Biomimetic encoding model for restoring touch in bionic hands through a nerve interface

Objective. Hand function can be restored in upper-limb amputees by equipping them with anthropomorphic prostheses controlled with signals from residual muscles. The dexterity of these bionic hands is severely limited in large part by the absence of tactile feedback about interactions with objects. We propose that, to the extent that artificial touch mimics its natural counterpart, these sensory signals will be more easily integrated into the motor plan for object manipulation. Approach. We describe an approach to convey tactile feedback through electrical stimulation of the residual somatosensory nerves that mimics the aggregate activity of tactile fibers that would be produced in the nerve of a native hand during object interactions. Specifically, we build a parsimonious model that maps the stimulus—described as time-varying indentation depth, indentation rate, and acceleration—into continuous estimates of the time-varying population firing rate and of the size of the recruited afferent population. Main results. The simple model can reconstruct aggregate afferent responses to a wide range of stimuli, including those experienced during activities of daily living. Significance. We discuss how the proposed model can be implemented with a peripheral nerve interface and anticipate it will lead to improved dexterity for prosthetic hands.


Introduction
to low and high frequency vibrations, respectively (Saal and Bensmaia 2015). Without these tactile signals, dexterity is severely compromised (Augurelle 2002, Witney et al 2004.
Much of what is known about neural coding in the periph eral nerve stems from recordings from individual nerve fibers in anesthetized monkeys or awake humans (Talbot andMountcastle 1968, Vallbo andHagbarth 1968). Attempts to reconstruct the responses of afferent populations based on single afferent recordings typically involve estimating time averaged firing rates across afferent populations. The prevailing conclu sion from this body of work is that individual tactile fibers carry ambiguous information about a contacted object and that tactile information is distributed over populations of fibers (Johnson 2001, Muniak et al 2007, Saal and Bensmaia 2014.
We have recently developed a computational modeldubbed TouchSim-that simulates the responses of all tactile fibers to any spatiotemporal deformation of the skin of the hand (Saal et al 2017). With this model, we can characterize with unprecedented spatial and temporal precision how tactile information is distributed across afferent populations. In addi tion to its potential to address basic questions about sensory coding in the somatosensory nerves, this newfound capability can inform precisely how to restore the sense of touch in bionic hands through electrical activation of tactile nerve fibers (Kim et al 2009, Saal and Bensmaia 2015. Indeed, given the importance of touch to dexterity, to con struct an agile bionic hand requires not only the ability to move the hand precisely but also the means to receive tactile signals about the consequences of these movements, particularly as they pertain to object interactions Miller 2014, Saal andBensmaia 2015). In principle, TouchSim provides us with a precise blueprint of tactile restoration as it describes how each tactile nerve fiber will respond to object contact. However, manual interactions with objects evoke responses that differ across fibers depending on their type, their loca tion with respect to the stimulus, and even idiosyncratic differences across nerve fibers of a given type (Vallbo and Hagbarth 1968, Johnson 2001, Johansson and Flanagan 2009, Dong et al 2013. Accordingly, to restore natural touch would require stimulating each fiber independently with its own idi osyncratic stimulation pattern, a feat that current technologies are nowhere near ready to accomplish. Indeed, stateoftheart electrical interfaces with the nerve comprise tens or hundreds of channels, not the 12 or so thousand that would be required for fully biomimetic restoration of touch on the palmar sur face of the hand. Furthermore, at typical stimulation levels, each channel activates tens or hundreds of fibers and evokes highly unnatural synchronous responses in these fibers. Until much denser and more selective neural interfaces become available, then, attempts to mimic nerve responses will have to settle for mimicking aggregate neural responses Bensmaia 2015, Delhaye et al 2016).
TouchSim can be used to simulate the aggregate behavior of hundreds or thousands of fibers by pooling simulated responses across small afferent populations. From the per spective of engineering a bionic hand, however, simulating tens of thousands of fibers to then collapse them into a small number of unidimensional signals is highly inefficient.
With this in mind, we have developed a new, intuitive, computationally inexpensive encoding algorithm, one that comprises only a handful of parameters but that reconstructs with high accuracy the aggregate response of the nerve to timevarying pressure applied to the fingertip. We examine the properties of this population signal and demonstrate that it far outperforms more traditional sensory encoding algorithms in reconstructing the nerve activity evoked during activities of daily living (Gurpreet Singh Dhillon and Horch 2005, Clark et al 2014, Raspopovic 2014, Tan et al 2014, Graczyk et al 2016. We propose that this simple model is precisely what is needed to convert the output of force or pressure sensors on bionic hands into biologically realistic patterns of electrical stimulation of the nerve. Bionic hands endowed with this algorithm will provide more realistic tactile feedback to the user thereby supporting dexterous interactions with objects. More naturalistic feedback may also improve the embodiment of bionic hands and the confidence of users in using them (Marasco et al 2011.

Results
The proposed strategy to restore touch consists of converting the output of sensors on the prosthetic hand into patterns of electrical stimulation to evoke naturalistic patterns of aggre gate activity in the residual nerve (figure 1). To this end, we simulate, using TouchSim (Saal et al 2017), the spiking responses of a population of nerve fibers when a tactile stim ulus is applied to a localized patch of skin. We then pool all the simulated responses to obtain the timevarying population firing rate (FR t ). We also evaluate the timevarying surface of afferent activation by inscribing all active afferent locations in a polygon and computing its area (A t ). This latter quanti ty repre sents the size of the activated population, which is related to but not identical with the population firing rate. Indeed, increasing stimulus intensity results not only in an increase in the firing rate of activated tactile fibers but also in the recruitment of addi tional fibers with receptive fields away from the point of contact (Muniak et al 2007). As discussed below, these two aspects of the response-firing rate and activated area-are required to map neural response onto parameters of electrical stimulation. Next, we develop a simple mapping between the stimulusdecomposed into its time varying indentation, indentation rate, and acceleration-and the aggregate response representations (firing rate, area of activation) to obviate the need for the com putationally demanding and excessively detailed simulation of the entire nerve. Finally, we compare the resulting biomimetic encoding model to a more conventional encoding model that signals instantaneous pressure.

Biomimetic encoding model
First, we simulated the responses to mechanical noise whose frequency composition matched that of natural interactions with objects and of indentations of varying durations and amplitudes as the latter are overrepresented during manual interactions with objects (during maintained grasp, for example). Stimulus amplitudes spanned the range experi enced during activities of daily living (0 to 3 mm). The training set was thus selected to yield a model that is well suited for common manual tasks (see below). Having simulated the aggregate response, we then regressed the timevarying firing rate (FR t ) and timevarying area of activation ( A t ) onto the indentation depth, rate, and acceleration of the stimulus. For area, this linear regression was the input to a sigmoidal func tion to capture the levelingoff of activated area at high ampl itudes (figure 1 and supplementary figure 1(C) (stacks.iop.org/ JNE/15/066033/mmedia)). Both models included several time points for all three variables to capture stimulus dynamics (five time points, spanning a total of 10 ms for each variable in firing rate model, two lags spanning a total of 20 ms for each variable in area model, see methods). The resulting models thus mapped the timevarying response onto the timevarying stimulus with up to 15 stimulusrelated parameters and an intercept (with three additional parameters for the area com putation to capture saturation).

Model performance
Noise, sinusoids, and steps. First, we examined the ability of the model to account for responses to parametric stimuli Figure 1. Biomimetic tactile feedback in a bionic hand. Top flow: contact with an object produces temporal patterns of pressure on a sensor at the fingertip of the prosthetic hand. In principle, the sensor output could be used as input to TouchSim, which would simulate the responses of each afferent innervating the glabrous skin. Spikes could then be pooled across all afferents and binned to yield the firing rate of the whole nerve (FR t ), as well as the recruitment of nerve fibers (A t ). These two metrics indicate how to modulate frequency and pulse charge to produce a biomimetic pattern of nerve activation. Bottom flow: the computationally demanding simulation of TouchSim can be replaced with a simpler model that comprises only a handful of parameters to predict aggregate nerve activity. To this end, we find a mapping between stimulus (pressure) and population activity (firing rate and recruitment) using a combination of linear and nonlinear filters.
including sinusoids over a range of frequencies, pink noise with different bandpasses, and sustained indentations vary ing in duration and amplitude (figure 2(A)). We found that model performance was high for these stimuli, accounting for the bulk of the variance in the simulated aggregate firing rate (R 2 = 0.85, 0.87, 0.9 for noise, sinusoids and steps, respec tively; figure 2(B)-red) and area of activation (R 2 = 0.83, 0.61, and 0.71; figure 2(B)-blue). Note that the model pre cisely captured the hallmark response of the nerve to indenta tions, which is dominated by onset and offset transients and is very weak during static indentation. This property of the nerve response is overlooked in standard encoding models that track timevarying pressure (Gurpreet Singh Dhillon and Horch 2005, Clark et al 2014, Raspopovic 2014, Tan et al 2014, Grac zyk et al 2016. Testing the model across a wider range of frequencies, we found that performance dete riorated for highfrequency stimuli, especially for sinusoidal stimuli (>60 Hz) (figure 2(C) and supplementary figure 2), a phenomenon that can be attributed to two causes. First, the nerve is differentially sensitive at different frequencies and the Main: examples of model fits. Top: timevarying stimulus trace. Middle: population firing rate (FR t ) computed using the full afferent model (TouchSim, black) and using the simplified biomimetic model (red). Bottom: time varying area of activation computed using TouchSim (black) and using the biomimetic model (blue). R 2 denotes the match between TouchSim and the simple model predictions for that trace. (B) Mean goodnessoffit for the firing rate and area models trained to reconstruct low frequency stimuli (up to 10 Hz). The test sample consisted of noise filtered below 10 Hz (different seed), steps (of random amplitudes and durations), and sinusoids (from 1 to 10 Hz). The simple model captures most of the variance in both the aggregate firing rate and activated area over this range of frequencies. (C) Mean goodnessoffit of firing rate (red) and area (blue) predictions as a function of the lowpass cutoff frequency of the stimuli for noise, sinusoids, and steps. Forty models were trained with varying cutoff frequencies (5 Hz-200 Hz) and tested on sinusoids and noise (comprising components with frequencies at or below the training cutoff) and steps of random amplitudes and duration. At high frequencies, the aggregate response becomes tonic rather than oscillatory so performance plummets for sinusoids and noise (see detailed fits in supplementary figure 2). model does not comprise a term that explicitly incorporates this frequency dependence (supplementary figure 1(C)). Sec ond, although individual afferents-particularly RA and PC fibers-produce phaselocked responses to highfrequency vibrations (Talbot andMountcastle 1968, Mackevicius et al 2012), which in principle the model could follow, this signal vanishes when responses are pooled because different fibers spike at different phases within each cycle (Manfredi et al 2012).
Natural stimuli. Next, we tested the model's ability to account for responses evoked during manual interactions with objects. Specifically, we measured the timevarying pressure at the fin gertips and palm as a subject performed a series of activities of daily living (ADL), including grasping a cup, writing with a pen, typing, using a computer mouse, and opening a door. The pressure traces evoked during ADLs are dominated by low frequencies and informed the selection of training stimuli to fit the model. Timevarying skin deformations at each skin location were estimated from the pressure output of the sensor and were used as input to the model. We then compared model predictions to aggregate responses simulated using TouchSim and found that the linear model accounted for a large propor tion of the variance in the ADLevoked responses (figures 3(A) and (B), R 2 = 0.84).
Next, we compared the performance of the biomimetic encoding model to that of the standard encoding model, which simply tracks pressure. We found that the biomimetic model massively outperformed the standard model on the ADL evoked responses (∆R 2 = 0.6, paired ttest: t(15) = 17.86, p = 1.6 × 10 −11 ). As a further test of the model, we simu lated the responses to 200 stimuli designed to mimic ADLs (see methods) and found that the biomimetic model far out performed the standard algorithm for these stimuli as well Sample traces from pressure sensors on the fingertips and the palm along with the firing rate (FR t ) estimated using TouchSim or the biomimetic model for four activities of daily living: opening a door, typing on a keyboard, using a mouse, and picking up a cup. Top: each trace denotes the stimulus, color coded by location (see inset). Bottom traces: population firing rate (black) versus predicted firing rate computed for each task and each projection field (same color as the corresponding stimulus). R 2 denotes match between TouchSim and simple model predictions for that trace. (B) Model performance, averaged across all sessions and hand locations with significant sensor output. The green and orange bars denote the performance of the conventional and biomimetic encoding models, respectively. Error bars show standard errors in each sample. (C) Performance of the two models for simulated tactile stimuli mimicking natural stimuli (n = 200).
(∆R 2 = 0.57, paired ttest: t(199) = 159, p = 9.8 × 10 −212 , figure 3(C)). The biomimetic encoding model outperforms the standard one primarily because it takes into account the fact that the nerve is much more responsive to contact transientsby including velocity and acceleration terms-and responds only weakly to sustained pressure (figures 2(A) and 3(A)).

Stimulation strategy
The proposed biomimetic model provides a faithful estimate of the response that one would wish to elicit in populations of tactile fibers. The overall firing rate (FR t ) evoked in the nerve, given the spatially restricted stimulus, is likely confined to a single fascicle. The firing rate is determined by the activation charge rate, essentially the amount of suprathreshold current delivered to the fascicle (Graczyk et al 2016). However, stan dard electrical pulse trains comprise two parameters-pulse charge and frequency-and population firing rate can be con trolled by modulating either parameter. In contrast, area of activation is a proxy for the crosssection of the fascicle that is activated at any given time, a quantity that can be controlled by modulating pulse charge. The ratio of firing rate to area con stitutes an estimate of the mean firing rate of activated neu rons, a quantity that can be controlled by modulating pulse frequency. We find that the ratio (of population firing rate to number of activated fibers) estimated using our model accu rately reproduces the ratio derived from simulated responses with TouchSim (supplementary figure 3). The simple model proposed here can then be used to specify the values of these two parameters of electrical stimulation as a function of time to produce naturalistic patterns of nerve activation based on the timevarying output of pressure sensors on a prosthetic hand.
The accuracy of our modeling approach places greater emphasis on understanding precisely how stimulation regime-pulse charge, pulse frequency, and pulse wave form-maps onto evoked afferent activation. To predict the neuronal response evoked by a pattern of electrical stimula tion requires a realistic biophysical model of somatosensory nerves. Recently, singlecell and populationlevel models have been developed to describe the response of the nerve to different patterns of injected current (O'Brien 2016). These models, however, are specific to the neural interface used for stimulation. Indeed, intrafascicular and extrafascicular inter faces imply different tissue conductivities and electric field distributions and, thus, different patterns of afferent recruit ment with the changes in injected current (Veltink et al 1988, Grinberg et al 2008. Intraneural interfaces consist of elec trodes that penetrate the epineurium and make direct contact with nerve fibers (TIME  Durand 2002, FINE-Leventhal andDurand 2004), however, the stimulating electrodes do not directly contact their neuronal targets and neuronal activation also depends on spatial factors, such as electrode configuration (Miller et al 2003), pulse polarity (Rattay 1989), electrodefiber distance (Mino et al 2004), and nerve fiber geometry (Woo et al 2010). In many cases, spatial factors are idiosyncratic and must be assessed on a subject by subject basis, for example, the distribution of nerve fascicles at the current injection site and the geometry of the channel rela tive to the nerve fibers (Gustafson et al 2009, Brill and Tyler 2011. Furthermore, stimulation regimes must be evalu ated for their potential to cause damage to the neural tissue with chronic deployment (Briaire and Frijns 2006). While a detailed discussion of how to design a precise and accurate mapping between electrical stimulation and neuronal activa tion falls outside the scope of the present paper, the proposed encoding model establishes a need for such a mapping, which would make possible the elicitation of neuronal patterns of activation whose naturalism is limited only by the capabilities of the neural interface.

Submodality-specific models
Some evidence suggests that tactile nerve fibers are clustered according to their modalities (Hallin et al 1991, Niu et al 2013. That is, handfuls of fibers of a single class (SA1, RA, PC) are grouped together, and these bundles are interleaved seemingly randomly throughout the fascicle. However, the spatial scale over which this clustering occurs is too small and its distribution over the fascicle too idiosyncratic to be reli ably exploited by a neural interface. Nevertheless, once spa tial selectivity of stimulation is improved, the present model can be used to stimulate each tactile submodality appropri ately (supplementary figure 4). For lowfrequency stimuli, the submodalityspecific models are accurate for SA1 and RA responses (supplementary figure 4(C)). As might be expected, however, the reconstruction of PC responses is poor because this class of fibers responds poorly at low frequencies (supple mentary figures 4(A) and (B)).

Implementation notes
The sampling rate of sensors on the bionic hand is a key design specification for the proposed biomimetic model. Indeed, afferent responses cannot be accurately estimated if the tem poral resolution of the input is too coarse (less than 10 ms, figure 4(D)). If a sufficient resolution cannot be achieved, model performance can be rescued to an extent by resampling the sensor values through interpolation.
Another important consideration relates to the size and loca tion of the projection field as the model parameters depend on the size of the estimated afferent population and the location of their receptive fields. Indeed, the number of tactile fibers and the relative proportions of afferents of each type depend on both of these factors. We designed the model for a contact area with a diameter of 6 mm on the fingertip, thus corresponding to a projection field of equivalent size. However, this specific model breaks down when the contact area is much smaller or much bigger (see figure 4(E)), because of the concomitant changes in the sizes and composition of the activated nerve fibers. In light of this, successful deployment of the model requires that the projection field of each electrode be mapped precisely, for example by having the subject report the location and spatial extent of electrically evoked sensations (see Clark et al (2014) and Tan et al (2014), e.g.). The idea is to design the model for each electrode such that the contact area matches the spatial extent of the projection field. As a result, stimulation will produce a sensation whose spatial extent is commensurate with that of a stimulus of equivalent contact area. Otherwise, a mismatch between the size of the projection field and the resulting sensations might occur. Regarding location, models designed for one digit can be applied to other digits. However, the distal fingertips and the rest of the hand yield different models given the pronounced differences in innervation densi ties of the three classes of tactile nerve fibers across these skin locations (see figures 4(A)-(C)). Be that as it may, the model for each electrode can readily be designed for the location and spatial extent of its projection field to optim ize naturalness.

Limitations of the approach
As discussed above, the ideal somatosensory prosthesis would stimulate each nerve fiber independently with a pulse train designed to mimic that fiber's idiosyncratic response. However, given the limitations of current neural interfaces, we developed a linear model to describe the relationship between the timevarying stimulus and the pooled responses of nerve fibers that are liable to be activated by a given stimu lating electrode. While the relationship between pooled firing rates and indentation depth is approximately linear at low frequencies, which dominate during activities of daily living, this linearity breaks down at high frequencies (supplementary figure 1(C)). Another source of lack of fit, described above, is the frequencydependence of the afferent response, par ticularly at high frequencies, which is not explicitly taken into consideration in the model. These nonlinearities result in a reduction in the prediction accuracy of the model, which is based on a linear mapping, particularly at the higher frequen cies. Even at the low frequencies, the proposed model does not capture all of the variance in the neuronal response, as might be expected given the complex nonlinearities between the stimulus and the responses of individual afferents. However, in the frequency range relevant for daily interactions with objects, model predictions of aggregate afferent activity are substantially more faithful to the natural neural response than are predictions from the standard model.
The critical bottleneck for the proposed approach, however, is not the failure of the linear modeling approach to capture the fine spatiotemporal structure of the neural response but rather the limited selectivity of current stimulation technologies. Indeed, synchronous stimulation of many afferents limits the spatial resolution of the sensory feedback, obscuring spatial patterning in the stimulus that falls within the aggregate recep tive field of the stimulated afferents. Furthermore, while the aggregate response of the stimulated afferents will be approxi mately biomimetic, the response of individual afferents will not, a feature that is likely to compromise the naturalness of the resulting percept. However, the model provides a close approximation of the response at the level that can be manipu lated with existing technologies, so paves the way for the most biomimetic response that can be achieved given technological limitations. To the extent that the spatiotemporal dynamics of the aggregate nerve response matter, and given that afferent signals converge as they ascend the somatosensory neuraxis, the proposed sensory encoding algorithm is likely to improve the intuitiveness and utility of the resulting sensory feedback.

Computing population firing rate and activated area from TouchSim simulations
TouchSim simulates afferent responses in two steps. First, the stresses resulting from a stimulus applied at the surface of the skin are estimated as two distinct components, one quasistatic, the other dynamic. The quasistatic component confers to tactile fibers response properties resulting from contact mechanics, such as edge enhancement and surround suppression. The dynamic component propagates through the skin surface as a wave and confers to afferents the ability to respond to vibration at a distance from contact. Second, TouchSim computes the spiking responses of SA1, RA and PC nerve fibers 5 -which tile the hand at their known densi ties (Johansson and Westling 1984)-based on these two stress components using an integrateandfire mechanism. Responses simulated by TouchSim have been shown to match their measured counter parts closely-with singledigit milli second precision-across a wide range of experimental condi tions (Saal et al 2017).
Simulated responses of all afferents with receptive fields on the palmar surface of the hand were pooled to obtain the timevarying population firing rate of the nerve (FR t ) in time increments of 2 ms ( figure 1 and supplementary figure 2(B)).
To estimate area of activation, we pooled the coordinates of all the SA1 and RA fibers that were activated within each 10 ms bin and inscribed them in a polygon of minimum area, A t ( figure 1 and supplementary figure 1(B)). We excluded PC fibers in this computation because their receptive fields are so large as to span most of the hand, and a given PC fiber is activated by touch almost anywhere on the hand.

Training stimulus
The firing rate of populations of afferents has been shown to be approximately linear (Muniak et al 2007) (supplemen tary figure 1(C)), but the slope of this function is dependent on stimulus frequency. To keep the model simple, we did not incorporate any frequencydependent terms. As a result, the parameters of the model were dependent on the (training) stimulus used to obtain them. Indeed, the frequency composi tion of the training stimulus will determine the degree to which different frequency components are weighted in the determi nation of these parameters. Second, sustained indentations of the skin are common during natural interactions with objectsduring maintained grasp, for instance-but absent in a stimulus consisting entirely of noise. With this in mind, we designed a training stimulus that comprises both aspects observed in natural scenes. The stimulus comprised a mechanical noise component with power spectrum that decreases with frequency proportional to 1/f (pink noise) − . The noise was lowpass fil tered to truncate high frequency components (see results sec tion on performance dependence on cutoff frequency) and the resulting stimulus was scaled to a maximum indentation amplitude of 3 mm (supplementary figure 1(A)). The training stimulus also contained skin indentations of varying dura tion-ranging from 1 to 5 s-and varying amplitude-ranging from 0 to 3 mm. We verified that the indentation rates of the resulting stimulus fell within a physiologically plausible range and did not exceed 80-90 cm s −1 , the maximum indentation rate observed during object interactions (Säfström and Edin 2008). A stimulus as short as 100 s was sufficient to train both the firing rate and the area models.

Biomimetic encoding model
We estimate timevarying firing rate ( FR t ) and dynamic area of activation (Â t ) using the following models (see figure 1): is a vector of stimulus features including indentation depth (s), rate (ṡ), and acceleration (s), with k denoting the number of time lags. The model was trained with a contact area of diameter of 2, 4, and 6 mm, respectively, then was tested with different smaller/larger contact areas with diameters ranging from 0.1 to 7 mm. For all analyses, the model was trained using sustained indentations and pink noise filtered below 5 Hz. Test set consisted of steps of varying length and amplitude, noise of random seed and sinusoids of varying frequencies (<5 Hz). Model must be tailored to the size of the projection field.
h FR (.) is a nonlinearity of the form h FR (x) = ® x, x > 0 0, x 0 to guarantee that firing rate is always nonnegative; h A (.) is a nonlinearity defined by a sigmoid function to cap ture the observed saturation of activated area at high amplitudes: We estimate parameters of the firing rate model (W FR ) using least squares regression and parameters of the area model (W A , b) using nonlinear optimization with the Levenberg-Marquardt algorithm. We optimized the number of lags k to achieve stable crossvalidation performance across all test stimuli with both models (k = 5 for firing rate and k = 2 for activation area).

Conventional encoding model
In the majority of sensory feedback algorithms implemented to date in experiments with human amputees (see Dhillon and Horch (2005), Clark et al (2014), Raspopovic (2014), Tan et al (2014), Graczyk et al (2016) and Schiefer et al (2016)), the firing rate of the nerve FR t linearly tracks the timevarying stimulus s t , such that FR t ∝ s t . We used this model as a baseline, linearly scaling it to best fit the simulated response.

Model validation
To test the model, we first assessed the degree to which it could reproduce the timevarying firing rate and activated area of afferent population simulated with TouchSim using a set of parametric stimuli. Specifically, we computed the output of the model to sinusoids varying in frequency and amplitude, noise stimuli with the same spectral profile used to obtain the parameters but with a different random seed, and step inden tations varying in duration and amplitude. We then compared this output with the aggregate firing rate computed using TouchSim. The coefficient of determination (R 2 ) was used to gauge model fit.
Next, we assessed the model performance on stimuli that reproduce those experienced during every day interactions with objects. To this end, we instrumented an adult male participant with a sensorized glove (FingerTPS, PPS, Inc., Los Angeles, CA) with six pressure sensors-one on each fingertip and one on the palm-and had him perform five standard manual tasks: grasping a cup, writing with a pen, typing, clicking a computer mouse and opening a door (for detailed description of the data collection, see Kim et al (2011)). The output of each sensor was converted to indentation depth by scaling it to a maximum of 3 mm. We resampled the pressure output from 64 Hz to 512 Hz using spline interpolation and filtered the resulting trace with a lowpass cutoff of 5 Hz to eliminate highfrequency noise. The resulting trace was used as input to TouchSim and to the biomimetic encoding model. Models were tailored to the location of the projection field, with dif ferent sets of coefficients for different sensor locations.
To further test the biomimetic model, we generated a set of synthetic stimuli designed to mimic ADLs in terms of their spectral profile. Specifically, we pooled all ADL samples (n = 23) with indentation depths greater than 1 mm and esti mated their power spectrum using Multitaper Power Spectral Density estimate (Chronux, Matlab). We then generated 200 white noise samples, each 10 s long, converted them to the frequency domain, adjusted their power spectrum to match that of ADLs, then converted the resulting spectra back to time domain. The code for computing parameters of the bio mimetic model is available at http://bensmaialab.org/code/ touchmime/.