Motor cortex stimulation: role of computer modeling.

Motor cortex stimulation (MCS) is a promising clinical technique used to treat chronic, otherwise intractable pain. However, the mechanisms by which the neural elements that are stimulated during MCS induce pain relief are not understood. Neither is it known which of the main neural elements, i.e. cell bodies, dendrites or fibers are immediately excited by the electrical pulses in MCS. Moreover, it is not known what are the effects of MCS on fibers which are parallel or perpendicular to the cortical layers, below or away from the electrode. The therapy and its efficacy are less likely to be improved until it is better understood how it may work. In this chapter, we present our efforts to resolve this issue. Our computer model of MCS is introduced and some of its predictions are discussed. In particular, the influence of stimulus polarity and electrode position on the electrical field and excitation thresholds of different neural elements is addressed. Such predictions, supported with clinical evidence, should help to elucidate the immediate effects of an electrical stimulus applied over the motor cortex and may ultimately lead to optimizations of the therapy.

Cathodal, anodal or bifocal stimulation of the motor cortex in the management of chronic pain?

The conditions of motor cortex stimulation (MCS) applied with epidural electrodes, in particular monopolar (cathodal or anodal) and bipolar stimulation, are discussed. The results of theoretical studies, animal experiments and clinical studies lead to similar conclusions. Basically, cortical nerve fibres pointing at the epidural electrode and those normal to this direction are activated by anodal and cathodal stimulation, respectively. Because MCS for the relief of chronic pain is generally applied bipolarly with electrodes at a distance of at least 10 mm, stimulation may actually be bifocal. The polarity and magnitude of a stimulus needed to recruit cortical nerve fibres varies with the calibre and shape of the fibres, their distance from the electrode and their position in the folded cortex (gyri and sulci). A detailed analysis of intra-operative stimulation data suggests that in bipolar MCS the anode of the bipole giving the largest motor response in the pain region is generally the best electrode for pain management as well, when connected as a cathode. These electrode positions are most likely confined to area 4.

Modelling motor cortex stimulation for chronic pain control: electrical potential field, activating functions and responses of simple nerve fibre models.

This computer modelling study on motor cortex stimulation (MCS) introduced a motor cortex model, developed to calculate the imposed electrical potential field characteristics and the initial response of simple fibre models to stimulation of the precentral gyrus by an epidural electrode, as applied in the treatment of chronic, intractable pain. The model consisted of two parts: a three-dimensional volume conductor based on tissue conductivities and human anatomical data, in which the stimulation-induced potential field was computed, and myelinated nerve fibre models allowing the calculation of their response to this field. A simple afferent fibre branch and three simple efferent fibres leaving the cortex at different positions in the precentral gyrus were implemented. It was shown that the thickness of the cerebrospinal fluid (CSF) layer between the dura mater and the cortex below the stimulating electrode substantially affected the distribution of the electrical potential field in the precentral gyrus and thus the threshold stimulus for motor responses and the therapeutic stimulation amplitude. When the CSF thickness was increased from 0 to 2.5 mm, the load impedance decreased by 28%, and the stimulation amplitude increased by 6.6 V for each millimetre of CSF. Owing to the large anode-cathode distance (10 mm centre-to-centre) in MCS, the cathodal fields in mono- and bipolar stimulation were almost identical. Calculation of activating functions and fibre responses showed that only nerve fibres with a directional component parallel to the electrode surface were excitable by a cathode, whereas fibres perpendicular to the electrode surface were excitable under an anode.

A simple method for the construction of electrode arrays.

A simple method is described for the construction of electrode arrays consisting of insulated metal wires (33 microns diameter) spaced at small, equal distances (0.1 mm). No specialized instrumentation and techniques are needed, as only simple mechanical tools are sufficient. The electrode arrays are used for field potential recording from in vitro brain slice preparations.

Chronaxie calculated from current-duration and voltage-duration data.

To determine the rheobase and the chronaxie of excitable cells from strength-duration curves both constant-current pulses and constant-voltage pulses are applied. Since the complex impedance of the electrode-tissue interface varies with both the pulsewidth and the stimulation voltage, chronaxie values estimated from voltage-duration measurements will differ from the proper values as determined from current-duration measurements. To allow a comparison of chronaxie values obtained by the two stimulation methods, voltage-duration curves were measured in human subjects with a deep brain stimulation electrode implanted, while the current and the load impedance of the stimulation circuit were determined in vitro as a function of both stimulation voltage and pulsewidth. Chronaxie values calculated from voltage-duration data were shown to be 30-40% below those estimated from current-duration data. It was also shown that in the normal range of stimulation amplitudes (up to 7 V) the load impedance increases almost linearly with the pulsewidth. This result led us to present a simple method to convert voltage-duration data into current-duration data, thereby reducing the error in the calculated chronaxie values to approximately 6%. For this purpose voltage-duration data have to be measured for pulses up to 10-20 times the expected chronaxie.

A nerve stimulation method to selectively recruit smaller motor-units in rat skeletal muscle.

Electrical stimulation of peripheral nerve results in a motor-unit recruitment order opposite to that attained by natural neural control, i.e. from large, fast-fatiguing to progressively smaller, fatigue-resistant motor-units. Yet animal studies involving physiological exercise protocols of low intensity and long duration require minimal fatigue. The present study sought to apply a nerve stimulation method to selectively recruit smaller motor-units in rat skeletal muscle. Two pulse generators were used, independently supplying short supramaximal cathodal stimulating pulses (0.5 ms) and long subthreshold cathodal inactivating pulses (1.5 s) to the sciatic nerve. Propagation of action potentials was selectively blocked in nerve fibres of different diameter by adjusting the strength of the inactivating current. A tensile-testing machine was used to gauge isometric muscle force of the plantaris and both heads of the gastrocnemius muscle. The order of motor-unit recruitment was estimated from twitch characteristics, i.e. peak force and relaxation time. The results showed prolonged relaxation at lower twitch peak forces as the intensity of the inactivating current increased, indicating a reduction of the number of large motor-units to force production. It is shown that the nerve stimulation method described is effective in mimicking physiological muscle control.

The double dipole model of theta rhythm generation: simulation of laminar field potential profiles in dorsal hippocampus of the rat.

A set of compartmental models of CA1 pyramidal, granular and polymorph cells of the dorsal hippocampus have been used to simulate membrane potentials generated by synaptic activation at various levels along these cells. From the membrane potential distributions the field potentials in dorsal CA1 and the dorsal blade of the dentate area have been simulated using a model based on volume conduction theory. Field potential profiles similar to laminar profiles, found experimentally in the dorsal hippocampus during theta rhythm, could only be simulated by assuming (almost) simultaneous synaptic excitation of the 3 cell types at given sites. The results lead to 2 alternative models for the simultaneous excitation of CA1 pyramidal cells and dentate granular cells during theta rhythm. Other electrophysiological evidence favours the model in which the two neuronal populations are activated distally near the fissure.

MR assessment of the normal position of the spinal cord in the spinal canal.

PURPOSE: To investigate intradural geometry, which strongly influences the effects of epidural spinal cord stimulation. METHODS: Axial MR images with turbo spin-echo were made of 26 healthy subjects at C-4 through C-6, T-5 and T-6, and T-11 and T-12, at T-11 and T-12 both in the supine and the prone position. Measurements were made of the dorsomedial and the ventromedial cerebrospinal fluid layer and the anteroposterior and transverse sizes of both the spinal cord and the dural sac. The samples of all variables were analyzed statistically. The distance between spinal and vertebral midline was also determined. RESULTS: The dorsal cerebrospinal fluid layer was 1.5 to 4.0 mm at C-4 through C-6 and 4.0 to 8.5 mm at T-5 and T-6. At T-11 it was 2.0 to 6.0 mm in the supine position and was increased by approximately 2.2 mm in the prone position. At T-12 these values were 1.5 to 4.5 mm and approximately 3.4 mm, respectively. Differences between the spinal and vertebral midline up to 1.5 to 2.0 mm occurred in approximately 40% of the images. CONCLUSIONS: Because there are variations of the dorsal cerebrospinal fluid layer among subjects by more than a factor of 2, and significant variations of the mediolateral position of the spinal cord, information on these parameters in patients will be essential for the optimal application of epidural spinal cord stimulation.

Effectiveness of spinal cord stimulation in the management of chronic pain: analysis of technical drawbacks and solutions.

OBJECTIVE: A major drawback of currently available spinal cord stimulation (SCS) systems for the management of chronic intractable pain, especially of widespread pain patterns as in reflex sympathetic dystrophy, is the generally limited paresthesia coverage. The aim of this study is to analyze the origin of this problem and to provide solutions. METHODS: Results from theoretical studies, in which a computer model was used to mimic the effects of SCS on spinal nerve fibers, were used to analyze which factors may limit paresthesia coverage. Model predictions were verified by empirical data from clinical literature. RESULTS: When using common SCS electrodes, both perception threshold and motor/discomfort threshold are generally related to dorsal root stimulation. Because these thresholds have a small ratio (approximately 1:1.4), stimulation of dorsal column fibers and paresthesia coverage is limited by this small range of stimulation. When the distance between the epidural electrode and spinal cord is large (midthoracically), the threshold for dorsal column stimulation exceeds discomfort threshold, resulting only in segmental paresthesia. The range of dorsal column stimulation and paresthesia coverage can be improved when using either an optimally dimensioned rostrocaudal bi-/tripole or a transverse tripole ("guarded cathode"). When applying the latter in combination with a dual channel pulse generator providing simultaneous pulses, paresthesias can simply be changed to optimally cover the painful area. CONCLUSION: Paresthesia coverage and pain management by SCS can be improved when using electrodes as proposed.

Effect of anode-cathode configuration on paresthesia coverage in spinal cord stimulation.

OBJECTIVE: To provide a theoretical basis for the selection of the anode-cathode configuration in spinal cord stimulation for the management pain when one percutaneous epidural electrode or two electrodes in parallel are used. METHODS: A computer model of spinal cord stimulation at T8-T9 was used to calculate the dorsal column areas recruited in stimulation by various configurations used in clinical practice. RESULTS: Tripolar (or bipolar) stimulation by a single electrode, symmetrically placed over the dorsal columns, recruits the largest area and will give the widest paresthesia coverage. Stimulation by two symmetrically placed electrodes connected in parallel to a single channel pulse generator may give similar results, because of their generally smaller distance from the spinal cord, but a "summation effect" does not exist. A smaller dorsal column area is activated when two offset electrodes are used. An electrode placed laterally or transverse bipolar stimulation results in unilateral, usually segmentary, paresthesia. CONCLUSIONS: The relative positions of cathodes and anodes and their distance from the spinal cord are the major determinants of dorsal column/dorsal root activation and paresthesia distribution. The large interpatient variability of the intraspinal geometry is the main cause of differences in paresthesia coverage among patients having optimally placed electrode(s). Changes of paresthesia coverage over time are more probable when multiple electrodes are used.

Clinical evaluation of paresthesia steering with a new system for spinal cord stimulation.

OBJECTIVE: The goal was to evaluate, in a clinical study, the predicted performance of the transverse tripolar system for spinal cord stimulation, particularly the steering of paresthesia, paresthesia coverage, and the therapeutic range of stimulation. METHODS: Six transverse tripolar electrodes were implanted in the lower thoracic region in four patients experiencing chronic neuropathic pain. Electrode positions, relative to the spinal cord, were estimated from computed tomographic scans. A dual-channel stimulator was used for initial percutaneous tests, and an implanted single-channel stimulator was used for follow-up test sessions. Nine "balance" settings and several cathode-anode combinations were used with the dual-channel and single-channel stimulator, respectively. In each test, the increase of paresthesia coverage from the perception threshold to the discomfort threshold was registered on a body map and the corresponding voltages were recorded. RESULTS: Paresthesia steering occurred in all but one patient. The normalized steering score, enabling quantitative comparisons of paresthesia steering among tests and patients, showed that maximum paresthesia steering occurred when the electrode was at least 3 mm dorsal to the spinal cord and centered <2 mm from its midline. Paresthesia coverage included 70 to 100% of the body up to the electrode level, unless the electrode migrated or had broken wires. The therapeutic range, defined as the discomfort/perception of paresthesia threshold ratio, varied from 1.6 to 4.0. CONCLUSION: The clinical performance of transverse tripolar stimulation is in accordance with the characteristics predicted by computer modeling. It enables finer control of paresthesia than that achieved by polarity changes in conventional spinal cord stimulation systems.

Excitation of dorsal root fibers in spinal cord stimulation: a theoretical study.

In epidural spinal cord stimulation it is likely that not only dorsal column fibers are activated, but that dorsal root fibers will be involved as well. In this investigation a volume conductor model of the spinal cord was used and dorsal root fibers were modeled by an electrical network including fiber excitation. The effects of varying some geometrical fiber characteristics, as well as the influence of the dorsal cerebrospinal fluid layer and the electrode configuration on the threshold stimulus for their excitation, were assessed. The threshold values were compared with those of dorsal column fibers. The results of this modeling study predict that, besides the well known influence of fiber diameter, the curvature of the dorsal root fibers and the angle between these fibers and the spinal cord axis were of major influence on their threshold values. Because of these effects, threshold stimuli of dorsal root fibers were relatively low as compared to dorsal column fibers. Excitation of the dorsal root fibers occurred near the entry point of the fibers.

Position-selective activation of peripheral nerve fibers with a cuff electrode.

The degree of spatial selectivity which can be obtained with longitudinal dot tripoles in an insulating cuff was quantified in terms of the overlap between fiber populations activated by different tripoles. Previous studies have failed to take into account the relative influences of transverse current and longitudinal current on position-selective activation, and furthermore have not controlled for the differing sensitivities of large and small nerve fibers to electrical stimuli. In this study, these factors were taken into account. Transverse current from an anode positioned opposite the stimulating cathode was found to improve spatial selectivity, and selectivity was enhanced when the ratio of transverse current to longitudinal current was increased. Large fibers were excited before small fibers, irrespective of fiber position, indicating a combination of position and size selectivity.

Epidural spinal cord stimulation: calculation of field potentials with special reference to dorsal column nerve fibers.

The effect of electrical stimulation with several electrode combinations on nerve fibers with different orientations in the spinal cord was investigated by computing the steady-state field potentials and activating functions. At first an infinite homogeneous model was used while secondly the spinal cord and its surrounding tissues were modeled as an inhomogeneous anisotropic volume conductor. The effect of mediodorsal epidural stimulation was calculated. It was concluded that with cathodal stimulation, mediodorsally in the epidural space, longitudinal fibers are depolarized, but dorsoventral ones are hyperpolarized. With anodal stimulation the opposite will occur. It was found that parameters substantially affecting the potential distribution in the dorsal columns are the conductivity of the white matter and the width and the conductivity of the csf layer.

Recruitment of dorsal column fibers in spinal cord stimulation: influence of collateral branching.

An electrical network model of myelinated dorsal column nerve fibers is presented. The effect of electrical stimulation was investigated using both a homogeneous volume conductor and a more realistic model of the spinal cord. An important feature of dorsal column nerve fibers is the presence of myelinated collaterals perpendicular to the rostro-caudal fibers. It was found that transmembrane potentials, due to external monopolar stimulation, at the node at which a collateral is attached, is significantly influenced by the presence of the collateral. It is concluded that both excitation threshold and blocking threshold of dorsal column fibers are decreased up to 50% compared to unbranched fibers.

A modeling study of nerve fascicle stimulation.

A nerve stimulation model has been developed, incorporating realistic cross-sectional nerve geometries and conductivities. The potential field in the volume conductor was calculated numerically using the variational method. Nerve fiber excitation was described by the model of McNeal. Cross-sectional geometries of small monofascicular rat common peroneal nerve and multifascicular human deep peroneal nerve were taken as sample geometries. Selective stimulation of a fascicle was theoretically analyzed for several electrode positions: outside the nerve, in the connective tissue of the nerve, and inside a fascicle. The model results predict that the use of intraneural or even intrafascicular electrodes is necessary for selective stimulation of fascicles not lying at the surface of the nerve. Model predictions corresponded with experimental results of Veltink et al. on intrafascicular and extraneural stimulation of rat common peroneal nerve and to results of McNeal and Bowman on muscle selective stimulation in multifascicular dog sciatic nerve using an extraneural multielectrode configuration.

Selective stimulation of sacral nerve roots for bladder control: a study by computer modeling.

The aim of this study was to investigate theoretically the conditions for the activation of the detrusor muscle without activation of the urethral sphincter and afferent fibers, when stimulating the related sacral roots. Therefore, the sensitivity of excitation and blocking thresholds of nerve fibers within a sacral root to geometric and electrical parameters in tripolar stimulation using a cuff electrode, have been stimulated by a computer model. A 3-D rotationally symmetrical model, representing the geometry and electrical conductivity of a nerve root surrounded by cerebrospinal fluid and a cuff was used, in combination with a model representing the electrical properties of a myelinated nerve fiber. The electric behavior of nerve fibers having different diameters and positions in a sacral root was analyzed and the optimal geometric and electrical parameters to be used for sacral root stimulation were determined. The model predicts that an asymmetrical tripolar cuff can generate unidirectional action potentials in small nerve fibers while blocking the large fibers bidirectionally. This result shows that selective activation of the detrusor may be possible without activation of the urethral sphincter and the afferent fibers.

Estimation of fiber diameters in the spinal dorsal columns from clinical data.

Lack of human morphometric data regarding the largest nerve fibers in the dorsal columns (DC's) of the spinal cord has lead to the estimation of the diameters of these fibers from clinical data retrieved from patients with a new spinal cord stimulation (SCS) system. These patients indicated the perception threshold of stimulation induced paresthesia in various body segments, while the stimulation amplitude was increased. The fiber diameters were calculated with a computer model, developed to calculate the effects of SCS on spinal nerve fibers. This computer model consists of two parts: 1) a three-dimensional (3-D) volume conductor model of a spinal cord segment in which the potential distribution due to electrical stimulation is calculated and 2) an electrical equivalent cable model of myelinated nerve fiber, which uses the calculated potential field to determine the threshold stimulus needed for activation. It is shown that the largest fibers in the medial DC's are significantly smaller than the largest fibers in the lateral parts. This finding is in accordance with the fiber distribution in cat, derived from the corresponding propagation velocities. Moreover, it is shown that the mediolateral increase in fiber diameter is mainly confined to the lateral parts of the DC's. Implementation of this mediolateral fiber diameter distribution of the DC's in the computer model enables the prediction of the recruitment order of dermatomal paresthesias following increasing electrical stimulation amplitude.

Significance of the spinal cord position in spinal cord stimulation.

The effects of the antero-posterior and medio-lateral positions of the spinal cord in the dural sac on the perception threshold and paresthesia coverage in spinal cord stimulation were analyzed. The distributions of the dorsal cerebrospinal fluid (CSF) layer thickness, measured from transverse MR scans of normal subjects at various spinal levels, were used to calculate the distributions of threshold voltages for the stimulation of spinal nerve fibers by a computer model. These theoretical threshold distributions were shown to fit well to the corresponding distributions of perception threshold measured in patients. It is concluded that the thickness of the dorsal csf layer is the main factor determining the perception threshold and paresthesia coverage in spinal cord stimulation: an increasing thickness raises the threshold and reduces the coverage, and vice versa. The effects of an asymmetrical electrode position with respect to the spinal cord midline were also analyzed by computer modeling. It is concluded that a lateral asymmetry of less than 1 mm gives a significant reduction of perception threshold and may result in unilateral paresthesiae.

Application of a dual channel peroneal nerve stimulator in a patient with a "central" drop foot.

Dropped foot is a common mobility problem amongst patients after a cerebro vascular accident. The condition arises from paresis of the muscles that control the foot movement during the swing phase of gait. If the abnormal movement is not compensated for, it results in a significant decrease in the mobility and hence quality of life. Compensation for the drop foot can be achieved through the application of functional electrical stimulation. To date, in the clinical environment, the stimulation has been applied through electrodes placed on the skin over the common peroneal nerve, and using a single channel implant device. It is well known that with these techniques it is difficult to establish a balanced response of the foot. An implantable dual channel system for stimulation of the deep and superficial peroneal nerve has now been developed for patients with a drop foot following a stroke. By stimulation of the two branches of the common peroneal nerve separately it is possible to achieve a precisely balanced dorsal flexion and eversion of the foot. Stimulation occurs via small bipolar electrodes which are placed subepineural. After successful tests on animals we have now started the two channel peroneal nerve stimulator implantation in patients. The preliminary results of the first implants are presented.