A model for compound action potentials and currents in a nerve bundle. I: The forward calculation

Computational models of compound nerve action potentials: Efficient filter-based methods to quantify effects of tissue conductivities, conduction distance, and nerve fiber parameters

BACKGROUND

Peripheral nerve recordings can enhance the efficacy of neurostimulation therapies by providing a feedback signal to adjust stimulation settings for greater efficacy or reduced side effects. Computational models can accelerate the development of interfaces with high signal-to-noise ratio and selective recording. However, validation and tuning of model outputs against in vivo recordings remains computationally prohibitive due to the large number of fibers in a nerve.

METHODS

We designed and implemented highly efficient modeling methods for simulating electrically evoked compound nerve action potential (CNAP) signals. The method simulated a subset of fiber diameters present in the nerve using NEURON, interpolated action potential templates across fiber diameters, and filtered the templates with a weighting function derived from fiber-specific conduction velocity and electromagnetic reciprocity outputs of a volume conductor model. We applied the methods to simulate CNAPs from rat cervical vagus nerve.

RESULTS

Brute force simulation of a rat vagal CNAP with all 1,759 myelinated and 13,283 unmyelinated fibers in NEURON required 286 and 15,860 CPU hours, respectively, while filtering interpolated templates required 30 and 38 seconds on a desktop computer while maintaining accuracy. Modeled CNAP amplitude could vary by over two orders of magnitude depending on tissue conductivities and cuff opening within experimentally relevant ranges. Conduction distance and fiber diameter distribution also strongly influenced the modeled CNAP amplitude, shape, and latency. Modeled and in vivo signals had comparable shape, amplitude, and latency for myelinated fibers but not for unmyelinated fibers.

CONCLUSIONS

Highly efficient methods of modeling neural recordings quantified the large impact that tissue properties, conduction distance, and nerve fiber parameters have on CNAPs. These methods expand the computational accessibility of neural recording models, enable efficient model tuning for validation, and facilitate the design of novel recording interfaces for neurostimulation feedback and understanding physiological systems.

Neuromuscular Magnetic Field Measurement Based on Superconducting Bio-Sensors

These years, disease-causing and disabling diseases have caused great concern. Neurological musculoskeletal disorders are diverse and affect people of a wide range of ages. And the lack of comprehensive diagnostic methods places a huge burden on healthcare systems and social economies. In this paper, the current status of clinical research on neuromuscular diseases is introduced, and the advantages of magnetic field measurement compared with clinical diagnostic methods are illustrated. A comprehensive description of the related technology of superconducting quantum interference devices (SQUIDs), magnetic field detection noise suppression scheme, the development trend of the sensor detection system, and the application and model establishment of the neuromuscular magnetic field is also given in this paper. The current research and development trends worldwide are compared simultaneously, and finally the conclusions and outlook are put forward. Based on the description of the existing literature and the ideas of other researchers, the next development trends and my own research ideas are presented in this paper, that is, starting from the establishment of a neuromuscular model, combining medical and industrial work, designing a sensor system that meets clinical needs, and laying the foundation for the clinical application of a bio-magnetic system. This review promotes a combination between medicine and industry, and guides researchers on considering the challenges of sensor development in terms of clinical needs. In addition, in this paper, the development trends are described, including the establishment of the model, the clinical demand for sensors, and the challenges of system development so as to give certain guidance to researchers.

Biomagnetism: The First Sixty Years

Biomagnetism is the measurement of the weak magnetic fields produced by nerves and muscle. The magnetic field of the heart-the magnetocardiogram (MCG)-is the largest biomagnetic signal generated by the body and was the first measured. Magnetic fields have been detected from isolated tissue, such as a peripheral nerve or cardiac muscle, and these studies have provided insights into the fundamental properties of biomagnetism. The magnetic field of the brain-the magnetoencephalogram (MEG)-has generated much interest and has potential clinical applications to epilepsy, migraine, and psychiatric disorders. The biomagnetic inverse problem, calculating the electrical sources inside the brain from magnetic field recordings made outside the head, is difficult, but several techniques have been introduced to solve it. Traditionally, biomagnetic fields are recorded using superconducting quantum interference device (SQUID) magnetometers, but recently, new sensors have been developed that allow magnetic measurements without the cryogenic technology required for SQUIDs.

Comparative study of extracellular recording methods for analysis of afferent sensory information: Empirical modeling, data analysis and interpretation

BACKGROUND

Physiological studies of sensorial systems often require the acquisition and processing of data extracted from their multiple components to evaluate how the neural information changes in relation to the environment changes. In this work, a comparative study about methodological aspects of two electrophysiological approaches is described.

NEW METHOD

Extracellular recordings from deep vibrissal nerves were obtained by using a customized microelectrode Utah array during passive mechanical stimulation of rat´s whiskers. These recordings were compared with those obtained with bipolar electrodes. We also propose here a simplified empirical model of the electrophysiological activity obtained from a bundle of myelinated nerve fibers.

RESULTS

The peripheral activity of the vibrissal system was characterized through the temporal and spectral features obtained with both recording methods. The empirical model not only allows the correlation between anatomical structures and functional features, but also allows to predict changes in the CAPs morphology when the arrangement and the geometry of the electrodes changes.

COMPARISON WITH EXISTING METHOD(S)

This study compares two extracellular recording methods based on analysis techniques, empirical modeling and data processing of vibrissal sensory information.

CONCLUSIONS

This comparative study reveals a close relationship between the electrophysiological techniques and the processing methods necessary to extract sensory information. This relationship is the result of maximizing the extraction of information from recordings of sensory activity.

Axonal excitability and conduction alterations caused by levobupivacaine in rat

In this study, effects of the long-acting amide-type local anesthetic levobupivacaine on axonal conduction and excitability parameters of the rat sciatic nerve were thoroughly examined both in vitro and in vivo. In order to deduce its effects on isolated nerve conduction, compound nerve action potential (CNAP) recordings were performed using the suction method over sciatic nerves of Wistar rats before and after administration of 0.05 % (1.7 mmol L-1) levobupivacaine. Levobupivacaine caused complete CNAP area and amplitude depression by blocking conduction in a time-dependent manner. To assess the influence of levobupivacaine on in vivo excitability properties, threshold-tracking (TT) protocols were performed at sciatic nerves of rats injected with perineural 0.05 % (1.7 mmol L-1) levobupivacaine or vehicle alone. Charge-duration TT results revealed that levobupivacaine increases the rheobase and decreases the strength-duration time constant, suggesting interference of the anesthetic with the opening of Na+ channels. Twenty and 40 % threshold electrotonus curves were found for both groups to follow the same paths, suggesting no significant effect of levobupivacaine on K+ channels for either the fastest or relatively slow conducting fibers. Current-threshold relationship results revealed no significant effect on axonal rectifying channels. However, according to the results of the recovery cycle protocol yielding the pattern of excitability changes following the impulse, potential deviation was found in the recovery characteristics of Na+ channels from the absolute refractory period. Consequently, conduction blockage caused by levobupivacaine may not be due to the passive (capacitive) properties of axon or the conductance of potassium channels but to the decrease in sodium channel conductance.

Non-invasive detection of animal nerve impulses with an atomic magnetometer operating near quantum limited sensitivity

Magnetic fields generated by human and animal organs, such as the heart, brain and nervous system carry information useful for biological and medical purposes. These magnetic fields are most commonly detected using cryogenically-cooled superconducting magnetometers. Here we present the first detection of action potentials from an animal nerve using an optical atomic magnetometer. Using an optimal design we are able to achieve the sensitivity dominated by the quantum shot noise of light and quantum projection noise of atomic spins. Such sensitivity allows us to measure the nerve impulse with a miniature room-temperature sensor which is a critical advantage for biomedical applications. Positioning the sensor at a distance of a few millimeters from the nerve, corresponding to the distance between the skin and nerves in biological studies, we detect the magnetic field generated by an action potential of a frog sciatic nerve. From the magnetic field measurements we determine the activity of the nerve and the temporal shape of the nerve impulse. This work opens new ways towards implementing optical magnetometers as practical devices for medical diagnostics.

A model of evoked potentials in spinal cord stimulation

Electrical stimulation of the spinal cord is used for pain relief, and is in use for hundreds of thousands of cases of chronic neuropathic pain. In spinal cord stimulation (SCS), an array of electrodes is implanted in the epidural space of the cord, and electrical currents are used to stimulate nearby nerve fibers, believed to be in the dorsal columns of the cord. Despite the long history of SCS for pain, stretching over 30 years, its underlying mechanisms are poorly understood, and the therapy has evolved very little in this time. Recent work has resulted in the ability to record complex compound action potential waveforms during therapy. These waveforms reflect the neural activity evoked by the therapeutic stimulation, and reveal information about the underlying physiological processes. We aim to simulate these processes to the point of reproducing these recordings. We establish a hybrid model of SCS, composed of a three dimensional electrical model and a neural model. The 3D model describes the geometry of the spinal regions under consideration, and the electric fields that result from any flow of current within them. The neural model simulates the behaviour of spinal nerve fibers, which are the target tissues of the therapy. The combination of these two models is used to predict which fibers may be recruited by a given stimulus, as well as to predict the ensuing recorded waveforms. The model is shown to reproduce major features of spinal compound action potentials, such as threshold and propagation behaviour, which have been observed in experiments. The model's coverage of processes from stimulation to recording allows it to be compared side-by-side with actual experimental data, and will permit its refinement to a substantial level of accuracy.

Investigating the effect of thermal stress on nerve action potential using the soliton model

The thermal mechanism of acoustic modulation of the reversible electrical activities of peripheral nerves is investigated using the soliton model, and a numerical solution is presented for its non-homogenous version. Our results indicate that heating a small segment of the nerve will increase the action potential conduction velocity and decrease its amplitude. Moreover, cooling the nerve will have the reverse effects, and cooling to temperatures below the nerve melting point can reflect back a significant portion of the action potentials. These results are consistent with the theory of the soliton model, as well as with the experimental findings. Although there exists a discrepancy between the results of the soliton model and experimental pulse amplitude data, from the free energy point of view, the experiments are compatible with Heimburg and Jackson theory. We conclude that the presented model accompanied by the free energy view is capable of simulating the effects of thermal energy on nerve function. One potential application of the developed theoretical model will be investigation of the reversible and irreversible effects of thermal energy induced by various energy modalities, including therapeutic ultrasound, on nerve function.

A simulation study of the combined thermoelectric extracellular stimulation of the sciatic nerve of the Xenopus laevis: the localized transient heat block

The electrical behavior of the Xenopus laevis nerve fibers was studied when combined electrical (cuff electrodes) and optical (infrared laser, low power sub-5 mW) stimulations are applied. Assuming that the main effect of the laser irradiation on the nerve tissue is the localized temperature increase, this paper analyzes and gives new insights into the function of the combined thermoelectric stimulation on both excitation and blocking of the nerve action potentials (AP). The calculations involve a finite-element model (COMSOL) to represent the electrical properties of the nerve and cuff. Electric-field distribution along the nerve was computed for the given stimulation current profile and imported into a NEURON model, which was built to simulate the electrical behavior of myelinated nerve fiber under extracellular stimulation. The main result of this study of combined thermoelectric stimulation showed that local temperature increase, for the given electric field, can create a transient block of both the generation and propagation of the APs. Some preliminary experimental data in support of this conclusion are also shown.

Magnetic measurements of peripheral nerve function using a neuromagnetic current probe

The progress made during the last three decades in mathematical modeling and technology development for the recording of magnetic fields associated with cellular current flow in biological tissues has provided a means of examining action currents more accurately than that of using traditional electrical recordings. It is well known to the biomedical research community that the room-temperature miniature toroidal pickup coil called the neuromagnetic current probe can be employed to measure biologically generated magnetic fields in nerve and muscle fibers. In contrast to the magnetic resonance imaging technique, which relies on the interaction between an externally applied magnetic field and the magnetic properties of individual atomic nuclei, this device, along with its room-temperature, low-noise amplifier, can detect currents in the nano-Ampere range. The recorded magnetic signals using neuromagnetic current probes are relatively insensitive to muscle movement since these probes are not directly connected to the tissue, and distortions of the recorded data due to changes in the electrochemical interface between the probes and the tissue are minimal. Contrary to the methods used in electric recordings, these probes can be employed to measure action currents of tissues while they are lying in their own natural settings or in saline baths, thereby reducing the risk associated with elevating and drying the tissue in the air during experiments. This review primarily describes the investigations performed on peripheral nerves using the neuromagnetic current probe. Since there are relatively few publications on these topics, a comprehensive review of the field is given. First, magnetic field measurements of isolated nerve axons and muscle fibers are described. One of the important applications of the neuromagnetic current probe to the intraoperative assessment of damaged and reconstructed nerve bundles is summarized. The magnetic signals of crushed nerve axons and the determination of the conduction velocity distribution of nerve bundles are also reviewed. Finally, the capabilities and limitations of the probe and the magnetic recordings are discussed.

Recovery of neurophysiological features with time after rat sciatic nerve repair: a magneto-neurographic study

Experimental assessment of peripheral nerve regeneration in rats by electrophysiology is controversial due to low reproducibility of electrophysiological indicators and diminished quantitative evaluation in conventional experimental set-ups. Magnetoneurography (MNG) counteracts these drawbacks by magnetically recording electrophysiological signals ex vivo, thereby providing accurate and quantitative data. In 50 rats, sciatic nerve transection was followed by direct repair. MNG outcome parameters, footprints [static toe spread factor (TSF); function] and muscle weight (MW) were studied for their recovery pattern from 2 to 24 weeks. By using MNG, we showed that the regeneration process still continues when functional recovery (static TSF) becomes stagnant. With regression analysis, MNG parameters amplitude, amplitude area and conduction velocity (CV) demonstrated moderate significant correlation with MW, whereas CV was not significantly associated with static TSF. No significant association exists between MW and static TSF. A Kaplan-Meier survival curve revealed that autotomy/contracture of rat hind paws was not related to decreased MNG outcome values. In conclusion, this study highlights and discusses the dissimilarities between direct (MNG) and indirect (static TSF and MW) assessment techniques of the regeneration process. We emphasise the significance of MNG as a direct derivative of axon regeneration in experimental rat studies. Additionally, we stress the must for right-left ratios, as neurophysiological indicators vary with age, and we confute possible bias in footprint analysis caused by exclusion of autotomy/contracture animals.

Nerve compound action current (NCAC) measurements and morphometric analysis in the proximal segment after nerve transection and repair in a rabbit model

In the evaluation of nerve regeneration using magneto-neurography (MNG), the proximal segment showed a reproducible decrease in peak-peak amplitude of the nerve compound action current's (NCAC) of 60%. To explain these changes, morphometry of myelinated axons in the proximal segment is compared to the MNG signals. A standardised nerve transection and reconstruction was performed in rabbits. NCACs were measured approximately 5 cm proximal to the lesion from operated and control nerves after 12 weeks. Histological samples were taken from the same area of the nerve where the NCACs were obtained. Results showed a decrease of the peak-peak amplitude of the NCAC of 57% compared to the control. Conduction velocity decreased 15% (not significant). Morphometry elicited a decrease in larger (10-15 microm) axons (284 +/- 134 vs 82 +/- 55) and an increase in smaller (2-5 microm) axons (1445 +/- 360 vs 1921 +/- 393). A strong correlation existed between the decrease in amplitude and the decrease in larger axons (0.85). Peak-peak amplitude varies approximately with the square of the diameter axon. Therefore, because peak-peak amplitude is mainly dependent on the larger-diameter axons, the decrease in peak-peak amplitude of the NCACs may be explained by a decrease in numbers of 10-15-microm axons.

Selective recording of electroneurograms from the sciatic nerve of a dog with multi-electrode spiral cuffs

Electroneurograms (ENGs) from superficial regions of the sciatic nerve of a Beagle dog were recorded selectively with a chronically implanted 33-electrode spiral cuff (cuff). By delivering stimulating pulses to groups of three electrodes (GTEs) within the cuff we could define the relative positions of the particular superficial regions that selectively innervated the tibialis anterior (TA) and gastrocnemius muscles (GM). GTEs with and without contractions of the TA and GM muscles were selected and connected to a 4-channel ENG system designed to amplify ENGs by 100,000 times and to pass frequencies between 500 Hz and 10 kHz. In our study, 12 experiments were conducted on three Beagle dogs with a cuff implanted for up to 2 years. We present the results obtained in four experiments conducted on one animal. With the implanted leg mounted in a special electronic brace we applied extending forces to the ankle, rotating it by up to 37 degrees according to the neutral position, eliciting torque to stretch the TA muscle. Only the ENG from a GTE eliciting maximum contraction of the TA muscle showed activities corresponding to the trajectory of the mechanical load of the muscle. Next, we dissected the calcanean tendon (CT) of the implanted leg and applied repetitive pull forces to the CT. Only the ENG from the GTE eliciting maximum contraction of the GM muscle was activated in correspondence to the trajectory of the mechanical load applied on the CT. The results suggest that the cuff, implanted chronically on the sciatic nerve, is useful to record ENGs of the afferent fibers from TA and GM muscles selectively and that the technique could be extended for human use in the field of rehabilitation for paralysis.

Water diffusion, T(2), and compartmentation in frog sciatic nerve

A potential relationship between structural compartments in neural tissue and NMR parameters may increase the specificity of MRI in diagnosing diseases. Nevertheless, our understanding of MR of nerves and white matter is limited, particularly the influence of various water compartments on the MR signal is not known. In this study, components of the (1)H transverse relaxation decay curve in frog peripheral nerve were correlated with the diffusion characteristics of the water in the nerve. Three T(2) values were identified with nerve. Water mobility was found to be unrestricted on the timescale of 100 msec in the component of the signal with the intermediate T(2) time, suggesting some contribution from the interstitial space to this T(2) component. Restricted diffusion was observed in the component with the longest T(2) time, supporting the assignment of at least part of the spins contributing to this component to an intracellular compartment. The observed nonexponential behavior of the diffusion attenuation curves was investigated and shown to be potentially caused by the wide range of axon sizes in the nerve. Magn Reson Med 42:911-918, 1999.

A magnetic evaluation of peripheral nerve regeneration: I. The discrepancy between magnetic and histologic data from the proximal segment

Histologic techniques can quantify the number of axons in a nerve, but give no information about electrical conductibility. The number of functional myelinated neuronal units in a nerve can be quantified based on a magnetic recording technique. When studying reconstructed peripheral nerves a significant difference between the results found with these two techniques can be observed. A comparison was made between the long-term changes in the number of histologically and magnetoneurophysiologically measured neuronal units proximal to a nerve reconstruction. This study was performed on 6 New Zealand White rabbits, 20 weeks after the peroneal nerve had been reconstructed. The contralateral nerves were used as a control. Histologic examination demonstrates a statistically significant decrease of approximately 5% in the number of myelinated fibers. The magnetoneurophysiological results demonstrate a decrease which is estimated to be caused by the loss of approximately 50% of the functional myelinated neuronal units in the nerve. Therefore we conclude that of the initially available myelinated neuronal units, 5% degenerate completely, 45% are vital but lose their signal conducting capability, and the remaining 50% are vital and continue to conduct signals. Apparently, only this latter group of 50% of the initially available functional neuronal units appears to remain available for functional recovery.

A magnetic evaluation of peripheral nerve regeneration: II. The signal amplitude in the distal segment in relation to functional recovery

Motor and sensory function in a healthy nerve is strongly related to the number of neuronal units connecting to the distal target organs. In the regenerating nerve the amplitudes of magnetically recorded nerve compound action currents (NCACs) seem to relate to the number of functional neuronal units with larger diameters regenerating across the lesion. The goal of this experiment was to compare the signal amplitudes recorded from the distal segment of a reconstructed nerve to functional recovery. To this end, the peroneal nerves of 30 rabbits were unilaterally transected and reconstructed. After 6, 8, 12, 20, and 36 weeks of regeneration time the functional recovery was studied based on the toe-spread test, and the nerve regeneration based on the magnetically recorded NCACs. The results demonstrate that the signal amplitudes recorded magnetically from the reconstructed nerves increase in the first 12 weeks from 0% to 21% of the amplitudes recorded from the control nerves and from 21% to 25% in the following 23 weeks. The functional recovery increases from absent to good between the 8th and the 20th week after the reconstruction. A statistically significant relation was demonstrated between the signal amplitude and the functional recovery (P < 0.001). It is concluded that the magnetic recording technique can be used to evaluate the quality of a peripheral nerve reconstruction and seems to be able to predict, shortly after the reconstruction, the eventual functional recovery.

Axon conduction and survival in CNS white matter during energy deprivation: a developmental study

We investigated the postnatal development of axon sensitivity to the withdrawal of oxygen, glucose, or the combined withdrawal of oxygen + glucose in the isolated rat optic nerve (a CNS white matter tract). Removal of either oxygen or glucose for 60 min resulted in irreversible injury in optic nerves from adult rats, assessed by loss of the evoked compound action potential (CAP). Optic nerves at ages <P10 showed no permanent loss of function. CAP sensitivity to the withdrawal of oxygen or glucose emerged during a critical period in development between postnatal days 10-20 (P10-P20). The CAP was unchanged in adult optic nerve for 45 min after the withdrawal of glucose, demonstrating the presence of a significant energy reserve. Periods of glucose withdrawal >45 min caused the selective loss of late CAP components; this was not seen with oxygen deprivation. The amplitude of the early component recovered to 94.8% of control after 60 min of glucose withdrawal, although total CAP area recovered to only 42.3%. Combined oxygen + glucose withdrawal for 60 min produced a greater degree of permanent CAP loss than 60 min of glucose or oxygen withdrawal individually in optic nerves from rats older than P4. Younger than P4 optic nerves showed no permanent loss of function from 60 min of combined oxygen + glucose withdrawal. Unexpectedly, optic nerves from P21-P49 rats recovered significantly less after all three conditions than adult opticnerves (>P50). It is probable that this period of final myelination corresponds to a time of heightened metabolic activity in white matter. The tolerance of CNS white matter to energy deprivation can be categorized into four stages that are correlated with specific developmental features: premyelination (P0-P4), highly tolerant to anoxia, aglycemia and combined anoxia/aglycemia; early myelination (P5-P20), partially tolerant of anoxia and aglycemia but not to combined anoxia/aglycemia; late myelination (P21-P49), very low tolerance of anoxia, aglycemia and combined anoxia/aglycemia; and mature (>P50), low tolerance of anoxia, aglycemia and combined anoxia/aglycemia. The relative resistance of optic nerve function to glucose withdrawal in the presence of oxygen, compared with glucose withdrawal in the absence of oxygen, is presumably due to the presence of oxygen-dependent energy reserves such as astrocytic glycogen, amino acids. and phospholipids.

The extracellular potential of a myelinated nerve fiber in an unbounded medium and in nerve cuff models

A model is presented for the calculation of single myelinated fiber action potentials in an unbounded homogeneous medium and in nerve cuff electrodes. The model consists of a fiber model, used to calculate the action currents at the nodes of Ranvier, and a cylindrically symmetrical volume conductor model in which the fiber's nodes are represented as point current sources. The extracellular action potentials were shown to remain unchanged if the fiber diameter and the volume conductor geometry are scaled by the same factor (principle of corresponding states), both in an unbounded homogeneous medium and in an inhomogeneous volume conductor. The influence of several cuff electrode parameters, among others, cuff length and cuff diameter, were studied, and the results were compared, where possible, with theoretical and experimental results as reported in the literature.

A four sphere model for calculating the magnetic field associated with spreading cortical depression

In our previous model, we ascertained that the large amplitude waves (LAWs), reported by Barkley and coworkers (1990) in time series magnetoencephalography (MEG) recordings from migraine patients, could be simulated and compared with the recorded signals using a simple plane volume conductor model (Tepley and Wijesinghe 1996). In this paper, we model LAWs using the help of more complicated yet reliable four-sphere model. This mathematical model furthermore assumes that the LAWs arise from propagation of Spreading Cortical Depression (SCD) across a sulcus and these simulated signals are more similar to the recorded signals than the ones we obtained from our previous model. SCD propagates slowly across the cortex in all species in which it has been observed. In our model, current dipoles represent the excitable neurons in the cortex and magnetic fields created by these individual dipoles are calculated using a four-sphere model. The magnetic field arising from the excited area of cortex is obtained by summing the fields due to these individual dipoles. Sulci shapes are represented by simple mathematical formulae.

Correlation between electrophysiological effects of mexiletine and ischemic protection in central nervous system white matter

Protection of CNS white matter tracts in brain and spinal cord is essential for maximizing clinical recovery from disorders such as stroke or spinal cord injury. Central myelinated axons are damaged by anoxia/ischemia in a Ca(2+)-dependent manner. Leakage of Na+ into the axoplasm through Na+ channels causes Ca2+ overload mainly by reverse Na(+)-Ca2+ exchange. Na+ channel blockers have thus been shown to be protective in an in vitro anoxic rat optic nerve model. Mexiletine (10 microM-1 mM), an antiarrhythmic and use-dependent Na+ channel blocker, was also significantly protective, as measured by recovery of the compound action potential after a 60 min anoxic exposure in vitro. More importantly, mexiletine (80 mg/kg, i.p.) also significantly protected optic nerves from injury in a model of in situ ischemia. This in situ model is more clinically relevant as it addresses drug pharmacokinetics, toxicity and CNS penetration. Optic nerve recovery cycles (defined as shifts in latency of compound action potentials with paired stimulation) were used to measure the concentration of mexiletine in optic nerves after systemic administration, estimated at approximately 42 microM 1 h after a single dose of 80 mg/kg, i.p. These results indicate that mexiletine is able to penetrate into the CNS at concentrations sufficient to confer significant protection. Na+ channel blockers such as mexiletine may prove to be effective clinical therapeutic agents for protecting CNS white matter tracts against anoxic/ischemic injury.

Autoprotective mechanisms in the CNS: some new lessons from white matter

Anoxia/ischemia in the CNS is a common and devastating phenomenon. It is possible that the best hopes for protection against anoxic/ischemic injury may involve recruiting and/or augmenting any autoprotective systems that evolution has provided for the CNS. We describe here the existence of such an autoprotective system present in CNS white matter. White matter is both well suited to studying extrasynaptic systems, such as the system we describe here, and is a highly appropriate target for research into anoxic-ischemic injury in its own right. We show that white matter contains functional GABAB and adenosine receptors that respond to an anoxic efflux of GABA and adenosine by recruiting a convergent intracellular mechanism involving protein kinase C (PKC). The net result of this receptor-mediated cascade is an increase in resistance to anoxia, which presumably allows CNS white matter to tolerate better a common class of ischemic events that are located solely in white matter and that comprises approximately 25% of all strokes seen clinically.

Loss of viable neuronal units in the proximal stump as possible cause for poor function recovery following nerve reconstructions

Function recovery after nerve reconstructions is often poor. Could this be caused by a loss of viable neuronal units proximal to the nerve reconstruction? The number of neuronal units (i.e., a motor or sensory neuron, including its axon and axonal branches) in the proximal segments of reconstructed peripheral nerves were studied using a novel magnetic recording technique. In five rabbits a common personal nerve was transected and microsurgically reconstructed. After 8 weeks regeneration time the nerve compound action signals were recorded magnetically from the reconstructed as well as from the healthy contralateral peroneal nerve and from peroneal nerves of five unoperated control animals. The amplitudes of the recorded signals were compared and the diameter distribution histograms were calculated. These calculations were based on the conduction distance between the stimulator and the sensor and the conduction velocities of 30 different axon diameter classes ranging from 3 to 18 microns. Our results indicate that there is a reduction of approximately 50% in the number of viable neuronal units at 10 mm proximal to a simple nerve reconstruction after 8 weeks regeneration time. The number of neuronal units innervating a hand is strongly correlated with clinical function in a healthy hand. The reduction in viable neuronal units after a reconstruction, demonstrated in our experiments, corresponds with a frequently clinically observed decrease in function after nerve reconstructions. Therefore, we suggest that the number of viable neuronal units may be a good indicator of final functional recovery.

Muscle electric activity. I: A model study on the effect of needle electrodes on single fiber action potentials

Needle recorded electromyographic signals can be expected to be influenced by the presence of the needle, the electrical double layer at the metal-electrolyte interface, and by an edematous layer around the needle electrode. The magnitude of each of these effects is derived from a cylinder symmetrical volume conductor model. Analytical solutions of Laplace's equation have been derived. These are used for simulating single muscle fiber action potentials (SFAPs) recorded by a typical single fiber electrode. The results indicate that there is no short-circuiting effect, in spite of the presence of a highly conducting needle shaft, which is due to the high impedance of the electrical double layer. The insulating properties of the double layer cause the SFAP amplitudes to increase, when the muscle fiber passes the electrode at the side of the leading-off point. The edematous layer counteracts this increase depending on the thickness and the conductivity of this layer. Only slight SFAP wave-form changes are found.

Protection of the axonal cytoskeleton in anoxic optic nerve by decreased extracellular calcium

Since CNS white matter tracts contain axons, oligodendrocytes and astrocytes but not synapses, it is likely that anoxic injury of white matter is mediated by cellular mechanisms that do not involve synapses. In order to test the hypothesis, that anoxic injury of white matter is mediated by an influx of Ca2+ into the intracellular compartment of axons, we compared the ultrastructure of axons in rat optic nerve exposed to 60 min of anoxia in artificial cerebrospinal fluid (aCSF) containing normal (2 mM) Ca2+, and in aCSF containing zero-Ca2+ together with 5 mM EGTA. Optic nerves fixed at the end of 60 min of anoxia in 2 mM Ca2+ exhibit extensive ultrastructural alterations including disruption of microtubules and neurofilaments within the axonal cytoskeleton, development of membranous profiles and empty spaces between the axon and the ensheathing myelin, and swelling of mitochondria with loss of cristae. Bathing the nerves in zero-Ca2+ aCSF during anoxia protected the axons from cytoskeletal changes; after 60 min of anoxia, optic nerve axons retained normal-appearing microtubules and neurofilaments. Membranous profiles were rare, and empty spaces between axons and myelin did not develop in anoxic optic nerves bathed in zero-Ca2+ aCSF. Disorganization of cristae in axonal mitochondria was observed in anoxic optic nerves even when Ca2+ was omitted from the medium. Because Ca(2+)-mediated injury is known to disrupt the axonal cytoskeleton, these results support the hypothesis that anoxia triggers an abnormal influx of Ca2+ into myelinated axons in CNS white matter.

A comparison of electric and magnetic compound action signals as quantitative assays of peripheral nerve regeneration

The evaluation of peripheral nerve regeneration is of great interest in clinical as well as in experimental situations. However, there are few techniques that give early and quantitative information on the status of the regeneration process. If quantitative assays would be available, different surgical techniques and medications could be evaluated more accurately in relation to axonal ingrowth and functional recovery. The purpose of this study was to investigate the merits of nerve compound action signals (NCASs) recorded electrically and signals recorded with a novel magnetic recording technique. We compared the two techniques in the rabbit peroneal nerve, 2, 4, 6, and 8 weeks after a nerve reconstruction. Our conclusions are that the signals recorded with the magnetic sensor are far more reproducible and less prone to stimulus artifact than the electrically recorded signals. Furthermore, the magnetic recording shows that the number of axons that have regenerated increases with time. Previously, this could only be determined with histological studies. Other ingrowth parameters that can be quantified are the average ingrowth distance, and the variation between axons in ingrowth velocity.

Ultrastructural concomitants of anoxic injury and early post-anoxic recovery in rat optic nerve

To study the effects of anoxia on CNS white matter, we examined the ultrastructure of axons and glial cells in a white matter tract, the rat optic nerve, that was subjected to a standardized anoxic insult in vitro. Previous electrophysiological studies showed that in this model, action potential conduction is rapidly abolished by anoxia, and conduction is restored after reoxygenation in about 30% of axons following a 60-min anoxic period. The present study examined the ultrastructural correlates of anoxic injury and early post-anoxic recovery in this model. Optic nerves examined immediately following 60 min of anoxia displayed numerous large, apparently empty zones located within myelin sheaths adjacent to the axon. The myelin remained compact and retained its periodicity. In some regions, the extracellular space was enlarged. There was mitochondrial swelling with loss of normal cristae. There was also loss of microtubules and, to a smaller degree, of neurofilaments in large-diameter axons. Some nodes of Ranvier in anoxic optic nerves displayed detachment of terminal oligodendroglial loops or retraction of the myelin from the node; the presence of tongue-like processes, extending from nearby cells under the detached myelin loops, suggested a possible role of cell-mediated damage to the paranodal myelin. Bundles of dense astrocyte processes were present, and there was vesicular degeneration of perinodal astrocyte processes. In optic nerves that had been permitted to recover for 60 min in oxygenated Ringers following the anoxic period, empty zones were only rarely observed within myelin sheaths and, when present, were smaller than in optic nerves immediately following 60 min of anoxia. The axoplasm of large fibers continued to show loss of microtubules and neurofilaments, as well as mitochondrial swelling. Myelin appeared normal, and only rare paranodal oligodendroglial processes remained unattached from the axon membrane. These results provide support for the idea that, during anoxia, myelinated axons are damaged with significant injury to cytoskeletal elements, probably due to an influx of calcium. The ultrastructural results, together with our earlier observations on the physiological correlates of anoxia and re-oxygenation, suggest that the development of intramyelinic spaces or damage to paranodes lead to conduction block in the anoxic optic nerve. These results also suggest that repair of these structural abnormalities may provide a morphological basis for the early recovery of conduction that occurs after re-oxygenation.

A model for compound action potentials and currents in a nerve bundle. III: A comparison of the conduction velocity distributions calculated from compound action currents and potentials

In this paper, we present the experimentally measured Compound Action Current (CACs) and Compound Action Potentials (CAPs) from frog sciatic nerves and earthworm nerve cords. We used histologically prepared cross sections of these nerve bundles to determine the distribution of fiber diameters. A modified volume conduction model that includes frequency-dependent conductivities was used to compute the Single Fiber Action Signals (SFASs). The recorded CACs and CAPs are used to predict the Conduction Velocity Distributions (CVDs) from the nerve bundles. The predicted CVDs are then compared with the histological CVDs. Analysis of Compound Action Signals from the three giant axons in the earthworm nerve cord and microelectrode data for the transmembrane action potential demonstrate the validity of our mathematical model. We found that the CVDs predicted from the recorded CACs and CAPs differ from the histological CVD for a variety of reasons. The validity of the assumption of a linear relationship between axon diameter and conduction velocity of a propagating action signal was investigated using CVDs from both the CAC and CAP. Variations of the CVDs with the propagation distance of the CASs and the recording temperature were investigated.

A model for compound action potentials and currents in a nerve bundle. II: A sensitivity analysis of model parameters for the forward and inverse calculations

We present a detailed analysis of the sensitivity of simulated Compound Action Current (CAC) and Compound Action Potential (CAP) recordings to specific model parameters, including the Single Fiber Action Currents (SFACs) and Single Fiber Action Potentials (SFAPs) that represent the contributions of each axon in the nerve bundle. In the preceding paper, we described a general method for simulating CACs and CAPs. This method uses a volume conduction model that incorporates the effects of the nerve bundle and other anisotropic properties of the region of the bundle that surrounds an individual nerve axon. In this paper, we present a complete analysis of the effects of incorrectly assigned model parameters on the simulated CAC and CAP. We also investigate the effects of incorrectly assigned parameters, recording noise, and data smoothing on the Conduction Velocity Distributions (CVDs) predicted from the CAC and CAP. We find that the simulated CAC is less sensitive to most of the parameters than is the CAP.