Cortical preparatory activity indexes learned motor memories.

The brain's remarkable ability to learn and execute various motor behaviours harnesses the capacity of neural populations to generate a variety of activity patterns. Here we explore systematic changes in preparatory activity in motor cortex that accompany motor learning. We trained rhesus monkeys to learn an arm-reaching task1 in a curl force field that elicited new muscle forces for some, but not all, movement directions2,3. We found that in a neural subspace predictive of hand forces, changes in preparatory activity tracked the learned behavioural modifications and reassociated4 existing activity patterns with updated movements. Along a neural population dimension orthogonal to the force-predictive subspace, we discovered that preparatory activity shifted uniformly for all movement directions, including those unaltered by learning. During a washout period when the curl field was removed, preparatory activity gradually reverted in the force-predictive subspace, but the uniform shift persisted. These persistent preparatory activity patterns may retain a motor memory of the learned field5,6 and support accelerated relearning of the same curl field. When a set of distinct curl fields was learned in sequence, we observed a corresponding set of field-specific uniform shifts which separated the associated motor memories in the neural state space7-9. The precise geometry of these uniform shifts in preparatory activity could serve to index motor memories, facilitating the acquisition, retention and retrieval of a broad motor repertoire.

Decoding and perturbing decision states in real time.

In dynamic environments, subjects often integrate multiple samples of a signal and combine them to reach a categorical judgment1. The process of deliberation can be described by a time-varying decision variable (DV), decoded from neural population activity, that predicts a subject's upcoming decision2. Within single trials, however, there are large moment-to-moment fluctuations in the DV, the behavioural significance of which is unclear. Here, using real-time, neural feedback control of stimulus duration, we show that within-trial DV fluctuations, decoded from motor cortex, are tightly linked to decision state in macaques, predicting behavioural choices substantially better than the condition-averaged DV or the visual stimulus alone. Furthermore, robust changes in DV sign have the statistical regularities expected from behavioural studies of changes of mind3. Probing the decision process on single trials with weak stimulus pulses, we find evidence for time-varying absorbing decision bounds, enabling us to distinguish between specific models of decision making.

Inferring single-trial neural population dynamics using sequential auto-encoders.

Neuroscience is experiencing a revolution in which simultaneous recording of thousands of neurons is revealing population dynamics that are not apparent from single-neuron responses. This structure is typically extracted from data averaged across many trials, but deeper understanding requires studying phenomena detected in single trials, which is challenging due to incomplete sampling of the neural population, trial-to-trial variability, and fluctuations in action potential timing. We introduce latent factor analysis via dynamical systems, a deep learning method to infer latent dynamics from single-trial neural spiking data. When applied to a variety of macaque and human motor cortical datasets, latent factor analysis via dynamical systems accurately predicts observed behavioral variables, extracts precise firing rate estimates of neural dynamics on single trials, infers perturbations to those dynamics that correlate with behavioral choices, and combines data from non-overlapping recording sessions spanning months to improve inference of underlying dynamics.

Structure and variability of delay activity in premotor cortex.

Voluntary movements are widely considered to be planned before they are executed. Recent studies have hypothesized that neural activity in motor cortex during preparation acts as an 'initial condition' which seeds the proceeding neural dynamics. Here, we studied these initial conditions in detail by investigating 1) the organization of neural states for different reaches and 2) the variance of these neural states from trial to trial. We examined population-level responses in macaque premotor cortex (PMd) during the preparatory stage of an instructed-delay center-out reaching task with dense target configurations. We found that after target onset the neural activity on single trials converges to neural states that have a clear low-dimensional structure which is organized by both the reach endpoint and maximum speed of the following reach. Further, we found that variability of the neural states during preparation resembles the spatial variability of reaches made in the absence of visual feedback: there is less variability in direction than distance in neural state space. We also used offline decoding to understand the implications of this neural population structure for brain-machine interfaces (BMIs). We found that decoding of angle between reaches is dependent on reach distance, while decoding of arc-length is independent. Thus, it might be more appropriate to quantify decoding performance for discrete BMIs by using arc-length between reach end-points rather than the angle between them. Lastly, we show that in contrast to the common notion that direction can better be decoded than distance, their decoding capabilities are comparable. These results provide new insights into the dynamical neural processes that underline motor control and can inform the design of BMIs.

Neural constraints on learning.

Learning, whether motor, sensory or cognitive, requires networks of neurons to generate new activity patterns. As some behaviours are easier to learn than others, we asked if some neural activity patterns are easier to generate than others. Here we investigate whether an existing network constrains the patterns that a subset of its neurons is capable of exhibiting, and if so, what principles define this constraint. We employed a closed-loop intracortical brain-computer interface learning paradigm in which Rhesus macaques (Macaca mulatta) controlled a computer cursor by modulating neural activity patterns in the primary motor cortex. Using the brain-computer interface paradigm, we could specify and alter how neural activity mapped to cursor velocity. At the start of each session, we observed the characteristic activity patterns of the recorded neural population. The activity of a neural population can be represented in a high-dimensional space (termed the neural space), wherein each dimension corresponds to the activity of one neuron. These characteristic activity patterns comprise a low-dimensional subspace (termed the intrinsic manifold) within the neural space. The intrinsic manifold presumably reflects constraints imposed by the underlying neural circuitry. Here we show that the animals could readily learn to proficiently control the cursor using neural activity patterns that were within the intrinsic manifold. However, animals were less able to learn to proficiently control the cursor using activity patterns that were outside of the intrinsic manifold. These results suggest that the existing structure of a network can shape learning. On a timescale of hours, it seems to be difficult to learn to generate neural activity patterns that are not consistent with the existing network structure. These findings offer a network-level explanation for the observation that we are more readily able to learn new skills when they are related to the skills that we already possess.

Trial-by-Trial Motor Cortical Correlates of a Rapidly Adapting Visuomotor Internal Model.

Accurate motor control is mediated by internal models of how neural activity generates movement. We examined neural correlates of an adapting internal model of visuomotor gain in motor cortex while two macaques performed a reaching task in which the gain scaling between the hand and a presented cursor was varied. Previous studies of cortical changes during visuomotor adaptation focused on preparatory and perimovement epochs and analyzed trial-averaged neural data. Here, we recorded simultaneous neural population activity using multielectrode arrays and focused our analysis on neural differences in the period before the target appeared. We found that we could estimate the monkey's internal model of the gain using the neural population state during this pretarget epoch. This neural correlate depended on the gain experienced during recent trials and it predicted the speed of the subsequent reach. To explore the utility of this internal model estimate for brain-machine interfaces, we performed an offline analysis showing that it can be used to compensate for upcoming reach extent errors. Together, these results demonstrate that pretarget neural activity in motor cortex reflects the monkey's internal model of visuomotor gain on single trials and can potentially be used to improve neural prostheses.SIGNIFICANCE STATEMENT When generating movement commands, the brain is believed to use internal models of the relationship between neural activity and the body's movement. Visuomotor adaptation tasks have revealed neural correlates of these computations in multiple brain areas during movement preparation and execution. Here, we describe motor cortical changes in a visuomotor gain change task even before a specific movement is cued. We were able to estimate the gain internal model from these pretarget neural correlates and relate it to single-trial behavior. This is an important step toward understanding the sensorimotor system's algorithms for updating its internal models after specific movements and errors. Furthermore, the ability to estimate the internal model before movement could improve motor neural prostheses being developed for people with paralysis.

Neural population dynamics during reaching.

Most theories of motor cortex have assumed that neural activity represents movement parameters. This view derives from what is known about primary visual cortex, where neural activity represents patterns of light. Yet it is unclear how well the analogy between motor and visual cortex holds. Single-neuron responses in motor cortex are complex, and there is marked disagreement regarding which movement parameters are represented. A better analogy might be with other motor systems, where a common principle is rhythmic neural activity. Here we find that motor cortex responses during reaching contain a brief but strong oscillatory component, something quite unexpected for a non-periodic behaviour. Oscillation amplitude and phase followed naturally from the preparatory state, suggesting a mechanistic role for preparatory neural activity. These results demonstrate an unexpected yet surprisingly simple structure in the population response. This underlying structure explains many of the confusing features of individual neural responses.

Tensor Analysis Reveals Distinct Population Structure that Parallels the Different Computational Roles of Areas M1 and V1.

Cortical firing rates frequently display elaborate and heterogeneous temporal structure. One often wishes to compute quantitative summaries of such structure-a basic example is the frequency spectrum-and compare with model-based predictions. The advent of large-scale population recordings affords the opportunity to do so in new ways, with the hope of distinguishing between potential explanations for why responses vary with time. We introduce a method that assesses a basic but previously unexplored form of population-level structure: when data contain responses across multiple neurons, conditions, and times, they are naturally expressed as a third-order tensor. We examined tensor structure for multiple datasets from primary visual cortex (V1) and primary motor cortex (M1). All V1 datasets were 'simplest' (there were relatively few degrees of freedom) along the neuron mode, while all M1 datasets were simplest along the condition mode. These differences could not be inferred from surface-level response features. Formal considerations suggest why tensor structure might differ across modes. For idealized linear models, structure is simplest across the neuron mode when responses reflect external variables, and simplest across the condition mode when responses reflect population dynamics. This same pattern was present for existing models that seek to explain motor cortex responses. Critically, only dynamical models displayed tensor structure that agreed with the empirical M1 data. These results illustrate that tensor structure is a basic feature of the data. For M1 the tensor structure was compatible with only a subset of existing models.

A Non-Human Primate Brain-Computer Typing Interface.

Brain-computer interfaces (BCIs) record brain activity and translate the information into useful control signals. They can be used to restore function to people with paralysis by controlling end effectors such as computer cursors and robotic limbs. Communication neural prostheses are BCIs that control user interfaces on computers or mobile devices. Here we demonstrate a communication prosthesis by simulating a typing task with two rhesus macaques implanted with electrode arrays. The monkeys used two of the highest known performing BCI decoders to type out words and sentences when prompted one symbol/letter at a time. On average, Monkeys J and L achieved typing rates of 10.0 and 7.2 words per minute (wpm), respectively, copying text from a newspaper article using a velocity-only two dimensional BCI decoder with dwell-based symbol selection. With a BCI decoder that also featured a discrete click for key selection, typing rates increased to 12.0 and 7.8 wpm. These represent the highest known achieved communication rates using a BCI. We then quantified the relationship between bitrate and typing rate and found it approximately linear: typing rate in wpm is nearly three times bitrate in bits per second. We also compared the metrics of achieved bitrate and information transfer rate and discuss their applicability to real-world typing scenarios. Although this study cannot model the impact of cognitive load of word and sentence planning, the findings here demonstrate the feasibility of BCIs to serve as communication interfaces and represent an upper bound on the expected achieved typing rate for a given BCI throughput.

Single-unit activity, threshold crossings, and local field potentials in motor cortex differentially encode reach kinematics.

A diversity of signals can be recorded with extracellular electrodes. It remains unclear whether different signal types convey similar or different information and whether they capture the same or different underlying neural phenomena. Some researchers focus on spiking activity, while others examine local field potentials, and still others posit that these are fundamentally the same signals. We examined the similarities and differences in the information contained in four signal types recorded simultaneously from multielectrode arrays implanted in primary motor cortex: well-isolated action potentials from putative single units, multiunit threshold crossings, and local field potentials (LFPs) at two distinct frequency bands. We quantified the tuning of these signal types to kinematic parameters of reaching movements. We found 1) threshold crossing activity is not a proxy for single-unit activity; 2) when examined on individual electrodes, threshold crossing activity more closely resembles LFP activity at frequencies between 100 and 300 Hz than it does single-unit activity; 3) when examined across multiple electrodes, threshold crossing activity and LFP integrate neural activity at different spatial scales; and 4) LFP power in the "beta band" (between 10 and 40 Hz) is a reliable indicator of movement onset but does not encode kinematic features on an instant-by-instant basis. These results show that the diverse signals recorded from extracellular electrodes provide somewhat distinct and complementary information. It may be that these signal types arise from biological phenomena that are partially distinct. These results also have practical implications for harnessing richer signals to improve brain-machine interface control.

An Integrated 3-Dimentional Navigation System Increases the Accuracy, Efficiency, and Safety of Percutaneous Thoracolumbar Pedicle Screw Placement in Minimally Invasive Approaches: A Randomized Cadaveric Study.

STUDY DESIGN: Cadaveric study. OBJECTIVES: The purpose of this study was to compare a novel, integrated 3D navigational system (NAV) and conventional fluoroscopy in the accuracy, efficiency, and radiation exposure of thoracolumbar percutaneous pedicle screw (PPS) placement. METHODS: Twelve skeletally mature cadaveric specimens were obtained for twelve individual surgeons. Each participant placed bilateral PS at 11 segments, from T8 to S1. Prior to insertion, surgeons were randomized to the sequence of techniques and the side (left or right). Following placement, a CT scan of the spine was obtained for each cadaver, and an independent reviewer assessed the accuracy of screw placement using the Gertzbein grading system. Outcome metrics of interest included a comparison of breach incidence/severity, screw placement time, total procedure time, and radiation exposure between the techniques. Bivariate statistics were employed to compare outcomes at each level. RESULTS: A total of 262 screws (131 using each technique) were placed. The incidence of cortical breaches was significantly lower with NAV compared to FG (9% vs 18%; P = .048). Of breaches with NAV, 25% were graded as moderate or severe compared to 39% in the FG subgroup (P = .034). Median time for screw placement was significantly lower with NAV (2.7 vs 4.1 min/screw; P = .012), exclusive of registration time. Cumulative radiation exposure to the surgeon was significantly lower for NAV-guided placement (9.4 vs 134 µGy, P = .02). CONCLUSIONS: The use of NAV significantly decreased the incidence of cortical breaches, the severity of screw breeches, screw placement time, and radiation exposure to the surgeon when compared to traditional FG.

Learning leaves a memory trace in motor cortex.

How are we able to learn new behaviors without disrupting previously learned ones? To understand how the brain achieves this, we used a brain-computer interface (BCI) learning paradigm, which enables us to detect the presence of a memory of one behavior while performing another. We found that learning to use a new BCI map altered the neural activity that monkeys produced when they returned to using a familiar BCI map in a way that was specific to the learning experience. That is, learning left a "memory trace" in the primary motor cortex. This memory trace coexisted with proficient performance under the familiar map, primarily by altering neural activity in dimensions that did not impact behavior. Forming memory traces might be how the brain is able to provide for the joint learning of multiple behaviors without interference.

A high-performance brain-computer interface.

Recent studies have demonstrated that monkeys and humans can use signals from the brain to guide computer cursors. Brain-computer interfaces (BCIs) may one day assist patients suffering from neurological injury or disease, but relatively low system performance remains a major obstacle. In fact, the speed and accuracy with which keys can be selected using BCIs is still far lower than for systems relying on eye movements. This is true whether BCIs use recordings from populations of individual neurons using invasive electrode techniques or electroencephalogram recordings using less- or non-invasive techniques. Here we present the design and demonstration, using electrode arrays implanted in monkey dorsal premotor cortex, of a manyfold higher performance BCI than previously reported. These results indicate that a fast and accurate key selection system, capable of operating with a range of keyboard sizes, is possible (up to 6.5 bits per second, or approximately 15 words per minute, with 96 electrodes). The highest information throughput is achieved with unprecedentedly brief neural recordings, even as recording quality degrades over time. These performance results and their implications for system design should substantially increase the clinical viability of BCIs in humans.

A closed-loop human simulator for investigating the role of feedback control in brain-machine interfaces.

Neural prosthetic systems seek to improve the lives of severely disabled people by decoding neural activity into useful behavioral commands. These systems and their decoding algorithms are typically developed "offline," using neural activity previously gathered from a healthy animal, and the decoded movement is then compared with the true movement that accompanied the recorded neural activity. However, this offline design and testing may neglect important features of a real prosthesis, most notably the critical role of feedback control, which enables the user to adjust neural activity while using the prosthesis. We hypothesize that understanding and optimally designing high-performance decoders require an experimental platform where humans are in closed-loop with the various candidate decode systems and algorithms. It remains unexplored the extent to which the subject can, for a particular decode system, algorithm, or parameter, engage feedback and other strategies to improve decode performance. Closed-loop testing may suggest different choices than offline analyses. Here we ask if a healthy human subject, using a closed-loop neural prosthesis driven by synthetic neural activity, can inform system design. We use this online prosthesis simulator (OPS) to optimize "online" decode performance based on a key parameter of a current state-of-the-art decode algorithm, the bin width of a Kalman filter. First, we show that offline and online analyses indeed suggest different parameter choices. Previous literature and our offline analyses agree that neural activity should be analyzed in bins of 100- to 300-ms width. OPS analysis, which incorporates feedback control, suggests that much shorter bin widths (25-50 ms) yield higher decode performance. Second, we confirm this surprising finding using a closed-loop rhesus monkey prosthetic system. These findings illustrate the type of discovery made possible by the OPS, and so we hypothesize that this novel testing approach will help in the design of prosthetic systems that will translate well to human patients.

Evaluation of volumetric modulated arc therapy for cranial radiosurgery using multiple noncoplanar arcs.

PURPOSE: To evaluate a commercial volumetric modulated arc therapy (VMAT), using multiple noncoplanar arcs, for linac-based cranial radiosurgery, as well as evaluate the combined accuracy of the VMAT dose calculations and delivery. METHODS: Twelve patients with cranial lesions of variable size (0.1-29 cc) and two multiple metastases patients were planned (Eclipse RapidArc AAA algorithm, v8.6.15) using VMAT (1-6 noncoplanar arcs), dynamic conformal arc (DCA, ∼4 arcs), and IMRT (nine static fields). All plans were evaluated according to a conformity index (CI), healthy brain tissue doses and volumes, and the dose to organs at risk. A 2D dose distribution was measured (Varian Novalis Tx, HD120 MLC, 1000 MU/min, 6 MV beam) for the ∼4 arc VMAT treatment plans using calibrated film dosimetry. RESULTS: The CI (0-1 best) average for all plans was best for ∼4 noncoplanar arc VMAT at 0.86 compared with ∼0.78 for IMRT and a single arc VMAT and 0.68 for DCA. The volumes of healthy brain receiving 50% of the prescribed target coverage dose or more (V(50%)) were lowest for the four arc VMAT [RA(4)] and DCA plans. The average ratio of the V(50%) for the other plans to the RA(4) V(50%) were 1.9 for a single noncoplanar arc VMAT [RA(1nc)], 1.4 for single full coplanar arc VMAT [RA(1f)] and 1.3 for IMRT. The V(50%) improved significantly for single isocenter multiple metastases plan when two noncoplanar VMAT arcs were added to a full single coplanar one. The maximum dose to 5 cc of the outer 1 cm rim of healthy brain which one may want to keep below nonconsequential doses of 300-400 cGy, was 2-3 times greater for IMRT, RA(1nc) and RA(1f) plans compared with the multiple noncoplanar arc DCA and RA(4) techniques. Organs at risk near (0-4 mm) to targets were best spared by (i) single noncoplanar arcs when the targets are lateral to the organ at risk and (ii) by skewed nonvertical planes of IMRT fields when the targets are not lateral to the organ at risk. The highest dose gradient observed between an organ at risk and a target at the edge of a VMAT arc plane or plane of IMRT fields was 17%/mm. The average absolute percent difference between the measured and calculated central axis dose for all the VMAT plans was 3.6 ± 2.2%. The measured perpendicular profile widths and shifts were on average within 0.5 mm of planned values. The average total MUs for VMAT plans was double the DCA average and similar to the IMRT average. CONCLUSIONS: For the aforementioned planning and delivery system and cranial lesions greater than 7 mm in diameter, multiple noncoplanar arc VMAT consistently provides accurate and high quality cranial radiosurgery dose distributions with low doses to healthy brain tissue and high dose conformity to the target. These qualities may make multiple noncoplanar arc VMAT suitable for a greater range of prescription doses or larger and more irregular lesions. For smaller and/or rounder lesions there are other clinically acceptable treatment techniques that may involve fewer couch angles or arcs and reduce treatment times.

Learning is shaped by abrupt changes in neural engagement.

Internal states such as arousal, attention and motivation modulate brain-wide neural activity, but how these processes interact with learning is not well understood. During learning, the brain modifies its neural activity to improve behavior. How do internal states affect this process? Using a brain-computer interface learning paradigm in monkeys, we identified large, abrupt fluctuations in neural population activity in motor cortex indicative of arousal-like internal state changes, which we term 'neural engagement.' In a brain-computer interface, the causal relationship between neural activity and behavior is known, allowing us to understand how neural engagement impacted behavioral performance for different task goals. We observed stereotyped changes in neural engagement that occurred regardless of how they impacted performance. This allowed us to predict how quickly different task goals were learned. These results suggest that changes in internal states, even those seemingly unrelated to goal-seeking behavior, can systematically influence how behavior improves with learning.

Dendritic calcium signals in rhesus macaque motor cortex drive an optical brain-computer interface.

Calcium imaging is a powerful tool for recording from large populations of neurons in vivo. Imaging in rhesus macaque motor cortex can enable the discovery of fundamental principles of motor cortical function and can inform the design of next generation brain-computer interfaces (BCIs). Surface two-photon imaging, however, cannot presently access somatic calcium signals of neurons from all layers of macaque motor cortex due to photon scattering. Here, we demonstrate an implant and imaging system capable of chronic, motion-stabilized two-photon imaging of neuronal calcium signals from macaques engaged in a motor task. By imaging apical dendrites, we achieved optical access to large populations of deep and superficial cortical neurons across dorsal premotor (PMd) and gyral primary motor (M1) cortices. Dendritic signals from individual neurons displayed tuning for different directions of arm movement. Combining several technical advances, we developed an optical BCI (oBCI) driven by these dendritic signalswhich successfully decoded movement direction online. By fusing two-photon functional imaging with CLARITY volumetric imaging, we verified that many imaged dendrites which contributed to oBCI decoding originated from layer 5 output neurons, including a putative Betz cell. This approach establishes new opportunities for studying motor control and designing BCIs via two photon imaging.

Roles of monkey premotor neuron classes in movement preparation and execution.

Dorsal premotor cortex (PMd) is known to be involved in the planning and execution of reaching movements. However, it is not understood how PMd plan activity-often present in the very same neurons that respond during movement-is prevented from itself producing movement. We investigated whether inhibitory interneurons might "gate" output from PMd, by maintaining high levels of inhibition during planning and reducing inhibition during execution. Recently developed methods permit distinguishing interneurons from pyramidal neurons using extracellular recordings. We extend these methods here for use with chronically implanted multi-electrode arrays. We then applied these methods to single- and multi-electrode recordings in PMd of two monkeys performing delayed-reach tasks. Responses of putative interneurons were not generally in agreement with the hypothesis that they act to gate output from the area: in particular it was not the case that interneurons tended to reduce their firing rates around the time of movement. In fact, interneurons increased their rates more than putative pyramidal neurons during both the planning and movement epochs. The two classes of neurons also differed in a number of other ways, including greater modulation across conditions for interneurons, and interneurons more frequently exhibiting increases in firing rate during movement planning and execution. These findings provide novel information about the greater responsiveness of putative PMd interneurons in motor planning and execution and suggest that we may need to consider new possibilities for how planning activity is structured such that it does not itself produce movement.

Structure in Neural Activity during Observed and Executed Movements Is Shared at the Neural Population Level, Not in Single Neurons.

In multiple cortical areas, including the motor cortex, neurons have similar firing rate statistics whether we observe or execute movements. These "congruent" neurons are hypothesized to support action understanding by participating in a neural circuit consistently activated in both observed and executed movements. We examined this hypothesis by analyzing neural population structure and dynamics between observed and executed movements. We find that observed and executed movements exhibit similar neural population covariation in a shared subspace capturing significant neural variance. Further, neural dynamics are more similar between observed and executed movements within the shared subspace than outside it. Finally, we find that this shared subspace has a heterogeneous composition of congruent and incongruent neurons. Together, these results argue that similar neural covariation and dynamics between observed and executed movements do not occur via activation of a subpopulation of congruent single neurons, but through consistent temporal activation of a heterogeneous neural population.

Causal Role of Motor Preparation during Error-Driven Learning.

Current theories suggest that an error-driven learning process updates trial-by-trial to facilitate motor adaptation. How this process interacts with motor cortical preparatory activity-which current models suggest plays a critical role in movement initiation-remains unknown. Here, we evaluated the role of motor preparation during visuomotor adaptation. We found that preparation time was inversely correlated to variance of errors on current trials and mean error on subsequent trials. We also found causal evidence that intracortical microstimulation during motor preparation was sufficient to disrupt learning. Surprisingly, stimulation did not affect current trials, but instead disrupted the update computation of a learning process, thereby affecting subsequent trials. This is consistent with a Bayesian estimation framework where the motor system reduces its learning rate by virtue of lowering error sensitivity when faced with uncertainty. This interaction between motor preparation and the error-driven learning system may facilitate new probes into mechanisms underlying trial-by-trial adaptation.