigue ( Boksem & Tops , 2008 ) refers to the inability to maintain optimal cognitive performance in continuous task of the high demand of cognitive activity . Such inability in the context of driver could lead to accidents with severe consequences . Individuals may find themselves in a mental fatigue state because of lack of sleep , continuous driving for longtime , midnight driving , monotonous driving , and driving during the influence of sleeping drugs or sleep disorders ( Ji et al. , 2004 ; Ting et al. , 2008 ) . In response to these critical issues , several methods ( Jap et al. , 2009 ; Wascher et al. , 2014 ; Cook et al. , 2007 ; Lal et al. , 2003 ; de Naurois et al. , 2017 ) have been proposed to estimate and predict the mental fatigue based on EEG and RT ( Fig . 1a ) . Some of these methods , however , performed considerably well for some participants but failed for others due to lack of robustness . There are several challenges behind such instability and one of such problem is how to use RT effectively . RT is the most resourceful piece of information to predict mental fatigue . However , it is easily affected by the instrumental error , mind wandering or any other task non-related factor . A previous study ( Wei et al. , 2015 ) tried to overcome this problem by providing different techniques to adjust RT , they also tried removing outliers nevertheless , failed to make it work for all participants . The regression assumption of this method between EEG signals and RT is not correct . Human ’ s RT is usually the result of preference ( Izuma & Adolphs , 2013 ) in brain dynamics during the task , than just a single value . These preferences of human can be affected by different cognition ( Möckel et al. , 2015 ) like mind wandering ( Lin et al. , 2016 ) , and/or lower level of attention ( Chuang et al. , 2018 ) . Therefore , the relationship between EEG and RT including the extreme/abnormal RT should be taken care in the way that reflect human brain dynamics preferences by the developed technique itself . Another important problem is related to different brain regions , which are normally responsible for different functionalities . There was an attempt to choose different brain regions ( Wascher et al. , 2014 ) for a method during mental fatigue prediction but these regions of the brain are not necessary same for all participants ( Gramann et al. , 2006 ) . For example , existing work ( Wascher et al. , 2014 ) used frontal theta to represent a different level of mental fatigue for all participants . In such case learning model ’ s reliability would inevitably degrade because of possibly noisy channels chosen , on different brain regions , by the method . Some previous work ( de Naurois et al. , 2017 ) , attempted to solve this issue using artificial neural network models but still failed to provide convincing results . Again these mentioned work reflect developed methods should be based on brain dynamics preferences rather than fix model or regions of brain . To overcome the above-mentioned problems , a new approach has been proposed . We called it BDrank such that brain dynamics ranking . This approach not only learns from brain dynamics preferences for mental fatigue but also other cognitive states ( Lal et al. , 2003 ) , while effectively preserving the exact ordering of RT ( Fig . 1b ) . This approach surprisingly improved over defects of previous models and their performance due to noisy and extreme RT . Furthermore , BDrank model also proposes to use transition matrix to evaluate the high confidence BDrank ( HC-BDrank ) sources among different EEG channels , which contributes highly toward task performance . In order to handle large-scale EEG signals and obtain higher generalization , an online-generalized Expectation Maximum ( OnlineGEM ) ( Roche , 2011 ) algorithm also has been proposed . Comprehensive empirical experiments on EEG signals from 44 participants show that BDrank model together with OnlineGEM algorithm delivers substantial improvements and robust performance while simultaneously providing the information about noisy or less informative EEG channels . 2 MATERIALS AND METHODS : . Huang et al . Information transfer during drowsy driving FIGURE 1 | Sustained-attention driving task . ( A ) Event-related lane-deviation paradigm . ( B–C ) EEG and behavior were recorded simultaneously . ( D ) The experimental paradigm was implemented in a VR-based driving simulator , where a 3-D surrounding view simulated a monotonous highway scene and a vehicle was mounted on a six degree-of-freedom dynamic platform . ( E ) The car speed was fixed at 100 km/h and the subject was asked to keep the car cruising on the central of the lane . processes X and Y . We assume that each of these processes can be approximated by a stationary Markov Process of finite order d. Thus , we can reconstruct the state space of the process X by a delay embedded vector of dimension d with past values . Representing the two time series as X = xt and Y = yt , the delay embedded vector is defined as x d t = ( xt , xt−τ , xt−2τ , · · · , xt− ( d−1 ) τ ) ; similar representation can also be made for ydt . The dimension of the embedding space is d , and the delay is τ . Under the assumption that the system X can be approximated by a stationary Markov process of order d , the transition probabilities that describe the system are given by : p ( xt+1 ∣ ∣ ∣ xdt ) . ( 1 ) The entropy rate of the systemX is the average number of bits that is required to represent an additional state provided all previous states are known . Thus , the entropy rate can be computed as follows h ( xt+ u ∣ ∣ ∣ xdt ) = − ∑ xt+ u , x d t p ( xt+ u , x d t ) log p ( xt+u ∣ ∣ ∣ xdt ) , ( 2 ) where p ( xt+u ∣ ∣ ∣ xdt ) = p ( xt+u , x d t ) /p ( x d t ) , u is the prediction time , and p ( ∗ ) is the probability . If the two processes are independent , there will be no transfer of information and p ( xt+u ∣ ∣ ∣ xdt ) = p ( xt+u ∣ ∣ ∣ xdt , y m t ) . As proposed by Schreiber ( 2000 ) , a measure of deviation from this generalized Markov property can be computed using Kullback divergence or mutual information and that is a directedmeasure of information transfer from Y to X . The amount of information transferred ( i.e. , transfer entropy ) from process Y to process X , denoted as TE ( Y → X ) , is computed as ( Schreiber , 2000 ; HlaváèkováSchindler et al. , 2007 ; Vicente et al. , 2011 ) TE ( Y → X ) = ∑ p ( xt+u , x d t , y m t ) log p ( xt+u ∣ ∣ ∣ xdt , y m t ) p ( xt+u ∣ ∣ ∣ xdt ) , ( 3 ) where ymt = { yt , yt−τ , · · · , yt− ( m−1 ) τ } indicating that the process X depends onm states of Y . The Equation ( 3 ) can be rewritten in terms of differential entropy as the following TE ( Y → X ) = H ( xdt , y m t ) −H ( xt+u , x d t , y m t ) + H ( xt+u , x d t ) −H ( X d t ) . ( 4 ) Note that TE is inherently asymmetric , that is TE ( Y → X ) 6= TE ( X → Y ) . In addition , when the processes are mutually independent then TE ( Y → X ) = TE ( X → Y ) = 0 . The estimation of parameters and the calculation of TE were performed by TRENTOOL ( version 2.0.4 ) ( Lindner et al. , 2011 ) . Specifically , the TE values were estimated by the k-nearest neighbor approach ( Kraskov et al. , 2004 ; Vicente et al. , 2011 ) , with k = 4 as suggested by Kraskov et al . ( 2004 ) . The embedding delay ( τ ) was determined based on the Cao criterion ( Cao , 1997 ) , and the dimension ( d andm ) was obtained by an effective search algorithm ( Cormen et al. , 2001 ; Lindner et al. , 2011 ; Vicente et al. , 2011 ) . Theiler correction tries to remove autocorrelation effect from the density estimation . For the nearest neighbor search , it discards all samples which are very close in time with respect to a reference point . Here the Theiler correction window ( T ) was set to 1 . In this study the prediction time u was set to 5 . This was determined by finding the maximum value of TE over a set of choices : ( 5 , 10 , 20 , 40 , 60 , 80 , and 100ms ) . Frontiers in Human Neuroscience | www.frontiersin.org 3 October 2015 | Volume 9 | Article 570 Figure 2 : Sustained-attention riving tas a ) Experiment Paradigm : This paper utilized the 33-channels EEG data recorded in the previous study ( Huang et al. , 2015 ) from 44 adult participants while performing long sustained attention task . The experiment has been conducted using a virtual-reality ( VR ) dynamic driving simulator ( Fig . 2D-E ) . The task involves driving on the fourlane highway while lane-departure events were randomly induced deviation toward the side of the road from the original position . Each participant was instructed to quickly respond to steer back to original position . A complete trial in this study ( Fig . 2A ) , includes 10s baseline , deviation onset , response onset , and response offset ( Fig . 2B-C ) . The next trial occurs within an interval of 5-10s after finishing the current trial . Each participant completed T trials within 1.5h . For each trial i , the EEG signals { xn , i } Nn=1 from N different channels were recorded simultaneously and the corresponding response time RTi was also collected afterwards . If a participant fell asleep during the experiment , there was no feedback to wake him up . 2 The response time is an intuitive indicator used to assess human mental fatigue . Therefore , the common practice for mental fatigue monitoring is to find a robust mapping for humans ’ response time ( RT ) to an emergent situation using the EEG signals recorded beforehand . The natural way to forecast the response time with the EEG signals is to formulate it as a regression task ( Fig . 1a ) , namely finding a nonlinear mapping ( e.g . neural network , SVR ) from the EEG signals x to the corresponding RT . However , due to the easily corrupted properties of the EEG signals and the existence of extreme values in response times during data collection , focusing on predicting the exact value of a noisy and non-smooth measurement ( the response time ) is easier to create a near-perfectly fitted model with poor generalization performance ( See Table 1 and Fig . 3 for more details ) . This creates a dilemma : it requires a powerful learning model to predict response time with the complex EEG signals ( indeed , it is exactly our target ) but it is not so significant to excessively approximate the exact value of response time , especially the extreme values . Here comes the problem , how to find an efficient way to learn from the noisy response time while the exact value is not so significant ? Actually , the RTs are defined in the totally ordered space R. The totally ordered space owns its structure meanings , which are preserved by the pairwise comparisons between the RTs . The pairwise comparisons indeed preserve the whole relative structure information between the response times while ignoring their absolute numerical information . Therefore , predicting the orderings of the pairwise comparisons can be accepted as a regularized alternative of previous regression model . Further , it makes it more flexible to consider more powerful learning unit in the proposed model . Therefore , there is no longer requirement to estimate the RT with a regression model . Instead , the proposed approach will transform it into an ordinal classification problem , and focus on correctly preserving the whole orderings between the pairwise RT comparisons ( Fig . 1b ) . First , the preference propositions1 could be constructed as follows , D1 = { ρm } M1m=1 = { RTm,1 > RTm,2 } M1 m=1 , D2 = { ρm′ } M2 m′=1 = { RTm′,1 ≈ RTm′,2 } M2 m′=1 . ( 1 ) where M1 and M2 denote the number of type-1 and type-2 preference propositions . D1 denotes the type-1 preference propositions that the orderings between the RTs are significant ; D2 denotes the type-2 preference propositions that the RTs in each comparison are comparable . Then , the brain dynamics preference was constructed for each proposition with the corresponding pairwise EEG signals recorded from each channel . For brevity of notations , new index ( the notation in Eq.1 ) is adopted in the following , instead of the original index used in sustained-attention driving task ( Fig . 1 ) . Namely , the m-th proposition ρm ∈D1 ⋃ D2 denotes the pairwise comparison RTm,1 > RTm,2 or RTm,1 ≈ RTm,2 . And the pairwise brain dynamics preference ( x1n , m , x2n , m ) denotes the features recorded within the n-th channel for each preference proposition ρm ∀m = 1,2 , · · · , M1 +M2 . In this paper , the 10s baseline ( Fig . 2B ) as the feature vector has been adopted , which is assumed to be long enough to detect any significant changes in brain activity ( Zhang , 2000 ) . This followed by exploring the relation between the 10s baseline x ( ∈ Rk ) and the preference proposition ρm under the following four assumptions : ( 1 ) different participants are independent during the data collection process ; ( 2 ) Different EEG sensors used for recording are recorded independently from scalp without influencing other sensors ( Homan et al. , 1987 ; Teplan et al. , 2002 ) ; ( 3 ) Different trials are conducted independently during the data collection process ; ( 4 ) The collected response time are slightly corrupted by inherent ( basically irremovable ) sources of noise , but the ranking relationships are preserved to some extents . b ) Brain Dynamics Preferences : Again , instead of modelling the dependence between the RT and the 10s baseline as a regression problem , we aim to predict the orderings of the pairwise comparisons using the brain dynamics preferences , namely f ( x1 , x2 ) → ρ . Further , a preference proposition ρ has three states : 1,0 , −1 , denoting win ( RT1 > RT2 ) , tie ( RT1 ≈ RT2 ) and loss ( RT1 < RT2 ) , respectively . However , classical classification models , e.g . logistic ordinal regression ( Harrell , 2001 ) , are infeasible for our problem , due to the lack of a normalized probability definition for three states . Since two types of preference propositions D1 and D2 are considered in our problem , we tailor-define a normalized probability definition , namely first normalizing the probabilities of the states ( 1 , −1 ) 1We used the term “ preference ” intentionally to show that brain dynamics keep changing w.r.t . human behaviours and it happens because the human brain prefers one decision over others . Therefore , we prefer to call it “ preference ” than “ classification ” . ( exclusively to D1 ) to 1 , then generalize the probability definition to state 0 . To be specific , it can be mathematically formulated as follows , P ( ρ|w , x1 , x2 ) = σ ( wT ∆x ) [ 1−κ ( wT ∆x ) ] ρ = 1 κ ( wT ∆x ) ρ = 0 σ ( −wT ∆x ) [ 1−κ ( wT ∆x ) ] ρ =−1 ( 2 ) where σ ( z ) = 1/ ( 1+ e−z ) is the sigmoid function and σ ( −z ) = 1−σ ( z ) . The symbol ∆x denotes the subtraction ( x1− x2 ) between the brain dynamics preferences ( x1 , x2 ) . Following Weng & Lin ( 2011 ) , the probability of a tie is modelled as the geometric mean between a win and a loss , namely κ ( wT ∆x ) = √ σ ( wT ∆x ) [ 1−σ ( wT ∆x ) ] . c ) Preference State Transition : Furthermore , considering the different functions of different regions in the human brain , the relative contributions of different channels to human response time may vary a lot . For example , the information conveyed by positive channels is positive related to the RT , while negative channels may convey the information which is negative related to the RT . There are also some noisy ( non-relevant ) channels which are independent to the learning task . Therefore , if we directly model the EEG preferences recorded in each channel without making any distinctions about the channel state ( i.e . positive , noisy and negative ) , the model ’ s reliability would inevitably degrade . Note that a channel is called as “ noise ” if the current algorithms could not extract useful brain information with EEG signals from this channel ( Alharbi , 2018 ; Lin et al. , 2018 ) . In the following , a transition matrix Πn is introduced to characterize the reliability of each channel n w.r.t the corresponding task . Let ρ denote the preference proposition and ρ ( n ) denote the prediction from the n-th channel . They are defined on the finite state space S = { 1,0 , −1 } . Then we have Πn = P ( ρ|ρ ( n ) ) = πn 0 ( 1−πn ) 0 1 0 ( 1−πn ) 0 πn , ( 3 ) where Pi , j ( ρ|ρ ( n ) ) =P ( ρ = S j|ρ ( n ) = Si ) . Note that we do not consider the transition between the type1 and type-2 preference propositions ( i.e . P ( ρ = { 1 , −1 } |ρ ( n ) = 0 ) = 0 and P ( ρ = 0|ρ ( n ) = { 1 , −1 } ) = 0 ) , since the equal cases are hard to measure when do prediction . A promising approach to generalize the transition matrix Πn ( Eq.3 ) is to introduce the concept of the confidence region to measure the equal cases ( Pregibon et al. , 1981 ) . Remark : The parameter πn in the transition matrix Πn actually indicates the reliability of the n-th channel ∀n = 1,2 , · · · , N. It additionally helps to divide the channels into three states : ( 1 ) positive channels with πn close to 1 , the ranking model ( Eq.2 ) can extract enough information from the n-th channel , and exactly predict the state of the preference proposition . ( 2 ) Noisy channels with πn approximating to 0.5 , the ranking model can not extract any useful information from the n-th channel . ( 3 ) Negative channels with πn close to 0 , the ranking model can extract enough information from the n-th channel , but the prediction states are exactly opposite to the proposition states . The identified positive and negative channels are all considered as informative EEG channels , which helps in learning reliable models for the corresponding task . With the introduced transition matrix Πn , the marginal likelihood function for each proposition ρ can be further represented as P ( ρ ) = Eρ ( n ) [ P ( ρ|ρ ( n ) ) P ( ρ ( n ) ) ] . Specifically , P ( ρ|w , Πn , x1 , x2 ) = [ πnσ ( wT ∆x ) + ( 1−πn ) σ ( −wT ∆x ) ] [ 1−κ ( wT ∆xn , m ) ] ρ = 1 κ ( wT ∆xn , m ) ρ = 0 [ ( 1−πn ) σ ( wT ∆x ) +πnσ ( −wT ∆x ) ] [ 1−κ ( wT ∆xn , m ) ] ρ =−1 ( 4 ) For sake of simplicity , the subscripts ( n , m ) are omitted . Let D =D1 ⋃ D2 denotes all the preference propositions and X represents the recorded EEG signals from N different channels . We further extend our robust ordinal classification ( Eq.4 ) for BDrank into the Bayesian version . A Gaussian prior is introduced for w ( i.e. , w ∼ N ( µ , Σ ) ) . Since the transition matrix Πn only depends on the parameter πn , we only focus on estimate the parameter πn ∀n = 1,2 , · · · , N in the following . Let π denote { πn } Nn=1 , and we introduce a Beta prior for each πn ( i.e. , π ∼ B ( α , β ) = ∏Nn=1 B ( αn , βn ) ) . Then , our BDrank can be formulated into a maximum a posteriori ( MAP ) estimate as follows , argmax π , w P0 ( π ) P0 ( w ) P ( D |π , w , X ) = P0 ( π ) P0 ( w ) P ( D1|π , w , X ) P ( D2|π , w , X ) = P0 ( π ) P0 ( w ) N ∏ n=1 [ M1 ∏ m=1 P ( ρm = 1|πn , w , ∆xn , m ) M2 ∏ m′=1 P ( ρm′ = 0|πn , w , ∆xn , m′ ) ] ( 5 ) = B ( π|α , β ) N ( w|µ , Σ ) N ∏ n=1 [ M1 ∏ m=1 ( [ πnσ ( wT ∆x ) + ( 1−πn ) σ ( −wT ∆x ) ] [ 1−κ ( wT ∆xn , m ) ] ) M2 ∏ m′=1 κ ( wT ∆xn , m′ ) ] . Note that due to the symmetry of the state probability ( Eq.2 ) and transition matrix ( Eq.3 ) w.r.t . state 1 and −1 , the resultant marginal likelihood ( Eq.4 ) remains symmetry w.r.t . state 1 and −1 . For simplicity , D1 is constructed using the preference propositions with state ρ = 1 only . M1 and M2 denote the number of type-1 and type-2 preference propositions , namely |D1|= M1 and |D2|= M2 . The variable n iterates over the channels . m and m′ iterate over two types of preference propositions , respectively . Now our aim is to estimate the model parameters ( w and π ) by maximizing Eq.5 . In principle , any solution strategies for MAP can be considered to solve this problem . See Section 3 for optimization details . d ) Reliability analysis and channel state estimation Note that our BDrank ( Eq.5 ) indeed trains a mixture of two complementary classifiers , which share the same parameter w. It is different from classical mixture models , since it clusters at the channel level instead of the sample level . In particular , in terms of the positive channels with πn close to 1 , BDrank relies on the first classifier to update the shared parameter w. In terms of the negative channels with πn close to 0 , Eq.5 automatically switches to the opposite classifier which can extract correct information from the negative channels and update the shared parameter w accordingly . Further , BDrank is robust to the noisy channels with πn approximating to 0.5 , because Eq.5 gives up extracting information from the noisy channels by assigning a constant likelihood ( i.e . 0.5 ) to each brain dynamics preference . Note that the estimated πn can be leveraged as the indicator to detect noisy channels with πn ≈ 0.5 , ∀n = 1,2 , · · · , N. See Fig . 4 in the experimental section for more details .

Summary: The mental fatigue is an important factor in road accidents. Finding a direct mapping between EEG features and reaction time is difficult and error-prone, combining the noise measurement of EEG and individual variation of RT.  The authors introduce a measure called BDrank based on partial ordering instead of regression. Formulating the measure as a MAP problem, the authors propose a generalized EM algorithm for prediction. An online extension, relying on iterative L-BFGS optimization over mini-batches.