Research in Electrical Stimulation Fundamentals

Being new to the field, I was curious to understand the remarkable differences observed between intra- and extracellular stimulation. As an example, the anodic extracellular stimulation threshold is often about four times the cathodic one; as another, excitation can be blocked by strong cathodic stimuli. For extracellular stimulation such phenomena are well known in the electrical stimulation community, but they had not been observed in experiments with intracellular electrode placement. Inspired by Ranck’s exceptional review on electrical stimulation and his appeal for more theoretical work 2, I found compartment modeling to be a useful tool to explain many missing links in the understanding of the fundamentals of electrical nerve stimulation 3–8. The excitable cell of interest is segmented into small compartments, and every compartment is connected with its neighbors by intracellular current flow.

Electrophysiological phenomena are usually explored by current injection into a nerve or muscle cell. A small positive injected current will raise the cell membrane voltage in the vicinity of a penetrating microelectrode without generating hyperpolarization anywhere along the neuron. External stimulation can be explained by a virtual current injection in every compartment. Here, in contrast to intracellular stimulation, positive and negative currents are applied in a balanced way, leading to both depolarized and hyperpolarized regions, even for stimulation with a single monophasic impulse. I introduced the “activating function” as a simple formula to describe these virtual currents 3–5. For a long homogeneous fiber, the activating function is proportional to the second derivative of the extracellular potential along the fiber 3, 4. In regions with positive activating function, the fiber is depolarized; negative values cause hyperpolarization. In this way we obtain not only a first approach for spike initiation zones but also hints for specific events like unidirectional firing 4. Quantitative results, such as calculation of threshold currents, require more complex models that include individual ion channel gating processes in the membrane of an excitable target cell. Type and density of sodium channels are important excitability parameters.

Besides the pioneering work in cochlear implant technology, a second Vienna group around Herwig Thoma and Winfried Mayr achieved surprising progress in functional electrical stimulation in the early 1980s. They developed fully implantable multichannel devices to restore mobility to paraplegic individuals as well as for the fatigue-free stimulation of phrenic nerves to reactivate physiological respiration in patients with complete ventilatory insufficiency. Fatigue resistance was achieved with four-electrode arrangements placed locally at the epineurium and delivering impulses via varying combinations of two or three active electrodes. For modeling of this specific electrode arrangement, the activating function concept was used to estimate the populations of activated axons in different electrode arrangements 8.

The Vienna group also has long experience with the transcutaneous stimulation of denervated muscles. Muscle fibers without nerve supply react to electrical stimuli with much longer impulse width in comparison to nerve fibers. Denervated muscle fibers react most sensitively either in their central region or at one of the fiber ends. The same modeling principles can be applied with some modifications. The compartment model method evaluates the currents in a compartment of interest by including the axial currents from the neighboring compartments. For central compartments, this results in virtual injected currents as described above. However, at the ends there is a compartment with only one neighboring compartment; consequently, the activating function is reduced and becomes proportional to the first derivative of the extracellular potential. In most cases the first derivative of the external potential decreases less with distance to the electrode than the second derivative. Therefore, most denervated fibers are expected to be most sensitive to stimulating field gradients at their ends, especially if they are situated in deeper tissue regions 9, 10. Biophysical modeling revealed the following relationship between applied electrical field and excitation of denervated muscle fibers: in the near field, denervated muscle fibers are considerably more sensitive in the central region than toward the ends. When electrode–fiber distance is increased, the electrode location for optimal stimulation efficacy shifts from the central region to the fiber ends for cathodic stimulation and to a position in front of the terminating part of the fiber for anodic currents 6.

Miniaturization of the devices broadened the field to include novel neuroprosthetic applications, such as deep-brain and spinal cord stimulation and visual prostheses. Individual electrical and geometrical characteristics of neural substructures can have surprising effects on artificially controlled neural signaling. A rule of thumb approved for the stimulation of long peripheral axons, for example “cathodic thresholds are lower than anodic ones,” may not hold in closely packed neuronal networks in the central nervous system 5, 7, 11, 12.

Selective activation of different groups of neural elements has always been a basic problem in functional electrical stimulation. Central nervous system stimulation with microelectrodes demands additional theoretical investigation into the substructures of neurons. As an example, previously it was assumed that cortical stimulation would excite neurons whose cell bodies were in the close vicinity of the tip of the stimulating microelectrode. However, low-current cortex stimulation produces a sparse and distributed set of activated cells, often with distances of several hundred micrometers between cell bodies and the microelectrode 7. Although the axon initial segment and nodes of Ranvier are the most excitable segments for external stimulation, many thin axons and dendrites close to the electrode in the densely packed cortical regions are also proper candidates for spike initiation sites. These numerous thin processes have better chances to be excited; for example, a 0.2-μm-diameter axon passing the electrode tip at a 10-μm distance can be activated by a 2.6-μA cathodic pulse of 100 μs. Because of the low sodium channel densities in their membranes, dendrites are expected to have about three times higher thresholds. According to biophysical model analysis, direct cathodic excitation of dendrites requires a minimum electrode–fiber distance, which increases with dendrite diameter. Therefore, thin dendrites can profit from the stronger electrical field close to the electrode, where low-current stimulation cannot activate large-diameter dendrites. This phenomenon of a dendritic recruitment order that favors the thin fibers is contrary to the reverse recruitment order known from peripheral nerve stimulation, where large-diameter axons have the lowest threshold 7.

A quadratic current–distance relationship (I = Kr²) for effective current spread is often used as a rough approach to estimate excitation threshold as a function of electrode distance. This rule is based on experiments conducted in the late 1960s in which the distance r between the electrode and activated pyramidal cell bodies was varied between 100 and 450 μm. However, the last example disproves such a simple current–distance relationship for typical central nervous system neurons like pyramidal cells, mainly because of the complex fiber branching in the dendritic tree and in the axon terminal regions. For straight homogeneous fibers we have shown that the exponent in the current–distance relationship changes gradually with r, and the relationship becomes linear for short distances (I = Kr), whereas a cubic trend is observed for large distances (I = Kr³) 4, 6, 7. It is important to note that the coefficient K depends essentially on the ion channel composition of the excited cell segment. The high density of sodium channels in the axon initial segment favors spike initiation in this region. Fortunately, in epiretinal implants this sensitivity characteristic supports visual perception quality elicited by focal stimulation with multielectrode arrays, as bypassing axons from distal retinal regions need higher stimuli than closely situated retina cells.

The temporal characteristics of excitable structures are described by strength–duration curves showing threshold current for a specific electrode as function of stimulus pulse duration. Chronaxy is defined as the time on such a strength–duration curve for twice the minimum threshold (rheobase) current needed for very long pulses. As different neural structures have different chronaxies, stimulus pulse duration is an important control parameter for selective stimulation. For example, the shorter chronaxy of myelinated motor neurons compared with that of unmyelinated fibers of the myocardium allows safe stimulation with short pulses during artificial respiration. Established by experimental findings, the classical excitability parameter chronaxy was assumed to be more or less independent from the distance between the current source and the excited cell. Based on theoretical considerations, chronaxy had been suggested to be about 0.7 times the time constant of the cell membrane, implying the same chronaxy values whether a stimulating electrode is on the inside or on the outside. Therefore many authors did not trust experimental observations of smaller chronaxy values for external cell stimulation than for internal. We were able to explain this controversy, demonstrating that extracellular stimulation also generates hyperpolarized regions in the cell membrane, hindering a steady excitation as seen in the intracellular case 13. The largest inside/outside chronaxy ratio for microelectrode stimulation is found in the close vicinity of the cell. Chronaxy values up to 20 times larger are expected when the stimulating electrode is moved from 50 μm away to the inside of the cell. In the case of monophasic cathodic stimulation, the length of the primarily excited zone, which is situated between the hyperpolarized regions, increases with electrode–cell distance, and for distant electrodes the excitation process is more comparable with the temporal behavior of intracellular stimulation. Chronaxy also varies along the neural axis, being small for electrode positions at neural segments with high sodium channel density (nodes of Ranvier and axon initial segment) and larger at the soma and dendrites. For a constant electrode position, the spike initiation site can change for short and long pulses; for example, a short current pulse intracellularly applied at the dendrite may cause a dendritic spike, whereas a longer weaker pulse may initiate a spike via intracellular current flow within the axon initial segment. As a consequence, strength–duration curves have in some cases a bimodal shape, and thus, they deviate from a classical monotonic curve as described by the formulas of Lapicque and Weiss 13. The usual fit of experimental strength–duration curves according to these classical formulas can be misleading.

My scientific contributions were shaped by developments that matured biophysical modeling from early beginnings to becoming a relevant tool for helping to explain phenomena that are not or only indirectly accessible to experimental measurement techniques. In particular, I have dedicated my scientific life to modeling of electrophysiological mechanisms in complex neural structures and nerve and muscle cells. My introduction of the activating function in neural modeling has improved the understanding of electrophysiological phenomena at both the microscopic and macroscopic scales, at the cell level and in the whole-body view. As I have tried to demonstrate above in my discussion of own work, the method offers a wide spectrum of applications in the analysis of the underlying mechanisms of complex neural functions. I am happy that this work has been recognized by numerous colleagues around the world applying my methodology to many other issues in their own scientific work. Examples are electrode arrangements for unidirectional firing, stimulation with magnetic coils, and an extension of the concept of the activating function to explain the mechanisms of defibrillation.

The support of brain research by generous funding programs like the “Decade of the Brain” and the Human Brain Project has positive effects for related fields like neuroprosthetics. However, important findings commonly raise a plethora of new questions and technological problems that have to be solved before the findings can be applied in a neural interface system.