Rheobase

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. 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). 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. 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. 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, and ALS.

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. 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.

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. Thus, the strength duration time constant is a reflection of persistent Na+ channel function, and is furthermore 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. As a result, sensory nerves have a longer strength duration time constant and a lower rheobase than motor nerves. 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. 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 in the strength duration time constant 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.

Axonal degeneration and regeneration are common processes in many nerve disorders. As a consequence of myelin remodeling, the internodal length is known to remain persistently short. Little is known about how neurons cope with the increased number of nodes except that there may be a compensatory increase in Na+ channels so that the internodal density is restored. Nevertheless, most extant research findings maintain that regenerated axons may be functionally deficient, as the access to the K+ channel under the paranodal myelin may be increased. In the clinical setting, the function of the internode can only be explored by excitability studies (see Measurement). Experimental observations utilizing threshold measurements to assess excitability of myelinated nerve fibers have indicated that the function of regenerated internodes indeed remains persistently abnormal, with regenerated motor axons displaying increased rheobase and decreased chronaxie—changes that are consistent with abnormal active membrane properties. These studies have furthermore determined that activity dependent conduction block in myelination was due to hyperpolarization, as well as abnormally increased Na+ currents and increased availability of fast K+ rectifiers. Listed below are findings on the changes in nerve excitability, and therefore the strength duration time constant, that have been observed within several of the most pervasive nerve disorders.

Amyotrophic lateral sclerosis (ALS) affects upper and lower motor systems, with symptoms ranging from 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 and lower values for rheobase 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 (MJD) is a triplet repeat disease characterized by cerebellar ataxia, pyramidal signs, ophthalmoplegia, 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, and this corresponds to a significant reduction in rheobase. Combined with findings on Na+ channel blockers, these data suggest that the cramps in MJD are likely caused by the increased persistent Na+ channel conductance that may be unregulated during axonal reinnervation (which results from long term axonal degeneration).

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. Measurement of sensory conduction in distal nerve segments have shown salient defects in diabetic patients, suggesting that the function of persistent Na+ channels is decreased in diabetics. These experiments have furthermore opened new avenues for preventative drug efficacy. Measurement of chronaxie and rheobase in sural sensory fibers has revealed mild reductions in excitability in diabetics, as evidenced by significant reductions in conduction velocity and chronaxie of sensory fibers with corresponding increases in rheobase. These effects are attributed to the reduced Na+ K+ ATPase activity in axon of diabetic patients, which causes Na+ ions to accumulation intracellularly, as well as a subsequent a decrease in the transmembrane Na+ gradient.

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. Measurement of chronaxie and rheobase for these diseased nerves has concluded that electrophysiologically, a patient with demyelinating (Type I) CMT demonstrates slow nerve conduction velocity, frequently accompanied by reduced amplitudes of motor and sensory action potentials; moreover, axonal (Type II) CMT can be attributed to impaired interaction between Schwann cells and axons. Changes in excitability measures are typically universal and vary little between patients, and this is likely due to the diffuse distribution of demyelination, suggesting changed cable properties associated with short internodes.

Multifocal motor neuropathy (MMN) is a rare clinical case, characterized almost entirely by muscle weakness, atrophy, and fasciculations. An important feature of MMN is that the strength duration constant is significantly small, corresponding to an appreciable increase in rheobase. Both measurements have been shown to become normalized following intravenous immunoglobulin therapy.

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