Mass spectrometry coupled to gas chromatography (GC-MS) has been widely applied in the field of metabolomics. Success of this application has benefited greatly from computational workflows that process the complex raw mass spectrometry data and extract the qualitative and quantitative information of metabolites. Among the computational algorithms within a workflow, deconvolution is critical since it reconstructs a pure mass spectrum for each component that the mass spectrometer observes. Based on the pure spectrum, the corresponding component can be eventually identified and quantified. Deconvolution is challenging due to the existence of co-elution. In this review, we focus on progress that has been made in the development of deconvolution algorithms and provide thoughts on future developments that will expand the application of GC-MS in metabolomics. Metabolomics is the comprehensive qualitative and/or quantitative study of a metabolome  and as such provides measurements essential for systems biology approaches for the study of health and disease. It has benefited greatly from advances in analytical technologies including nuclear magnetic resonance (NMR) and mass spectrometry (MS) coupled to separation techniques. The advantages of NMR are the minimal requirements for sample preparation and the non-discriminating and non-destructive nature of the technique. However, the low sensitivity of NMR makes it difficult to detect low-abundance metabolites that could constitute key discoveries of new biomarkers or biological mechanisms. Mass spectrometry-based metabolomics offers high selectivity and sensitivity and, more importantly, the potential to identify metabolites. Combining MS with separation techniques reduces the complexity of the mass spectra due to metabolite separation in the time dimension and provides additional information about the physical and chemical properties of the metabolites , 2. Due Obtaining a full coverage of the metabolome generally requires multiple separation approaches since metabolites are heterogeneous, low molecular-weight components  that are characterized by a wide variation in physical and chemical properties  . Three tGC combined with electron ionization (EI) mass spectrometry allows for the identification and quantification of volatile and thermally stable compounds of low polarity from sources such as biological tissues and foods . The fraComplementary to GC-MS, LC-MS enables identification and quantification of high polarity compounds including organic acids, fatty acids, amino acids, and steroids. LC-MS-based metabolomics is generally performed using soft ionization techniques such as electrospray ionization (ESI) and atmospheric pressure chemical ionization (APCI), which do not cause fragmentation of the molecular ions and thus allow for the determination of elemental compositions. In addition, LC-MS/MS can be used to identify metabolites , 13.The third separation technique, CE, is suited for the separation of polar and charged compounds, as compounds are separated on the basis of their electrophoretic mobility. However, the repeatability of migration time in CE is very poor compared to that of the retention time in GC and LC. This factor is especially critical in metabolomics because a high accuracy of metabolite peak alignment must be achieved prior to downstream data analyses. Large variations in migration time make alignment very challenging .MS-based metabolomics experiments using these separation techniques can be conducted using three approaches: 1) non-targeted metabolic profiling where the identity and relative quantity of as many metabolites as possible are obtained; 2) targeted profiling where the absolute quantity of a pre-selected smaller set of metabolites, typically related by chemical or biological similarity, are obtained using internal standards and reference compounds, and 3) metabolic fingerprinting where a global snapshot of the metabolism is acquired and compared without performing quantification and chemical identification. Biologically interesting components can then be subjected to targeted profiling for identification and quantification.These aforementioned analytical platforms  and metabolomic approaches (profiling and fingerprinting) have been applied widely in metabolomics research. A number of excellent review articles have been published summarizing this work , 15–24. For metabolic profiling where identification and quantitation (semi-quantitation for non-targeted and absolute quantitation for targeted profiling) are performed, bioinformatics includes three sequential steps: (1) data processing converts mass spectral data into tables of known or unknown metabolites with their identity and quantity, (2) data analysis identifies interesting metabolites or metabolic patterns through statistical analyses, clustering, and classification, and (3) data interpretation places the metabolomics data in the context of metabolic pathways and integrates metabolomics data with data from other omics platforms. Combination of the three steps is essential for knowledge discovery from the metabolomics experiments.deconvolution in GC-MS data processing.Among the three data handling steps, processing of raw mass spectral data is critical because any inaccuracy in this stage will propagate to the subsequent two steps. For a GC-MS based metabolomics study, data processing is even more critical due to co-elution of two or more compounds and the in-source fragmentation of molecular ions caused by the hard EI ionization. Co-elution and in-source fragmentation cause the resulting raw mass spectra to consist of mass peaks from all of the co-eluting metabolites. In order to identify and extract the quantitative information of the corresponding metabolites, the spectrum for each single metabolite has to be constructed based on the composite spectra. This spectrum construction step is called Considering the importance of GC-MS for analyzing compounds commonly observed in fruits, vegetables, nutritional and medicinal plants, and human biofluids after food digestion, we would focus on the deconvolution aspect of GC-MS data processing in this review. We will review the progress that has been made so far, and provide our thoughts on future developments that will enable further progress in metabolomics research. For the other aspects of data processing and the subsequent data analysis and interpretation, we refer readers to the research article by Stein el al. , review For GC-MS data, deconvolution is the process of computationally separating co-eluting components and creating a pure spectrum for each component. Specifically, for each observed EIC that results from two or more components, deconvolution calculates the contribution of each component to the EIC. Deconvolution had evolved based on the work of a number of researchers , 29 and The overall deconvolution process in AMDIS consists of four sequential steps: 1) noise analysis, 2) component perception, 3) model shape determination , this segment is accepted and the median deviation from the mean abundance for that segment is found  are divided into segments of a certain number of scans . For eais found . This desequentially examines scans starting at the scan of maximization and proceeds in the forward and reverse directions up to a pre-set maximum number of scans (12 is the default). If a signal abundance is encountered that is more than five noise units greater than the smallest abundance between that scan and the starting scan , then it is presumed that another component has been found and the window length is set to the preceding scan. Also, if the intensity falls below 5% of the maximum intensity, the window is fixed at that scan.”The second step, component perception, perceives individual chromatographic components. The rationale behind component perception is that a component exists when a sufficient magnitude of ions maximize together. It is achieved through a process as illustrated in Amax, and an abundance value located n scans from the maximum, An is defined as:The third step determines the model peaks to be used in the next step for deconvolution. The model shape for each perceived component is taken as the sum of the individual ion chromatograms that maximize together and whose sharpness values are within 75% of the maximum value for this component. The sharpness value between the maximum abundance, The maximum sharpness values on each side of the maximum scan are averaged as the sharpness value of this ion chromatogram.The last step, deconvolution, extracts ‘purified’ spectra from individual ion chromatograms for each component using the model shapes and the least-squares method. Briefly, each ion chromatogram is fit to the model profiles allowing a linear baseline:This four-step process of deconvolution that AMDIS uses forms the basis of deconvolution in MetaboliteDetector  and ADAPDeconvolution in MetaboliteDetector differs from AMDIS in component perception and model peak determination. For component perception, it detects the beginning and ending of chromatographic peaks by calculating the first derivative of the smoothed intensity values :4f'(x)=-discrepancy index, is defined based on the assumption that all values of the first derivative of an ideal single peak must be positive from the peak beginning to the peak maximum and negative from the peak maximum to the peak ending. The absolute values of the first derivatives that agree with this assumption are summed as ideal slopes and the absolute values of the first derivatives that disagree with this assumption are summed as nonideal slopes. The discrepancy index qp of a peak shape is formally defined as the ratio of the nonideal to ideal slopes:A resulting peak is counted as valid if three criteria are met: the peak must consist of more than three values, the height above the baseline in signal-to-noise units of the maximum peak value must exceed a predefined threshold, and the quality of the peak shape must be in a certain range. The quality of a peak shape, named qp are in the range between 0% and 10%.Reasonable values of qp values below 10% by their sharpness values. The top 25% of the peaks in terms of the sharpness value are summed to form the model peak for this compound.To determine the model peak shape for each perceived component, MetaboliteDetector sorts all single ion peaks of a compound having Deconvolution in ADAP-GC 2.0 differs from AMDIS and MetaboliteDetector in terms of component perception, noise analysis, and model peak determination . Specifisimple CPF, and a CPF that results from two or more components is defined as a composite CPF. A simple CPF has only one local maximum, and a composite CPF could have one, two, or more local maxima. ADAP-GC 2.0 detects a CPF by determining the beginning, ending, and apex time of each local peak based on local maximum (for peak apex) and minimum (for beginning and ending). To determine if a peak is a simple CPF or part of a composite CPF, the algorithm calculates the ratio of intensity values at the boundaries to the intensity value at the peak apex. If one of the ratios is higher than a configurable threshold, this peak is considered part of a composite CPF. All of the neighboring incomplete peaks are then merged to form a composite CPF.A CPF is the elution profile of a minimum number of components that makes the elution profile complete, with ‘complete’ meaning that the elution profile lasts from the beginning to the end of the elution of the component(s). A CPF that results from a single component is defined as a Subsequently, ADAP-GC 2.0 determines the deconvolution windows based on both the TIC and EIC. Basically, the beginning and ending of a TIC CPF delimit a window and any EIC CPF whose peak apex falls in the window will participate in the window-specific deconvolution. For each deconvolution window, ADAP determines the number of components and the model peak shape for each component. Unlike the model peak in AMDIS and MetaboliteDetector, ADAP-GC 2.0 defines a model CPF as the elution profile of a compound when it elutes from a chromatography system alone and its concentration is within the linear dynamic range of the mass spectrometer. As such, a model peak can result from the elution of a single component only. To determine the model CPF, ADAP first calculates five quality metrics of each CPF. These five metrics are sharpness, signal-to-noise ratio (SNR), peak intensity, Gaussian similarity, and the mass. The sharpness value of a CPF is calculated asN is the total number of time points for a CPF, p is the time index of the apex, and Ii is the abundance value at time index i. The SNR is estimated based on the high- and low-frequency signal components of the CPF, which is calculated using the continuous wavelet transform. For details about other metrics, please refer to the original article.Where Following the calculation of the five metrics, ADAP selects those CPFs with high values of sharpness, SNR, and Gaussian similarity. Each of the filter-passing CPFs is assigned a total quality score calculated asThose CPFs whose total score pass the following threshold are considered good candidates of model CPFs:Finally, all of the good candidates for model CPFs participate in a hierarchical clustering process for ADAP to determine the most likely number of components in the current deconvolution window and the corresponding model peak for each component.Noise analysis: Mass spectra and chromatograms that are obtained from the spectra are inherently noisy. All of the three algorithms we described above incorporated noise analysis. AMDIS and MetaboliteDetector calculate the noise factor of a GC-MS data file and then convert the signal magnitude in noise units in some of the subsequent calculations. ADAP-GC 2.0 uses a completely different approach by directly computing the signal-to-noise ratio of each CPF and uses it as a filter to prevent noisy CPFs from being selected as model CPFs. Without direct comparison between these two approaches, it is challenging to state which one leads to better performance.Determination of deconvolution windows: AMDIS's approach often causes deconvolution windows to be narrower than optimal for quantitation, as pointed out in the original article . This haIn order to resolve this issue, ADAP-GC 2.0 tries to detect composite CPFs and ensure that their deconvolution windows contain the entire CPF. Conceptually, this should increase the accuracy of the quantitative information that ADAP extracts about metabolites from the data.In MeteboliteDetector, how deconvolution windows are determined was not explicitly described. Regardless of the specific approach, it must utilize the information about the beginning and ending of chromatographic peaks. MetaboliteDetector determines the beginnings and endings using first derivatives as in c * M (nmax) in nmax denotes the scan with the maximum model peak abundance, will be used as the abundance for the corresponding m/z in the extracted spectrum. Conceptually, it should be preferred that each model peak corresponds to one single component only. However, since both AMDIS and MetaboliteDetector use a summation of peaks as the model peak and one or more of the constituent peaks could consist of signals from multiple co-eluting components, the likelihood that the final model peak also consists of signals from multiple co-eluting components is very high. Consequently, the magnitude of the mass peaks in the extracted spectrum will be inaccurate, which could ultimately cause both false positive and false negative metabolite identifications. Moreover, the quantitative information for corresponding components will be inaccurate as well since it is calculated based on the extracted spectrum.Determination of model peaks: The central goal of deconvolution is to decompose a composite CPF into the weighted summation of the model peaks and then form the spectrum of a single component based on the weights in ADAP, however, selects only the purest peak for model peaks by using five peak quality metrics. On the other hand, ADAP has a weakness too in determining model peaks. It favors model peaks that are symmetric and resemble a Gaussian curve. In reality, fronting and tailing do occur and cause asymmetric peak shapes even when a compound elutes alone from the chromatography system. This issue can conceptually be alleviated or eliminated by decreasing the weighting factor that is assigned to the Gaussian similarity in Each of the aforementioned computational steps plays an important role in determining whether or not metabolic changes can be detected in metabolomics studies.Based on the above description, we can see that it will be worthwhile to carry out a detailed comparison about the performance of the critical computational steps and come up with the best overall deconvolution strategy. Even though the aforementioned three algorithms have not been directly compared, a comparison between AMDIS and two commercial software packages, ChromaTOF  and AnalFor AMDIS, it was originally developed for automated identification of chemical weapons and related compounds . TherefoAppropriate configuration of processing parameters can help alleviate the challenge to find an acceptable balance between false positive and false negative identifications. However, without prior knowledge about the sample composition in un-targeted metabolic profiling experiments, researchers usually do not know what parameter setting is appropriate for their datasets. This issue exists in other algorithms as well.More efficient and reliable deconvolution algorithms need to be developed for identification and quantification of metabolites due to the aforementioned limitations of existing deconvolution algorithms. Newly developed algorithms need to be implemented into user-friendly and high-throughput software tools. These software tools should be equipped with visualization capabilities that will allow metabolomics researchers to visually examine intermediate and final results for verifying the correctness of significant metabolites detected in the data analysis and data interpretation stages. Development of these algorithms and software tools will benefit greatly from an interdisciplinary team of researchers and software engineers with engineering, chemistry, math, and computer science background.Computational algorithms and software tools are also needed for identifying unknown metabolites. This is because, with unprecedented sensitivity, dynamic range, and throughput, both GC-MS and LC-MS analytical platforms can now detect many metabolites in a short time frame that could not be observed before. However, the power of the detection methods has outstripped our ability to process the data. Often, the number of unidentified metabolites in a sample is 2-3-fold more than the number of identified metabolites even after extensive data processing. This is because even the largest and most comprehensive of currently available libraries contain only a small portion of the endogenous metabolites found in biological samples –41.The past decade has witnessed tremendous progress on metabolomics bioinformatics research. However, the progress has not been as fast as that on the instrumentation side as mass spectrometry coupled to chromatography is becoming increasingly sensitive and their operations are becoming increasingly high-throughput. Next, we provide our thoughts on new bioinformatics capabilities for GC-MS data processing that are needed for metabolomics to progress further.Arabidopsis thaliana has a large number of enzymes whose substrates and products remain unknown [Identifying these unknown metabolites is currently a major bottleneck in metabolomics , 43. Thi unknown . MeanwhiTherefore, a pressing need in the metabolomics community is the development of effective methods for prioritizing, studying, and ultimately identifying uncharacterized metabolites . To addrFor GC-MS-based metabolomics, some progress has been made in the effort to use and catalogue unidentified GC-MS spectra in metabolomics studies , 46–64. In addition to the above approaches, the widely used GOLM GC-MS mass spectral database incorporated mass spectra of unidentified metabolites. However, similar to the vocBinBase database, no derivation of consensus spectra or determination of the best representative spectra was implemented . For LC-This lack of capabilities to handle unidentified GC-MS and LC-MS spectra reveals that metabolomics bioinformatics is lagging behind technological advances in analytical instrumentation, and this is hindering investigators from taking advantage of data that the instruments already capture.


Fifty years ago, FitzHugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of simple dynamical models to unfold complex firing patterns. To date, in spite of the enormous progresses in qualitative and quantitative neural modeling, this phase portrait has remained a core picture of neuronal excitability. Yet, a major difference between the neurophysiology of 1961 and of 2011 is the recognition of the prominent role of calcium channels in firing mechanisms. We show that including this extra current in Hodgkin-Huxley dynamics leads to a revision of FitzHugh-Nagumo phase portrait that affects in a fundamental way the reduced modeling of neural excitability. The revisited model considerably enlarges the modeling power of the original one. In particular, it captures essential electrophysiological signatures that otherwise require non-physiological alteration or considerable complexification of the classical model. As a basic illustration, the new model is shown to highlight a core dynamical mechanism by which calcium channels control the two distinct firing modes of thalamocortical neurons. Rooted in the seminal work of Hodgkin and Huxley The Hodgkin-Huxley model and all reduced models derived from it The inclusion of calcium currents in the HH model before its planar reduction leads to a novel phase portrait that seems to have been disregarded to date. Mimicking earlier classical work, we perform a normal form reduction of the global HH reduced planar model. The mathematical normal form reduction is fundamentally different in the classical and new phase portrait because it involves a different bifurcation. The classical fold bifurcation is replaced by a transcritical bifurcation.The results of these mathematical analysis lead to a novel simple model that further enriches the modeling power of the popular hybrid model of Izhikevich. A single parameter in the new model controls the neuron calcium conductance. In low calcium conductance mode, the model captures the standard behavior of earlier models. But in high calcium conductance mode, the same model captures the electrophysiological signature of neurons with a high density of calcium channels, in agreement with many experimental observations. For this reason, the novel reduced model is particularly relevant to understand the firing mechanisms of neurons that switch from a low calcium-conductance mode to a high calcium-conductance mode. Because thalamocortical (TC) neurons provide a prominent example of such neurons, they are chosen as a proof of concept of the present paper, the benefits of which should extend to a much broader class of neurons.Calcium channels participate in the spiking pattern by providing, together with sodium channels, a source of depolarizing currents. In contrast to sodium channels whose gating kinetics are fast, calcium channels activate on a slower time-scale, similar to that of potassium channels A illustrates the spiking behavior induced by the action of an external square current A left), the presence of the calcium current is characterized by a triple electrophysiological signature (see A right):HH model A left, ture see A right:spike latency: the spike train (burst) is delayed with respect to the onset of the stimulationplateau oscillations: the spike train oscillations occur at a more depolarized potential than the hyperpolarized stateafter-depolarization potential (ADP): the burst terminates with a small depolarizationThis electrophysiological signature is typical of neurons with sufficiently strong calcium currents. See for instance: spike latency B (left). This phase portrait and the associated reduced dynamics are well studied in the literature (see A left).Following the standard reduction of HH model ions cf. A left.B (right). In the resting mode, the hyperpolarized state is a stable node lying on the far left of the phase-plane. The In the presence of the calcium current, the phase-portrait changes drastically, as shown in A (right) in the presence of the calcium current  explains the presence of plateau oscillations. As the stimulation is turned off the spiking limit cycle disappears in a saddle-homoclinic bifurcation (see below), and the resting state recovers its attractivity.When the stimulation is turned on, the see also . In addiThe presence of the lower branch of the alue of  , left. I nature) , right. i.e. high-voltage, state).A bifurcation diagram with ng modes . We use llations  (for larB(top right). The node and the saddle coalesce in a supercritical fold bifurcation at The power of mathematical analysis of the reduced planar model (1) is fully revealed by introducing two further simplifications.Time-scale separation: we exploit that the voltage dynamics are much faster than the recovery dynamics by assuming a small ratio B(right) for . This particular phase portrait contains a transcritical bifurcation (red circle) which is the key ruler of excitability. This is because, as illustrated in B for A, these hyberbolic objects degenerate to a critical manifold that coincides with the voltage nullcline near the transcritical bifurcation. It is in that sense that the X-shape of the voltage nullcline completely organizes the excitability, i.e. the transition from resting state to limit cycle.The critical current The persistence of the manifold where B left  is familiar to most neuroscientists since the work of FitzHugh. Likewise, the conceptual sketch of the transcritical bifurcation will be familiar to all readers of basic textbooks in bifurcation analysis. For instance, the sketch is found in B, the missing connection is brought to life by calcium channels. Their particular kinetics renders the transcritical bifurcation of HH model physiological in the presence of a high-conductance calcium current.It is of interest to realize that the addition of the calcium current in the HH model unmasks a global view of its phase portrait that has been disregarded to date for its lack of physiological relevance. The singular limit of planar reduced models reveals that the excitability properties of spiking neurons are essentially determined by a local normal form of bifurcation of the resting equilibrium. This property is at the core of mathematical analysis of neuronal excitability  spike down-stroke, is able to reproduce the behavior of a large family of neurons with a high degree of fidelity The proposed transcritical hybrid model is highly reminiscent of the hybrid model of Izhikevich, but it consideraly enlarges its modeling power by including two features of importance:the transcritical normal form the new parameter The parameter ullcline ; likewisullcline ; likewisA) or a plateau burst spiking (B) in vitro and in vivo recordings Thalamocortical (TC) relay neurons are the input to sensory cortices. These neurons exhibit two distinct firing patterns: either a continuous regular spiking A or a p spiking B [27]–[Because TC relay cells have an important role in physiology and pathology, they have been widely studied in the literature. In particular, their electrophysiological activity has been successfully reproduced in various conductance-based models A, black solid curves). The accompanying transcritical singularity appears at non-physiological values of the gating variable A, light gray solid curve), the fixed point looses its stability to a limit cycle that relaxes to the resting state when the stimulation is switched off. Likewise, no plateau is observed and the repolarization phase is strictly monotonic (no ADP can be exhibited).B, upper-left, black gray solid curves). When a depolarizing current step is applied, this branch falls below the B, upper-left, light gray solid curves). In order to generate the first spike, the state travels the narrow region between the two nullclines, resulting in a pronounced latency. This latency relies on the small level of The situation is very different when the neuron is initially hyperpolarized, because T-type calcium channels are then deinactivated, critically affecting the phase portrait: a lower B, upper-right). At the end of the burst, the system converges toward the hyperpolarized state, being attracted first by the upper part of the B, lower-left). Note the presence of a transcritical bifurcation in the phase portrait for a particular value of T-type calcium channel inactivation . Finally, when the stimulation is relaxed, the neuron recovers its initial hyperpolarized state and the inactivation of T-type calcium channels is released .These high frequency plateau oscillations continue until the T-type calcium channel inactivation dominates , both in the low and high calcium conductance modes. As discussed above, the small calcium conductance mode is obtained by choosing a positive A, left). When the hyperpolarized state belongs to the upper branch of the A, left). Furthermore, the relaxation toward the hyperpolarized state is necessarily monotone (i.e. no ADP), as stressed in B, left. , left, tpossible A, left.B, left).At the generation of the first spike, is fired B, left.A, right). In order to generate the first spike, the state travels in the narrow region between the two nullclines, resulting in a pronounced latency. Furthermore, the relative position of the hyperpolarized state (lower branch) with respect to (hybrid) spiking cycle (upper branch) clearly explains the generation mechanism of plateau oscillations, as in the reduced TC model. These high frequency plateau oscillations (burst) continue until A, right).When  , right, ullcline A, righturcation A, rightB, right). A finer and more physiological modeling of the intracellular calcium dynamics could reproduce in vitro recordings with a higher degree of fidelity. Note that the ADP trajectories are slightly different in the reduced conductance based and the transcritical hybrid models. This minor difference is due to a lower time-scale separation in the reduced TC model for low values of At the end of the burst, the system converges toward the hyperpolarized state following the left branch of the  calcium B, rightNeuron environment, based on the configuration files freely available at http://cns.iaf.cnrs-gif.fr/alain_demos.html) and a fold hybrid model In order to further verify the physiological consistence of the transcritical model, we compare its behavior with the simulated step response of another quantitative one compartment model There is a striking similarity between the projection of the trajectories between both quantitative models and the phase portrait of the second-order transcritical model. In both cases, the ADP is generated during a decrease of the activation variable, and plateau oscillations are exhibited far from the resting state. Moreover, the spike latency is a robust property of the transcritical model because the trajectory must visit the neighborhood of both the nullclines set rule . This unFor a neuron model to be biologically relevant, it should be robust to exogenous disturbances . The firing pattern, in particular, should remain unchanged. The difference in robustness is explained by the different ADP generation mechanisms, as illustrated in om below . The absConversely, ADP generation in the transcritical hybrid model is robustly governed by the attractor The ADP apex is the most excitable part of the trajectory. A physiologically relevant external stimulation can easily generate a spike during this small period, whereas the neuron is barely excitable in the preceding and following periods. This suggests a major role for this ADP in the modulation of external inputs by neuron endogenous rhythm. This excitability can be finely tuned through variations of channel kinetics. For instance, the presence of a “buckle” in the ADP trajectory of the reduced conductance based model in The inclusion of calcium channels in Hodgkin-Huxley model has a dramatic impact on its mathematical reduction: the firing mechanisms are governed by the local normal form of a transcritical rather than fold bifurcation. It results in the presence of a new voltage nullcline branch in the phase portrait, which lies below the classical inverted N-shaped one. When the calcium channel density is high, neuronal excitability is governed by this lower branch, which accounts for the physiological signature of these currents: spike latency, plateau oscillations and afterdepolarization potential.Interestingly, it is not the phase portrait of the reduced HH model that is affected by calcium, but only the subregion of the plane where it is physiologically relevant. Indeed, the transcritical singularity is the core mechanism of the classical Hodgkin-Huxley model as well, and the well known fold bifurcation derives from it. As a consequence, the classical FitzHugh Nagumo phase portrait is a particular  view of the more complete picture studied in the present paper. This complete picture and its dynamical consequences are brought to live by any slowly activating depolarizing current, calcium currents being the most representative. Note that it may be generated by a slowly activating persistent sodium current as well.The proposed planar model is distinctively different from earlier reduced models that include calcium channels in that its slow variable  assuming an instantaneous sodium activation, The complete TC neuron model reads , apart from the 200-compartment model, which was simulated with the NEURON software environment. . The numerical bifurcation analysis has been obtained with XPP environment.  and with calcium current (right).(EPS)Click here for additional data file.Figure S2Nullcline intersections in the reduced model (5) with calcium current for different values of the calcium conductance. The (EPS)Click here for additional data file.Figure S3Comparison of the step response and phase-portrait in the transcritical hybrid model, a quantitative one compartment model of TC neuron , a 200-compartment model of TC neurons  and the fold hybrid model  in large calcium conductance mode. In the phase-portrait of the hybrid models, (EPS)Click here for additional data file.Figure S4Time-courses of the calcium activation gating variable  The black line shows the d = 1.5 n3. The calcium activation gating variable is well approximated as a static function of the potassium activation gating variable in this region of interest.(EPS)Click here for additional data file.Figure S5Comparison of the complete and reduced conductance based models of TC relay cells, in tonic and bursting modes. Black lines show the complete model step responses in both modes. Red lines show the reduced model step responses in both modes. The complete and reduced models has similar kinetics in our range of interest. Note that the reduced model shows an artifact at the apex of the ADP in bursting mode.(EPS)Click here for additional data file.


Virtual reality (VR) is not commonly used in clinical rehabilitation, and commercial VR gaming systems may have mixed effects in patients with stroke. Therefore, we developed RehabMaster™, a task-specific interactive game-based VR system for post-stroke rehabilitation of the upper extremities, and assessed its usability and clinical efficacy.A participatory design and usability tests were carried out for development of RehabMaster with representative user groups. Two clinical trials were then performed. The first was an observational study in which seven patients with chronic stroke received 30 minutes of RehabMaster intervention per day for two weeks. The second was a randomised controlled trial of 16 patients with acute or subacute stroke who received 10 sessions of conventional occupational therapy only (OT-only group) or conventional occupational therapy plus 20 minutes of RehabMaster intervention (RehabMaster + OT group). The Fugl-Meyer Assessment score (FMA), modified Barthel Index (MBI), adverse effects, and drop-out rate were recorded.P = .03) and MBI (P = .04) across evaluation times. The second trial revealed that the addition of RehabMaster intervention tended to enhance the improvement in the FMA (P = .07) but did not affect the improvement in the MBI. One patient with chronic stroke left the trial, and no adverse effects were reported.The requirements of a VR system for stroke rehabilitation were established and incorporated into RehabMaster. The reported advantages from the usability tests were improved attention, the immersive flow experience, and individualised intervention. The first clinical trial showed that the RehabMaster intervention improved the FMA (The RehabMaster is a feasible and safe VR system for enhancing upper extremity function in patients with stroke. Upper extremity (UE) functional deficits after stroke have received a great deal of attention because they are strongly related to the quality of life of stroke survivors,2. Such However, it remains challenging to implement high-intensity repetitive training in the real clinical setting because the necessary resources may be limited. In addiVR is a computer-generated interactive simulation that imitates reality and provides users with an artificial environment including sensory information similar to real-world experience. It began to be employed specifically for rehabilitation about 15 years ago. PreviouTM-based system could be used as a rehabilitation tool in children with cerebral palsy and acquired muscle atrophy, and Ustinova et al.[meaningful play[challenges for scaffolding skill improvement[Recently, VR-based off-the-shelf commercial gaming systems, e.g. the Nintendo® Wii and Playstation EyeToy, have exhibited general physical effects when used in UE rehabilitation of stroke patients-12. Somea et al. demonstra et al.. To addrgful play and chalprovement,18. The We developed a task-specific game-based VR rehabilitation system, called the RehabMaster™, which provides a rich interactive rehabilitation setting; this system is depicted in Figureuser management module that contains information about each participant , an assessment module that tracks the patient’s rehabilitation progress, a rehabilitation training program that asks the patients to imitate some of the 40 different motions performed by an avatar, and rehabilitation games that provide an engaging form of rehabilitation exercise using gaming concepts.The main user interface for the RehabMaster comprises four elements: a Underwater fire, Goalkeeper, Bug hunter, and Rollercoaster  hands on the display to catch a football (or bug). The speed, location, trajectory of the football, and pattern in which the bugs appeared could be controlled by the occupational therapist. Finally, the Rollercoaster game was designed to increase the control, speed, and accuracy of UE and trunk movements. The game consists of imitating the postures displayed by the system, which simulate those adopted during a rollercoaster ride. That is, the patient is instructed to position his or her arms and trunk as shown by the avatar. The difficulty of the game is defined by the difficulty level of the postures and the speed of the rollercoaster. The patient’s actual movements during the entire gaming session are recorded and played back at the end of the session in order to provide feedback.In detail, the assessment consists of evaluations of range of motion and movement evaluation with reference to such commonly used instruments as the Fugl-Meyer Assessment, Action Rr Figure. UnderwaPrior to each RehabMaster intervention session, a physiatrist outlined the customised training and gaming tasks, which were then further modified by the occupational therapists during the actual training sessions.Three representative user groups, i.e. stroke patients, occupational therapists, and physiatrists, were involved in designing the RehabMaster. Each stroke patient’s routine tasks and procedures were evaluated individually and focus group studies were held once a week for around half a year. Feedback and suggestions were categorised and incorporated into the development process.A usability study was then carried out in the same types of representative users. The main purpose of the usability test was to assess the RehabMaster from the perspective of each stakeholder group. The patients with stroke performed 20-minute RehabMaster sessions at regular intervals twice a week for two weeks under the supervision of occupational therapists and physiatrists. All three representative user groups completed a self-report-style five-point Likert questionnaire at the end of the RehabMaster intervention. The questionnaire was different for each user group in order to accommodate their different concerns.As patient’s engagement is a key benefit of the RehabMaster intervention, the primary user group, i.e. the patients with stroke, assessed the ability of the RehabMaster to provide strong motivation, enjoyment, and consequently, an optimal flow experience. The secPatients with hemiparetic upper limb dysfunction secondary to first-ever stroke were recruited from two rehabilitation hospitals and the neurorehabilitation unit of a university hospital. All of them exhibited mild-to-severe deficits of the paretic upper extremity , and the level of statistical significance was We used several focus-group studies and interviews with the representative user groups  to establish the key design elements of an interactive VR rehabilitation system Table. Those kThe advantages reported by each stakeholder group after initial testing of the RehabMaster can be summarised as follows: improved attention and an immersive flow experience for the patients with stroke; ability to follow the prescription and efficiently manage the intervention programs for the occupational therapists; and ability to administer effective individualised intervention for the physiatrists.To see if RehabMaster afforded the stroke patients a desirable level of rehabilitation, we conducted a usability test in 20 patients with stroke and collected their responses as to whether they were highly engaged and considered the user experience pleasant, so that they were further motivated to take an active part in the RehabMaster intervention. TableTo see if the challenges presented by the RehabMaster were of a level with which the patients with stroke could cope, we collected the field responses from three occupational therapists who employed the RehabMaster. All of them strongly agreed (5 out of 5) with both statements, ‘I was able to improvise the rehabilitation program using the RehabMaster in accordance with the actual performance of each patient’ and ‘I was easily able to manage the prescription using RehabMaster’. One of the occupational therapists stated that ‘Many patients were very satisfied with the adjustable difficulty of the rehabilitation program and were pleased to see that they were able to imitate the movements of the avatar on the screen correctly’.To evaluate whether the game play constituted meaningful rehabilitation for the stroke patients, a semi-structured interview was administered to seven physiatrists who had employed the RehabMaster in patients with stroke. Most of the physiatrists strongly agreed that they had been able to design an effective rehabilitation program using the RehabMaster (six of seven physiatrists agreed that the RehabMaster seemed to be an effective method for administering OT) that could be tailored to the current state of each patient . Further, all participating physiatrists felt that the RehabMaster was able to provide a record of relevant information concerning a patient’s rehabilitation progress. However, these statements were not amenable to any statistical evaluation because of the ceiling effect.Only one patient with chronic stroke discontinued the trial because of a personal issue unrelated to any adverse effect of the RehabMaster. None of the patients who participated in the RehabMaster intervention suffered from any adverse effect that would be likely to result from VR, such as dizziness or disorientation.P = .18) and between T5 and T10 (P = .25); although the FMA score then decreased by 0.67 between T10 to T25, this change was also not statistically significant (P = .61). Conversely, the MBI increased during all three intervals, T0 to T5 (P = .68), T5 to T10 (P = .68), and T10 to T25 (P = .44), indicating a steady and persistent effect over time.In the first clinical experiment in patients with chronic stroke, six patients  completed two weeks of intervention and a follow-up evaluation during the fourth week. FigureP = .07; TableP = .16; TableThe second clinical experiment was performed in patients with acute or subacute stroke. None of the baseline characteristics differed significantly between the two groups Table. The impThe RehabMaster, a task-specific interactive game-based VR rehabilitation system, was developed to facilitate motor recovery after stroke. Our study included the first randomised controlled trial to assess the effects of a depth sensor-based VR gaming system on functional outcomes in patients with stroke; in addition, the testing of usability and clinical efficacy for upper extremity function in patients with stroke yielded favourable responses.We employed a novel type of VR system, the RehabMaster, an OpenNI™-compliant depth sensor-based rehabilitation system that responds to the participant’s motions without the need for a controller or any attachments. This allows participants who have not regained sufficient hand power to use a game controller to interact with the system. In contrast, previous VR gaming systems have required the participants to be able to grasp a controller or to wear gloves and coloured patches on their upper extremities,29,30. OThe FMA and MBI improved during the RehabMaster intervention in patients with chronic stroke. As none of the patients with chronic stroke in our clinical trials was receiving any other kind of therapy at the time of recruitment, these improvements appeared to indicate that the RehabMaster intervention was effective in patients with chronic stroke. In addition, the randomised controlled trial in patients with acute/subacute stroke also showed that RehabMaster + OT elicited greater improvement in FMA or MBI compared to OT-only groups, although this trend did not reach statistical significance. Therefore, RehabMaster might be a useful novel tool for rehabilitation of the upper extremities in patients with stroke. We speculated that these functional improvements stemmed from the greater focus of the RehabMaster intervention on the affected upper extremity. As seenAs the observation of action contributes to motor recovery by mirror motor neuron activation, the patiMoreover, the usability test indicated that the stroke patients received a ‘flow experience’. We suspect that this flow experience results from a combination of intrinsic motivation and complete immersion in the intervention. This maAnother main concern in the real-world rehabilitation setting is how to treat patients safely. This may be an important advantage of the RehabMaster when considered as a legitimate rehabilitation intervention to be adopted by a medical institution or medical insurance system. The complete absence of adverse effects during the intervention suggests that the RehabMaster is a safe rehabilitation tool. As the intervention is performed in the sitting position, there is a lower risk of falling, which is a common hazard in patients with stroke and the elderly. The supervision by occupational therapists also increases the level of safety.Our study has several limitations that must be considered when interpreting the results. We first tested the RehabMaster in patients with chronic stroke, as most previous studies using VR were performed in such patients. Once itAnother limitation is that the assessments in the clinical experiments were restricted to functional outcomes (FMA and MBI) and a few motor-related factors (range of motion and strength). The present study would have been strengthened by the use of measures based on the participants’ natural environments, which might have indicated whether the effects of VR rehabilitation are generalisable to the real world. In addition, we did not appraise other factors, such as cognitive function, motivation, and depression, which are commonly examined in patients with stroke. Finally, we evaluated the satisfaction or enjoyment in the usability test but did not compare it between the groups in the clinical trial.Therefore, various aspects of the effects of the RehabMaster should be confirmed in future comparative studies with the comparison between groups receiving the same total amount of intervention time in order to eliminate any confounding by this factor. Finally, we plan in the future to evaluate the kinematic data recorded in real time during the RehabMaster intervention.™, and presented the results of a usability test and clinical trials. The RehabMaster proved to be a feasible and safe rehabilitation tool to enhance motor function among patients in various stages of recovery after stroke. It also encouraged the patient’s skill development, improved immersion, and motivated further rehabilitation by providing meaningful play, optimal challenge, and a flow experience.The present study described the development of a task-specific, interactive, game-based VR rehabilitation system, called the RehabMasterUE: Upper extremity; VR: Virtual reality; FMA: Fugl-Meyer Assessment; MBI: Modified Barthel Index; OT: Occupational therapy; EXCITE: Extremity constraint induced therapy evaluation.The authors declare that they have no conflicts of interest with respect to the authorship and/or publication of this article.JHS contributed to the conception and design of the RehabMaster, data acquisition, analysis and interpretation of data, and drafting of the manuscript. HR designed and analysed the usability test, provided technical and material support, and revised the present manuscript. SHJ designed the study, completed the statistical analysis, interpreted data, obtained funding, and critically reviewed the manuscript for important intellectual content. All authors read and approved the final manuscript.


ART) for extracting informative intermediate level visual features during the learning process, which also makes this model stable against the destruction of previously learned information while learning new information. Such a mechanism has been suggested to be embedded within known laminar microcircuits of the cerebral cortex. To reveal the strength of the proposed visual feature learning mechanism, we show that when we use this mechanism in the training process of a well-known biologically motivated object recognition model (the HMAX model), it performs better than the HMAX model in face/non-face classification tasks. Furthermore, we demonstrate that our proposed mechanism is capable of following similar trends in performance as humans in a psychophysical experiment using a face versus non-face rapid categorization task.The brain mechanism of extracting visual features for recognizing various objects has consistently been a controversial issue in computational models of object recognition. To extract visual features, we introduce a new, biologically motivated model for facial categorization, which is an extension of the Hubel and Wiesel simple-to-complex cell hierarchy. To address the synaptic stability versus plasticity dilemma, we apply the Adaptive Resonance Theory ( V1, continues over the extrastriate visual areas, V2 and V4, to the inferotemporal cortex (IT) and then to prefrontal cortex (PFC) HMAX model, which is based on the classical simple-to-complex cells model by Hubel & Wiesel. The HMAX model attempts to quantitatively resemble visual processing in the ventral visual pathway. A significant degree of invariance to scale and translation are some characteristic of the HMAX model. Furthermore, this model outperforms some state-of-the-art computer vision systems in applications such as object recognition and scene understanding Although real-world object recognition is one of the most complex and difficult of tasks, it is robustly and rapidly performed by the primate visual system. The visual system can easily adapt itself to real-world object recognition, where objects are presented in cluttered backgrounds that can vary in illumination, viewpoint, position and scale. Neurobiological evidence demonstrates that object recognition in the visual cortex is mediated by the ventral visual pathway LAMINART and SMART models, does not fall into the category of object recognition models. These models try to implement details of circuits and layers of the visual cortex. The LAMINART model LGN), and the V1 and V2 areas of the visual cortex. The Synchronous Matching ART model (SMART) Another group of models, including the LAMINART and SMART models attempt to show how the ART mechanism may be embedded in the cerebral cortex and attempt to propose a solution to the stability-plasticity dilemma observed in the cerebral cortex.Solving the stability-plasticity dilemma together with achieving memory stability in an evolving input environment is considered as a fundamental goal. The stability-plasticity dilemma is related to how our brain learns enormous amounts of information and can remain stable against forgetting previously learned material. The PFC) to extract informative visual features. Their method uses an optimization algorithm to select informative patches from a large pool of patches STDP) learning rule in an architecture on the basis of the Serre et al. model. Although this is a biologically-plausible approach, it is not stable due to the forgetting of previously learned information. Furthermore, each input is required to be presented several hundred times, whereas usually our brain is able to learn scenes at first glance.Extracting biologically plausible visual features that can mimic visual processing in the primate brain has been a challenging goal for computational models of object recognition. For example, learning in the model proposed by Serre et al. involves a simple mechanism of selecting random patches from the training images HMAX model), that is based on the hierarchical model of Hubel and Wiesel. The HMAX model is a feedforward network of four layers of alternating simple and complex units . The HMAX model with our proposed feature learning mechanism, inspired by the ART system, suggests a mechanism for solving the problem of stability versus plasticity in object recognition systems. Both the ART mechanism, which is employed in our model, and the STDP rule are biologically plausible. However, the ART mechanism enables our model to learn informative features in a single presentation of the input image. This is in contrast to the STDP rule, which requires hundred times of image presentation.In this paper, by using a stable visual feature learning mechanism, we propose a model which incorporates one of the well-know object recognition models  while suppresses the activities of irrelevant cells in the non-matched portion (the surround) (One theory that addresses the stability-plasticity dilemma is the  pathway . The ARTurround) . The topV1 and V2, which demonstrates that the visual cortex not only has feed-forward connections , but also possesses feedback connections, which is thought to have a key role in the stabilization of both development and learning within multiple cortical areas including the V1 and V2 areas ART matching in the visual cortex.As previously described, top-down connections exist in the early layers of the visual cortex such as LAMINART model LGN, V1, and V2 areas in the visual cortex. The Synchronous Matching ART model LAMINART model and implements interactions between laminar cortical circuits and higher-order thalamic nuclei. The LAMINART and SMART models are based on the adaptive resonance theory, which suggests a solution for the stability-plasticity dilemma.How the visual cortex automatically develops circuits and can still remain stable is a major question for which several models have been developed, including the V1 area receive direct inputs from the LGN and also from an on-center, off-surround network V2 circuitry also demonstrates a similar pattern to that of V1, but on a larger spatial scale.Simple cells in the HMAX model, and uses a stable learning method, inspired by the ART mechanism, to solve the stability-plasticity dilemma. The proposed model is generally based on NeocognitronHMAX  proposed by Riesenhuber and Poggio HMAX model in facial categorization tasks . Furthermore, to solve the stability-plasticity dilemma, we used the ART mechanism to extract more informative features of intermediate complexity, and this consequently provides a more realistic biologically inspired model.We propose a biologically motivated object recognition model which incorporates the S) units correspond to the simple cells in the visual cortex, which combine their inputs according to a bell-shaped tuning function to increase selectivity. Complex (C) units correspond to the complex cells in the visual cortex, which show tolerance to a shift in the position and size of the stimuli within their receptive field. These units pool their inputs through a maximum (max) operation 1S units take the form of the Gabor function V1. The 1S units include 16 filter sizes, spanning a range of sizes from 7×7 to 37×37 pixels in steps of two pixels, and four orientations . Totally, there are 64 different 1S units. These 64 filters are then divided into eight bands where each band contains two adjacent filter sizes The proposed model has a hierarchical structure and intends to emulate rapid object categorization in the visual cortex. The model consists of alternating simple and complex units: simple  and compared them with a vigilance parameter to determine the matching degree between the prototypes and the input image. These selected units are shown separately at the 2C level  for classification.http://www.vision.caltech.edu/Image_Data sets/Caltech101  datasets HMAX model in face/non-face categorization tasks. The images were converted to grayscale values and rescaled to be 140 pixels in height. The width was rescaled accordingly to preserve the aspect ratio. In all experiments, the following procedure was performed:We designed various experiments to compare the proposed model with the 2-level features:Extracting C Our stable fast learning algorithm was performed on the training dataset to extract a set of 2C-level features.Training the SVM classifier: All of the training set images were applied one by one to the model, and 2C responses were calculated. The 2C responses with labels (1 for positive and -1 for negative examples) were used to train a classifier . It is noteworthy that layers are fixed at this stage, and learning in lower levels of the system is stopped.Evaluating the extracted features: The performance of the classifier on the test set was evaluated. The overall procedure was repeated 20 times, and the average performance and standard deviation (SD) were reported.2C-level features and training the SVM classifier, and the second subset was used for evaluating the classification performance.In the first experiment, we evaluated the performance of the proposed model in a face/non-face classification task. For this purpose, the datasets were randomly divided into two subsets with equal number of images, i.e., for the training and test sets. The first subset was used for extracting In the next experiment, we studied the effect of the number of training samples on the classification performance. The model was evaluated using different numbers of positive training samples . We used 50 negative training samples, 50 positive test samples, and 50 negative test samples. To demonstrate that our model extracts informative and as few intermediate-level features as possible from the images, we measured the classification performance across different number of extracted features.For further studies regarding the biologically plausibility of the proposed model, we compared the performance of the face/non-face categorization task in humans with the model.HMAX), and human subjects. First, the results of the proposed model are compared against the HMAX model in three different experiments. As a follow-up to these results, we compare the performance of the human subjects in a psychophysical test (rapid categorization of faces versus non-faces) with the performance of our proposed model.In the next two sections, we report the results of different comparisons made between the proposed model, another biologically plausible model  exceeding an observation from the second population (Y) is not equal to 0.05. Rejection of the null hypothesis is at the 0.05 significance level. The reported p-values using these methods were 0.009 and 0.059, respectively.In the first experiment, the face and background datasets were randomly divided into two separate sets of equal sizes. Next, we applied our stable fast-learning algorithm to the training dataset to extract the most informative intermediate-level features from the images. The vigilance parameter in the model was determined such that the most informative features with the highest possible performance were extracted. After this stage, the prototype learning was stopped, and the obtained features were applied in the face/non-face classification task. The classification performance of these features was then computed. In the classification stage, we used a linear 2C-level-features were extracted and subsequently used to train the classifier for the face/non-face classification task. We then implemented the benchmark model using the same number of features. To make the comparison more challenging for our proposed model, we also performed the benchmark model using 1,000 features. As shown in To study the potential effects of using a different number of training examples on the performance of the system, we selected 1, 3, 6, 15, 30, and 40 positive training samples. We used 50 negative training samples together with 50 positive and 50 negative test samples. The performances of the proposed model and the benchmark model using different number of training images are compared in HMAX model using different numbers of features. In this case, the parameters of the proposed model were set to extract a number of features, and these features were then used in the classification task. The datasets were randomly divided into two separate subsets of equal size (the training set and the test set). As shown in HAMX model using very few features in contrast to the HMAX model with randomly extracted features. This finding illustrates that our mechanism has extracted more informative features from the input images than did the standard HMAX model. With such a biologically plausible learning mechanism, we addressed the stability-plasticity dilemma and also solved the problem of extracting redundant features.In the next experiment, we compared the performance of the proposed model with the Moreover, the proposed model suggests a stable biologically plausible learning mechanism for extracting intermediate level visual features (for more information regarding the stability of the proposed model please refer to the stability of the proposed model section).We performed a psychophysical experiment for categorizing faces versus non-faces to compare the proposed model with human observers. For this purpose, we selected the Caltech face and background datasets as positive samples and distractors, respectively. In addition, we added various levels of salt and pepper noise to these images. The noisy images were shown to human subjects using a computer screen in a random order. The human subjects were instructed to respond as fast and as accurately as possible to determine whether the image contains a human face or a distractor by pressing the ‘‘YES’’ or ‘‘NO’’ key. The results obtained from the human subjects were compared with those obtained using the proposed model on the same image set.SOA) in this test was a fixed SOA of 30 ms  of 10 ms). The experiment was performed in a dark room. The participants were seated 0.5 m away from the computer screen (Intel core 2 duo processor (2.66 GHz), 4 GB RAM). We used the MATLAB software with the psychophysics toolbox ms, and this was followed by the presentation of a random noise mask. The mask appeared after a fixed ISI for duration of 80 ms (which corresponded to an SOA of 30 ms). Please refer to We used 16 human subjects in this experiment (18–36 years old) with an equal number of male and female subjects. The Stimulus Onset Asynchrony . These five sets correspond to various levels of noise  and the proposed model in the face/non-face classification task is shown in d′, which combines both the hit and false-alarm rates of each observer into a single standardized score. The responses of both the proposed model and the human subjects were roughly similar. The proposed model was capable of following similar trends in responses as humans in this experiment. The performance of the HMAX model for this experiment is also demonstrated in A comparison between the average performance of the human observers . For more clarification, imagine the model has learned some features from an input image, then, by adding a new image to the model, it may require learning new features or may not. Therefore, the model learns new features only when the previously learned features are insufficient for describing the new input image. As a result, the average minimum distance decreases in each stage because the model does not forget previously learned features and only extracts new required features. If the model was not stable, it would extract non-required features in every stage which would result in an increase to the average minimum distance. As observed, the proposed model exhibited steeper downward slopes in most cases unlike the HMAX model, which mostly shows upward trends. In We also probed the relationship between the performance and stability of the model by running an experiment for all of the patch sizes separately using a different number of training images. In this experiment, the classification performance was measured for each patch size. As shown in V1), and then continues to the extrastriate visual areas (V2 and V4), which are next followed by the inferotemporal cortex (IT) and the prefrontal cortex (PFC).The most widely accepted biological evidence shows that visual processing in the brain exhibits a hierarchical structure, which starts from the primary visual cortex (IT and PFC1C and 2S which is a simple mechanism of indiscriminately selecting patches from the training images STDP learning rule to extract intermediate-complexity visual features STDP rule, which causes forgetting previously learned information, this approach is unstable. Furthermore, for the sake of learning by this rule, each input must be presented several hundred times, whereas our brain is able to learn scenes at a glance. In contrast to the STDP rule, we proposed another approach for the learning of intermediate-level features, which is not only a biologically plausible method but also addresses the problems of instability, the need for repeated image presentation, and the issue of the redundancy of the extracted visual features in the HMAX model. Whereas other models do not illustrate how the visual cortex is stable against the destruction of previously learned information over time, our model applied the ART mechanism, which solves the stability-plasticity dilemma. We showed that the proposed model is capable of learning new information without losing previously learned information. We also demonstrated that there is a direct relationship between the stability of the model and its performance. This means that if the model is trained with more stable patches, it performs better. This mechanism was implemented in a hierarchical feed-forward model of the visual cortex and used in face categorization. We also compared our results with the HMAX model in face/non-face categorization tasks, and the obtained results showed that it performed better than the HMAX model in ‘different number of training images’ experiment although not significant. However, our model significantly outperformed the HMAX model in ‘different numbers of features’ experiment, particularly with fewer numbers of features. Performed experiments using different numbers of features showed that our model extracts as fewest as possible features from the training images, which are the most informative features; and yet achieves an acceptable performance. In contrast, the HMAX model requires extracting more features to reach the similar performance. This showed that features learned by the proposed mechanism are highly informative which makes them capable of giving much better representation of the input images in higher processing layers. This thus results in improving the classification performance while using fewer numbers of features, as shown in It is thought that plasticity and learning probably occurs at all stages, in particular, at the level of the To determine to what extent the proposed model can mimic the performance of human subjects, we performed the same face/non-face categorization task on humans in a rapid categorization psychophysical test. Our results showed a trend using the model that approximately resembles the trend observed in human subjects.


There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1) Does this new stochastic formulation produce similar results to the agent-based version? (2) Can these methods be used interchangeably? (3) Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm. In previous work, three case studies using established mathematical models of immune interactions with early-stage cancer were considered in order to investigate the additional contribution of ABMS to ODE models simulation In this work we apply the Gillespie algorithm To the best of our knowledge, current literature regarding the direct comparison of the Gillespie algorithm and ABMS is scarce. We want therefore to answer research questions such as: (1) Does this new stochastic formulation produce similar results to ABMS? (2) Can these methods be used interchangeably for our case studies? (3) Does the stochastic model implemented using the Gillespie algorithm also find the extra patterns revealed by the ABMS? We aim to establish a methodological discussion regarding the benefits of each approach for biological simulation, rather than provide further insights into the biological aspects of the problems studied. We therefore intend to compare the dynamics of each approach and observe the outcomes produced over time. We hope that this study provides further insights into the potential usability and contribution of ABMS to systems simulation.The case studies used for our comparison regard models with different population sizes, varying modelling effort and model complexity. We hope that by tackling problems with different characteristics, a more robust analysis of our experiments is performed. The features of each case study are shown in The first case study considered is based on an ODE model involving interactions between generic tumour and effector cells. The second case study adds to the previous model the influence of the IL-2 cytokine molecules in the immune responses. The third case study comprises a model of interactions between effector cells, tumour cells, and IL-2 and TGF-The remainder of this paper is organized as follows. The next section introduces the literature review comparing stochastic ODE models and ABMS for different simulation domains. First, we show general work that has been carried out in areas such as economics and operations research, and then we focus on research concerned with the comparison for immunological problems. Finally, we discuss gaps in the literature regarding cancer research. In the following section we introduce our Gillespie and agent-based modelling development processes and the methods used for conducting the experimentation. Subsequently we present our case studies, comparison results and discussions. In the final section we draw our overall conclusions and outline future research opportunities.in-silico approaches used in early-stage cancer research include computational simulation of compartmental models, individual-based models and rule-based models. Compartmental models adopt an aggregate representation of the elements in the system. They include deterministic methods such as ordinary differential equation (ODE) models, system dynamics (SD) models and partial differential equation (PDE) models. These models have been largely employed in the study of dynamics between cancer cells and tumour cells Current The differences between deterministic compartmental models and individual-based models are well known in operations research As mentioned previously, there are few studies that compare the Gillespie algorithm with ABMS. Most of these studies regard research in economic models and immunology. To the best of our knowledge there is no literature regarding the direct comparison of these methods to early-stage interactions between the immune system and tumour cells. This section describes relevant researches in several areas, which provided further insights into the gaps in the current literature and the research questions addressed in this paper.et al.is an objective obstacle for quantitative modeling and needs further studying.There are a few attempts of re-conceptualizing agent-based models into simpler stochastic models of complex systems in economics. For instance, Daniunas et al.Stracquadanio et al.Karkutla In our work we further study the differences between the approaches outcomes and investigate whether under different problem characteristics for early-stage cancer we still obtain similar results. In the next section we introduce the methodology used to conduct our investigations.This section introduces the research methodology used for the development of our simulation models and for the experimentation performed in the following sections. As mentioned previously, our investigations concern the use of three cases to answer research questions regarding the application of the Gillespie algorithm and ABMS interchangeably for early-stage cancer models. For each case study, there is a well established ODE model from the literature and its correspondent agent-based model, that we previously developed in The Gillespie algorithm is implemented by the direct conversion of the original mathematical equations into reactions and simulating them under the COPASI http://anytips.cs.nott.ac.uk/wiki/index.php/Resources).ABMS is a modelling and simulation technique that employs autonomous agents that interact with each other. The agents' behaviour is described by rules that determines how they learn, interact and adapt. The overall system behaviour is given by the agents individual dynamics as well as their interactions. Our agent-based models are implemented using the As the Gillespie and ABMS are both stochastic simulation methods, we ran five hundred replications for each case study and calculated the mean values for the outputs. For all approaches, the rates  employed were the same as those established by the mathematical model.In addition, in order to investigate any statically significant differences between the ABMS and Gillespie techniques for the case studies, we implement a mixed effect model. This is a type of regression that considers both fixed and random effects. This method accounts for correlation caused by repeating the measure over time . The mixed effect analysis was implemented in the programming language R using the package NLME As a mixed effect model requires finding parameters for a regression model, it is not suitable when considering the whole time period. This is because in cases 2 and 3 the tumour dynamics has a damping oscillation and the function describing this dynamics is unknown (see pages 11 and 14). Instead, the sequence of local maxima and minima are used. It can been seen that these are converging and any statistical deviation between these sequences for the different simulation techniques indicate differences between the output of the techniques. If the simulations from the ABMS and the Gillespie technique come from the same distribution, then there would be no statistical difference between the maxima and minima over time. Therefore, we investigate two null hypotheses. The first is that the function of local maxima is the same for the ABMS and the Gillespie algorithm simulations. And the second is that the function of local minima is the same for the ABMS and the Gillespie algorithm simulations. We use a 1% significance level.There is no standard technique for estimating the required sample size for non-linear mixed effect models for a defined power when the measure of effect is known The first case considers tumour cells growth and their interactions with general immune effector cells, as defined in Mathematically, the interactions between tumour cells and immune effector cells are defined as follows The Kuznetsov model In the agent-based model there are two classes of agents, the tumor cells and the effector cells, as described in Similarly to the experiments from Results for Scenario 1 appear similar for the three approaches, although the effector cells curve from the ABMS show more variability. To evaluate whether the results are significantly different for the two simulation methods, we apply a mixed effect model. The null hypothesis is that there is no significant difference between the methods (and therefore there will be no significant fixed effect for the method type). We use a 1% significance level. We are testing the similarity for the population of effector cells.The effector cells follow a dynamic similar to 1/x for the time between 1 and 100:We apply a mixed-effect model where the simulation run is considered to have a random effect on the parameter We believe that the variability observed in the ABMS and Gillespie curves, given their stochasticity, also influenced the statistical test results. The number of effector cells for all simulations follow a similar pattern, although the similarity hypothesis was rejected. This variability of Gillespie and ABMS is very evident with regards to the effector cells population as the size of the populations involved in the first scenario is relatively small, which increases the impacts of stochasticity in the outcomes.Results for scenario 2 are shown in the second row of For scenarios 3 and 4, shown in third and fourth rows of In the fourth scenario, although effector cells appear to decay in a similar trend for both approaches, the results for tumour cells vary largely. In the ODE simulation, the numbers of effector cells reached a value close to zero after twenty days and then increased to a value smaller than one. For the ABMS simulation, however, these cells reached zero and never increased again. For the Gillespie model results, a similar pattern as that from the ABMS model occurs, although there seems to be less variance in the outcome curve. In addition, the mean numbers for tumour cells for the Gillespie approach seem smaller that those observed in the ABMS.An outcome comparison between an ABMS and a Gillespie algorithm model was performed for case study 1. We considered an ODE model of tumour cells growth and their interactions with general immune effector cells as the baseline for results validation. Four scenarios considering small population numbers were investigated and results from ABMS and Gillespie were different for both populations for all scenarios. Furthermore, both approaches differed largely from the original mathematical outcomes. These results indicate that, for this case study, the stochasticity applied to the population as a whole when compared to that applied to the individual has a higher impact given the small population sizes. The result analysis also reveals that conceptualizing the stochastic approaches from the mathematical equations does not always produce statistically similar outputs.Case two regards the interactions between tumour cells, effector cells and the cytokine IL-2. It extends the previous study as it considers IL-2 as molecules mediating the immune response towards tumour cells. These molecules interfere in the proliferation of effector cells, which occurs proportionally to the number of tumour cells in the system. For this case, there are two types of treatment, the injection of effector cells or the addition of cytokines.The mathematical model used in case 2 is obtained from As described in The experiment is conducted assuming the same parameters as those of the mathematical model . For theThe results obtained are shown in The local maxima sequence follows a second order polynomial function of the form:The local minima sequence follows a second order polynomial function of the form:For the mixed-effect model, we consider Interactions between tumour cells, effector cells and the cytokine IL-2 were considered to investigate the potential differences and similarities of ABMS and Gillespie algorithm outcomes. Statistical comparison between the Gillespie and the ABMS results show a significant difference in the outcomes. Compared to the original ODE model used as validation, ABMS displayed a little more variability in the results, whereas the Gillespie algorithm followed mostly the same patterns as those produced by the ODEs for all populations in the simulation. As for these simulations a bigger number of individuals was required, it was also observed that, regarding the use of computational resources, ABMS was far more time- and memory-consuming than the Gillespie approach.et al. in Case study three comprises interactions between tumour cells and immune effector cells, as well as the immune-stimulatory and suppressive cytokines IL-2 and TGF-effector cells are assumed to be recruited to a tumour site as a direct result of the presence of tumour cells. The parameter c in experimental evidence suggests that TGF-. This switch in TGF-The mathematical model is described by the differential equations below:The agents established for the ABMS represent the effector cells, tumour cells, IL-2 and TGF-The ABMS model rates corresponding to the mathematical model are given in The experiment is conducted assuming the same parameters as those defined for the mathematical model . SimilarThe mean results of 500 runs for the Gillespie algorithm and the ABMS contrasted with the ODE model are shown in The use of ABS modelling has therefore led to the discovery of additional “rare” patterns, which we would have not been able to derive by using analytical methods or the dynamic Monte Carlo method, i.e. the Gillespie algorithm. These “extreme cases” found by ABMS suggest that there might be circumstances where the tumour cells are completely eliminated by the immune system, without the need of any cancer therapies.We believe that ABMS when compared to Gillespie produces extra patterns because of the agents individual behaviour and their interactions. While ODEs and the Gillespie algorithm always use the same values for the parameters over the entire population aggregate, ABMS rates vary with time and number of individuals. Each agent is likely to have distinct numbers for their probabilities and therefore have its own memory of past events . The agents individual interactions, which give raise to the overall behaviour of the system, are also influenced by the scenario determined by the random numbers used. By running the ABMS multiple times with different sets of random numbers, the outcomes vary according to these sets and the emerging interactions of the agents also produce the rare outcome patterns.For further statistical comparison of the results that follow the same pattern of behaviour for ABMS and Gillespie, a mixed-effect model is used. In 236 of the 500 ABMS simulations the tumour cell population dies out early in time. The remaining 264 ABMS simulations  is compared with the 500 Gillespie simulations by a non-linear mixed effect model.The local maxima sequence follows a second order polynomial function of the form:The local minima sequence follows a second order polynomial function of the form:For the mixed-effect model we considered Regarding the TGF-The third case study simulations investigated interactions between effector cells, tumour cells and two types of cytokines, namely IL-2 and TGF-In this work, we employed three case studies to investigate circumstances where we can use ABMS and the Gillespie algorithm interchangeably. We aimed at reproducing the variability embedded in the ABMS systems to the mathematical formulation and verify whether results resemble. Current literature regarding the comparison of the Gillespie algorithm and ABMS is scarce and we wanted therefore to answer the questions: (1) Does the Gillespie algorithm produce similar results to ABMS? (2) Can these two methods be used interchangeably for our case studies? (3) Does the Gillespie algorithm also find the extra patterns revealed by the ABMS in the third case study? The case studies investigated regarded models with different characteristics, such as population sizes, modelling effort demanded and model complexity.The first case study involved interactions with general immune effector cells and tumour cells. Four different scenarios regarding distinct sets of parameters were investigated and in the first three scenarios treatment was included. ABMS and Gillespie produced different results for all scenarios. It appears that two major characteristics of this model influenced the differences obtained: (1) The small quantities of individuals considered in the simulations  that significantly increased the variability of both stochastic approaches; and (2) the stochasticity of the Gillespie algorithm is applied to the aggregates, while in the ABMS there is individual variability.Case study 2 referred to the investigation of a scenario containing interactions between effector cells, cytokines IL-2 and tumour cells. For this case the Gillespie and ABMS approaches produced similar outcome curves, which also matched the pattern of behaviour of the mathematical model used for validation. As populations' sizes had a magnitude of Case study 3 includes the influence of the cytokine TGF-In response to our research questions, we conclude that regarding the interchangeable use of Gillespie and ABMS, population size has a positive impact on result similarity. This means that bigger populations tend to result in close simulation output patterns. However, the stochasticity of both approaches and the memory present in the ABMS produce outcome differences which are statistically significant, although visually the outcomes look similar. Finally, the emergent behaviour of ABMS can contribute additional insight (extra patterns), which was not obtained by the aggregate stochasticity present in Gillespie, given its incapacity of retaining memory of past events for their elements.Currently, it is acknowledged that the necessary levels of detail present a system's conceptual model might require the adoption of multiple simulation approaches, under different scales of abstraction, in order to produce satisfactory outcomes. For certain cases, multi-scale and multi-modelling solutions represent the only possible manner to properly implement a set of requirements, even though these practices are generally more resource-intensive.Several models, especially those regarding biological systems, encompass elements with distinct time and length scales coupled together. Multiple layers involving different levels of granularity need therefore to be considered. Phenomena such as cellular gradient-based chemotaxis and nutrient-dependent cell cycles are better implemented by employing numerical simulation . On the other hand, cellular random movement, memory, adaptability, explicit representation of space, heterogeneous populations, etc. represent suitable concepts to be represented within an agent-based approach. There are also subsets of characteristics in a system that can be implemented under more than one approach.Despite of the well-known domains of applicability of each simulation technique, other factors such as the real-world data availability, the computing resources, the required granularity of the model, the time available to develop the simulation, the research questions and the expertise of the simulation developer also influence the decision on the paradigms to be adopted. By understanding the strengths and weaknesses of each approach, it is possible decide on which route to take and also the implications of this decision to the final outcome. We hope that our study results can assist simulation researchers on this debate.