Shock Wave Applications in Musculoskeletal Disorders

1 Physical Characteristics of Shock Waves

Physics

Shock waves are the result of the phenomenon that creates intense changes in pressure, as evidenced in lightning or supersonic aircraft. These huge changes in pressure produce strong waves of compressive and tensile forces that can travel through any elastic medium such as air, water, or certain solid substances.

A shock wave is defined as an acoustic wave, at the front of which pressure rises from the ambient value to its maximum within a few nanoseconds (Krause 1997, Ogden et al. 2001, Ueberle 1997, Wess et al. 1997). Typical characteristics are high peak-pressure amplitudes (500 bar) withrisetimesoflessthan10nanoseconds, a short lifecycle (10 ms), and a frequency spectrum ranging from the audible to the far end of the ultrasonic scale (16Hz-20MHz).

As shown in Figure 1.1, the pressure rapidly rises from ambient values to the peak value, the so-called peak positive pressure (P+), then drops exponentially to zero and negative values within microseconds. This pressure versus time curve describes the transient shock wave at one specific point-like location of the pressure field.

The pressure disturbance is transient and propagates in three-dimensional space. To obtain spatial information on the total shock wave field, numerous samples of the shock waves have to be collected. Three-dimensional plots of the P+-values may then give an impression of the pressure field distribution.

The pulse energy needs to be focused in order to be applied where treatment is needed. According to the spatial distribution of the pressure, the focus of the shock wave is defined as the location of the maximum peak positive acoustic pressure P+. In relation to P+ as the reference, the -6 dB focal extent in the x, y, and z-directions is physically defined by the -6dB contour around the focus location. In other words, the focal dimensions are determined by half of the peak positive pressure (P+/2) contour (Fig. 1.2). This typical "cigarshaped" focal extent of the device usually covers an area of about 50 mm in the axis of the shock wave axis, with a diameter of 4.0 mm perpendicular to the shock wave axis (focal width). Concentrating the focus of the shock wave field therefore is of paramount importance for successful therapy (Hagelauer et al. 2001).

Fig. 1.1 A typical shock wave is characterized by a positive pressure step (P+) having an extremely short rise time (tr), followed by an exponential decay to ambient pressure. It typically lasts several hundred nanoseconds.

Fig. 1.2 Three-dimensional pressure distribution within the x, y, and z plane.

Many physical effects depend on the energy involved. Thus, shock wave energy is deemed to be an important parameter for clinical application, too. The energy of the shock wave field is calculated by taking the time integral over the pressure/time function (Fig. 1.1) at each particular location of the pressure field, for example, in the focal area:

Energy (E) = 1?c?(?p2(t,A)dt)dA

Unit: millijoule (mJ)

A: area in which the shock wave is existent

?: density of the propagation medium

c: propagation velocity

p: pressure

t: time

The concentrated shock wave energy per area is another important parameter. Physicists use the term "energy flux density" to illustrate the fact that the shock wave energy flows through an area with perpendicular orientation to the direction of propagation. It is a measure of the energy per square area that is being released by the sonic pulse at a specific point:

Energy Flux Density (ED) = dE/dA = 1/?c?(?p2(t)dt)

Unit: millijoule/millimeter2 (mJ/mm2)

Acoustic Properties of Media

Media are distinguished by their different mechanical properties, such as elasticity and compressibility. These parameters affect sonic waves by determining the propagation speed c, as well as the acoustic impedance Z = ? c, the product of density and speed of sound c (unit: newtonsecond/meter3; Ns/m3). Water (1.48 × 106 Ns/m3), fat tissue (1.33 × 106 Ns/m3), and muscle tissue (1.67 106Ns/m3) have a similar impedance. The impedance of air is much lower (429 Ns/m3); the impedance of bone is much higher (6.6 × 106 Ns/m3). If the impedance of two media is different, a part of the shock wave energy is reflected. The specific reflected sound amplitude pr is calculated as follows: pr = p0 (Z2 - Z1/(Z2 + Z1)

where Z1 and Z2 are the impedances of medium 1and of medium 2, respectively. The reflected energy is calculated from the square of the amplitude.

If the impedance of the second medium is lower than the first, the polarity of the reflected pressure is reversed, i.e., positive pressure becomes negative pressure or underpressure.

This is especially the case at interfaces between tissue and air, for example, at the interface of lung tissue. Because nearly all the energy is reflected at this interface, the delicate alveolar tissue is unable to resist the mechanical forces of the shock wave and will disrupt.

Fig. 1.3 If concretions are impacted in the surrounding tissue, the so-called Hopkins effect leads to destruction beginning at the rear side of the concretion because the tensile strength is exceeded due to the underpressure.

The effect of pressure reversal also occurs at another interface: When the shock wave transmitted into a calcific deposit or into bone hits the posterior border of this medium, a portion of the shock wave is reflected into the deposit or into the bone as negative pressure, because the muscle tissue at the back of the deposit or the bone has a lower impedance than the deposit or the bone. This reflected wave is then superimposed with the later overpressure portion of the incident wave so that particularly strong tensile forces act on the rear of the deposit or the bone (Hopkins effect) (Fig. 1.3).

Cavitation

Cavitation is defined as the occurrence of gasfilled hollow bodies in a liquid medium. Stable cavitation bubbles are in equilibrium when the vapor pressure inside the bubble is equal to the external pressure of the liquid.

When a shock wave hits a cavitation bubble, the increased external pressure causes the bubble to shrink, whereby the latter absorbs part of the sonic energy. If the excitant energies and consequent forces are strong enough, the bubble collapses, thereby releasing part of the energy stored in the bubble to the liquid medium as a secondary shock wave. The radius of a cavitation bubble is about 500 micrometer in water. The bubble collapses about 2-3 microseconds after being hit by the shock wave. The resulting collapse pressure of the secondary wave is about one-tenth of the initial shock wave pressure and exists for about 30 nanoseconds. Thus, the sonic energy released by the collapsing bubble is less by a factor of 1000 than that of the excitant shock wave.

Due to the one-sided impact of the excitant shock wave the bubble collapses asymmetrically, sending out a jet of water. This jet can reach speeds of 100-800 m/s, sufficient, for example, to perforate aluminum membranes or plastics. The needle-shaped hemorrhages (petechiae) on the skin after shock wave therapy (SWT) are attributed to this cavitation effect.

Fig. 1.4 Gas-filled bubbles are first compressed by the positive peak pressure of the shock wave, then expand dramatically due to the underpressure component of the shock wave.

The underpressure part of the initial shock wave leads to a contrary effect: microbubbles grow during underpressure. They may reach a stable size which can be three orders of magnitude larger than the nucleus and can exist for several hundred microseconds. If these bubbles are hit by a following shock wave, once again a collapse with cavitation effects is produced (Fig. 1.4).

Shock Wave Generation

Extracorporeal shock waves used in medicine today are emitted as a result of electromagnetic, piezoelectric, or electrohydraulic generation. All studies presented in this book were done using a source of electromagnetic shock waves.

Electromagnetic systems utilize an electromagnetic coil and an opposing metal membrane. A high current impulse is released through the coil to generate a strong magnetic field, which induces a high current in the opposing membrane, accelerating the metal membrane away from the coil to the 100,000-fold of gravity, thus producing an acoustic impulse in surrounding water. The impulse is focused by an acoustic lens to direct the shock wave energy to the target tissue. The lens controls the focus size and the amount of energy produced within the target (Fig. 1.5).

Piezoelectric systems are characterized by mounting piezoelectric crystals to a spherical surface. When a high voltage is applied to the crystals they immediately contract and expand, thus generating a pressure pulse in surrounding water. The pulse is focused by means of the geometrical shape of the sphere (Fig. 1.6).

Electrohydraulic systems incorporate an electrode, submerged in a water-filled housing comprised of an ellipsoid and a patient interface. The electrohydraulic generator initiates the shock wave by an electrical spark produced between the tips of the electrode. Vaporization of the water molecules between the tips of the electrode produce an explosion, thus creating a spherical shock wave. The wave is then reflected from the inside wall of a...