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| [[File:Rheobase chronaxie.svg|thumb|350px|alt=Alt text|Fig. 1 - Rheobase and chronaxie are points defined on the strength-duration curve for stimulus of an excitable tissue.]]
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| '''Rheobase''' is a measure of [[Membrane potential|membrane excitability]]. In [[neuroscience]], rheobase is the minimal current [[amplitude]] of infinite duration (in a practical sense, about 300 milliseconds) that results in the [[depolarization]] [[threshold potential|threshold]] of the cell membranes being reached, such as an [[action potential]] or the [[Muscle contraction|contraction]] of a muscle.<ref>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</ref> In [[List of Greek and Latin roots in English|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.
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| Rheobase can be best understood in the context of the strength-duration relationship (Fig. 1).<ref>Fleshman et al. "Rheobase, input resistance, and motor-unit type in medial gastrocnemius motoneurons in the cat." ''Journal of Neurophysiology'', 1981.</ref> The ease with which a [[membrane]] can be stimulated depends on two variables: the strength of the [[stimulus (physiology)|stimulus]], and the duration for which the stimulus is applied.<ref name="Boinagrov, D. 2010">Boinagrov, D., et al. (2010). "Strength-duration relationship for extracellular neural stimulation: Numerical and analytical models". ''Journal of Neurophysiology'', 194(2010), 2236–2248.</ref> 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.<ref name="Boinagrov, D. 2010"/> 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.<ref name="Boinagrov, D. 2010"/>
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| 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".<ref name= "Geddes, 2004" /> Many studies are being conducted in relation to rheobase values and the dynamic changes throughout maturation and between different nerve fibers.<ref>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.</ref> 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 as [[Diabetic neuropathy]], [[Chronic inflammatory demyelinating polyneuropathy|CIDP]], [[Machado-Joseph Disease]],<ref name="Nodera">Nodera, H., & Kaji, R. (2006). "Nerve excitability testing in its clinical application to neuromuscular diseases". ''Clinical Neurophysiology'', 117(2006), 1902–1916.</ref> and [[Amyotrophic lateral sclerosis|ALS]].<ref name= "Mogyoros, 1998">Mogyoros, I., et al. (1998). "Strength-duration properties of sensory and motor axons in amyotrophic lateral sclerosis". ''Brain'', 121(1998), 851–859.</ref>
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| ==Strength-Duration Curve==
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| 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.
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| The strength-duration curve is a plot of the threshold current (I) versus pulse duration (d) required to stimulate [[excitable medium|excitable tissue]].<ref name= "Geddes, 2004">Geddes, L. A. (2004). "Accuracy limitations of chronaxie values". ''IEEE Transactions on Biomedical Engineering'', 51(1).</ref> 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.<ref>Geddes, L.A., & Bourland, J. D. (1985) "The Strength-Duration Curve". ''IEEE Transactions on Biomedical Engineering'', 32 (6). 458–459.</ref>
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| ===Lapicque's Equation===
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| In 1907, Louis Lapicque, a French [[neuroscience|neuroscientist]], proposed his exponential equation for the strength-duration curve. His equation for determining current ''I'':
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| :<math>I = b (1 + {c \over d} \,) ,</math>
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| where ''b'' relates to the rheobase value and ''c'' relates to the chronaxie value over duration ''d''.
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| 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 objects, reflecting an urgent need at the turn of the 20th century.<ref name= "Geddes, 2004" /> Lapicque used constant-current, [[capacitor]]-discharge pulses to obtain chronaxie for a wide variety of excitable tissues.<ref name= "Geddes, 2004" /> Rheobase in the Lapicque equation is the [[asymptote]] of the [[exponential growth|exponential curve]] at very long durations.
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| ===Weiss's Equation===
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| In 1901, G. Weiss proposed another [[linear equation]] using a [[electric charge|charge]] ''Q'' duration curve. The electrical charge ''Q'' can be calculated with the following equation:
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| :<math>Q = b (d + c)</math> or <math>Q = Id,</math>
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| again, where ''I'' is the [[electric current|current]] is measured in [[ampere]]s multiplied by duration ''d''. ''b'' relates to the rheobase value and ''c'' relates to the chronaxie value.
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| 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.
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| 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.<ref name= "Geddes, 2004" /> 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.<ref name= "Geddes, 2004" /> When the duration of a stimulus is prolonged, charge transfer and membrane potential rise exponentially to a plateau (instead of increasing linearly with time).<ref name= "Geddes, 2004" /><ref name= "Nodera" /> 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.<ref name= "Geddes, 2004" /><ref name= "Nodera" /> Weiss' equation predicts the relationship between stimulus strength and duration for an ideal capacitor with no leakage resistance.
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| 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.<ref name= "Mogyoros, 1995" /> Weiss used rectangular, constant-current [[Pulse (signal processing)|pulses]] and found that threshold charge required for stimulation increased linearly with pulse duration.<ref name= "Geddes, 2004" /> He also found that [[Stimulus (physiology)|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.<ref name= "Nodera" />
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| ==Measurement==
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| The use of strength-duration curves in was developed in the 1930s, followed by the use of [[Threshold potential|threshold current]] measurements for the study of human [[axon]]al excitability in the 1970s.<ref name="Nodera" /> Use of these methods in [[Toxicity|toxic]] [[Peripheral neuropathy|neuropathies]] has enabled researchers to designate protective factors for many [[Neuralgia|peripheral nerve disorders]], and several diseases of the [[central nervous system]] (see [[#Clinical Significance|Clinical Significance]]).
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| Nerve excitability examination complements conventional nerve conduction studies by allowing insight into [[Biophysics|biophysical]] characteristics of [[axon]]s, as well as their ion-channel functioning.<ref name= "Krarup, 2009" /> 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]].<ref name= "Krarup, 2009" /> 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.<ref name= "Mogyoros, 1997" /> 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|Clinical Significance]]).<ref name= "Krarup, 2009" /><ref name= "Mogyoros, 1997" /> 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.<ref name= "Krarup, 2009" /><ref name= "Mogyoros, 1997" /> Additionally, multiple measures of excitability in the TROND protocol permit assessment of ion channels (transient and persistent Na<sup>+</sup> channels, slow K<sup>+</sup> 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.<ref name= "Krarup, 2009" /> This is accomplished by applying long polarizing currents to the nerve and measuring the influence of voltage on voltage gated-ion channels beneath myelin.<ref name= "Krarup, 2009" />
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| ==Neurobiological Significance==
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| The properties of the [[Myelin sheath gap|nodal membrane]] largely determine the [[axon|axon's]] strength-duration properties, and these will change with changes in membrane potential, with temperature, and with [[myelin|demyelination]] as the exposed membrane is effectively enlarged by the inclusion of paranodal and intermodal membrane.<ref name= "Mogyoros, 1995">Mogyoros, I., et al. (1995). "Strength-duration properties of human peripheral nerve". ''Brain'', 119(1996), 439–447.</ref> Thus, the strength-duration time constant is a reflection of persistent Na<sup>+</sup> channel function, and is furthermore influenced by membrane potential and passive membrane properties.<ref name= "Krarup, 2009">Krarup, C., & Mihai, M. (2009). "Nerve conduction and excitability studies in peripheral nerve disorders". ''Current Opinion in Neurology'', 22(5), 460–466.</ref> 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 signaling|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.<ref name= "Mogyoros, 1998" />
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| Rheobase is influenced by excitability of the nodal membrane, which increases with [[Hyperpolarization (biology)|hyperpolarization]] and decreases with [[depolarization]]. Its voltage-dependence follows the behavior of persistent [[sodium channel]]s that are active near [[threshold potential|threshold]] and have rapidly activating, slowly inactivating channel properties.<ref name= "Nodera" /> [[Depolarization]] increases the Na<sup>+</sup> current through the persistent channels, resulting in a lower rheobase; hyperpolarization has the opposite effect. The strength-duration time constant increases with demyelination, as the exposed membrane is enlarged by inclusion of paranodal and internodal membrane. The function of the latter of these is to maintain [[resting membrane potential]], so internodal dysfunction significantly affects excitability in a diseased nerve. Such implications are further discussed in [[#Clinical Significance|Clinical Significance]].
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| ===Sensory Nerves vs. Motor Nerves===
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| Nerve excitability studies have established a number of [[biophysics|biophysical]] differences between human [[Sensory neuron|sensory]] and [[motor neuron|motor]] axons.<ref name="Nodera" /> Even though the [[diameter]]s and [[Nerve conduction velocity|conduction velocities]] of the most excitable [[motor neuron|motor]] and [[Sensory neuron|sensory]] fibers are similar, sensory fibers have significantly longer strength-duration time constants.<ref name= "Mogyoros, 1997">Mogyoros, I. et al. (1997). "Excitability changes in human sensory and motor axons during hyperventilation and ischaemia”. ‘’Brain’’ (1997), 120, 317–325.</ref> As a result, sensory nerves have a longer strength-duration time constant and a lower rheobase than [[motor neuron|motor]] nerves.<ref name= "Mogyoros, 1998" />
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| Many studies have suggested that differences in the expression of [[Threshold potential|threshold]] channels could account for the sensory/motor differences in strength-duration time constant.<ref name= "Mogyoros, 1997" /> 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<sup>+</sup> [[Electrical resistance and conductance|conductance]].<ref name= "Bostock, 1997">Bostock H. & Rockwell J. C. (1997) "Latent addition in motor and sensory fibres of human peripheral nerve". '' J Physiol'' (Lond) 1997; 498: 277–94.</ref> Additionally, sensory axons accommodate more to long-lasting hyperpolarizing currents than do motor axons, suggesting a greater expression of the [[Hyperpolarization (biology)|hyperpolarization]]-activated inward rectifier channels.<ref name= "Bostock, 1997" /> Finally, the [[Bioelectrogenesis|electrogenic]] [[Na+/K+-ATPase|Na<sup>+</sup>/K<sup>+</sup>-ATPase]] is more active in sensory nerves, which have a greater dependence on this pump to maintain [[resting membrane potential]] than do motor nerves.<ref name="Nodera" />
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| Increases in the strength-duration time constant are observed when this [[Electrical resistance and conductance|conductance]] is activated by [[depolarization]], or by [[hyperventilation]].<ref name= "Mogyoros, 1998" /> 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.<ref>Bostock, H., et al. (1983) "The spatial distribution of excitability and membrane current in normal and demyelinated mammalian nerve fibers". ''The Journal of Physiology''. (341) 41–58.</ref>
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| The strength-duration time constant of both [[skin|cutaneous]] and motor [[afferent]]s decreases with age, and this corresponds to an increase in rheobase.<ref name= "Mogyoros, 1998" /> 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<sup>+</sup> conductance might decrease [[Developmental biology|maturation]]. Significant decreases in threshold for sensory and motor fibers have been observed during [[ischemia]].<ref name = "Mogyoros, 1998" /> 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 [[sodium channels|Na<sup>+</sup> channels]], which are active at [[resting membrane potential|resting potential]].
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| ==Clinical Significance==
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| Axonal degeneration and regeneration are common processes in many nerve disorders.<ref name= "Krarup, 2009" /> As a consequence of myelin remodeling, the internodal length is known to remain persistently short.<ref name= "Krarup, 2009" /> Little is known about how neurons cope with the increased number of nodes except that there may be a compensatory increase in Na<sup>+</sup> channels so that the internodal density is restored.<ref name= "Nodera" /> Nevertheless, most extant research findings maintain that regenerated axons may be functionally deficient, as the access to the K<sup>+</sup> channel under the paranodal myelin may be increased.<ref name="Nodera" /><ref name= "Krarup, 2009" />
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| In the clinical setting, the function of the internode can only be explored by excitability studies (see [[#Measurement|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.<ref name= "Krarup, 2009" /> These studies have furthermore determined that activity-dependent conduction block in myelination was due to hyperpolarization, as well as abnormally increased Na<sup>+</sup> currents and increased availability of fast K<sup>+</sup> rectifiers.<ref name= "Krarup, 2009" /> 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.
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| ===Amyotrophic Lateral Sclerosis===
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| [[Amyotrophic lateral sclerosis|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.<ref name= "Mogyoros, 1998" /> Many studies have concluded that abnormally decreased K<sup>+</sup> conductance results in axonal [[depolarization]], leading to axonal [[Hyperactivity|hyperexcitability]] and the generation of [[fasciculation]].<ref name="Nodera" /><ref name= "Mogyoros, 1998" /> ALS patients in these studies demonstrated longer strength-duration time constants and lower values for rheobase than in [[scientific control|control]] subjects.<ref name="Nodera" /><ref name= "Mogyoros, 1998" />
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| 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.<ref name= "Mogyoros, 1998" /> 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 neuron]]s.<ref name= "Mogyoros, 1998" /> Changes in the [[geometry]] of the nerve due to loss of axons within the [[peripheral nerve]] likely cause this shift in rheobase.<ref name= "Mogyoros, 1998" /> A logical conclusion of the present data is that there is a greater persistent Na<sup>+</sup> conductance at rest in motor axons of patients with ALS than normal.<ref name= "Mogyoros, 1998" />
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| ===Machado-Joseph Disease===
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| [[Machado-Joseph Disease|Machado-Joseph Disease (MJD)]] is a triplet repeat disease characterized by [[cerebellar ataxia]], [[Pyramidal tracts|pyramidal signs]], [[ophthalmoplegia]], and [[polyneuropathy]].<ref name="Nodera" /> Since [[muscle cramp]]s are a frequent occurrence in MJD, axonal hyperexcitability has been considered to play a role in the disease.<ref name="Nodera" /><ref name= "Krarup, 2009" /> 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.<ref name="Nodera" /><ref name= "Krarup, 2009" /> Combined with findings on [[Sodium channel blocker|Na<sup>+</sup> channel blockers]], this data suggests that the cramps in MJD are likely caused by the increased persistent Na<sup>+</sup> channel conductance that may be unregulated during axonal [[reinnervation]] (which results from long-term axonal degeneration).<ref name="Nodera" /><ref name= "Krarup, 2009" /> | |
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| ===Diabetic Polyneuropathy===
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| The hallmark feature of [[diabetic neuropathy|diabetic polyneuropathy]] is a blend of axonal and [[demyelinating disease|demyelinating]] damage, which results from mechanical [[demyelination]] and channel/pump dysfunctions.<ref name="Nodera" /> [[Diabetic]] patients have been found to experience a significantly shorter strength-duration time constant and a much higher rheobase than normal patients.<ref name="Nodera" />
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| Measurement of sensory conduction in distal nerve segments have shown salient defects in diabetic patients, suggesting that the function of persistent Na<sup>+</sup> channels is decreased in diabetics.<ref name= "Nodera" /> These experiments have furthermore opened new avenues for preventative drug efficacy. Measurement of chronaxie and rheobase in [[sural nerve|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.<ref name="Nodera" /> These effects are attributed to the reduced Na<sup>+</sup>-K<sup>+</sup>-ATPase activity in axon of diabetic patients, which causes Na<sup>+</sup> ions to accumulation intracellularly, as well as a subsequent a decrease in the transmembrane Na<sup>+</sup> gradient.<ref name="Nodera" />
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| ===Charcot-Marie-Tooth Disease===
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| [[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.<ref name="Nodera" /> Measurement of chronaxie and rheobase for these diseased nerves have 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 potential]]s; moreover, axonal (Type II) CMT can be attributed to impaired interaction between Schwann cells and axons.<ref name="Nodera" /><ref name= "Krarup, 2009" /> 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 theory|cable properties]] associated with short internodes.<ref name= "Krarup, 2009" />
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| ===Multifocal Motor Neuropathy===
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| [[Multifocal motor neuropathy|Multifocal motor neuropathy (MMN)]] is a rare clinical case, characterized almost entirely by [[muscle weakness]], [[atrophy]], and [[fasciculation]]s.<ref name="Nodera" /> An important feature of MMN is that the strength-duration constant is significantly small, corresponding to an appreciable increase in rheobase.<ref name="Nodera" /> Both measurements have been shown to been shown to become normalized following [[intravenous immunoglobulin]] therapy.<ref name="Nodera" />
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| ===Chronic Inflammatory Demyelinating Polyneuropathy===
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| [[Chronic inflammatory demyelinating polyneuropathy|Chronic inflammatory demyelinating polyneuropathy (CIDP)]] is an [[immunological]] demyelinating [[polyneuropathy]].<ref name="Nodera" /><ref name= "Krarup, 2009" /> As a result of increased paranodal [[capacitance]] from demyelination, patients experience increased stimulation threshold, shorter strength-duration time constant, and increased rheobase.<ref name="Nodera" /><ref name= "Krarup, 2009" />
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| ==See also==
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| * [[Chronaxie]]
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| ==References==
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| {{reflist}}
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| [[Category:Neurology]]
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