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PubMed1975

Convergence in a thermal afferent pathway in the rat.

1. In anaesthetized rats, unit activity was recorded in the afferent somatosensory pathway leading from the scrotum. Recording sites were in the dorsal horn near the entry zone of the scrotal nerve, in the ventrobasal complex of the thalamus and in the somatosensory (SI) cortex. During recording, the temperatures of the left and right sides of the scrotum were varied independently. 2. Almost all (64/67) the units in dorsal horn, thalamus and cortex responding specifically to scrotal temperature were equally affected by temperature changes on either side of the scrotum. The receptive fields of these units were bilateral and large, implying a massive convergence of fibres from thermoreceptors on to each central unit. In contrast, mechanosensitive units responded only to unilateral stimulation. 3. As a consequence of the convergence in the thermal pathway, the firing rate of each central unit was a function of an additive combination, often simply the sum, of the temperatures of the two sides of the scrotum. 4. The relationship between firing rate and the temperature of one side of the scrotum was sigmoid, the position, but not the shape, of the curve depending on the temperature at which the opposite side was maintained. An increase in the maintained temperature shifted the sigmoid response curve towards lower temperatures and vice versa. 5. The convergence which this pathway exhibits would be well suited to integration of the temperature of the scrotal skin, but not to spatial discrimination.

Action Potentials↗

PubMed2004

Speed and convergence properties of gradient algorithms for optimization of IMRT.

Gradient algorithms are the most commonly employed search methods in the routine optimization of IMRT plans. It is well known that local minima can exist for dose-volume-based and biology-based objective functions. The purpose of this paper is to compare the relative speed of different gradient algorithms, to investigate the strategies for accelerating the optimization process, to assess the validity of these strategies, and to study the convergence properties of these algorithms for dose-volume and biological objective functions. With these aims in mind, we implemented Newton's, conjugate gradient (CG), and the steepest decent (SD) algorithms for dose-volume- and EUD-based objective functions. Our implementation of Newton's algorithm approximates the second derivative matrix (Hessian) by its diagonal. The standard SD algorithm and the CG algorithm with "line minimization" were also implemented. In addition, we investigated the use of a variation of the CG algorithm, called the "scaled conjugate gradient" (SCG) algorithm. To accelerate the optimization process, we investigated the validity of the use of a "hybrid optimization" strategy, in which approximations to calculated dose distributions are used during most of the iterations. Published studies have indicated that getting trapped in local minima is not a significant problem. To investigate this issue further, we first obtained, by trial and error, and starting with uniform intensity distributions, the parameters of the dose-volume- or EUD-based objective functions which produced IMRT plans that satisfied the clinical requirements. Using the resulting optimized intensity distributions as the initial guess, we investigated the possibility of getting trapped in a local minimum. For most of the results presented, we used a lung cancer case. To illustrate the generality of our methods, the results for a prostate case are also presented. For both dose-volume and EUD based objective functions, Newton's method far outperforms other algorithms in terms of speed. The SCG algorithm, which avoids expensive "line minimization," can speed up the standard CG algorithm by at least a factor of 2. For the same initial conditions, all algorithms converge essentially to the same plan. However, we demonstrate that for any of the algorithms studied, starting with previously optimized intensity distributions as the initial guess but for different objective function parameters, the solution frequently gets trapped in local minima. We found that the initial intensity distribution obtained from IMRT optimization utilizing objective function parameters, which favor a specific anatomic structure, would lead to a local minimum corresponding to that structure. Our results indicate that from among the gradient algorithms tested, Newton's method appears to be the fastest by far. Different gradient algorithms have the same convergence properties for dose-volume- and EUD-based objective functions. The hybrid dose calculation strategy is valid and can significantly accelerate the optimization process. The degree of acceleration achieved depends on the type of optimization problem being addressed (e.g., IMRT optimization, intensity modulated beam configuration optimization, or objective function parameter optimization). Under special conditions, gradient algorithms will get trapped in local minima, and reoptimization, starting with the results of previous optimization, will lead to solutions that are generally not significantly different from the local minimum.

Algorithms↗

PubMed1994

Improving the convergence of iterative filtered backprojection algorithms.

Several authors have proposed variations of the iterative filtered backprojection (IFBP) reconstruction algorithms claiming fast initial convergence rates. We have found that these algorithms are trying to minimize an unusual squared-error criterion in a suboptimal way. As a result, existing IFBP algorithms are inefficient in the minimization of the criterion, and may become unstable at higher iteration numbers. We show that existing IFBP algorithms can be modified to use the steepest descent technique by simply optimizing the step size at each iteration. Further gains in convergence rates can be achieved with conjugate gradient IFBP algorithms derived from the same criterion. The steepest descent and conjugate gradient IFBP algorithms are guaranteed to converge, unlike some IFBP algorithms, and will do so in fewer iterations than existing IFBP algorithms.

Algorithms↗

PubMed1997

Analysis and convergence of the iterative convolution/superposition dose reconstruction technique for multiple treatment beams and tomotherapy.

An iterative convolution/superposition (C/S) algorithm has been created to reconstruct dose distributions in patients from exit dose measurements during a radiotherapy treatment. The method is based on an extended phantom which includes the patient CT representation and an electronic portal imaging device (EPID). The patient CT is assumed to be a true and rigid representation of the patient at the time of treatment. The C/S method computes the dose throughout the extended phantom which allows the exit dose to be predicted in the EPID. The process is then reversed to take the exit dose measurement and infer what the dose distribution must have been to produce the measured exit dose. The dose distribution is modeled without knowledge of the incident intensity distribution, and includes the effects of scatter in the computation. The iterative method begins by assuming that the exit primary energy fluence (PEF) is equal to the exit dose, the PEF is then backprojected through the extended phantom and superposed with the dose deposition kernel to determine a new prediction of the exit dose. The ratio of the computed PEF to exit dose is then multiplied by the measured exit dose image to produce a better representation of the exit PEF. Successive iterations then converge to the exit PEF image that would produce the measured exit dose image. Once convergence is established, the dose distribution is determined by backprojecting the exit PEF followed by superposition with the dose deposition kernel. The method is used to reconstruct the dose from a stimulated dynamic wedge and verified with film. Convergence and termination of the algorithm is then investigated with no noise and in the presence of noise. The method is then expanded to handle multiple treatment beams by separating the representation of the EPID from the patient or phantom representation in the computation process. Investigation of the effects of noise during the process of iterative dose reconstruction is necessary to understand the capabilities of the algorithm using exit dose images that may contain significant amounts of noise. The capability of the algorithm is evaluated for multiple field treatments to a cube phantom and a prostate patient CT representation in the presence of noise. The method is then used to simulate the dose reconstruction process for tomotherapy using 72 intensity-modulated fan beams. Dose reconstruction is shown to be capable of verifying the dose distributions in patients including multiple beams and dynamic collimation, provided the patient CT is known at the time of treatment.

Algorithms↗

PubMed2006

On phonetic convergence during conversational interaction.

Following research that found imitation in single-word shadowing, this study examines the degree to which interacting talkers increase similarity in phonetic repertoire during conversational interaction. Between-talker repetitions of the same lexical items produced in a conversational task were examined for phonetic convergence by asking a separate set of listeners to detect similarity in pronunciation across items in a perceptual task. In general, a listener judged a repeated item spoken by one talker in the task to be more similar to a sample production spoken by the talker's partner than corresponding pre- and postinteraction utterances. Both the role of a participant in the task and the sex of the pair of talkers affected the degree of convergence. These results suggest that talkers in conversational settings are susceptible to phonetic convergence, which can mark nonlinguistic functions in social discourse and can form the basis for phenomena such as accent change and dialect formation.

Adolescent↗

PubMed1998

Space geodetic observations of nazca-south america convergence across the central andes

Space geodetic data recorded rates and directions of motion across the convergent boundary zone between the oceanic Nazca and continental South American plates in Peru and Bolivia. Roughly half of the overall convergence, about 30 to 40 millimeters per year, accumulated on the locked plate interface and can be released in future earthquakes. About 10 to 15 millimeters per year of crustal shortening occurred inland at the sub-Andean foreland fold and thrust belt, indicating that the Andes are continuing to build. Little (5 to 10 millimeters per year) along-trench motion of coastal forearc slivers was observed, despite the oblique convergence.

Journal Article↗

PubMed2001

A fast and convergent stochastic MLP learning algorithm.

We propose a stochastic learning algorithm for multilayer perceptrons of linear-threshold function units, which theoretically converges with probability one and experimentally exhibits 100% convergence rate and remarkable speed on parity and classification problems with typical generalization accuracy. For learning the n bit parity function with n hidden units, the algorithm converged on all the trials we tested (n=2 to 12) after 5.8 x 4.1(n) presentations for 0.23 x 4.0(n-6) seconds on a 533MHz Alpha 21164A chip on average, which is five to ten times faster than Levenberg-Marquardt algorithm with restarts. For a medium size classification problem known as Thyroid in UCI repository, the algorithm is faster in speed and comparative in generalization accuracy than the standard backpropagation and Levenberg-Marquardt algorithms.

Algorithms↗

PubMed1994

A constructive algorithm that converges for real-valued input patterns.

A constructive algorithm is presented which combines the architecture of Cascade Correlation and the training of perceptron-like hidden units with the specific error-correcting roles of Upstart. Convergence to zero errors is proved for any consistent classification of real-valued pattern vectors. Addition of one extra element to each pattern allows hyper-spherical decision regions and enables convergence on real-valued inputs for existing constructive algorithms. Simulations demonstrate robust convergence and economical construction of hidden units in the benchmark "N-bit parity" and "twin spirals" problems.

Algorithms↗

PubMed1997

The convergence of backpropagation trained neural networks for various weight update frequencies.

One of the problems concerning the backpropagation training of feed-forward neural networks is the effect of the weight update frequency. This aspect influences the efficiency of parallel implementations of the training algorithm where the training vectors are distributed among processors. In this paper the convergence of two applications for various weight update intervals is reported. Further, several models are proposed for describing convergence and learning rate aspects in the context of a set of weight update intervals. The results show that the convergence by updating the weights after each training vector leads to about 10 times less number of training iterations compared to updating the weights only ones for the whole training set.

Algorithms↗

PubMed2003

Pain mechanisms: labeled lines versus convergence in central processing.

The issue of whether pain is represented by specific neural elements or by patterned activity within a convergent somatosensory subsystem has been debated for over a century. The gate control theory introduced in 1965 denied central specificity, and since then most authors have endorsed convergent wide-dynamic-range neurons. Recent functional and anatomical findings provide compelling support for a new perspective that views pain in humans as a homeostatic emotion that integrates both specific labeled lines and convergent somatic activity.

Afferent Pathways↗

PubMed1977

Distortion in converging collimator scintiphotography.

Distortion is intrinsic to converging collimator scintiphotography although converging collimation offers improved resolution and sensitivity. The nature of the distortion is defined and compared to nondistorted parallel-hole collimator images. The analogy between long and short focal-film-distance radiographs, and parallel and converging hole collimators, is discussed.

Humans↗

PubMed1994

Splanchnic and somatic afferent convergence on cervical spinal neurons of the rat.

The rostral cervical spinal cord is increasingly being considered the source of important propriospinal regulation. To better understand the substrate for this function, we investigated the effects of stimulation of the greater splanchnic nerve (GSN) and both thoracic and cervical somatic afferents on the activity of cervical spinal neurons. Extracellular single-neuron recordings were made in the C2-C5 spinal segments of chloralose-anesthetized, paralyzed, and artificially ventilated rats. Neurons were classified according to their responses to GSN stimulation. Neurons were inhibited by this stimulation as frequently as they were excited. We then studied the characteristics of cervical and thoracic convergent somatic input to each class of neurons. Although all cervical neurons that responded to GSN stimulation responded to electrical stimulation of the iliohypogastric nerve (IHN), only the few neurons that exhibited whole body receptive fields (RF) responded to natural thoracic somatic stimuli. Responses to electrical stimulation of the GSN and IHN were similar for most neurons; most exhibited nociceptive cutaneous RFs in cervical dermatomes. These data indicate that input from cervical somatic afferents and from both thoracic visceral and thoracic somatic afferents converge on individual splanchnic-receptive cervical neurons. Although these neurons exhibited the predicted cervical somatic RFs, responses from thoracic levels did not exhibit discrete RFs, requiring instead more synchronous or more spatially convergent input.

Abdomen↗

PubMed2005

Dynamic-clamp analysis of the effects of convergence on spike timing. I. Many synaptic inputs.

Precise action potential timing is crucial in sensory acuity and motor control. Convergence of many synaptic inputs is thought to provide a means of decreasing spike-timing variability ("jitter"), but its effectiveness has never been tested in real neurons. We used the dynamic-clamp technique in mouse auditory brain stem slices to examine how convergence controls spike timing. We tested the roles of several synaptic properties that are influenced by ongoing activity in vivo: the number of active inputs (N), their total synaptic conductance (G(tot)), and their timing, which can resemble an alpha or a Gaussian distribution. Jitter was reduced most with large N, up to a factor of over 20. Variability in N is likely to occur in vivo, but this added little jitter. Jitter reduction also depended on the timing of inputs: alpha-distributed inputs were more effective than Gaussian-distributed inputs. Furthermore, the two distributions differed in their sensitivity to synaptic conductance: for Gaussian-distributed inputs, jitter was most reduced when G(tot) was 2-3 times threshold, whereas alpha-distributed inputs showed continued jitter reduction with higher G(tot). However, very high G(tot) caused the postsynaptic cell to fire multiple times, particularly when the input jitter outlasted the cell's refractory period, which interfered with jitter reduction. G(tot) also greatly affected the response latency, which could influence downstream computations. Changes in G(tot) are likely to arise in vivo through activity-dependent changes in synaptic strength. High rates of postsynaptic activity increased the number of synaptic inputs required to evoke a postsynaptic response. Despite this, jitter was still effectively reduced, particularly in cases when this increased threshold eliminated secondary spikes. Thus these studies provide insight into how specific features of converging inputs control spike timing.

Action Potentials↗

PubMed1986

Visual, auditory, and somatosensory convergence on cells in superior colliculus results in multisensory integration.

Convergence of inputs from different sensory modalities onto individual neurons is a phenomenon that occurs widely throughout the brain at many phyletic levels and appears to represent a basic neural mechanism by which an organism integrates complex environmental stimuli. In the present study, neurons in the superior colliculus (SC) were used as a model to examine how single neurons deal with simultaneous cues from different sensory modalities (e.g., visual, auditory, somatosensory). The functional result of multisensory convergence on an individual cell was determined by comparing the responses evoked from it by a combined-modality (multimodal) stimulus with those elicited by each (unimodal) component of that stimulus presented alone. Superior colliculus cells exhibited profound changes in their activity when individual sensory stimuli were combined. These "multisensory interactions" were found to be widespread among deep laminae cells and fell into one of two functional categories: response enhancement, characterized by a significant increase in the number of discharges evoked; and response depression, characterized by a significant decrease in the discharges elicited. Multisensory response interactions most often reflected a multiplicative, rather than summative, change in activity. Their absolute magnitude varied from cell to cell and, when stimulus conditions were altered, within the same cell. However, the percentage change of enhanced interactions was generally inversely related to the vigor of the responses that could be evoked by presenting each unimodal stimulus alone and suggest that the potential for response amplification was greatest when responses evoked by individual stimuli were weakest. The majority of cells exhibiting multi-sensory characteristics were demonstrated to have descending efferent projections and thus had access to premotor and motor areas of the brain stem and spinal cord involved in SC-mediated attentive and orientation behaviors. These data show that multisensory convergence provides the descending efferent cells of the SC with a dynamic response character. The responses of these cells and the SC-mediated behaviors that they underlie need not be immutably tied to the presence of any single stimulus, but can vary in response to the particular complex of stimuli present in the environment at any given moment.

Afferent Pathways↗

PubMed1988

Convergence of retinal W-cell and corticotectal input to cells of the cat superior colliculus.

1. Conduction velocities of retinotectal W-cell afferents were estimated from differences among latencies of collicular unit responses to supramaximal stimulation of the contralateral optic disk (OD), optic chiasm (OX), and ipsilateral optic tract (OT). W-cell afferents driving collicular neurons had very slowly conducting axons, nearly all below 8 m/s (mean = 5.3 m/s). These match the conduction velocities of W-cell axons terminating in the uppermost superficial gray layer and triggering juxtazonal potentials (JZPs). Such slow conduction velocities are typical of W-cells belonging to the W2 subclass ("phasic W-cells"), but are slower than nearly all W1 cells ("tonic W-cells"). 2. Most W-driven cells were activated at latencies longer than expected for monosynaptic input from these W-cell afferents. However, comparable delays were observed among JZPs, which signal monosynaptic excitation of collicular neurons by W-cell terminals. This suggests that the delayed activation of W-driven cells reflects slowed conduction in the preterminal segments of W-cell afferents rather than polysynaptic transmission of W-cell signals through intermediary neurons in the brain stem or cortex. Thus monosynaptic inputs from retinal W2 cells appear to drive most neurons of the superficial collicular layers. 3. Convergence of retinotectal W-cell and corticotectal pathways was assessed by recording responses of W-driven collicular cells to intracortical stimulation of area 17. The great majority of W-driven collicular cells were activated by cortical stimulation (41/52; 79%), indicating that such convergence is widespread. 4. The population of corticotectal cells influencing W-driven collicular cells may differ from that mediating Hoffmann's Y-indirect pathway. W-driven collicular cells were activated from the striate cortex at longer latencies (mean = 6.3 ms) than cells driven by the Y-indirect pathway (mean = 2.5 ms). In addition, cortically activated W-driven cells were common throughout the superficial gray layer, whereas cells driven by the Y-indirect input were encountered only in the deepest part of the superficial gray and below. 5. W2 cells, apparently the dominant retinotectal cell type, nearly all project contralaterally and are tuned for slow stimulus velocities. Thus the binocularity of W-driven collicular cells and their sensitivity to moderately fast stimulus motion probably reflect the convergent cortical input described here.

Action Potentials↗

PubMed1990

Evidence for restricted central convergence of cutaneous afferents on an excitatory reflex pathway to medial gastrocnemius motoneurons.

1. We previously reported that excitatory postsynaptic potentials (EPSPs) produced by low-threshold electrical stimulation of the caudal cutaneous sural nerve (CCS) occur preferentially and with the shortest central latencies in the medial gastrocnemius (MG) portion of the triceps surae motor nuclei. The present study employs the spatial facilitation technique to assess interneuronal convergence on the short-latency excitatory pathway from CCS to MG by several other ipsilateral hindlimb afferents [the lateral cutaneous sural (LCS), caudal cutaneous femoral (CCF), saphenous (SAPH), superficial peroneal (SP), posterior tibial (TIB), and posterior articular (Joint) nerves]. 2. Spatial facilitation of CCF EPSPs in MG motoneurons was demonstrated with conditioning stimulation of the LCS, CCF, SAPH, SP, and TIB nerves, but was most readily and consistently observed with CCF conditioning. Facilitation of CCS and CCF EPSPs was obtained in individual MG motoneurons with a wide range of condition-test intervals. 3. CCF EPSPs in MG motoneurons produced by twice threshold (2T) afferent stimulation had a mean latency of 4.8 ms and often appeared as slowly rising, asynchronous potentials. On the other hand, 2T CCS EPSPs had a mean latency of 2.8 ms and appeared as sharper rising, less variable depolarizations. The optimum condition-test interval for facilitation of CCS and CCF EPSPs was found to be 5.2 ms on average, with CCS stimulation delayed from that of CCF. The longer latency of CCF EPSPs and the finding that the minimum condition-test interval was on the order of 3.9 ms suggests that convergence occurs late in the excitatory CCF pathway to MG motoneurons. 4. Convergence between excitatory pathways to MG from CCF and CCS afferents is discussed with regard to the original observations of Hagbarth on the location of cutaneous receptive fields and excitation of ankle extensors. In addition, evidence for the segregation of these specialized reflex pathways from those involved in general flexion reflexes is discussed.

Afferent Pathways↗

PubMed1993

Converging influences from visual, auditory, and somatosensory cortices onto output neurons of the superior colliculus.

1. Physiological methods were used to examine the pattern of inputs from different sensory cortices onto individual superior colliculus neurons. 2. Visual, auditory, and somatosensory influences from anterior ectosylvian sulcus (AES) and visual influences from lateral suprasylvian (LS) cortex were found to converge onto individual multisensory neurons in the cat superior colliculus. An excellent topographic relationship was found between the different sensory cortices and their target neurons in the superior colliculus. 3. Corticotectal inputs were derived solely from unimodal neurons. Multisensory neurons in AES and LS were not antidromically activated from the superior colliculus. 4. Orthodromic and antidromic latencies were consistent with monosynaptic corticotectal inputs arising from LS and the three subdivisions of AES (SIV, Field AES, and AEV). 5. Superior colliculus neurons that received convergent cortical inputs formed a principal component of the tecto-reticulospinal tract. Thus there appears to be extensive cortical control over the output neurons through which the superior colliculus mediates attentive and orientation behaviors. 6. Two other multisensory circuits were identified. A population of multisensory superior colliculus neurons was found, which neither received convergent cortical input nor projected into the tecto-reticulo-spinal tract. In addition, multisensory neurons in AES and LS proved to be independent of the superior colliculus (i.e., they were not corticotectal). While it is likely that these three distinct multisensory neural circuits have different functional roles, their constituent neurons appear to integrate their various sensory inputs in much the same way.

Animals↗

PubMed1998

Convergence properties of solitary tract neurons responsive to cardiac receptor stimulation in the anesthetized cat.

The convergence pattern of cardiac receptors, pulmonary C-fibers, carotid chemoreceptor, and baroreceptor afferents onto neurons within the nucleus of the solitary tract (NTS) was studied in the anesthetized (pentobarbitone sodium, 40 mg/kg,) paralyzed and artificially ventilated cat. Extra- and intracellular recordings were made from NTS neurons while stimulating both cardiac receptors by aortic root injections of veratridine (1-3 micrograms/kg) and pulmonary C-fibers by a right atrial injection of phenylbiguanide (10-20 micrograms/kg). The ipsilateral carotid body was stimulated by using arterial injection of CO2-saturated bicarbonate solution, whereas inflation of the ipsilateral carotid sinus was used to activate baroreceptors. The ipsilateral cardiac vagal branch, cervical vagus, and carotid sinus nerves were stimulated electrically (1 Hz, 0.2-1 ms, 1-35 V). In 78 NTS neurons recorded either extracellularly (n = 47) or intracellularly (n = 31), electrical stimulation of the cardiac branch of the vagus nerve evoked synaptic potentials (spikes and/or excitatory postsynaptic potentials) with an onset latency between 4 and 220 ms. Some neurons displayed both short and long latency inputs(15.5 +/- 1.8 and 160.0 +/- 8.5 ms; n = 14). Of these 78 neurons, 24 responded to veratridine stimulation of cardiac receptors (i.e., cardioreceptive neurons) by exhibiting an augmenting-decrementing discharge of 37 +/- 4 s in duration with a peak frequency of 30 +/- 5 Hz. Convergence from other cardiorespiratory receptors was noted involving either carotid chemoreceptors (n = 7) or pulmonary C-fibers (n = 4) or from both carotid chemoreceptors and pulmonary C-fibers (n = 6). In contrast, only one cardioreceptive NTS neuron was activated by distension of the carotid sinus. Recording sites recovered were confined to the medial NTS at the level of the area postrema and extended caudally into the commissural subnucleus. Our results indicate a convergence of carotid chemoreceptor and pulmonary C-fiber afferent inputs to cardioreceptive NTS neurons. With the paucity of baroreceptor inputs to these neurons it is suggested that sensory integration within the NTS may reflect regulatory versus defensive or protective reflex control.

Afferent Pathways↗