No abstract

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.

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.

In spinal cord stimulation (SCS) large diameter cutaneous (Abeta) fibres in the dorsal columns (DCs) are activated and have an inhibiting effect on the transmission of pain signals by Adelta and C fibres from the corresponding dermatome(s). The largest Abeta fibres can be activated up to a maximum depth of about 0.25 mm in the DCs. No data are available on the distribution of the large fibres in this superficial human DC layer at the common SCS levels Th(10-11). Such data are indispensable to improve the predictive capability of a computer model of SCS. The whole myelinated fibre population in the superficial 300 microm of the dorsal column (DC(0-300)) at Th(10-11 )of two human subjects was morphometrically analysed. Some data was obtained from a third subject. The superficial dorsolateral column (DLC(0-300)) was included in this analysis because it was hypothesized that large dorsal spinocerebellar tract fibres could also be activated by SCS. Only very few fibres larger than 10.7 microm were found: a mean of 68 (0.5%) in DC(0-300) and 114 (2%) in DLC(0-300). Considering that the effect of SCS is primarily attributed to activation of these largest fibres, it is concluded that a surprisingly small average amount of 2.4 fibres per running 0.1 mm width and 6 fibres per segmental division of the DC is involved. Distinct mediolateral heterogeneity in fibre composition was found in both DC(0-300) and DLC(0-300). In the DC(0-300), the mean diameter of fibres > or =7.1 microm increases significantly by 5% from medial to lateral. Density (i.e. number of fibres per 1000 microm(2)) and frequency (i.e. percentage of a fibre size group compared to its parent population) of the large fibres increase significantly from medial to lateral in the DC(0-300). For fibres > or =10.7 microm, these parameters increase by 200 and 269%, respectively. It is concluded that the difference in stimulation threshold of large Abeta fibres in the median and lateral DC can be mainly attributed to the absence and presence, respectively, of collaterals at the stimulation site. Marked differences were found between DC(0-300) and DLC(0-300). The largest DLC(0-300) fibres (> or =10.7 microm) have a 320% higher frequency and a 473% higher density. Their mean diameter is, however, only 2% larger. The largest DLC(0-300) fibres are not likely to be recruited by SCS, since they are not larger than their DC(0-300) counterparts, they lack collaterals (which would reduce the threshold stimulus substantially) and they are more remote from the stimulation electrode.

No abstract

An overview of computer models developed since the late seventies, which enable the simulation of the primary e ects of spinal cord stimulation (SCS) on nerve ®bres, is presented. These models consist of a 3-dimensional volume conductor model, representing anatomical structures and their electrical conductivities, and cable models representing the electrical behaviour of nerve ®bres. The characteristics of these models and their relation to anatomy and physiology, as well as the calculation of stimulation-induced electrical ®elds and their e ect on nerve ®bre models, are reviewed. It is shown that most characteristics of SCS as predicted by computer modelling correspond well with empirical data. Accordingly, a theoretical framework describing the relations between relevant parameters in SCS is presented. Finally, it is shown how theory and computer modeling are applied to improve the e cacy of SCS by the optimization of its technique, primarily by the design of new epidural electrodes.

The potential distributions produced in the spinal cord and surrounding tissues by dorsal epidural stimulation at the midcervical, midthoracic, and low thoracic levels were calculated with the use of a volume conductor model. Stimulus thresholds of myelinated dorsal column fibers and dorsal root fibers were calculated at each level in models in which the thickness of the dorsal csf layer was varied. Calculated stimulus thresholds were compared with paresthesia thresholds obtained from measurements at the corresponding spinal levels in patients. The influences of the csf layer thickness, the contact separation in bipolar stimulation and the laterality of the electrodes on the calculated thresholds were in general agreement with the clinical data.

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.