H.B.K. Boom

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

In epidural spinal cord stimulation it is likely not only that dorsal column fibers are activated, but also 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 geometric 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 are a 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.<<ETX>>

Automatic stance-swing phase detection from accelerometer data for peroneal nerve stimulation

The development of implantable peroneal nerve stimulators has increased interest in sensors which can detect the different phases of walking (stance and swing). Accelerometers with a potential for implantation are studied as detectors for the swing phase of walking to replace footswitches. Theoretically, one can show that accelerometers can be used to distinguish between stance and swing phase. Using accelerometers attached between the ankle and knee joints, the equivalent acceleration of the ankle joint was calculated. This resulted in a typical and reproducible signal in which the different walking phases were identified. Automatic detection algorithms based on cross-correlation calculations were developed and tested. Measurements from four healthy and four hemiplegic subjects resulted in a total of 317 and 272 steps, respectively. The testing of one of the hemiplegic subjects was considered to be a failure due to large disturbances in the acceleration signal during the swing phase of walking, which may be related to the use of crutches.<<ETX>>

Real-time gait assessment utilizing a new way of accelerometry

Real-time registration of body segment angles is essential in artificial body position control. A new method is presented for the real-time calculation of the lower extremity angles using data obtained from pairs of two one-dimensional accelerometers. It is shown that, assuming rigid-body dynamics and simple hinge joints, relative angles (i.e. angles between segments) can be calculated without integration, thereby solving the problem of integration drift normally associated with accelerometry. During the stance phase of walking, the relative angles can be transformed to absolute angles (i.e. relative to the gravitational field direction) for the different leg segments. The feasibility of relative angle calculation is demonstrated by calculation of the knee angle of a healthy subject. Stability and resolution were demonstrated with measurements during standing. Measurements during standing up, sitting down and walking showed that shock (heel-strike) and skin movements, due to movements of the underlying muscle tissue, are the main error sources. Additional signal processing, e.g. low-pass filtering, can be used to diminish this error. The accuracy of the knee angle found is shown to be high enough to be used in a feedback controller for functional electrostimulation of the lower extremities.

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 simulation 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.<<ETX>>

The median frequency of the surface EMG power spectrum in relation to motor unit firing and action potential properties

Three components determine the power spectrum of the surface EMG signal: the auto- and cross-power spectra of the firing processes and the power spectra of the motor unit action potential (MUAP). To clarify the relative contribution of these components to the median frequency (MF) of the power spectrum, a stochastic simulation model was used in which most input parameters [e.g., MUAP peak-peak time (PPT), mean interpulse interval time, and synchronization parameters] were described in terms of distribution functions. Simulation clearly predicts that MF is especially sensitive to variations in MUAP shape, the MUAP PPT, and synchronization. The influence of the firing process parameters was predicted to be marginal. To obtain values for the MUAP parameters, a needle-triggered averaging technique was used to gather surface MUAPs from the m. biceps brachii. With use of these MUAPs as input for the model, it was found that intrasubject variability of MF is caused by variations in both MUAP PPT and MUAP shape, whereas intersubject variability in MF is caused primarily by variations in PPT.

Paresthesia thresholds in spinal cord stimulation: a comparison of theoretical results with clinical data

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 cerebrospinal fluid (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. >

A model of the electrical behaviour of myelinated sensory nerve fibres based on human data

Calculation of the response of human myelinated sensory nerve fibres to spinal cord stimulation initiated the development of a fibre model based on electro-physiological and morphometric data for human sensory nerve fibres. The model encompasses a mathematical description of the kinetics of the nodal membrane, and a non-linear fibre geometry. Fine tuning of only a few, not well-established parameters was performed by fitting the shape of a propagating action potential and its diameter-dependent propagation velocity. The quantitative behaviour of this model corresponds better to experimentally determined human fibre properties than other mammalian, non-human models do. Typical characteristics, such as the shape of the action potential, the propagation velocity and the strength-duration behaviour show a good fit with experimental data. The introduced diameter-dependent parameters did not result in a noticeable diameter dependency of action potential duration and refractory period. The presented model provides an improved tool to analyse the electrical behaviour of human myelinated sensory nerve fibres.

A modeling study of nerve fascicle stimulation

A nerve-stimulation model incorporating realistic cross-sectional nerve geometries and conductivities is discussed. The potential field in the volume conductor was calculated numerically using the variational method. Nerve fiber excitation was described by the model of McNeal (ibid., vol.BME-23, p.329-37, 1976). 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 correspond to experimental results on intrafascicular and extraneural stimulation of rat common peroneal nerve and to results on muscle selective stimulation in multifascicular dog sciatic nerve using an extraneural multielectrode configuration.<<ETX>>

Lower extremity angle measurement with accelerometers-error and sensitivity analysis

The use of accelerometers for angle assessment of the lower extremities is investigated. This method is evaluated by an error-and-sensitivity analysis using healthy subject data. Of three potential error sources (the reference system, the accelerometers, and the model assumptions) the last is found to be the most important. Model calculations based on data obtained by the Elite video motion analysis system showed the rigid-body assumption error to be dominant for high frequencies (>10 Hz), with vibrations in the order of 1 mm resulting in errors of one radial or more. For low frequencies (<5 Hz), the imperfect fixation of the accelerometers combined with a nonhinge-type knee joint gave an error contribution of +or-0.03 rad. The walking pattern was assumed to be two-dimensional, which was shown to result in an error of +or-0.04 rad. Accelerations due to rotations of the segments could be neglected. The total error computed for low frequencies (+or-0.07 rad) is comparable to the experimental difference between the current and the reference system.<<ETX>>

Transverse tripolar stimulation of peripheral nerve: a modelling study of spatial selectivity

Various anode-cathode configurations in a nerve cuff are modelled to predict their spatial selectivity characteristics for functional nerve stimulation. A 3D volume conductor model of a monofascicular nerve is used for the computation of stimulation-induced field potentials, whereas a cable model of myelinated nerve fibre is used for the calculation of the excitation thresholds of fibres. As well as the usual configurations (monopole, bipole, longitudinal tripole, ‘steering’ anode), a transverse tripolar configuration (central cathode) is examined. It is found that the transverse tripole is the only configuration giving convex recruitment contours and therefore maximises activation selectivity for a small (cylindrical) bundle of fibres in the periphery of a monofascicular nerve trunk. As the electrode configuration is changed to achieve greater selectivity, the threshold current increases. Therefore threshold currents for fibre excitation with a transverse tripole are relatively high. Inverse recruitment is less extreme than for the other configurations. The influences of several geometrical parameters and model conductivities of the transverse tripole on selectivity and threshold current are analysed. In chronic implantation, when electrodes are encapsulated by a layer of fibrous tissue, threshold currents are low, whereas the shape of the recruitment contours in transverse tripolar stimulation does not change.