Extracellular stimulation of nerve cells with electric current spikes induced by voltage steps
📝 Abstract
A new stimulation paradigm is presented for the stimulation of nerve cells by extracellular electric currents. In the new paradigm stimulation is achieved with the current spike induced by a voltage step whenever the voltage step is applied to a live biological tissue. By experimental evidence and theoretical arguments, it is shown that this spike is well suited for the stimulation of nerve cells. Stimulation of the human tongue is used for proof of principle. Charge injection thresholds are measured for various voltages. The time-profile of the current spike used in the experiment has a half-width of about 1 microsecond. The decay of the spike is non-exponential. The spike has at least three distinctly different phases. A Maxwell phase is followed by a charge-rearrangement phase. Charging of cell membranes is completed in a third phase. All three phases contribute to depolarization or hyperpolarization of cell membranes. Due to the short duration of the spike the charge transfer is very small. The activation time (time of no return) of nerve cell membranes leading to an action potential is measured and found to be unexpectedly short. It can become as short as 3 microseconds for a voltage step of 10 V or higher.
💡 Analysis
A new stimulation paradigm is presented for the stimulation of nerve cells by extracellular electric currents. In the new paradigm stimulation is achieved with the current spike induced by a voltage step whenever the voltage step is applied to a live biological tissue. By experimental evidence and theoretical arguments, it is shown that this spike is well suited for the stimulation of nerve cells. Stimulation of the human tongue is used for proof of principle. Charge injection thresholds are measured for various voltages. The time-profile of the current spike used in the experiment has a half-width of about 1 microsecond. The decay of the spike is non-exponential. The spike has at least three distinctly different phases. A Maxwell phase is followed by a charge-rearrangement phase. Charging of cell membranes is completed in a third phase. All three phases contribute to depolarization or hyperpolarization of cell membranes. Due to the short duration of the spike the charge transfer is very small. The activation time (time of no return) of nerve cell membranes leading to an action potential is measured and found to be unexpectedly short. It can become as short as 3 microseconds for a voltage step of 10 V or higher.
📄 Content
Extracellular stimulation of nerve cells with electric current spikes induced by voltage steps
Erich W. Schmid
Institute of Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14,
72076 Tübingen, Germany, erich.schmid(at)uni-tuebingen.de
Abstract
A new stimulation paradigm is presented for the stimulation of nerve cells by extracellular
electric currents. In the new paradigm stimulation is achieved with the current spike induced
by a voltage step whenever the voltage step is applied to a live biological tissue. By
experimental evidence and theoretical arguments, it is shown that this spike is well suited
for the stimulation of nerve cells. Stimulation of the human tongue is used for proof of
principle. Charge injection thresholds are measured for various voltages. The time-profile of
the current spike used in the experiment has a half-width of about 1 µs. The decay of the spike
is non-exponential. The spike has at least three distinctly different phases. A Maxwell phase
is followed by a charge-rearrangement phase. Charging of cell membranes is completed in a
third phase. All three phases contribute to depolarization or hyperpolarization of cell
membranes. Due to the short duration of the spike the charge transfer is very small. The
activation time (time of no return) of nerve cell membranes leading to an action potential is
measured and found to be unexpectedly short. It can become as short as 3 µs for a voltage
step of 10 V or higher.
Keywords
Stimulation paradigm, transverse stimulation,
longitudinal stimulation, electrical
stimulation, retinal prosthesis, epi-retinal implant, subretinal implant.
- Introduction
The electrical properties of biological tissues have been of great interest for over 200 years
of research. According to the historical review of Foster and Schwan [Fo 1989] it has been
known in 1837, already, that a voltage step applied to a biological tissue induces a current
spike followed by a constant current. The current spike and its time profile have been studied
by many researchers. It became clear that there is something like “tissue-polarization”, in the
sense that the tissue takes up electricity when the voltage is switched on and gives it back
when the voltage is switched off. Theoretical understanding became possible only after the
discovery of the cell membrane and its property as an insulator in 1902. It became clear that
during the current spike a polarization current passes the cell membrane vertically to its
surface and leaves behind a polarized membrane, with opposite polarization of the
membrane at opposite sides of the cell. In the 20th century studies with alternating currents
revealed many details and resulted in realistic models. Parameters were adjusted to many
types of human tissue [Ga 1996].
External electrical stimulation of nerve cells has been discovered by Luigi Galvani [Ga 1791]
at the end of the 18th century. In a first experiment he found and studied what we now call
transverse stimulation. In a second experiment he found and studied longitudinal
stimulation. An understanding of microscopic details was not possible at Galvani’s time. By
the work of Hodgkin and Huxley [Ho 1952] we now understand that in both experiments the
membrane of a nerve cell got depolarized and an action potential emerged.
As has been said above, the polarization current passing the tissue during the current spike
causes depolarization at one side of a cell and hyperpolarization at the opposite side of the
same cell. If the depolarization is bigger than a certain threshold it can give rise to an action
potential and thus to the so-called external electrical stimulation. Since the polarization
current passes the cell membrane vertically to its surface, we call this kind of stimulation
transverse stimulation.
The fact that depolarization of the cell membrane can give rise to an action potential led to new interest in Heaviside’s cable equation. This equation was meant to describe a telegraph cable in the ocean, but it can also describe an axon or a dendrite in a biological tissue. In the cable model, the stimulation current is not a polarization current. It is an ohmic current that flows parallel to the membrane, which means in longitudinal direction with respect to the cylinder axis of an axon or dendrite. The stimulation is caused by the voltage drop of the ohmic current along its course, which then affects the membrane. This kind of stimulation is described in text books [Jo 1995]. In the present paper we call it longitudinal stimulation.
The main difference between longitudinal stimulation and transverse stimulation can be described as follows. For longitudinal stimulation the polarization (depolarization or hyperpolarization) of the cell membrane is the same at all sides of a cell, or of a compartment of an axon or dendrite. For transverse stimulation, in contrast, the polarization changes si
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