Linear Convolution Model Research Articles

Laser-sound reproduction by pulse amplitude modulation audio streams

Recently, the possibility to reproduce complex continuous acoustic signals via pulsed laser-plasma sound sources was demonstrated. This was achieved by optoacoustic transduction of dense laser pulse trains, modulated via single- or multi-bit Sigma–Delta, in the air or on solid targets. In this work, we extend the laser-sound concept to amplitude modulation techniques. Particularly, we demonstrate the possibility of transcoding audio streams directly into acoustic pulse streams by analog pulsed amplitude modulation. For this purpose, an electro-optic modulator is used to achieve pulse-to-pulse amplitude modulation of the laser radiation, similarly to the multi-level Sigma–Delta method. The modulator is directly driven by the analog input stream through an audio interface. The performance of the system is evaluated at a proof-of-principle level for the reproduction of test audio signals such as single tones, double tones and sine sweeps, within a limited frequency range of the audible spectrum. The results are supported by computational simulations of the reproduced acoustic signals using a linear convolution model that takes as input the audio signal and the laser-generated acoustic pulse profile. The study shows that amplitude modulation allows for significant relaxation of the laser repetition rate requirements compared to the Sigma–Delta-based implementation, albeit at the potential cost of increased distortion of the reproduced sound signal. The nature of the distortions is analyzed and a preliminary experimental and computational investigation for their suppression is presented.

Hemodynamic matrix factorization for functional magnetic resonance imaging

The General Linear Model (GLM) used in task-fMRI relates activated brain areas to extrinsic task conditions. The translation of resulting neural activation into a hemodynamic response is commonly approximated with a linear convolution model using a hemodynamic response function (HRF). There are two major limitations in GLM analysis. Firstly, the GLM assumes that neural activation is either on or off and matches the exact stimulus duration in the corresponding task timings. Secondly, brain networks observed in resting-state fMRI experiments present also during task experiments, but the GLM approach models these task-unrelated brain activity as noise. A novel kernel matrix factorization approach, called hemodynamic matrix factorization (HMF), is therefore proposed that addresses both limitations by assuming that task-related and task-unrelated brain activity can be modeled with the same convolution model as in GLM analysis. By contrast to the GLM, the proposed HMF is a blind source separation (BSS) technique, which decomposes fMRI data into modes. Each mode comprises of a neural activation time course and a spatial mapping. Two versions of HMF are proposed in which the neural activation time course of each mode is convolved with either the canonical HRF or predetermined subject-specific HRFs.Firstly, HMF with the canonical HRF is applied to two open-source cohorts. These cohorts comprise of several task experiments including motor, incidental memory, spatial coherence discrimination, verbal discrimination task and a very short localization task, engaging multiple parts of the eloquent cortex. HMF modes were obtained whose neural activation time course followed original task timings and whose corresponding spatial map matched cortical areas known to be involved in the respective task processing.Secondly, the alignment of these neural activation time courses to task timings were further improved by replacing the canonical HRF with subject-specific HRFs during HMF mode computation.In addition to task-related modes, HMF also produced seemingly task-unrelated modes whose spatial maps matched known resting-state networks.The validity of a fMRI task experiment relies on the assumption that the exposure to a stimulus for a given time causes an imminent increase in neural activation of equal duration. The proposed HMF is an attempt to falsify this assumption and allows to identify subject task participation that does not comply with the experiment instructions.

LINEAR CONVOLUTION MODEL OF FETAL CIRCULATION FOR HEMODYNAMIC RESPONSES TO MATERNAL HYPEROXIA USING IN UTERO FUNCTIONAL MRI.

Functional MRI studies have started the hemodynamic responses of the placenta and fetal brain using maternal hyperoxia. While most studies have focused on analyzing the changes in magnitude of fMRI signals, few studies have analyzed the latency and duration of responses to hyperoxia. This paper proposes a linear convolution model of fetal circulation where a chain of responses to maternal hyperoxia are produced in the placenta and fetal brain. Specifically, an impulse response to hyperoxia was modeled as the hemodynamic response function (HRF) which consists of multiple gamma functions. Both time-to-peak and full width at half maximum of HRF were estimated using simulated annealing (SA). A Monte Carlo simulation was carried out to evaluate the performance of the SA-based method for estimating both parameters. Finally, we provided an example of estimating HRFs from fMRI time series of the placenta and fetal brain acquired during maternal hyperoxia in vivo.

Reconstructing material properties by deconvolution of full-field measurement images: The conductivity case

This study concerns the reconstruction of material parameters from full-field measurements. In this context the typical available data is a set of digital images that is seldom handled as such when solving the inverse problem. Therefore, this work investigates a direct method to compute constitutive parameter maps from full-field measurement images. Within the prototypical framework of the periodic conductivity model, the starting point for the proposed approach is the Lippmann–Schwinger equation, which is satisfied by the fields measured internally. This integral equation is reinterpreted as a linear convolution model for the sought conductivity field. Considering that multiple experiments might be available and then combined, this problem is solved in the least-square sense. To do so, the Krylov subspace-based LSQR algorithm is employed. Full advantage is taken of the convenient expression of the featured Green’s function in Fourier space and of the intensive use of the fast Fourier transform (FFT). Moreover, a spectral-based filtering regularization scheme is implemented to tackle noisy data. Overall, the proposed reconstruction algorithm only handles image-like quantities in an efficient mesh-free approach. The performance of the method is assessed on a set of synthetic 2D numerical examples both for isotropic and anisotropic material configurations.

Effects of Voluntary Locomotion and Calcitonin Gene-Related Peptide on the Dynamics of Single Dural Vessels in Awake Mice.

The dura mater is a vascularized membrane surrounding the brain and is heavily innervated by sensory nerves. Our knowledge of the dural vasculature has been limited to pathological conditions, such as headaches, but little is known about the dural blood flow regulation during behavior. To better understand the dynamics of dural vessels during behavior, we used two-photon laser scanning microscopy (2PLSM) to measure the diameter changes of single dural and pial vessels in the awake mouse during voluntary locomotion. Surprisingly, we found that voluntary locomotion drove the constriction of dural vessels, and the dynamics of these constrictions could be captured with a linear convolution model. Dural vessel constrictions did not mirror the large increases in intracranial pressure (ICP) during locomotion, indicating that dural vessel constriction was not caused passively by compression. To study how behaviorally driven dynamics of dural vessels might be altered in pathological states, we injected the vasodilator calcitonin gene-related peptide (CGRP), which induces headache in humans. CGRP dilated dural, but not pial, vessels and significantly reduced spontaneous locomotion but did not block locomotion-induced constrictions in dural vessels. Sumatriptan, a drug commonly used to treat headaches, blocked the vascular and behavioral the effects of CGRP. These findings suggest that, in the awake animal, the diameters of dural vessels are regulated dynamically during behavior and during drug-induced pathological states.

Brief anesthesia, but not voluntary locomotion, significantly alters cortical temperature.

Changes in brain temperature can alter electrical properties of neurons and cause changes in behavior. However, it is not well understood how behaviors, like locomotion, or experimental manipulations, like anesthesia, alter brain temperature. We implanted thermocouples in sensorimotor cortex of mice to understand how cortical temperature was affected by locomotion, as well as by brief and prolonged anesthesia. Voluntary locomotion induced small (∼ 0.1 °C) but reliable increases in cortical temperature that could be described using a linear convolution model. In contrast, brief (90-s) exposure to isoflurane anesthesia depressed cortical temperature by ∼ 2 °C, which lasted for up to 30 min after the cessation of anesthesia. Cortical temperature decreases were not accompanied by a concomitant decrease in the γ-band local field potential power, multiunit firing rate, or locomotion behavior, which all returned to baseline within a few minutes after the cessation of anesthesia. In anesthetized animals where core body temperature was kept constant, cortical temperature was still > 1 °C lower than in the awake animal. Thermocouples implanted in the subcortex showed similar temperature changes under anesthesia, suggesting these responses occur throughout the brain. Two-photon microscopy of individual blood vessel dynamics following brief isoflurane exposure revealed a large increase in vessel diameter that ceased before the brain temperature significantly decreased, indicating cerebral heat loss was not due to increased cerebral blood vessel dilation. These data should be considered in experimental designs recording in anesthetized preparations, computational models relating temperature and neural activity, and awake-behaving methods that require brief anesthesia before experimental procedures.

Control performance assessment for a class of nonlinear systems using second-order Volterra series models based on nonlinear generalised minimum variance control

In this paper, control performance assessment for a class of nonlinear systems modelled by autoregressive second-order Volterra series with a general linear additive disturbance is presented. The proposed approach employs the nonlinear generalised minimum variance (NGMV) controller concept. The Volterra series models provide a natural extension of a linear convolution model with the nonlinearity considered in an additive term. The polynomial operator form is used throughout this paper for the description of the system input–output model. The closed form formulation of NGMV controller for autoregressive second-order Volterra series is presented in a polynomial form then a control assessment criterion based on the NGMV control is given. Simulation results and comparison studies are used to show the effectiveness of the proposed approach for a class of nonlinear systems.

Quantitative separation of arterial and venous cerebral blood volume increases during voluntary locomotion

Voluntary locomotion is accompanied by large increases in cortical activity and localized increases in cerebral blood volume (CBV). We sought to quantitatively determine the spatial and temporal dynamics of voluntary locomotion-evoked cerebral hemodynamic changes. We measured single vessel dilations using two-photon microscopy and cortex-wide changes in CBV-related signal using intrinsic optical signal (IOS) imaging in head-fixed mice freely locomoting on a spherical treadmill. During bouts of locomotion, arteries dilated rapidly, while veins distended slightly and recovered slowly. The dynamics of diameter changes of both vessel types could be captured using a simple linear convolution model. Using these single vessel measurements, we developed a novel analysis approach to separate out spatially and temporally distinct arterial and venous components of the location-specific hemodynamic response functions (HRF) for IOS. The HRF of each pixel of was well fit by a sum of a fast arterial and a slow venous component. The HRFs of pixels in the limb representations of somatosensory cortex had a large arterial contribution, while in the frontal cortex the arterial contribution to the HRF was negligible. The venous contribution was much less localized, and was substantial in the frontal cortex. The spatial pattern and amplitude of these HRFs in response to locomotion in the cortex were robust across imaging sessions. Separating the more localized arterial component from the diffuse venous signals will be useful for dealing with the dynamic signals generated by naturalistic stimuli.

Dynamic stability of spinning viscoelastic cylinders at finite deformation

The study of spinning axisymmetric cylinders undergoing finite deformation is a classic problem in several industrial settings – the tire industry in particular. We present a stability analysis of spinning elastic and viscoelastic cylinders using ARPACK to compute eigenvalues and eigenfunctions of finite element discretizations of the linearized evolution operator. We show that the eigenmodes correspond to N-peak standing or traveling waves for the linearized problem with an additional index describing the number of oscillations in the radial direction. We find a second hierarchy of bifurcations to standing waves where these eigenvalues cross zero, and confirm numerically the existence of finite-amplitude standing waves for the nonlinear problem on one of the new branches. In the viscoelastic case, this analysis permits us to study the validity of two popular models of finite viscoelasticity. We show that a commonly used finite deformation linear convolution model results in non-physical energy growth and finite-time blow-up when the system is perturbed in a linearly unstable direction and followed nonlinearly in time. On the other hand, Sidoroff-style viscoelastic models are seen to be linearly and nonlinearly stable, as is physically required.

Non-linear generalised minimum variance control state space design for a second-order Volterra series model

This paper presents a non-linear generalised minimum variance (NGMV) controller for a second-order Volterra series model with a general linear additive disturbance. The Volterra series models provide a natural extension of a linear convolution model with the nonlinearity considered in an additive term. The design procedure is entirely carried out in the state space framework, which facilitates the application of other analysis and design methods in this framework. First, the non-linear minimum variance (NMV) controller is introduced and then by changing the cost function, NGMV controller is defined as an extended version of the linear cases. The cost function is used in the simplest form and can be easily extended to the general case. Simulation results show the effectiveness of the proposed non-linear method.

Fast optical signals in the sensorimotor cortex: General Linear Convolution Model applied to multiple source–detector distance-based data

In this study, we applied the General Linear Convolution Model to detect fast optical signals (FOS) in the somatosensory cortex, and to study their dependence on the source–detector separation distance (2.0 to 3.5cm) and irradiated light wavelength (690 and 830nm). We modeled the impulse response function as a rectangular function that lasted 30ms, with variable time delay with respect to the stimulus onset. The model was tested in a cohort of 20 healthy volunteers who underwent supra-motor threshold electrical stimulation of the median nerve. The impulse response function quantified the time delay for the maximal response at 70ms to 110ms after stimulus onset, in agreement with classical somatosensory-evoked potentials in the literature, previous optical imaging studies based on a grand-average approach, and grand-average based processing. Phase signals at longer wavelength were used to identify FOS for all the source–detector separation distances, but the shortest one. Intensity signals only detected FOS at the greatest distance; i.e., for the largest channel depth. There was no activation for the shorter wavelength light. Correlational analysis between the phase and intensity of FOS further confirmed diffusive rather than optical absorption changes associated with neuronal activity in the activated cortical volume. Our study demonstrates the reliability of our method based on the General Linear Convolution Model for the detection of fast cortical activation through FOS.

Fast optical signal in visual cortex: Improving detection by General Linear Convolution Model

In this study we applied the General Linear Convolution Model to fast optical signals (FOS). We modeled the Impulse Response Function (IRF) as a rectangular function lasting 30ms, with variable time delay with respect to the stimulus onset. Simulated data confirmed the feasibility of this approach and its capability of detecting simulated activations in case of very unfavorable Signal to Noise Ratio (SNR), providing better results than the grand average method. The model was tested in a cohort of 10 healthy volunteers who underwent to hemi-field visual stimulation. Experimental data quantified the IRF time delay at 80-100ms after the stimulus onset, in agreement with classical visual evoked potential literature and previous optical imaging studies based on grand average approach and a larger number of trails. FOS confirmed the expected contralateral activation in the occipital region. Correlational analysis between hemodynamic intensity signal, phase and intensity FOS supports diffusive rather than optical absorption changes associated with neuronal activity in the activated cortical volume. Our study provides a feasible method for detecting fast cortical activations by means of FOS.

Paradigm free mapping with sparse regression automatically detects single-trial functional magnetic resonance imaging blood oxygenation level dependent responses.

The ability to detect single trial responses in functional magnetic resonance imaging (fMRI) studies is essential, particularly if investigating learning or adaptation processes or unpredictable events. We recently introduced paradigm free mapping (PFM), an analysis method that detects single trial blood oxygenation level dependent (BOLD) responses without specifying prior information on the timing of the events. PFM is based on the deconvolution of the fMRI signal using a linear hemodynamic convolution model. Our previous PFM method (Caballero-Gaudes et al., 2011: Hum Brain Mapp) used the ridge regression estimator for signal deconvolution and required a baseline signal period for statistical inference. In this work, we investigate the application of sparse regression techniques in PFM. In particular, a novel PFM approach is developed using the Dantzig selector estimator, solved via an efficient homotopy procedure, along with statistical model selection criteria. Simulation results demonstrated that, using the Bayesian information criterion to select the regularization parameter, this method obtains high detection rates of the BOLD responses, comparable with a model-based analysis, but requiring no information on the timing of the events and being robust against hemodynamic response function variability. The practical operation of this sparse PFM method was assessed with single-trial fMRI data acquired at 7T, where it automatically detected all task-related events, and was an improvement on our previous PFM method, as it does not require the definition of a baseline state and amplitude thresholding and does not compromise on specificity and sensitivity.

Time-series analysis for rapid event-related skin conductance responses

Event-related skin conductance responses (SCRs) are traditionally analysed by comparing the amplitude of individual peaks against a pre-stimulus baseline. Many experimental manipulations in cognitive neuroscience dictate paradigms with short inter trial intervals, precluding accurate baseline estimation for SCR measurements. Here, we present a novel and general approach to SCR analysis, derived from methods used in neuroimaging that estimate responses using a linear convolution model. In effect, the method obviates peak-scoring and makes use of the full SCR. We demonstrate, across three experiments, that the method has face validity in analysing reactions to a loud white noise and emotional pictures, can be generalised to paradigms where the shape of the response function is unknown and can account for parametric trial-by-trial effects. We suggest our approach provides greater flexibility in analysing SCRs than existing methods.

Study of neurovascular coupling in humans via simultaneous magnetoencephalography and diffuse optical imaging acquisition

By combining diffuse optical imaging (DOI) and magnetoencephalography (MEG) we investigate neurovascular coupling non-invasively in human subjects using median-nerve stimulation. Previous fMRI studies have shown a habituation effect in the hemodynamic blood oxygen level-dependent (BOLD) response for stimulation periods longer than 2 s. With DOI and MEG we can test whether this effect in hemodynamic response can be accounted for by a habituation effect in the neural response. Our experimental results show that the habituation effect in the hemodynamic response is stronger than that in the earliest cortical neural response (N20). Using a linear convolution model to predict hemodynamic responses we found that including late neural components (≥30 ms) improves the prediction of the hemoglobin response. This finding suggests that in addition to the initial evoked-response deflections related to the talamic afferent input, later cortical activity is needed to predict the hemodynamic response.

Differential transient MEG and fMRI responses to visual stimulation onset rate

AbstractWhile recent analysis of functional magnetic resonance imaging (fMRI) data utilize a generalized nonlinear convolution model (e.g., dynamic causal modeling), most conventional analyses of local responses utilize a linear convolution model (e.g., the general linear model). These models assume a linear relationship between the blood oxygenated level dependent (BOLD) signal and the underlying neuronal response. While previous studies have shown that this “neurovascular coupling” process is approximately linear, short stimulus durations are known to produce a larger fMRI response than expected from a linear system. This divergence from linearity between the stimulus time‐course and BOLD signal could be caused by neuronal onset and offset transients, rather than a nonlinearity in the hemodynamics related to BOLD contrast. We tested this hypothesis by measuring MEG and fMRI responses to stimuli with ramped contrast onsets and offsets in place of abrupt transitions. MEG results show that the ramp successfully reduced the transient onset of neural activity. However, the nonlinearity in the fMRI response, while also reduced, remained. Predictions of fMRI responses from MEG signals show a weaker nonlinearity than observed in the actual fMRI data. These results suggest that the fMRI BOLD nonlinearity seen with short duration stimuli is not solely due to transient neuronal activity. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 18, 17–28, 2008

A novel method for integrating MEG and BOLD fMRI signals with the linear convolution model in human primary somatosensory cortex

Characterizing the neurovascular coupling between hemodynamic signals and their neural origins is crucial to functional neuroimaging research, even more so as new methods become available for integrating results from different functional neuroimaging modalities. We present a novel method to relate magnetoencephalography (MEG) and BOLD fMRI data from primary somatosensory cortex within the context of the linear convolution model. This model, which relates neural activity to BOLD signal change, has been widely used to predict BOLD signals but typically lacks experimentally derived measurements of neural activity. In this study, an fMRI experiment is performed using variable-duration (< or =1 s) vibrotactile stimuli applied at 22 Hz, analogous to a previously published MEG study (Nangini et al., [2006]: Neuroimage 33:252-262), testing whether MEG source waveforms from the previous study can inform the convolution model and improve BOLD signal estimates across all stimulus durations. The typical formulation of the convolution model in which the input is given by the stimulus profile is referred to as Model 1. Model 2 is based on an energy argument relating metabolic demand to the postsynaptic currents largely responsible for the MEG current dipoles, and uses the energy density of the estimated MEG source waveforms as input to the convolution model. It is shown that Model 2 improves the BOLD signal estimates compared to Model 1 under the experimental conditions implemented, suggesting that MEG energy density can be a useful index of hemodynamic activity.

Resolution of Uncertainty in Prefrontal Cortex

Making optimal decisions in the face of uncertain or incomplete information arises as a common problem in everyday behavior, but the neural processes underlying this ability remain poorly understood. A typical case is navigation, in which a subject has to search for a known goal from an unknown location. Navigating under uncertain conditions requires making decisions on the basis of the current belief about location and updating that belief based on incoming information. Here, we use functional magnetic resonance imaging during a maze navigation task to study neural activity relating to the resolution of uncertainty as subjects make sequential decisions to reach a goal. We show that distinct regions of prefrontal cortex are engaged in specific computational functions that are well described by a Bayesian model of decision making. This permits efficient goal-oriented navigation and provides new insights into decision making by humans.

Towards pointwise motion tracking in echocardiographic image sequences – Comparing the reliability of different features for speckle tracking

In this paper, we studied the problem of feature-based motion tracking in echocardiographic image sequences. We described the relation between possible feature variations and different kinds of tissue motion using a linear convolution model. We also showed that motion-feature decorrelation (which means that the motion parameters estimated using feature tracking fail to represent the underlying tissue motion) compensation is an ill-posed inverse problem. Instead of finding a method that may provide better compensation results than previous approaches, we used an quantitative measure to compare the reliability of tracking features. Experiment results showed that the use of the reliability measure improved the robustness of displacement estimation. With the help of the reliability measure, we compared the performance of different features using simulations and phantom examples. While we noticed that the radio frequency (RF) signal outperforms the B-mode (BM) signal in the analysis of small deformation (e.g., less than 0.1% compression), we also found out that the BM signal works better than the RF signal in the analysis of large deformation (e.g., larger than 2% compression). The use of a band-passed filtered feature does not result in significant improvement in tracking.

Long Duration Stimuli and Nonlinearities in the Neural–Haemodynamic Coupling

Recent studies have shown that the haemodynamic responses to brief (<2 secs) stimuli can be well characterised as a linear convolution of neural activity with a suitable haemodynamic impulse response. In this paper, we show that the linear convolution model cannot predict measurements of blood flow responses to stimuli of longer duration (>2 secs), regardless of the impulse response function chosen. Modifying the linear convolution scheme to a nonlinear convolution scheme was found to provide a good prediction of the observed data. Whereas several studies have found a nonlinear coupling between stimulus input and blood flow responses, the current modelling scheme uses neural activity as an input, and thus implies nonlinearity in the coupling between neural activity and blood flow responses. Neural activity was assessed by current source density analysis of depth-resolved evoked field potentials, while blood flow responses were measured using laser Doppler flowmetry. All measurements were made in rat whisker barrel cortex after electrical stimulation of the whisker pad for 1 to 16 secs at 5 Hz and 1.2 mA (individual pulse width 0.3 ms).