The figure at left represents an idealized nerve cell in which recordings are made from different regions along the axon at 1 mm increments. The cell body is impaled with a stimulating electrode connected to a battery, the value of which changes the potential of the cell body to mV the equivalent of putting a 10 o C rod on a o C hot plate.
This axon, even though it initially had a spatially uniform resting potential of mV, now has a potential of mV in the soma because that is the region in which the stimulus is applied. However, the potential is not mV all along the axon; it varies as a function of distance from the soma. One mm away the potential is mV; at 2 mm away it is even closer to mV; and far enough along the axon, the potential of the axon is mV, the resting potential.
In Figure 3. Thus, whereas the time constant is an index of how rapidly a membrane would respond to a stimulus in time, the space constant is an index of how well a subthreshold potential will spread along an axon as a function of distance.
The space constant is a passive property of membranes. Although it influences the rate of propagation of the action potentials, it is an independent process. It is like the surface of a race track and the action potential is like the race car. If the surface is muddy, the car will go slow, if it is firm and paved, the same car will be able to go much faster.
The length constant can be described in terms of the physical parameters of the axon, where d is the diameter of the axon, R m is, as before, the membrane resistance, the inverse of the permeability, and R i is the internal resistance resistance of the axoplasm. R i is an indicator of the ability of charges to move along the inner surface of the axon. A small subthreshold change in the charge distribution at one point along an axon will spread along the axon, but as it does some will diffuse back out of the membrane and some will continue to move along the axon.
If the resistance of the membrane R m is high, less will leak out and relatively more will move along the axon. Increasing R m is like putting insulation on a metal rod and heating the rod at one end. With more insulation more resistance to heat loss to the outside of the rod , more heat will travel along the inside of the rod.
Propagation Velocity. How are the time constant and the space constant related to propagation velocity of action potentials? The smaller the time constant, the more rapidly a depolarization will affect the adjacent region. If a depolarization more rapidly affects an adjacent region, it will bring the adjacent region to threshold sooner. Therefore, the smaller the time constant, the more rapid will be the propagation velocity.
If the space constant is large, a potential change at one point would spread a greater distance along the axon and bring distance regions to threshold sooner. Therefore, the greater the space constant, the more rapidly distant regions will be brought to threshold and the more rapid will be the propagation velocity. Thus, the propagation velocity is directly proportional to the space constant and inversely proportional to the time constant. There are separate equations that describe both the time constant and the space constant.
The insight above allows us to make a new equation that combines the two. The equation provides insights into how it is possible for different axons to have different propagation velocities. One way of endowing an axon with a high propagation velocity is to increase the diameter. However, there is one serious problem in changing the propagation velocity by simply changing the diameter.
To double the velocity, it is necessary to quadruple the diameter. Clearly there must be a better way of increasing propagation velocity than by simply increasing the diameter. Another way to increase the propagation velocity is to decrease the membrane capacitance. This can be achieved by coating axons with a thick insulating sheath known as myelin. Instead of coating the entire axon with the myelin, only sections are coated and some regions called nodes are left bare.
Propagation of action potentials in myelinated fibers is illustrated in Figure 3. They can be caused by brain diseases such as Alzheimer disease , which doctors believe is associated with plaques and tangles forming in the brain.
Delirium is sudden confusion that leads to changes in thinking and behavior. It is often due to illnesses that are not related to the brain. Infection can cause an older person to become severely confused. Certain medicines can also cause this. Thinking and behavior problems can also be caused by poorly controlled diabetes.
Rising and falling blood sugar levels can interfere with thought. Seek medical help right away if these symptoms occur suddenly or along with other symptoms. A change in thinking, memory, or behavior is important if it is different from your normal patterns or it affects your lifestyle. Differential diagnosis of spinal disease. In: Winn HR, ed. Youmans and Winn Neurological Surgery. Philadelphia, PA: Elsevier; chap Martin J, Li C. Normal cognitive aging. Brocklehurst's Textbook of Geriatric Medicine and Gerontology.
Arrows denote central sulcus. A corresponding analysis for the right-side injured participants failed to detect any effect in the contralesional primary sensorimotor cortex. However, a greater inter-individual variability in the location of the hand representation in the left than in the right hemisphere possibly remaining after the spatial normalization procedure could have prevented detection of an effect in the left primary sensorimotor cortex.
To address this issue, we repeated the SVC-analysis after realigning the smoothed brain image of each participant in the transaxial plane based on the coordinates of the cortical knob-like structure. In this slice, we identified for each participant and hemisphere the apex of the omega shaped cortical knob-structure and used the recorded X and Y coordinates for the realignment.
Defined as the Euclidian distance of the sampled coordinates to their centroid, the inter-individual variability compensated for by the realignment was 1. After the realignment, the SVC-analysis still failed to detect any significant effect for the right-side injured participants. Corresponding SVC analyses of the ipsilesional primary sensorimotor cortex for each group of injured participants did not reveal any significant effect. To investigate possible relationships between the functional impact of the injury in a subjective perspective and the size of observed structural changes, we correlated the DASH-scores with the standardized effect size for the area showing a structural effect in the right M1 of the left injured participants.
The failure of this analysis to reproduce the voxel gray matter effect in the right M1 observed in the SVC-analyses could be explained by a higher cluster threshold value in the whole brain analysis voxels. As for the whole brain analysis that contrasted the left- and right-side injured participants, no effects were observed in the primary sensorimotor cortices, but effects were detected in other brain areas. First, we found reduced gray matter volume in two lateral premotor regions.
Median nerve injury had no detectable effects on the gray matter volume in the homologous contralateral areas, i. Reduced gray and white matter volume in premotor areas of median nerve-injured participants. Green areas indicate extrastriate visual areas with increased gray matter volume.
R, right; L, left; A, anterior; P, posterior. Distribution of gray matter volume in the detected zones in left PMv and right PMd, and white matter volume in CC and RCC from areas in a among the nerve-injured participants red and blue filled circles and the control participants black open circles. For further details, see legend of Fig. Second, the nerve-injured participants also showed volume reductions in white matter tracts Fig.
Specifically, this reduction was observed in the midbody of the corpus callosum CC that interconnect the premotor areas of the two hemispheres 43 , 44 and in a sector of white matter radiating from corpus callosum RCC to the right PMd. Correlation of gray and white matter volumes in right premotor areas. Positive correlation between the gray matter volume in the right dorsal premotor cortex PMd and the white matter volume in the right radiation of corpus callosum RCC across the nerve-injured participants.
The solid line shows the orthogonal linear regression line; participants with left red and right blue sided injury pooled. Inlay of slice image from Fig. The left- and right-side injured groups showed similar structural effects in the abovementioned premotor areas and white matter tracts see red and blue filled circles in Fig. In the nerve-injured participants we also observed regional increases in gray matter volume, namely bilaterally in the posterior part of middle temporal gyrus near the occipito-temporal junction close to the intersection of BA 39, 37 and 19 Fig.
Similar effect sizes were found when analyzing the left- and right-side injured participants separately see red and blue symbols in Fig. For the left hemisphere, the effect size was 1. The corresponding values for the right hemisphere were 1.
Increased gray matter volume in extrastriate visual areas of median nerve-injured participants. Our findings indicate that median nerve transection followed by surgical repair and reinnervation of the hand can cause long-term structural changes in several brain areas, and in particular those that are functionally implicated in planning and control of skilled manual actions.
That the detected effects were synaptically remote from the lesioned neurons and involved reductions as well as increases of cortical gray matter volume strongly suggest that they represent complex activity-dependent adaptations in specific processing units in the brain 11 , 12 , 47 , Strikingly, the observed structural changes in the brain predominantly concerned higher-order rather than primary sensorimotor areas.
The lack of detectable effect in contralesional S1 and limited effects in contralesional M1 stands in contrast to the considerable gray matter effects in these areas reported in persons with sensorimotor deprivation caused by amputation or immobilization of an upper extremity 18 , 19 , A likely explanation for the overall spared primary sensorimotor areas in our nerve injured participants is that they regularly used their affected hand in everyday activities.
Indeed, the consequences of the injury were subtle enough for them to return to their usual jobs. Nevertheless, our nerve injured participants were unable to perform certain everyday tasks requiring fine finger dexterity, such as tying shoelaces. This behavioral restriction can be explained by the nerve injury preventing them from successfully executing one or more of the sequentially linked action phases involved in the performance of the impeded tasks We believe that the decrease in the gray matter volume detected in higher-order sensorimotor areas PMv, PMd reflected decreased neural processing associated with such limitations in the normal manual action repertoire.
For the effect found in extrastriatal visual cortex of the nerve-injured participants, we believe that the gray matter increase reflected increased visuomotor processing for compensation of a compromised tactile sensory innervation of the affected hand. For the primary sensorimotor cortex, we found gray matter volume reduction in a limited zone of the contralesional M1 for the left-side injured participants but not for the right-side injured.
This suggest that the activity in the left M1 after contralateral injury is maintained to a higher degree than the corresponding activity in the right M1. At least three different factors related to hemispheric specialization in the human brain of right-handers might contribute to such an asymmetry in M1 activity. First, compared with the left-side injured, participants with their right dominant side injured were probably more inclined to reclaim the use of the affected hand after reinnervation and would therefore have engaged the contralesional M1 to a higher degree.
The second factor relates to the observation that the engagement of the ipsilateral M1 differ for left and right hand actions. That is, left hand actions engage the left ipsilateral M1 to a higher degree than right hand actions engage the right ipsilateral M1 50 , Therefore, left hand actions performed by the right-side injured would tend to maintain processing in the left M1 to a higher degree after the injury than right hand actions performed by left-side injured would tend to do in the right M1.
Third, a restriction in the bimanual action repertoire due to the nerve injury is likely to reduce the processing in the contralesional M1 more in the left- than in the right-side injured participants. This is because the use of the left-hand, in relative terms, is more often associated with bimanual tasks compared to the use of the right dominant hand. Indeed, complex bimanual coordination involving fine finger dexterity characterizes most daily manual skills, such as dressing, personal hygiene, grooming, preparation of food and eating, and numerous work-related tasks often involving tool usage 52 , The lack of activity-dependent gray matter effects in the contralesional S1 irrespective of injured side is not entirely surprising since functional imaging studies in humans have reported that tactile stimulation of fingers can activate the contralateral S1 to a similar extent after median nerve injury and reinnervation as in healthy individuals 17 , 32 , Likewise, experimental studies in monkeys have shown that the median nerve largely recaptures its original cortical territory after transection and reinnervation, but with distortions of the somatotopic representation 24 , 25 , 26 , We suggest that the reduced gray matter volume detected in PMv and PMd of the nerve-injured participants were associated with decreased neural processing in these areas due to the restrictions in their natural manual action repertoire see above.
Through mutual interactions and interactions with M1, these premotor areas are responsible for higher-level planning and control of goal directed manual actions. To that end, they integrate information about action-goals from prefrontal cortex and multimodal sensory state information from parietal cortex, including somatosensory information from the hands 54 , 55 , 56 , 57 , 58 , 59 , That the effects observed in the premotor areas were lateralized in a hemispherical asymmetrical manner independent of side of injury is in accordance with evidence for hemispherical specialization in higher-level multi-modal processing that underlie implementation of learned skilled hand actions in right-handers 34 , 35 , 36 , Accordingly, the reduction in the gray matter of the left PMv irrespective of side of injury likely reflected a reduced, or even ceased, processing in certain neuronal assemblies representing compound motor acts that could not be realized because of the insufficient innervation of the affected hand.
In the same vein, a reduction of the gray matter lateralized to the right PMd irrespective of affected hand is consistent with a sub-population of PMd-neurons showing limb-independent processing 64 , 65 and that the right PMd has a special role in the kinematic processing of grip formations in humans irrespective of acting hand Similarly, dorsal parieto—premotor networks of the human right hemisphere are considered implicated in the processing of kinematic aspects of hand movements in haptic object exploration 67 and, more generally, in processing of spatial aspects of occurrences across and close to the entire body surface 68 , Moreover, since the right PMd seems particularly involved in complex bimanual coordination 70 , 71 , 72 , restrictions in the bimanual action repertoire due to impairment of one hand could have contributed to an activity-dependent reduction of gray matter.
In accordance with findings on activity-dependent changes in myelination 12 , the observed white matter reduction in the premotor commissural pathways would also be in agreement with restrictions in the bimanual action repertoire. The gray matter increase observed bilaterally in the posterior middle temporal gyrus of the nerve-injured participants matched the increased dependence on vision in activities requiring skillful object handling at impaired tactile innervation of a hand 4 , 73 , 74 , Likewise, manual visuomotor skill acquisition is associated with increased gray matter density especially in this extrastriate visual area 13 , To our knowledge, only one previous study has examined structural brain changes after injury and repair of the principal nerves innervating the hand In contrast to our findings, this study only reported reductions in gray matter and in areas not specifically associated with hand control, including areas of post-central gyrus seemingly distant from the primary hand representations.
Methodological factors presumably account for this difference: VBM and VBCT measures different structural characteristics and are considered complementary for local gray matter analysis, where VBM is additionally sensitive to local surface area and cortical folding 87 , 88 , In addition, the participant-groups in the two studies were heterogeneous regarding nerves injured. Our results are limited by several factors, including those inherent to the VBM technique Although the restricted sample size limited the statistical power of relevant analyses, the effects exposed in the premotor and the extrastriatal areas were seen in both the left- and right-side injured subgroups when analyzed separately.
That the detected structural effects only included fractions of the network of brain areas and pathways implicated in control of manual dexterity suggests that the identified areas were the most sensitive ones concerning activity-dependent structural plasticity associated with persistent dexterity impairments of the nerve-injured participants. Another weakness in our study concerns deficiencies in the characterization of the behavioral impairments of our nerve-injured participants, which could have prevented the detection of possible relationships between sizes of structural effects and functional impacts.
Neither established questionnaires, such as the DASH questionnaire, nor existing performance tests, which focus on what a person can do in a highly standardized environment, address systematically the natural diversity and complexity of fine finger dexterity at a level of detail required for quantification of the various more or less subtle aspects of the disabilities remaining after median nerve reinnervation 91 , Likewise, established performance tests do not explicitly address bimanual behaviors.
Moreover, the kind of cross-sectional study used here does not favor the discovery of quantitative relationships between behavioral and structural effect sizes. First, since the structural conditions of the individual brain prior to injury were not available as a reference, the amount of structural change after injury could not be assessed at the individual level.
Second, our study reveals little about the time course of structural brain changes after median nerve injury. Additional gray and white matter changes may have existed during the months-long period when the hand was partially paralyzed and deprived of sensations before reinnervation 7 , Depending on the degree of reengagement of the hand in daily assignments after reinnervation, some structural changes might have reversed totally whereas others only partially 47 , 93 , Resolution of both of these potentially confounding factors would require a longitudinal study design that maps the structure of each brain before it is affected by the nerve injury.
The study included 16 median nerve-injured right-handed adult participants four females and 16 healthy right-handers matched to age and sex. None of the participants suffered from diabetes or neurological disorders. All participants gave their informed written consent in accordance with the Declaration of Helsinki. Eleven of the participants had suffered sharp complete transection injury of the median nerve at the left distal forearm three females and five one female at the right distal forearm.
Injuries to tendons and arteries Table 1 were surgically repaired in the same session. A standard clinical assessment of the nerve-injured patients was performed more than two years after surgery. This concerned sudomotor function, range of motion and muscle atrophy of the affected hand, and static 2-point discrimination threshold at the tips of the reinnervated digits.
To assess the practical consequences of the nerve-injury, participants were asked to describe how the injury affected their everyday life including effects on working ability.
Thus, the responses to the DASH questionnaire do not indicate how the activities are conducted and to what extent behavioral compensatory strategies are used to deal with the effects of the injury.
For the healthy controls, the outcomes of these questionnaires was normal. Only two participants reported some cold intolerance where one scored 4 and the other 8 points. We used a three-dimensional fast spoiled gradient echo sequence to acquire a series of transaxial T1-weighted images with the following MR-parameters: TE, 3.
To improve the accuracy of inter-subject alignment we used diffeomorphic image registration DARTEL ; of the segmented gray and white matter images before we normalized the single-participant images to MNI space. We then entered the pre-processed single-participant gray and white matter images into group analyses using the voxel-based morphometry VBM software provided in SPM8 A general linear model analysis was performed at each voxel where group of participants constituted the predictor of prime interest.
Furthermore, to statistically control for influences of age and sex on regional gray and white matter volumes , in all analyses, age constituted a continuous predictor and sex a categorical predictor. To protect against false positives while at the same time retain the power to detect meaningful effects in the face of multiple comparisons across image voxels , in all statistical analyses of effects of nerve injury see below we subjected the preprocessed morphometric images to a two-step threshold approach Forman et al.
To test specifically our hypothesis of a change in gray matter volume within the contralesional M1 and S1, we compared each group of injured participants left- and right- side injury separately with the control participants using a small-volume correction SVC analysis implemented in SPM8 two-tailed t-test.
We based these coordinates on average local maxima of the 3-D peak coordinates for the primary sensorimotor cortex of the hand established in a meta-analysis based on functional brain imaging To maximize the power we included all 16 control-participants.
We also applied a whole brain analysis to seek for effects beyond the primary sensorimotor cortex. In these analyses, we looked for effects on gray and white matter that would depend on side of injury as well as effects that would be independent of side of injury. For this analysis, a cluster size threshold of one-half of that in the standard double-threshold approach was used to search for areas showing symmetrically localized bilateral effects on the gray and white matter volume. We motivate this approach with the argument that bilateral homologous effects with high probability indicate meaningful effects given the strong structural and functional connectivity between bilaterally connected areas 43 , 44 , , Effect sizes are also reported as the signed difference between the mean values obtained for the injured and the control group expressed as percentage of the mean value of the control group; the estimate of the standard error SE was based on the pooled variance of the two populations.
In data analysis, we used an alpha level of 0. Bonferroni corrections were used to compensate for multiple comparisons. The datasets analyzed during the current study are available from the corresponding author on reasonable request. However, in accordance with patient confidentiality, personal data from participants in the study will not be disclosed.
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