and Ultrasound Basics

Fig. A1.1 The Hagen–Poiseuille law. V = mean velocity; P − P*= ΔP = pressure gradient; l = vessel length; r = vessel radius, η = dynamic fluid viscosity.

Fig. A1.2 The pattern of flow of water in the Colorado river as it flows through the Grand Canyon (Colorado, USA). Note the normal, calm flow in the wider segments of the river and the increase in flow and turbulence in the narrow segment. (Reproduced from Google Earth, Mount View, USA.)

Flow Pattern and Flow Velocity

Flow in a vessel system can be linear or turbulent depending on the vessel size and flow velocity (Fig. A1.2, Fig. A1.3, Fig. A1.4). The example in Fig. A1.2 shows the water flow in a segment of the Colorado river as it flows through the Grand Canyon (Colorado, USA). The width of the river changes, from a relatively wide stretch with calm flow to a narrow section where cataracts can be seen. The river then widens again and the flow becomes calmer. Within the calm areas the water flow is steady but flow velocity increases noticeably within the narrowing, i.e., within the stenosis (Fig. A1.3). Flow in the wider segments of the river is laminar, but it becomes turbulent within the narrowed areas (Fig. A1.4). Similarly, in the human vasculature flow velocity increases in any case of vessel narrowing. In addition, this phenomenon can be observed in vessel segments with a raised pressure gradient, i.e., hyperperfusion within a normal-sized vessel. If flow velocity reaches a certain magnitude, it changes from laminar to turbulent. This is why turbulent flow is an ultrasound criterion always searched for in suspected vessel stenosis. However, turbulence can also be seen over varying lengths distally adjacent to a stenosis, in regions with vessel elongation, kinking, or hyperperfusion, which may limit its diagnostic value.

Fig. A1.3 Schematic of the changes in flow velocity around and within a vessel narrowing: Normal initial flow velocity, increased velocity within the stenosis and normalized flow afterward.

Ultrasound Principles

Doppler Effect

Diagnostic ultrasound enables the visualization and measurement of the phenomenon of flow dynamics. Ultrasound is generated by oscillating piezoelectric elements, emitting frequencies in the nonaudible range between 20 kHz and 1 GHz (Hz = Hertz = number of oscillations per second). This frequency travels through body tissues in the form of a wave. While traveling through tissue at a speed of ~1,500 m/s, the wave is reflected by various structures which may be resting (tissue) or moving (blood cells, mainly erythrocytes). The reflected wave is then analyzed. When there is a frequency shift between the emitted and received frequency, a “Doppler effect” has occurred, named after the Austrian physicist Christian A. Doppler (Fig. A1.5).

Fig. A1.4 Schematic of the flow pattern around and within a vessel narrowing: Initial laminar flow changing to turbulent flow within the stenosis and within a short segment distal to the narrowing, followed again by a normal laminar flow.

Fig. A1.5 Christian A. Doppler (1803–1853).

The Doppler effect can easily be explained using audible sound. Consider a tuning fork emitting sound with a frequency of A = 440 Hz (Fig. A1.6). This frequency travels through air with the speed of sound (330 m/s) toward an observer, who can hear exactly the same frequency of 440 Hz. However, if the observer rides a bicycle at a speed of 18 km/h (5 m/s) toward the tuning fork his speed would lead to the subjective experience of a higher frequency, i.e., 447 Hz in our example.

The human auditory system (Fig. A1.7) is able to recognize a Doppler shift of audible frequencies. A familiar example is that when an emergency ambulance passes us in the street we hear characteristic changes in the received sound pitch of its sirens. All ultrasound systems are constructed to a pattern which resembles the human hearing system (Fig. A1.8). The difference between emitted and received frequencies (Doppler shift) is caused by the reflection of ultrasound by various moving reflectors—the corpuscular blood components.

The received frequency is amplified (corresponding to the function of the tympanic membrane and ossicles). A demodulator subtracts the received from the emitted frequency (f* − f) which is then directly sent to a speaker, as the Doppler shift is within the audible kHz range of the human ear. In addition, flow direction is determined, depending on whether f* − f is positive or negative. Finally, the received frequency spectrum is processed by Fourier analysis. This calculation can be explained by the following example: An observer is asked to analyze the male voices of a choir. At time points 1, 2, and 3 seconds, he is asked to mark on a diagram how loud he can hear the tenor, baritone, and bass. At time points 1 and 2, the tenor is the loudest, the baritone is moderately loud, and the bass is the quietest. At time point 3, the tenor is silent while the bass is loudest (Fig. A1.9). Applying this to Doppler frequencies, a large Doppler shift translates into high flow velocity and a small Doppler shift translates into a low flow velocity, while the volume depends on the number of reflectors moving with a given flow velocity. In our example (Fig. A1.10), most erythrocytes are flowing fast, a moderate number are slower, and a small number are very slow, which is usually the case in regions with a laminar flow pattern.

Fig. A1.6 Example of the Doppler effect occurring within the range of the audible sound. An observer evaluates the sound emitted by a tuning fork. Top: The observer stands still. The emitted frequency is identical to the received frequency. Bottom: The observer is moving toward the acoustic source, therefore passing more quickly through the sound waves, resulting in a subjectively higher received frequency.

Fig. A1.7 Schematic of the human auditory apparatus and its ability to detect a frequency shift of a moving acoustic source.

Fig. A1.8 Schematic demonstrating the analogy of a diagnostic ultrasound machine to the human auditory system.

Fig. A1.9 Explanation of Fourier analysis, using a choir as an example. A frequency analysis is performed over time. At defined time points the song is analyzed and documented in colored boxes according to the active singers (= frequencies) and to the strength at which they sing, i.e., point 1 depicts the moment when the tenor is loudest, the baritone sings at moderate volume, and the bass has the weakest sound.

Extension of frequency step numbers of time points per second leads to a typical Doppler spectrum (Fig. A1.11). The exact number of frequency steps varies from 64 to 256 depending on the Doppler or duplex ultrasound system being used.

Doppler Shift and Flow Velocity

To convert the Doppler shift (measured as a frequency in kHz) into flow velocities (cm/s or m/s), the Doppler formula needs to be applied (Equation A1.1). As the formula includes the cosine of the insonation angle, exact flow velocity can only be calculated if the ultrasound beam is directly in line with the direction of blood flow in the vessel segment being analyzed (cosine of 0° insonation angle = 1). Therefore, whenever the insonation angle is greater than 0° the calculated velocity will be “false low.” As blood vessels hardly ever point directly toward the ultrasound transducer, an acceptable flow velocity can only be calculated if the insonation angle is less than 30° (error from real Doppler shift is ≤13%) or if the insonation angle is known and corrected for (Fig. A1.12). Every duplex ultrasound system offers the feature of angle correction, which is easily achieved by adjusting a flow-line-symbol visualized within the sample volume. For correct measurements, the sample volume needs to be in the center of flow and not too close to the edges of the visible vessel. The flow-line then needs to be adjusted in line with the blood flow or flow-jet seen in the color mode (see also Fig. A5.54). Most ultrasound systems offer the option to correct for angles from 0° to more than 70°, but a correction of more than 60° will result in additional system-dependent errors (falsely high velocities) that can be as high as 40% (Daigle et al 1990, Steinman et al 2005). Therefore, it is usually recommended not to correct for more than 60° to avoid inaccurate flow velocity measurements (Fig. A1.13). In general, it is desirable to apply angle correction for all vessels to minimize angle-dependent errors of velocity measurement. However, to avoid introducing additional errors or increasing inter- and intraobserver variability, angle correction is usually recommended in straight vessel segments that are visible over at least 1.5 cm of length (Giller 1994). Extracranially, this criterion is mostly fulfilled and therefore angle correction is an accepted and required part of every velocity measurement. This does not apply to intracranial insonation, however, as most vessel segments are tortuous, thus impeding exact angle correction (Fig. A1.14). Consequently, recommendations in the literature for transcranial color-coded duplex sonography (TCCS) vary from “correction” via “fixed correction” to “no correction.” For the above reasons, we do not recommend routine angle correction in TCCS examinations but registering the highest measurable velocity instead. In case of a specific question, for instance in unclear side-to-side velocity differences, it may be helpful to apply angle correction if the sample volume can be positioned in a satisfactory long vessel segment of at least 1 cm aligned with the direction of the vessel in the color-mode image (Nedelmann et al 2009b).

Fig. A1.10 Fourier analysis of ultrasound-generated Doppler signals: Transferring the example of the choir to blood flow analysis. The detected frequencies now resemble the detected Doppler shift, the amplification from the number of reflectors generating an equal Doppler shift.

Equation. A1.1

Fig. A1.11 Top: Doppler spectrum of a transcranial (TCD) ultra-sound system. Note the “systolic window,” i.e., in laminar flow most erythrocytes are fast flowing, therefore the highest intensities (orange colored) are close to the highest flow velocities. Intensity near the zero line is low as only few erythrocytes are slow. Bottom: Blood vessel with schematic laminar flow lines, fastest erythrocytes (and high number) in the vessel middle, slowest erythrocytes (and low number) near the vessel wall.

The reflected ultrasound waves contain a spectrum of frequencies. From these, several diagnostically relevant hemodynamic and blood flow parameters are generally calculated automatically by modern ultrasound machines, provided that a correct envelope curve has been fitted (Fig. A1.15) (for further details about hemodynamic parameters, see also Chapter 3, “Parameters of Cerebral Hemodynamics”).

Fig. A1.12 Relation of insonation angle and error in Doppler shift determination.

Fig. A1.13 Duplex ultrasound of the CCA, longitudinal plane. Identical vessel segments but different angulation of the ultrasound probe at the neck, subsequently requiring two different angle corrections (blue bar): 60° and 73°. The former leads to a correct flow velocity of 105 cm/s, the latter to a system-related false high velocity of 144 cm/s.

Fig. A1.14 Dilemma of exact angle correction in curved vessel segments. The blue circle (top left) indicates the segment of interest. Which angle correction would you choose: 0° (top right): 15° (bottom left), or 35° (bottom right)? Exact angle correction is not possible in short, curved vessel segments.

Fig. A1.15 Hemodynamic parameters derived from Doppler spectrum analysis. Top: TCD system. Bottom: Duplex ultrasound system. PSV = peak systolic velocity; EDV = end diastolic velocity; V_mean = TAV_mean = intensity-weighted mean velocity.

Ultrasound Systems

This section focuses on the characteristics and function of duplex ultrasound systems. The use of these systems for routine vascular diagnostics, particularly for determination of stenoses and occlusion, is the current standard for extracranial examinations and is the foreseeable standard for intracranial assessment. With systems becoming smaller and lighter, this applies not only to assessments in the ultrasound laboratory but also to assessments of patients in intensive care units. Pure Doppler ultrasound is being modified to perform functional tests. The majority of ultrasound diagnostics in the cases presented in this book are derived from duplex ultrasound. If data are derived from Doppler systems, the particular specifications are discussed. In general, the same basic principles are applied in Doppler and duplex systems, and system settings can be adjusted in a similar manner.

Fig. A1.16 Examples of the three transducer types and frequencies often used for insonation of the vessels supplying the brain. (A) Linear transducer, frequency range 5–18 MHz, for extracranial insonation; (B) Sector transducer, frequency range 4–8 MHz, for extracranial insonation; (C) Trapezoid transducer, 1–3 MHz, for transcranial insonation.

Fig. A1.17 Schematic visualization of the relationship between insonation frequency, achievable spatial resolution, and possible insonation depth. Usually, for each region of interest a compromise between the three variables has to be used.

Ultrasound Transducer

The transducer combines the emission of ultrasound waves into the tissue and the simultaneous registration of reflected ultrasound in quick succession to the emitted impulse. Duplex ultrasound transducers contain a series of piezoelectric elements working simultaneously. When exposed to an alternating voltage, these crystals start to vibrate and therefore emit mechanical waves into the surrounding tissues. This also works in reverse, enabling the detection of mechanical—i.e., ultrasound—waves, and their conversion into electrical current. More than 500 piezoelectric elements may be integrated into current modern transducers. Their configuration on the probe varies and determines the appearance of the image. Three main types of transducer configuration are usually used for insonation of the extra- and intracranial arteries and veins (Fig. A1.16). For extracranial insonation, high-frequency transducers with a frequency range between 5 MHz and 18 MHz and a linear or sector ultrasound beam configuration are used. The higher the frequency the higher the achievable spatial resolution, but the lower the potential insonation depth (Fig. A1.17 and Fig. A1.18).

The linear transducer has the advantage of providing undistorted images with high spatial resolution, but it requires a large contact surface. For extracranial insonation, this is generally not a problem, so that linear probes are most frequently used. The high-frequency sector transducer has the advantage of providing images from a wider fan-shaped range but causes image distortion. For transcranial insonation, lower frequencies in the range of 1–3 MHz are required to permit transmission and reception of sound through the bones of the skull. However, this is limited to regions of the skull where the bone is naturally thin, i.e., a “bone window” is present (for further details, see also Chapter 2, “Intracranial Arteries” under “Special Arterial Anatomy and Ultrasound Anatomy,” and Fig. A2.45). Using a linear transducer for transcranial insonation would result in small, narrow images, whereas the trapezoidal ultrasound field produced by a sector transducer allows insonation with maximum image information even through a small bone window (Fig. A1.16).

Fig. A1.18 Left: extracranial duplex sonography, longitudinal plane. Right: Transcranial duplex, axial insonation, midbrain plane. Example images acquired with one extracranial and transcranial probe adjusted to different insonation frequencies. Note: the lower the insonation frequency the brighter the image, but this is accompanied by a loss in spatial resolution.

The ultrasound fields of all transducer types are focused by the spatial arrangement of the piezoelectric elements on the surface of the transducer, by electronic control, or both. The ultrasound field can be divided into a near field and a far field. The transitional area between the two is the focal zone with the best lateral spatial image resolution, i.e., the ability to distinguish two objects that are adjacent to one another within the same insonation depth. A typical 2-MHz probe achieves a lateral resolution of up to 3 mm, a 15-MHz probe of up to 0.4 mm (David et al 2000). Modern ultrasound systems allow calculation of two or more focus zones simultaneously (Fig. A1.19). The localization of the focus zone can be adjusted in all duplex ultrasound systems and should always be optimized according to the insonated region of interest.