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The neural interface can be unidirectional or bidirectional. It is the bridge between the biotic and abiotic systems where information from an engineered system is transferred to the neural system and/or information from the neural system is transferred to an engineered system. Historically, transfer of information to the neural system has been called “stimulation,” and transfer of information from the neural system has been called “recording.” These terms, however, are limiting as they only consider the action potential as the goal of the interface.
It is more correct, especially in the field of neuromodulation, to consider electrical input to the neural systems as manipulation of membrane potential. Information transferred to the neural system includes traditional neuronal excitation plus important modulation techniques of inhibition, membrane hyperpolarization, blocked action potential propagation, and modulation of information content. All of these behaviors are controlled by the application of energy to the system. The modes are distinguished based on how the energy is applied.
Similarly, it is more correct to consider the definition of the transfer of information from the neural system as sensing the flow of ions and transmitters caused by activity of the neural system. Electrically, the interface senses the potential fields resulting from the distribution of charged molecules and ions in the tissue. The more general definition would also include other transduction methods of converting ion motion and, hence, electrochemical energy to electrical signals.
In all cases, the interface is an integral element in the process of information transfer and the design of the interface determines the capabilities of such a transfer. There are many examples of electrodes for the neural interface that have been developed since the electrical interface to the nervous system was first described by Galvani in . As well, there have been several reviews of various interface technologies (e.g., ). The purpose of this chapter, however, is to provide the reader a broader perspective of basic design principles in the design of neural interfaces.
Rationale electrode design requires knowledge of the biologic environment within which the electrode will interface. The size, morphology, tissues, vasculature, and organization dictate many aspects of the neural interface design. Some of the most important neural science fundamentals to consider are:
Section Neural Science Fundamentals | Section Related Design Principles |
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The anatomy of the nervous system is discussed in greater detail in other chapters. Here, the important anatomical features having significant impact on the design of the interface and the considerations imposed by the anatomy are briefly highlighted. It is important to remember that neurons are only one of multiple cell types in the nervous system. Equally prevalent, and more numerous than the neurons, are the important glial cells. These consist of microglia and three general types of macroglia, including the oligodendrocytes, astrocytes, and Schwann cells. The microglia are the macrophages of the nervous system. The macroglia are the supporting cells that keep the neurons healthy and functioning. The glia cells are important when considering the response of the nervous system to a neural electrode. These cells are responsible for most of cytokine and chemokine signaling in response to the foreign material of the electrode and any injury caused by its implant and chronic presence. Understanding and controlling their response to the electrode can significantly alter the quality and chronic stability of the neural interface.
The nervous system is composed of several anatomical divisions ( Fig. 20.1 ). The first distinction is between the central nervous system (CNS) and the peripheral nervous system (PNS). The CNS consists of the spinal cord, medulla oblongata, pons, cerebellum, midbrain, diencephalon, and cerebral hemispheres (or telencephalon). The diencephalon includes the thalamus and the hypothalmus. The cerebral hemispheres include the amygdaloid, hippocampus, basal ganglia, and cerebral cortex. The PNS consists of the autonomic and somatic systems. The autonomic nervous system (ANS) consists of the sympathetic, parasympathetic, and enteric nervous systems. Both somatic and autonomic divisions of the PNS contain both motor (efferent) and sensory (afferent) components. The somatic components are related to voluntary motor control and sensory awareness. The autonomic components are related to the mostly subconscious, involuntarily controlled organs and physiology. The components of the CNS perform most of the integrative and processing functions of the nervous system. Generally, higher-order processing, like behavior and abstraction, occur at the more rostral divisions, such as the cerebral hemispheres, while more rudimentary processing, such as reflexes occurs more caudally, such as in the spinal cord.
Neural interfaces have been developed and studied extensively in the somatic PNS, cerebral cortex, basal ganglia, diencephalon, and spinal cord. The ANS is an increasingly important target for neuromodulation therapeutic alternatives to pharmacologic interventions for homeostasis and well-being. Interest and efforts continue to explore interfaces for all of the major divisions of the nervous system. Each of the systems has anatomic differences that guide development of neural interfaces.
The motor components of the somatic and autonomic PNS are the last link in the output chain that terminates on an end organ to produce an action or function. The sensory components of the somatic and most of the autonomic PNS are the first input to the processing circuitry of the CNS. Neural interfaces with the PNS interact nearly exclusively with an axon to modulate or sense its activity. The somatic PNS neural interfaces have been implemented in several clinical therapies, such as cardiac pacemakers, vagal nerve stimulators, functional electrical stimulation systems, and auditory prostheses. Note that several of the interfaces are also applied to the cranial nerves, which are very similar to peripheral nerves, but the cell bodies are in the cranium.
Interfaces with CNS are more complicated, however, in that the interface includes cell bodies, dendrites, and cellular circuits in addition to axons. The effects of applied electric fields and the signals recorded by electrodes are significantly more complicated, affecting many more cells and different cell structures. The spinal cord is part of the CNS and epidural spinal simulators for pain management accounts for a large component of the neuromodulation market. Modulation of CNS structures can directly alter circuit behavior, higher level function, and transfer of information between various centers in the CNS. Placement of the neural interface in the CNS is more critical than in the PNS.
There are several hierarchical levels to the size scales in the nervous system. When considering the electrode design, it is important to know the size of the target tissue for the electrode. The smallest scale typically considered in present-day electrodes is that of the axon and cell body. The size of a cell body is in the range of 4–50 μm. An axon, if considered as a long uniform, cylindrical tube, has a diameter ranging from about 0.2 μm for unmyelinated fibers to 20 μm for myelinated fibers. The length of an axon, however, is highly variable, depending on its location. In the CNS, axon length is only a few tens of microns to nearly 1 m. In the PNS, axons are generally long, ranging from several centimeters to nearly 1 m. The axon of a motor neuron, for example, extends from the ventral horn of the spinal cord to the muscle. Sensory axons extend from the point of sensation, such as the skin, to the dorsal root ganglion (DRG) and into the dorsal horn of the spinal cord. Cranial nerves extend from their nucleus in the CNS to the end organ. These can range from several centimeters such as the optic nerve (CN II), to nearly 1 m for components of the vagus nerve (CN X). Dendrites are microns in diameter and general only microns in length. Electrodes that target individual axons need to be about the size of an axon or 10s of microns in cross-sectional dimensions.
There are many important collections of cell bodies throughout the nervous system. These are called either nuclei or ganglia in the CNS and are called ganglia in the ANS. They are typically ellipsoidal or capsular in shape, are 10s of microns to 1 mm in cross section and can extend several millimeters. In the spinal cord, for example, the nuclei exist in the gray matter of the cord and will extend over several vertebral segments. This provides for multisegmental reflexes and coordination. Electrodes that target nuclei can be larger than those that target individual axons but should be smaller than the target nucleus.
Peripheral nerves range from centimeters up to 1 m in length. The cross-sectional dimensions of peripheral nerves range from about 0.2 to 20 mm. Electrodes that remain external to the peripheral nerves can be larger than those that interact directly with the axons or cells but at the potential expense of selectivity.
In the somatic PNS, motor neuron cell bodies are located in the ventral horn of the spinal cord. Sensory neuron cell bodies are located in the DRG, which is inside the vertebral column, immediately adjacent to the spinal cord. The dendrites of the motor somatic PNS are located in the gray matter of the spinal cord, typically in the ventral horn regions.
The axons in the PNS are organized into bundles, called fascicles, within long cables, called peripheral nerves ( Fig. 20.2 ). The peripheral nerve is composed of three basic tissues: the epineurium, perineurium, and endoneurium. The fascicles are defined by a perineurium membrane, which consists of multiple layers of cells connected by zona occludens or tight junctions ( ). Between each layer of cells, there is a sheet of collagen fibrils ( ). The perineurium is a strong membrane, providing mechanical, as well as, chemical protection to the axons. It is an extension of the meninges from the CNS ( ).
The space within the fascicles is the endoneurium, and it contains the axons. There is very little extracellular space as the axons are well packed into the endoneurium. Schwann cells within the endoneurium wrap the myelinated axons and enclose the unmyelinated fibers. The Schwann cells are important to maintaining the axon health and repair following injury. The endoneurium also includes fibroblasts, perineurial fibroblasts, and resident macrophages ( ). Between the axons there is a loose connective tissue of mesh-like and longitudinal collagen fibrils ( ).
The fascicles are embedded within the epineurium, a mesh of adipose and thick collagen fibrils, to form the common nerve trunk. The collagen fibrils are flat, tape-like in shape with a 10–20 μm width ( ). The collagen fibrils have a wavy course that allows for stretching of the peripheral nerve during normal motion. The ulnar nerve, for example, will stretch by up to 29% during elbow flexion ( ). Fascicle diameters range from about 100 μm to about 1 mm with most being about 0.5 mm ( ). There is a positive internal pressure of about 1–5 mmHg ( ) in the fascicle relative to the surrounding tissue, and fascicles generally have a circular cross section. The fascicle size remains constant across species, even as the overall nerve size changes ( ).
The size of the electrode necessary to safely and selectively activate specific nerves and structures are defined by the size of those structures. To interact with individual axons, then the electrode must be only a few microns in size. Electrodes that interact with fascicles will be on the order of 1 mm, and electrodes to interface with entire peripheral nerve will be several millimeters.
The pathway and consistency of grouping of axons over the entire length of the peripheral nerve are important ( Fig. 20.3 ). It is known that the number of fascicles change significantly over the length of the nerve with fascicles combining and separating all along the length ( ; Brill and Tyler, 2016). As well, several nerves will join and divide, forming several plexiform structures along the length of the nerve. Just proximal to a motor nerve branching from a main trunk, there is an identifiable fascicle or fascicles that contain only fibers to the specific muscle. There is evidence ( ) that as the axons course proximally through the plexiform structures of the nerve, however, axons tend to maintain a somatotopic organization ( ). Sensory information from a given region of the fingers will be collocated within the proximal nerves of the brachial plexus ( ). Similarly, motor fibers to the same muscle have been shown to be collocated in the proximal nerve sections ( ).
The ANS innervates and controls the visceral organs. The ANS is divided into the sympathetic, parasympathetic, and enteric systems. Unlike in the somatic PNS, where axons travel directly between the spinal cord and target organ, the ANS has ganglia in the periphery where preganglionic and postganglionic fibers connect. The neuron between the spinal cord and the ganglia is the preganglionic cell, and the one between the ganglion and the target tissue is the postganglionic cell, irrespective of the direction of information flow. The axons of the ANS and somatic PNS often travel in common nerve trunks. Another important difference is that efferent axons of the ANS innervate smooth muscle and tend to spread over the entire target organ in a mesh-like network, while efferent fibers from the somatic PNS innervate striated muscle at a few well-defined motor points. In the somatic PNS, it is possible to activate large portions of a skeletal muscle with a single electrode at the motor point on the muscle. Since no single motor point exists for the ANS organs, it is difficult to activate the entire organ with a single electrode at the organ.
The sympathetic nervous system (SNS) arises from the T1 to L3 spinal nerves. It is characterized by a chain of ganglia, called the sympathetic chain, that is external, bilateral, and immediately adjacent to the vertebral bodies ( Fig. 20.4 ). Fibers from the dorsal and ventral roots communicate to the sympathetic chain via the gray and white ramus communicans, which are located just distal to the division of the spinal nerve into the ventral and dorsal rami. Fibers extend along the sympathetic trunk that connects the ganglia of the sympathetic chain. The postganglionic fibers form multiple plexi between the ganglia and innervations of the target organ. An electrode can possibly interact with the sympathetic system independently of the somatic system through the sympathetic chain and would use similar design principles as for peripheral nerves.
The parasympathetic nervous system arises in CN III, VII, IX, and X and the S2, S3, and S4 spinal nerves. CN X, also known as the vagus nerve, carries nearly 70% of the parasympathetic fibers. The ganglia of the parasympathetic nervous system are located directly at the target organ. The preganglionic fibers travel in well-defined and accessible nerves to the target organ and tend to have few plexi during their course compared with the SNS. The postganglionic fibers form a diffuse mesh within the organ.
The CNS is composed of six basic divisions ( Fig. 20.1 ). Starting most caudal and progressing rostrally, they include the spinal cord, medulla oblongata, pons, midbrain, diencephalon, and cerebral hemispheres. The divisions, in the order presented, correspond to a progression of higher levels of processing. The diencephalon consists of the thalamus and hypothalamus, which are central relay and early processing stations for incoming sensory information to the CNS. The cerebral hemispheres are composed of the amygdaloid, hippocampus, basal ganglia, and cerebral cortex.
Related to the discussion of electrode design, there are a few common anatomical features throughout the CNS to consider. First, the CNS is surrounded by three protective tissue layers that comprise the meninges. These are the outer, mechanically tough dura mater; the vessel rich arachnoid; and the thin pia mater immediately adjacent to the neural tissue. Between the arachnoid and pia mater is a subarachnoid space.
The structures of the CNS are divided by arrangements of axons and cell bodies but not separated by significant tissue structures. The cerebral cortex is the outermost 2–4 mm of the cerebral hemispheres. It consists of six distinct layers, numbered from 1 at the pial surface down to 6 ( Fig. 20.5 ). Generally, the axons and connections are arranged in columnar fashion. Layer 1 does not contain many neuron bodies but mostly axons that transverse laterally to synapse on apical dendrites of deeper cells in surrounding cortical regions and glial cells. Layers 2 and 3 contain pyramidal cells providing the output to other cortical regions. Layer 4 has many nonpyramidal cells and receives most of the input from the thalamus. Layer 5 has mostly very large pyramidal cells and is the main output layer with projections to other cortical and subcortical brain regions including the basal ganglia, brainstem, and spinal cord. Finally, layer 6 contains a heterogeneous population of cells with mostly projecting back to the thalamus. The tissue below layer 6 is largely composed of white matter and axons communicating between the cortex and other neural structures.
Below the cortex, there is a large “highway” of axons traveling between various nuclei and tracts, which are the other significant organizational elements of the CNS. A nucleus is a collection of cell bodies where information is processed. Fiber tracts are axonal bundles that carrying information to and from the nuclei within the CNS, the spinal cord, and out to the PNS. The reader is encouraged to review other sources for information about specific nuclei and tracts. The important aspect is that the nuclei and tracts exist at many different depths and locations throughout the CNS, requiring longer electrodes that must often penetrate through neural tissue to reach a nucleus. The boundaries of the different anatomical regions are often not well defined and tracts will run in close proximity to the nuclei. Stimulation and recording from specific nuclei or tracts require careful electrode design and placement. Nuclei are generally in the range of a few millimeters in size and often have ellipsoidal shapes, though they do vary between nuclei.
The fiber tracts can be considered cables that are 10s to 100s of microns in diameter and millimeters long when communicating between nuclei in the brain. The tracts usually have nonlinear paths through the brain, traveling in and around the different nuclei. The descending tracts, such as the corticospinal tract, are much longer and can be up to 1 m in length. These tracts are usually fairly linear, resembling a peripheral nerve buried in the CNS, and have generally known locations within the CNS.
The spinal cord travels down the spine within the central canal in the vertebra. The vertebra creates a bony case that surrounds the spinal cord and sets a defined space available for electrodes. The spinal column is divided into cervical, thoracic, lumbar, and sacral regions. The spinal cord is composed of a butterfly-shaped central region of gray matter surrounded by white matter ( Fig. 20.6 ). The gray matter contains cell bodies and the white matter contains myelinated axons. The axons of the white matter carry information to and from the brain and between the spinal levels. The white matter is divided into the dorsal column, lateral column, and ventral column and a ventral commissure. Generally, somatic sensory information travels in the dorsal column, motor, sensory, and autonomic information in the lateral column, and pain, thermal, and axial muscle control information travels in the ventral column. Information is transferred between the two sides of the spinal cord across the ventral commissure.
The gray matter is divided into 10 layers or lamina starting with lamina I on the dorsal aspect and increasing ventrally through lamina IX on the ventral aspect. Lamina X is in the center, around the central canal. The laminae contain collections of cell bodies that form nuclei for processing and integration of descending pathways and input information. The dorsal laminae generally receive sensory input from peripheral sensors and contain the connection to between peripheral sensors and ascending/descending tracts and/or local reflexive circuits. The ventral laminae are generally motor and contain the cell bodies of the lower motor neurons within motor nuclei of the ventral horn.
The axons that form the peripheral nerves enter and exit the dorsal and ventral horns in a series of rootlets along the length of the spinal cord. The rootlets within each of the vertebra join to form the dorsal and ventral spinal roots which then combine to form the common spinal root. There is one spinal root on each side that exits the vertebra through a foramen. There are 8 cervical, 12 thoracic, 5 lumbar, and 5 sacral nerves.
The spinal cord is surrounded by the same three meningeal layers as the brain, the dura mater, arachnoid, and pia matter. The rootlets and spinal roots are only accessible within the meninges. The meninges are continuous with and eventually form the epineurium and perineurium of the peripheral nerve.
The important anatomical structures and organization that determine the shape, size, placement, and potential complexity of the interface with the electrode have been reviewed very briefly. These anatomical characteristics also dictate the surgical techniques, invasiveness, and tools required to access the neurons and implant the interface. In addition to the physical characteristics of the electrode, functional anatomy dictates the types of interfaces and the potential modulation and information possible at each implant location. Typically, electrodes on the periphery are easiest to implant. They will control end organs directly or effect the sensory input to the first stages of information processing, such as reflex circuits. Electrodes in the spinal cord can interact with fiber tracts for multilevel influence and some of the fundamental circuits and pattern generators for motor coordination. Electrodes in the brainstem and diencephalon interact with functional systems, such as respiration, autonomic regulation, and overall motion coordination. Electrodes in the cortex interact with the highest levels of consciousness. The first approach to any electrode development is a careful determination of the tradeoffs between physical and surgical limitations and risks of location, the information or function available at that location, and the electrode characteristics required to interact effectively with the tissue.
The vessels that perfuse peripheral nerves typically run along the nerves and consist of extrinsic and intrinsic vessels ( Fig. 20.7 ). Larger intrinsic vessels run in the epineurium and communicate with the extrinsic vessels via collateral supplies. This arrangement allows for several centimeters ( ), up to 40 times the nerve diameter ( ), of the nerve can be exposed and freed from surrounding tissue without significant deficit in perfusion, as long as the extrinsic vascular supply is left intact.
To reach the axons, the vessels cross obliquely through the perineurium to transverse between the epineurium and endoneurium. As they pass through the perineurium, they tend to reduce in size and take an ellipsoidal cross-sectional shape ( ). Within the endoneurium, the blood flow is dependent on the intrafascicular pressure. Up to 20 mmHg, the capillary and arteriolar blood flow is unaffected and there is only a small decrease in venular flow. As pressure rises above 20 mmHg, the capillary and arteriolar flow begins to decrease. At about 60 mmHg, the venular flow is stopped. All blood flow is stopped at approximately 70 mmHg ( ). These pressures correspond to neural damage in compression neuropathies. In the carpal tunnel, for example, the normal resting pressure is 2.5 mmHg and the maximum pressure at full wrist extension and flexion is approximately 30 mmHg. In carpal tunnel syndrome, however, the resting and maximum pressures increase to 32 mmHg and approximately 100 mmHg, respectively. Even at rest, the pressure is high enough to impede blood flow, leading to painful neuropathies ( ). In addition to blood flow, axonal transport is affected by pressure. Up to 20 mmHg, there is no observed decrease in transport, but above 20 mmHg, there is a significant degradation of transport ( ). Therefore, 20 mmHg is an important pressure guideline for electrode development and 60 mmHg is a critical value as many of the neural processes in the peripheral nerves are significantly degraded or stopped altogether above this value.
In addition to intraneural pressure, blood flow is affected by stretching of the nerve. As with pressure, venular flow is affected first at approximately 8% strain. Arteriolar and capillary flow are first affected at approximately 10% strain. Complete cessation of blood flow occurs at approximately 15% strain ( ).
The permeability of the vessels within the endoneurium is different than in the epineurium. Large molecules that can freely cross in and out of the vessels in the epineurium are unable to do so in the endoneurium. This greater selectivity of the endoneurial vessels controls the osmotic and molecular environment within the fascicles to maintain an environment favorable to the axon function ( ). The selective permeability in the peripheral nerves is referred to as the blood–nerve barrier (BNB) and is analogous to the blood–brain barrier (BBB) of the CNS.
The blood supply to the brain is provided by the internal carotid arteries and the vertebral arteries. These vessels join to form the circle of Willis from which the anterior cerebral, middle cerebral, posterior cerebral, superior cerebellar, posterior inferior cerebellar, anterior cerebellar, anterior spinal, posterior communicating, and basilar arteries arise to supply the diencephalon and telencephalon CNS regions. The major vessels then continually divided to form a dense mesh network throughout the CNS tissue ( ). In cortical tissue, the large vessels are in the superficial pial layers and then descend into the cortical tissue with finer division and denser structure ( Fig. 20.8 ). The vascular network contributes significantly to the dynamics of the cortical tissue during electrode insertion ( ), and it is very likely that any device inserted into the tissue will damage some of the vasculature.
As in the PNS, the vessels within the brain have a more selective permeability, preventing large molecules from crossing out of the vessels and into the neural tissue, forming the BBB ( ). During insertion of electrodes, it is likely that damage will occur to the web-like microvasculature. The vascular damage disrupts the BBB, allowing foreign molecules and proinflammatory cells to enter the neural tissue. This contributes to the inflammatory response ( ) discussed further elsewhere in this book.
The arterial supply to the spinal cord consists predominantly of three vessels that run longitudinally along the spinal cord ( Fig. 20.9 ). The anterior spinal artery runs along the midline of the anterior surface of the spinal cord with connections via the anterior segmental medullary arteries to the vertebral arteries in the cervical region, the posterior intercostal arteries in the thoracic region, the lumbar arteries in the lumbar region, and the sacral arteries in the sacral region. Blood is then distributed segmentally into the gray matter via the anterior sulcal arteries through the ventral median fissure. The ventral and lateral columns of the white matter are segmentally supplied by the anterior segmental medullary arteries through the pial arterial plexus. On the dorsal surface, there are two posterior spinal arteries that run the length of the cord and lateral of midline. These are supplied via the posterior segmental medullary arteries by the vertebral arteries in the cervical region, the posterior intercostal arteries in the thoracic region, the lumbar arteries in the lumbar region, and the sacral arteries in the sacral region. The posterior medullary arteries also supply the dorsal horn of the gray matter. The posterior spinal arteries supply the segmentally supply the dorsal column of the white matter. Similar to the arterial supply, but in mirrored arrangement, there are two to four anterior spinal vein and a central posterior spinal vein that run the length of the cord. These veins provide segmental connection to the spinal cord regions to complete the circulatory loop. As with the vasculature of the PNS, the spinal cord blood supply is mostly segmental with long connecting major vessels that allow exposure of large surfaces of the structure without ischemia. The electrodes, however, should avoid damage to these vessels .
Having considered the anatomical basics of electrode design, we next need to consider the electrical properties of neural tissues. These properties will determine how currents flow within the neural tissue and, ultimately, the distribution of electrical fields that are created or sensed by the electrode. Note that all current within the body is carried via ionic mechanisms. The conversion from electron to ion current occurs at the electrochemical interface with the electrode. This is discussed in other sections of this book. Here, tissue impedance is presented in terms of electrical properties ( Table 20.1 ).
Tissue | Conductivity (S/m) | References |
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Saline | 1.3–2.0 | |
Encapsulation | 0.2–0.5 | |
Perineurium | 0.002 | and |
Epineurium | 0.083 | |
Endoneurium | 0.083 transverse | and |
0.571 longitudinal | ||
Scalp | 0.43 | |
Skull | 0.015 | |
Dura mater | 0.030 | |
Brain | 0.12–0.48 | and |
Skin | 0.00001–0.001 |
The most resistive of all tissues is the skin. At 1 kHz, the resistance of a 1-cm 2 patch of skin is between 10 and 1000 kΩ ( ). This corresponds to a conductance of between 0.00001 and 0.0001 S/m ( ). The low conductance of the skin significantly attenuates and filters the signal, both spatially and temporally. Consequently, electrodes outside the skin require the most energy to directly excite neural tissue with electric fields, are not very selective in their stimulation, cannot record small signals, and have poor spatial resolution in recording neural signals, such as in electroencephalographic (EEG) recordings.
Electrodes placed inside the body will be encapsulated by a collagenous layer of tissue. The impedance of encapsulation tissue is dependent on the maturity and organization of the tissue. Mature, compact tissue is closer to a pure resistor, while loose, poorly form encapsulation has a significant capacitive component. The conductivity of a well-formed capsule is approximately 0.15 S/m. The impedance of encapsulation with loose connective tissue and macrophage infiltrations is frequency dependent, ranging from 0.22 to 0.51 S/m between 10 Hz and 1 kHz, respectively, and stable at 0.51 S/m between 1 and 100 kHz ( ). Note that these numbers are guidelines, but the values can vary with changes in electromagnetic field frequency and signal amplitude.
In peripheral nerves, the resistivities of the perineurium, epineurium, and endoneurium are most important. The conductivities of these tissue are not exactly known and are quite variable. The following numbers, however, give a range of expected values. The conductivity of the perineurium and epineurium is 0.002 and 0.083 S/m, respectively ( ). The endoneurium, however, is anisotropic with a conductivity of 0.083 S/m across the axons and 0.571 S/m along the fibers ( ). The relatively low conductivity of the perineurium has a significant influence on the field distribution in peripheral nerves. If the electrode is external to the perineurium, an applied field is significantly attenuated and typically more uniform within the fascicle that if the perineurium did not exist. This makes stimulation of small subpopulations within the fascicle difficult. In contrast, an electrode within the perineurium will be isolated from other fascicles and is able to selectively activate small axon populations within the fascicle. The perineurium and size of one fascicle will also influence the fields within surrounding fascicles ( ). When recording neural signals, the perineurium significantly attenuates the field produced by neurons, making single-unit field recording virtually impossible outside the fascicle.
In central tissues, the meninges have low conductivity; the dura, for example, is reported to be around 0.030 S/m. The conductivity of the skull is also fairly low at 0.015 S/m. These low conductivities affect the selectivity and sensitivity of recording, that is, EEG, and stimulation with electrodes on the scalp just as surface electrodes for the peripheral nerves. EEG recording, however, is possible as the brain is relatively large and close to the surface compared with peripheral nerves.
In general, tissue is a viscoelastic material. The different tissues have a wide range of differing moduli. The elastic modulus of neural tissue is in the range of 0.1–1.5 kPa ( ), which is similar to jelly. This includes the endoneurium in the PNS and the gray and white matters of the CNS. The specific modulus depends on contend and orientation of connective tissues; orientation of axons; and the composition of cells bodies and glia versus axons in the various neural structures.
The protective tissues of the perineurium in the PNS and meninges in the CNS are stiff compared with other tissues. The properties of the spinal dura mater provide a representation of the modulus values. The dura mater is composed of a very tough outer fibroelastic layer, an intermediate fibrous layer, and an inner cellular layer with interdigitated cells, little extracellular collagen, few tight junctions, and significant extracellular space ( ). In the lumbar spinal cord, the dura mater has an elastic modulus of 5–140 MPa, depending on the orientation in which it is measured ( ). The perineurium has been estimated to have a modulus between 120 kPa in the frog sciatic ( ) and 2–10 MPa ( ) in mammalian nerves.
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