On the reorganization of sensory hand areas after mono-hemispheric lesion: a functional (MEG)/anatomical (MRI) integrative study

Frontal and parieto-temporal cortical ablations and diaschisis-like effects on auditory neurocognitive potentials evocable from apparently intact ipsilateral association areas in humans: five case reports

The aim of this study was to investigate the effects of disruption on the warning auditory S1-elicited ERP and CNV complexes recordable on the site and on remote ipsilateral apparently normal anatomo-functionally interconnected brain regions. These effects in some cases showed aspects of a probable diaschisis-like phenomenon, due to resections of extensive frontal association cortex or of primary and secondary sensory parieto-temporal areas damaged by differing pathological processes. Using a standard CNV paradigm, 21/19 EEG electrodes connected with three different references, and scalp-topographic bidimensional mapping analysis, the S1 auditory binaural/monaural clicks N1a,b,c, P2, N2, P3 and CNV waves were recorded in 10 normal subjects and 11 patients. Nine of the latter had been submitted to unilateral frontal dorsolateral cortex ablation, one to bihemispheric dorsomedial cortex ablation, and one to unilateral ablation of sensory parieto-temporal cortex and underlying white matter, verified through CT/MRI examinations. No true S1ERP/CNV components were recordable over the ablated cortical areas, whereas normal ERP/CNV complexes were observable on the intact hemispheres. In five patients, four of whom with frontocortical ablations, the S1 ERP/CNV complexes appeared severely diminished or disrupted, in two cases in a slow, partially-reversible manner, also in the neuroradiologically normal ipsilateral functionally-connected post-rolandic sensory and association areas. Similar deactivation of some ERP components was observed in reverse on the unilateral dorsolateral frontocortical region in the fifth patient with parieto-temporal cortex ablation. Even when they are partially reversible, these ipsilateral remote ERP changes in apparently intact brain regions, due to ablations of functionally-interconnected cortical formations, probably reflect cortical deactivation or simply dysfacilitation deriving from functional unilateral diaschisis. If these changes are instead irreversible they may probably be interpreted as transneuronal degeneration phenomena, though they are not at present easy to document either neuroradiologically or electroclinically.

Rapid mapping of finger representations in human primary somatosensory cortex applying neuromagnetic steady-state responses

We analyzed somatosensory evoked steady-state fields in order to localize finger representations in the hand area of the primary somatosensory cortex (S1). Using a 122-channel whole-head neuromagnetometer we recorded in six healthy subjects neuromagnetic responses to high frequency electrical stimuli delivered simultaneously to digit I, II, III and V at 22, 24, 27 and 30 Hz, respectively, and to transient stimulation of each single digit with a frequency of 3 Hz. Responses were averaged separately for each digit and were modeled by single equivalent current dipoles. Both conditions yielded the typical somatotopic finger representations within S1 hand area. Dipole locations did not differ significantly between the transient and the steady-state stimulation. Therefore, simultaneous high-frequency stimulation of the digits seems to be a reliable method for rapid and detailed mapping of the S1 hand area. This procedure has potential advantages over recording of transient responses. With simultaneous steady-state stimulation the measurement times are reduced to 2 min for mapping the whole hand area. Because of this our method probably increases spatial accuracy and permits repeated short interval recordings, e.g. in experiments studying short term plasticity.

Somatosensory processing during movement observation in humans

OBJECTIVES

A neural system matching action observation and execution seems to operate in the human brain, but its possible role in processing sensory inputs reaching the cortex during movement observation is unknown.

METHODS

We investigated somatosensory evoked potentials (SEPs), somatosensory evoked fields (SEFs) and the temporal spectral evolution of the brain rhythms (approximately 10 and approximately 20 Hz) following electrical stimulation of the right median nerve in 15 healthy subjects, during the following randomly intermingled conditions: a pure cognitive/attentive task (mental calculation); the observation of a motoric act (repetitive grasping) with low cognitive content ('Obs-grasp'); and the observation of a complex motoric act (finger movement sequence), that the subject had to recognize later on, therefore reflecting an adjunctive cognitive task ('Obs-seq'). These conditions were compared with an absence of tasks ('Relax') and actual motor performance.

RESULTS

The post-stimulus rebound of the approximately 20 Hz beta magnetoencephalographic rhythm was reduced during movement observation, in spite of little changes in the approximately 10 Hz rhythm. Novel findings were: selective amplitude increase of the pre-central N(30) SEP component during both 'Obs-grasp' and 'Obs-seq', as opposed to the 'gating effect' (i.e. amplitude decrease of the N(30)) occurring during movement execution. The strength increase of the 30 ms SEF cortical source significantly correlated with the decrease of the approximately 20 Hz post-stimulus rebound, suggesting a similar pre-central origin.

CONCLUSIONS

Changes took place regardless of either the complexity or the cognitive content of the observed movement, being related exclusively with the motoric content of the action. It is hypothesized that the frontal 'mirror neurons' system, known to directly facilitate motor output during observation of actions, may also modulate those somatosensory inputs which are directed to pre-central areas. These changes are evident even in the very first phases (i.e. few tens of milliseconds) of the sensory processing.

Neuroimaging of recovery of function after stroke: implications for rehabilitation

Stroke is a leading cause of morbidity and mortality in individuals. Many patients have good functional recovery after stroke. The mechanisms of recovery remain largely unknown. Neuroimaging of patients recovering from stroke may provide important insight into the mechanisms of recovery as well as assist in the development of new rehabilitation techniques. The first part of this article reviews previous neuroimaging studies that have monitored the reorganization within the motor and language areas after stroke. In the second section, a unifying theory based on John Hughlings Jackson's "Principles of Compensation" is presented as a possible theory for recovery of function. In the final portion of the article, possible implications and future applications of neuroimaging studies for rehabilitation are presented.

Brain plasticity for sensory and linguistic functions: a functional imaging study using magnetoencephalography with children and young adults

In this report, the newest of the functional imaging methods, magnetoencephalography, is described, and its use in addressing the issue of brain reorganization for basic sensory and linguistic functions is documented in a series of 10 children and young adults. These patients presented with a wide variety of conditions, ranging from tumors and focal epilepsy to reading disability. In all cases, clear evidence of reorganization of the brain mechanisms of either somatosensory or linguistic functions or both was obtained, demonstrating the utility of magnetoencephalography in studying, completely noninvasively, the issue of plasticity in the developing brain.

Cerebral networks in sensorimotor disturbances

Increasing evidence suggests that the human brain employs multiple, interconnected brain areas for information processing and control of behavior, including the performance of laboratory tasks. Brain diseases are expected to affect these networks directly by interference and indirectly as a consequence of deficit compensation. Covariance analyses applied to functional brain imaging data open the opportunity to study neural networks and their disease-related changes in the human brain. Here, we review our analytic approach based on principal component analysis (PCA) to address such questions. We will discuss its methodological foundations and applications in patients with sensorimotor disorders. We will show that PCA in combination with, both, hypothesis-driven testing and correlation statistics provides a powerful tool for elucidating disease-related abnormalities and postlesional reorganization of neural networks in the human brain.

Role of the mode of sensory stimulation in presurgical brain mapping in which functional magnetic resonance imaging is used

OBJECT

The aim of this study was to evaluate different types of sensory stimulation used to distinguish between microvasculature and venous drainage on functional magnetic resonance (fMR) images with blood oxygen level-dependent (BOLD) contrast.

METHODS

Seven volunteers received three sensory stimulations. One consisted of small discontinuous automated pokes to the ventral aspect of the right thumbtip. The other two were delivered by the investigator, who vigorously brushed the ventral aspect of the right thumbtip either alone or in combination with the thenar region. Seven contiguous axial slices of the head were acquired using echoplanar fMR imaging during each mode of stimulation. Boxcar analysis and Student's t-test were performed. Cluster analysis was used to determine significant differences between rest and activation phases. The major findings were 1) that a discontinuous sensory stimulation involving a small skin area was able to evoke a limited activated area in the postcentral gyrus with a low activation index (AI [2%]); 2) that this limited activated area was included in the activated area elicited by the continuous sensory stimulations; and 3) that this also evoked multiple activated areas exhibiting AIs of either approximately 2% or greater than 5%. This indicated that the limited discontinuous tactile stimulation evoked a BOLD-contrast fMR image essentially of microvasculature, whereas the more extensive continuous stimulations evoked a BOLD-contrast fMR image in both microvasculature and venous drainage.

CONCLUSIONS

Different sensory stimulations are necessary to differentiate primary sensory cortex from venous drainage for presurgical brain mapping.

Neuromagnetic integrated methods tracking human brain mechanisms of sensorimotor areas 'plastic' reorganisation

The potential for reorganization in the adult brain has been largely underestimated in the past and we are just beginning to understand the organisational principles involved in functional recovery. A bulk of experimental evidences have been accumulated in support of the hypothesis that neuronal aggregates adjacent to a lesion in the cortical brain areas can be progressively vicarious to the function of the damaged neurones. Such a reorganisation, if occurring in the affected hemisphere of a patient with a monohemispheric lesion, should significantly modify the interhemispheric symmetry of somatotopic organisation of the sensorimotor cortices, both in terms of absolute surfaces and number of "recruited" neurons, as well as of spatial coordinates. In fact, a roughly symmetrical organisation of sensorimotor - particularly for the hand contorl - in the right and left hemisphere has been observed in healthy humans by different methods of functional brain imaging, including fMRI, TMS, MEG, HD-EEG. Not uniform results about the functional brain activity related to sensory, motor and cognitive functions in normal and diseased subjects are often due to differences in the experimental paradigm designed as well as in the spatial and temporal resolution of the neuroimaging techniques used. The multi-modal integration of data obtained with several neuroimaging techniques allowed a coherent modelling of human brain higher functions. Functional magnetic resonance imaging (fMRI) provided fine spatial details (millimetres) of the brain responses, which were compared with the cortical maps of the motor output to different body districts obtained with transcranial magnetic stimulation (TMS). Magnetoencephalography (MEG) ability to study sensorimotor areas by analysing cortical magnetic fields, is also complementary to the motor cortex topographical mapping provided by TMS. MEG high temporal resolution allows to detect relatively restricted functional neuronal pools activated during cerebral processing of external stimuli. Moreover, these brain responses can be investigated with magnetoencephalography (MEG) and high density electroencephalography (EEG) techniques, with elevated time resolution (ms). With respect to the high resolution EEG technique, the MEG technique allowed a more precise localisation of the sites of neural activity buried into the cortical sulci, but was unable to detect the response of the crown of the cortical giri and of the frontal-mesial cortex (including the supplementary motor area), because of its poor sensitivity to radially oriented dipoles. The integration of functional and anatomical information provide cues on the relationship between brain activity and anatomic sites where this takes place, allowing the characterisation of the physiological activity of the cortical brain layers as well as to study the plastic reorganisation of the brain in different pathological conditions following stroke, limb amputation, spinal cord injury, hemisperectomy.

The somatosensory evoked magnetic fields

Averaged magnetoencephalography (MEG) following somatosensory stimulation, somatosensory evoked magnetic field(s) (SEF), in humans are reviewed. The equivalent current dipole(s) (ECD) of the primary and the following middle-latency components of SEF following electrical stimulation within 80-100 ms are estimated in area 3b of the primary somatosensory cortex (SI), the posterior bank of the central sulcus, in the hemisphere contralateral to the stimulated site. Their sites are generally compatible with the homunculus which was reported by Penfield using direct cortical stimulation during surgery. SEF to passive finger movement is generated in area 3a or 2 of SI, unlike with electrical stimulation. Long-latency components with peaks of approximately 80-120 ms are recorded in the bilateral hemispheres and their ECD are estimated in the secondary somatosensory cortex (SII) in the bilateral hemispheres. We also summarized (1) the gating effects on SEF by interference tactile stimulation or movement applied to the stimulus site, (2) clinical applications of SEF in the fields of neurosurgery and neurology and (3) cortical plasticity (reorganization) of the SI. SEF specific to painful stimulation is also recorded following painful stimulation by CO(2) laser beam. Pain-specific components are recorded over 150 ms after the stimulus and their ECD are estimated in the bilateral SII and the limbic system. We introduced a newly-developed multi (12)-channel gradiometer system with the smallest and highest quality superconducting quantum interference device (micro-SQUID) available to non-invasively detect the magnetic fields of a human peripheral nerve. Clear nerve action fields (NAFs) were consistently recorded from all subjects.

Environmental influence on brain-derived neurotrophic factor messenger RNA expression after middle cerebral artery occlusion in spontaneously hypertensive rats

Enriched environment significantly enhances postischemic functional outcome. We have tested the hypothesis that housing in enriched environment stimulates gene expression for brain-derived neurotrophic factor. After ligation of the middle cerebral artery in male spontaneously hypertensive rats, they were housed in individual cages for 30h, then housed either in standard cages or in an enriched environment. The rats were killed two to 30days after the ischemic event. Cryostat coronal sections through the dorsal hippocampus (Bregma -3.3) were processed for in situ hybridization using a rat-brain-derived neurotrophic factor messenger RNA antisense oligonucleotide probe. Postischemic gene expression was significantly higher in standard rats than in enriched rats in contralateral and peri-infarct cortex and in most parts of the hippocampus two, three and 12days after the ischemic event, with a trend for higher-than-baseline levels in standard rats and lower-than-baseline levels in enriched rats. At 20 and 30days the values for both groups were below baseline levels. Contrary to our hypothesis, gene expression in rats postoperatively housed in enriched environment was significantly lower than in standard rats at a time when other studies have reported hyperexcitability in the ipsilateral and contralateral cortex. Should the low messenger RNA levels correspond to low protein synthesis, this might indicate that dampening of the early postischemic hyperexcitability may be beneficial. Low levels in both groups at 20 and 30days may correspond to loss of callosal connections in the opposite hemisphere and to horizontal cortical connections in the lesioned hemisphere.

Morphology of somatosensory evoked fields: inter-hemispheric similarity as a parameter for physiological and pathological neural connectivity

The morphology of somatosensory evoked fields (SEF) following electrical separate stimulation of left and right median nerve in 22 healthy volunteers was explored. The analysis of morphological properties of individual SEFs has been performed, in order to quantify an inter-hemispheric correlation coefficient. Despite a high inter-subject variability of the SEF morphologies, a high intra-subject inter-hemispheric shape correlation occurs in the post-stimulus epoch of 100 ms from the stimulus onset. Accordingly, a normative value for the parameter describing the SEF inter-hemispheric correlation coefficient has been calculated. The present work establishes quantitative and normative descriptions of the shape similarity of SEFs from the two hands in the left and right hemispheres. This provides a database for a new parameter, which might be useful in detecting alterations in the primary sensory cortical activation due to possible unilateral alterations of sensory inflow because of either peripheral or central deficits. The described procedure has been successfully applied to a small number of patients affected by unilateral cerebrovascular lesion.

Magnetoencephalographic studies of functional organization and plasticity of the human auditory cortex

Magnetoencephalography has proven to be a powerful noninvasive tool for investigating the functional organization of the human auditory cortex and its plastic changes. The first part of this review summarizes some recent experiments on the tonotopic organization, which can be observed not only in the slow auditory evoked fields, but also in the middle-latency and the steady-state fields. In the second part of this review, recent studies on plasticity of the auditory cortex are outlined. These studies showed that the cortical representation of tones may change within hours after a reversible "functional deafferentation" (short-term plasticity) and that early musical training leads to an expansion in the cortical representation of complex harmonic sounds (long-term plasticity).

A pilot study of somatotopic mapping after cortical infarct

BACKGROUND AND PURPOSE

Animal studies have described remodeling of sensory and motor representational maps after cortical infarct. These changes may contribute to return of function after stroke.

METHODS

Functional MRI was used to compare sensory and motor maps obtained in 35 normal control subjects with results from 2 patients with good recovery 6 months after a cortical stroke.

RESULTS

During finger tapping in controls, precentral gyrus activation exceeded or matched postcentral gyrus activation in 40 of 42 cases. Patient 1 had a small infarct limited to precentral gyrus. Finger tapping activated only postcentral gyrus, a pattern not seen in any control subject. During tactile stimulation of a finger or hand in controls, postcentral gyrus activation exceeded or matched precentral gyrus activation in 11 of 14 cases. Patient 2 had a small infarct limited to postcentral gyrus and superior parietal lobule. Tactile stimulation of the finger activated only precentral gyrus, a pattern not seen in any control. In both patients, activation during pectoralis contraction was medial to the site activated during finger tapping.

CONCLUSIONS

Results during finger tapping (patient 1) and finger stimulation (patient 2) may reflect amplification of a preserved component of normal sensorimotor function, a shift in the cortical site of finger representation, or both. Cortical map reorganization along the infarct rim may be an important contributor to recovery of motor and sensory function after stroke. Functional MRI is useful for assessing motor and sensory representational maps.

Brain plasticity and stroke rehabilitation. The Willis lecture

Neuronal connections and cortical maps are continuously remodeled by our experience. Knowledge of the potential capabilityof the brain to compensate for lesions is a prerequisite for optimal stroke rehabilitation strategies. Experimental focal cortical lesions induce changes in adjacent cortex and in the contralateral hemisphere. Neuroimaging studies in stroke patients indicate altered poststroke activation patterns, which suggest some functional reorganization. To what extent functional imaging data correspond to outcome data needs to be evaluated. Reorganization may be the principle process responsible for recovery of function after stroke, but what are the limits, and to what extent can postischemic intervention facilitate such changes? Postoperative housing of animals in an enriched environment can significantly enhance functional outcome and can also interact with other interventions, including neocortical grafting. What role will neuronal progenitor cells play in future rehabilitation-stimulated in situ or as neural replacement? And what is the future for blocking neural growth inhibitory factors? Better knowledge of postischemic molecular and neurophysiological events, and close interaction between basic and applied research, will hopefully enable us to design rehabilitation strategies based on neurobiological principles in a not-too-distant future.

Environmental influence on gene expression and recovery from cerebral ischemia

An emerging concept in neurobiology is that the adult brain retains a capacity for plasticity and functional reorganization throughout the life span. Experimental data from electrophysiological, morphological and behavioral studies have documented experience dependent plasticity in the intact and injured adult brain. Neuroimaging clinical studies indicate altered post stroke functional activation patterns, usually including activation of the intact hemisphere. However, there is some disagreement regarding their functional significance and longitudinal studies correlating outcome and activation pattern are needed to solve some controversies. Postoperative housing of rats in activity stimulating environment after ligation of the middle cerebral artery significantly enhances outcome. Gene expression for brain derived neurotrophic factor and Ca2+/calmodulin-dependent protein kinase II, two substances with potential role in brain plasticity, show different patterns in animals housed in standard and in enriched environment. The functional significance of altered gene expression needs to be evaluated.

The role of diaschisis in stroke recovery

BACKGROUND AND PURPOSE

Recovery from hemiparesis after stroke has been shown to involve reorganization in motor and premotor cortical areas. However, whether poststroke recovery also depends on changes in remote brain structures, ie, diaschisis, is as yet unresolved. To address this question, we studied regional cerebral blood flow in 7 patients (mean+/-SD age, 54+/-8 years) after their first hemiparetic stroke.

METHODS

We analyzed imaging data voxel by voxel using a principal component analysis by which coherent changes in functional networks could be disclosed. Performance was assessed by a motor score and by the finger movement rate during the regional cerebral blood flow measurements.

RESULTS

The patients had recovered (P<0. 001) from severe hemiparesis after on average 6 months and were able to perform sequential finger movements with the recovered hand. Regional cerebral blood flow at rest differentiated patients and controls (P<0.05) by a network that was affected by the stroke lesion. During blindfolded performance of sequential finger movements, patients were differentiated from controls (P<0.05) by a recovery-related network and a movement-control network. These networks were spatially incongruent, involving motor, sensory, and visual cortex of both cerebral hemispheres, the basal ganglia, thalamus, and cerebellum. The lesion-affected and recovery-related networks overlapped in the contralesional thalamus and extrastriate occipital cortex.

CONCLUSIONS

Motor recovery after hemiparetic brain infarction is subserved by brain structures in locations remote from the stroke lesion. The topographic overlap of the lesion-affected and recovery-related networks suggests that diaschisis may play a critical role in stroke recovery.

Somatosensory evoked magnetic fields from the primary somatosensory cortex (SI) in acute stroke

We recorded somatosensory evoked magnetic fields (SEFs) to median nerve stimulation from 15 patients in the acute stage (1-15 days from the onset of the symptoms) of their first-ever unilateral stroke involving sensorimotor cortical and/or subcortical structures in the territory of the middle cerebral artery (MCA). Neuronal activity corresponding to the peaks of the N20m, P35m and P60m SEF deflections from the contralateral primary somatosensory cortex (SI) was modelled with equivalent current dipoles (ECDs), the locations and strengths of which were compared with those of an age-matched normal population. Four patients with pure motor stroke had symmetric SEFs. In one of the 4 patients with pure sensory stroke, and in 5 of the 7 patients with sensorimotor paresis, the SEFs were markedly attenuated or missing. All except one patient with abnormal SEFs had deficient two-point discrimination ability; especially the attenuation of N20m was more clearly correlated with two-point discrimination than with joint-position or vibration senses. Of the different SEF deflections, P35m and P60m were slightly more sensitive indicators of abnormality than N20m, the former being affected in two patients with symmetric N20m. Three patients with pure sensory stroke and lesions in the opercular cortex had normal SEFs from SI. We conclude that the SEF deflections N20m, P35m and P60m from SI are related to cutaneous sensation, in particular discriminative to touch. The results also demonstrate that basic somatosensory perception can be affected by lesions in the opercular cortex in patients with functionally intact SI.

Neuronal damage and plasticity identified by microtubule-associated protein 2, growth-associated protein 43, and cyclin D1 immunoreactivity after focal cerebral ischemia in rats

BACKGROUND AND PURPOSE

An objective of therapeutic intervention after cerebral ischemia is to promote improved functional outcome. Improved outcome may be associated with a reduction of the volume of cerebral infarction and the promotion of cerebral plasticity. In the developing brain, neuronal growth is concomitant with expression of particular proteins, including microtubule-associated protein 2 (MAP-2), growth-associated protein 43 (GAP-43), and cyclin D1. In the present study we measured the expression of select proteins associated with neurite damage and plasticity (MAP-2 and GAP-43) as well as cell cycle (cyclin D1) after induction of focal cerebral ischemia in the rat.

METHODS

Brains from rats (n=28) subjected to 2 hours of middle cerebral artery occlusion and 6 hours, 12 hours, and 2, 7, 14, 21, and 28 days (n=4 per time point) of reperfusion and control sham-operated (n=3) and normal (n=2) rats were processed by immunohistochemistry with antibodies raised against MAP-2, GAP-43, and cyclin D1. Double staining of these proteins for cellular colocalization was also performed.

RESULTS

Loss of immunoreactivity of both MAP-2 and GAP-43 was observed in most damaged neurons in the ischemic core. In contrast, MAP-2, GAP-43, and cyclin D1 were selectively increased in morphologically intact or altered neurons localized to the ischemic core at an early stage (eg, 6 hours) of reperfusion and in the boundary zone to the ischemic core (penumbra) during longer reperfusion times.

CONCLUSIONS

The selective expressions of the neuronal structural proteins (MAP-2 in dendrites and GAP-43 in axons) and the cyclin D1 cell cycle protein in neurons observed in the boundary zone to the ischemic core are suggestive of compensatory and repair mechanisms in ischemia-damaged neurons after transient focal cerebral ischemia.

A neuromagnetic normative data set for hemispheric sensory hand cortical representations and their interhemispheric differences

Somatotopy of human hand primary sensory cortex has been studied neuromagnetically [C. Baumgartner, A. Doppelbauer, L. Deecke, D.S. Barth, J. Zeitlhofer, G. Lindinger, W.W. Sutherling, Neuromagnetic investigation of somatotopy of human hand somatosensory cortex, Exp. Brain Res. 87 (1991) 641-648.] [1]. Investigation of sensory cortex devoted to the hand will be of major importance in relation to clinical recovery after sensorimotor deficits as well as an index of plasticity phenomena following alterations of peripheral nerves inputs. Here a normative data set has been constructed, on the basis of the neuromagnetic investigation of the primary sensory hand cortical representation in the two hemispheres of 20 healthy volunteers. This can be used to evaluate interhemispheric differences of the 'sensory' hand areas during experimental paradigms in the healthy as well as following patients with monohemispheric lesions. The localizations in each hemisphere of the cortical Equivalent Current Dipoles (ECDs) activated with the shortest latencies (N20m and P30m components) by separate stimulation of left and right median nerve, thumb and little finger were analysed. By considering the ECDs to thumb and little finger stimulation the boundaries of the hand cortical representation in primary sensory cortex, the 'hand extension' was measured as the distance between the two. For all the considered parameters (related to N20m and P30m ECDs: latency, strength, spatial position in the individual head, 'hand extension', interhemispheric differences) the appropriate variable distribution was considered and by including the 98% of the healthy population normative limits were calculated.