Population-response model for vibrotactile spatial summation

A computational model based on previous physiological and psychophysical data is presented for the human Pacinian (P) psychophysical channel. The model can predict the probability of detection in simple psychophysical tasks, and hence psychometric functions and thresholds. The model simulates stimulating variable and fixed glabrous skin sites with different-sized contactors and includes spatial variation of monkey P-fiber sensitivities. Therefore, it is especially suitable for studying spatial summation, i.e. the improvement of threshold with increasing contactor area. Selective contributions of neural integration (n.i.) and probability summation (p.s.) are also incorporated into the model. Model predictions are compared to psychophysical results of Gescheider et al. (). The performance of the model regarding the effects of contactor size is very good. In addition to predicting approximately 3?dB improvement of thresholds when the contactor area is doubled, the model also reveals nonlinear contributions of p.s. and n.i. Furthermore, the model asserts that thresholds are largely governed by neural integration when small contactors are used. These and other findings discussed in the article show that the presented model is a helpful tool for formulating testable hypotheses. Although the model can also simulate some temporal summation effects, simulation results do not conform well to previous data on temporal response properties. Thus, the model needs to be refined in that respect.     

Population-response model for vibrotactile spatial summation

A computational model based on previous physiological and psychophysical data is presented for the human Pacinian (P) psychophysical channel. The model can predict the probability of detection in simple psychophysical tasks, and hence psychometric functions and thresholds. The model simulates stimulating variable and fixed glabrous skin sites with different-sized contactors and includes spatial variation of monkey P-fiber sensitivities. Therefore, it is especially suitable for studying spatial summation, i.e. the improvement of threshold with increasing contactor area. Selective contributions of neural integration (n.i.) and probability summation (p.s.) are also incorporated into the model. Model predictions are compared to psychophysical results of Gescheider et al. (2005). The performance of the model regarding the effects of contactor size is very good. In addition to predicting approximately 3 dB improvement of thresholds when the contactor area is doubled, the model also reveals nonlinear contributions of p.s. and n.i. Furthermore, the model asserts that thresholds are largely governed by neural integration when small contactors are used. These and other findings discussed in the article show that the presented model is a helpful tool for formulating testable hypotheses. Although the model can also simulate some temporal summation effects, simulation results do not conform well to previous data on temporal response properties. Thus, the model needs to be refined in that respect.     

Modelling spatial vision at the threshold level.

Some available single- and multiple-channel models are reviewed. Multichannel models are generalized and tested against threshold data on various stimulus sets. Without using the explicit assumption of spatial probability summation, simple multichannel models are shown to provide good simultaneous predictions of threshold curves of sinewave gratings and other gratings. They fail in predicting threshold curves of disk-shaped stimuli. If global or local spatial probability summation within channels is incorporated into the models, correctly shaped threshold curves of disks can be predicted. However, the predicted curves appear still too low if compared to measured curves. The same holds for noise gratings. Possible extensions of the models, based on local summation between channel responses and/or models consisting of initial isotropic channels (retina) followed by anisotropic channels (cortex), are discussed.     

Evidence for different nonlinear summation schemes for lines and gratings at threshold

Within a wide class of multichannel models of the visual system it is suggested that spatial distributions of luminance are processed by the independent activation of grating detectors, or spatial frequency channels. Probability summation is often described in terms of Quick's nonlinear pooling model [Quick RF (1974) Kybernetik 16:65–67]. Using this model, we find evidence for the existence of different kinds of nonlinear summation at threshold; for compound gratings with well-separated spatial frequency components, the threshold functions indicate nonlinear summation which is not compatible with probability summation, while for line patterns well separated in the spatial domain the probability summation rule proves compatible with the data. Received: 24 June 1998 / Accepted in revised form: 16 March 1999     

Spatial summation in the tactile sensory system: probability summation and neural integration

Psychophysical thresholds for the detection of a 300-Hz burst of vibration applied to the thenar eminence were measured for stimuli applied to the skin through 1.5 cm2 and through 0.05 cm2 contactors. Thresholds were approximately 13 dB lower when the area of the contactor was 1.5 cm2 than when it was 0.05 cm2. The difference between the thresholds measured with the large and small contactors was significantly reduced when only the lowest thresholds obtained in the testing sessions were considered. This result supports the hypothesis that one component of spatial summation in the P channel is probability summation. In addition, threshold measurements within a session were less variable when measured with the 1.5 cm2 contactor. We conclude that spatial summation in the P channel is a joint function of two processes that occur as the areal extent of the stimulus increases: probability summation in which the probability of exceeding the psychophysical detection threshold increases as the number of receptors of varying sensitivities increases, and neural integration in which neural activity originating from separate receptors is combined within the central nervous system rendering the channel more sensitive to the stimulus.     

The effect of summation of contraction on acceleration signals in human skeletal muscle

The purpose of this study was to determine the effects of summation of contraction on acceleration signals in human skeletal muscle. The torque parameters of dorsiflexion and acceleration signals in the tibialis anterior muscle were measured during evoked isometric contractions. In an examination of two-pulse trains with different inter-pulse intervals, the torque and accelerometer responses to inter-pulse intervals of 10–100 ms were recorded. In an investigation of the effects of different numbers of stimuli, the torque and accelerometer responses to 1–8 pulses with a constant inter-pulse interval of 10 ms were recorded. The present study found that there was a difference in acceleration amplitude between the single-pulse and two-pulse trains with an inter-pulse interval of 10 ms but not two-pulse trains with an inter-pulse interval of 20 ms or more. In the investigation of different numbers of stimuli, we found a similar MMG amplitude across 2–8 pulses. Moreover, we observed that the maximal time to the peak acceleration signal was ～27 ms. In a comparison of torque parameters with acceleration signals, the present study clearly shows that acceleration amplitude is poorly correlated to changes in force parameters when the inter-pulse interval or the number of stimuli are increased. These results suggest that the absence of associated changes in acceleration peak is due to the long interval for the subsequent pulses relative to the time at which acceleration peak is achieved (～27 ms). These findings will provide useful information concerning the method for assessing summation of contraction with an accelerometer.     

Parallel and serial processes in the human oculomotor system: bimodal integration and express saccades

Saccadic reaction times (SRTs) were analyzed in the context of stochastic models of information processing (e.g., Townsend and Ashby 1983) to reveal the processing architecture(s) underlying integrative interactions between visual and auditory inputs and the mechanisms of express saccades. The results support the following conclusions. Bimodal (visual + auditory) targets are processed in parallel, and facilitate SRT to an extent that exceeds levels attainable by probability summation. This strongly implies neural summation between elements responding to spatially aligned visual and auditory inputs in the human oculomotor system. Second, express saccades are produced within a separable processing stage that is organized in series with that responsible for intersensory integration. A model is developed that implements this combination of parallel and serial processing. The activity in parallel input channels is summed within a sensory stage which is organized in series with a pre-motor and motor stage. The time course of each subprocess is considered a random variable, and different experimental manipulations can selectively influence different stages. Parallels between the model and physiological data are explored.     

Area summation in human vision at and above detection threshold

The initial image-processing stages of visual cortex are well suited to a local (patchwise) analysis of the viewed scene. But the world's structures extend over space as textures and surfaces, suggesting the need for spatial integration. Most models of contrast vision fall shy of this process because (i) the weak area summation at detection threshold is attributed to probability summation (PS) and (ii) there is little or no advantage of area well above threshold. Both of these views are challenged here. First, it is shown that results at threshold are consistent with linear summation of contrast following retinal inhomogeneity, spatial filtering, nonlinear contrast transduction and multiple sources of additive Gaussian noise. We suggest that the suprathreshold loss of the area advantage in previous studies is due to a concomitant increase in suppression from the pedestal. To overcome this confound, a novel stimulus class is designed where: (i) the observer operates on a constant retinal area, (ii) the target area is controlled within this summation field, and (iii) the pedestal is fixed in size. Using this arrangement, substantial summation is found along the entire masking function, including the region of facilitation. Our analysis shows that PS and uncertainty cannot account for the results, and that suprathreshold summation of contrast extends over at least seven target cycles of grating.     

Mechanisms for spatial integration in visual detection: a model based on lateral interactions

Recent studies of visual detection show a configuration dependent weak improvement of thresholds with the number of targets, which corresponds to a fourth-root power law. We find this result to be inconsistent with probability summation models, and account for it by a model of 'physiological' integration that is based on excitatory lateral interactions in the visual cortex. The model explains several phenomena which are confirmed by the experimental data, such as the absence of spatial and temporal uncertainty effects, temporal summation curves, and facilitation by a pedestal in 2AFC tasks. The summation exponents are dependent on the strength of the lateral interactions, and on the distance and orientation relationship between the elements.     

Interaction of spatial and temporal summation in the warmth sense.

Two experiments explored the interaction of spatial and temporal summation in the perception of radiant heat. The first experiment showed that the absolute threshold for detecting two brief (0.1 sec) pulses of heat, one presented to each side of the forehead, is lower than the threshold for detecting a single pulse, even when the two pulses are separated in time by as muchas 0l75 sec. The second experiment showed that a single, 4-sec pulse of heat presented to one side of the forehead feels no warmer than two successive, 2-sec pulses, one to each side. Spatial and temporal summation appear to take place at least partly in the central nervous system.     

A Two-Pulse Cellular Stimulation Test Elucidates Variability and Mechanisms in Signaling Pathways

Mammalian cells respond in a variable manner when provided with physiological pulses of ligand, such as low concentrations of acetylcholine present for just tens of seconds or TNFα for just tens of minutes. For a two-pulse stimulation, some cells respond to both pulses, some do not respond, and yet others respond to only one or the other pulse. Are these different response patterns the result of the small number of ligands being able to only stochastically activate the pathway at random times or an output pattern from a deterministic algorithm responding differently to different stimulation intervals? If the response is deterministic in nature, what parameters determine whether a response is generated or skipped? To answer these questions, we developed a two-pulse test that utilizes different rest periods between stimulation pulses. This “rest-period test” revealed that cells skip responses predictably as the rest period is shortened. By combining these experimental results with a mathematical model of the pathway, we further obtained mechanistic insight into potential sources of response variability. Our analysis indicates that in both intracellular calcium and NFκB signaling, response variability is consistent with extrinsic noise (cell-to-cell variability in protein levels), a short-term memory of stimulation, and high Hill coefficient processes. Furthermore, these results support recent works that have emphasized the role of deterministic processes for explaining apparently stochastic cellular response variability and indicate that even weak stimulations likely guide mammalian cells to appropriate fates rather than leaving outcomes to chance. We envision that the rest-period test can be applied to other signaling pathways to extract mechanistic insight.     

Comparison of hyperalgesia induced by capsaicin injection and controlled heat injury: effect on temporal summation

The relationship between induction of central sensitization and facilitation of temporal summation to repetitive stimulation is still unclear. The aim of this study was to investigate temporal summation before and after the induction of secondary hyperalgesia by two different experimental methods: capsaicin injection and controlled heat injury. The effect of each injury model was assessed on a separate day with an interval of at least 5 days. Twelve healthy volunteers participated. Each experiment was performed using electrical, radiant heat, mechanical impact, and punctuate stimuli consecutively. The pain threshold (PT) to a single stimulus and the summation threshold to five repetitive stimuli for electrical (2?Hz) and radiant heat (0.83?Hz) were assessed within the secondary hyperalgesic area. The degree of temporal summation for stimulus intensities of 0.8, 1.0, and 1.2 times the baseline pain thresholds were evaluated by the increase in visual analogue scale (VAS) scores from the first to the fifth stimulus of the train. Further, the degrees of temporal summation were assessed for mechanical impact and punctuate stimuli within the primary and secondary hyperalgesic areas. The contra-lateral forearm served as control (no injury). The pain threshold and the summation threshold to electrical and heat stimuli decreased significantly within the secondary hyperalgesic area after the injury induced by both heat injury or capsaicin injection. However, there was no temporal summation for heat and electrical stimuli in either model. In contrast, for the mechanical impact and punctuate mechanical stimuli the degree of temporal summation was significantly facilitated in the secondary hyperalgesic areas compared with the baseline and the control arm in both models. In the primary hyperalgesic area, the degree of temporal summation was facilitated to mechanical impact and punctuate stimuli but only following the capsaicin injection. In conclusion, the temporal summation mechanism for mechanical stimuli was facilitated in the secondary hyperalgesic area.     

Comparison of hyperalgesia induced by capsaicin injection and controlled heat injury: effect on temporal summation

The relationship between induction of central sensitization and facilitation of temporal summation to repetitive stimulation is still unclear. The aim of this study was to investigate temporal summation before and after the induction of secondary hyperalgesia by two different experimental methods: capsaicin injection and controlled heat injury. The effect of each injury model was assessed on a separate day with an interval of at least 5 days. Twelve healthy volunteers participated. Each experiment was performed using electrical, radiant heat, mechanical impact, and punctuate stimuli consecutively. The pain threshold (PT) to a single stimulus and the summation threshold to five repetitive stimuli for electrical (2 Hz) and radiant heat (0.83 Hz) were assessed within the secondary hyperalgesic area. The degree of temporal summation for stimulus intensities of 0.8, 1.0, and 1.2 times the baseline pain thresholds were evaluated by the increase in visual analogue scale (VAS) scores from the first to the fifth stimulus of the train. Further, the degrees of temporal summation were assessed for mechanical impact and punctuate stimuli within the primary and secondary hyperalgesic areas. The contra-lateral forearm served as control (no injury). The pain threshold and the summation threshold to electrical and heat stimuli decreased significantly within the secondary hyperalgesic area after the injury induced by both heat injury or capsaicin injection. However, there was no temporal summation for heat and electrical stimuli in either model. In contrast, for the mechanical impact and punctuate mechanical stimuli the degree of temporal summation was significantly facilitated in the secondary hyperalgesic areas compared with the baseline and the control arm in both models. In the primary hyperalgesic area, the degree of temporal summation was facilitated to mechanical impact and punctuate stimuli but only following the capsaicin injection. In conclusion, the temporal summation mechanism for mechanical stimuli was facilitated in the secondary hyperalgesic area.     

Detecting gustatory-olfactory flavor mixtures: models of probability summation

Odorants and flavorants typically contain many components. It is generally easier to detect multicomponent stimuli than to detect a single component, through either neural integration or probability summation (PS) (or both). PS assumes that the sensory effects of 2 (or more) stimulus components (e.g., gustatory and olfactory components of a flavorant) are detected in statistically independent channels, that each channel makes a separate decision whether a component is detected, and that the behavioral response depends solely on the separate decisions. Models of PS traditionally assume high thresholds for detecting each component, noise being irrelevant. The core assumptions may be adapted, however, to signal-detection theory, where noise limits detection. The present article derives predictions of high-threshold and signal-detection models of independent-decision PS in detecting gustatory-olfactory flavorants, comparing predictions in yes/no and 2-alternative forced-choice tasks using blocked and intermixed stimulus designs. The models also extend to measures of response times to suprathreshold flavorants. Predictions derived from high-threshold and signal-detection models differ markedly. Available empirical evidence on gustatory-olfactory flavor detection suggests that neither the high-threshold nor the signal-detection versions of PS can readily account for the results, which likely reflect neural integration in the flavor system.     

Space-variant visual processing: spatially limited visual channels

A multichannel model incorporating visual inhomogeneity is presented in this paper. The parameters that describe inhomogeneity have been experimentally obtained both at threshold and in several suprathreshold conditions. At threshold, probability summation is taken into account in order to determine the spatial extent of visual channels from experimental data showing an asymptotic increase in sensitivity with increasing grating area. At suprathreshold contrast, the region where luminance variations at several scales are visible has also been found. The results support a spatially limited multichannel model of early visual processing and set out a basis for studying perceptual phenomena from the viewpoint of linear space-variant visual processing.     

Arithmetic of subthreshold synaptic summation in a model CA1 pyramidal cell

The rules of synaptic integration in pyramidal cells remain obscure, in part due to conflicting interpretations of existing experimental data. To clarify issues, we developed a CA1 pyramidal cell model calibrated with a broad spectrum of in vitro data. Using simultaneous dendritic and somatic recordings and combining results for two different response measures (peak versus mean EPSP), two different stimulus formats (single shock versus 50 Hz trains), and two different spatial integration conditions (within versus between-branch summation), we found that the cell's subthreshold responses to paired inputs are best described as a sum of nonlinear subunit responses, where the subunits correspond to different dendritic branches. In addition to suggesting a new type of experiment and providing testable predictions, our model shows how conclusions regarding synaptic arithmetic can be influenced by an array of seemingly innocuous experimental design choices.     

Modelling the distributions and spatial coincidence of bluetongue vectors Culicoides imicola and the Culicoides obsoletus group throughout the Iberian peninsula

Data obtained by a Spanish national surveillance programme in 2005 were used to develop climatic models for predictions of the distribution of the bluetongue virus (BTV) vectors Culicoides imicola Kieffer (Diptera: Ceratopogonidae) and the Culicoides obsoletus group Meigen throughout the Iberian peninsula. Models were generated using logistic regression to predict the probability of species occurrence at an 8-km spatial resolution. Predictor variables included the annual mean values and seasonalities of a remotely sensed normalized difference vegetation index (NDVI), a sun index, interpolated precipitation and temperature. Using an information-theoretic paradigm based on Akaike's criterion, a set of best models accounting for 95% of model selection certainty were selected and used to generate an average predictive model for each vector. The predictive performances (i.e. the discrimination capacity and calibration) of the average models were evaluated by both internal and external validation. External validation was achieved by comparing average model predictions with surveillance programme data obtained in 2004 and 2006. The discriminatory capacity of both models was found to be reasonably high. The estimated areas under the receiver operating characteristic (ROC) curve (AUC) were 0.78 and 0.70 for the C. imicola and C. obsoletus group models, respectively, in external validation, and 0.81 and 0.75, respectively, in internal validation. The predictions of both models were in close agreement with the observed distribution patterns of both vectors. Both models, however, showed a systematic bias in their predicted probability of occurrence: observed occurrence was systematically overestimated for C. imicola and underestimated for the C. obsoletus group. Average models were used to determine the areas of spatial coincidence of the two vectors. Although their spatial distributions were highly complementary, areas of spatial coincidence were identified, mainly in Portugal and in the southwest of peninsular Spain. In a hypothetical scenario in which both Culicoides members had similar vectorial capacity for a BTV strain, these areas should be considered of special epidemiological concern because any epizootic event could be intensified by consecutive vector activity developed for both species during the year; consequently, the probability of BTV spreading to remaining areas occupied by both vectors might also be higher.     

A validated model of in vivo electric field distribution in tissues for electrochemotherapy and for DNA electrotransfer for gene therapy

Permeabilising electric pulses can be advantageously used for DNA electrotransfer in vivo for gene therapy, as well as for drug delivery. In both cases, it is essential to know the electric field distribution in the tissues: the targeted tissue must be submitted to electric field intensities above the reversible permeabilisation threshold (to actually permeabilise it) and below the irreversible permeabilisation threshold (to avoid toxic effects of the electric pulses). A three-dimensional finite element model was built. Needle electrodes of different diameters were modelled by applying appropriate boundary conditions in corresponding grid points of the model. The observations resulting from the numerical calculations, like the electric field distribution dependence on the diameter of the electrodes, were confirmed in appropriate experiments in rabbit liver tissue. The agreement between numerical predictions and experimental observations validated our model. Then it was possible to make the first precise determination of the magnitude of the electric field intensity for reversible (362+/-21 V/cm, mean +/- S.D.) and for irreversible (637+/-43 V/cm) permeabilisation thresholds of rabbit liver tissue in vivo. Therefore the maximum of induced transmembrane potential difference in a single cell of the rabbit liver tissue can be estimated to be 394+/-75 and 694+/-136 mV, respectively, for reversible and irreversible electroporation threshold. These results carry important practical implications.     

Life table analysis of leaf fall in Tasmanian cool temperate forests

The annual leaf fall of three species of cool temperate forest trees was examined for two different consecutive seasons at two localities in Tasmania. The reverse summation of the sequential fall of leaves throughout an annual cycle provided a population biomass that was amenable to life table analyses. Rates of leaf fall were compared between species at different times, and were related to temperature. The threshold temperature for leaf fall to commence was approximately 11–12°C. Estimates of the probability of leaves remaining on trees at different times through the cycle were also obtained.     

Electrophysiological and psychophysical quantification of temporal summation in the human nociceptive system

Animal experiments have shown that the nociceptive reflex can be used as an indicator of central temporal integration in the nociceptive system. The aim of the present study on humans was to investigate whether the nociceptive reflex, evoked by repetitive strong electrical sural nerve stimuli, increased when summation was reported by the volunteers. The reflexes were recorded from the biceps femoris and rectus femoris muscles in eight volunteers following a series of stimulations at 0.1, 1, 2, and 3 Hz. Each series consisted of five consecutive stimuli. Using 0.1- and 1-Hz stimulation, the reflex was not facilitated in the course of the five consecutive stimuli. Following 2- and 3-Hz stimulation, the reflex size (root mean square amplitude) increased significantly during the course of the fifth stimulus. This reflex facilitation was followed by a significant increase (summation) in the pain magnitude when compared with 1- and 0.1-Hz stimulation. Furthermore, the threshold for psychophysical summation could be determined. This threshold (stimulus intensity) decreased when the stimulus frequency (1–5 Hz) of the five consecutive stimuli was increased. The nociceptive reflex and the psychophysical summation threshold might be used to clarify and quantify aspects of temporal summation within the human nociceptive system.