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# (p. 386) Physics of Ultrasound and Nerve Stimulation

Physics of Ultrasound and Nerve Stimulation
Chapter:
Physics of Ultrasound and Nerve Stimulation
DOI:
10.1093/med/9780190856649.003.0029
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date: 22 October 2021

## 1. Ultrasonography

Ultrasound guidance has become the principal tool for the placement of peripheral nerve blocks since the beginning of this century. The evolution of point-of-care ultrasound imaging systems has made these systems more affordable, easy to use, and ubiquitous in the clinical environment. In the US military, point-of-care ultrasound systems are organic to role 2 and above levels of care, and new handheld devices are finding their way to the most austere areas of medical care.

As with any device or instrument, an understanding of the fundamentals of how ultrasound systems work and how they can be optimized affords the operator the greatest likelihood of safe, efficient, and successful placement of a needle adjacent to the target of interest.

## 2. Physics of Ultrasound

### 2.1. Properties of sound

Sound is a form of oscillating mechanical energy transmitted through a medium by the compression (condensation) and expansion (rarefication) of particles of matter. Ultrasound is emitted at frequencies above the threshold of human hearing (>20 kHz). The frequencies used for medical ultrasound imaging range between 1 MHz and 20 MHz. The wavelength ( λ‎) of a sound wave is the quotient of the speed of sound (v) and frequency (f).

$Display mathematics$

The speed of sound (v) is defined as the square root of the quotient of elasticity (or bulk modulus, B) and density (ρ‎).

$Display mathematics$

It is thus related to the characteristics of the conductive media and unrelated to frequency or amplitude. Harder materials (greater bulk modulus) conduct sound at greater velocity. However, in practice the speed of sound in solid is not exactly described by the equation above as it is also related to the geometry of the substance and the interactions of longitudinal and transverse waves.

Acoustic impedance (Z) is the resistance of a substance to conduct sound and is defined as the product of the velocity (v) of sound in and density (ρ‎) of a substance.

$Display mathematics$

Air and lung have low acoustic impedance, while bone and metal have high acoustic impedance. The difference between the acoustic impedance of 2 substances dictates how much sound energy is transmitted or reflected at their interface. Air-tissue and tissue-bone interfaces reflect nearly all the incident sound wave. Table 29.1 lists the velocity of sound and acoustic impedance of several biologic and man-made materials.

Table 29.1: Speed of sound and acoustic impedance in various media.

Substance

Speed of Sound (m / s)

Acoustic Impedance (g / [cm2∙ s])

Water (20°C)

1480

1.48 × 105

Blood

1570

1.61 × 105

Bone

3500

7.80 × 105

Fat

1450

1.38 × 105

Liver

1550

1.65 × 105

Muscle

1580

1.70 × 105

Polythene

2000

1.84 × 105

Air

330

0.0004 × 105

Soft tissue (average)

1540

1.63 × 105

Aluminum

6320

17.1 × 105

Steel (434)

5850

45.63 × 105

Adapted from Allan, P. (2006). Clinical Doppler ultrasound. Oxford: Churchill Livingstone/Elsevier.

### 2.2. Piezoelectric effect

Piezoelectricity is the fundamental principle driving the operation of ultrasound transducers. The prefix piezo is derived from the Greek “to compress,” and refers to the properties of some crystals to emit an electric impulse when deformed. This piezoelectric effect has 2 components: direct piezoelectric effect, which is the ability of a crystalline structure to emit an electric impulse following deformation, and the reverse piezoelectric effect, where the deformation of a crystalline structure occurs with the input of electrical energy to the material.

### 2.3. Attenuation, power, and intensity

Attenuation is the loss of sound energy within a medium. This lost energy represents information that cannot be processed or used in the imaging process. Such losses can be from absorption of the energy (conversion to heat) by the material, reflection and scattering as the sound wave encounters interfaces within the substance, and transmission through the medium (Figure 29.1). The coefficient of attenuation (ac) is the attenuation that occurs through each centimeter of a substance expressed as decibels per centimeter (dB/cm); as the attenuation coefficient and the length the sound wave travels through the substance increase, so will attenuation. For soft tissues, the attenuation coefficient is between 0.3 and 0.7 dB/cm. The most significant source of attenuation is through absorption of sound energy by a substance.

Figure 29.1 Causes of ultrasound dispersion in a medium.

Attenuation is also related to the frequency of the sound wave. As frequency of the wave increases, attenuation increases. The practical result is that as the frequency gets higher, more of the sound energy is lost to the tissue, diminishing the tissue penetration at a given amplitude.

Adjustments to both the power and the intensity of a sound wave can be used to overcome attenuation losses within a substance, providing more information for image processing. Power (P) is the rate at which energy is being delivered to a system described as units of energy over time and expressed as watts (W).

Intensity is the rate at which energy is delivered over a given area. For a point energy source, intensity (I) is expressed as:

$Display mathematics$

Thus, as a sound wave travels through a substance, the intensity decreases with the square of the distance from the source (r) (Figure 29.2). Increasing power will increase the intensity of the sound wave at a given distance from the source; however, this is at the price of a greater amount of heat imparted to the tissue through attenuation.

Figure 29.2 Power versus intensity. Power (P) is the amount of energy applied to a substance per unit time and is constant as the wave travels through the medium. Intensity (I) is the amount of energy delivered per unit area (A) and decreases with the square of the radius (r).

### 2.4. Frequency, resolution, and penetration

As was touched upon earlier, the attenuation through a medium (in dB) is related to frequency:

$Display mathematics$

where f is frequency and L is the depth traveled through the substance. Thus, lower frequency sound energy has lower attenuation and therefore better penetration into a medium. This has implications with regard to transducer selection; over a given power range, the lower the frequency, the greater the penetration of the sound wave into a tissue, allowing the imaging of deeper structures. Table 29.2 provides average tissue penetration (assuming an average soft tissue attenuation coefficient of 0.5 dB/cm) and attenuation relative to transducer frequency.

Table 29.2: Penetration and attenuation of sound at different frequencies.

Frequency (MHz)

Penetration

(cm)

Attenuation (dB)

15.0

4

7.5

10.0

6

5

7.5

8

3.8

5.0

12

2.5

3.5

17

1.8

2.0

30

1.0

Adapted from Kremkau, F., & Forsberg, F. (2016). Sonography: principles and instruments. St. Louis, MO: Elsevier.

However, with the greater penetration that comes with lower frequencies, there is a loss of resolution for objects within the tissue being imaged. Lateral resolution (LR) is the minimum distance 2 echogenic structures must be separated to be imaged as 2 distinct echo returns. It is directly related to the beam width (wb). Thus a 15 MHz wave has a lateral resolution of 0.1 mm while a 2 MHz wave has a lateral resolution of 0.8 mm. Axial resolution determines the minimum depth 2 echogenic structures must be separated to be resolved as discrete objects. Like lateral resolution, it is related to wavelength but also includes the spatial pulse length. Spatial pulse length (SPL) is the size of the pulse measured in millimeters as a factor of wave cycles:

$Display mathematics$

Where n is the number of cycles and λ‎ is wavelength. Axial resolution relates to frequency through the following equation (in mm):

$Display mathematics$

Most point-of-care ultrasounds emit a 2- to 3-cycle pulse; thus a 2 MHz transducer will have an axial resolution of 1.2 mm, and a 15 MHz transducer will have a resolution of 0.2 mm.

### 2.5. Reflection, refraction, and transmission

In the ultrasound transducer, the piezoelectric crystal array acts as both the emitter and the detector of ultrasound waves; as a result, only the energy from the echo return that reaches the probe can be processed for imaging. The strength of the ultrasound wave return depends on the nature of the reflective surface and the amount of energy lost to the tissue through attenuation.

Reflected waves are the echoes generated by the tissue; these are directed toward the transducer (perpendicular incidence), or at angles other than perpendicular to the incident wave (oblique incidence). The greater the component of perpendicular incidence, the better the quality of the image; thus optimal resolution of in-plane objects such as needles occurs at incident angles between 90° and 45° to the face of the object. Beyond 45° most of the ultrasound energy is reflected away from the probe face and is lost. Along a smooth echogenic boundary such as fascial sheaths, the diaphragm, walls of major vessels, and block needles, the reflected waves travel parallel to one another (Figure 29.3a) in a process called specular reflection. Irregular boundaries such as pleura and visceral organs, incident waves are reflected at variable angles, creating scatter (Figure 29.3b). This scatter directs energy away from the transducer, reducing image quality. This scattering may also result in signal noise that creates a hazy appearance to the structure and tissue beyond it known as backscatter.

Figure 29.3 Specular reflection (a) and scatter (b).

Transmission is the incident wave energy that passes into and through a media. Refraction is the change in the path taken by the sound wave when transiting a boundary between 2 dissimilar substances (see Figure 29.1). If the propagation speed of the deeper medium is higher than the superficial medium, then the transmitted wave will refract at an angle greater than the incident wave at the interface. Refraction may impact on image quality if the change in direction results in reflection of the transmitted wave obliquely to the incident wave.

### 2.6. Doppler ultrasound

The Doppler effect describes the change in frequency of a wave caused by motion of the reflector or emitter. The difference in the received (fR) versus emitted frequency (fO) is called the Doppler shift (fD) and is expressed using the following equation, where v is the velocity of the reflected wave and c is the speed of sound through the media:

$Display mathematics$

As the reflector moves toward the source, the received echo will increase in frequency, and then as the reflector moves away from the source, the frequency of the received wave will decrease.

The Doppler angle (θ‎ ) impacts on the degree of Doppler shift observed for a given emitter and reflector. The Doppler shift (fD) is related to the cosine of Doppler angle by the following equation, where v is the velocity of the reflected wave, c is the speed of sound in substance, and fO is the emitted frequency:

$Display mathematics$

Thus, the ideal Doppler angle for maximum detection of the flow of a substance (maximum Doppler shift) would be 0° or parallel to the direction of flow. At 90° the Doppler shift would be 0; thus placement of a transducer should be 60° or less to the direction of flow for best assessment of fluid flow. However, at angles less than 30° the ultrasound wave is reflected almost completely at the vessel wall-blood interface, preventing detection of blood flow.

By convention, color Doppler modes display the relative velocities of blood flow using a color scale, with blue hues indicating a negative Doppler shift (blood moving away) and red hues indicating a positive Doppler shift (blood moving toward) from the receiver. This can be remembered using the mnemonic BART (Blue Away, Red Toward). The numeric portion of the scale indicates the maximum velocity range that can be displayed.

## 3. The Ultrasound Machine

Point-of-care ultrasound machines are computerized instruments consisting of a transducer, pulsed beam generator, signal processor, and display. The transducer emits and detects the ultrasound energy used in tissue imaging. The pulsed beam generator drives the transducer, times the pulse and receive phases, sets the wave frequency, amplifies the return signal, and digitizes the data for the signal processor. The signal processor filters and analyzes the data from the pulse generator and then creates and stores the image for display. The display presents the processed information in a format usable by the ultrasound operator.

### 3.1. Transducers

The transducer both emits ultrasound waves and detects their echo returns using an array of piezoelectric crystals. Modern devices use synthetic lead zirconate titanate ceramics. These composite materials are imparted with specific piezoelectric properties during manufacture that determine its resonant frequency. An assembly of these piezo-composites is arranged in a linear or curved array of varying frequencies that dictate the resolution and penetration properties of the probe.

The ultrasound beam can be focused, allowing the sound energy to be concentrated over a narrow region. This results in a reduction in the beam width, improving lateral resolution. This can be accomplished through curvature of the array, placement of an acoustic lens, or electronically through phased arrays.

Coupling medium (ultrasound gel) is used as an interface between the probe and the skin. This layer fills gaps between the skin and the probe, eliminating air/probe and air/skin interfaces. The low acoustic impedance of air would result in total reflection of the ultrasound wave at the air/skin interface.

### 3.2. Pulsed beam generator

The pulsed beam generator is responsible for creating the specific ultrasound wave emitted by the transducer. Most manipulations performed by the operator to optimize the ultrasound image are effected through adjustments to the behavior of the pulsed beam generator. This includes gain, phased arrays, and compound spatial imaging.

### 3.3. Image formation

The ultrasound machine creates an image by correlating the depth of an echo return with the time taken for the signal to reach the detector following the pulse:

$Display mathematics$

where c is the propagation speed of sound through a substance and t is the pulse-return transit time. A pixel corresponding to a reflected wave is illuminated on a display, corresponding to the calculated depth of the reflected wave. Though this process is fundamental to the function of the ultrasound machine, it is also a source of error. The processing software must make specific assumptions with regard to the behavior of sound within the medium and the reflected waves:

1. 1. Sound waves propagate linearly from the source.

2. 2. The amplitude of the echo is directly related to the echogenic properties of the reflector.

3. 3. Echoes represent reflections from objects in the path of the wave.

4. 4. The distance to the imaged target correlates to the round-trip travel time of the pulse.

5. 5. The propagation speed is uniform through the tissue.

When any of these assumptions are inaccurate, improper representations of tissues or structures occur. These artifacts may confuse or mislead the operator if they are not recognized. One of the more common sources of artifact relates to the uniform propagation velocity of sound through tissues: most manufacturers use a soft tissue average of 1540 m/s as the propagation speed; however, tissues often contain a mixture of adipose, muscle, and connective tissues. Examples of specific artifacts will be detailed later in the chapter.

### 3.4. Gain and time gain compensation

Amplification of a signal is a form of processing that increases the amplitude of the input waveform without altering the frequency or pulse length. The signal processor receives the amplified signal and filters background noise from the data. In effect, waves below a certain amplitude are filtered from the processed image to provide the necessary contrast to identify structures. When significant attenuation occurs, the return echo may be weak and the default amplification fails to meet the threshold for display of the data. Gain on the ultrasound machine is the ratio of voltage of the amplified output wave to the original input wave and is expressed in decibels (dB). Gain adjustments increase the amplification of the input signal, bringing more of the waveform above the filter threshold of the signal processor, thereby improving resolution. This, however, occurs at the price of increased displayed noise or speckling, creating a grainy image and loss of contrast.

Time gain compensation takes advantage of the increased attenuation that occurs the deeper an ultrasound wave travels in a substance. It allows for progressively increased amplification of reflections from deeper structures. This is achieved by boosting the amplification of signals that arrive to the transducer later during the detection phase of the transmit/receive cycle. Manufacturers accomplish this by dividing the image into depth zones that correspond to return signals with greater transit times. User adjustment of these zones is accomplished through sliders, knobs, or keys, depending on the number of regions programmed by the instrument manufacturer (Figure 29.4).

Figure 29.4 Examples of time gain compensation adjustment buttons and sliders.

### 3.5. Spatial compound imaging

Phased array transducers are capable of selectively triggering individual piezoelectric elements. The array can be fired simultaneously, creating a beam wave front parallel to the transducer face, or can be fired sequentially with a small (<1 μ‎s) delay between each element, creating a directed wave front that propagates at an angle tangential to the array. These directed tangential waves image the tissue at differing angles, allowing visualization of structures that would otherwise be obscured by overlying objects. Compound spatial imaging combines a sequence of angled wave fronts to create a single image that can impart improved resolution and dimensionality to the target tissues (Figures 29.5a and 29.5b).

Figure 29.5 Compound spatial imaging. When the crystal array fires simultaneously (a), a wave front is generated that is parallel to the face of the probe. When the timing of the firing of the individual crystals of the array is offset (b), a wave tangential to the face of the probe is generated.

### 3.6. Exam modes and user-adjustable parameters

Most point-of-care ultrasound systems have preprogrammed examination modes designed to optimize the image to suit the specific procedure to be performed. These modes have preset gain adjustments, transducer frequency ranges, focal points, and postprocessing algorithms that are applied to the input signals to create the desired effects. For example, modes designed for nerve exams and block placement are designed to improve the contrast at interfaces of similar acoustic impedance and maximize resolution, while modes used for vascular access are designed to highlight vascular wall/blood interfaces with decreased affinity for small structures. Selecting the proper exam mode for the desired tissue and procedure is a significant determinant for the ease and precision of image acquisition.

Some manufacturers allow user selection of electronic focal points. Electronic focusing takes advantage of phased array systems to create an ultrasound wave front that converges to concentration point in much the same way a physical acoustic lens focuses the sound energy. However, unlike a fixed acoustic lens, the wave generated by the phased array can be adjusted so that the depth of the convergence point can be changed. Through the use of submenus or hot keys, operators can adjust the depth of the convergence point on these machines to maximize the resolution of specific structures.

### 3.7. Contrast agents

Differentiation of tissues with comparable echogenic properties, such as nerves within adipose containing connective tissue or highly vascularized organs, is difficult as the sound will tend to propagate through the various tissues without significant reflection at the interfaces. The use of injectable media with differing acoustic properties than the target tissues can create the necessary interfaces between tissue planes to allow echogenic reflection between the tissues, enhancing differentiation of the anatomic structures. To aid in the identification of nerves, injection of saline or local anesthetic can create such an interface where reflection rather than transmission occurs between the solution and surrounding structures, improving image quality.

For vascular tissues, the use of engineered injectable encapsulated microbubble contrast agents improves the resolution of the vessels and detection of flow using Doppler due to the high difference in acoustic impedance between the air-filled spheroids and the surrounding blood.

## 4. Transducer Manipulation

There are 4 cardinal transducer movements used in image acquisition embodied by the mnemonic PART: Pressure, Alignment, Rotation, and Tilt.

### 4.1. Pressure

Pressure movements (Figure 29.6a) are the axial forces applied to the patient through the transducer used to improve coupling of the transducer to the tissue surface, compress structures, and improve resolution of objects at the limit of the transducer’s penetration range. These movements may be quite forceful and can lead to patient discomfort. Furthermore, these manipulations can lead to compression of structures such as veins, obscuring them from view. Two variations on pressure movements are often used to optimize imaging of objects: heel-toe and roll. Heel-toe (or press) manipulations (Figure 29.6b) apply distal pressure while relaxing the proximal side of the probe face. This, in effect, aligns the probe face tangentially to the skin surface, angling the wave front so that it better aligns with the reflective surface of the target structure. Roll is a similar maneuver performed using the curved edge of a curvilinear probe (Figure 29.6c). Roll and heel-toe can also be used to image structures deep to tissues of high acoustic impedance such as bone by angling the incident beam to a plane where the target structures are no longer obscured.

Figure 29.6 (a) Pressure; (b) press or heel-toe; (c) roll.

### 4.2. Alignment

Alignment movements are longitudinal and transverse movements (Figure 29.7) of the transducer along the body surface. These are the primary movements used in performance of the ultrasound examination and in aligning a nerve block needle with the target structure. The operator glides the transducer along the skin to image the underlying structures and acquire the desired objects.

Figure 29.7 Alignment.

### 4.3. Rotation

Rotation movements are clockwise and counterclockwise movements along the long axis of the probe (Figure 29.8). These manipulations are used to optimize the orientation of the probe to the desired imaging plane (transverse or longitudinal) of the target structure. They fine-tune the alignment maneuvers during in-plane procedural techniques. Rotational alignment errors are the most common source of improper needle placement during in-plane approaches. It is for this reason that the “bevel-up” (Figure 29.9) or bevel oriented toward the probe orientation of the needle is emphasized during needle advancement. With the “bevel-up” orientation the classic step appearance of the needle is visualized. This appearance is due to the length difference between the front and back walls of the needle due to the slope of the bevel. Other orientations may mask the front wall due to shadowing by the back wall, making determination of the needle tip unreliable.

Figure 29.8 Rotation.

Figure 29.9 Bevel-up orientation (top figure) with classic step-down appearance of the needle bevel (arrows). With the bevel down (bottom figure), the bevel is not visible and the shaft can be confused with the needle tip.

### 4.4. Tilt

Tilt manipulations change the angle of the ultrasound beam relative to the probe face (Figure 29.10). Much like pressure movements, these adjustments can be used to image structures obscured by other echogenic objects or to align the ultrasound beam with multiple target structures so that they are viewed in the same plane. Tilt maneuvers also allow the operator to take advantage of a property of specular reflective objects called anisotropy. Anisotropy is the difference in the reflective properties of a material due to changes in the incident angle of the wave source. The optimal reflective angle for nerves lie within 10 degrees from perpendicular to the fascia; thus the transducer must be within this 20 degree band, otherwise the signal will be lost to attenuation. When tracing a structure along its course, the path it takes may be altered and deviate from the plane of the skin. As the path the probe advances along the skin diverges from that taken by the target, the angle of incidence will deviate as the plane of the skin is no longer parallel to the tissue plane. Tilting the probe realigns the incident beam with the target plane. The degree of anisotropy can also be used to differentiate among tissue types: tendons have an anisotropy of about 2 degrees; thus, by titling the probe one can distinguish nerve from tendon using the difference in reflective behavior.

Figure 29.10 Tilt.

## 5. Artifacts

Artifacts are false displays of anatomy due to errors or distortions in echo signal processing and display. These errors result in incorrect display of structures that are nonexistent, missing, distorted, or in the incorrect anatomic location. Artifacts can be due to operator error and misconfiguration of the machine for the exam to be performed, resulting in poor resolution of the desired anatomic structures. Most artifacts that result in anatomic distortions or misrepresentations are due to the behavior of the incident and reflected ultrasound waves in the differing tissues and the consequence of the computational assumptions made by the engineers who designed the system discussed earlier in the chapter. The following artifacts are due either to differences in the actual propagation speed of sound from the assumed propagation speed for tissues, or to delays in echo returns as the return echo meets interfaces of differing acoustic impedance.

### 5.1. Bayonet sign

The bayonet sign is an apparent kink and step-off of the needle shaft, giving the impression of a bayonet under the barrel of a rifle (Figure 29.11). This is due to the needle transiting between 2 tissues of dramatically different propagation speeds. In the instance where the tip of the needle looks to have kinked deep to the needle, the segment of the needle that appears to be more superficial is in a substance with faster propagation velocity, such as muscle, while the segment that appears deeper has a slower propagation speed, such as a fluid-filled space.

Figure 29.11 Bayonet sign. Apparent bend in a needle (arrows) due to change in acoustic properties between different tissues.

### 5.2. Refraction error

Refraction error occurs when the reflected wave transits between tissues of differing acoustic impedance, resulting in a shift in the path of the wave off its initial axis. This causes the machine to interpret the source of the echo to be along the deviated path rather than from its actual origin.

### 5.3. Reverberation artifact

Reverberation artifacts (Figure 29.12) occur when the incident wave strikes 2 strong reflectors or between the transducer and reflector. These artifacts are the result of 2 possible acoustical interactions.

Figure 29.12 Reverberation artifact (arrows).

In the first mechanism, the incident beam strikes the strong reflector and the typical reflection occurs; however, the reflected beam then strikes a surface with greater acoustic impedance, causing a portion of the energy to be transmitted to the transducer and a reflection occurs back into the tissue toward the first highly reflective surface. This process repeats until attenuation results in the loss of detectable echo, or the next pulse cycle begins.

The second process involves reflections of sound waves between 2 highly echogenic surfaces such as the walls of a needle. The incident beam reflects off the shallower reflective surface, with transmission through the first surface followed by reflection by the deeper surface, resulting in repeated echoes of the same structure, the extent of which is determined by the extent of attenuation and the length of the pulse-return cycle.

In both cases, each return echo occurs at a later time point than the one before. This causes the machine to interpret the reverberations as having taken a longer transit time, which is falsely displayed as a deeper object.

Comet tail artifact (Figure 29.13) is a form of reverberation artifact that occurs along an irregular reflective plane such as pleura, diaphragm, and lung. A significant amount of the reflected energy is scattered; however, some of the planes will be perpendicular to the incident wave. Since the interface between the pleura and underlying lung represents a transition between an area of relatively high acoustic impedance (the pleura, diaphragm, and lung tissue) and low acoustic impedance (air within the alveoli), alternating reflection and transmission occurs, leading to the reverberation. Since only certain portions of the echoes are reflected back to the transducer, the reverberations are restricted to a limited area. This artifact can be used to aid in the identification of pleura or diaphragm and may appear to shift position with ventilation as the reflective surface changes with movement of the structures.

Figure 29.13 Comet tail artifact (arrows).

Posterior acoustic enhancement (Figure 29.14) is a reverberation artifact observed in cystic structures or vessels. The vascular or cystic walls are specular reflectors with high acoustic impedance, while the fluids within have a low acoustic impedance. This creates a system where reverberations occur between the walls of the structures, creating false echoes of the back wall deep to the object.

Figure 29.14 Posterior acoustic enhancement (arrows).

These reverberation artifacts can obscure the ability to identify deeper structures as the reflections may overwhelm any echoes from those tissues that lie within the path of the reverberations. This is why advancing a needle superior to a target structure may lead to obscuring of the target due to reverberations. This may also be observed in imaging the radial nerve at the level of the axilla, due to its lying behind the artery in relation to the transducer, and may thus be masked by any posterior acoustic enhancement that may occur. One means of differentiating posterior acoustic enhancement artifacts from actual structures is to observe the behavior of the sonographic image: if it pulses in synchrony with the vessel, this likely represents reflection of the vessel wall; if it is static, it is likely the nerve, since it is not adherent to the vessel and would not oscillate with pulsations.

Acoustic shadowing (Figure 29.15) artifacts occur at the interface between media of significantly differing acoustic impedance such as muscle and bone or air and tissue, with the tissue of higher acoustic impedance deep to the lesser. This results in near-total reflection of incident energy at the interface with minimal transmission, causing an image dropout deep to the reflective surface. Any objects deep to the shadow will be unresolvable.

Figure 29.15 Acoustic shadowing (arrows) resulting from near-total reflection of ultrasound waves at the interface between the paraspinous muscles and lamina of the vertebral bodies.

## 6. Nerve Stimulation

Prior to nerve stimulation–guided blockade techniques, block placement was guided by external or palpable anatomy and paresthesia. These methods were relatively unreliable and placed the patient at risk for injury during the performance of the nerve block. The development of techniques utilizing electrical stimulation of motor and sensory nerves to confirm needle localization in the late 1970s greatly improved the safety and reliability of nerve blockade and led to wide adoption of regional anesthetic procedures for surgical and postoperative analgesia.

## (p. 401) 7. Physics of Nerve Stimulation

Peripheral nerve stimulators generate a pulsed electrical current that triggers depolarization of the target nerve. This depolarization results in muscle stimulation along the distribution of the targeted motor nerve or electrical tingling referred to the cutaneous distribution of sensory nerves. To accomplish this nerve stimulation, the device must be designed such that the characteristics of the electrical waveform will trigger depolarization and can be adjusted to allow detection of the minimal stimulation threshold. The user observes the strength of the motor or sensory reaction to impulses at a set intensity (current). The needle is advanced until brisk response is noted. The current is reduced until the motor or sensory twitch is lost. If the loss occurs at the desired threshold current, the needle is at the target location. If the loss occurs at a current lower than the threshold, then the needle is too close to the nerve and should be withdrawn. If the loss is at a higher than desired current, then the needle is advanced until reaction to the stimulus is observed. This process is repeated until the needle placement is optimized to the desired current level. The nature of the waveform and current required is dictated by the physical properties of the nerve, such as degree of myelination or density of ion channels. These histologic features determine the rebase and chronaxie for a nerve type.

### 7.1. Rebase and chronaxie

Rebase is the minimum amount of continuous current required to depolarize a nerve, and chronaxie is the minimum duration of a current impulse to stimulate a nerve at 2 times the rebase. The current (I) required to stimulate a nerve is related to rebase (P), chonaxie (κ‎), and duration of the impulse (t) through the following equation:

$Display mathematics$

Each nerve type has a distinct rebase and chronaxie, which influence the current required to stimulate depolarization. Large A-alpha motor fibers have the lowest chonaxie (0.05–0.1 ms), while smaller A-delta sensory and C-fibers have higher chonaxie (0.150 ms and 0.4 ms, respectively); thus it is possible to selectively stimulate motor fibers using pulse lengths of 50 to 100 ms and minimize or prevent stimulation-related pain as it is below the threshold for sensory A-delta (140 ms) and C-fibers (400 ms). Adjustments to impulse duration allow for selective nerve stimulation or stimulation of physiologically deranged nerves; for example, glycosylation of nerves in diabetic patients alters the chonaxie; by increasing pulse duration, stimulation of these nerves may be possible without the need for excess current.

### 7.2. Cathodic versus anodic stimulation

The polarity of the nerve tip dictates the way in which the current behaves as the needle is passed through tissue and the current/distance relationship with the target nerve. In nerve stimulation, the cathode is the negative terminal and acts as the electron donor; the anode (or grounding lead) is the positive terminal and acts as the electron acceptor. Current thus flows from the cathode to the anode, counter to electron flow. In anodic stimulation, the cations are discharged from the anode on the skin and flow through the body to the needle cathode, where stimulation occurs.

Conventional peripheral nerve stimulators make use of cathodic stimulation for 2 principal reasons: (1) anodic stimulation results in an increase in the concentration of cations under the anode, resulting in a hyperpolarization of the nerve under the anode, placing the nerve in a refractory state and thus resistant to depolarization; and (2) significantly higher current (3–4 times) is required to depolarize a nerve using anodic stimulation.

### 7.3. Peripheral nerve stimulator

The peripheral nerve stimulator (Figure 29.16) consists of a needle lead, a grounding lead, microprocessor controller, timing clock, display system, and controls. Modern nerve stimulators are capable of delivering a constant current by adjusting output voltage to accommodate for differences in impedance as the needle advances through different tissue planes.

Figure 29.16 Nerve stimulator.

Using timing inputs from the clock, the microprocessor controller creates the stimulating impulse at the desired pulse width dictated by the rebase and chronaxie of the target nerve type.

The user adjusts the delivered current to the patient using an analog or digitally controlled potentiometer. Many peripheral nerve stimulators also allow the user to adjust the pulse width to allow stimulation of motor or sensory fibers. Users are also able to set the rate at which the machine produces a pulse wave. This frequency adjustment is typically between 1 Hz and 2.5 Hz. The higher the frequency, the more pulses are generated per second, and the easier it is to detect changes in response to movement of the needle. However, higher frequency pulses may lead to greater discomfort in patients with fractures or other musculoskeletal injury due to more frequent contracture of traumatized tissue. In cases of injury along the motor distribution of the target nerve, a lower frequency is used to decrease the amount of stimulation, but slower and more cautious needle manipulations should be performed so as not to miss the desired stimulation.

### 7.4. Insulated needles

The energy density at the needle tip is the current that stimulates the target nerve. Uninsulated needles suffer from greater current dispersion as the entire needle shaft is in contact with potentially conductive body tissues. This may lead to alternate electrical paths that draw current away from the target area, necessitating increasing current to overcome these losses. Insulated needles have a nonconductive covering along the shaft. This prevents loss of energy to surrounding tissue through dispersion currents and concentrates the energy at the needle tip. This concentration effect restricts dispersion to the tip alone and greatly reduces the current necessary to depolarize the target nerve.

### 7.5. Needle tip to nerve distance estimation

Nerve stimulation–guided techniques rely on correlation between the amount of current necessary to achieve the threshold for stimulation and the distance the needle tip is from the nerve. The greater the distance from the nerve, the more current is required for depolarization. This current/distance relationship is described by Coulomb’s law:

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Where E is the threshold depolarization current, K is Coulomb’s constant, Q is the needle tip current, and r is the distance of the needle tip from the nerve. Expressed in terms of the needle tip current:

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Thus, the amount of emitted current necessary to attain the threshold depolarization current is proportional to the square of the needle distance from the nerve. The needle tip requires 16 times more current when it is 4 mm from the nerve than when it is 1 mm from the nerve to achieve depolarization.

In practice, for peripheral nerve localization, depolarization currents of 0.2 to 0.5 mA correspond to needle tip placement adjacent to the nerve; at current less than 0.2 mA there is significant risk for intraneural placement.

### 7.6. Limitations of peripheral nerve stimulation

There are several factors that impact on the reliability and utility of nerve stimulation–based block techniques. Anatomic derangements may impact on the ability to use such techniques. For example, an amputee may no longer have a limb distal to the point of stimulation to observe response; in such cases a sensory stimulator could be used, with the patient describing the perceived location of the stimulus; this perceived stimulation is known as phantom stimulation. Patients with contractures may also not demonstrate motor responses at the desired threshold for determination of needle tip proximity to the nerve.

Patients with neurologic pathology such as glycosylation of nerves in diabetics, demyelination disorders, or nerve trauma may not respond to nerve stimulation or may require significantly higher current to achieve the same degree of motor response as would a nonaffected individual.

Because this is a stimulating procedure, patients traditionally received moderate sedation in the performance of these techniques. Furthermore, patients with trauma along the distribution of the stimulated nerve may not tolerate the motor contractions and might require significantly more sedation to perform the procedure. Use of these techniques is limited when the patient is under general anesthesia with motor blockade.

In vivo and in vitro study of cathodic stimulation demonstrated biphasic variability in intensity of motor stimulation with increasing current as the needle approached the nerve. In a rat sciatic model, at currents over 0.5 mA the intensity of the muscle twitch decreased by 60%, and at >1.0 mA complete conduction block occurred in vitro. In vivo a 10% to 30% conduction block was observed as current was increased beyond 1.0 mA. This paradoxical decrease in nerve conduction with closer proximity to the nerve began to manifest at about 2 to 4 cm from the nerve depending on the current. Intraneural needle placement demonstrated an expected return in nerve stimulation and a threefold decrease in threshold activation current. Anodic stimulation showed a linear relationship between nerve distance and current with nerve response and was proportionate to increasing current. This biphasic behavior of cathodic stimulation may explain the relatively high incidence of intraneural injections using nerve stimulation techniques when evaluated using ultrasound.

## 8. Conclusion

A sound understanding of the basic physical principles that underlie the instruments used to aid in the performance of nerve blocks provides the clinician with the tools to safely guide the needle to the target nerve. Whether nerve stimulators, ultrasound machines, or both are used to perform regional anesthesia, this basic understanding of how these technologies function when used on a patient is an important addition to, but not a substitute for, detailed anatomic knowledge. This technology can only confirm and refine correct needle placement for regional blocks; it should never be considered a substitute for the physician’s understanding of the anatomic basis for each block.