Neural Delays Research Articles

Adaptive Neural Delay Feedback Control of a Typical Robot on a Slope

ABSTRACTIn this article, an adaptive neural delay feedback control strategy is proposed for the motion control of a two‐wheel self‐balancing robot (TWSBR) on a slope with an input delay. Based on the Lagrange equation, the dynamic model of the robot is derived. Given a target trajectory vector, the corresponding error system is obtained. An input delay and uncertainties are considered. First, the system with an input delay is transformed into a delay‐free one. Second, a quadratic performance optimization criterion is defined, and a linear quadratic regulator (LQR) controller is designed to minimize the error between the system's state vector and the target vector. Thirdly, an integral sliding mode controller is added to the LQR controller to enhance the system's robustness. To reduce the “chattering” phenomenon, an adaptive neural delay feedback control scheme is developed based on the adaptive learning of the uncertainties' upper bound by a radial basis function neural network (RBFNN). It is demonstrated that a relaxation process exists at the beginning of the upslope motion. As the input delay increases, the swing range of the center of gravity of the pendulum expands. The angle can converge to the steady state more quickly, but the relaxation time is still 0.031 s which has nothing to do with the input delay. An example of the back‐and‐forth motion of a TWSBR on a slope can verify an excellent agreement between theoretical analysis and numerical results.

Neural Delays in Processing Speech in Background Noise Minimized after Short-Term Auditory Training.

Background noise disrupts the neural processing of sound, resulting in delayed and diminished far-field auditory-evoked responses. In young adults, we previously provided evidence that cognitively based short-term auditory training can ameliorate the impact of background noise on the frequency-following response (FFR), leading to greater neural synchrony to the speech fundamental frequency(F0) in noisy listening conditions. In this same dataset (55 healthy young adults), we now examine whether training-related changes extend to the latency of the FFR, with the prediction of faster neural timing after training. FFRs were measured on two days separated by ~8 weeks. FFRs were elicited by the syllable "da" presented at a signal-to-noise ratio (SNR) of +10 dB SPL relative to a background of multi-talker noise. Half of the participants participated in 20 sessions of computerized training (Listening and Communication Enhancement Program, LACE) between test sessions, while the other half served as Controls. In both groups, half of the participants were non-native speakers of English. In the Control Group, response latencies were unchanged at retest, but for the training group, response latencies were earlier. Findings suggest that auditory training can improve how the adult nervous system responds in noisy listening conditions, as demonstrated by decreased response latencies.

A sensorimotor enhanced neuromusculoskeletal model for simulating postural control of upright standing.

The human's upright standing is a complex control process that is not yet fully understood. Postural control models can provide insights into the body's internal control processes of balance behavior. Using physiologically plausible models can also help explaining pathophysiological motion behavior. In this paper, we introduce a neuromusculoskeletal postural control model using sensor feedback consisting of somatosensory, vestibular and visual information. The sagittal plane model was restricted to effectively six degrees of freedom and consisted of nine muscles per leg. Physiologically plausible neural delays were considered for balance control. We applied forward dynamic simulations and a single shooting approach to generate healthy reactive balance behavior during quiet and perturbed upright standing. Control parameters were optimized to minimize muscle effort. We showed that our model is capable of fulfilling the applied tasks successfully. We observed joint angles and ranges of motion in physiologically plausible ranges and comparable to experimental data. This model represents the starting point for subsequent simulations of pathophysiological postural control behavior.

Corrective mechanisms of motion extrapolation.

Transmission and processing of sensory information in the visual system takes time. For motion perception, our brain can overcome this intrinsic neural delay through extrapolation mechanisms and accurately predict the current position of a continuously moving object. But how does the system behave when the motion abruptly changes and the prediction becomes wrong? Here we address this question by studying the perceived position of a moving object with various abrupt motion changes by human observers. We developed a task in which a bar is monotonously moving horizontally, and then motion suddenly stops, reverses, or disappears-then-reverses around two vertical stationary reference lines. Our results showed that participants overestimated the position of the stopping bar but did not perceive an overshoot in the motion reversal condition. When a temporal gap was added at the reverse point, the perceptual overshoot of the end point scaled with the gap durations. Our model suggests that the overestimation of the object position when it disappears is not linear as a function of its speeds but gradually fades out. These results can thus be reconciled in a single process where there is an interplay of the cortical motion prediction mechanisms and the late sensory transient visual inputs.

Investigating sources for variability in volunteer kinematics in a braking maneuver, a sensitivity analysis with an active human body model.

Occupant kinematics during evasive maneuvers, such as crash avoidance braking or steering, varies within the population. Studies have tried to correlate the response to occupant characteristics such as sex, stature, age, and BMI, but these characteristics explain no or very little of the variation. Therefore, hypothesis have been made that the difference in occupant response stems from voluntary behavior. The aim of this study was to investigate the effect from other sources of variability: in neural delay, in passive stiffness of fat, muscle tissues and skin, in muscle size and in spinal alignment, as a first step towards explaining the variability seen among occupants in evasive maneuvers. A sensitivity analysis with simulations of the SAFER Human Body Model in braking was performed, and the displacements from the simulations were compared to those of volunteers. The results suggest that the head and torso kinematics were most sensitive to spinal alignment, followed by muscle size. For head and torso vertical displacements, the range in model kinematics was comparable to the range in volunteer kinematics. However, for forward displacements, the included parameters only explain some of the variability seen in the volunteer experiment. To conclude, the results indicate that the variation in volunteer vertical kinematics could be partly attributed to the variability in human characteristics analyzed in this study, while these cannot alone explain the variability in forward kinematics. The results can be used in future tuning of HBMs, and in future volunteer studies, when further investigating the potential causes of the large variability seen in occupant kinematics in evasive maneuvers.

What, if anything, is coincidence detection?

Neural delays and coincidence detection are neural operations posited as key elements in temporal processing, in the auditory system and beyond. Although longstanding physiological evidence for coincidence detectors exists at a phenomenological level, mechanistic examinations have only recently been performed. We review intracellular recordings from two cell types which are traditionally regarded as prototypes of coincidence detectors. Neurons in the medial superior olive (MSO) are sensitive to “coincidences” in action potentials from the ipsi- and contralateral ear, making the neurons sensitive to interaural temporal differences. Octopus cells in the cochlear nucleus are sensitive to “coincidences” of action potentials across inputs tuned to a wide range of frequencies. We found that in both cases, the spike output of neurons does not simply reflect coincidences of input spikes. When inputs vary in strength, their sequence of activation is an important determinant of response strength. Maximal output is not just determined by the maximal number of coincidences, but reflects temporal input structure in interaction with intrinsic (membrane) properties. These observations suggest a simpler mechanism of temporal sensitivity than traditional lag and coincidence proposals.

Spike-timing dependent plasticity partially compensates for neural delays in a multi-layered network of motion-sensitive neurons.

The ability of the brain to represent the external world in real-time is impacted by the fact that neural processing takes time. Because neural delays accumulate as information progresses through the visual system, representations encoded at each hierarchical level are based upon input that is progressively outdated with respect to the external world. This 'representational lag' is particularly relevant to the task of localizing a moving object-because the object's location changes with time, neural representations of its location potentially lag behind its true location. Converging evidence suggests that the brain has evolved mechanisms that allow it to compensate for its inherent delays by extrapolating the position of moving objects along their trajectory. We have previously shown how spike-timing dependent plasticity (STDP) can achieve motion extrapolation in a two-layer, feedforward network of velocity-tuned neurons, by shifting the receptive fields of second layer neurons in the opposite direction to a moving stimulus. The current study extends this work by implementing two important changes to the network to bring it more into line with biology: we expanded the network to multiple layers to reflect the depth of the visual hierarchy, and we implemented more realistic synaptic time-courses. We investigate the accumulation of STDP-driven receptive field shifts across several layers, observing a velocity-dependent reduction in representational lag. These results highlight the role of STDP, operating purely along the feedforward pathway, as a developmental strategy for delay compensation.

Visual Information Is Predictively Encoded in Occipital Alpha/Low-Beta Oscillations.

Hierarchical predictive coding networks are a general model of sensory processing in the brain. Under neural delays, these networks have been suggested to naturally generate oscillatory activity in approximately the α frequency range (∼8-12 Hz). This suggests that α oscillations, a prominent feature of EEG recordings, may be a spectral "fingerprint" of predictive sensory processing. Here, we probed this possibility by investigating whether oscillations over the visual cortex predictively encode visual information. Specifically, we examined whether their power carries information about the position of a moving stimulus, in a temporally predictive fashion. In two experiments (N = 32, 18 female; N = 34, 17 female), participants viewed an apparent-motion stimulus moving along a circular path while EEG was recorded. To investigate the encoding of stimulus-position information, we developed a method of deriving probabilistic spatial maps from oscillatory power estimates. With this method, we demonstrate that it is possible to reconstruct the trajectory of a moving stimulus from α/low-β oscillations, tracking its position even across unexpected motion reversals. We also show that future position representations are activated in the absence of direct visual input, demonstrating that temporally predictive mechanisms manifest in α/β band oscillations. In a second experiment, we replicate these findings and show that the encoding of information in this range is not driven by visual entrainment. By demonstrating that occipital α/β oscillations carry stimulus-related information, in a temporally predictive fashion, we provide empirical evidence of these rhythms as a spectral "fingerprint" of hierarchical predictive processing in the human visual system.SIGNIFICANCE STATEMENT "Hierarchical predictive coding" is a general model of sensory information processing in the brain. When in silico predictive coding models are constrained by neural transmission delays, their activity naturally oscillates in roughly the α range (∼8-12 Hz). Using time-resolved EEG decoding, we show that neural rhythms in this approximate range (α/low-β) over the human visual cortex predictively encode the position of a moving stimulus. From the amplitude of these oscillations, we are able to reconstruct the stimulus' trajectory, revealing signatures of temporally predictive processing. This provides direct neural evidence linking occipital α/β rhythms to predictive visual processing, supporting the emerging view of such oscillations as a potential spectral "fingerprint" of hierarchical predictive processing in the human visual system.

Robust and efficient representations of dynamic stimuli in hierarchical neural networks via temporal smoothing.

Efficient coding that minimizes informational redundancy of neural representations is a widely accepted neural coding principle. Despite the benefit, maximizing efficiency in neural coding can make neural representation vulnerable to random noise. One way to achieve robustness against random noise is smoothening neural responses. However, it is not clear whether the smoothness of neural responses can hold robust neural representations when dynamic stimuli are processed through a hierarchical brain structure, in which not only random noise but also systematic error due to temporal lag can be induced. In the present study, we showed that smoothness via spatio-temporally efficient coding can achieve both efficiency and robustness by effectively dealing with noise and neural delay in the visual hierarchy when processing dynamic visual stimuli. The simulation results demonstrated that a hierarchical neural network whose bidirectional synaptic connections were learned through spatio-temporally efficient coding with natural scenes could elicit neural responses to visual moving bars similar to those to static bars with the identical position and orientation, indicating robust neural responses against erroneous neural information. It implies that spatio-temporally efficient coding preserves the structure of visual environments locally in the neural responses of hierarchical structures. The present results suggest the importance of a balance between efficiency and robustness in neural coding for visual processing of dynamic stimuli across hierarchical brain structures.

Real-Time Target Tracking System With Spiking Neural Networks Implemented on Neuromorphic Chips

Real-time target tracking is a usual task for humans despite the neural delays during the nervous system’s axonal transfer and neural processing. A plausible explanation is that the human brain employs predictive mechanisms to compensate for the delay. Inspired by the brain, this paper adopts a prediction network based on spiking neural networks (SNNs) to implement a real-time tracking task on a neuromorphic chip with low power consumption. The SNN-based prediction network outperforms the long short-term memory (LSTM) network on a small dataset and reduces 90% to 98% computations compared with LSTM. The quantized SNN-based network is deployed on a neuromorphic chip, and it takes 25ms and only 442 626nJ for a single prediction. The tracking performance of the system is also verified in real-life scenarios. Furthermore, the proposed real-time target tracking system can be easily ported to other neuromorphic platforms.

Position representations of moving objects align with real-time position in the early visual response.

When interacting with the dynamic world, the brain receives outdated sensory information, due to the time required for neural transmission and processing. In motion perception, the brain may overcome these fundamental delays through predictively encoding the position of moving objects using information from their past trajectories. In the present study, we evaluated this proposition using multivariate analysis of high temporal resolution electroencephalographic data. We tracked neural position representations of moving objects at different stages of visual processing, relative to the real-time position of the object. During early stimulus-evoked activity, position representations of moving objects were activated substantially earlier than the equivalent activity evoked by unpredictable flashes, aligning the earliest representations of moving stimuli with their real-time positions. These findings indicate that the predictability of straight trajectories enables full compensation for the neural delays accumulated early in stimulus processing, but that delays still accumulate across later stages of cortical processing.

Interocular Transfer: The Dichoptic Flash-Lag Effect in Controls and Amblyopes.

PurposeThe mammalian brain can take into account the neural delays in visual information transmission from the retina to the cortex when accurately localizing the instantaneous position of moving objects by motion extrapolation. In this study, we wanted to investigate whether such extrapolation mechanism operates in a comparable fashion between the eyes in normally sighted and amblyopic observers.MethodsTo measure interocular extrapolation, we adapted a dichoptic version of the flash-lag effect (FLE) paradigm, in which a flashed bar is perceived to lag behind a moving bar when their two positions are physically aligned. Twelve adult subjects with amblyopia and 12 healthy controls participated in the experiment. We measured the FLE magnitude of the subjects under binocular, monocular, and dichoptic conditions.ResultsIn controls, the FLE magnitude of binocular condition was significantly smaller than that of monocular conditions (P ≤ 0.023), but there was no difference between monocular and dichoptic conditions. Subject with amblyopia exhibited a smaller FLE magnitude in the dichoptic condition when the moving bar was presented to the amblyopic eye and the flash to the fellow eye (DA condition) compared to the opposite way around (DF condition), consistent with a delay in the processing of the amblyopic eye (P = 0.041).ConclusionsOur observations confirm that trajectory extrapolation mechanisms transfer between the eyes of normal observers. However, such transfer may be impaired in amblyopia. The smaller FLE magnitude in DA compared to DF in patients with amblyopia could be due to an interocular delay in the amblyopic visual system. The observation that normal controls present a smaller FLE in binocular conditions raises the question whether a larger FLE is or is not an indicator of better motion processing and extrapolation.

Facilitation and inhibition effects of anodal and cathodal tDCS over areas MT+ on the flash-lag effect.

The perceived position of a moving object in vision entails an accumulation of neural signals over space and time. Due to neural signal transmission delays, the visual system cannot acquire immediate information about the moving object's position. Although physiological and psychophysical studies on the flash-lag effect (FLE), a moving object is perceived ahead of a flash even when they are aligned at the same location, have shown that the visual system develops the mechanisms of predicting the object's location to compensate for the neural delays, the neural mechanisms of motion-induced location prediction are not still understood well. Here, we investigated the role of neural activity changes in areas MT+ (specialized for motion processing) and the potential contralateral processing preference of MT+ in modulating the FLE. Using transcranial direct current stimulations (tDCS) over the left and right MT+ between pre- and posttests of the FLE in different motion directions, we measured the effects of tDCS on the FLE. The results found that anodal and cathodal tDCS enhanced and reduced the FLE with the moving object heading to but not deviating from the side of the brain stimulated, respectively, compared with sham tDCS. These findings suggest a causal role of area MT+ in motion-induced location prediction, which may involve the integration of position information.NEW & NOTEWORTHY Perceived positions of moving objects are related to neural activities in areas MT+. We demonstrate that tDCS over areas MT+ can modulate the FLE, and further anodal and cathodal tDCS facilitated and inhibited the FLE with a moving object heading to but not deviating from the side of the brain stimulated, respectively. These findings suggest a causal role of area MT+ in motion-induced location prediction and contribute to understanding the neural mechanism of the FLE.

Musical experience partially counteracts temporal speech processing deficits in putative mild cognitive impairment.

Mild cognitive impairment (MCI) commonly results in more rapid cognitive and behavioral declines than typical aging. Individuals with MCI can exhibit impaired receptive speech abilities that may reflect neurophysiological changes in auditory-sensory processing prior to usual cognitive deficits. Benefits from current interventions targeting communication difficulties in MCI are limited. Yet, neuroplasticity associated with musical experience has been implicated in improving neural representations of speech and offsetting age-related declines in perception. Here, we asked whether these experience-dependent effects of musical experience might extend to aberrant aging and offer some degree of cognitive protection against MCI. During a vowel categorization task, we recorded single-channel electroencephalograms (EEGs) in older adults with putative MCI to evaluate speech encoding across subcortical and cortical levels of the auditory system. Critically, listeners varied in their duration of formal musical experience (0-21 years). Musical experience sharpened temporal precision in auditory cortical responses, suggesting that musical experience produces more efficient processing of acoustic features by counteracting age-related neural delays. Additionally, robustness of brainstem responses predicted the severity of cognitive decline, suggesting that early speech representations are sensitive to preclinical stages of cognitive impairment. Our results extend prior studies by demonstrating positive benefits of musical experience in older adults with emergent cognitive impairments.

Neural Piecewise-Constant Delay Differential Equations

Continuous-depth neural networks, such as the Neural Ordinary Differential Equations (ODEs), have aroused a great deal of interest from the communities of machine learning and data science in recent years, which bridge the connection between deep neural networks and dynamical systems. In this article, we introduce a new sort of continuous-depth neural network, called the Neural Piecewise-Constant Delay Differential Equations (PCDDEs). Here, unlike the recently proposed framework of the Neural Delay Differential Equations (DDEs), we transform the single delay into the piecewise-constant delay(s). The Neural PCDDEs with such a transformation, on one hand, inherit the strength of universal approximating capability in Neural DDEs. On the other hand, the Neural PCDDEs, leveraging the contributions of the information from the multiple previous time steps, further promote the modeling capability without augmenting the network dimension. With such a promotion, we show that the Neural PCDDEs do outperform the several existing continuous-depth neural frameworks on the one-dimensional piecewise-constant delay population dynamics and real-world datasets, including MNIST, CIFAR10, and SVHN.

Evaluating auditory brainstem response to a level-dependent chirp designed based on derived-band latencies.

The best cochlear-neural delay model for designing a chirp that can produce the largest auditory brainstem response (ABR) has not been established. This study comprised two experiments. Experiment I aimed to estimate the delay model by measuring derived-band ABR latencies at different levels. The results demonstrated that, as the level decreased, the delay between the center frequencies of 0.7 and 5.7 kHz increased. The aim of experiment II was to compare ABRs generated by three stimuli: (1) a level-dependent derived-band (DB)-Chirp, designed based on the model in experiment I; (2) a level-dependent level specific (LS)-Chirp from Kristensen and Elberling [(2012). J. Am. Acad. Audiol. 23, 712-721]; and (3) a click. The results demonstrated that the DB-Chirp produced significantly larger wave V than the LS-Chirp at 45 dB normal hearing level (nHL); however, no differences were observed at other levels. The wave I generated by the DB-Chirp and LS-Chirp were significantly larger than those evoked by the click at 45 and 60 dB nHL and at 30 and 45 dB nHL, respectively; however, at all levels, no differences between these two chirps were observed. The DB-Chirp may be a valuable stimulus for producing ABRs for clinical applications such as assessing cochlear synaptopathy and estimating hearing sensitivity.

Time for Space and the Stability of Prospective Control: Reaching-to-Grasp Gibson.

Gibson formulated an approach to goal-directed behavior using prospective information in the context of visually guided locomotion and manual behavior. The former was Gibson's paradigm case, but it is the rapidity of targeted reaching that has provided the special challenge for stable control. Recent treatments of visually guided reaching assume that internal forward models are required to generate stable behavior given delays caused by neural transmission times. Internal models are representations of the sort eschewed by Gibson in favor of prospective information. Reaching is usually described as guided using relative distances of hand and target, but prospective information is usually temporal rather than spatial. We describe proportional rate control models that incorporate time dimensioned prospective information and show they remain stable in the face of delays. The use of time-dimensioned prospective information removes the need for internal models for stable behavior despite neural transmission delays and allows Gibson's approach to prevail.

Neural closure models for dynamical systems

Complex dynamical systems are used for predictions in many domains. Because of computational costs, models are truncated, coarsened or aggregated. As the neglected and unresolved terms become important, the utility of model predictions diminishes. We develop a novel, versatile and rigorous methodology to learn non-Markovian closure parametrizations for known-physics/low-fidelity models using data from high-fidelity simulations. The new neural closure models augment low-fidelity models with neural delay differential equations (nDDEs), motivated by the Mori–Zwanzig formulation and the inherent delays in complex dynamical systems. We demonstrate that neural closures efficiently account for truncated modes in reduced-order-models, capture the effects of subgrid-scale processes in coarse models and augment the simplification of complex biological and physical–biogeochemical models. We find that using non-Markovian over Markovian closures improves long-term prediction accuracy and requires smaller networks. We derive adjoint equations and network architectures needed to efficiently implement the new discrete and distributed nDDEs, for any time-integration schemes and allowing non-uniformly spaced temporal training data. The performance of discrete over distributed delays in closure models is explained using information theory, and we find an optimal amount of past information for a specified architecture. Finally, we analyse computational complexity and explain the limited additional cost due to neural closure models.

Nonlinear postural control paradigm for larger perturbations in the presence of neural delays.

Maintaining balance is an essential skill regulated by the central nervous system (CNS) that helps humans to function effectively. Developing a physiologically motivated computational model of a neural controller with good performance is a central component for a large range of potential applications, such as the development of therapeutic and assistive devices, diagnosis of balance disorders, and designing robotic control systems. In this paper, we characterize the biomechanics of postural control system by considering the musculoskeletal dynamics in the sagittal plane, proprioceptive feedback, and a neural controller. The model includes several physiological structures, such as the feedforward and feedback mechanism, sensory noise, and proprioceptive feedback delays. A high-gain observer (HGO)-based feedback linearization controller represents the CNS analog in the modeling paradigm. The HGO gives an estimation of delayed states and the feedback linearization control law generates the feedback torques at joints to execute postural recovery movements. The whole scheme is simulated in MATLAB/Simulink. The simulation results show that our proposed scheme is robust against larger perturbations, sensory noises, feedback delays and retains a strong disturbance rejection and trajectory tracking capability. Overall, these results demonstrate that the nonlinear system dynamics, the feedforward and feedback mechanism, and physiological latencies play a key role in shaping the motor control process.

Slacklining as therapy to address non-specific low back pain in the presence of multifidus arthrogenic muscle inhibition.

Low back pain (LBP) represents the most prevalent, problematic and painful of musculoskeletal conditions that affects both the individual and society with health and economic concerns. LBP is a heterogeneous condition with multiple diagnoses and causes. In the absence of consensus definitions, partly because of terminology inconsistency, it is further referred to as non-specific LBP (NSLBP). In NSLBP patients, the lumbar multifidus (MF), a key stabilizing muscle, has a depleted role due to recognized myocellular lipid infiltration and wasting, with the potential primary cause hypothesized as arthrogenic muscle inhibition (AMI). This link between AMI and NSLBP continues to gain increasing recognition. To date there is no ‘gold standard’ or consensus treatment to alleviate symptoms and disability due to NSLBP, though the advocated interventions are numerous, with marked variations in costs and levels of supportive evidence. However, there is consensus that NSLBP management be cost-effective, self-administered, educational, exercise-based, and use multi-modal and multi-disciplinary approaches. An adjuvant therapy fulfilling these consensus criteria is ‘slacklining’, within an overall rehabilitation program. Slacklining, the neuromechanical action of balance retention on a tightened band, induces strategic indirect-involuntary therapeutic muscle activation exercise incorporating spinal motor control. Though several models have been proposed, understanding slacklining’s neuro-motor mechanism of action remains incomplete. Slacklining has demonstrated clinical effects to overcome AMI in peripheral joints, particularly the knee, and is reported in clinical case-studies as showing promising results in reducing NSLBP related to MF deficiency induced through AMI (MF-AMI). Therefore, this paper aims to: rationalize why and how adjuvant, slacklining therapeutic exercise may positively affect patients with NSLBP, due to MF-AMI induced depletion of spinal stabilization; considers current understandings and interventions for NSLBP, including the contributing role of MF-AMI; and details the reasons why slacklining could be considered as a potential adjuvant intervention for NSLBP through its indirect-involuntary action. This action is hypothesized to occur through an over-ride or inhibition of central down-regulatory induced muscle insufficiency, present due to AMI. This subsequently allows neuroplasticity, normal neuro-motor sequencing and muscle re-activation, which facilitates innate advantageous spinal stabilization. This in-turn addresses and reduces NSLBP, its concurrent symptoms and functional disability. This process is hypothesized to occur through four neuro-physiological processing pathways: finite neural delay; movement-control phenotypes; inhibition of action and the innate primordial imperative; and accentuated corticospinal drive. Further research is recommended to investigate these hypotheses and the effect of slacklining as an adjuvant therapy in cohort and control studies of NSLBP populations.