Rheobase is a measure of membrane potential excitability. In neuroscience, rheobase is the minimal current amplitude of infinite duration that results in the depolarization threshold of the cell membranes being reached, such as an action potential or the contraction of a muscle.Ashley, et al. "Determination of the Chronaxie and Rheobase of Denervated Limb Muscles in Conscious Rabbits". Artificial Organs, Volume 29 Issue 3 Page 212 - March 2005 In Greek, the root rhe translates to "current or flow", and basi means "bottom or foundation": thus the rheobase is the minimum current that will produce an action potential or muscle contraction.
Rheobase can be best understood in the context of the strength-duration relationship (Fig. 1).Fleshman et al. "Rheobase, input resistance, and motor-unit type in medial gastrocnemius motoneurons in the cat." Journal of Neurophysiology, 1981. The ease with which a membrane can be stimulated depends on two variables: the strength of the stimulus, and the duration for which the stimulus is applied.Boinagrov, D., et al. (2010). "Strength-duration relationship for extracellular neural stimulation: Numerical and analytical models". Journal of Neurophysiology, 194(2010), 2236–2248. These variables are inversely related: as the strength of the applied current increases, the time required to stimulate the membrane decreases (and vice versa) to maintain a constant effect. Mathematically, rheobase is equivalent to half the current that needs to be applied for the duration of chronaxie, which is a strength-duration time constant that corresponds to the duration of time that elicits a response when the nerve is stimulated at twice rheobasic strength.
The strength-duration curve was first discovered by G. Weiss in 1901, but it was not until 1909 that Louis Lapicque coined the term rheobase. Many studies are being conducted in relation to rheobase values and the dynamic changes throughout maturation and between different nerve fibers.Carrascal, et al. (2005). "Changes during postnatal development in physiological and anatomical characteristics of rat motoneurons studied in vitro". Brain Research Reviews, 49(2005), 377–387. In the past strength-duration curves and rheobase determinations were used to assess nerve injury; today, they play a role in clinical identification of many neurological pathologies, including diabetic neuropathy, CIDP, Machado–Joseph disease,Nodera, H., & Kaji, R. (2006). "Nerve excitability testing in its clinical application to neuromuscular diseases". Clinical Neurophysiology, 117(2006), 1902–1916. and ALS.Mogyoros, I., et al. (1998). "Strength-duration properties of sensory and motor axons in amyotrophic lateral sclerosis". Brain, 121(1998), 851–859.
Strength-Duration Curve The strength-duration time constant (chronaxie) and rheobase are parameters that describe the strength-duration curve—the curve that relates the intensity of a threshold stimulus to its duration. As the duration of a test stimulus increases, the strength of the current required to activate a single fiber action potential decreases.
The strength-duration curve is a plot of the threshold current (I) versus pulse duration (d) required to stimulate excitable tissue.Geddes, L. A. (2004). "Accuracy limitations of chronaxie values". IEEE Transactions on Biomedical Engineering, 51(1). As mentioned, the two important points on the curve are rheobase (b) and chronaxie (c), which correlates to twice the rheobase (2b). Strength-duration curves are useful in studies where the current required is changed when the pulse duration is changed.Geddes, L.A., & Bourland, J. D. (1985) "The Strength-Duration Curve". IEEE Transactions on Biomedical Engineering, 32 (6). 458–459.
Lapicque's Equation
In 1907, Louis Lapicque, a French neuroscientist, proposed his exponential equation for the strength-duration curve. His equation for determining current I:
where b relates to the rheobase value and c relates to the chronaxie value over duration d.
Lapicque's hyperbolic formula combines the threshold amplitude of a stimulus with its duration. This represents the first manageable with physiologically defined parameters that could compare excitability of different tissues, reflecting an urgent need at the turn of the 20th century. Lapicque used constant-current, capacitor-discharge pulses to obtain chronaxie for a wide variety of excitable tissues. Rheobase in the Lapicque equation is the asymptote of the hyperbolic curve at very long durations.
Weiss's Equation
In 1901, G. Weiss proposed another linear equation using a charge Q duration curve. The electrical charge Q can be calculated with the following equation:
or
again, where I is the current is measured in amperes multiplied by duration d. b relates to the rheobase value and c relates to the chronaxie value.
Rheobase in the Weiss formula is the slope of the graph. The x-intercept of the Weiss equation is equal to b x c, or rheobase times chronaxie.
This equation suggests that a graph of threshold stimulus strength versus stimulus duration should show a decay toward zero as stimulus duration is increased, so the stimulus strength required to reach threshold is predicted to increase during more protracted stimulation. The strength-duration curve for a typical nerve membrane is slightly skewed from the predicted graph, in that the curve flattens out in response to repetitive stimulation reaching an asymptote representing rheobase. When the duration of a stimulus is prolonged, charge transfer and membrane potential rise exponentially to a plateau (instead of increasing linearly with time). When rheobase exceeds the strength of the stimulus, stimulation fails to generate action potentials (even with large values of t); thus if the stimulus is too small, the membrane potential never reaches threshold. The disparity between the shape of the strength-duration curve predicted by Weiss's equation and the one actually observed in neural membranes can be attributed to leakage of charge that occurs under physiological conditions, a feature of the electrical resistance of the membrane. Weiss' equation predicts the relationship between stimulus strength and duration for an ideal capacitor with no leakage resistance.
Despite this limitation, Weiss’s equation provides the best fit for strength-duration data and indicates that rheobase and time constant (chronaxie) can be measured from the charge duration curve with a very small margin of error. Weiss used rectangular, constant-current pulses and found that threshold charge required for stimulation increased linearly with pulse duration. He also found that stimulus charge, the product of stimulus current and stimulus duration is proportional to rheobase, so that only two stimulus durations are necessary to calculate rheobase.
Measurement The use of strength-duration curves was developed in the 1930s, followed by the use of threshold current measurements for the study of human axonal excitability in the 1970s. Use of these methods in toxic neuropathies has enabled researchers to designate protective factors for many peripheral nerve disorders, and several diseases of the central nervous system (see Clinical Significance).
Nerve excitability examination complements conventional nerve conduction studies by allowing insight into biophysical characteristics of axons, as well as their ion-channel functioning. The protocol is aimed at providing information about nodal as well as internodal ion channels, and the indices are extremely sensitive to axon membrane potential. These studies have provided insight into conditions characterized by changes in resting potential, such as electrolyte concentration and pH, as well as specific ion-channel and pump function in normal and diseased nerves. Furthermore, software programs enabling the calculation of rheobasic and time constant values from both normal and diseased nerves have recently enabled researchers to pinpoint some important factors for a number of pervasive nerve disorders, many of which involve substantial demyelination (see Clinical Significance). Supraximal electrical stimulation and measurement of conduction velocity and amplitudes of compound motor (CMAP) and sensory (SNAP) responses provide measures of the number and conduction velocities of large myelinated fibers. Additionally, multiple measures of excitability in the TROND protocol permit assessment of ion channels (transient and persistent Na+ channels, slow K+ channels) at nodes of Ranvier by computing stimulus response curves, strength duration time constant (chronaxie), rheobase, and the recovery cycle after passage of an action potential. This is accomplished by applying long polarizing currents to the nerve and measuring the influence of voltage on voltage gated-ion channels beneath myelin.
In Neurons In neurons, the rheobase is defined as the smallest injected step current, of infinite duration, that results in one action potential. In practice, there are several challenges of measuring the rheobase. The general protocol is to inject currents of various amplitudes, observe if any action potentials were produced, and then further refine the injected current magnitude until the boundary between spiking and non-spiking behavior is identified.
Duration
Because it is not possible to wait an infinite amount of time, trial currents are injected for finite durations. The current duration varies among publications, but is on the order of 0.1-5 seconds. However, this also implies that an injected current that did not result in spikes could have resulted in spikes if the duration was longer. For this reason, the current duration should be specified when reporting a cell's rheobase.
Precision
In addition to current duration, it is not possible to find the exact rheobase value in a real cell. In publications, a common method is to try various currents at some increments (e.g. 10 pA), and find the two consecutive current amplitudes that do and do not result in action potentials. The smallest difference between the lower and upper currents used is the rheobase search precision: the "true" rheobase is somewhere between the two tested current values.
Precision is also affected by thermal noise and stochastic nature of ion channels. If a cell does not reliably spike at a certain current amplitude, the search method could be modified to include multiple repeated current injections to find such current that reliably results in spikes.
Maximum Current Amplitude Range
When searching for the rheobase, a proper current amplitude range must be chosen. If the maximum current used is too small, no spikes will be produced. If too large, cell health might be compromised. Before starting the search, the cell's membrane input resistance (from negative current injections) can be measured and used to estimate the current necessary to activate the cell (e.g. if -10pA reduces the potential by 20mV, then a cell that rests at -60mV will likely spike at least once in response to +30pA injections).
Negative Rheobase
The standard rheobase definition assumes that a given cell does not spike when a current is not injected. However, some cells are spontaneously spiking (e.g. Cardiac pacemaker cells). For such cells, a negative (inhibitory) current will quiet them, while a slightly less negative current will result in action potentials. In such cases, stimulation protocols that utilize the rheobase and assume that spiking rates are proportional to the rheobase will produce nonsense results (e.g. spike rate in response to 2X rheobase will not be greater than at 1.5X rheobase).
Bursting cells
Bursting cells will produce multiple spikes once activated. For such cells, it can be very difficult to find the current that produces only a single spike within a given time frame. For such cells, finding the boundary between currents that result in bursts and no bursts could be used.