Electrical neuroimaging reveals intensity-dependent activation of human cortical gustatory and somatosensory areas by electric taste.

To analyze the neural basis of electric taste we performed electrical neuroimaging analyses of event-related potentials (ERPs) recorded while participants received electrical pulses to the tongue. Pulses were presented at individual taste threshold to excite gustatory fibers selectively without concomitant excitation of trigeminal fibers and at high intensity evoking a prickling and, thus, activating trigeminal fibers. Sour, salty and metallic tastes were reported at both intensities while clear prickling was reported at high intensity only. ERPs exhibited augmented amplitudes and shorter latencies for high intensity. First activations of gustatory areas (bilateral anterior insula, medial orbitofrontal cortex) were observed at 70-80ms. Common somatosensory regions were more strongly, but not exclusively, activated at high intensity. Our data provide a comprehensive view on the dynamics of cortical processing of the gustatory and trigeminal portions of electric taste and suggest that gustatory and trigeminal afferents project to overlapping cortical areas.

Early processing in the human lateral occipital complex is highly responsive to illusory contours but not to salient regions.

Human electrophysiological studies support a model whereby sensitivity to so-called illusory contour stimuli is first seen within the lateral occipital complex. A challenge to this model posits that the lateral occipital complex is a general site for crude region-based segmentation, based on findings of equivalent hemodynamic activations in the lateral occipital complex to illusory contour and so-called salient region stimuli, a stimulus class that lacks the classic bounding contours of illusory contours. Using high-density electrical mapping of visual evoked potentials, we show that early lateral occipital cortex activity is substantially stronger to illusory contour than to salient region stimuli, whereas later lateral occipital complex activity is stronger to salient region than to illusory contour stimuli. Our results suggest that equivalent hemodynamic activity to illusory contour and salient region stimuli probably reflects temporally integrated responses, a result of the poor temporal resolution of hemodynamic imaging. The temporal precision of visual evoked potentials is critical for establishing viable models of completion processes and visual scene analysis. We propose that crude spatial segmentation analyses, which are insensitive to illusory contours, occur first within dorsal visual regions, not the lateral occipital complex, and that initial illusory contour sensitivity is a function of the lateral occipital complex.

Epileptogenic zone, electrode location and clinical outcome in hippocampal electrical stimulation for mesial temporal lobe epilepsy : a correlation study

Objectif : Etudier les résultats cliniques du traitement de patients atteints pai- une épilepsie mésiale du lobe temporal (MTLE) réfractaire, par stimulation cérébrale profonde (DBS) de l'hippocampe, en fonction de l'emplacement de l'électrode. Méthodes : Huit patients atteints de MTLE implantés dans l'hippocampe et stimulés par DBS à haute fréquence ont été inclus dans cette étude. Cinq ont subi des enregistrements invasifs avec des électrodes profondes dans le but d'estimer la localisation du foyer ictal avant de procéder à une DBS chronique. La position des contacts actifs de l'électrode a été mesurée en utilisant une imagerie post-opératoire. Les distances par rapport au foyer ictal ont été calculées, et les structures hippocampiques influencées par la stimulation ont été identifiées au moyen d'un atlas neuro-anatomique. Ces deux paramètres ont été corrélés avec la réduction de la fréquence d'apparition des crises. Résultats : Les distances entre la localisation estimée des contacts actifs de l'électrode et le foyer ictal étaient respectivement 11.0 +/- 4.3 ou 9.1 +/- 2.3 mm pour les patients présentant une réduction de > 50% ou < 50% de la fréquence des crises. Chez les patients (N = 6) montrant une réduction de > 50% de la fréquence des crises, 100% avaient des contacts actifs situés à < 3 mm du subiculum (p < 0,05). Les 2 patients ne répondant pas au traitement étaient stimulés par des contacts situés à > 3mm du subiculum. Conclusion : La diminution de l'activité épileptogène induite par DBS sur l'hippocampe dans les cas de MTLE réfractaires : 1) ne semble pas directement liée à la proximité des contacts actifs de l'électrode au foyer ictal déterminé par les enregistrements invasifs ; 2) pourrait être obtenue par une neuro-modulation du subiculum.

Twitch potentia induced by two different modalities of neuromuscular electrical stimulation: implications for motor unit recruitment.

INTRODUCTION: We tested the hypothesis that twitch potentiation would be greater following conventional (CONV) neuromuscular electrical stimulation (50-µs pulse width and 25-Hz frequency) compared with wide-pulse high-frequency (WPHF) neuromuscular electrical stimulation (1-ms, 100-Hz) and voluntary (VOL) contractions, because of specificities in motor unit recruitment (random in CONV vs. random and orderly in WPHF vs. orderly in VOL). METHODS: A single twitch was evoked by means of tibial nerve stimulation before and 2 s after CONV, WPHF, and VOL conditioning contractions of the plantar flexors (intensity: 10% maximal voluntary contraction; duration: 10 s) in 13 young healthy subjects. RESULTS: Peak twitch increased (P<0.05) after CONV (+4.5±4.0%) and WPHF (+3.3±5.9%), with no difference between the 2 modalities, whereas no changes were observed after VOL (+0.8±2.6%). CONCLUSIONS: Our results demonstrate that presumed differences in motor unit recruitment between WPHF and CONV do not seem to influence twitch potentiation results.

Glucose and lactate are equally effective in energizing activity-dependent synaptic vesicle turnover in purified cortical neurons.

This study examines the role of glucose and lactate as energy substrates to sustain synaptic vesicle cycling. Synaptic vesicle turnover was assessed in a quantitative manner by fluorescence microscopy in primary cultures of mouse cortical neurons. An electrode-equipped perfusion chamber was used to stimulate cells both by electrical field and potassium depolarization during image acquisition. An image analysis procedure was elaborated to select in an unbiased manner synaptic boutons loaded with the fluorescent dye N-(3-triethylammoniumpropyl)-4-(4-(dibutylamino)styryl)pyridinium dibromide (FM1-43). Whereas a minority of the sites fully released their dye content following electrical stimulation, others needed subsequent K(+) depolarization to achieve full release. This functional heterogeneity was not significantly altered by the nature of metabolic substrates. Repetitive stimulation sequences of FM1-43 uptake and release were then performed in the absence of any metabolic substrate and showed that the number of active sites dramatically decreased after the first cycle of loading/unloading. The presence of 1 mM glucose or lactate was sufficient to sustain synaptic vesicle cycling under these conditions. Moreover, both substrates were equivalent for recovery of function after a phase of decreased metabolic substrate availability. Thus, lactate appears to be equivalent to glucose for sustaining synaptic vesicle turnover in cultured cortical neurons during activity.

Distinct neuronal circuits underlying the bahavioral and physiological components of the fear response

Abstract : Expression of fear involves changes in a number of behavioral and physiological parameters that are triggered by the central amygdala (CeA). The fear circuit also includes a series of brain stem nuclei that are the final effectors of the changes induced by the fear reaction. The CeA expresses many different neuropeptide receptors that can modulate fear responses. Today, the precise organization and the modulation of projections from the amygdala to the brain stem are still poorly understood. The aim of this project was to better understand the organization and the modulation of the fear circuit. To investigate this we first determined whether the CeA is composed of separate neuronal populations, where each one projects to specific brain stem nuclei, or whether single CeA neurons project to several nuclei. For this purpose, we first selected two brain stem nuclei implicated in the modulation of different components of the fear reactions, the periaqueductal gray (implicated in freezing) and the nucleus of solitary tract (implicated in heart rate modulation). We then performed double injections of two different retrograde tracers in these two nuclei and we quantified the subsequent presence of co-labelling in the CeA. We found that neurons projecting to the PAG and to the NTS are organized in separate populations. Subsequent electrophysiological recordings of the two populations revealed that PAG and NTS projecting neurons also have different electrophysiological characteristics. We then verified in vitro whether the neurons projecting to different brain stem nuclei express specific combinations of neuropeptide receptors, and whether a neuropeptide acting pre-synaptically (oxytocin) specifically modulates one of these two projections. We did not find differences at the level of expression of neurópeptide receptors, but we observed that oxytocin, a neuropeptide with anxiolytic properties, modulates PAG projecting neurons without affecting NTS projecting neurons. As oxytocin appeared to specifically modulate projections to the PAG, involved in the modulation of the freezing reaction, but did not affect the projections to the NTS, implicated in the modulation of cardiovascular parameters, we verified how this modulation translates in living animals. We investigated the effects of infra-amygdala injection of oxytocin on cardiovascular and behavioral changes induced by contextual fear conditioning. We found that oxytocin decreased the freezing response without affecting the cardiovascular system. Finally, as neuropeptides are considered potential future anxiolytics, we investigated whether diazepam and oxytocin, acting on the same circuit, had additive effects. This question was addressed exclusively with an in vitro electrophysiological approach. We obtained that oxytocin and diazepam, when co-applied, had an additive effect on both synaptic transmission and neuronal activity. These results open new perspectives for the possible clinical applications of oxytocin. Résumé : L'expression de la peur est accompagnée par de nombreux changements physiologiques et comportementaux qui sont déclenchés par l'amygdale centrale (CeA). Le circuit inclue aussi une série de noyaux du tronc cérébrale qui sont les effecteurs des différentes composantes de la réaction de peur. On sait que CeA envoie des projections aux noyaux du tronc cérébral et que ces neurones expriment une grande variété de récepteurs aux neuropeptides. Par contre, l'organisation des projections, ainsi que la modulation de ces projections par les neuropeptides reste encore peu connue. Avec ce projet, on premièrement voulu déterminer si CeA est composée de populations neuronales séparées qui projettent vers un noyau spécifique, ou bien si chaque neurones envoie des projections vers plusieurs noyaux. A ce propos, on a effectué des doubles injections de deux traceurs rétrogrades différentes dans deux noyaux du tronc cérébral impliqués dans des différentes composantes des réactions de peur. On a injecté la substance grise périaqueducale (PAG), qui est impliquée dans la réponse d'immobilisation, ainsi que le noyau du tractus solitaire (NTS) qui est responsable des changements cardiovasculaires. On a ensuite quantifié la présence de neurones contenant les deux traceurs dans CeA. On a trouvé que la plupart des neurones de l'amygdale centrale projettent vers un noyau spécifique, et on peut donc dire que l'amygdale semble être composée de populations neuronales séparées. On a ensuite mesuré les caractéristiques électrophysiologiques de ces deux projections et on a trouvé des différences substantielles concernant la résistance membranaire, la capacitance, le potentiel membranaire de repos ainsi que la fréquence des potentiels d'action spontanés. Puis, comme beaucoup de neuropéptides dans l'amygdale exercent un effet modulatoire sûr les réactions de peur et sur l'anxiété, on a étudié les effets directs et indirects d'une série de neuropeptides sur les différentes projections pour évaluer s'il y a des neuropeptides qui agissent spécifiquement sur une. On n'a pas trouvé de différences entre neurones qui projettent vers le PAG et neurones qui projettent vers le NTS concernant les effets de neuropeptides qui agissent directement sur ces cellules. Par contre, on a trouvé que l'ocytocine, un neuropeptide qui se lie à des récepteurs dans la partie latérale de l'amygdale centrale et inhibe de façon indirecte les neurones de l'amygdala centrale médiale, module les projections vers le PAG sans affecter celles qui vont vers le NTS. Comme le PAG est impliqué dans la réponse d'immobilisation, alors que le NTS est impliqué dans la modulation cardiovasculaire, on a ensuite étudié les effets de l'ocytocine injectée dans l'amygdale de rat vivants sur les réactions de peur conditionnées. On a trouvé que l'ocytocine diminue la réponse d'immobilisation sans par contre affecter la réponse cardiovasculaire. Pour terminer, on a vérifié si l'ocytocine potentialise les effets d'un médicament anxiolytique, le diazeparn. Avec une étude in vitro on a trouvé qu'une co-application d'ocytocine et diazeparn résulte en un effet additionnel à la fois sur la transmission synaptique ainsi que sur l'activité neuronale des neurones de l'amygdale centrale médiale. Ces résultats ouvrent des nouvelles perspectives pour une potentielle utilisation clinique de l'ocytocine.

A new paradigm of neuromuscular electrical stimulation for the quadriceps femoris muscle.

PURPOSE: Neuromuscular electrical stimulation (NMES) with large electrodes and multiple current pathways (m-NMES) has recently been proposed as a valid alternative to conventional NMES (c-NMES) for quadriceps muscle (re)training. The main aim of this study was to compare discomfort, evoked force and fatigue between m-NMES and c-NMES of the quadriceps femoris muscle in healthy subjects. METHODS: Ten healthy subjects completed two experimental sessions (c-NMES and m-NMES), that were randomly presented in a cross-over design. Maximal electrically evoked force at pain threshold, self-reported discomfort at different levels of evoked force, and fatigue-induced force declines during and following a series of 20 NMES contractions were compared between c-NMES and m-NMES. RESULTS: m-NMES resulted in greater evoked force (P < 0.05) and lower discomfort in comparison to c-NMES (P < 0.05-0.001), but fatigue time course and magnitude did not differ between the two conditions. CONCLUSIONS: The use of quadriceps m-NMES appears legitimate for (re)training purposes because it generated stronger contractions and was less discomfortable than c-NMES (due to multiple current pathways and/or lower current density with larger electrodes).

Metabolic equivalent: one size does not fit all.

The metabolic equivalent (MET) is a widely used physiological concept that represents a simple procedure for expressing energy cost of physical activities as multiples of resting metabolic rate (RMR). The value equating 1 MET (3.5 ml O2 x kg(-1) x min(-1) or 1 kcal x kg(-1) x h(-1)) was first derived from the resting O2 consumption (VO2) of one person, a 70-kg, 40-yr-old man. Given the extensive use of MET levels to quantify physical activity level or work output, we investigated the adequacy of this scientific convention. Subjects consisted of 642 women and 127 men, 18-74 yr of age, 35-186 kg in weight, who were weight stable and healthy, albeit obese in some cases. RMR was measured by indirect calorimetry using a ventilated hood system, and the energy cost of walking on a treadmill at 5.6 km/h was measured in a subsample of 49 men and 49 women (26-45 kg/m2; 29-47 yr). Average VO2 and energy cost corresponding with rest (2.6 +/- 0.4 ml O2 x kg(-1) x min(-1) and 0.84 +/- 0.16 kcal x kg(-1) x h(-1), respectively) were significantly lower than the commonly accepted 1-MET values of 3.5 ml O2 x kg(-1) x min(-1) and 1 kcal x kg(-1) x h(-1), respectively. Body composition (fat mass and fat-free mass) accounted for 62% of the variance in resting VO2 compared with age, which accounted for only 14%. For a large heterogeneous sample, the 1-MET value of 3.5 ml O2 x kg(-1) x min(-1) overestimates the actual resting VO2 value on average by 35%, and the 1-MET of 1 kcal/h overestimates resting energy expenditure by 20%. Using measured or predicted RMR (ml O2 x kg(-1) x min(-1) or kcal x kg(-1) x h(-1)) as a correction factor can appropriately adjust for individual differences when estimating the energy cost of moderate intensity walking (5.6 km/h).

Neurally Adjusted Ventilatory Assist (NAVA) improves the matching of diaphragmatic electrical activity and tidal volume in comparison to pressure support (PS) under non invasive ventilation

INTRODUCTION. Patient-ventilator asynchrony is a frequent issue in non invasivemechanical ventilation (NIV) and leaks at the patient-mask interface play a major role in itspathogenesis. NIV algorithms alleviate the deleterious impact of leaks and improve patient-ventilator interaction. Neurally adusted ventilatory assist (NAVA), a neurally triggered modethat avoids interferences between leaks and the usual pneumatic trigger, could further improvepatient-ventilator interaction in NIV patients.OBJECTIVES. To evaluate the feasibility ofNAVAin patients receiving a prophylactic postextubationNIV and to compare the respective impact ofPSVandNAVAwith and withoutNIValgorithm on patient-ventilator interaction.METHODS. Prospective study conducted in 16 beds adult critical care unit (ICU) in a tertiaryuniversity hospital. Over a 2 months period, were included 17 adult medical ICU patientsextubated for less than 2 h and in whom a prophylactic post-extubation NIV was indicated.Patients were randomly mechanically ventilated for 10 min with: PSV without NIV algorithm(PSV-NIV-), PSV with NIV algorithm (PSV-NIV+),NAVAwithout NIV algorithm (NAVANIV-)and NAVA with NIV algorithm (NAVA-NIV+). Breathing pattern descriptors, diaphragmelectrical activity, leaks volume, inspiratory trigger delay (Tdinsp), inspiratory time inexcess (Tiexcess) and the five main asynchronies were quantified. Asynchrony index (AI) andasynchrony index influenced by leaks (AIleaks) were computed.RESULTS. Peak inspiratory pressure and diaphragm electrical activity were similar in thefour conditions. With both PSV and NAVA, NIV algorithm significantly reduced the level ofleak (p\0.01). Tdinsp was not affected by NIV algorithm but was shorter in NAVA than inPSV (p\0.01). Tiexcess was shorter in NAVA and PSV-NIV+ than in PSV-NIV- (p\0.05).The prevalence of double triggering was significantly lower in PSV-NIV+ than in NAVANIV+.As compared to PSV,NAVAsignificantly reduced the prevalence of premature cyclingand late cycling while NIV algorithm did not influenced premature cycling. AI was not affectedby NIV algorithm but was significantly lower in NAVA than in PSV (p\0.05). AIleaks wasquasi null with NAVA and significantly lower than in PSV (p\0.05).CONCLUSIONS. NAVA is feasible in patients receiving a post-extubation prophylacticNIV. NAVA and NIV improve patient-ventilator synchrony in different manners. NAVANIV+offers the best patient-ventilator interaction. Clinical studies are required to assess thepotential clinical benefit of NAVA in patients receiving NIV.

Brain tissue properties differentiate between motor and limbic basal ganglia circuits.

Despite advances in understanding basic organizational principles of the human basal ganglia, accurate in vivo assessment of their anatomical properties is essential to improve early diagnosis in disorders with corticosubcortical pathology and optimize target planning in deep brain stimulation. Main goal of this study was the detailed topological characterization of limbic, associative, and motor subdivisions of the subthalamic nucleus (STN) in relation to corresponding corticosubcortical circuits. To this aim, we used magnetic resonance imaging and investigated independently anatomical connectivity via white matter tracts next to brain tissue properties. On the basis of probabilistic diffusion tractography we identified STN subregions with predominantly motor, associative, and limbic connectivity. We then computed for each of the nonoverlapping STN subregions the covariance between local brain tissue properties and the rest of the brain using high-resolution maps of magnetization transfer (MT) saturation and longitudinal (R1) and transverse relaxation rate (R2*). The demonstrated spatial distribution pattern of covariance between brain tissue properties linked to myelin (R1 and MT) and iron (R2*) content clearly segregates between motor and limbic basal ganglia circuits. We interpret the demonstrated covariance pattern as evidence for shared tissue properties within a functional circuit, which is closely linked to its function. Our findings open new possibilities for investigation of changes in the established covariance pattern aiming at accurate diagnosis of basal ganglia disorders and prediction of treatment outcome.

Mutism and Amnesia following High-Voltage Electrical Injury: Psychogenic Symptomatology Triggered by Organic Dysfunction?

Background: Mutism and dense retrograde amnesia are found both in organic and dissociative contexts. Moreover, dissociative symptoms may be modulated by right prefrontal activity. A single case, M.R., developed left hemiparesis, mutism and retrograde amnesia after a high-voltage electric shock without evidence of lasting brain lesions. M.R. suddenly recovered from his mutism following a mild brain trauma 2 years later. Methods: M.R.'s neuropsychological pattern and anatomoclinical correlations were studied through (i) language and memory assessment to characterize his deficits, (ii) functional neuroimaging during a standard language paradigm, and (iii) assessment of frontal and left insular connectivity through diffusion tractography imaging and transcranial magnetic stimulation. A control evaluation was repeated after recovery. Findings: M.R. recovered from the left hemiparesis within 90 days of the accident, which indicated a transient right brain impairment. One year later, neurobehavioral, language and memory evaluations strongly suggested a dissociative component in the mutism and retrograde amnesia. Investigations (including MRI, fMRI, diffusion tensor imaging, EEG and r-TMS) were normal. Twenty-seven months after the electrical injury, M.R. had a very mild head injury which was followed by a rapid recovery of speech. However, the retrograde amnesia persisted. Discussion: This case indicates an interaction of both organic and dissociative mechanisms in order to explain the patient's symptoms. The study also illustrates dissociation in the time course of the two different dissociative symptoms in the same patient.

Visual functions in the healthy and schizophrenic brain : from stimulus control to illusory perceptions using electrical neuroimaging

ABSTRACT (FRENCH)Ce travail de thèse basé sur le système visuel chez les sujets sains et chez les patients schizophrènes, s'articule autour de trois articles scientifiques publiés ou en cours de publication. Ces articles traitent des sujets suivants : le premier article présente une nouvelle méthode de traitement des composantes physiques des stimuli (luminance et fréquence spatiale). Le second article montre, à l'aide d'analyses de données EEG, un déficit de la voie magnocellulaire dans le traitement visuel des illusions chez les patients schizophrènes. Ceci est démontré par l'absence de modulation de la composante PI chez les patients schizophrènes contrairement aux sujets sains. Cette absence est induite par des stimuli de type illusion Kanizsa de différentes excentricités. Finalement, le troisième article, également à l'aide de méthodes de neuroimagerie électrique (EEG), montre que le traitement des contours illusoires se trouve dans le complexe latéro-occipital (LOC), à l'aide d'illusion « misaligned gratings ». De plus il révèle que les activités démontrées précédemment dans les aires visuelles primaires sont dues à des inférences « top- down ».Afin de permettre la compréhension de ces trois articles, l'introduction de ce manuscrit présente les concepts essentiels. De plus des méthodes d'analyses de temps-fréquence sont présentées. L'introduction est divisée en quatre parties : la première présente le système visuel depuis les cellules retino-corticales aux deux voix du traitement de l'information en passant par les régions composant le système visuel. La deuxième partie présente la schizophrénie par son diagnostic, ces déficits de bas niveau de traitement des stimuli visuel et ces déficits cognitifs. La troisième partie présente le traitement des contours illusoires et les trois modèles utilisés dans le dernier article. Finalement, les méthodes de traitement des données EEG seront explicitées, y compris les méthodes de temps-fréquences.Les résultats des trois articles sont présentés dans le chapitre éponyme (du même nom). De plus ce chapitre comprendra les résultats obtenus à l'aide des méthodes de temps-fréquenceFinalement, la discussion sera orientée selon trois axes : les méthodes de temps-fréquence ainsi qu'une proposition de traitement de ces données par une méthode statistique indépendante de la référence. La discussion du premier article en montrera la qualité du traitement de ces stimuli. La discussion des deux articles neurophysiologiques, proposera de nouvelles d'expériences afin d'affiner les résultats actuels sur les déficits des schizophrènes. Ceci pourrait permettre d'établir un marqueur biologique fiable de la schizophrénie.ABSTRACT (ENGLISH)This thesis focuses on the visual system in healthy subjects and schizophrenic patients. To address this research, advanced methods of analysis of electroencephalographic (EEG) data were used and developed. This manuscript is comprised of three scientific articles. The first article showed a novel method to control the physical features of visual stimuli (luminance and spatial frequencies). The second article showed, using electrical neuroimaging of EEG, a deficit in spatial processing associated with the dorsal pathway in chronic schizophrenic patients. This deficit was elicited by an absent modulation of the PI component in terms of response strength and topography as well as source estimations. This deficit was orthogonal to the preserved ability to process Kanizsa-type illusory contours. Finally, the third article resolved ongoing debates concerning the neural mechanism mediating illusory contour sensitivity by using electrical neuroimaging to show that the first differentiation of illusory contour presence vs. absence is localized within the lateral occipital complex. This effect was subsequent to modulations due to the orientation of misaligned grating stimuli. Collectively, these results support a model where effects in V1/V2 are mediated by "top-down" modulation from the LOC.To understand these three articles, the Introduction of this thesis presents the major concepts used in these articles. Additionally, a section is devoted to time-frequency analysis methods not presented in the articles themselves. The introduction is divided in four parts. The first part presents three aspects of the visual system: cellular, regional, and its functional interactions. The second part presents an overview of schizophrenia and its sensoiy-cognitive deficits. The third part presents an overview of illusory contour processing and the three models examined in the third article. Finally, advanced analysis methods for EEG are presented, including time- frequency methodology.The Introduction is followed by a synopsis of the main results in the articles as well as those obtained from the time-frequency analyses.Finally, the Discussion chapter is divided along three axes. The first axis discusses the time frequency analysis and proposes a novel statistical approach that is independent of the reference. The second axis contextualizes the first article and discusses the quality of the stimulus control and direction for further improvements. Finally, both neurophysiologic articles are contextualized by proposing future experiments and hypotheses that may serve to improve our understanding of schizophrenia on the one hand and visual functions more generally.