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Extracellular electrical stimulation recruits axons in an order that is opposite to the normal sequence, inducing rapid fatigue

The recruitment order of motor units is the order in which different neural fiber types are activated under load. A motor unit is made up of a peripheral neuron and the muscle fibers on which it synapses. Large peripheral neurons typically innervate larger, fast-fatiguable muscle fibers. Smaller peripheral neurons typically innervate smaller, slow-fatiguable muscle fibers. Physiologically, small, slowly-fatiguing motor units are recruited first, followed by large, quickly fatiguing motor units ^[1]. This helps the body naturally delay neuromuscular fatigue and sustain muscle forces for as long as possible ^[2].

Under neural stimulation, the natural recruitment order of motor units is reversed. Neural stimulation applies extracellular electrical currents to the peripheral nerves in order to induce neural excitation that leads to muscle contraction. Neural stimulation of peripheral nerves has been used in people with spinal cord injury to restore function below the level of injury and for other neuromuscular disorders. Due to the shape of extracellular electric fields and the dynamics of nerve fiber activation, neural stimulation recruits large, fast-fatiguable motor units first. This leads to rapid fatigue that limits the performance of functional electrical stimulation systems. While the mechanisms of reversed recruitment order are well understood, research is still underway to circumvent this phenomenon and delay neuromuscular fatigue due to neural stimulation.

Background

The physiologic motor unit recruitment order was most famously elucidated by Henneman and colleagues in the 1960s. In a series of well known experiments performed on the feline soleus and gastrocnemius muscles, these researchers found that the number of muscle fibers a motor neuron innervated was proportional to that neuron's size. Small neurons innervate few muscle fibers compared to large neurons that innervate many fibers. Furthermore, they found that small amplitude external stimuli, in this case small stretches in the cat tricep muscle, resulted in small amounts of force generation. This indicated that low level stimuli results in small motor unit recruitment. The opposite was true with larger stimuli. Large stretches in the tricep muscle resulted in larger amounts of force generation, thus indicating the recruitment of larger motor units ^[1]. Based on these observations, the Henneman Size Principle was established. In short, this principle states that the natural recruitment order is from small to large motor units.

While this principle has been confirmed in many subsequent experiments and holds true for physiologic, intracellular stimulation, advancement in the use of extracellular stimulation for rehabilitation purposes has exposed an exception to this rule. Electrical stimulation of peripheral nerves was used clinically as early as 1961 by Liberson and colleagues. Liberson was able to electrically activate the peroneal nerve, which controls muscles responsible for plantarflexion and dorsiflexion about the ankle. By activating the peroneal nerve on the leg in the swing phase of walking, researchers were able to evoke dorsiflexion of the suspended foot. This enabled them to prevent foot drop in patients with hemiplegia, or paralysis that affects only one side of the body ^[3]. Since then, Functional Electric Stimulation (FES) has been used for a variety of rehabilitative and therapeutic purposes for people with spinal cord injury, stroke, multiple sclerosis, and other ailments that effect neuromuscular control ^[4].

Despite the initial and ongoing success of extracellular stimulation of peripheral nerves, a common limitation has been observed across research studies attempting to use this technology to create, control, and maintain muscle forces. That limitation is rapid muscle fatigue. Early studies using electrical stimulation reported that the maximum force output of the muscles being activated through the stimulated nerves declined much more quickly than expected ^[5] . To quantify this, one study published by B. Bigland-Ritchie directly compared electromyogram (EMG) and fatigue characteristics of human muscles contracted voluntarily to that of the same human muscles contracted through external stimulation. Researchers stimulated the nerve just enough to produce the same contractile force as the subject's maximum voluntary contraction (MVC). When the time course of the force output from the stimulated contraction was compared to the force output time course from the voluntary contraction, it was found that the muscle fatigued much more quickly under electrical stimulation. The MVC could be maintained voluntarily for significantly longer periods of time, indicating a clear difference in the way motor units were fatiguing physiologically versus under external control ^[6].

This observation remained largely unexplained until 1978, when a study by J.A. Stephens, R. Garnett, and R.P. Buller revealed the physiologic reason for increased fatigue from electrical stimulation. In their submission to Nature, they revealed findings that showed transcutaneous stimulation of an intact human muscle reverses the recruitment order compared with the recruitment order seen under voluntary contraction ^[7]. This means that when the muscle was stimulated through the subject's own volition, slowly fatiguing, smaller diameter fibers were found to fire first, followed by larger, fast-fatiguing fibers. The recruitment order was as predicted by Henneman's size principle. However, when the same muscle was then stimulated through electrodes placed on the surface of the skin, the larger neural fibers were the first to fire action potentials and evoke muscle contraction. This recruitment order was opposite of that predicted by the size principle. When the external stimulation was then taken away and the muscle was again contracted voluntarily, the original recruitment order returned. This discovery gave insight into why electrical stimulation induces rapid fatigue. Because fast-fatiguable fibers are activated immediately at the onset of stimulation, as opposed to only once needed as in normal circumstances, the force they are able to contribute is quickly used up and the overall muscle force that can be maintained declines rapidly. Therefore, the accelerated excitation of larger motor units through extracellular stimulation ultimately manifests in rapid fatigue ^[8].

Rapid fatigue can now be understood as resulting from the reversed recruitment order of motor units that occurs under extracellular electrical excitation. The reason that the recruitment order is switched in this way under electrical stimulation is the focus of the rest of this article.

Peripheral Nerve Anatomy

Before physiologic and extracellular activation dynamics may be evaluated, it is necessary to understand the anatomical layout of a peripheral nerve. A peripheral nerve is a nerve that lies outside of the central nervous system. Thus, it is not encased by bone. Peripheral nerves, such as the human sciatic nerve, can be tens of centimeters long depending on its target. If one were to transversely slice a peripheral nerve and observe its cross-section, several features would be readily apparent. First, the whole nerve itself is made up of hundreds of individual axons. Second, axons are arranged within the nerve into larger structures called fascicles, which typically contain axons responsible for innervating muscle fibers of the same effector or effectors with similar function or anatomical location. Fasicles can branch off of the peripheral nerve as they move distally along the nerve's length in order to allow axons to synapse on their target ^[9].

The whole nerve is surrounded by the epineurium, which enables nutrient exchange into the nerve fiber. Each individual fascicle is surrounded by the perineurium, which is a structure containing many more tight junctions. The closer arrangement of the perineurium forms the blood-nerve barrier and protects the axons within from outside pathogens. The space between axons within a fascicle is termed the endoneurium. Each axon within a peripheral nerve itself is surrounded by multiple Schwann cells. Schwann cells are a type of glial cell that provide a peripheral nerve with its myelin sheath, by wrapping around a section of the axon multiple times. Myelinated regions, or internodes, enable axons to transmit signals down their lengths more effectively, as current can "jump" from one unmyelinated region, or node, to another ^[9]. The length of an internode is proportional to the axon's diameter. Larger diameter axons have longer internodal regions, and thus have increased action potential propagation velocities. Smaller diameter axons have shorter internodal regions, and thus their typical action potential propagation speeds are lower ^[10]. The relative lengths of internodal regions becomes extremely important for reversed activation orders under extracellular stimulation.

Physiologic Stimulation

In a normally functioning nervous system, signals are transmitted from one neuron to another through synapses. When a presynaptic neuron has been stimulated and fires action potentials, it releases neurotransmitters into the synapse, or the space between neurons. Receptors on the postsynaptic cell can then bind these neurotransmitters and thus receive information from the cell before it. Depending on the type and amount of neurotransmitter released as well as several properties of the synapse, the postsynaptic cell can either experience depolarizing or hyperpolarizing postsynaptic potentials (PSPs). Depolarizing PSPs make the membrane potential of the neuron more positive, moving it towards its threshold value. They are thus also termed excitatory postsynaptic potentials, or EPSPs. Hyperpolarizing PSPs, on the other hand, are inhibitory and are also known as inhibitory postsynaptic potentials, or IPSPs. They make the membrane potential of the post-synaptic neuron more negative and move it further away from the threshold potential necessary to fire action potentials.

Henneman's Size Principle

Whether a neuron in the peripheral nervous system fires an action potential and continues to relay a signal through physiologic stimulation is dependent on the sum of the EPSPs and IPSPs at that neuron's soma. The neuron's dendrites, which function as the inputs of the neuron, receive information from surrounding neurons in the form of those post-synaptic potentials, and relay that information to the soma, or cell body. The soma acts as an integrator, summing together all of the incoming PSPs from its dendrites for an overall membrane potential effect. The overall membrane potential of the whole soma must be depolarized sufficiently before the soma will allow action potential initiation and propagation down its axon.

The amount of stimulus and time required to alter the membrane potential of the soma heavily depends on the input resistance of the neuron's dendrites. The voltage of a dendrite at the point of current injection, or where the presynaptic neuron interacts with the dendrite in question, can be described by the equation :

${\displaystyle V_{0}=Ir_{input}=I{\frac {1}{\pi }}{\sqrt {\frac {R_{i}}{g_{m}d^{3}}}},\quad {\text{(Equation 1)}}}$

As can be seen from the equation, the input resistance $r_{input}$ is inversely proportional to the dendrite diameter. Larger diameter dendrites on larger neurons thus have smaller voltage changes than smaller diameter dendrites on small neurons in response to the same injected current. This smaller voltage in the larger dendrites translates to less excitation of the soma, thus causing large diameter fibers to require more stimulus, and enabling smaller diameter fibers to fire first at lower stimulus thresholds. This is the physiologic explanation behind Henneman's size principle.

As determined by Henneman and colleagues, small neurons (with high input resistance) innervate a small, slowly fatiguing muscle fibers. Large neurons (with low input resistance) innervate large, fast fatiguing muscle fibers ^[1]. Because small neurons require less stimulus and less time to reach threshold, they fire first under physiologic stimulation. This results in activation of slowly fatiguing muscle fibers first, which are solely responsible for producing force until the demand is increased. Larger neurons that require more time and more stimulus do not reach threshold until neural input is increased, such as under heavier loads or once the slowly fatiguing fibers finally begin to fail.

Action Potential Propagation - The Cable Equation

Once an action potential is initiated in a neuron, it travels from the initial segment of the axon, called the axon hillock, down the length of the axon to the terminal branches. The movement of this action potential can be precisely modeled according to Cable Theory ^[11]. Based on the laws of cable theory, the membrane voltage at any point in time and at any location on an axon can be approximated using the passive cable equation:

${\displaystyle \lambda ^{2}{\frac {\partial ^{2}V_{m}(x,t)}{\partial x^{2}}}-\tau {\frac {\partial V_{m}(x,t)}{\partial t}}-V_{m}(x,t)-I_{inj}=0.\quad {\text{(Equation 2)}}}$

It should be noted that the $I_{inj}$ term here represents the overall current injected into the neuron. Physiologically, this current influx would come from the binding of neurotransmitters to receptors on the neuron in question, which can alter ion channel permeability and allow current to flow into or out of the cell. The rest of the constants in the equation, namely the time constant $\tau$ and length constant $\lambda$ , are parameters that depend on the neuron's geometry and composition. The equation is set equal to zero, as (aside from neurotransmitter input in the form of injected current), no extracellular factors influence the way in which the action potential propagates once it is initiated.

Extracellular Stimulation

Whereas physiologic stimulation and signal transmission occurs through neurotransmitters and synapses that affect dendritic and ultimately soma membrane potentials, extracellular stimulation bypasses these components and alters the membrane potentials of axons directly.

Modified Cable Equation

In the presence of extracellular stimulation, the cable equation that governs the change in membrane potential of the axon across time and space becomes:

${\displaystyle \lambda ^{2}{\frac {\partial ^{2}V_{m}(x,t)}{\partial x^{2}}}-\tau {\frac {\partial V_{m}(x,t)}{\partial t}}-V_{m}(x,t)={\frac {\partial ^{2}V_{e}(x,t)}{\partial x^{2}}}.\quad {\text{(Equation 3)}}}$

The first three terms in Equation 3 are identical to those in Equation 2. The $I_{inj}$ term is now missing, however, as extracellular stimulation is used in the absence of physiological signaling, as would be the case for participants with spinal cord injury or other neural disorders where impulses from the central nervous system (CNS) are not properly transmitted to the periphery. An additional term denoting the second derivative of the extracellular voltage profile produced by the stimulating electrode, ${\frac {\partial ^{2}V_{e}(x,t)}{\partial x^{2}}}$ , is now the sole activating function^[12]. Thus, the degree to which the voltage across an axon's membrane changes depends on how the extracellular voltage differs from one section of the axon to the next.

Recruitment Order Reversal

File:Kxg277VoltageProfile license.png

Figure 1: Extracellular voltage profile produced by a single simulating electrode, with its relative effects on small and large diameter axons.

A typical voltage profile produced from a monopolar stimulating electrode is shown as the black trace in Figure 1. Extracellular voltage is highest directly underneath the electrode. The extracellular voltage decays exponentially moving away from the electrode, producing the symmetric, concave curve shown. Therefore, any axon underneath such an electrode will have the highest voltage difference across the patch of membrane beneath the probe, creating an area of maximum excitation. A reduced voltage difference across the membrane is seen traveling down the length of the axon in either direction, following the voltage profile from the electrode.

Recall, as discussed in the above section, that the activation of a neuron through extracellular stimulation depends on the second derivative of the extracellular voltage. This means that the propagation of an action potential at one node of a myelinated axon depends on the difference between the extracellular voltage it experiences compared to the extracellular voltages experienced by the two nodes on either side of it. This difference is also known as the second spatial difference. A larger second spatial difference corresponds to stronger activation of that neuron ^[12].

The theoretical second spatial difference for a small diameter neuron versus that of a large diameter neuron is represented in Figure 1 by the blue and green lines respectively. From the illustration, it is obvious that the second spatial difference is much larger for the larger neuron than the smaller one. The reason for this increased difference calls back to the physiology of myelinated peripheral nerves. The myelin sheaths around neurons of differing sizes are not created equal. In fact, the length of each myelinated section (internode) varies proportionately with the axon's diameter, approximately according to the equation:

$L_{internode}=100D_{axon}$ ^[13]

An increased axon diameter results in an increased internodal length. This in turn results in a larger space between one node and its neighbor, and because of the exponential decay of the extracellular voltage profile, a significant increase in second spatial difference. The much higher activating function causes axons of larger diameters to fire action potentials at a lower stimulus threshold than smaller axons, effectively reversing the natural recruitement order of motor units under extracellular stimulation ^[12].

It should be noted that this analysis of activation using the second spatial difference is considered more intuitive, requires less computational time, and gives more accurate results than the analysis of activation presented by Rattay et al., which bases recruitment of an axon solely off of the amount of current that flows through each respective diameter as a function of the stimulation ^[14]. However, the second spatial difference approach may only hold for myelinated fibers, as the difference in myelinated region lengths is what drives the analysis. Rattay's approach gives explanation to the reversed recruitment order seen in unmyelinated fibers as well. Both approaches are valuable for understanding and evaluating the difference in recruitment order seen with extracellular stimulation, and since the motor nerves targeted by FES are typically myelinated, either may be used.

Research

Despite the recruitment order reversal and the associated early onset muscle fatigue that comes with the use of extracellular electrodes, they are still widely used in research involving neural stimulation. The main argument for using them over intracellualr electrodes, that would inject current directly into the cell and more closely mimic physiology, is that they are much less invasive. Intracellular electrodes would have to pierce the perineurium to gain access to the inside of a neural cell. This would result in a breach of the blood-nerve barrier and could easily result in infection or nerve damage. Furthermore, intracellular electrodes pose a great manufacturing challenge as they must be much smaller and require much more accuracy to properly place ^[15].

The increasing popularity of extracellular electrodes have sparked the need for more research to be done to circumvent the inherent reversed recruitment order and resulting fatigue in order to maximize their applications and benefits.

Modified Electrode Arrays

One approach to avoiding a reversed recruitment order involves complex electrode arrays. Instead of stimulating through a single electrode that produces an exponentially decaying voltage profile and preferentially activates large neural fibers, complex electrode arrays could produce voltage fields of various shapes and sizes and thus have a different effect on nearby axons ^[16] . A study published by Lertmanorat and Durand used computer simulations to model the extracellular voltage profiles of different electrode arrays. These arrays reshaped the typical voltage profile shown in Figure 1 to different degrees depending on the number of individual electrodes used and the spacing between them within the array.

Using these arrays and very low values of stimulation parameters, researchers found that, theoretically, physiologic recruitment order of peripheral nerves with extracellular stimulation may be returned using 5-7 electrodes within an array ^[17]. This is because stimulating through each of the electrodes within the array at once results in a voltage profile intricately shaped such that the second spatial difference is actually greater in the smaller fibers rather than the large fibers.

A major limitation of this approach is the number of electrical contacts required to stimulate one set of axons. Many stimulation systems require stimulation of more than one muscle fiber group to achieve a desired movement or posture. Dedicating multiple electrodes to preferentially activate each individual axon population would result in an overly large functional electrical stimulation system.

Advanced Stimulation Paradigms

Complex electrode arrays, while possible in theory, are very difficult to successfully implement. Another approach to delaying the rapid fatigue induced by extracellular stimulation, therefore, is to simply accept the reversed recruitment order, but use advanced stimulation paradigms that allow muscle fibers to intermittently recover from the induced fatigue. This has been made possible by the selectivity of composite flat-interface nerve cuff electrodes, or CFINEs ^[18].

File:Kxg277ASPs.png

Figure 2: Advanced Stimulation Paradigms make use of nerve cuff selectivity to circumvent fatigue. These paradigms allow muscle fibers to periodically rest and recover to offset the effects of reversed recruitment order with extracellular stimulation.

CFINEs are nerve cuffs that can be implanted around the epineurium of a nerve bundle. They surround the nerve with multiple individual electrodes, henceforth referred to as contacts. CFINEs have been used in the Advanced Platform Technology Center in the Louis Stokes Cleveland VA Hospital and in partnership with Case Western Reserve University to restore function in people with spinal cord injury and with upper or lower limb amputations. These electrodes differ from the electrode arrays referenced above because the contacts are spread further apart and are used independently of one another. Every contact is responsible for stimulating the axon population closest to it; multiple contacts are not used to target a single axon pool. Each contact can thus be simplified down to the single electrode example and produces the familiar extracellular voltage profile from Figure 1. While the configuration of the CFINE electrodes themselves cannot fix the reversed recruitment order, the selectivity that these nerve cuffs provide can allow researchers to cycle through independent motor unit pools that have agonistic effects ^[19].

Figure 2 illustrates two stimulation paradigms that could theoretically exploit this selectivity to delay fatigue. In Carousel Stimulation, one motor unit pool is stimulated at a time to produce a desired moment, while other motor unit pools are allowed to rest and recover as a way to offset the effects of initially recruiting fast-fatiguable muscle fibers. In Sum of Phase-Shifted Sinusoids (SOPS) stimulation, the stimulation parameters are continually modulated in order to produce a sinusoidal moment from each independent contact. When these sinusoidal moments are then phase-shifted to the correct degree, the total resulting moment is the sum of all of the individual sinusoids, which comes out to a constant value greater than that of any one contact alone. In this way, less stimulation can be used to achieve higher moment outputs. This, along with the varying degrees of stimulation each contact received, could enable rest and recovery similar to the Carousel paradigm.

Infrared Neuromodulation

A quickly emerging technology within the neural stimulation world is Infrared Optical Stimulation. Instead of applying electrical stimulation to neural fibers, optical stimulation is used to create a temperature change that has the ability to control temperature-gated ion channels on a neuron's membrane and lead to either excitation or neural block. Interestingly, this modality has been reported to effect axons in their normal, physiologic order, from small to large ^[20]. This technology could thus be another potential way to delay fatigue from neural stimulation, as it could lead to the excitation of slowly fatiguable fibers before fast fatiguable fibers, but certain limitations such as energy efficiency, selectivity, and safety factors must first be considered.

References

^ ^a ^b ^c Hennemann; Somjen; Carpenter (1965). "Functional significance of cell size in spinal motoneurons". Journal of Neurophysiology. 28: 560-580.
^ Conwit; Stashuk; Tracy; McHugh; Brown; Metter (1999). "The relationship of motor unit size, firing rate and force". Clinical Neurophysiology. 7: 1270-1275.
^ Liberson; Holmquest; Scot; Dow (1961). "Functional electrotherapy: stimulation of the peroneal nerve synchronized with the swing phase of the gait of hemiplegic patients". Arch Phys Med Rehabil. 42: 101-105.
^ Niloy; Peckham. "Peripheral nerve Stimulation for restoration of Motor Function". Journal of Clinical Neurophysiology. 14: 378-393.
^ Hayashibe, Mitsuhiro; Zhang, Win; Guiraud, David; Fatal, Charles (2011). "Evoked EMG-based torque predition under muscle fatigue in imlanted neural stimulation" (PDF). Journal of Neural Engineering. 8.
^ Bigland-Ritche; Jones; Hosking; Edwards (1978). "Central and peripheral fatigue in sustained maximum voluntary contractions of human quadriceps muscles" (PDF). Clinical Science and Molecular Medicine. 54: 609-614.
^ Stephens, J.A.; Garnett, R.; Buller, R.P. (1978). "Reversal of recruitment order of single motor units produced by cutaneous stimulation during voluntary muscle contraction in man". Nature. 272: 362–364.
^ Bickel; Gregory; Dean. "Motor unit recruitment during neuromuscular electrical stimulation: a critical appraisal". European Journal of Applied Physiology. 111: 2399-2402.
^ ^a ^b Romero-Ortega, M. (March 2015). Peripheral Nerves, Anatomy and Physiology of. In: Encyclopedia of Computational Neuroscience. New York, NY: Springer.
^ Waxman, S.G. (1980). "Determinants of conduction velocity in myelinated nerve fibers". Muscle & Nerve. 3 (2): 141-150. doi:10.1002/mus.880030207.
^ Rall, W. (2011). "Core Conductor Theory and Cable Properties of Neurons". Comprehensive Physiology: 39-97. doi:10.1002/cphy.cp010103.
^ ^a ^b ^c Peterson, EJ; Izad, O; Tyler, DJ (August 2011). "Predicting myelinated axon activation using spatial characteristics of the extracellular field". J. Neural Eng. 8 (4). doi:10.1088/1741-2560/8/4/046030.
^ Hursh, J.B. (1939). "Conduction velocity and diameter of nerve fibers". Am. J. Physiol. 127: 131-139.
^ Rattay, F. (1986). "Analysis of models for external stimulation of axons". IEEE Trans Biomed Eng. 33 (10): 947-7. doi:10.1109/TBME.1986.325670.
^ Breckenridge, L.J.; Wilson, R.J.A.; Connolly, P. (1995). "Advantages of using microfabricated extracellular electrodes for in vitro neuronal recording". J. Neuroscience Research. 42 (1): 266-276. doi:10.1002/jnr.490420215.
^ Petrofsky; Phillips (1981). "Impact of recruitment order on electrode design for neural prosthetics of skeletal muscle". American Journal of Physical Medicine. 60: 243-253.
^ Lertmanorat; Durand. "Extracellular voltage profile for reversing the recruitment order of peripheral nerve stimulation: a simulation study". Journal of neural Engineering.
^ Schiefer, MA; Polasek, KH; Triolo, RJ; Pinault, GCJ; Tyler, DJ (2010). "Selective stimulation of the human femoral nerve with a flat interface nerve electrode". J. Neural Engineering. 7 (2).
^ Fisher; Tyler; Triolo. "Optimization of selective stimulation patterns for multi-contact electrodes". Journal of NeuroEngineering and Rehabilitation.
^ Lothet, EH; Shaw, KM; Zhuo, J; Wang, YT; Gu, S; Stolz, DB; Jansen, ED; Horn, CC; Chiel, HJ; Jenkins, MW (2017). "Selective inhibition of small-diameter axons using infrared light". Scientific Reports. 7: 3275. doi:10.1038/s41598-017-03374-9.

External Links

The Nervous System

Action Potential Propogation Animation in Myelinated Axons

Action Potential Propogation Animation in Unmyelinated Axons

Cable Equation Derivation

FES FAQs

APT Center Research

[Hen-1] Hennemann; Somjen; Carpenter (1965). "Functional significance of cell size in spinal motoneurons". Journal of Neurophysiology. 28: 560-580.

[2] Conwit; Stashuk; Tracy; McHugh; Brown; Metter (1999). "The relationship of motor unit size, firing rate and force". Clinical Neurophysiology. 7: 1270-1275.

[3] Liberson; Holmquest; Scot; Dow (1961). "Functional electrotherapy: stimulation of the peroneal nerve synchronized with the swing phase of the gait of hemiplegic patients". Arch Phys Med Rehabil. 42: 101-105.

[4] Niloy; Peckham. "Peripheral nerve Stimulation for restoration of Motor Function". Journal of Clinical Neurophysiology. 14: 378-393.

[5] Hayashibe, Mitsuhiro; Zhang, Win; Guiraud, David; Fatal, Charles (2011). "Evoked EMG-based torque predition under muscle fatigue in imlanted neural stimulation" (PDF). Journal of Neural Engineering. 8.

[6] Bigland-Ritche; Jones; Hosking; Edwards (1978). "Central and peripheral fatigue in sustained maximum voluntary contractions of human quadriceps muscles" (PDF). Clinical Science and Molecular Medicine. 54: 609-614.

[7] Stephens, J.A.; Garnett, R.; Buller, R.P. (1978). "Reversal of recruitment order of single motor units produced by cutaneous stimulation during voluntary muscle contraction in man". Nature. 272: 362–364.

[8] Bickel; Gregory; Dean. "Motor unit recruitment during neuromuscular electrical stimulation: a critical appraisal". European Journal of Applied Physiology. 111: 2399-2402.

[phys-9] Romero-Ortega, M. (March 2015). Peripheral Nerves, Anatomy and Physiology of. In: Encyclopedia of Computational Neuroscience. New York, NY: Springer.

[10] Waxman, S.G. (1980). "Determinants of conduction velocity in myelinated nerve fibers". Muscle & Nerve. 3 (2): 141-150. doi:10.1002/mus.880030207.

[11] Rall, W. (2011). "Core Conductor Theory and Cable Properties of Neurons". Comprehensive Physiology: 39-97. doi:10.1002/cphy.cp010103.

[Tyler-12] Peterson, EJ; Izad, O; Tyler, DJ (August 2011). "Predicting myelinated axon activation using spatial characteristics of the extracellular field". J. Neural Eng. 8 (4). doi:10.1088/1741-2560/8/4/046030.

[13] Hursh, J.B. (1939). "Conduction velocity and diameter of nerve fibers". Am. J. Physiol. 127: 131-139.

[14] Rattay, F. (1986). "Analysis of models for external stimulation of axons". IEEE Trans Biomed Eng. 33 (10): 947-7. doi:10.1109/TBME.1986.325670.

[15] Breckenridge, L.J.; Wilson, R.J.A.; Connolly, P. (1995). "Advantages of using microfabricated extracellular electrodes for in vitro neuronal recording". J. Neuroscience Research. 42 (1): 266-276. doi:10.1002/jnr.490420215.

[16] Petrofsky; Phillips (1981). "Impact of recruitment order on electrode design for neural prosthetics of skeletal muscle". American Journal of Physical Medicine. 60: 243-253.

[17] Lertmanorat; Durand. "Extracellular voltage profile for reversing the recruitment order of peripheral nerve stimulation: a simulation study". Journal of neural Engineering.

[18] Schiefer, MA; Polasek, KH; Triolo, RJ; Pinault, GCJ; Tyler, DJ (2010). "Selective stimulation of the human femoral nerve with a flat interface nerve electrode". J. Neural Engineering. 7 (2).

[Triolo-19] Fisher; Tyler; Triolo. "Optimization of selective stimulation patterns for multi-contact electrodes". Journal of NeuroEngineering and Rehabilitation.

[20] Lothet, EH; Shaw, KM; Zhuo, J; Wang, YT; Gu, S; Stolz, DB; Jansen, ED; Horn, CC; Chiel, HJ; Jenkins, MW (2017). "Selective inhibition of small-diameter axons using infrared light". Scientific Reports. 7: 3275. doi:10.1038/s41598-017-03374-9.

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