Summation

About: Summation is a research topic. Over the lifetime, 954 publications have been published within this topic receiving 45593 citations. The topic is also known as: summation & sum of a sequence.

The contrast sensitivity of retinal ganglion cells of the cat.

Abstract: 1. Spatial summation within cat retinal receptive fields was studied by recording from optic-tract fibres the responses of ganglion cells to grating patterns whose luminance perpendicular to the bars varied sinusoidally about the mean level. 2. Summation over the receptive fields of some cells (X-cells) was found to be approximately linear, while for other cells (Y-cells) summation was very non-linear. 3. The mean discharge frequency of Y-cells (unlike that of X-cells) was greatly increased when grating patterns drifted across their receptive fields. 4. In twenty-one X-cells the relation between the contrast and spatial frequency of drifting sinusoidal gratings which evoked the same small response was measured. In every case it was found that the reciprocal of this relation, the contrast sensitivity function, could be satisfactorily described by the difference of two Gaussian functions. 5. This finding supports the hypothesis that the sensitivities of the antagonistic centre and surround summating regions of ganglion cell receptive fields fall off as Gaussian functions of the distance from the field centre. 6. The way in which the sensitivity of an X-cell for a contrast-edge pattern varied with the distance of the edge from the receptive field centre was determined and found to be consistent with the cell's measured contrast sensitivity function. 7. Reducing the retinal illumination produced changes in the contrast sensitivity function of an X-cell which suggested that the diameters of the summating regions of the receptive field increased while the surround region became relatively ineffective.

Spatial summation in the receptive fields of simple cells in the cat's striate cortex.

Abstract: 1. We have examined the responses of simple cells in the cat's atriate cortex to visual patterns that were designed to reveal the extent to which these cells may be considered to sum light-evoked influences linearly across their receptive fields. We used one-dimensional luminance-modulated bars and grating as stimuli; their orientation was always the same as the preferred orientation of the neurone under study. The stimuli were presented on an oscilloscope screen by a digital computer, which also accumulated neuronal responses and controlled a randomized sequence of stimulus presentations. 2. The majority of simple cells respond to sinusoidal gratings that are moving or whose contrast is modulated in time in a manner consistent with the hypothesis that they have linear spatial summation. Their responses to moving gratings of all spatial frequencies are modulated in synchrony with the passage of the gratings' bars across their receptive fields, and they do not produce unmodulated responses even at the highest spatial frequencies. Many of these cells respond to temporally modulated stationary gratings simply by changing their response amplitude sinusoidally as the spatial phase of the grating the grating is varied. Nonetheless, their behavior appears to indicate linear spatial summation, since we show in an Appendix that the absence of a 'null' phase in a visual neurone need not indicate non-linear spatial summation, and further that a linear neurone lacking a 'null' phase should give responses of the form that we have observed in this type of simple cell. 3. A minority of simple cells appears to have significant non-linearities of spatial summation. These neurones respond to moving gratings of high spatial frequency with a partially or totally unmodulated elevation of firing rate. They have no 'null' phases when tested with stationary gratings, and reveal their non-linearity by giving responses to gratings of some spatial phases that are composed partly or wholly of even harmonics of the stimulus frequency ('on-off' responses). 4. We compared simple receptive fields with their sensitivity to sinusoidal gratings of different spatial frequencies. Qualitatively, the most sensitive subregions of simple cells' receptive fields are roughly the same width as the individual bars of the gratings to which they are most sensitive. Quantitatively, their receptive field profiles measured with thin stationary lines, agree well with predicted profiles derived by Fourier synthesis of their spatial frequency tuning curves.

Dendritic Hyperpolarization-Activated Currents Modify the Integrative Properties of Hippocampal CA1 Pyramidal Neurons

Abstract: Step hyperpolarizations evoked slowly activating, noninactivating, and slowly deactivating inward currents from membrane patches recorded in the cell-attached patch configuration from the soma and apical dendrites of hippocampal CA1 pyramidal neurons. The density of these hyperpolarization-activated currents (Ih) increased over sixfold from soma to distal dendrites. Activation curves demonstrate that a significant fraction of Ih channels is active near rest and that the range is hyperpolarized relatively more in the distal dendrites. Ih activation and deactivation kinetics are voltage-and temperature-dependent, with time constants of activation and deactivation decreasing with hyperpolarization and depolarization, respectively. Ih demonstrated a mixed Na+-K+ conductance and was sensitive to low concentrations of external CsCl. Dual whole-cell recordings revealed regional differences in input resistance (Rin) and membrane polarization rates (taumem) across the somatodendritic axis that are attributable to the spatial gradient of Ih channels. As a result of these membrane effects the propagation of subthreshold voltage transients is directionally specific. The elevated dendritic Ih density decreases EPSP amplitude and duration and reduces the time window over which temporal summation takes place. The backpropagation of action potentials into the dendritic arborization was impacted only slightly by dendritic Ih, with the most consistent effect being a decrease in dendritic action potential duration and an increase in afterhyperpolarization. Overall, Ih acts to dampen dendritic excitability, but its largest impact is on the subthreshold range of membrane potentials where the integration of inhibitory and excitatory synaptic inputs takes place.

Abnormal sensitization and temporal summation of second pain (wind-up) in patients with fibromyalgia syndrome

Abstract: Although individuals with fibromyalgia syndrome (FMS) consistently report wide-spread pain, clear evidence of structural abnormalities or other sources of chronic stimulation of pain afferents in the involved body areas is lacking. Without convincing evidence for peripheral tissue abnormalities in FMS patients, it seems likely that a central pathophysiological process is at least partly responsible for FMS, as is the case for many chronic pain conditions. Therefore, the present study sought to obtain psychophysical evidence for the possibility that input to central nociceptive pathways is abnormally processed in individuals with long standing FMS. In particular, temporal summation of pain (wind-up) was assessed, using series of repetitive thermal stimulation of the glabrous skin of the hands. Although wind-up was evoked both in control and FMS subjects, clear differences were observed. The perceived magnitude of the sensory response to the first stimulus within a series was greater for FMS subjects compared to controls, as was the amount of temporal summation within a series. Within series of stimuli, FMS subjects reported increases in sensory magnitude to painful levels for interstimulus intervals of 2-5 s, but pain was evoked infrequently at intervals greater than 2 s for control subjects. Following the last stimulus in a series, after-sensations were greater in magnitude, lasted longer and were more frequently painful in FMS subjects. These results have multiple implications for the general characterization of pain in FMS and for an understanding of the underlying pathophysiological basis.

Temporal and spatial summation in human vision at different background intensities

Abstract: The present experiments were undertaken as part of an investigation of the suggestion made by Rose (1942, 1948) and de Vries (1943) that human visual performance is limited by the inevitable fluctuations in the numbers of quanta absorbed in the retina. In a previous paper (Barlow, 1957) it was shown that this idea (modified by assuming that there is also a weak intrinsic source of noise) leads to theoretical curves which fit experimental determinations of increment threshold made with a short duration small area test stimulus superimposed upon a large uniform adapting field. It was also shown that big changes in the amount of temporal and spatial summation occur when the background intensity is changed, with the result that when thresholds are determined with a long duration large area test stimulus the experimental points deviate from the appropriate theoretical curve and tend to obey the Weber law instead. In following up this finding there were two objectives. The quantum fluctuation hypothesis predicts that the increment threshold intensity should be inversely proportional to the square root ofthe area and duration ofthe stimulus, and the first object was to find whether the occurrence of these laws fitted in with the hypothesis: the results show that the predicted laws of summation do hold over certain ranges, but when they hold the actual values of the thresholds are higher than the theory predicts. The second objective was to determine the parameters oc and r which were introduced in the previous paper; these are the area and time over which quanta absorbed from the background light are liable to be confused with those absorbed from a short duration small area stimulus light, and here the results obtained are disappointing, for one can only derive lower limits to these quantities. On the other hand, the results do show up the complicated interrelations between temporal and spatial summation and background intensity; tentative explanations of these effects, and of the failure to perform up to the quantal fluctuation limit, are put forward. 22 PHYSIO. CXLI