Extracellular Stimulation

In clinical practice, the stimulation methods used to elucidate the electrical properties of excitable cells are simply not suitable. To start with, clinically useful stimulation requires stimulating much more than a single nerve or muscle cell, making it impractical to build electrode arrays that can impale a large number of cells simultaneously. Next, even if a sufficient number of cells could be impaled with microelectrodes, it is next to impossible to keep them in place in a living, moving being. Because of this, in vivo stimulation almost always involves delivering the stimulating currents between a pair of electrodes placed near (but not inside) the target cells. Consider the simple model of Figure 7.3. Here the vector current flux is indicated by arrows and transmembrane current is assumed to flow only at the anode and cathode (in reality it flows at all parts of the cell) when the switch closes. As shown in Figure 7.3b, the current through the membrane will hyperpolarize the intracellu-lar membrane region under the anode and depolarize the intracellular region under the cathode. Stimulation will occur when the transmembrane potential at the cathode crosses the

Inside of Cell

Inside of Cell

Figure 7.3 Simplified model of electrical stimulation of a cell by a current applied through extracellular electrodes. (a) A transmembrane current is assumed to flow only at the anode and cathode. The vector current flux is indicated by arrows. (b) The current through the membrane hyperpolarizes the intracellular membrane region under the anode and depolarizes the intracellular region under the cathode. Stimulation occurs when the transmembrane potential at the cathode crosses the membrane's threshold voltage.

membrane's threshold voltage. Note that this is the reverse of what happens with intracellular stimulation, where excitation occurs at the anode.

Depending on the arrangement of the electrodes, three stimulation modes can be distinguished:

1. Bipolar. Both electrodes are close to the target tissue.

2. Monopolar (also called unipolar). One electrode, normally the cathode, is close to the target tissue, and the other (anode) is remote from the target tissue, making its size and exact placement irrelevant.

3. Field stimulation. Both electrodes are remote from the target tissue.

The efficiency of bipolar and monopolar stimulation is similar. However, the current delivered in the monopolar mode often crosses through nontarget tissue on its way to the anode (yes, the conventional direction for current is in the opposite direction, but you know what we mean) and is sometimes capable of stimulating these nontarget excitable cells undesirably. Field stimulation is the most inefficient method but is very commonly the preferred mode of current delivery in nonchronic applications since it allows tissues to be stimulated using noninvasive skin-surface electrodes.

A stimulus must be of adequate intensity and duration to evoke a response. If it is too short, even a strong pulse will not be effective. The stimulation threshold is defined as the minimum strength of stimulus (expressed either in volts or in milliamperes) required for activation of a target tissue for a given stimulus duration. When thresholds for several durations are put together on the same graph, a strength-duration curve is formed. The nice thing about the strength-duration curve is that with one quick look one can determine whether or not a stimulus will be effective. Any stimulus that falls above the curve will excite the target tissue.

As shown in the stylized strength-duration curve of Figure 7.4, stimulus current and duration can be mutually traded off over a certain range. For a short pulse, the effectiveness of a stimulus is characterized by the product of current I and duration t, where delivered charge Q = It. Hence if the amount of charge required to activate the target tissue is Qthreshold and the stimulus duration is t, the current /threshold required to achieve activation wiU be /threshold = Qthreshold/t.

It would seem from this relationship that the strength-duration curve should show a decline to near zero as stimulus duration is increased. However, the strength-duration curve of real excitable tissue flattens out with long stimulus durations, reaching an asymptote called the rheobase. The root rheo means current and base means foundation; thus, the rheobase is the foundation, or minimum, current (stimulus strength) that will produce a response. When the stimulus strength is below the rheobase, stimulation is ineffective even when stimulus duration is very long.

The reason for the difference between the actual behavior and that predicted by /threshold = Qthreshold/t is that the latter assumes that the membrane is an ideal capacitor. This is not the case, and the leakage resistance shows its effect during prolonged stimulation (large values of t). The equation fails to predict the charge transfer across the cell membrane because under these conditions, more membrane current is carried by the leakage resistance and less is used to charge the membrane capacitance. Membrane potential thus rises exponentially to a plateau during prolonged stimulation instead of increasing linearly with time.

The strength-duration curve was characterized by Lapicque [1909] by the value of the rheobase (in volts or milliamperes) and a second number called the chronaxie. The root chron means time and axie means axis. The chronaxie is measured along the time axis and is defined as the stimulus duration (in milliseconds) that yields excitation of the tissue when stimulated at twice the rheobase strength. In the strength-duration curve of Figure 7.4, the

Figure 7.4 It is possible to see from this stylized strength-duration curve that stimulus current and duration can be mutually traded off over a certain range. The strength-duration curve was characterized by Lapicque by the value of the rheobase (in volts or milliamperes) and the chronaxie, which is measured along the time axis and defined as the stimulus duration (in milliseconds) that yields excitation of the tissue when stimulated at twice the rheobase strength. In this example, rheobase = 3.5 mA and chronaxie = 0.22ms.

Figure 7.4 It is possible to see from this stylized strength-duration curve that stimulus current and duration can be mutually traded off over a certain range. The strength-duration curve was characterized by Lapicque by the value of the rheobase (in volts or milliamperes) and the chronaxie, which is measured along the time axis and defined as the stimulus duration (in milliseconds) that yields excitation of the tissue when stimulated at twice the rheobase strength. In this example, rheobase = 3.5 mA and chronaxie = 0.22ms.

rheobase is the minimum stimulus strength that will produce a response, which is the point at which the curve asymptotes, about 3.5mA. To determine the chronaxie, simply look for the stimulus duration that yields a response when the stimulus strength is set to exactly twice rheobase, or 7 mA. In this example, the chronaxie is 0.22 ms.

The strength-duration curve is highly dependent on the type of tissue being stimulated. For example, the chronaxie of human motor nerve is approximately 0.01 ms, about 0.25 ms for pain receptors, and approximately 2 ms for mammalian cardiac muscle. That is why there is rarely a need for pulses longer than 2 ms in nerve stimulation, whereas a pulse width as long as 10 ms is often necessary for direct stimulation of certain smooth muscles.

The empirical equations for the threshold current, charge, and energy for a rectangular stimulation pulse are

'threshold = rheobase X I 1

chronaxie |

^threshold ^ rheobase X t X 1l + Xonaxie j

Figure 7.5 The strength-duration relationship can be expressed in terms of threshold current, threshold charge, or threshold energy needed to excite a tissue. For a rectangular current stimulus of duration t delivered to a load of resistance r, these relationships are given by /threshold = rheobase X (1 + chronaxie/t), Gthreshold = rheobase X t X (1 + chronaxie/t), and £threshold = rheobase2 X r X t X (1 + chronaxie/t)2.

Figure 7.5 The strength-duration relationship can be expressed in terms of threshold current, threshold charge, or threshold energy needed to excite a tissue. For a rectangular current stimulus of duration t delivered to a load of resistance r, these relationships are given by /threshold = rheobase X (1 + chronaxie/t), Gthreshold = rheobase X t X (1 + chronaxie/t), and £threshold = rheobase2 X r X t X (1 + chronaxie/t)2.

^threshold = (rheobase)2 X r Xt X ^ 1 + a^a j where t is the stimulus duration and r is the resistance of the path through which the current flows (resistance of the wires, ionic resistance of the medium, and electrode-tissue interface impedance). Figure 7.5 presents the three strength-duration curves in a single graph.

In practice, stimulation parameters close to those of the strength-duration curve are seldom used. Owing to small fluctuations of excitability, the target tissue may not always be excited if the stimulus is only slightly above threshold. For this reason, the stimulus parameters are usually set to at least twice the threshold in applications that require reliable stimulation.

Binaural Beats Healing

Binaural Beats Healing

Heal Yourself With Powerful Binaural Beats. If you search the Net for binaural beats you'll promptly discover there's a whole industry built upon the idea that listening to binaural beats may produce all sorts of desired effects in your brain.

Get My Free Ebook


Post a comment