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Fig. 1 - Rheobase and chronaxie are points defined on the strength-duration curve for stimulus of an excitable tissue.

Rheobase is a measure of membrane excitability. The ease with which a membrane can be stimulated depends on two variables: the strength of the stimulus, as well as the duration for which the stimulus is applied. These variables are related inversely: as the strength of the applied current increases, the time required to stimulate the membrane decreases (and vice versa) to maintain a constant effect. In neuroscience, rheobase is the minimal current amplitude of indefinite duration (in a practical sense, about 300 milliseconds) that results in the depolarization threshold of the cell membranes being reached, such as an action potential or the contraction of a muscle. This can be understood better by looking at a strength duration relationship (Fig. 1).

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. In the case of a nerve or single muscle cell, rheobase is half the current that needs to be applied for the duration of chronaxie. Mathematically, rheobase is equivalent to half 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 properties of the nodal membrane largely determine the axon's strength-duration properties, and these will change with changes in membrane potential, with temperature, and with demyelination as the exposed membrane is effectively enlarged by the inclusion of paranodal and intermodal membrane. 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 In the past strength duration curves and rheobase determinations were used to assess nerve injury and today, plays a role in many diseases such as Diabetic neuropathy, CIDP, Machado-Joseph Disease , and ALS .

Strength-Duration Curve

The strength-duration curve is a plot of the threshold current (I) versus pulse duration (d) required to stimulate excitable tissue. There are two important points on the curve: 1) Rheobase (b) and 2) 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.

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:

$I=b(1+{c \over d}\,),$

where b relates to the rheobase value and c relates to the chronaxie value over duration d.

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 exponential 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:

$Q=b(d+c)$ or $Q=Id,$

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.

Weiss’s equation provides the best fit for strength duration data and indicates that rheobase and time constant (chronaxie) can be measured simply from the charge duration curve. 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. 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.

Experimental Findings

The use of strength-duration curves in 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 have enabled researchers to designate protective factors for many peripheral nerve disorders, and several diseases of the central nervous system (see Clinical Significance).

The strength-duration time constant is a reflection of persistent Na+ channel function, but is also influenced by membrane potential and passive membrane properties . As such, many aspects of nerve excitability testing depend on sodium channel functions: namely, the strength-duration time constant, the recovery cycle, the stimulus-response curve, and the current-threshold relationship. Measuring responses in nerve that are related to nodal function (including strength-duration time constant and rheobase) and internodal function has allowed insight into normal axon physiology as well as normal fluctuations of electrolyte concentrations .

The function of internodes is to maintain resting membrane potential. Internodal dysfunction significantly affects nerve excitability in a diseased nerve. Rheobase is influenced by excitability of the nodal membrane, which increases with hyperpolarization and decreases with depolarization. Its voltage-dependence follows the behavior of persistent sodium channels that are active near threshold and have rapidly activating, slowly inactivating channel properties . Depolarization increases the Na+ current through the persistent channels, resulting in a lower rheobase; hyperpolarization has the opposite effect.

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.

Sensory Nerves vs. Motor Nerves

Nerve excitability studies have established a number of biophysical differences between human sensory and motor axons . Even though the diameters and conduction velocities of the most excitable motor and sensory fibers are similar, sensory fibers have significantly longer strength-duration time constants. As a result, sensory nerves have a longer strength-duration time constant and a lower rheobase than motor nerves.

Many studies have suggested that differences in the expression of threshold channels could account for the sensory/motor differences in strength-duration time constant. The differences in strength-duration time constant and rheobase of normal sensory and motor axons are thought to reflect differences in expression of a persistent Na+ conductance . Additionally, sensory axons accommodate more to long-lasting hyperpolarizing currents than do motor axons, suggesting a greater expression of the hyperpolarization-activated inward rectifier channels. Finally, the electrogenic Na⁺/K⁺-ATPase is more active in sensory nerves, which have a greater dependence on this pump to maintain resting membrane potential than do motor nerves.

Increases in the strength-duration time constant are observed when this conductance is activated by depolarization, or by hyperventilation . However, demyelination, which exposes internodal membrane with a higher membrane time constant than that of the original node, can also increase strength duration time constant .

The strength-duration time constant of both cutaneous and motor afferents decreases with age, and this corresponds to an increase in rheobase. Two possible reasons for this age-related decrease have been proposed. First, nerve geometry might change with age because of axonal loss and neural fibrosis. Secondly, the persistent Na+ conductance might decrease maturation. Significant decreases in threshold for sensory and motor fibers have been observed during ischemia . These decreases in threshold were furthermore associated with significant increases in the strength-duration time constant, appreciably indicating a significant decrease in rheobase current. These changes are thought to be the result of non-inactivating, voltage-dependent Na+ channels, which are active at resting potential.

Clinical Significane

Diabetic polyneuropathy

The hallmark feature of diabetic polyneuropathy is a blend of axonal and demyelinating damage, which results from mechanical demyelination and channel/pump dysfunctions. Diabetic patients have been found to experience a significantly shorter strength-duration time constant and a much higher rheobase than normal patients.

Charcot-Marie-tooth disease

Charcot–Marie–Tooth disease (CMT) is the most common form of hereditary neuropathy and can be further subdivided into two types: Type 1: demyelinating, and Type 2: axonal. A patient with Type 1 CMT shows slow nerve conduction velocity and often times low amplitudes of motor and sensory action potentials.

Multifocal motor neuropathy

Multifocal motor neuropathy (MMN) is a rare clinical case, characterized almost exclusively by muscle weakness, atrophy, and fasciculations. An important feature of MMN is that the strength-duration constant is significantly small, but becomes normalized followed intravenous immunoglobulin therapy .

Chronic Inflammatory Demyelinating Polyneuropathy

Chronic inflammatory demyelinating polyneuropathy (CIDP) is an immunological demyelinating polyneuropathy. As a result of increased paranodal capacitance from demyelination, patients experience increased stimulation threshold and shorter strength-duration time constant.

Amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis (ALS) affects upper and lower motor systems. Symptoms include muscle atrophy, hyperreflexia, and fasciculations, all of which suggest increased axonal excitability. Many studies have concluded that abnormally decreased K+ conductance results in axonal depolarization, leading to axonal hyperexcitability and the generation of fasciculation. ALS patients in these studies demonstrated longer strength-duration time constants than in control subjects.

Another study has demonstrated that sensory rheobases were no different in patients from those in age-matched control subjects, whereas motor rheobases were significantly lower . Discovering that motor axons have both a lower rheobase and a longer strength-duration time constant in ALS has prompted the conclusion that motor neurons are abnormally excitable in ALS, with properties more like those of sensory neurons. Changes in the geometry of the nerve due to loss of axons within the peripheral nerve likely cause this shift in rheobase. A logical conclusion of the present data is that there is a greater persistent Na+ conductance at rest in motor axons of patients with ALS than normal.

Machado-Joseph disease

Machado-Joseph Disease (MJD) is a triplet repeat disease characterized by cerebellar ataxia, pyramidal signs, opthalmoplegia, and polyneuropathy . Since muscle cramps are a frequent occurrence in MJD, axonal hyperexcitability has been considered to play a role in the disease. Research has demonstrated that the strength-duration time constant in MJD patients is significantly longer than in controls. Combined with findings on Na+ channel blockers, this data suggests that the cramps in MJD are likely caused by the increased persistent Na+ channel conductance that may be unregulated during axonal reinnervation.

See also

• Chronaxie