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Assessing convergence of Markov chain Monte Carlo simulations in hierarchical Bayesian models for population pharmacokinetics.

Advances in computer hardware and the associated computer-intensive algorithms made feasible by these advances [like Markov chain Monte Carlo (MCMC) data analysis techniques] have made possible the application of hierarchical full Bayesian methods in analyzing pharmacokinetic and pharmacodynamic (PK-PD) data sets that are multivariate in nature. Pharmacokinetic data analysis in particular has been one area that has seized upon this technology to refine estimates of drug parameters from sparse data gathered in a large, highly variable population of patients. A drawback in this type of analysis is that it is difficult to quantitatively assess convergence of the Markov chains to a target distribution, and thus, it is sometimes difficult to assess the reliability of estimates gained from this procedure. Another complicating factor is that, although the application of MCMC methods to population PK-PD problems has been facilitated by new software designed for the PK-PD domain (specifically PKBUGS), experts in PK-PD may not have the necessary experience with MCMC methods to detect and understand problems with model convergence. The objective of this work is to provide an example of a set of diagnostics useful to investigators, by analyzing in detail three convergence criteria (namely the Raftery and Lewis, Geweke, and Heidelberger and Welch methods) on a simulated problem and with a rule of thumb of 10,000 chain elements in the Markov chain. We used two publicly available software packages to assess convergence of MCMC parameter estimates; the first performs Bayesian parameter estimation (PKBUGS/WinBUGS), and the second is focused on posterior analysis of estimates (BOA). The main message that seems to emerge is that accurately estimating confidence regions for the parameters of interest is more demanding than estimating the parameter means. Together, these tools provide numerical means by which an investigator can establish confidence in convergence and thus in the estimated parameters derived from hierarchical full Bayesian pharmacokinetic data analysis.

Algorithms↗

The vascular converging points of the right pulmonary hilus and their diagnostic significance.

The shadows of the right descending pulmonary artery, the superior pulmonary vein crossing it, the middle lobe artery, and branches of the artery supplying the superior segment of the lower lobe converge distinctly at the right hilus. Because the right pulmonary artery bifurcates within the mediastinum, the arteries of the right upper lobe form a second though less obvious converging point above this level. In contrast, the left pulmonary artery does not bifurcate until it reaches the left hilus, providing only a single converging point on that side. A survey of 100 chest radiographs showed that the two converging points on the right could be distinguished in 95 cases, with the upper one being situated somewhat above the single point on the left in 83. In the absence of lobar resection, finding only one converging point on the right is suggestive of collapse of either the upper or lower lobe, whereas visualization of both points excludes major atelectasis.

Humans↗

Pathophysiologic mechanism of convergence nystagmus.

The convergent eye movements in convergence nystagmus are reported to be opposed adducting saccades under excessive convergence drive. What occurs is a horizontal saccade of the adducting eye and a quick reversal of the abducting eye immediately after initiation of the original saccade. Accordingly, the opposed adducting saccades of the abducting eye have been explained by the dynamic overshoot mechanism. However, by electro-oculographic analysis of eye movements in a patient with convergence nystagmus, we found that the opposed adducting saccades of the abducting eye occurred not only after but also just before initiation of the original saccade. Our observation indicates that the opposed adducting saccades can occur without dynamic overshoot as the starter mechanism. Possibly, cessation of the discharge of omnipause neurons may lead to firing of the burst neurons for the medial rectus subnucleus via activation by the excessive convergence drive.

Aged↗

Convergent extension, planar-cell-polarity signalling and initiation of mouse neural tube closure.

Planar-cell-polarity (PCP) signalling is necessary for initiation of neural tube closure in higher vertebrates. In mice with PCP gene mutations, a broad embryonic midline prevents the onset of neurulation through wide spacing of the neural folds. In order to evaluate the role of convergent extension in this defect, we vitally labelled the midline of loop-tail (Lp) embryos mutant for the PCP gene Vangl2. Injection of DiI into the node, and electroporation of a GFP expression vector into the midline neural plate, revealed defective convergent extension in both axial mesoderm and neuroepithelium, before the onset of neurulation. Chimeras containing both wild-type and Lp-mutant cells exhibited mainly wild-type cells in the midline neural plate and notochordal plate, consistent with a cell-autonomous disturbance of convergent extension. Inhibitor studies in whole-embryo culture demonstrated a requirement for signalling via RhoA-Rho kinase, but not jun N-terminal kinase, in convergent extension and the onset of neural tube closure. These findings identify a cell-autonomous defect of convergent extension, requiring PCP signalling via RhoA-Rho kinase, during the development of severe neural tube defects in the mouse.

Animals↗

Caudalization by the amphibian organizer: brachyury, convergent extension and retinoic acid.

Caudalization, which is proposed to be one of two functions of the amphibian organizer, initiates posterior pathways of neural development in the dorsalized ectoderm. In the absence of caudalization, dorsalized ectoderm only expresses the most anterior (archencephalic) differentiation. In the presence of caudalization, dorsalized ectorderm develops various levels of posterior neural tissues, depending on the extent of caudalization. A series of induction experiments have shown that caudalization is mediated by convergent extension: cell motility that is based on directed cell intercalation, and is essential for the morphogenesis of posterior axial tissues. During amphibian development, convergent extension is first expressed all-over the mesoderm and, after mesoderm involution, it becomes localized to the posterior mid-dorsal mesoderm, which produces notochord. This expression pattern of specific down regulation of convergent extension is also followed by the expression of the brachyury homolog. Furthermore, mouse brachyury has been implicated in the regulation of tissue elongation on the one hand, and in the control of posterior differentiation on the other. These observations suggest that protein encoded by the brachyury homolog controls the expression of convergent extension in the mesoderm. The idea is fully corroborated by a genetic study of mouse brachyury, which demonstrates that the gene product produces elongation of the posterior embryonic axis. However, there exists evidence for the induction of posterior dorsal mesodermal tissues, if brachyury homolog protein is expressed in the ectoderm. In both cases the brachyury homolog contributes to caudalization. A number of other genes appear to be involved in caudalization. The most important of these is pintavallis, which contains a fork-head DNA binding domain. It is first expressed in the marginal zone. After mesoderm involution, it is present not only in the presumptive notochord, but also in the floor plate. This is in contrast to the brachyury homolog, whose expression is restricted to mesoderm. The morphogenetic effects of exogenous RA on anteroposterior specification during amphibian embryogenesis are reviewed. The agent inhibits archencephalic differentiation and enhances differentiation of deuterencephalic and trunk levels. Thus the effect of exogenous RA on morphogenesis of CNS is very similar to that of caudalization, which is proposed to occur through the normal action of the organizer. According to a detailed analysis of the effect of lithium on morphogenesis induced by the Cynops organizer, lithium has a caudalizing effect closely comparable with that of RA. Furthermore, lithium induces convergent extension in the prechordal plate, which normally does not show cell motility.(ABSTRACT TRUNCATED AT 400 WORDS)

Amphibians↗

Convergence accommodation.

Steady-state accommodation responses were measured in both eyes as a function of vergence angle and direction of lateral gaze. The measurements were made with a binocular laser optometer. Small speckle patterns were used as fusional stimuli in an otherwise dark field. These patterns have the advantage of providing no blur stimulus to accommodation. Convergence accommodation for vergence angles ranging from 0 to 25 deg was measured for lateral-gaze angles of +32, -32, and 0 deg. The average accommodation of the two eyes was linearly related to vergence angle over the observer's accommodation range but was independent of the angle of lateral gaze. The mean convergence accommodation/convergence ratio for three subjects, in diopters per meter-angle, was 0.9. Our measurements of convergence accommodation using laser-speckle targets are in good agreement with previous studies that used small pupils. Accommodation responses for binocular viewing of letters of a Snellen chart were also measured. When luminance was reduced, night myopia was observed. No similar effect was found for convergence accommodation. Accommodation to a dim target corresponded closely to the convergence accommodation.

Accommodation, Ocular↗

Spatial convergence and divergence between cutaneous afferent axons and dorsal horn cells are not constant.

We have proposed a quantitative model of the development of dorsal horn cell receptive fields (RFs) and somatotopic organization (Brown et al. [1997] Somatosens. Motor Res. 14:93-106). One component of that model is a hypothesis that convergence and divergence of connections between low-threshold primary afferent mechanoreceptive axons and dorsal horn cells are invariant over skin location and dorsal horn location. The more limited, and more easily tested, hypothesis that spatial convergence and divergence between cutaneous mechanoreceptors and dorsal horn cell are constant was examined. Spatial divergence is the number of dorsal horn cells whose RFs overlap the RF center of a primary afferent, and spatial convergence is the number of afferent RF centers that lie within the RF of a dorsal horn cell. Innervation density was determined as a function of location on the hindlimb by using peripheral nerve recording and axon counting. A descriptive model of dorsal horn cell receptive fields (Brown et al. [1998] J. Neurophysiol. 31:833-848) was used to simulate RFs of the entire dorsal horn cell population in order to estimate RF area and map scale as a function of location on the hindlimb. Previously reported correlations among innervation density, map scale, and RF size were confirmed. However, these correlations were not linear. The hypothesis that spatial convergence and divergence are constant was rejected. The previously proposed model of development of dorsal horn cell somatotopy and RF geometries must be revised to take variable spatial convergence and divergence into account.

Afferent Pathways↗

Nonsurgical treatment of convergent strabismus.

It is generally agreed that surgical treatment of convergent strabismus should be withheld until all other less traumatic approaches have proved ineffectual. There are four categories of nonsurgical treatment. One is psychiatric. Too often psychiatric problems in the causation of convergent strabismus are either overlooked or unrecognized. Another is the proper employment of optical devices. For example, spectacle lenses to eliminate the need for excessive accommodation with its associated convergence excess, and the employment of prisms in the lenses to permit the two eyes to see as a unit even though they may not be properly anatomically oriented. Another kind of treatment is orthoptics, the use of exercises and rather complex optical equipment in a laboratory to train the patient in coordination between the two eyes. Treatment with drugs is based on the fact that certain drugs reduce the effort necessary for accommodation (much as eye-glasses do) and therefore lessen the stimulus toward convergence which may possibly tend toward the development of convergent strabismus.

Accommodation, Ocular↗

Delamination of neuroepithelium and nonneural ectoderm and its relation to the convergence step in chick neurulation.

We have analysed the characteristics of the neuroectoderm-nonneural ectoderm meeting point at several axial levels in relation to the mechanics of neurulation in each level. The results show wide differences at cephalic and somitic levels. At cephalic levels, where convergence plays an important role, the delamination process appears at the beginning of the convergence step. This phenomenon produces a major isolation of the basal lamina, forming a space between this structure and the epithelial sheet in whose basal surface a new basal lamina begins to form. This cavity contains abundant extracellular matrix stained with ruthenium red (RR) and tannic acid (TA), and its increase in volume correlates with the progressive convergence of neural folds. At somitic levels, where the convergence is not important, delamination involves the progressive formation of a half-moon-shaped cavity. This structure appears between a dorsal attachment point, in the tip of neuroectodermal wall, and a ventral attachment point which coincides with the point of bending that determines the bilateral furrow, if it exists. In this small cavity, delamination is not related to an isolation of basal lamina. The RR-staining of the extracellular matrix in this cavity is scarce and the volume increase is smaller than in the cephalic region. These results are discussed in terms of neural fold convergence and neural tube closure.

Animals↗

Convergence and the multidimensional niche.

Convergent evolution has played an important role in the development of the ecological niche concept. We investigated patterns of convergent and divergent evolution of Caribbean Anolis lizards. These lizards diversified independently on each of the islands of the Greater Antilles, producing the same set of habitat specialists on each island. Using a phylogenetic comparative framework, we examined patterns of morphological convergence in five functionally distinct sets of morphological characters: body size, body shape, head shape, lamella number, and sexual size dimorphism. We find evidence for convergence among members of the habitat specialist types for each of these five datasets. Furthermore, the patterns of convergence differ among at least four of the five datasets; habitat specialists that are similar for one set of characters are often greatly different for another. This suggests that the habitat specialist niches into which these anoles have evolved are multidimensional, involving several distinct and independent aspects of morphology.

Adaptation, Biological↗

The distribution of rolling neutrophils in venular convergences.

The aim of this study was to characterize the distribution of adherent leukocytes in branched venular convergences in vivo. Intravital microscopy was used to obtain video images of leukocyte adhesion in multiple branched sites in mouse cremaster muscle, during the mild inflammatory response induced by surgical preparation. The average number of cells/vessel length was obtained over several minutes for seven venular convergences with varying geometrical configurations. Results from this study demonstrate a strong tendency of leukocytes to adhere at junctional points between converging vessels. Different vessel configurations were studied and results were shown to be insensitive to precise vessel geometry. Thus, in post-capillary venules, leukocytes are most likely to adhere at points between converging vessels, regardless of the precise geometrical properties or configuration of the vessels. Hydrodynamic mechanisms due to flow behavior through convergences likely play a significant role in determining locations of cellular adhesion. Future work should concentrate on quantifying the relative contributions of hydrodynamic and biochemical mechanisms to aid in understanding disease processes and development of treatments or therapeutics.

Animals↗

[A study on tooth preparation by means of the newly developed parallelometer and its educational effect, with primary regard to convergence angles of abutment tooth].

Proper tooth preparation is one of the fundamental requirements in crown & bridge prosthodontics. However, it is difficult for students in particular to prepare adequate convergence angles of abutment tooth in the limited environment of patient's mouth. Therefore, the parallelometer was developed to improve the preparations as a supplementary device which informs the person by a signal of alarming simultaneously when a bur is not properly installed to convergence angles of abutment tooth. Sixty subjects were selected from students of Kanagawa Dental College and they were divided into two groups (A and B) to prepare abutment tooth of lower right 1st molar for full cast crown on typodont mounted into the manikin. A preliminary training was performed for once without the parallelometer for group A and with it for group B prior to a comparative experiment. The following results were obtained with primary regard to convergence angles of abutment tooth. 1. Related to each of four convergence angles, group B is superior to group A in all mean values with a statistical significance (P less than 0.01). 2. Related to a total of four convergence angles by the maximum number of subjects, group B is also superior to group A in a mean value by about ten degrees. 3. A newly developed parallelometer proved to be an efficient supplementary device for training of students to master a technique of preparation for adequate abutment tooth.

Crowns↗

[Development of a converging collimator for thyroid scintigraphy].

Thyroid scintigraphy is generally performed using a pin-hole or a parallel-hole collimator. The former yields a high resolution image, however, the acquisition time prolongs because the collimation system magnifies a thyroid image. The latter has somewhat low resolution, because the collimation system cannot magnify the thyroid image and it is difficult to close the collimator surface to a patient thyroid. The defects of the above two collimators are distortion or blurs at the thyroid edge of the acquired image. To improve the image quality of the thyroid scintigram, we made computer simulations concerning contrast resolution in comparison of a parallel-hole, pin-hole and converging collimator. The simulations results showed that the contrast resolution by the converging collimator is superior to the other collimators. According to the results, we developed a specially-designed converging collimator (thickness: 100 mm, focal length: 195 mm). We cut an edge of the collimator to decrease the distance between the neck and the collimator surface. Under almost the same conditions for spatial resolution and sensitivity, we compared the effectiveness of the converging collimator with that of the other two collimators; the pin-hole type [medium resolution] and the parallel-hole type [high resolution]. As a result of experiments using a phantom, the converging collimator showed less distortion compared with the other collimators at the deep area of the thyroid phantom.(ABSTRACT TRUNCATED AT 250 WORDS)

Computer Simulation↗

Convergence amplitude insufficiency.

There is a frequently overlooked group of patients, usually under 20 years of age, with typical symptoms of convergence insufficiency and diminished convergence amplitudes, but with normal near point of convergence. We studied ten cases of this type, which we call convergence amplitude insufficiency. The diagnosis in such patients will not be missed if convergence amplitudes are measured on every patient complaining of asthenopic symptoms during close work.

Accommodation, Ocular↗

[Dynamic focusing of informational convergence in basal ganglia].

Data in the literature support two apparently contradictory hypotheses: that of parallel processing and that of informational convergence in the basal ganglia. We present electrophysiological data supporting one and the other. Thus, at the output of the basal ganglia, in the intact monkey, neurons of the pallidum respond almost exclusively and in small number to passive limb movement. The specificity of the responses supports the parallel processing hypothesis. However, when the monkey is rendered parkinsonian by the neurotoxin MPTP, the dopaminergic deficit discloses a strong convergence upon pallidal neurons of information originating from different body parts. Such a convergence is also observed in the case of pallidal responses to electrical stimulation of the striatum. According to data in the recent literature, it is more likely that this information converges into the pallidum through the subthalamo-pallidal rather than the striato-pallidal pathway. On the other hand, pallidal responses to electrical stimulation of the striatum display a topological antagonistic center-surround organization, probably resulting from lateral inhibition. Moreover, changes in neuronal activities induced in the external pallidal segment by local injection of bicuculline display a similar organization and suggest the occurrence of a wide and powerful lateral inhibition in this pallidal segment. Such focusing mechanisms would be useless in an exclusively parallel system. One may therefore think that, in the normal individual, the level of dopamine dynamically focuses the system on the appropriate information. This would allow parallel processing in neuronal channels that are only relatively independent, since they can also demonstrate informational convergence.

Animals↗

Application of the flow convergence region method to the determination of stroke volume and cardiac output in patients with mitral stenosis.

OBJECTIVE: This study was undertaken to investigate the feasibility and accuracy of determination of stroke volume and cardiac output by calculating transmitral flow volume using the flow convergence region method in patients with mitral stenosis. PATIENTS AND INTERVENTIONS: Fifty-six patients with rheumatic mitral stenosis were studied using imaging and Doppler echocardiography. Aliasing velocities of 20 to 23 cm/s were used to record the flow vonvergence region proximal to the stenotic mitral orifice. The stroke volume (mL) was calculated by multiplying peak transmitral flow rate which was obtained using an angle-corrected hemispheric flow convergence equation, by transmitral velocity time integral (cm) divided by peak transmitral velocity (cm/s) recorded using continuous wave Doppler method. MAIN RESULTS: Stroke volume calculated using the flow convergence region method was not significantly different from that calculated using aortic Doppler two-dimensional echocardiographic method in 39 patients with pure mitral stenosis (75+/-19 [mean+/-1SD] versus 73+/-19 mL, P=0.12), and from that calculated using pulmonic Doppler two-dimensional echocardiographic method in nine patients with mitral stenosis with associated>2+ aortic regurgitation (77+/-12 versus 75+/-14 mL, P=0.49). No significant difference existed between the cardiac output obtained using the flow convergence region method and that obtained using Fick method in 12 patients with pure mitral stenosis. The stroke volume was overestimated by the flow convergence region method when compared with those obtained using aortic Doppler two-dimensional echocardiographic method in patients with mitral stenosis with associated >2+ mitral regurgitation (123+/-40 versus 67+/-15 mL, P=0.001). CONCLUSIONS: The present study provided an alternative way to calculate the stroke volume and cardiac output in patients with mitral stenosis.

Adult↗

Adult aphasics: relationship between convergent and divergent semantic behavior.

The purpose of the present study was to empirically evaluate the relationship between the ability of 30 aphasic subjects to produce a number and a variety of semantic responses with their ability to produce highly, knowledge-oriented, automatic responses. That is, the relationship between divergent and convergent semantic behaviors was explored. Use of both types of tasks will more adequately reflect the semantic strategies needed for spontaneous communication in day-to-day life situations. Results of the present study show that divergent and convergent behavior seem to require separate and distinct abilities for aphasic subjects. The strong and significant correlations between subject performance on the verbal, gestural and graphic convergent variables and subject ability to produce a number and a variety of relevant semantic responses confirms the fact that aphasia is both a divergent and a convergent semantic disorder. The findings of the present study therefore indicate the need to create diagnostic and therapeutic paradigms with divergent tasks that emphasize a variety, quantity and relevance of output from the same source, as well as the more traditional convergent tasks that are more highly knowledge oriented.

Adult↗

Randomised clinical trial of the effectiveness of base-in prism reading glasses versus placebo reading glasses for symptomatic convergence insufficiency in children.

PURPOSE: To compare base-in prism reading glasses with placebo reading glasses for the treatment of symptomatic convergence insufficiency (CI) in children aged 9 to <18 years. METHODS: In a randomised clinical trial, 72 children aged 9 to <18 years with symptomatic CI were assigned to either base-in prism glasses or placebo reading glasses. Symptom level, measured with a quantitative symptom questionnaire (CI Symptom Survey-V15), was the primary outcome measure. Near point of convergence and positive fusional vergence at near were secondary outcomes. RESULTS: The mean (SD) CI Symptom Survey score decreased (that is, less symptomatic) in both groups (base-in prism glasses from 31.6 (10.4) to 16.5 (9.2); placebo glasses from 28.4 (8.8) to 17.5 (12.3)). The change in the CI Symptom Survey scores (p = 0.33), near point of convergence (p = 0.91), and positive fusional vergence (p = 0.59) were not significantly different between the two groups after 6 weeks of wearing glasses. CONCLUSIONS: Base-in prism reading glasses were found to be no more effective in alleviating symptoms, improving the near point of convergence, or improving positive fusional vergence at near than placebo reading glasses for the treatment of children aged 9 to <18 years with symptomatic CI.

Adolescent↗